Power Studies & Solver Engine Reference

16 Comprehensive Power Studies & Numerical Engines

In-depth technical breakdown of all power system studies in DevEN: why each study is performed, international standards, comparison of available numerical methods ("Which is best and why"), input parameters, exact simulation outputs, and real-time visualization guide.

Select Study (Interactive DevEN App Tab Switcher):

Click to view study methods, options, outputs & real-time tools

1-Phase Load Flow Analysis (LFA)

Steady-State · Nodal Power Balance Standard: IEEE 399 / IEEE 3004.2 / IEC 60909-0

Why Solve this Study? (Engineering Objective & Physical Importance)

Load Flow Analysis calculates the steady-state operating state of an interconnected power transmission or distribution network. It determines voltage magnitudes ($V_i$), phase angles ($\theta_i$), active power flows ($P_{ij}$), reactive power flows ($Q_{ij}$), and system active/reactive losses ($P_{loss}, Q_{loss}$) under normal and emergency operating conditions. It is the fundamental prerequisite for equipment sizing, contingency evaluation, thermal overload mitigation, and voltage stability.

Verdict / Recommended Best: Full Newton-Raphson (NR) with KLU Sparse LU factorization is the overall BEST choice for general meshed transmission grids. Fast-Decoupled (XB) is best for high X/R lines requiring sub-second real-time EMS runs. Levenberg-Marquardt is best when solving heavily loaded systems near voltage collapse.

Numerical Methods & Algorithms Comparison (Why those methods & Which is Best)

Table 1.1 — Solver Method Evaluation

Algorithm / Method	Mathematical Formulation	Convergence Rate	Best d For	Limitations / Trade-offs	Verdict
Newton-Raphson (Polar)	Full analytical Jacobian matrix factorization with quadratic convergence.	Quadratic $O(N^2)$	Standard meshed transmission networks ($\le 10,000$ buses)	Requires recomputing Jacobian every iteration	BEST FOR GENERAL TRANSMISSION
Fast-Decoupled (XB / BX)	Decouples active power-angle ($P-\theta$) and reactive power-voltage ($Q-V$) into constant $B'$ and $B''$ sub-matrices.	Linear $O(N)$	High $X/R$ ratio transmission systems (> 3.0)	May diverge on low $X/R$ cables or distribution networks	BEST FOR LARGE REAL-TIME EMS
Levenberg-Marquardt (LM)	Damped trust-region regularized Jacobian: $(\mathbf{J}^T \mathbf{J} + \lambda \mathbf{I}) \Delta x = -\mathbf{J}^T F(x)$.	Super-linear	Heavily stressed systems, ill-conditioned grids, low voltage knees	Slightly higher computation per step	BEST FOR ILL-CONDITIONED & STRESSED GRIDS
Gauss-Seidel (GS)	Successive nodal substitution using admittance matrix directly without Jacobian.	Linear	Small radial systems or academic teaching (< 50 buses)	Extremely slow convergence (100+ iterations) on large systems	NOT RECOMMENDED FOR COMMERCIAL GRIDS
Continuation Power Flow (CPF)	Predictor-corrector tangent continuation along parameter path to trace PV nose curves.	Quadratic along curve	Maximum transfer capability (MTC) and voltage collapse analysis	Requires multiple sequential power flow solves	BEST FOR VOLTAGE STABILITY & P-V CURVES

Study Input Parameters, Options & Recommended Ranges

Table 1.2 — Configuration Options

Option / Param	CLI Slot	Data Type	Default Value	Recommended Range	Engineering Impact & Description
engine	Slot 1	int	0 (NR)	{0: NR, 1: FDLF, 2: GS, 3: LM, 4: CPF}	Solver engine algorithm to execute for nonlinear power flow.
v_init	Slot 2	int	0 (Flat)	{0: Flat (1.0 p.u., 0°), 1: Warm Start}	Voltage phasor initialization strategy before first iteration.
tol	Slot 3	float	1e-6	[1e-12, 1e-3]	Active and reactive nodal power mismatch tolerance threshold in p.u. (e.g. 1e-6 = 0.1 kW on 100 MVA base).
max_iter	Slot 4	int	20	[5, 100]	Maximum allowable iterations before solver declares divergence.
q_limit	Slot 5	int	1 (Enabled)	{0: Disabled, 1: Enabled}	Enforces generator reactive limits ($Q_{min} \le Q_g \le Q_{max}$), switching PV buses to PQ when violated.
line_charging	Slot 6	int	1 (Enabled)	{0: Ignore, 1: Include}	Includes transmission line shunt charging susceptance ($B/2$) in $\mathbf{Y}_{bus}$.
auto_tap	Slot 7	int	1 (Enabled)	{0: Fixed, 1: Automatic}	Enables On-Load Tap Changers (OLTC) stepping to maintain secondary bus voltages within deadband.
shunt_stepping	Slot 8	int	0 (Fixed)	{0: Fixed, 1: Automatic}	Enables automatic discrete stepping of switched shunt capacitor/reactor banks.
vmin_thresh	Slot 9	float	0.90	[0.70, 1.00]	Lower statutory voltage threshold for generating low-voltage violation warnings (p.u.).
vmax_thresh	Slot 10	float	1.10	[1.00, 1.30]	Upper statutory voltage threshold for generating over-voltage violation warnings (p.u.).

Study Outputs & Engineering Meaning (What are those outputs & Why?)

Table 1.3 — Simulation Outputs

Output Variable	Description	Data Type & Unit	Why is this output needed? (Physical & Safety Meaning)	Storage Table
vm_pu	Bus Voltage Magnitude	float (p.u.)	Statutory limit verification (0.95 to 1.05 p.u.). Detects under-voltage or over-voltage conditions.	res_bus
va_deg	Bus Voltage Phase Angle	float (deg)	Determines active power flow direction across transmission corridors and verifies steady-state stability limit.	res_bus
p_mw	Active Power Flow	float (MW)	Branch active power throughput. Essential for determining transmission capacity allocation and export limits.	res_line / res_trafo
q_mvar	Reactive Power Flow	float (MVAr)	Branch reactive power throughput. Identifies inductive/capacitive requirements across lines.	res_line / res_trafo
loading_percent	MVA Thermal Loading	float (%)	Direct percentage loading against continuous MVA rating. Highlights thermal bottlenecks and line overloads.	res_line / res_trafo
ploss_mw	Active Power Losses	float (MW)	Heat losses in conductor resistance ($I^2 R$). Used for economic loss evaluation and tariff calculations.	res_line / res_trafo
qloss_mvar	Reactive Power Losses	float (MVAr)	Series inductive reactive losses ($I^2 X$). Sizing reactive compensation and shunt capacitors.	res_line / res_trafo
iterations	Solver Iterations	int	Convergence performance metric. Verifies solver conditioning (typically 3-5 iterations for healthy grids).	res_summary

How to See These Outputs in Real Time in DevEN Workstation:

CAD Canvas Live Heatmap

Buses glow dynamically based on voltage: GREEN (0.95-1.05 p.u.), AMBER (0.90-0.95 / 1.05-1.10 p.u.), and FLASHING RED (<0.90 or >1.10 p.u.).

Animated Flow Direction Arrows

Transmission lines and transformers show animated arrows moving in real-time in the direction of active power flow, with speed proportional to MW throughput.

Real-Time Results Inspector Dock

Dockable side panel displays instant sortable columns for all bus voltages and line loadings. Click any row to automatically zoom the CAD canvas to that component.

Direct SQLite Storage Tables

Writes complete nodal and branch results to tables 'res_bus', 'res_line', 'res_trafo', and 'res_gen' within the .db container.

Core Mathematical Formulation

$$\begin{bmatrix} \Delta P \ \Delta Q \end{bmatrix} = \begin{bmatrix} J_{P\theta} & J_{PV} \ J_{Q\theta} & J_{QV} \end{bmatrix} \begin{bmatrix} \Delta \theta \ \Delta V / V \end{bmatrix}, \quad P_i = \sum_{j=1}^N V_i V_j (G_{ij}\cos\theta_{ij} + B_{ij}\sin\theta_{ij})$$

Three-Phase Unbalanced Power Flow (3P LFA)

Multi-Phase · Mutual Coupling · VUF% Standard: IEEE Std 1159 / NEMA MG 1 / IEC 61000-4-30

Why Solve this Study? (Engineering Objective & Physical Importance)

Single-phase positive-sequence approximations break down in modern distribution grids due to untransposed distribution lines, rooftop single-phase solar PV feeding random phases, electric vehicle single-phase charging, and heavy single-phase railway/industrial loads. Three-Phase Unbalanced LFA solves the full coupled 3-phase nodal equations ($\mathbf{Y}_{abc} \mathbf{V}_{abc} = \mathbf{I}_{abc}$), calculates neutral conductor voltage rise ($V_n$), individual phase loadings, and quantifies the Voltage Unbalance Factor ($VUF\%$). Excessive unbalance causes catastrophic counter-rotating negative-sequence fields in three-phase induction motors, overheating windings, tripping sensitive inverter protections, and increasing neutral ground losses.

Input Data Requirements & Parameter Guide

Table 2.1 — 3-Phase Parameters

Parameter Name	Applies To	Type & Unit	Physical Meaning & Engineering Impact	Database Field
z_matrix_abc	Line / Cable	3x3 matrix (Ω/km)	Phase self and mutual impedances ($Z_{aa}, Z_{bb}, Z_{cc}, Z_{ab}, Z_{bc}, Z_{ca}$) derived from Carson's equations with neutral reduction.	lines_3ph
load_p_a, b, c	3-Phase Load	float (kW per phase)	Active power consumed independently on Phase A, Phase B, and Phase C (Wye-N or Delta connected).	loads_3ph
xfmr_winding_conn	Transformer	text (Dyn11, Yyn0, etc.)	Vector group determining phase angle shift ($\pm 30^\circ$) and zero-sequence grounding path between primary and secondary.	transformers

Study Outputs & Engineering Meaning

Table 2.2 — Solved Results

Output Variable	Description	Data Type & Unit	Engineering & Physical Significance	Storage Table
v_a, v_b, v_c	Phase Voltages	float (kV / p.u.)	Line-to-neutral or line-to-line voltage on each phase. Highlights severe undervoltage on overloaded phases.	res_bus_3ph
vuf_percent	Voltage Unbalance Factor	float (%)	True sequence unbalance $\|V_2\|/\|V_1\| \times 100\%$. Utility limit is strictly $\lt 2.0\%$ under IEC 61000-4-30 Class A.	res_bus_3ph
i_neutral_a	Neutral Return Current	float (Amperes)	Unbalanced return current flowing back through neutral conductor and earth ground electrodes.	res_line_3ph

How to See These Outputs in Real Time in DevEN Workstation:

3-Phase Phasor Polar Diagram

Interactive HUD overlay showing $V_a, V_b, V_c$ vectors rotated in complex space with sequence decomposition ellipse.

VUF% Bus Heatmap Overlay

Color-codes all CAD network buses dynamically: Green ($\lt 1\%$), Amber ($1-2\%$), and Flashing Red ($\gt 2\%$).

Core Mathematical Formulation

$$\begin{bmatrix} \mathbf{I}_a \ \mathbf{I}_b \ \mathbf{I}_c \end{bmatrix} = \begin{bmatrix} \mathbf{Y}_{aa} & \mathbf{Y}_{ab} & \mathbf{Y}_{ac} \ \mathbf{Y}_{ba} & \mathbf{Y}_{bb} & \mathbf{Y}_{bc} \ \mathbf{Y}_{ca} & \mathbf{Y}_{cb} & \mathbf{Y}_{cc} \end{bmatrix} \begin{bmatrix} \mathbf{V}_a \ \mathbf{V}_b \ \mathbf{V}_c \end{bmatrix}, \quad VUF\% = \frac{|V_2|}{|V_1|} \times 100\% = \frac{|V_a + a^2 V_b + a V_c|}{|V_a + a V_b + a^2 V_c|} \times 100\%$$

CLI Engine: DevEN_3PH_Engine.exe --project network.sqlite --vuf-limit 2.0 C-Accelerated Sparse LU Factorization

Short Circuit Study (SCS - IEC 60909 & Classical ANSI C37)

Fault Analysis · IEC 60909 · ANSI C37 · IEEE Std 3002.3 · CEA 80% Margin Standard: IEC 60909-2016 / IEEE C37.010 / ANSI C37.13 / IEEE Std 3002.3 / CEA Section 6.1

Why Solve this Study? (Engineering Objective & Physical Importance)

Short Circuit Analysis calculates prospective fault currents, symmetrical breaking/making duties, and sequence component distributions across all standard IEEE/IEC fault categories: symmetrical (Three-Phase 3PH), asymmetrical shunt (Single Line-to-Ground SLG, Line-to-Line LL, Double Line-to-Ground LLG/DLG), and series open conductor faults (1-Phase Broken Conductor, 2-Phases Open). The engine supports dual calculation methodologies: the global IEC 60909 Equivalent Voltage Source method ($c \cdot U_n / \sqrt{3}$) and Classical ANSI C37 / Symmetrical Components ($Z_{bus}^{(1)}, Z_{bus}^{(2)}, Z_{bus}^{(0)}$) with operating pre-fault voltage superposition from Load Flow (LFA). It performs automated circuit breaker interrupting duty verification against IEEE Std 3002.3 and Central Electricity Authority (CEA) Section 6.1 80% design margins, computes neutral grounding resistor (NGR) power dissipation ($P_{NGR}$), and provides both system-wide and multi-attribute filtered bus scans.

Verdict / Recommended Best: The IEC 60909 Equivalent Voltage Source method is the globally accepted standard for equipment ratings and protective coordination. The Classical Symmetrical Components method with pre-fault load flow voltage superposition (LFA) is best for operational post-trip forensic analysis and real-time planning.

Numerical Methods & Algorithms Comparison (Why those methods & Which is Best)

Table 2.1 — Solver Method Evaluation

Algorithm / Method	Mathematical Formulation	Convergence Rate	Best d For	Limitations / Trade-offs	Verdict
IEC 60909 Standard Method	Applies voltage factor $c$ to nominal voltage at fault bus: $V_f = c \cdot U_n / \sqrt{3}$. Uses subtransient impedances with temperature correction, peak factor $\kappa$, and breaking factor $\mu$.	Analytical matrix inversion	All industrial, transmission, and distribution systems	Requires sequence impedances ($Z_1, Z_2, Z_0$)	BEST FOR GLOBAL COMPLIANCE & EQUIPMENT SIZING
Classical ANSI C37 / Symmetrical Components	Direct sequence impedance network matrix inversion ($\mathbf{Z}_{bus}^{(1)}, \mathbf{Z}_{bus}^{(2)}, \mathbf{Z}_{bus}^{(0)}$) utilizing actual pre-fault operating voltages from solved load flow ($V_{prefault}$).	Analytical network reduction	North American ANSI/IEEE installations and forensic trip analysis	Requires converged load flow before fault calculation	BEST FOR OPERATIONAL PLANNING & FAULT FORENSICS
From Load Flow (LFA) Superposition	Superimposes fault currents directly onto operating voltages from active database memory or loaded CSV / .out0 / .json load flow result files.	Two-stage solve: LFA then fault	Operational contingency and post-event fault investigations	Requires active load flow solution	BEST FOR REAL-TIME DISPATCH INTEGRATION
Series Open Conductor (Broken Phase)	Models longitudinal phase discontinuities (1-Phase Broken Conductor, 2-Phases Open) via series-connected sequence networks.	Two-port symmetrical components	Overhead transmission lines and distribution feeder safety audits	Requires branch terminal indexing	BEST FOR BROKEN CONDUCTOR HAZARD AUDITS

Study Input Parameters, Options & Recommended Ranges

Table 2.2 — Configuration Options

Option / Param	CLI Slot	Data Type	Default Value	Recommended Range	Engineering Impact & Description
method	Option 1	str	iec	{'iec': IEC 60909 (Standard), 'classical': Classical (ANSI C37 / Symmetrical Components)}	Calculation methodology governing equivalent voltage source vs sequence matrix inversion.
units	Option 2	str	ka	{'ka': kA (Fault Current), 'mva': MVA (Fault Power)}	Display engineering units for results reporting and SLD visualization.
scope	Option 3	str	all_buses	{'all_buses': All Buses, 'select_bus': Select Bus}	Target bus evaluation scope: system-wide scan across all buses or targeted custom bus subset.
bus_filter	Option 4	dialog	Modal	Search by Bus #/Name, kV Filter, Area Filter, Zone Filter, Reset, Batch Select/Deselect	Comprehensive multi-attribute dialog for interactive target bus selection with live counter.
fault_type	Option 5	str	3phase	{'3phase': 3-Phase Symmetrical (3PH), 'slg': Single Line-to-Ground (SLG / L-G), 'll': Line-to-Line (L-L), 'dlg': Double Line-to-Ground (LLG / L-L-G), 'open1p': Open 1-Phase (Broken Conductor), 'open2p': Open 2-Phases Open}	Standard shunt or series fault category.
fault_phase	Option 6	str	All (ABC)	{'abc': All (ABC), 'a': Phase A, 'b': Phase B, 'c': Phase C, 'ab': Phase AB, 'bc': Phase BC, 'ca': Phase CA}	Target faulted phase or conductor combination.
fault_loc	Option 7	str	bus	{'bus': At Bus, 'line': On Line}	Fault location: bolted at substation busbar node or along transmission line branch.
fault_bus	Option 8	int	1	[1, 999999]	Target bus index where fault is applied.
fault_line	Option 9	int	1	[1, 999999]	Target line branch index when fault location is set to 'On Line'.
fault_dist	Option 10	float	50.0%	[0.0%, 100.0%]	Distance slider percentage along line from sending bus (from_bus) to fault point.
fault_z	Option 11	float	0.0 + j0.0	Rf: [0, 1000 Ω], Xf: [0, 1000 Ω]	Fault arc / contact impedance in ohms ($Z_f = R_f + jX_f$). Default 0.0 = bolted fault.
c_factor	Option 12	float	1.10	[0.95, 1.15]	IEC 60909 voltage factor $c$: 1.10 for maximum fault current, 0.95/1.00 for minimum.
v_method	Option 13	str	lfa	{'lfa': From Load Flow (LFA), 'nominal': Flat Start 1.0 pu}	Pre-fault bus voltage source: active DB memory / CSV result file vs flat start (1.0 pu).
breaker_check	Option 14	bool	True (Enabled)	{True: Check Enabled, False: Disabled}	IEEE Std 3002.3 and Central Electricity Authority (CEA) Section 6.1 80% circuit breaker duty design margin check.

Study Outputs & Engineering Meaning (What are those outputs & Why?)

Table 2.3 — Simulation Outputs

Output Variable	Description	Data Type & Unit	Why is this output needed? (Physical & Safety Meaning)	Storage Table
ik_ss_ka	Initial Symmetrical Fault Current ($I_k''$)	float (kA rms)	Initial symmetrical AC fault current magnitude. Sizing circuit breaker breaking duty.	res_scs
sk_mva	Short Circuit Apparent Power ($S_k''$)	float (MVA)	Grid fault power level at bus: $S_k'' = \sqrt{3} \cdot U_n \cdot I_k''$. Determines grid stiffness.	res_scs
ia_ib_ic	Phase Fault Currents ($I_a, I_b, I_c$)	float (kA rms & deg)	Individual phase current magnitudes and phase angles at fault location.	res_scs
i0_i1_i2	Symmetrical Component Currents ($I_0, I_1, I_2$)	float (p.u. & kA)	Zero, positive, and negative sequence currents for protective relay coordination.	res_scs
va_vb_vc	Post-Fault Bus Phase Voltages	float (p.u. & kV)	Voltage profiles across all system buses during primary fault condition.	res_scs
cb_duty_margin	Circuit Breaker Duty & CEA 80% Margin	str / %	Automated compliance evaluation: flags if fault current exceeds 80% of rated breaker MVA.	res_scs
p_ngr_kw	Neutral Grounding Resistor Dissipation ($P_{NGR}$)	float (kW / MW)	Active power loss in neutral grounding resistor: $P_{NGR} = 3 I_0^2 R_{NGR}$.	res_scs
multi_bus_summary	Multi-Bus Short Circuit Summary Table	table	Summary across target buses comparing 3-Phase, SLG/LG, L-L, DLG/LLG, and Fault MVA.	res_scs

How to See These Outputs in Real Time in DevEN Workstation:

Target Bus Scope 2-Option Selector

Streamlined toggle between 'All Buses' and 'Select Bus' with inline [ 📋 Select Bus(es)... ] button and live selection summary badge.

Multi-Attribute Filter Modal Dialog

Interactive dialog with real-time text search (number or name), voltage level dropdown, area filter, zone filter, reset button, and quick batch selection tools.

Configurable SLD Heatmap Canvas Overlay

SLD canvas dynamically displays user-selected fault variable: Max Fault Current (Ik''), Fault Power (Sk'' MVA), Phase Currents (Ia, Ib, Ic), or Sequence Currents (I0, I1, I2).

Master Unified Monospace Report Console

Complete study report with Primary Fault Location Details, Post-Fault Bus Voltages, Multi-Bus Summary Table, and CEA 80% Margin Check with Copy and Save buttons.

Core Mathematical Formulation

$$I_k'' = \frac{c \cdot U_n}{\sqrt{3} \cdot |Z_{th}|}, \quad I_{sc,SLG} = \frac{3 \cdot c \cdot U_n / \sqrt{3}}{|Z^{(1)} + Z^{(2)} + Z^{(0)} + 3Z_f|}, \quad S_k'' = \sqrt{3} \cdot U_n \cdot I_k''$$

Contingency Analysis (CA - N-1 / N-k)

Grid Reliability · Security Assessment Standard: NERC TPL-001 / ENTSO-E Operational Security / IEEE 1459

Why Solve this Study? (Engineering Objective & Physical Importance)

Contingency Analysis evaluates grid resilience under the unexpected outage of critical power system assets (transmission lines, transformers, generators). By evaluating $N-1$ and $N-k$ outage combinations, it identifies single points of failure, computes post-contingency line loading, detects voltage collapse risks, and computes Line Outage Distribution Factors ($LODF$).

Verdict / Recommended Best: Full AC Contingency Screening is the BEST and only method that accurately predicts both thermal line overloads and bus voltage violations. DC Contingency Screening is recommended for initial fast ranking across thousands of lines.

Numerical Methods & Algorithms Comparison (Why those methods & Which is Best)

Table 3.1 — Solver Method Evaluation

Algorithm / Method	Mathematical Formulation	Convergence Rate	Best d For	Limitations / Trade-offs	Verdict
Full AC Contingency Screening	Solves full AC Newton-Raphson power flow for every single branch and generator outage.	Quadratic per outage	All transmission grids and compliance audits (NERC TPL)	Higher computational time on 10,000+ branch grids	BEST FOR ACCURATE RELIABILITY COMPLIANCE
DC Contingency (PTDF / LODF)	Linearized DC power flow using pre-computed Line Outage Distribution Factors: $\Delta P_l = LODF_{l,k} \cdot P_k$.	Instantaneous linear matrix multiply	Fast automated contingency ranking and market screening	Ignores reactive power, losses, and voltage collapse	BEST FOR ULTRA-FAST INITIAL CONTINGENCY RANKING

Study Input Parameters, Options & Recommended Ranges

Table 3.2 — Configuration Options

Option / Param	CLI Slot	Data Type	Default Value	Recommended Range	Engineering Impact & Description
contingency_type	Option 1	str	branch	{'branch': Line/Transformer, 'gen': Generator, 'all': Branch + Gen}	Asset category to screen for outages.
ranking_metric	Option 2	str	pi_v	{'pi_v': Voltage Index, 'pi_mw': Thermal Index, 'composite': Both}	Performance Index formulation used to rank contingency severity.
max_contingencies	Option 3	int	100	[1, 5000]	Maximum number of contingencies to evaluate in single run.
v_dip_thresh	Option 4	float	0.05	[0.01, 0.20]	Maximum allowable post-contingency bus voltage change ($\Delta V$) before flagging violation.
branch_rating_pcent	Option 5	float	100.0	[80.0, 150.0]	Emergency thermal rating threshold for branch overloads.
islanding_detection	Option 6	int	1 (Enabled)	{0: Disabled, 1: Enabled}	Automatically isolates and flags electrical islands formed by line trips.

Study Outputs & Engineering Meaning (What are those outputs & Why?)

Table 3.3 — Simulation Outputs

Output Variable	Description	Data Type & Unit	Why is this output needed? (Physical & Safety Meaning)	Storage Table
contingency_id	Contingency Identifier	str	Tag of tripped element (e.g. 'LINE_4_9' or 'GEN_1'). Identifies the single point of failure.	res_contingency
max_overload_pct	Worst Branch Overload	float (%)	Maximum post-outage thermal percentage on any remaining branch in the network. Triggers emergency dispatch.	res_contingency
min_voltage_pu	Worst Bus Voltage	float (p.u.)	Lowest post-outage bus voltage recorded across the grid. Verifies voltage stability margin.	res_contingency
severity_index_pi	Performance Index (PI)	float	Normalized severity ranking composite score. Ranks the most dangerous contingencies to top of operator queue.	res_contingency
islands_formed	Islands Count	int	Number of independent asynchronous electrical islands formed by the outage.	res_contingency

How to See These Outputs in Real Time in DevEN Workstation:

Worst-Case Contingency Matrix

Dynamic matrix widget sorted from worst to mildest outage. Click any contingency to instantly see post-trip grid state on CAD canvas.

Post-Trip Overload Overlays

Overloaded branches pulse with red hatched highlights, showing emergency MVA loading and available relief options.

Core Mathematical Formulation

$$LODF_{l,k} = \frac{PTDF_{l,i} - PTDF_{l,j}}{1 - (PTDF_{k,i} - PTDF_{k,j})}, \quad PI_v = \sum_{i=1}^{N_{bus}} \left(\frac{|V_i| - V_{nom}}{\Delta V_{max}}\right)^{2m}$$

1-Phase Time Series Simulation (TS)

Quasi-Static Time-Series (QSTS) · Chronological Profiles Standard: IEEE Std 1547 / ANSI C84.1 / EN 50160 / IEC 60287 / CIGRE TB 299

Why Solve this Study? (Engineering Objective & Physical Importance)

Time Series Simulation evaluates the behavior of power systems across continuous chronological timelines (seconds, minutes, 24-hour daily profiles, weekly curves, or 8760-hour annual operations). While snapshot load flow only analyzes a single peak-demand instant, Time Series tracks real-world time-dependent dynamics:

Voltage Envelope Compliance: Verifies that bus voltages remain strictly within ANSI C84.1 Range A (0.95–1.05 p.u.) across varying load and midday solar generation cycles.
Thermal Ampacity Duration Curves: Identifies the exact duration (hours) transformers and underground cables operate near or above 100% rated capacity.
Cumulative Technical Energy Losses (MWh): Integrates active and reactive power losses over time to determine true economic losses rather than peak-instant estimates.
Renewable & BESS Coordination: Models PV solar intermittency, wind fluctuations, and battery energy storage charging/discharging dispatch schedules.

Verdict / Recommended Best: Sequential Newton-Raphson with Voltage Warm-Starting is the industry standard BEST choice. By initializing step $t_k$ from the solved state of step $t_{k-1}$, simulation executes 4–8x faster while maintaining full non-linear AC convergence accuracy.

Numerical Methods & Algorithms Comparison

Table 4.1 — Time Series Solver Evaluation

Algorithm / Method	Mathematical Formulation	Speed & Acceleration	Best d For	Limitations	Verdict
Sequential Warm-Start NR (DevEN Default)	Initializes step $t_k$ with solved state $\mathbf{V}(t_{k-1})$ and $\boldsymbol{\theta}(t_{k-1})$. Solves full AC Jacobian.	4–8x Faster (1–3 iters/step)	Daily (24h) and annual (8760h) multi-period studies	Requires fallback if step diverges	RECOMMENDED BEST
Sequential Fast Decoupled (FDLF)	Constant $B'$ and $B''$ admittance matrices; pre-factorized once for entire timeline.	Ultra Fast (Matrix reuse)	High-voltage transmission grids with high X/R ratios	Inaccurate on high-R distribution cables	FAST FOR TRANSMISSION
Independent Flat-Start	Solves each time point independently starting from $1.0ngle 0^\circ$ p.u.	Baseline (4–7 iters/step)	Robust auto-recovery after abrupt topology switching	High computational cost for 8760h	FALLBACK MODE

Governing Physical Equations & Mathematical Formulations

Table 4.2 — Governing Physics

Physical Concept	Governing Mathematical Equation	Physical Meaning & Application
Time-Varying AC Power Balance	$$P_i(t) - P_{Li}(t) = V_i(t) \sum_{k=1}^N V_k(t) [G_{ik}\cos\theta_{ik}(t) + B_{ik}\sin\theta_{ik}(t)]$$ $$Q_i(t) - Q_{Li}(t) = V_i(t) \sum_{k=1}^N V_k(t) [G_{ik}\sin\theta_{ik}(t) - B_{ik}\cos\theta_{ik}(t)]$$	Non-linear algebraic power flow balance enforced continuously at every time point $t \in [0, T]$.
Sequential Warm-Starting	$$\mathbf{x}^{(0)}(t_k) = \mathbf{x}^*(t_{k-1}), \quad \mathbf{x} = [\boldsymbol{\theta}, \mathbf{V}]^T$$	Propagates the converged voltage state of step $t_{k-1}$ as the initial estimate for step $t_k$, reducing iterations to 1–2 per step.
Cumulative Energy Loss Integration	$$E_{loss} = \sum_{k=1}^{M} P_{loss}(t_k) \cdot \Delta t \quad \text{[MWh]}$$	Calculates total technical energy losses over the simulation horizon for economic loss evaluation.
Profile Imputation Engine (13 Methods)	$$P(t) = \text{Interpolate}(P_{raw}, t, \text{method})$$	Handles missing timestamps or mismatched sampling rates (supports Linear, PCHIP, Akima, Spline, Forward Fill, Mean).

Engineering Inputs & Solver Parameters

Table 4.3 — Parameters Reference

Parameter	Default Value	Allowable Range / Options	Engineering Purpose
duration / unit	24.0 Hours	Seconds, Minutes, Hours, Days	Defines the total chronological study span (e.g. 24h daily dispatch, 168h weekly, 8760h annual).
step_size / unit	1.0 Hour	1s to 24h	Temporal resolution between successive AC power flow evaluations.
csv_file	None (Optional)	Valid .csv file path	Universal Time Series CSV containing chronological multiplier curves for loads, PV solar, and wind.
imputation_method	linear	linear, pchip, akima, spline, ffill	Method used to interpolate between profile points when profile timestamps differ from simulation step size.
v_init_step	warm	warm, flat, initial	Sequential initialization mode. 'warm' re-uses prior step solution for 4-8x acceleration.
continue_on_divergence	True	True / False	Prevents batch failure; logs divergent timestamps and proceeds with remaining steps.

How to See Time Series Outputs in DevEN Workstation:

Time Series Tab

Dedicated study tab in DevEN interface allowing one-click duration setup, step configuration, and automated execution.

Universal CSV Template

Click 'Download Universal Template' to export pre-formatted CSV containing all network elements ready for profile entry.

HTML & CSV Reports

Generates rich interactive HTML report with voltage envelope charts, line loading curves, and complete hourly CSV exports.

Three-Phase Chronological Time Series (3P TS)

8760h Annual · Multi-Phase Solar & EV Dynamics Standard: IEEE 1547-2018 / IEEE PES Time Series Guidelines

Why Solve this Study? (Engineering Objective & Physical Importance)

Simulates continuous 24-hour diurnal or full 8760-hour annual grid operations where individual phases experience asynchronous load and generation swings. Accurately tracks transformer on-load tap changer (OLTC) mechanical wear per phase, battery storage cycling, and hours where rooftop PV injection pushes voltage unbalance above utility limits during midday solar peaks.

How to See These Outputs in Real Time in DevEN Workstation:

24-Hour 3-Phase Interactive Strip Chart

Plot $V_a(t), V_b(t), V_c(t)$ alongside $VUF\%(t)$ with pan, zoom, and threshold violation marker highlights.

OLTC Tap Step Histogram

Visualizes daily tap change counts for each regulating transformer to forecast substation maintenance intervals.

Core Mathematical Formulation

$$E_{loss}^{\phi} = \sum_{t=1}^{T} I_{\phi}(t)^2 R_{\phi} \Delta t, \quad \text{TAP}(t+1) = \text{TAP}(t) + f(\Delta V(t), \tau_{delay}), \quad \max_{t} VUF(t) \le 2.0\%$$

CLI Engine: DevEN_TS_Engine.exe --project network.sqlite --phases 3 --steps 8760 Multi-Core OpenMP Parallelized Time Steps

Hosting Capacity Analysis (HC)

Renewable Integration · Distributed Energy Standard: IEEE 1547-2018 / IEC 62786 / EPRI HC Framework

Why Solve this Study? (Engineering Objective & Physical Importance)

Hosting Capacity Analysis determines the maximum quantity of Distributed Energy Resources (Solar PV, Wind, EV Chargers, BESS) that can be connected to individual feeder buses without violating statutory grid limits (voltage rise $\gt 1.05$ p.u., conductor thermal capacity $\gt 100\%$, reverse power flow through substation transformers, or protection desensitization).

Verdict / Recommended Best: Iterative Feeder-Head Injection Scan is the utility BEST choice for interconnection approvals because it captures exact nonlinear voltage rise and tap changer interaction. Analytical Linear Sensitivity is best for wide-area regional screening.

Numerical Methods & Algorithms Comparison (Why those methods & Which is Best)

Table 5.1 — Solver Method Evaluation

Algorithm / Method	Mathematical Formulation	Convergence Rate	Best d For	Limitations / Trade-offs	Verdict
Iterative Feeder-Head Injection Scan	Progressively increments DER active power injection in steps ($\Delta P$) until any feeder voltage exceeds 1.05 p.u. or line loading exceeds 100%.	Multi-run Newton-Raphson	Feeder-by-feeder utility interconnection studies	Requires solving power flow at each incremental MW step	BEST FOR ACCURATE UTILITY INTERCONNECTION APPROVAL
Analytical Linearized Sensitivity ($dV/dP$)	Computes hosting capacity analytically from inverted bus impedance sensitivity: $\Delta V = Z_{bus,ii} \cdot \Delta P$.	Single-step matrix multiply	High-level regional renewable potential mapping	Approximation error increases near statutory voltage limits	BEST FOR MACRO-LEVEL REGIONAL CAPACITY SCREENING
Stochastic Monte Carlo Placement	Randomly distributes solar rooftop systems with probabilistic generation and load profiles.	Probabilistic 1,000+ runs	Urban residential low-voltage distribution planning	High computation time	BEST FOR PROBABILISTIC DISTRIBUTION PLANNING

Study Input Parameters, Options & Recommended Ranges

Table 5.2 — Configuration Options

Option / Param	CLI Slot	Data Type	Default Value	Recommended Range	Engineering Impact & Description
max_der_mw	Option 1	float	10.0	[0.1, 100.0]	Maximum DER generation search upper bound in MW.
step_mw	Option 2	float	0.25	[0.01, 5.0]	MW step increment for iterative capacity scan.
power_factor	Option 3	float	1.0	[-0.90, 1.0]	Inverter power factor: 1.0 (unity), or 0.95 absorbing for Volt-VAr support.
v_upper_lim	Option 4	float	1.05	[1.02, 1.10]	Upper statutory voltage limit threshold in p.u. (ANSI C84.1 Range A).
v_lower_lim	Option 5	float	0.95	[0.90, 0.98]	Lower statutory voltage limit threshold in p.u.
thermal_lim_pct	Option 6	float	100.0	[80.0, 120.0]	Maximum allowable feeder branch thermal loading percentage.

Study Outputs & Engineering Meaning (What are those outputs & Why?)

Table 5.3 — Simulation Outputs

Output Variable	Description	Data Type & Unit	Why is this output needed? (Physical & Safety Meaning)	Storage Table
hc_mw	Maximum Hosting Capacity	float (MW)	Maximum DER active power capacity allowable at this bus before violating any statutory limit.	res_hc
limiting_factor	Governing Constraint	str	Identifies root limitation: 'Overvoltage (1.05 p.u.)', 'Thermal Overload (100%)', or 'Substation Reverse Power'.	res_hc
curtailment_risk	Curtailment Risk Level	str	Assesses probability of solar PV curtailment during light load sunny hours ('LOW', 'MEDIUM', 'HIGH').	res_hc
volt_var_uplift_mw	Volt-VAr Potential Uplift	float (MW)	Additional MW capacity unlocked by enabling smart inverter Volt-VAr reactive absorption ($Q(V)$).	res_hc

How to See These Outputs in Real Time in DevEN Workstation:

Feeder Hosting Capacity Heatmap

Feeder nodes color-coded by allowable solar MW: DARK GREEN (> 5 MW), YELLOW (1-5 MW), RED (< 0.5 MW / Congested).

Limitation Breakdown Inspector

Clicking any bus displays whether voltage rise or cable ampacity is the binding constraint.

Core Mathematical Formulation

$$V_{DER} \approx V_{sub} + \frac{P_{DER} \cdot R_{feeder} + Q_{DER} \cdot X_{feeder}}{V_{sub}}, \quad P_{HC,max} = \frac{(V_{max} - V_{sub}) V_{sub}}{R_{feeder} + X_{feeder} an\phi}$$

Voltage & Power Sensitivity Analysis (SEN)

System Sensitivities · V-Q / P-V Slopes Standard: IEEE PES Task Force on Voltage Stability / CIGRE 397

Why Solve this Study? (Engineering Objective & Physical Importance)

Sensitivity Analysis computes the linearized mathematical response of power grid voltages, angles, and line loadings to incremental changes in generation, load, and reactive compensation ($dV/dQ, dV/dP, d\theta/dP$). It identifies weak grid areas prone to voltage instability, ranks candidate buses for capacitor/reactor installation, and generates Power Transfer Distribution Factors ($PTDF$) for market bidding.

Verdict / Recommended Best: Inverted Analytical Jacobian Sub-Matrix Inversion is the BEST method for local reactive margin and voltage stability assessment. PTDF / GSF DC Shift Factors are best for real-time market congestion screening.

Numerical Methods & Algorithms Comparison (Why those methods & Which is Best)

Table 6.1 — Solver Method Evaluation

Algorithm / Method	Mathematical Formulation	Convergence Rate	Best d For	Limitations / Trade-offs	Verdict
Full Jacobian Inversion ($J^{-1}$)	Inverts converged power flow Jacobian: $\begin{bmatrix} \Delta \theta \ \Delta V \end{bmatrix} = \begin{bmatrix} J_{P\theta} & J_{PV} \ J_{Q\theta} & J_{QV} \end{bmatrix}^{-1} \begin{bmatrix} \Delta P \ \Delta Q \end{bmatrix}$.	Analytical matrix solve	Weak bus identification and reactive power planning	Valid only around the specific operating point	BEST FOR VOLTAGE MARGIN & CAPACITOR SIZING
Power Transfer Distribution Factors (PTDF)	Calculates branch power flow sensitivity to transaction between buses: $PTDF_{l,ij} = \frac{\Delta P_l}{P_i - P_j}$.	Linear admittance solve	ISO/RTO market management and export/import limits	Assumes fixed nominal voltage and ignores reactive flow	BEST FOR TRANSMISSION CAPACITY ALLOCATION
Modal / Eigenvalue Stability Analysis	Computes eigenvalues ($\lambda_i$) and eigenvectors of reduced Jacobian matrix $J_R = J_{QV} - J_{Q\theta} J_{P\theta}^{-1} J_{PV}$.	Sparse eigensolver	Wide-area transmission voltage security analysis	Requires specialized eigensolver library (ARPACK)	BEST FOR SYSTEMIC VOLTAGE COLLAPSE RISK ASSESSMENT

Study Input Parameters, Options & Recommended Ranges

Table 6.2 — Configuration Options

Option / Param	CLI Slot	Data Type	Default Value	Recommended Range	Engineering Impact & Description
bus_target	Option 1	int	1	[1, 999999]	Target bus index for evaluating injection sensitivity.
delta_q_mvar	Option 2	float	1.0	[0.1, 50.0]	Reactive power perturbation step in MVAr for numeric verification.
delta_p_mw	Option 3	float	1.0	[0.1, 50.0]	Active power perturbation step in MW.
monitored_branch	Option 4	str	1-2	None or 'from-to'	Branch monitored for transfer sensitivity ($PTDF$).
modal_eigenvalues	Option 5	int	5	[1, 20]	Number of smallest eigenvalues to compute for modal analysis.

Study Outputs & Engineering Meaning (What are those outputs & Why?)

Table 6.3 — Simulation Outputs

Output Variable	Description	Data Type & Unit	Why is this output needed? (Physical & Safety Meaning)	Storage Table
dv_dq	V-Q Sensitivity Slope	float (kV/MVAr)	Rate of voltage change with reactive injection. Highest values identify the weakest buses in the grid.	res_sensitivity
dv_dp	V-P Sensitivity Slope	float (kV/MW)	Rate of voltage change with active power injection. Measures vulnerability to renewable curtailment.	res_sensitivity
ptdf_factor	Power Transfer Distribution Factor	float	Fraction of power transferred between bus A and B that flows across monitored line L.	res_ptdf
min_eigenvalue	Minimum Jacobian Eigenvalue	float	Magnitude of smallest eigenvalue $\lambda_{min}$. Approaches zero as system nears voltage collapse.	res_modal

How to See These Outputs in Real Time in DevEN Workstation:

Weak Bus Ranking Dashboard

Sorts and displays the top 10 weakest buses requiring capacitor banks or STATCOM compensation.

Sensitivity Contour Gradient

Overlays smooth color gradient over geographic CAD canvas displaying wide-area voltage stiffness contours.

Core Mathematical Formulation

$$\mathbf{J}_R = \mathbf{J}_{QV} - \mathbf{J}_{Q\theta} \mathbf{J}_{P\theta}^{-1} \mathbf{J}_{PV}, \quad \Delta \mathbf{V} = \mathbf{J}_R^{-1} \Delta \mathbf{Q}, \quad \mathbf{J}_R = \mathbf{\Xi} \mathbf{\Lambda} \mathbf{\Psi}$$

Harmonic Analysis (HAR - IEEE 519 & IEC 61000)

Power Quality · THD/TDD · IEEE Std 519-2022 · IEC 61000-3-6 · Resonance Scan Standard: IEEE Std 519-2022 / IEC 61000-3-6 / IEEE 3002.8

Why Solve this Study? (Engineering Objective & Physical Importance)

Harmonic Analysis calculates voltage and current harmonic distortion caused by non-linear loads (variable frequency drives, 6-pulse / 12-pulse / 24-pulse rectifiers, electric arc furnaces, switched-mode power supplies, and renewable inverter systems). It performs multi-frequency decoupled nodal admittance solves [Y_bus(h) * V_bus(h) = I_inj(h)] with frequency-dependent modeling of branch conductor resistance (skin effect R1*sqrt(h)), shunt charging susceptance (h*B1), transformer leakage reactance, and passive filters. The engine computes Total Harmonic Distortion (THD_V, THD_I), Total Demand Distortion (TDD_I), Telephone Interference Factor (TIF), Transformer K-Factor (UL 1561), and performs driving-point impedance frequency scans [|Z(f)| vs f] to identify parallel resonance peaks and size passive mitigation filters.

Verdict / Recommended Best: Decoupled Multi-Frequency Direct Admittance Inversion [Y(h)^-1 * I(h)] is the globally recognized industry standard for harmonic penetration studies under IEEE 519 and IEC 61000. Driving-Point Impedance Scan [Z_ii(f)] with adaptive frequency step is best for detecting dangerous parallel resonance and sizing detuned filter reactors.

Numerical Methods & Algorithms Comparison (Why those methods & Which is Best)

Table 9.1 — Solver Method Evaluation

Algorithm / Method	Mathematical Formulation	Convergence Rate	Best d For	Limitations / Trade-offs	Verdict
Decoupled Multi-Frequency Nodal Solver	Assembles complex admittance matrix $\mathbf{Y}_{bus}(h)$ for each harmonic order $h$ ($h = 2, 3, \dots, 50$) with skin effect $R(h) = R_1 \sqrt{h}$ and $X(h) = h X_1$. Solves $\mathbf{V}(h) = \mathbf{Y}_{bus}(h)^{-1} \mathbf{I}_{bus}(h)$ independently per harmonic frequency.	Direct sparse LU solve	All transmission, distribution, and industrial power systems	Requires harmonic spectrum data for non-linear loads	MANDATED STANDARD FOR IEEE 519 COMPLIANCE
Driving-Point Frequency Scan (Resonance Scan)	Injects unit 1.0 A current across continuous frequency spectrum (50 Hz to 2500 Hz in user-defined steps) at target bus to compute driving-point impedance magnitude $\|Z(f)\| = \|V_{scan}(f)\|$.	Multi-frequency sweep	Capacitor bank placement, harmonic filter tuning, PFC design	Identifies resonance frequencies $f_r$ and amplification factors	BEST FOR RESONANCE RISK DETECTION & FILTER SIZING
Passive Harmonic Filter Synthesis	Synthesizes passive filter topologies: single-tuned $R-L-C$, second-order high-pass, and C-type filters. Automatically calculates notch frequency $f_n = 1 / (2\pi \sqrt{LC})$, quality factor $Q = X_0 / R$, and fundamental reactive MVAr injection.	Analytical filter synthesis	Industrial facilities with high VFD / arc furnace penetration	Sizes filter components based on required reactive MVAr and targeted harmonic order	BEST FOR HARMONIC MITIGATION DESIGN

Study Input Parameters, Options & Recommended Ranges

Table 9.2 — Configuration Options

Option / Param	CLI Slot	Data Type	Default Value	Recommended Range	Engineering Impact & Description
max_harmonic	Option 1	int	50	[25, 100]	Maximum harmonic order evaluated (typically 50th order / 2500 Hz for 50 Hz, 3000 Hz for 60 Hz).
fundamental_freq	Option 2	float	50.0	{50.0: 50 Hz, 60.0: 60 Hz}	Nominal system fundamental operating frequency in Hertz.
skin_effect	Option 3	bool	True (Enabled)	{True: Enabled, False: Disabled}	Applies skin effect resistance correction to branch conductors: R(h) = R_1 * sqrt(h).
scan_start_hz	Option 4	float	50.0	[10.0, 500.0]	Starting frequency for driving-point impedance scan in Hertz.
scan_end_hz	Option 5	float	2500.0	[500.0, 5000.0]	Ending frequency for driving-point impedance scan in Hertz.
scan_step_hz	Option 6	float	2.0	[0.5, 25.0]	Frequency sweep resolution step size in Hertz.
scan_bus	Option 7	int	1	[1, 999999]	Target bus index for driving-point impedance scan and resonance detection.
ieee519_pcc_bus	Option 8	int	1	[1, 999999]	Designated Point of Common Coupling (PCC) bus index for IEEE 519 compliance verification.
isc_il_ratio	Option 9	float	50.0	[10.0, 1000.0]	Short-circuit ratio I_sc / I_L at the PCC determining IEEE 519 allowable harmonic distortion limits.

Study Outputs & Engineering Meaning (What are those outputs & Why?)

Table 9.3 — Simulation Outputs

Output Variable	Description	Data Type & Unit	Why is this output needed? (Physical & Safety Meaning)	Storage Table
thd_v_pct	Bus Voltage THD (%THD_V)	float (%)	Total harmonic voltage distortion across all evaluated orders: THD_V = sqrt(sum(V_h^2)) / V_1 * 100%. Flags buses exceeding IEEE 519 limit (5.0% or 8.0%).	res_harmonic_bus
individual_vhd_pct	Individual Harmonic Distortion (%VHD_h)	float (%)	Distortion per harmonic order (h=3, 5, 7, 11, 13, etc.). IEEE 519 enforces 3.0% maximum per order.	res_harmonic_spectrum
thd_i_pct	Branch Current THD (%THD_I)	float (%)	Total harmonic current distortion flowing through lines, cables, and transformers.	res_harmonic_branch
tdd_i_pct	Total Demand Distortion (TDD %)	float (%)	Harmonic current distortion evaluated against maximum customer demand load current (I_L) at the PCC.	res_harmonic_branch
k_factor	Transformer K-Factor	float	Underwriters Laboratories (UL 1561) rating metric for eddy-current heating in transformers supplying non-linear loads.	res_harmonic_trafo
tif	Telephone Interference Factor (TIF)	float	Weighting metric for audio-frequency telephone circuit inductive interference from nearby power lines.	res_harmonic_bus
parallel_resonance_peaks	Parallel Resonance Peak Frequencies	list (Hz, Ω)	Identifies frequencies where system impedance peaks, causing extreme voltage amplification.	res_harmonic_scan
ieee519_status	IEEE Std 519 Compliance Status	str	Overall compliance verdict at the PCC: 'COMPLIANT' or 'VIOLATION' with breakdown of offending orders.	res_harmonic_summary

How to See These Outputs in Real Time in DevEN Workstation:

Interactive Bus THD & %VHD Table

Real-time table displaying THD_V (%), individual harmonic orders (3rd, 5th, 7th, 11th, 13th, etc.), and color-coded IEEE 519 status (PASS / VIOLATION).

Branch Flow & Transformer K-Factor Dock

Displays branch harmonic current flows (A), %THD_I, TDD (%), and UL K-factor ratings to prevent transformer overheating.

Dynamic Frequency Scan & Resonance Curve

Interactive canvas plot of driving-point impedance magnitude |Z(f)| (ohms) vs frequency (Hz) with automated resonance peak tagging.

Harmonic Source & Filter Library Dialog

Modal dialog to inspect, add, or configure non-linear harmonic sources (Amp RMS, % Fund, p.u.) with preset wave libraries (6-pulse, 12-pulse, VFD, arc furnace) and passive R-L-C filters.

Core Mathematical Formulation

$$\mathbf{Y}_{bus}(h) \mathbf{V}_{bus}(h) = \mathbf{I}_{bus}(h), \quad \text{THD}_V = \frac{\sqrt{\sum_{h=2}^{H} V_h^2}}{V_1} \times 100\%, \quad K\text{-Factor} = \frac{\sum_{h=1}^H I_h^2 h^2}{\sum_{h=1}^H I_h^2}$$

Arc Flash Hazard Analysis (AF - IEEE 1584)

Personnel Safety · Incident Energy Standard: IEEE 1584-2018 / NFPA 70E-2024 / OSHA 1910.269

Why Solve this Study? (Engineering Objective & Physical Importance)

Arc Flash Analysis calculates the thermal incident energy ($cal/cm^2$) released during an arcing fault in electrical equipment (switchgear, MCCs, panelboards). It determines the Arc Flash Boundary (AFB) distance, assigns Personal Protective Equipment (PPE) Categories (1 through 4), and generates compliant equipment warning labels required by OSHA.

Verdict / Recommended Best: The IEEE 1584-2018 Empirical Model is the globally mandated BEST method for systems from 208V to 15kV. The Lee Theoretical Model is used only as a fallback for high-voltage open-air transmission substations above 15kV.

Numerical Methods & Algorithms Comparison (Why those methods & Which is Best)

Table 8.1 — Solver Method Evaluation

Algorithm / Method	Mathematical Formulation	Convergence Rate	Best d For	Limitations / Trade-offs	Verdict
IEEE 1584-2018 Empirical Model	Five electrode configurations (VCB, VCBB, HCB, VOA, HOA) derived from 1,800+ physical arc explosion lab tests.	Nonlinear logarithmic regression	All low-voltage and medium-voltage switchgear (208V to 15kV)	Complex iterative calculation of arcing current $I_{arc}$	MANDATED STANDARD FOR INDUSTRIAL SWITCHGEAR
Lee Theoretical Model	Open-air theoretical radiant spherical power dissipation: $E = 2.142 \times 10^6 V I_{bf} t / d^2$.	Closed-form analytical	Outdoor transmission switchyards and open-air busbars	Severely over-predicts incident energy inside metal-clad enclosures	BEST FOR OUTDOOR OPEN-AIR TRANSMISSION YARDS

Study Input Parameters, Options & Recommended Ranges

Table 8.2 — Configuration Options

Option / Param	CLI Slot	Data Type	Default Value	Recommended Range	Engineering Impact & Description
bus_id	Option 1	int	1	[1, 999999]	Target bus or switchgear enclosure to evaluate.
working_dist_mm	Option 2	float	457.2	[304.8, 914.4]	Working distance between worker and arc source (457.2 mm = 18 inches).
gap_mm	Option 3	float	32.0	[13.0, 152.0]	Conductor gap between phases in mm (e.g. 32 mm for 480V switchgear).
box_width_mm	Option 4	float	508.0	[254.0, 1270.0]	Enclosure box width in mm (508 mm = 20 inches).
box_height_mm	Option 5	float	508.0	[254.0, 1270.0]	Enclosure box height in mm.
electrode_config	Option 6	str	VCB	{'VCB': Vertical in Box, 'VCBB': Vert + Barrier, 'HCB': Horizontal in Box, 'VOA': Vert Open, 'HOA': Horiz Open}	Electrode orientation inside switchgear.

Study Outputs & Engineering Meaning (What are those outputs & Why?)

Table 8.3 — Simulation Outputs

Output Variable	Description	Data Type & Unit	Why is this output needed? (Physical & Safety Meaning)	Storage Table
incident_energy_cal	Incident Thermal Energy (E)	float (cal/cm²)	Thermal energy delivered to worker's chest at working distance. Determines exact NFPA 70E PPE rating required.	res_arcflash
afb_mm	Arc Flash Boundary (AFB)	float (mm / inches)	Distance at which incident energy drops to onset of second-degree burn (1.2 cal/cm²). Unqualified personnel must remain outside this boundary.	res_arcflash
ppe_category	NFPA 70E PPE Category	int (1, 2, 3, 4, or DANGER)	Official safety category (Cat 1: 4 cal, Cat 2: 8 cal, Cat 3: 25 cal, Cat 4: 40 cal, DANGER: >40 cal/cm²).	res_arcflash
i_arc_ka	Arcing Current ($I_{arc}$)	float (kA rms)	Actual sustained current through the electric arc in air (always lower than bolted short-circuit current).	res_arcflash
trip_time_s	Protective Clearing Time ($t$)	float (seconds)	Time required for upstream breaker/fuse to extinguish the arc. Directly proportional to total incident energy.	res_arcflash

How to See These Outputs in Real Time in DevEN Workstation:

Arc Flash Warning Label Designer

Generates compliant, printable ANSI/OSHA adhesive warning labels with QR code, incident energy, PPE category, and boundaries.

3D Switchgear Safety Zone View

Displays expanding spherical arc flash boundary zones around 3D switchgear models on the CAD canvas.

Core Mathematical Formulation

$$\log_{10} I_{arc} = k_1 + k_2 \log_{10} I_{bf} + k_3 \log_{10} G, \quad E = 12.552 \times 10^{A + B \log_{10} I_{arc} + C \log_{10} d} \cdot \left(\frac{t}{0.2}\right) \cdot CF$$

BESS Battery Energy Storage Dispatch

Time-Series Optimization · SOC Tracking Standard: IEEE 2030.2.1 / IEC 62933-2 / EPRI Energy Storage

Why Solve this Study? (Engineering Objective & Physical Importance)

BESS Dispatch optimizes the charging and discharging schedule of utility-scale battery energy storage systems across a 24-hour to 7-day operational horizon. It models battery degradation, maintains State of Charge (SOC) within safe operational boundaries, maximizes energy arbitrage revenue, performs solar/wind peak smoothing, and provides spinning reserve.

Verdict / Recommended Best: Linear Programming (LP) using the HiGHS or CLP interior-point solver is the industry BEST choice for economic dispatch. Mixed-Integer Linear Programming (MILP) is preferred when binary charge/discharge interlocks are strictly required.

Numerical Methods & Algorithms Comparison (Why those methods & Which is Best)

Table 7.1 — Solver Method Evaluation

Algorithm / Method	Mathematical Formulation	Convergence Rate	Best d For	Limitations / Trade-offs	Verdict
Linear Programming (LP / HiGHS)	Formulates continuous multi-period convex cost objective subject to linear battery efficiency and SOC bounds.	Polynomial $O(N^3)$	Utility economic arbitrage and peak shaving scheduling	Requires separate linear penalty to prevent simultaneous charge/discharge	BEST FOR WHOLESALE ARBITRAGE & ANNUAL DISPATCH
Mixed-Integer Linear Programming (MILP)	Adds binary status flags ($u_{chg}, u_{dis} \in \{0, 1\}$) to strictly forbid simultaneous charging and discharging.	Branch-and-bound	Rigorous contract modeling and ancillary service bidding	Computation time scales exponentially with time steps	BEST FOR CONTRACT BINDING & MICROGRID CONTROL
Rule-Based Threshold Dispatch	Heuristic logic: charge when solar generation exceeds feeder load, discharge when substation load exceeds setpoint.	Instantaneous logic	Behind-the-meter industrial peak shaving	Sub-optimal economic yield compared to LP/MILP	BEST FOR EMBEDDED CONTROLLER DEPLOYMENT

Study Input Parameters, Options & Recommended Ranges

Table 7.2 — Configuration Options

Option / Param	CLI Slot	Data Type	Default Value	Recommended Range	Engineering Impact & Description
mode	Option 1	str	peak_shaving	{'peak_shaving': Peak Cut, 'arbitrage': Price Arbitrage, 'smoothing': Renewable Firming}	Operational dispatch strategy.
soc_min	Option 2	float	0.10	[0.05, 0.30]	Minimum allowable state of charge (10% to prevent deep cycle degradation).
soc_max	Option 3	float	0.90	[0.70, 1.00]	Maximum allowable state of charge (90% to prevent thermal stress).
efficiency	Option 4	float	0.92	[0.75, 0.98]	Round-trip battery converter and electrochemical efficiency.
peak_price_start	Option 5	int	17	[0, 23]	Start hour for peak price tariff window (e.g. 17:00).
peak_price_end	Option 6	int	21	[0, 23]	End hour for peak price tariff window (e.g. 21:00).

Study Outputs & Engineering Meaning (What are those outputs & Why?)

Table 7.3 — Simulation Outputs

Output Variable	Description	Data Type & Unit	Why is this output needed? (Physical & Safety Meaning)	Storage Table
p_bess_profile	Hourly Dispatch Schedule P(t)	array [MW]	Optimized active power output (+discharging, -charging) for each hour of the operational schedule.	res_bess
soc_profile	State of Charge Timeline SOC(t)	array [%]	Hourly battery energy inventory, verifying SOC remains strictly within statutory 10%-90% limits.	res_bess
arbitrage_revenue	Net Arbitrage Revenue	float ($)	Total economic profit generated by charging at off-peak tariff and discharging at peak tariff.	res_bess
peak_shaved_mw	Peak Demand Reduction	float (MW)	Substation maximum load reduction achieved, lowering utility demand charges.	res_bess
cycle_count	Equivalent Full Cycles	float	Number of full charging cycles completed, used to estimate battery cell degradation and lifetime.	res_bess

How to See These Outputs in Real Time in DevEN Workstation:

Interactive 24-Hour SOC & Power Chart

Dual-axis time-series chart showing battery SOC curve (blue) synchronized with charge/discharge MW bars (green/red) and tariff price line (amber).

Real-Time Microgrid BESS Gauge

Circular gauge on CAD canvas displaying instantaneous battery SOC % and remaining energy (MWh) at POI.

Core Mathematical Formulation

$$SOC(t) = SOC(t-1) + \left( \eta_{chg} P_{chg}(t) - \frac{P_{dis}(t)}{\eta_{dis}} \right) \frac{\Delta t}{E_{rated}}, \quad SOC_{min} \le SOC(t) \le SOC_{max}$$

Total & Available Transfer Capability (TTC / ATC)

Inter-Area Power Transfer · NERC Compliance · N-1 Constrained Standard: NERC MOD-001-1a / MOD-029 / FERC Order 888

Why Solve this Study? (Engineering Objective & Physical Importance)

Determines the physical maximum electric power (MW) that can be reliably transferred between two control areas or across a transmission interface without violating thermal branch ratings, bus voltage thresholds, or system angular stability under normal (N-0) and all single contingency (N-1) outage conditions. Formulates commercial transfer margins for open-access transmission service.

Study Outputs & Commercial Transfer Metrics

Table 12.1 — NERC Transfer Capabilities

Metric	Description	Type & Unit	Engineering & Grid Security Meaning	Storage Table
TTC	Total Transfer Capability	float (MW)	Maximum MW transferable across transmission interface before any branch or voltage limit binds.	res_ttc_atc
ATC	Available Transfer Capability	float (MW)	Commercial power remaining for trade after reserving TRM, CBM, and existing commitments: $ATC = TTC - TRM - CBM - ETC$.	res_ttc_atc
limiting_element	Bottleneck Branch / Outage	text	Identifies specific critical transmission line or transformer that overloads first, preventing further transfer increase.	res_ttc_atc

Core Mathematical Formulation

$$ATC = TTC - TRM - CBM - ETC, \quad PTDF_{ij,mn} = \frac{\Delta P_{ij}}{\Delta P_{m o n}}, \quad OTDF_{ij,mn}^k = PTDF_{ij,mn} + LODF_{ij,k} \cdot PTDF_{k,mn}$$

CLI Engine: DevEN_TTC_Engine.exe --project network.sqlite --source Area1 --sink Area2 Iterative AC-Newton Raphson & Linear OTDF Fast Screening

Continuation Power Flow & Voltage Stability (CPF)

P-V Nose Curves · Saddle-Node Bifurcation · Blackout Margin Standard: IEEE Std 3002.1 / IEEE PES Voltage Stability Guidelines

Why Solve this Study? (Engineering Objective & Physical Importance)

Conventional Newton-Raphson solvers diverge near the maximum transfer limit because the standard power flow Jacobian matrix becomes singular ($\det(\mathbf{J}) o 0$). Continuation Power Flow (CPF) overcomes this limitation using a predictor-corrector continuation technique with an augmented parameter state space. It traces the full upper and lower branches of P-V and Q-V curves, identifying the exact voltage collapse point (saddle-node bifurcation), calculating the MW/MVAr distance to collapse, and pinpointing the most vulnerable load buses in the network.

Core Mathematical Formulation

$$\mathbf{F}(\mathbf{x}, \lambda) = \mathbf{0}, \quad \begin{bmatrix} \mathbf{J} & -\mathbf{K} \ \mathbf{t}_k & \tau_k \end{bmatrix} \begin{bmatrix} d\mathbf{x} \ d\lambda \end{bmatrix} = \begin{bmatrix} \mathbf{0} \ 1 \end{bmatrix}, \quad \mathbf{x}_{corr} = \mathbf{x}_{pred} - \mathbf{J}_{aug}^{-1} \mathbf{F}_{aug}$$

CLI Engine: DevEN_CPF_Engine.exe --project network.sqlite --step 0.05 --lambda-max 3.0 Tangent Predictor & Orthogonal Continuation Corrector

Dynamic Motor Starting Analysis (MS)

Direct-On-Line · Soft Starters · Voltage Dip Flicker Standard: IEEE Std 3002.7 / NEMA MG 1 / API 541 / IEEE 399

Why Solve this Study? (Engineering Objective & Physical Importance)

When large induction or synchronous motors start from rest, they draw massive locked-rotor currents ($500\% - 700\%$ of rated full-load current). This sudden low-power-factor surge causes deep voltage dips across the plant distribution bus. Severe voltage sags can cause adjacent running motors to stall, drop out critical contactors, flicker plant illumination, or prevent the starting motor from developing sufficient acceleration torque to reach rated speed.

Core Mathematical Formulation

$$J \frac{d\omega}{dt} = T_e(\omega, V) - T_L(\omega), \quad T_e \propto V^2, \quad \Delta V_{bus}\% \approx \frac{S_{start}}{S_{sc} + S_{start}} \times 100\%$$

CLI Engine: DevEN_MS_Engine.exe --project network.sqlite --motor-id MOT_101 --starter soft Runge-Kutta 4th Order Electromechanical Solver

Substation Ground Grid Design (GND)

Human Safety · Touch & Step Potentials · Soil Resistivity Standard: IEEE Std 80-2013 / IEEE Std 81 / IEC 60479-1

Why Solve this Study? (Engineering Objective & Physical Importance)

During earth faults at high-voltage substations, massive ground currents flow through the grounding electrode grid into the surrounding earth, creating dangerous potential gradients on the ground surface. Ground Grid Analysis calculates grid resistance ($R_g$), Ground Potential Rise (GPR), Mesh Voltage ($E_m$), and Step Voltage ($E_s$). It verifies that touch and step voltages remain strictly below lethal ventricular fibrillation thresholds for human bodies (50 kg and 70 kg models) under IEEE 80-2013 safety limits.

Core Mathematical Formulation

$$R_g = \rho \left[ \frac{1}{L_T} + \frac{1}{\sqrt{20 A}} \left(1 + \frac{1}{1 + h \sqrt{20/A}}\right) \right], \quad E_{touch50} = \frac{1000 + 1.5 C_s \rho_s}{\sqrt{t_s}} \times 0.116$$

CLI Engine: DevEN_GND_Engine.exe --project network.sqlite --grid-id SUB_GND_01 Sverak & Schwarz Analytical Mesh Integration

Distribution Reliability Evaluation (REL)

SAIFI · SAIDI · CAIDI · ASAI · EENS MWh Standard: IEEE Std 1366 / IEEE Std 493 (Gold Book)

Why Solve this Study? (Engineering Objective & Physical Importance)

Quantifies customer power supply continuity and long-term service reliability across medium- and low-voltage distribution networks. Based on component historical failure rates ($\lambda$ in failures/km/yr), mean repair durations ($r$), and automated recloser switching actions, it computes regulatory performance indices mandated by public utility commissions, including SAIFI, SAIDI, CAIDI, and Expected Energy Not Served (EENS in MWh/yr).

Core Mathematical Formulation

$$\text{SAIFI} = \frac{\sum \lambda_i N_i}{\sum N_i}, \quad \text{SAIDI} = \frac{\sum r_i \lambda_i N_i}{\sum N_i}, \quad \text{CAIDI} = \frac{\text{SAIDI}}{\text{SAIFI}}, \quad \text{EENS} = \sum L_i \lambda_i r_i$$

CLI Engine: DevEN_REL_Engine.exe --project network.sqlite --reclosers auto FMEA Failure Mode & Effects Analysis Algorithm

Power Grid Components & Multi-Study Results

11 Core Power Elements

Component-by-component electrical data model: definitions, physical parameters, data types, defaults, and multi-study output results.

0. Master Grid Components Directory (Click any component to jump directly)

11 Model Elements

Bus / Busbar

14 params · 9 studies

Transmission Line & Cable

19 params · 9 studies

Two-Winding Power Transformer

19 params · 9 studies

Three-Winding Transformer

11 params · 5 studies

Synchronous Generator

21 params · 8 studies

External Grid / Slack Bus

7 params · 5 studies

Electrical Load

7 params · 7 studies

Shunt Capacitor & Reactor

9 params · 6 studies

Static VAr Compensator

7 params · 3 studies

Battery Energy Storage System

11 params · 7 studies

Harmonic Filter

10 params · 3 studies

Bus / Busbar (Substation Node)

Node Model · Core Topology

What is this Component?

A Busbar represents a physical electrical node within a substation or transmission switching yard where generators, transmission lines, transformers, shunts, and loads interconnect. In algebraic network formulations, each bus defines one complex nodal voltage phasor $V_i \angle \theta_i$ and forms the primary row/column index in the nodal admittance matrix $\mathbf{Y}_{bus}$. Buses are categorized into PQ (Load) buses, PV (Generator voltage-controlled) buses, and $V\theta$ (Slack/Swing) buses.

Input Data Model & Physical Parameters

Table 1.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
idx / bus_num	i	int	—	auto (1..N)	Unique integer bus identifier and topological index.
name	Name	str	—	Bus_i	Descriptive station/substation alphanumeric label (e.g. 'SUB_132_BAY1').
type	Type	int	—	1 (PQ)	Nodal operational classification in power flow formulation.
base_kV	V_{base}	float	kV	132.0	Nominal line-to-line phase voltage base of the busbar section.
V_init / Vm	V_{init}	float	p.u.	1.0	Flat-start initial voltage magnitude estimate for iterative solvers.
angle_init / Va	\theta_{init}	float	deg	0.0	Initial voltage phase angle estimate (set to 0.0° for Slack bus).
Vmax	V_{max}	float	p.u.	1.10	Upper statutory voltage limit for over-voltage alarm and tap-changer limits.
Vmin	V_{min}	float	p.u.	0.90	Lower statutory voltage limit for under-voltage alarm and load shedding.
area	Area	int	—	1	Control area number for regional Active Power Generation Control (AGC).
zone	Zone	int	—	1	Loss allocation and tariff zone division for market dispatch.
owner	Owner	int	—	1	Utility ownership boundary code for joint transmission assets.
shunt_G	G_{sh}	float	MW	0.0	Lumped static shunt conductance connected directly to bus (losses at 1.0 p.u.).
shunt_B	B_{sh}	float	MVAr	0.0	Lumped static shunt susceptance connected to bus (+ for Cap, - for Reactor).
cb_mva / CB_Rating	S_{CB}	float	MVA	500.0	Circuit breaker interrupting capacity rating in MVA for IEEE Std 3002.3 and Central Electricity Authority (CEA) Section 6.1 80% duty margin verification.

Multi-Study Results Output Matrix

Table 1.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
LFA (Load Flow Analysis)	Solved Voltage Magnitude ($V_i$)	Reported in per-unit (p.u.) and actual kilovolts (kV = $V_i \times V_{base}$). Identifies weak buses.
	Voltage Phase Angle ($\theta_i$)	Reported in degrees (°). Determines electrical angular separation and power flow direction across lines.
	Net Injected Active Power ($P_i$)	Net algebraic active power injection (Generation - Load - Shunt Losses) in MW.
	Net Injected Reactive Power ($Q_i$)	Net algebraic reactive power injection (Generation - Load + Capacitive Shunt) in MVAr.
	Voltage Violation Flags	Status indicator: 'NORMAL', 'UNDER-VOLTAGE' ($V_i \lt V_{min}$), or 'OVER-VOLTAGE' ($V_i \gt V_{max}$).
	Actual Shunt Injection	Operating reactive injection of attached shunts at solved voltage: $Q_{sh} = V_i^2 \cdot B_{sh}$ (MVAr).
SCS (Short Circuit Study - IEC 60909)	Initial Symmetrical Fault Current ($I_k''$)	Subtransient RMS symmetrical fault current (kA) for 3-phase, SLG, LL, and DLG faults.
	Peak Make Current ($i_p$)	Maximum instantaneous asymmetrical peak current (kA) with DC offset: $i_p = \kappa \sqrt{2} I_k''$.
	Symmetrical Breaking Current ($I_b$)	RMS current (kA) at circuit breaker contact separation time (typically 20ms to 100ms).
	Steady-State Fault Current ($I_k$)	Sustained fault current (kA) after subtransient and transient decay.
	Thevenin Grid Impedance ($Z_{th}$)	Complex driving-point impedance seen at the bus: $Z_{th} = R_{th} + jX_{th}$ and $X/R$ ratio.
	Short-Circuit Capacity ($S_k''$)	Fault level MVA at the bus: $S_k'' = \sqrt{3} \cdot V_{base} \cdot I_k''$ (MVA).
	Sequence Voltages ($V_1, V_2, V_0$)	Positive, negative, and zero sequence voltage magnitudes during unbalance faults.
	Circuit Breaker Duty Margin (%)	Percentage ratio of prospective short-circuit breaking current to rated breaker capacity: $I_k'' / I_{CB}$. Automated CEA 80% design margin verification.
	Target Bus Scope	Targeted single-bus detailed investigation vs system-wide multi-bus scan with multi-attribute filtering (kV, Area, Zone).
CA (Contingency Analysis - N-1)	Post-Contingency Voltage ($V_{i}^{post}$)	Bus voltage under line or generator trip events across all N-1 scenarios.
	Voltage Deviation ($\Delta V_i$)	Maximum voltage dip/swell $\Delta V = \|V_i^{post} - V_i^{base}\|$ across all contingency cases.
	Voltage Performance Index ($PI_V$)	Contribution to system voltage security penalty: $PI_V = \sum \left(\frac{V_i - V_i^{nom}}{\Delta V_i^{max}}\right)^{2m}$.
	Voltage Collapse Margin	Distance to low-voltage limit before contingency-induced voltage collapse.
TS (Time Series Simulation)	Dynamic Voltage Trajectory ($V_i(t)$)	Time-domain voltage waveform across 0 to 10 seconds following fault inception and clearing.
	Dynamic Bus Frequency ($f_i(t)$)	Local instantaneous bus frequency in Hz: $f_i(t) = f_0 + \frac{1}{2\pi}\frac{d\theta_i(t)}{dt}$.
	Voltage Dip Duration ($t_{dip}$)	Duration in milliseconds that bus voltage remains below 0.70 p.u. or 0.80 p.u. (LVRT compliance).
	Under-Voltage Load Shedding Trigger	Flag indicating whether UVLS relays on this bus would trip feeder breakers.
HC (Hosting Capacity)	Max DER Penetration ($MW_{HC}$)	Maximum distributed solar PV or wind capacity that can be connected at this bus without overvoltage.
	Voltage Rise Gradient ($\frac{dV_i}{dP}$)	Analytical sensitivity of bus voltage to active power generation injection (kV/MW).
	Voltage Limit Constraining Metric	Indicates whether $V_{max}$ statutory limit (typically 1.05 p.u.) or thermal limit bounds hosting capacity.
SEN (Sensitivity Analysis)	Voltage-to-Active Sensitivity ($\frac{\partial V_i}{\partial P_j}$)	Partial derivative from inverse Jacobian indicating voltage change per MW transaction.
	Voltage-to-Reactive Sensitivity ($\frac{\partial V_i}{\partial Q_j}$)	dV/dQ sensitivity indicating local reactive power stiffness and capacitor bank effectiveness.
	Q-V Modal Critical Knee Point	Minimum reactive power margin (MVAr) before the bus reaches the dQ/dV = 0 voltage instability bifurcation.
BESS (Battery Energy Storage)	Bus Voltage Stabilization Impact	Reduction in voltage volatility ($\Delta V_{rms}$) achieved by co-located BESS active/reactive dispatch.
BESS (Battery Energy Storage)	Local Inverter Reactive Support	MVAr injection capacity available from 4-quadrant BESS inverter at current bus voltage.
AF (Arc Flash Hazard - IEEE 1584)	Three-Phase Bolted Fault ($I_{bf}$)	Available bolted fault current at the switchgear bus (kA) used as primary arc flash input.
	Arcing Current ($I_{arc}$)	Calculated plasma arc current in kA based on bus enclosure configuration (VCB, VCBB, HCB, VOA).
	Incident Energy ($E$)	Thermal energy dissipated at normalized working distance: reported in $\text{cal/cm}^2$ and $\text{J/cm}^2$.
	Arc Flash Boundary ($AFB$)	Distance in mm (and inches) where incident energy drops to second-degree burn threshold (1.2 $\text{cal/cm}^2$).
	NFPA 70E PPE Category	Mandated Personal Protective Equipment category (Category 1, 2, 3, 4, or DANGER > 40 $\text{cal/cm}^2$).
HAR (Harmonic Analysis - IEEE 519)	Bus Voltage THD (%THD_V)	Total harmonic voltage distortion: THD_V = sqrt(sum(V_h^2)) / V_1 * 100%. Evaluated against IEEE 519 statutory thresholds (5.0% or 8.0%).
	Individual Voltage Distortion (%VHD_h)	Magnitude of distortion per individual harmonic order (3rd, 5th, 7th, 11th, 13th, etc.). Limits: 3.0% max per order.
	Point of Common Coupling (PCC) Status	Automated compliance pass/fail indicator based on short-circuit ratio I_sc / I_L at the utility interface.
	Telephone Interference Factor (TIF)	Inductive interference weighting index on neighboring communications and audio-frequency circuits.
	Driving-Point Parallel Resonance Peaks	Identifies sharp impedance peaks (\|Z(f)\|) that cause catastrophic harmonic voltage magnification.

DevEN Modeling Rule: For large networks, ensure base_kV matches the nominal rating of all connected branches to avoid artificial tap mismatches.

2. Transmission Line & Cable

Branch Model · Pi-Equivalent

What is this Component?

A Transmission Line or Underground Cable is modeled as a lumped-parameter nominal $\pi$-equivalent circuit. It connects two buses ($from\_bus \to to\_bus$) and consists of series resistance $R$, series inductive reactance $X$, total shunt charging susceptance $B$, and shunt conductance $G$. In addition to positive-sequence parameters ($R_1, X_1, B_1$), zero-sequence parameters ($R_0, X_0, B_0$) are required for asymmetrical fault analysis. Lines support up to three seasonal thermal MVA ratings ($Rate\_A, Rate\_B, Rate\_C$).

Input Data Model & Physical Parameters

Table 2.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
line_num / branch_id	k	int	—	auto (1..N)	Unique branch identification number.
from_bus	i	int	—	required	Sending-end terminal bus index.
to_bus	j	int	—	required	Receiving-end terminal bus index.
circuit_id	ckt	str/int	—	'1'	Parallel circuit identifier for double/multi-circuit corridors.
r	R_1	float	p.u.	0.01	Positive-sequence series resistance on system base.
x	X_1	float	p.u.	0.10	Positive-sequence series inductive reactance on system base ($X = 2\pi f L$).
b	B_1	float	p.u.	0.0	Total positive-sequence shunt line charging susceptance ($B = 2\pi f C$).
g	G_1	float	p.u.	0.0	Total shunt dielectric/corona leakage conductance (typically 0.0).
r0	R_0	float	p.u.	0.03	Zero-sequence series resistance (includes earth return impedance).
x0	X_0	float	p.u.	0.30	Zero-sequence series reactance (typically $3 \times X_1$ for overhead lines).
b0	B_0	float	p.u.	0.0	Zero-sequence shunt charging susceptance.
rate_a	S_{max,A}	float	MVA	100.0	Continuous normal thermal power rating (MVA) for steady-state operation.
rate_b	S_{max,B}	float	MVA	120.0	Short-term emergency thermal rating (MVA) (typically 2-hour rating).
rate_c	S_{max,C}	float	MVA	140.0	Transient contingency rating (MVA) (typically 15-minute rating).
length	L	float	km	10.0	Physical line route length for specific impedance and sag calculations.
status	Status	int	—	1 (in-service)	Branch operational switching status (1 = closed, 0 = open).
fault_fraction	d_{fault}	float	%	50.0	Line fault distance location slider percentage from sending bus (from_bus) to receiving bus.
open_conductor	Fault_{series}	str	—	None	Series phase discontinuity fault mode: Broken 1-Phase conductor or 2-Phases open.
z0_mutual / zm0	Z_{m0}	float	p.u.	0.0	Zero-sequence mutual coupling impedance with parallel transmission line corridors.

Multi-Study Results Output Matrix

Table 2.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
LFA (Load Flow Analysis)	Sending-End Power Flow ($P_{from}, Q_{from}$)	Active (MW) and Reactive (MVAr) power injected into the line at from_bus.
	Receiving-End Power Flow ($P_{to}, Q_{to}$)	Active (MW) and Reactive (MVAr) power arriving at to_bus (negative denotes export).
	Apparent Power Flow ($S_{line}$)	Total apparent power loading: $S_{line} = \max(\sqrt{P_{from}^2 + Q_{from}^2}, \sqrt{P_{to}^2 + Q_{to}^2})$ in MVA.
	Active Line Losses ($P_{loss}$)	Total active joule/copper losses: $P_{loss} = P_{from} + P_{to} = I^2 R$ (MW).
	Reactive Line Losses ($Q_{loss}$)	Net reactive losses including series absorption and shunt generation: $Q_{loss} = Q_{from} + Q_{to}$ (MVAr).
	Percentage Thermal Loading	Ratio of operating MVA to continuous rating: $\% \text{Loading} = \frac{S_{line}}{Rate\_A} \times 100\%$.
	Thermal Overload Alarm	Warning trigger if loading exceeds 100% Rate A (Normal) or 100% Rate B (Emergency).
SCS (Short Circuit Study)	Branch Fault Current Flow ($I_{branch}$)	Current (kA) carried by the line during a fault located on either terminal bus or on the line itself.
	Zero-Sequence Current ($3I_0$)	Residual zero-sequence current flowing during single-line-to-ground (SLG) faults.
	Thermal Short-Circuit Stress ($I^2 t$)	Thermal withstand energy: verifies conductor annealing limit is not exceeded before protection clears.
	Series Open Conductor Fault Analysis	Computes sequence voltage unbalance and current redistribution during broken conductor (1-phase open) or 2-phases open series faults.
	Intermediate Line Fault Current	Exact fault current ($I_k''$, $i_p$) when fault occurs at intermediate distance along line.
CA (Contingency Analysis)	Post-Contingency MVA Flow ($S_{line}^{post}$)	Line power loading when an adjacent parallel circuit, line, or generator is removed.
	Line Outage Distribution Factor ($LODF_{l,k}$)	Linear sensitivity factor: fraction of active flow on tripped line $k$ redirected onto line $l$.
	Cascading Tripping Risk	Flags if line loading exceeds Rate C, indicating high risk of immediate cascading thermal tripping.
TS (Time Series Simulation)	Dynamic Power Swings ($P_{line}(t)$)	Oscillatory active power flows during power system oscillations and inter-area modes.
	Apparent Impedance Trajectory ($Z_{app}(t)$)	Dynamic impedance $Z_{app} = \frac{V_{from}(t)}{I_{line}(t)}$ tracked against Distance Relay Mho/Quadrilateral zones (Zones 1, 2, 3).
	Out-of-Step (OOS) Tripping Indicator	Identifies whether the line power swing trajectory enters the generator out-of-step trip boundary.
HC (Hosting Capacity)	Line Thermal Bottleneck Margin	Remaining MW capacity before reverse power flow from solar PV causes line loading to exceed Rate A.
HC (Hosting Capacity)	Reverse Power Flow Direction	Flag indicating whether renewable generation causes net power to flow backwards toward transmission grid.
SEN (Sensitivity Analysis)	Power Transfer Distribution Factor ($PTDF_{l, i-j}$)	MW flow change on this line for a 1 MW power transfer between bus $i$ and bus $j$.
SEN (Sensitivity Analysis)	Loss Sensitivity Factor ($\frac{\partial P_{loss}}{\partial P_i}$)	Marginal transmission loss impact of injecting active power at bus $i$.
BESS (Battery Energy Storage)	Peak Shaving Congestion Relief	Reduction in peak line loading (MW/MVA) achieved by downstream battery discharging during peak demand.
AF (Arc Flash Hazard)	Line Thevenin Contribution to Remote Fault	Line series impedance directly limits the magnitude of remote bolted fault current $I_{bf}$.
AF (Arc Flash Hazard)	Primary Clearing Time ($t_{clr}$)	Line protection relay operating time (Instantaneous Zone 1 vs Time-delayed Zone 2) dictating arcing time $t$.
HAR (Harmonic Analysis)	Branch Harmonic Current Flows ($I_h$)	Spectral breakdown of harmonic currents traversing the cable/line across orders 2 through 50.
	Current Total Harmonic Distortion (%THD_I)	Total harmonic current loading: THD_I = sqrt(sum(I_h^2)) / I_1 * 100%.
	Conductor Skin Effect Resistance	Frequency-dependent copper/aluminum AC resistance rise: R(h) = R_1 * sqrt(h).
	Charging Susceptance Amplification	Line capacitive susceptance escalates linearly with frequency: B(h) = h * B_1.

DevEN Modeling Rule: Always verify X/R ratio. Underground cables typically have high charging susceptance B and lower X/R compared to overhead lines.

Two-Winding Power Transformer

Branch Model · Complex Tap Ratio

What is this Component?

A Two-Winding Power Transformer couples two different voltage levels through electromagnetic induction. Modeled with series leakage impedance ($R + jX$), an off-nominal complex tap ratio $a = \tau \cdot e^{j\theta_{shift}}$ on the primary side, and magnetizing shunt admittance. It features On-Load Tap Changer (OLTC) capabilities to maintain downstream bus voltages within prescribed voltage bandwidths. Zero-sequence impedance modeling accounts for transformer core construction and vector group winding connections (e.g. Dyn11, YNyn0).

Input Data Model & Physical Parameters

Table 3.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
trans_num	t	int	—	auto (1..N)	Unique transformer identification number.
from_bus	i	int	—	required	Primary (HV) terminal bus index.
to_bus	j	int	—	required	Secondary (LV) terminal bus index.
r	R_T	float	p.u.	0.005	Transformer copper winding resistance on system MVA base.
x	X_T	float	p.u.	0.08	Transformer short-circuit leakage reactance on system base ($X = %Z / 100$).
tap	\tau	float	p.u.	1.0	Off-nominal turns ratio ($V_{pri,tap} / V_{pri,nom}$). Default 1.0.
shift	\theta_{shift}	float	deg	0.0	Phase-shifting angle (e.g. 30.0° for standard Dyn11 / Yd1 delta-star shift).
rate_a	S_{n,A}	float	MVA	50.0	Continuous self-cooled MVA rating (ONAN rating).
rate_b	S_{n,B}	float	MVA	65.0	Forced-air cooled MVA rating (ONAF rating).
rate_c	S_{n,C}	float	MVA	80.0	Emergency forced-oil/air rating (OFAF rating).
tap_min	\tau_{min}	float	p.u.	0.90	Lower mechanical limit of OLTC tap range.
tap_max	\tau_{max}	float	p.u.	1.10	Upper mechanical limit of OLTC tap range.
step_size	\Delta\tau	float	p.u.	0.00625	Voltage adjustment resolution per tap step (e.g. 0.625% = 1/160 p.u.).
controlled_bus	bus_{ctrl}	int	—	to_bus	Bus index whose voltage magnitude is monitored and regulated by OLTC.
vector_group	Vector	str	—	'Dyn11'	Winding configuration code dictating zero-sequence isolation and angular shift.
r0, x0	Z_0	float	p.u.	0.005, 0.08	Zero-sequence impedance (dependent on core design: 3-limb vs 5-limb).
grounding_r	R_g	float	ohms	0.0	Neutral Grounding Resistor (NGR) value for ground fault limitation.
grounding_x	X_g	float	ohms	0.0	Neutral grounding reactance in ohms.
core_type	Core	str	—	'3-limb'	Transformer core magnetic topology dictating zero-sequence magnetic reluctance path.

Multi-Study Results Output Matrix

Table 3.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
LFA (Load Flow Analysis)	Primary / Secondary Power Flows	Active (MW) and Reactive (MVAr) power at both HV and LV terminals.
	Copper ($I^2 R$) & Core Losses	Active winding losses (MW) and reactive leakage consumption (MVAr).
	Transformer Percentage Loading	Ratio of throughput MVA to ONAN/ONAF rating: $\% \text{Loading} = \frac{S}{S_n} \times 100\%$.
	Final Solved OLTC Tap Position	Actual discrete tap step selected by automatic tap changer to satisfy voltage deadband.
SCS (Short Circuit Study)	Through-Fault Current ($I_{sc}$)	Symmetrical short-circuit current passing through the transformer during downstream faults.
	Zero-Sequence Trapping (Delta)	Delta winding provides open-circuit to zero-sequence upstream; traps zero-sequence circulation.
	Neutral Grounding Current ($3I_0$)	Current flowing through neutral grounding resistor during single-line-to-ground faults.
CA (Contingency Analysis)	Parallel Unit Outage Loading	Checks if loss of parallel transformer causes remaining unit to exceed emergency ONAF/OFAF rating.
CA (Contingency Analysis)	Automatic OLTC Response	Simulates post-contingency tap-changer stepping to restore sagging secondary voltages.
TS (Time Series Simulation)	Reactive Absorption During Faults	Elevated reactive power consumption by transformer leakage inductance during low voltage.
TS (Time Series Simulation)	Flux Saturation Trajectory	Monitors core saturation effects following severe close-in fault recovery.
HC (Hosting Capacity)	Reverse Power Flow Limitation	Permissible reverse power (LV to HV) before violating thermal rating or causing OLTC hunting.
SEN (Sensitivity Analysis)	Tap-to-Voltage Sensitivity ($\frac{\partial V}{\partial \tau}$)	Direct analytical response of secondary voltage per tap step change.
BESS (Battery Energy Storage)	Transformer Substation Deferral	BESS discharging during peak hours prevents upgrading transformer to higher MVA rating.
AF (Arc Flash Hazard)	Downstream LV Switchgear Hazard	Transformer impedance $X_T$ is the primary determinant of bolted fault current $I_{bf}$ on LV switchgear.
AF (Arc Flash Hazard)	Primary Fuse / Relay Clearing Time	Upstream HV protection clearing curve defines arcing time $t$ for secondary arc flash calculations.
HAR (Harmonic Analysis)	Transformer Harmonic Current ($I_{tr,h}$)	Multi-frequency current flows through primary and secondary windings.
	UL 1561 Transformer K-Factor	Standardized metric quantifying eddy-current winding losses: K = sum(I_h^2 * h^2) / sum(I_h^2). Sizing K-rated transformers.
	Eddy Current Loss Derating Factor	Thermal derating required when conventional non-K-rated transformers supply non-linear harmonic loads.
	Triplen Harmonic Trapping (Delta)	Delta tertiary/primary windings trap zero-sequence triplen harmonics (3rd, 9th, 15th), preventing network propagation.

DevEN Modeling Rule: Set vector_group carefully (e.g. Dyn11 vs YNyn0) as zero-sequence fault currents depend entirely on delta/wye connections.

4. Three-Winding Transformer

Three-Port Network · Star Equivalent

What is this Component?

A Three-Winding Transformer connects three independent voltage levels (Primary, Secondary, and Tertiary) inside a single magnetic core tank. In power flow and short-circuit algorithms, it is converted into a three-branch fictitious star ($Y$) equivalent network with a central internal star point $T$. The branch impedances ($Z_p, Z_s, Z_t$) are calculated from standard factory short-circuit test pair measurements ($Z_{12}, Z_{23}, Z_{31}$). The tertiary winding is frequently connected in delta to suppress third-harmonic voltages and provide auxiliary station service.

Input Data Model & Physical Parameters

Table 4.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
trans3w_num	t3	int	—	auto (1..N)	Unique 3-winding transformer identifier.
bus1, bus2, bus3	p, s, t	int	—	required	Primary (HV), Secondary (MV), and Tertiary (LV) bus indices.
r12, x12	Z_{12}	float	p.u.	0.005, 0.10	Positive-sequence leakage impedance between Primary and Secondary.
r23, x23	Z_{23}	float	p.u.	0.008, 0.15	Positive-sequence leakage impedance between Secondary and Tertiary.
r31, x31	Z_{31}	float	p.u.	0.006, 0.12	Positive-sequence leakage impedance between Tertiary and Primary.
rate12, rate23, rate31	S_n	float	MVA	100, 60, 30	Nameplate MVA ratings for each winding pair.
tap1, tap2, tap3	\tau_{1,2,3}	float	p.u.	1.0, 1.0, 1.0	Individual winding off-nominal tap ratios.
shift1, shift2, shift3	\theta_{1,2,3}	float	deg	0.0, 30.0, 30.0	Individual winding phase shift angles.
status	Status	int	—	1 (in-service)	Operational service status.
r0_12..31, x0_12..31	Z_{0,ij}	float	p.u.	0.006, 0.10	Zero-sequence pair test impedances for three-winding equivalent star network.
tertiary_delta	Delta_{tert}	str	—	'closed'	Tertiary delta winding state for harmonic suppression and zero-sequence circulating path.

Multi-Study Results Output Matrix

Table 4.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
LFA (Load Flow Analysis)	Individual Winding Power Flows	Active (MW) and Reactive (MVAr) power flowing into Primary, Secondary, and Tertiary.
	Internal Star-Point Voltage	Calculated voltage magnitude and phase angle at fictitious central node $T$.
	Per-Winding Percentage Loading	Loading percentage computed independently for each winding against its own MVA rating.
SCS (Short Circuit Study)	Multi-Port Fault Current Contribution	Fault current contributions through all three ports during external or internal bus faults.
SCS (Short Circuit Study)	Delta Tertiary Circulating Current	Zero-sequence current circulating inside closed tertiary delta during ground faults.
CA (Contingency Analysis)	Winding Overload Screening	Identifies if high power transfer across secondary causes tertiary winding overload.
TS (Time Series Simulation)	Three-Port Voltage Support Dynamics	Dynamic reactive power distribution across all three coupled voltage levels.
AF (Arc Flash Hazard)	Tertiary Switchgear Hazard Assessment	Calculates arc flash incident energy on lower-voltage tertiary auxiliary switchboard.

DevEN Modeling Rule: Notice that Z_p, Z_s, or Z_t can sometimes yield a negative equivalent reactance in the fictitious star; this is mathematically normal.

5. Synchronous Generator (Power Source)

Active Source · AVR Voltage Control

What is this Component?

A Synchronous Generator represents a large centralized power generation unit (thermal, hydro, nuclear, gas turbine). In steady-state load flow, it is modeled as a PV bus with active power setpoint $P_g$ and target terminal voltage $V_{set}$, constrained by reactive power capability limits $[Q_{min}, Q_{max}]$. When reactive limits are hit, the solver converts the bus to PQ mode. In dynamic simulations, 6th-order or 4th-order machine models represent transient and subtransient fluxes along with exciter/AVR and governor controls.

Input Data Model & Physical Parameters

Table 5.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
gen_num	g	int	—	auto (1..N)	Unique generator machine identifier.
bus	i	int	—	required	Terminal bus index where generator is connected.
P_out / Pg	P_g	float	MW	100.0	Dispatched active power generation setpoint.
Q_out / Qg	Q_g	float	MVAr	20.0	Initial/dispatched reactive power generation.
V_set / Vg	V_{set}	float	p.u.	1.02	Target regulated terminal voltage magnitude for AVR.
Qmax	Q_{max}	float	MVAr	60.0	Maximum reactive power output (rotor thermal/field heating limit).
Qmin	Q_{min}	float	MVAr	-30.0	Minimum reactive power absorption (stator end-iron heating/underexcitation limit).
Pmax	P_{max}	float	MW	150.0	Turbine maximum prime-mover active power capability.
Pmin	P_{min}	float	MW	20.0	Boiler/turbine technical minimum stable active power limit.
mbase	S_{base,m}	float	MVA	120.0	Machine rated apparent power base.
r1, x1 / xdpp	X_d''	float	p.u.	0.02, 0.15	Direct-axis subtransient reactance on machine base for short-circuit.
r2, x2	X_2	float	p.u.	0.02, 0.15	Negative-sequence impedance for unbalanced fault calculations.
r0, x0	X_0	float	p.u.	0.01, 0.08	Zero-sequence leakage impedance.
H	H	float	s	4.0	Inertia constant: stored kinetic energy per rated MVA ($\text{MW}\cdot\text{s}/\text{MVA}$).
D	D	float	p.u.	0.0	Damping coefficient representing asynchronous damper winding torque.
status	Status	int	—	1 (in-service)	Generator commitment status.
xd_sync / Xd	X_d	float	p.u.	1.20	Direct-axis steady-state synchronous reactance on machine MVA base.
xd_p / Xd'	X_d'	float	p.u.	0.30	Direct-axis transient reactance on machine MVA base.
grounding_type	Gnd	str	—	'solid'	Neutral grounding scheme configuration for zero-sequence impedance network.
rg / R_ground	R_g	float	ohms	0.0	Generator neutral grounding resistance in ohms.
xg / X_ground	X_g	float	ohms	0.0	Generator neutral grounding reactance in ohms.

Multi-Study Results Output Matrix

Table 5.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
LFA (Load Flow Analysis)	Generated Active Power ($P_g$)	Final dispatched active power output in MW.
	Generated Reactive Power ($Q_g$)	Actual reactive power injected in MVAr to maintain $V_{set}$.
	Q-Limit Status (PV $\to$ PQ Switch)	Indicates whether generator is operating in normal voltage control or clamped at $Q_{max}$ / $Q_{min}$.
	Available Reactive Reserve ($\Delta Q$)	Remaining reactive margin: $\Delta Q_{cap} = Q_{max} - Q_g$ and $\Delta Q_{ind} = Q_g - Q_{min}$.
SCS (Short Circuit Study)	Subtransient Fault Current ($I_k''$)	Initial instantaneous fault current contribution: $I_k'' = \frac{c \cdot V_n}{\sqrt{3} \cdot X_d''}$ (kA).
	Decaying AC Component ($I_b$)	Symmetrical breaking current after subtransient decay factor $\mu$.
	DC Offset Current ($i_{dc}$)	Exponentially decaying DC component governed by armature time constant $T_a = X_d'' / (2\pi f R_a)$.
	Neutral Grounding Resistor Loss ($P_{NGR}$)	Active thermal dissipation in neutral grounding resistor: $P_{NGR} = 3 I_0^2 R_g$ in kW / MW.
	Asymmetrical Fault Feeds	Individual phase fault contributions ($I_a, I_b, I_c$) and sequence currents ($I_1, I_2, I_0$) into ground and line-to-line faults.
CA (Contingency Analysis)	Generator Outage ($N-1$ Gen)	Simulates sudden loss of this generator: evaluates system frequency dip and spinning reserve pickup.
CA (Contingency Analysis)	Post-Contingency Reactive Loading	Monitors surviving generators picking up reactive burden to prevent field breaker tripping.
TS (Time Series Simulation)	Rotor Angle Swing Curve ($\delta(t)$)	Rotor angular displacement over time: monitors first-swing stability and multi-swing damping.
	Rotor Speed Deviation ($\Delta\omega(t)$)	Instantaneous machine frequency deviation (p.u. and Hz).
	Critical Clearing Time (CCT)	Maximum allowable fault duration (in ms) before the generator loses synchronism (pole slips).
HC (Hosting Capacity)	System Inertia Displacement Metric	Evaluates reduction in system total $H_{sys}$ as solar/wind generation curtails synchronous units.
SEN (Sensitivity Analysis)	Generator Participation Factors	Determines active power re-dispatch allocation factor for loss compensation.
BESS (Battery Energy Storage)	Fast Frequency Response (FFR)	BESS sub-second active power injection reduces generator governor ramp strain during sudden trips.
AF (Arc Flash Hazard)	Generator Fault Contribution	Direct subtransient fault feed into power plant medium-voltage switchgear arc flash calculations.

DevEN Modeling Rule: Always check Qmax and Qmin. If Qmax=Qmin, the generator is treated strictly as a fixed PQ generator.

6. External Grid / Slack Bus (Swing Node)

Infinite Bus · System Reference

What is this Component?

The External Grid or Slack Bus acts as the mathematical and physical balance point of the power system. It fixes the global phase reference angle $\theta = 0.0^\circ$ and provides arbitrary active and reactive power injection to balance network transmission losses and load discrepancies: $P_{slack} = \sum P_{load} + \sum P_{loss} - \sum P_{gen}$. In short-circuit studies, it represents the upstream interconnecting transmission grid defined by its short-circuit MVA level $S_k''$ and $R/X$ ratio.

Input Data Model & Physical Parameters

Table 6.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
bus	i	int	—	required	Terminal bus designated as system reference bus.
V_set	V_{slack}	float	p.u.	1.0	Fixed reference voltage magnitude.
angle_set	\theta_{slack}	float	deg	0.0	Global reference phase angle for all network phasors.
Pmin, Pmax	P_{limits}	float	MW	-9999, 9999	Import/export boundary limits on transmission intertie.
Qmin, Qmax	Q_{limits}	float	MVAr	-9999, 9999	Reactive power limits on grid intertie connection.
Sk_max	S_k''	float	MVA	5000.0	Upstream grid short-circuit MVA capacity for Thevenin equivalent.
Rx_ratio	R/X	float	—	0.10	Upstream grid equivalent resistance to reactance ratio.

Multi-Study Results Output Matrix

Table 6.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
LFA (Load Flow Analysis)	Total Net Slack Active Power ($P_{slack}$)	Total MW imported from (or exported to) external grid to balance all system loads and losses.
LFA (Load Flow Analysis)	Total Net Slack Reactive Power ($Q_{slack}$)	Total MVAr required to maintain slack bus target voltage magnitude.
SCS (Short Circuit Study)	Grid Thevenin Source Impedance	Upstream source impedance: $Z_{grid} = \frac{1.1 \cdot V_n^2}{S_k''}$ in ohms on system base.
SCS (Short Circuit Study)	Upstream Grid Fault Contribution	Current (kA) delivered by external transmission grid to the fault location.
CA (Contingency Analysis)	Grid Tie Overload Check	Verifies that local generator outages do not violate intertie import MVA contract limits.
TS (Time Series Simulation)	Infinite Bus Inertial Reference	Acts as the rigid center of inertia against which local synchronous generators swing.
AF (Arc Flash Hazard)	Utility Source Short-Circuit Strength	Upstream grid $S_k''$ directly establishes the available bolted fault current $I_{bf}$ at incoming switchgear.

DevEN Modeling Rule: A power system must have at least one Slack bus to establish the angle reference and solve power balance.

Electrical Load (ZIP Model)

Demand Model · Voltage Dependent

What is this Component?

An Electrical Load consumes active power $P_d$ and reactive power $Q_d$. DevEN supports constant power (PQ), constant current (I), constant impedance (Z), and composite voltage-dependent polynomial ZIP models. Active and reactive power vary nonlinearly with actual operating bus voltage $V$ based on user-configured polynomial shares ($p_1, p_2, p_3$ and $q_1, q_2, q_3$), enabling realistic representation of industrial induction motors, resistive heating, and electronic power supplies.

Input Data Model & Physical Parameters

Table 7.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
load_num	d	int	—	auto (1..N)	Unique load identifier.
bus	i	int	—	required	Connection bus index.
P_demand / Pd	P_0	float	MW	10.0	Base nominal active power demand at nominal voltage $V_0$.
Q_demand / Qd	Q_0	float	MVAr	3.0	Base nominal reactive power demand (positive denotes inductive lag).
p1, p2, p3	p_{Z,I,P}	float	—	0, 0, 1	ZIP active power coefficients ($p_1 + p_2 + p_3 = 1.0$): Z=const imp, I=const cur, P=const pwr.
q1, q2, q3	q_{Z,I,P}	float	—	0, 0, 1	ZIP reactive power coefficients ($q_1 + q_2 + q_3 = 1.0$).
status	Status	int	—	1 (in-service)	Load operational service status (1 = connected, 0 = disconnected).

Multi-Study Results Output Matrix

Table 7.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
LFA (Load Flow Analysis)	Actual Realized Demand ($P_{actual}, Q_{actual}$)	Realized active/reactive power consumed at the bus under solved operating voltage $V_i$.
LFA (Load Flow Analysis)	Load Power Factor ($\cos\phi$)	Operating power factor: $PF = \frac{P}{\sqrt{P^2 + Q^2}}$ (lagging/leading).
SCS (Short Circuit Study)	Large Industrial Motor Infeed	If load includes large medium-voltage induction motors, calculates their short-circuit infeed current.
CA (Contingency Analysis)	Under-Voltage Load Shedding (UVLS)	Identifies automated load shedding blocks triggered by severe low voltage.
TS (Time Series Simulation)	Dynamic Voltage Recovery (FIDVR)	Simulates Fault Induced Delayed Voltage Recovery caused by air conditioning and motor stalling.
HC (Hosting Capacity)	Minimum Daytime Load Threshold	Minimum load valley determines worst-case reverse power flow during peak solar hours.
SEN (Sensitivity Analysis)	Voltage Collapse Indicator	Evaluates load margin to saddle-node bifurcation as demand increases.
HAR (Harmonic Analysis)	Non-Linear Harmonic Injection ($I_{inj}(h)$)	Nodal current spectrum injected into grid from VFDs, rectifiers, arc furnaces, and power electronic converters.
	Harmonic Spectrum Units	Supports direct input in Ampere RMS, Percentage of Fundamental (%), or per-unit (p.u.).
	Sequence Angle Rotation	Applies characteristic 3-phase sequence rotation: 6k-1 negative, 6k+1 positive, 3k zero sequence.
	Standard Harmonic Preset Library	Built-in typical spectrum profiles: 6-pulse converter, 12-pulse converter, PWM VFD, AC arc furnace, and SMPS/LED drivers.

DevEN Modeling Rule: Default is pure constant power (p3=1, q3=1). For distribution studies with voltage-sensitive loads, set p1=0.4, p2=0.3, p3=0.3.

8. Shunt Capacitor & Reactor

VAr Compensation · Voltage Support

What is this Component?

Shunt Capacitors inject reactive power to boost low voltages and improve power factors ($Q_{sh} = +V^2 B$), while Shunt Reactors absorb surplus capacitive charging reactive power on lightly loaded high-voltage lines to prevent the Ferranti overvoltage effect ($Q_{sh} = -V^2 B$). Shunts can be fixed or automatically stepped to maintain bus voltage within a designated target deadband.

Input Data Model & Physical Parameters

Table 8.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
shunt_num	sh	int	—	auto (1..N)	Unique shunt device identifier.
bus	i	int	—	required	Bus where shunt bank is installed.
B_mvar	B_{nom}	float	MVAr	10.0	Nominal reactive rating at 1.0 p.u. voltage (+ for Cap, - for Reactor).
G_mw	G_{nom}	float	MW	0.0	Active dielectric loss component (typically 0.0).
steps	N_{steps}	int	—	1	Number of switchable capacitor/reactor steps.
control_mode	Mode	int	—	0 (Fixed)	Operational switching control mode.
status	Status	int	—	1 (in-service)	Shunt bank in-service status.
ngr_r / R_ngr	R_{NGR}	float	ohms	0.0	Neutral Grounding Resistor (NGR) value connected at substation neutral.
p_ngr_kw	P_{NGR}	float	kW	0.0	Maximum continuous / short-time thermal power rating of the NGR (kW).

Multi-Study Results Output Matrix

Table 8.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
LFA (Load Flow Analysis)	Actual Operating Reactive Output ($Q_{actual}$)	Delivered reactive power at solved bus voltage: $Q_{actual} = V_i^2 \cdot B_{nom}$ (MVAr).
LFA (Load Flow Analysis)	Voltage Elevation ($\Delta V$)	Bus voltage improvement achieved by shunt capacitor connection: $\Delta V \approx \frac{Q_{actual}}{S_{sc}}$ (p.u.).
SCS (Short Circuit Study)	Fault Current Effect	Shunt capacitor contribution to power-frequency fault current is negligible and automatically bypassed.
CA (Contingency Analysis)	Post-Contingency Shunt Switching	Simulates automatic capacitor bank step-in during line outage to prevent low voltage alarms.
TS (Time Series Simulation)	Capacitor Energization Surge	Voltage transient and high-frequency inrush current during capacitor bank switching.
SEN (Sensitivity Analysis)	dV/dQ Effectiveness Check	Verifies whether shunt placement provides optimal voltage control leverage.
HAR (Harmonic Analysis)	Parallel Resonance Order ($h_r$)	Calculates resonance harmonic order: h_r = sqrt(S_sc / Q_cap). Flags high risk of harmonic amplification.
	Frequency-Dependent Admittance	Capacitive susceptance multiplies with order (Y_C = jhB), whereas inductive reactance diminishes (Y_L = -j*B/h).
	Harmonic Overvoltage & Overcurrent Stress	Verifies capacitor duty margins against IEEE Std 18 limits (110% peak V, 180% rms I, 135% kvar).

DevEN Modeling Rule: Because capacitor output is proportional to V^2, its reactive support drops precisely when the grid needs it most during low-voltage dips.

9. Static VAr Compensator (SVC) & STATCOM

FACTS Controller · Fast Dynamic VAr

What is this Component?

A Static VAr Compensator (SVC) or Static Synchronous Compensator (STATCOM) is a fast-acting Power Electronics Flexible AC Transmission System (FACTS) device. It modulates reactive power output continuously between an inductive limit $Q_{min}$ and a capacitive limit $Q_{max}$ according to a defined voltage-current slope characteristic to maintain voltage stability at a critical transmission bus.

Input Data Model & Physical Parameters

Table 9.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
svc_num	svc	int	—	auto (1..N)	Unique FACTS device identifier.
bus	i	int	—	required	Connection bus index.
V_set	V_{ref}	float	p.u.	1.0	Target voltage setpoint.
slope	X_{sl}	float	p.u.	0.03	V-I slope / droop characteristic ($V = V_{ref} + X_{sl} \cdot I$).
Q_max	Q_{max}	float	MVAr	100.0	Maximum capacitive reactive power capability at 1.0 p.u.
Q_min	Q_{min}	float	MVAr	-100.0	Maximum inductive reactive power capability at 1.0 p.u.
status	Status	int	—	1 (in-service)	Operational service status.

Multi-Study Results Output Matrix

Table 9.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
LFA (Load Flow Analysis)	Operating Reactive Dispatch ($Q_{svc}$)	Continuous reactive output within $[Q_{min}, Q_{max}]$ maintaining voltage within slope.
LFA (Load Flow Analysis)	Operating Region Indicator	Reports whether SVC is in Linear Control, Clamped Capacitive, or Clamped Inductive limit.
TS (Time Series Simulation)	Dynamic Power Swing Damping	Sub-cycle reactive modulation to rapidly damp electromechanical inter-area power swings.
CA (Contingency Analysis)	Voltage Collapse Prevention	Instantaneous reactive injection prevents voltage collapse during severe transmission tripping.

DevEN Modeling Rule: STATCOM maintains full rated capacitive current even at depressed voltages (I=const), whereas SVC output drops with V^2.

Battery Energy Storage System (BESS)

Electrochemical Storage · 4-Quadrant PCS

What is this Component?

A Battery Energy Storage System (BESS) pairs electrochemical battery cells (Lithium-ion, Flow, NaS) with a 4-quadrant bi-directional Power Conversion System (PCS) inverter. It can inject or absorb active power ($P \gt 0$ discharge, $P \lt 0$ charge) subject to State-of-Charge constraints ($SOC_{min} \le SOC(t) \le SOC_{max}$) while simultaneously providing independent reactive power support ($Q_{min} \le Q \le Q_{max}$) for voltage regulation, renewable smoothing, and peak shaving.

Input Data Model & Physical Parameters

Table 10.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
bess_num	bess	int	—	auto (1..N)	Unique BESS installation identifier.
bus	i	int	—	required	Grid connection bus index.
P_rated_mw	P_{rated}	float	MW	20.0	Maximum continuous active power charge/discharge rating.
E_rated_mwh	E_{rated}	float	MWh	80.0	Total rated nameplate electrical energy storage capacity.
SOC_init	SOC_0	float	p.u.	0.50	Initial state-of-charge fraction at start of simulation.
SOC_min, SOC_max	SOC_{lim}	float	p.u.	0.10, 0.90	Usable operational battery state-of-charge limits to prolong cell life.
efficiency_chg	\eta_{chg}	float	—	0.95	One-way battery charging roundtrip efficiency.
efficiency_dis	\eta_{dis}	float	—	0.95	One-way battery discharging roundtrip efficiency.
Q_max, Q_min	Q_{lim}	float	MVAr	15.0, -15.0	Inverter 4-quadrant reactive power capability limits: $S_{pcs} = \sqrt{P^2 + Q^2}$.
dispatch_mode	Mode	str	—	'Peak Shaving'	Control strategy: Peak Shaving, Solar Smoothing, Frequency Regulation, Energy Arbitrage.
status	Status	int	—	1 (in-service)	Operational service status.

Multi-Study Results Output Matrix

Table 10.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
LFA (Load Flow Analysis)	Active Power Injection ($P_{bess}$)	Dispatched power: positive denotes discharging into grid, negative denotes charging from grid.
	Inverter Reactive Injection ($Q_{bess}$)	Active voltage support provided by 4-quadrant inverter without depleting battery energy storage.
	Net Bus Impact	Alleviates upstream transformer and feeder loading.
SCS (Short Circuit Study)	Inverter Current-Limiting Contribution	Inverter-based short circuit current limited to $1.1 - 1.2 \times I_{rated}$ (no subtransient peak).
SCS (Short Circuit Study)	Zero-Sequence Current	Zero-sequence current is zero unless grounding transformer is explicitly added.
CA (Contingency Analysis)	Emergency Islanding Backup	Provides rapid active/reactive injection to support critical islanded microgrid loads during line trips.
TS (Time Series Simulation)	Virtual Inertia & Fast Frequency Response (FFR)	Sub-cycle active power injection ($P_{synth} = -2H_{virt} \frac{df}{dt}$) arresting frequency nadir.
HC (Hosting Capacity)	Feeder Solar Hosting Capacity Multiplier	Absorbs peak midday solar PV generation, doubling or tripling feeder hosting capacity without overvoltage.
BESS Optimization	24-Hour State-of-Charge Curve ($SOC(t)$)	Hourly battery energy tracking across 24 hours verifying bounds ($SOC_{min} \le SOC \le SOC_{max}$).
	Optimal Charge/Discharge Schedule	Time-of-use cost arbitrage and renewable curtailment reduction schedule.
	Battery Degradation & Cycle Life	Estimated equivalent full cycles (EFC) and battery health depreciation.
AF (Arc Flash Hazard)	DC Rack Arc Flash Hazard	NFPA 70E DC arc flash incident energy calculation inside battery rack containers.
AF (Arc Flash Hazard)	AC Inverter Terminal Hazard	Incident energy at low-voltage AC terminals of Power Conversion System.

DevEN Modeling Rule: BESS inverters can operate in Grid-Following (PQ control) or Grid-Forming (V-f droop control) mode during microgrid islanding.

Harmonic Filter (Passive R-L-C Shunt Filter)

Power Quality · Resonant Trap · Notch Filter

What is this Component?

A Passive Harmonic Filter connects directly to a bus to provide a low-impedance bypass path (resonant trap) for specific harmonic orders while providing fundamental power frequency reactive compensation (MVAr). DevEN models three standard topologies: Single-Tuned R-L-C, Second-Order High-Pass, and C-Type Damped filters.

Input Data Model & Physical Parameters

Table 11.1 — Parameter Specifications

Parameter	Symbol	Data Type	Unit	Default	Physical Meaning & Valid Range
filter_num	f	int	—	auto (1..N)	Unique passive filter branch identifier.
bus	i	int	—	required	Connection bus index where filter is installed.
filter_type	Type	str	—	'single_tuned'	Filter circuit configuration topology.
tuned_harmonic	h_n	float	—	5.0	Harmonic order to which the filter branch is tuned (e.g. 4.7 for 5th harmonic detuned trap).
q_mvar	Q_f	float	MVAr	5.0	Nominal fundamental reactive power generated by filter capacitor at 1.0 p.u. voltage.
quality_factor	Q	float	—	30.0	Quality sharpness factor: Q = X_0 / R where X_0 = sqrt(L/C).
r_ohms	R	float	ohms	0.50	Damping series resistance in ohms.
l_mh	L	float	mH	12.5	Series reactor tuning inductance in millihenries.
c_uf	C	float	µF	68.0	Capacitor bank capacitance in microfarads.
status	Status	int	—	1 (in-service)	Filter operational connection status.

Multi-Study Results Output Matrix

Table 11.2 — Simulation Outputs

Simulation Study	Component Output Variable	Engineering Interpretation & Impact
HAR (Harmonic Analysis - IEEE 519)	Harmonic Notch Impedance ($Z_{filter}(h)$)	Branch impedance magnitude across harmonic frequencies: minimum at notch frequency f_n.
	Absorbed Harmonic Current ($I_{filter,h}$)	Spectral current shunted away from the main grid into the filter trap.
	Post-Mitigation Bus THD Reduction	Immediate drop in bus %THD_V to achieve full IEEE 519 compliance.
	Resonance Damping Efficacy	Suppresses dangerous parallel resonance peaks between capacitor banks and utility grid impedance.
LFA (Load Flow Analysis)	Fundamental Reactive Injection ($Q_{fund}$)	Steady-state capacitive MVAr delivered at power frequency to improve power factor.
SCS (Short Circuit Study)	Subtransient Fault Infeed	High-frequency infeed during bus faults evaluated for breaker transient recovery voltage (TRV).

DevEN Modeling Rule: Filters are typically detuned slightly below target harmonic (e.g. 4.7th instead of 5.0th) to account for component tolerances and avoid resonant interaction.

Engine CLI & Headless Solvers · All 16 Studies Supported in Headless Binary Execution

CLI Headless Solvers & Script Automation

DevEN delivers 16 ultra-fast C++ and Python-native headless simulation binaries for automated HPC cluster runs, continuous parameter sweeps, CI/CD pipeline verification, and enterprise integration without requiring a graphical display.

Quick jump:

0. Architecture 1. LFA 2. 3P LFA 3. SCS 4. CA 5. TS 6. 3P TS 7. HC 8. SEN 9. HAR 10. AF 11. BESS 12. TTC 13. CPF 14. MS 15. GND 16. REL

CLI Architecture, Engine Roster & Execution Paradigms

Headless Execution · Multi-Study Integration · Automated Data Pipeline

How DevEN CLI Engines Work:

Every computational solver in DevEN is compiled into an independent, zero-dependency native Windows executable. Each binary reads input network cases from a standard SQLite database file (.db), executes high-speed numerical calculations using optimized sparse linear algebra (Eigen / Sparse), and commits solution tables directly back into the SQLite database.

Unified Calling Convention: All 16 study engines support simple default invocation (run_engine.exe case.db) or advanced parameterization using either individual command-line flags or the unified 22-slot compact hyphen-delimited string.

Complete Directory of 16 CLI Study Solvers:

run_loadflow.exe 1

1-Phase Load Flow Analysis (LFA)

run_3ph_lfa.exe 2

Three-Phase Unbalanced Power Flow (3P LFA)

run_scs.exe 3

Short Circuit Study (SCS - IEC 60909 & ANSI C37)

run_contingency.exe 4

Contingency Analysis & N-1 Security (CA)

run_timeseries.exe 5

1-Phase Time Series Simulation (TS)

run_3ph_ts.exe 6

Three-Phase Chronological Time Series (3P TS)

run_hosting.exe 7

DER & Hosting Capacity Analysis (HC)

run_sensitivity.exe 8

Voltage & Power Sensitivity Analysis (SEN)

run_harmonics.exe 9

Harmonic Analysis & Power Quality (HAR - IEEE 519)

run_arcflash.exe 10

Arc Flash Hazard Analysis (AF - IEEE 1584)

run_bess.exe 11

Battery Energy Storage Dispatch (BESS)

run_ttc.exe 12

Total & Available Transfer Capability (TTC / ATC)

run_cpf.exe 13

Continuation Power Flow & Voltage Stability (CPF)

run_motor_starting.exe 14

Dynamic Motor Starting Analysis (MS)

run_grounding.exe 15

Substation Ground Grid Design (GND - IEEE 80)

run_reliability.exe 16

Distribution System Reliability Evaluation (REL - IEEE 1366)

run_py2sqlite.exe

Database Converter (Py <-> SQLite)

DevEN.exe

Commercial Desktop GUI

Compact Format

22-Slot Compact CLI String

Batch Scripts

Automation (.bat / PowerShell)

run_loadflow.exe

1-Phase Load Flow Analysis (LFA)

LFA Engine · Sparse Newton-Raphson / FDLF / LM

High-performance steady-state power flow solver utilizing sparse analytical Newton-Raphson, Fast-Decoupled, or Levenberg-Marquardt engines with automatic tap stepping and generator Q-limit enforcement.

What Happens When Executed? (Internal Solver Workflow)

1. Opens binary SQLite database (.db) or parses text SQL/Python case.
2. Assembles complex nodal bus admittance matrix Y_bus using CSC sparse compression.
3. Solves nonlinear power mismatch equations until active/reactive tolerance (1e-6 p.u.) is satisfied.
4. Enforces generator reactive limits (Qmin/Qmax) and updates transformer tap positions.
5. Writes converged nodal voltages and branch flows into 'res_bus' and 'res_line' tables.
6. Returns exit code 0 on convergence, or exit code 1 on divergence.

Input Parameters & CLI Flags

Table 1.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to IEEE/custom case SQLite database (.db).
method	Alg	int	—	0 (NR)	0=Newton-Raphson Polar, 1=Fast-Decoupled (XB), 2=Gauss-Seidel, 3=Levenberg-Marquardt.
tol	ε	float	p.u.	1e-6	Active and reactive power convergence mismatch tolerance.
max_iter	N_max	int	iter	20	Maximum iterative solver steps before flagging divergence.
enforce_q_lims	Q_lim	int	—	1 (enforce)	1=Enforce generator reactive capability limits; 0=Relax to unlimited.
v_min / v_max	V_lim	float	p.u.	0.90 / 1.10	Statutory voltage operating envelope.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_loadflow.exe IEEE14_case.db

2. Advanced Parameterized Execution:

run_loadflow.exe IEEE14_case.db 0-0-0.000001-20-1-1-1-0-0.90-1.10

# Executes Polar Newton-Raphson with 1e-6 p.u. tolerance, 20 max iterations, enforcing generator Q-limits and automatic tap stepping.

Output Data Tables & Results in SQLite Database:

res_bus Nodal Voltage Results Table

bus vm_pu va_degree p_mw q_mvar

res_line Branch Flow & Thermal Loading Results Table

line p_from_mw q_from_mvar loading_percent losses_mw

res_trafo Transformer Loading & Tap States

trafo loading_percent tap_pos losses_mw losses_mvar

run_3ph_lfa.exe

Three-Phase Unbalanced Power Flow (3P LFA)

3P Phase Coordinates · a-b-c Admittance · VUF% & Ground Current

Full 3-phase 4-wire unbalanced power flow solver formulated in phase coordinates (a-b-c). Computes sequence voltages (zero, positive, negative), neutral wire current $I_n$, ground return current $I_g$, and voltage unbalance factor $VUF\%$.

What Happens When Executed? (Internal Solver Workflow)

1. Reads phase-wise line configurations, untransposed tower geometries, and 3-phase load models.
2. Assembles 3N x 3N coupled multi-conductor bus admittance matrix Y_bus_3ph.
3. Solves coupled nonlinear phase mismatch equations via 3-phase Newton-Raphson.
4. Computes sequence transformation matrices: V_0, V_1, V_2 = A_inv * V_abc.
5. Calculates Voltage Unbalance Factor (VUF% = |V_2| / |V_1| * 100%) and neutral wire current In.
6. Stores phase-resolved voltages and currents into 'res_bus_3ph' and 'res_line_3ph'.

Input Parameters & CLI Flags

Table 2.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to 3-phase SQLite database (.db).
tol	ε	float	p.u.	1e-6	Per-phase active and reactive power convergence tolerance.
max_iter	N_max	int	iter	25	Maximum iterative steps in 3-phase Newton-Raphson.
neutral_model	Neut	str	—	multi_grounded	multi_grounded, ungrounded, or impedance_grounded.
vuf_limit	VUF_max	float	%	2.0	Statutory Voltage Unbalance Factor threshold (IEC/IEEE).

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_3ph_lfa.exe IEEE13_unbalanced.db

2. Advanced Parameterized Execution:

run_3ph_lfa.exe IEEE13_unbalanced.db --tol 1e-6 --max-iter 25 --enforce-neutral

# Performs 3-phase unbalanced Newton-Raphson power flow on IEEE 13-bus feeder, evaluating per-phase voltage magnitudes, angles, and neutral current.

Output Data Tables & Results in SQLite Database:

res_bus_3ph Phase-Resolved Bus Voltages

bus va_pu vb_pu vc_pu vuf_percent vn_v

res_line_3ph Per-Phase Branch Current & Flow

line ia_a ib_a ic_a in_a loading_max_pct

run_scs.exe

Short Circuit Study (SCS - IEC 60909 & ANSI C37)

IEC 60909-0:2016 · Symmetrical Components · Breaking & Peak Current

Multi-standard short circuit computation engine implementing IEC 60909-0 (2016) and classical ANSI/IEEE C37. Computes symmetrical initial short-circuit current $I_k''$, peak current $i_p$, breaking current $I_b$, and thermal equivalent current $I_{th}$.

What Happens When Executed? (Internal Solver Workflow)

1. Builds positive, negative, and zero sequence admittance matrices Y_1, Y_2, Y_0.
2. Factors sequence admittance matrices into sparse LU representations.
3. Applies voltage factor c_max (1.05 or 1.10) to the faulted bus in the positive sequence.
4. Calculates driving-point impedances Z_th(1), Z_th(2), Z_th(0) at fault location.
5. Computes fault currents for 3-phase, single line-to-ground (SLG), line-to-line (LL), and double line-to-ground (DLG).
6. Exports branch contributions and breaker breaking duties into 'res_scs' and 'res_scs_branch'.

Input Parameters & CLI Flags

Table 3.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to case database with positive and zero sequence data.
fault_bus	i_flt	int	—	-1 (all)	Specific faulted bus index, or -1 to run all buses sequentially.
fault_type	Type	str	—	3P	Fault type: '3P', 'SLG', 'LL', or 'DLG'.
std	Std	str	—	IEC60909	Standard: 'IEC60909' or 'ANSI_C37'.
c_factor	c	float	—	1.10	Voltage factor c: 1.00 (min), 1.05 (MV max), or 1.10 (HV max).
breaker_time	t_b	float	s	0.05	Circuit breaker opening time for breaking current Ib evaluation.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_scs.exe IEEE14_case.db --fault-all

2. Advanced Parameterized Execution:

run_scs.exe IEEE14_case.db --bus 4 --fault-type 3P --std IEC60909 --c-factor 1.10

# Calculates IEC 60909 3-phase bolted fault at Bus 4, outputting initial short-circuit current Ik'', peak current ip, and breaker rating requirements.

Output Data Tables & Results in SQLite Database:

res_scs Bus Short-Circuit Results Table

bus fault_type ik_ss_ka ip_ka ib_ka sk_ss_mva

res_scs_branch Branch Fault Current Contributions

branch from_bus to_bus ik_contrib_ka

run_contingency.exe

Contingency Analysis & N-1 Security (CA)

N-1 / N-k Screening · Fast Decoupled / AC · Voltage & Thermal Severity

High-speed parallel contingency processor executing automated N-1 branch outages, generator trips, and multi-element outages with automatic ranking via composite voltage and active thermal performance indices.

What Happens When Executed? (Internal Solver Workflow)

1. Performs base case AC power flow to establish pre-contingency baseline state.
2. Enumerates contingency list: all N-1 lines, transformers, and generators.
3. Applies compensation method or updates factorized Y_bus using Sherman-Morrison rank-1 update.
4. Solves post-contingency state via 1-iteration Fast-Decoupled screening or full AC Newton-Raphson.
5. Calculates Voltage Performance Index (PI_v) and Active Power Performance Index (PI_p).
6. Sorts contingencies by severity rank and writes violations to 'res_contingency'.

Input Parameters & CLI Flags

Table 4.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to SQLite database.
mode	Mode	str	—	n-1-all	'n-1-lines', 'n-1-gens', 'n-1-all', or custom contingency file.
solver	Solv	str	—	ac	'ac' (full Newton-Raphson) or 'dc' (fast PTDF/LODF screening).
v_min / v_max	V_lim	float	p.u.	0.90 / 1.10	Post-contingency emergency voltage limits.
line_rating	MVA	str	—	rate_a	Thermal limit rating set to check ('rate_a' or 'rate_b' emergency).

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_contingency.exe IEEE14_case.db --n-1-all

2. Advanced Parameterized Execution:

run_contingency.exe IEEE14_case.db --n-1-lines --rank PI --top 10 --ac-verify

# Screens all N-1 line outages, ranks them by composite Performance Index (PI), and performs full AC verification on top 10 severe outages.

Output Data Tables & Results in SQLite Database:

res_contingency Contingency Severity Ranking

contingency_id outage_element status pi_score max_loading_pct

res_contingency_violations Post-Contingency Violations

contingency_id violated_element type value limit

run_timeseries.exe

1-Phase Time Series Simulation (TS)

Quasi-Dynamic · Chronological Profiles · 8760h Annual Analytics

High-throughput quasi-static chronological time-series solver capable of processing 1-minute to 1-hour resolution profiles over 24-hour, weekly, or 8,760-hour annual planning cycles with solar PV and wind variations.

What Happens When Executed? (Internal Solver Workflow)

1. Loads 1-minute to 1-hour chronological load, solar PV, and wind generation profiles.
2. Steps sequentially through time intervals: t = 1, 2, ..., N_steps.
3. Updates P_load(t), Q_load(t), and P_gen(t) based on active profile multipliers.
4. Uses prior converged solution x*(t-1) as warm-start initial guess for step t.
5. Solves power flow and tracks energy losses, tap movements, and line thermal stress.
6. Stores full trajectory into 'res_ts_bus' and 'res_ts_line' tables.

Input Parameters & CLI Flags

Table 5.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to SQLite database containing profile tables.
steps	N_t	int	steps	24	Number of chronological simulation time points.
interval	Δt	int	min	60	Time step duration in minutes (e.g. 15, 30, 60).
warm_start	Warm	int	—	1	1=Use previous time step solution as initial guess (3x faster).

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_timeseries.exe IEEE14_annual.db --steps 8760

2. Advanced Parameterized Execution:

run_timeseries.exe IEEE14_annual.db --start 0 --end 1440 --interval 15 --warm-start

# Executes 24-hour chronological simulation at 15-minute resolution (96 steps) with warm-start convergence acceleration.

Output Data Tables & Results in SQLite Database:

res_ts_bus Time-Series Bus Voltage Trajectory

time_step bus vm_pu va_degree

res_ts_line Time-Series Line Loading & Losses

time_step line loading_percent losses_mw

run_3ph_ts.exe

Three-Phase Chronological Time Series (3P TS)

Unbalanced Profiles · Dynamic Neutral & Tap Tracking · 24h Phase Simulation

Combines 3-phase phase-coordinate power flow with chronological daily and seasonal dispatch profiles. Tracks phase unbalance evolution, single-phase rooftop solar ramping, individual phase regulator tap movements, and daily line thermal loading.

What Happens When Executed? (Internal Solver Workflow)

1. Reads phase-separated load profiles (A, B, C) and distributed solar generation data.
2. Initializes 3-phase multi-conductor network state at time step t=0.
3. Dispatches per-phase active and reactive injections for current chronological interval.
4. Solves 3-phase Newton-Raphson power flow and updates individual step voltage regulators.
5. Logs neutral wire current In(t) and Voltage Unbalance Factor VUF%(t) over time.
6. Records chronological phase trajectories into 'res_3pts_bus' and 'res_3pts_line'.

Input Parameters & CLI Flags

Table 6.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to 3-phase time-series database.
steps	N_t	int	steps	96	Number of simulation intervals (e.g. 96 for 15-min 24h cycle).
tap_delays	Delays	int	—	1	1=Simulate realistic electromechanical tap changer time delays.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_3ph_ts.exe IEEE13_24h.db

2. Advanced Parameterized Execution:

run_3ph_ts.exe IEEE13_24h.db --profile solar_pv_cloudy --steps 96 --tap-delays

# Simulates 24-hour unbalanced feeder behavior with high solar PV variability, capturing instantaneous phase unbalance peaks.

Output Data Tables & Results in SQLite Database:

res_3pts_bus Chronological Phase Voltages & VUF

step bus va_pu vb_pu vc_pu vuf_pct

res_3pts_line Chronological Phase Currents & Losses

step line ia_a ib_a ic_a in_a

run_hosting.exe

DER & Hosting Capacity Analysis (HC)

Renewable Integration · Voltage Rise & Thermal Limits · PV/Wind Allocation

Evaluates maximum distributed energy resource (DER) solar PV and wind penetration capacity allowable at each substation and feeder bus without violating upper voltage limits (typically 1.05 p.u.) or transformer reverse power thermal constraints.

What Happens When Executed? (Internal Solver Workflow)

1. Establishes minimum-load / maximum-generation baseline operating condition.
2. Iteratively increases solar PV active power injection P_der at target bus in increments.
3. Computes analytical voltage rise gradient (dV/dP) and reverse power flow on substation transformer.
4. Checks statutory criteria: upper voltage limit V_max (1.05 p.u.) and branch MVA rating.
5. Pinpoints exact binding constraint: statutory voltage ceiling or thermal ampacity.
6. Records maximum hosting capacity (MW) into 'res_hosting_capacity'.

Input Parameters & CLI Flags

Table 7.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to SQLite database.
target_bus	i_bus	int	—	-1 (all)	Target bus to evaluate hosting capacity, or -1 for all buses.
step_mw	ΔP	float	MW	0.50	Generation injection step size during iteration.
pf_der	PF	float	—	1.0	DER operating power factor (e.g. 1.0 unity or 0.95 inductive).
v_max	V_max	float	p.u.	1.05	Statutory upper voltage limit ceiling.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_hosting.exe IEEE14_case.db --hc-all

2. Advanced Parameterized Execution:

run_hosting.exe IEEE14_case.db --bus 9 --power-factor 0.95-cap --step 0.25 --max-v 1.05

# Computes solar PV hosting capacity at Bus 9 with 0.25 MW resolution, enforcing a strict 1.05 p.u. statutory voltage limit.

Output Data Tables & Results in SQLite Database:

res_hosting_capacity DER Hosting Capacity Results

bus max_hosting_mw limiting_constraint voltage_at_max_pu reverse_flow_mw

run_sensitivity.exe

Voltage & Power Sensitivity Analysis (SEN)

Inverse Jacobian · dV/dQ Slopes · PTDF Matrices · Modal Q-V Curves

Analytical sensitivity engine computing inverted Jacobian submatrices, bus voltage-to-reactive power sensitivities ($dV/dQ$), active power transfer distribution factors ($PTDF$), and modal eigenvalue decomposition for voltage instability detection.

What Happens When Executed? (Internal Solver Workflow)

1. Inverts converged load flow Jacobian matrix to obtain sensitivity submatrices.
2. Computes reduced Jacobian J_R and derives exact dV/dQ slopes for all buses.
3. Evaluates PTDF shift factor matrices for transaction paths between zones.
4. Performs eigenvalue decomposition to determine proximity to voltage collapse (minimum eigenvalue lambda_min).
5. Populates 'res_sensitivity' and 'res_ptdf' with analytical sensitivities.
6. Returns exit code 0 on successful completion.

Input Parameters & CLI Flags

Table 8.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to SQLite database.
bus	i	int	—	-1 (all)	Target bus for dV/dQ evaluation, or -1 for full system matrix.
delta_q	ΔQ	float	MVAr	1.0	Reactive injection perturbation magnitude.
pv_qv	PV/QV	int	—	1	1=Compute full PV/QV modal eigenvalue decomposition.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_sensitivity.exe IEEE14_case.db --pv-qv

2. Advanced Parameterized Execution:

run_sensitivity.exe IEEE14_case.db --bus 4 --delta-q 1.0 --branch 1-2 --modal 5

# Computes exact dV/dQ slope at Bus 4, calculates PTDF on branch 1-2, and evaluates the smallest 5 modal eigenvalues.

Output Data Tables & Results in SQLite Database:

res_sensitivity Voltage & Reactive Sensitivity Table

bus dv_dq dv_dp critical_margin_mvar

res_ptdf Power Transfer Distribution Factors

from_bus to_bus branch ptdf_factor

run_harmonics.exe

Harmonic Analysis & Power Quality (HAR - IEEE 519)

IEEE 519-2022 · IEC 61000 · THD / TDD · Multi-Frequency Y_bus

Multi-frequency harmonic frequency scan and current injection solver evaluating harmonic propagation from orders $h=2$ to $h=50$. Computes total harmonic distortion ($THD_V, THD_I$), total demand distortion ($TDD$), telephone influence factor ($TIF$), and transformer K-Factor.

What Happens When Executed? (Internal Solver Workflow)

1. Reads nonlinear harmonic source injection spectra (e.g. 6-pulse, 12-pulse VFDs, inverters).
2. Reassembles multi-frequency nodal admittance matrix Y_bus(h) for each harmonic order h.
3. Inverts Y_bus(h) to solve harmonic voltages: V(h) = Y_bus(h)^(-1) * I(h).
4. Calculates Total Harmonic Distortion: THD_V = sqrt(sum(V_h^2)) / V_1 * 100%.
5. Computes Total Demand Distortion (TDD) and Transformer K-Factor.
6. Exports distortion spectra and IEEE 519 compliance flags into 'res_harmonics'.

Input Parameters & CLI Flags

Table 9.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to database containing harmonic source profiles.
orders	h_range	str	—	2-50	Harmonic order range to simulate (e.g. '2-50' or '3,5,7,11,13').
standard	Std	str	—	IEEE519	Standards verification rules: 'IEEE519' or 'IEC61000'.
thd_v_limit	THD_max	float	%	5.0	Maximum permissible Total Harmonic Distortion threshold.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_harmonics.exe IEEE14_harm.db --orders 2-50

2. Advanced Parameterized Execution:

run_harmonics.exe IEEE14_harm.db --bus 5 --scan 60-3000Hz --step 5Hz --filter-check

# Executes detailed frequency sweep from 60 Hz to 3,000 Hz at Bus 5 to detect parallel resonance anti-resonant impedance peaks.

Output Data Tables & Results in SQLite Database:

res_harmonics_bus Harmonic Bus Distortion Results

bus thd_v_pct tdd_pct k_factor ieee519_pass

res_harmonics_spectrum Harmonic Voltage Spectra

bus harmonic_order frequency_hz vh_pu

run_arcflash.exe

Arc Flash Hazard Analysis (AF - IEEE 1584)

IEEE 1584-2018 · NFPA 70E · Incident Energy & Arc Boundaries

Comprehensive personnel arc safety evaluation engine conforming to IEEE 1584-2018, NFPA 70E, and OSHA 1910.269. Computes arcing current $I_{arc}$, incident energy $E$ ($cal/cm^2$), arc flash boundary ($AFB$), and PPE Category 1-4 selection.

What Happens When Executed? (Internal Solver Workflow)

1. Reads bolted three-phase short-circuit current I_bf from SCS simulation.
2. Determines enclosure configuration (VCB, VCBB, HCB, VOA, HOA) and bus dimensions.
3. Computes reduced intermediate arcing currents I_arc using IEEE 1584 polynomial equations.
4. Determines arcing duration t from upstream protective relay and circuit breaker TCC curves.
5. Calculates Incident Energy at working distance: E = 4.184 * C_f * E_n * (t / 0.2) * (d_ref / d)^x.
6. Exports arc boundaries and NFPA 70E PPE categories into 'res_arcflash'.

Input Parameters & CLI Flags

Table 10.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to database with short-circuit and equipment data.
bus	i	int	—	-1 (all)	Target switchgear bus, or -1 for all substations.
electrode_config	Config	str	—	VCB	Electrode orientation: 'VCB', 'VCBB', 'HCB', 'VOA', or 'HOA'.
working_dist	d	float	mm	457 (18 in)	Working distance from arcing source to worker chest.
clearance_time	t	float	s	0.08	Upstream protection fault clearing time in seconds.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_arcflash.exe IEEE14_case.db --af-all

2. Advanced Parameterized Execution:

run_arcflash.exe IEEE14_case.db --bus 4 --electrode VCB --working-dist 457 --clearance-time 0.08

# Performs IEEE 1584-2018 arc flash assessment at Bus 4 switchgear, determining incident energy in cal/cm2 and NFPA 70E PPE Category.

Output Data Tables & Results in SQLite Database:

res_arcflash Arc Flash Incident Energy & PPE Table

bus bolted_fault_ka arcing_current_ka incident_energy_cal_cm2 afb_mm ppe_category

run_bess.exe

Battery Energy Storage Dispatch (BESS)

LP / MILP Optimizer · 24-Hour Peak Shaving · SOC Constraints

Executes linear and mixed-integer programming (LP/MILP) to generate optimal 24-hour battery charge/discharge schedules. Enforces state-of-charge ($SOC_{min} \le SOC(t) \le SOC_{max}$), round-trip efficiency ($\eta$), degradation penalties, and feeder thermal limits.

What Happens When Executed? (Internal Solver Workflow)

1. Reads hourly electricity tariff structure (TOU / real-time dynamic pricing).
2. Constructs linear cost objective function: min sum(Cost_grid(t) * P_grid(t) + Cost_deg * P_dis(t)).
3. Applies state-of-charge (SOC) dynamic continuity constraints: SOC(t) = SOC(t-1) + (eta_ch * P_ch - P_dis / eta_dis) * dt / E_rated.
4. Enforces inverter capacity limits: sqrt(P_bess^2 + Q_bess^2) <= S_max.
5. Solves MILP dispatch problem using HiGHS / interior-point solver.
6. Exports 24-hour optimal dispatch schedules into 'res_bess_dispatch'.

Input Parameters & CLI Flags

Table 11.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to database with BESS parameters and load profiles.
capacity_mwh	E_nom	float	MWh	5.0	Usable battery storage energy capacity.
power_mw	P_nom	float	MW	2.0	Four-quadrant inverter power rating.
soc_min / max	SOC	float	%	10 / 90	Permissible state-of-charge operational boundaries.
objective	Obj	str	—	peak_shaving	'peak_shaving', 'arbitrage', or 'loss_minimization'.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_bess.exe IEEE14_bess.db --peak-shave

2. Advanced Parameterized Execution:

run_bess.exe IEEE14_bess.db --bess-bus 9 --capacity 5.0 --power 2.0 --tariff tou_industrial

# Solves 24-hour optimal BESS dispatch at Bus 9 under time-of-use industrial tariffs, minimizing demand charges and peak loading.

Output Data Tables & Results in SQLite Database:

res_bess_dispatch Optimal BESS Dispatch Schedule

hour p_ch_mw p_dis_mw soc_percent cost_savings_usd

run_ttc.exe

Total & Available Transfer Capability (TTC / ATC)

Inter-Area Power Transfer · NERC / FERC Standards · TRM & CBM Margins

Computes maximum allowable power exchange across inter-area transmission ties and interfaces in accordance with NERC standards. Evaluates Total Transfer Capability ($TTC$), Transmission Reliability Margin ($TRM$), Capacity Benefit Margin ($CBM$), and Available Transfer Capability ($ATC$).

What Happens When Executed? (Internal Solver Workflow)

1. Reads inter-area tie-line boundaries and base power transfer schedule.
2. Calculates power transfer distribution factors (PTDF) and outage transfer distribution factors (OTDF).
3. Ramps bilateral power transactions from Source Area to Sink Area in discrete increments.
4. Evaluates branch thermal ratings and bus voltage limits under both base case and N-1 contingencies.
5. Determines First Contingency Incremental Transfer Capability (FCITC) and Total Transfer Capability (TTC).
6. Subtracts TRM and CBM margins to determine Available Transfer Capability (ATC) and records results into 'res_ttc_atc'.

Input Parameters & CLI Flags

Table 12.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to multi-area power system database.
from_area	Area_src	int	—	1	Source generating area index.
to_area	Area_sink	int	—	2	Sink load area index.
trm_mw	TRM	float	MW	10.0	Transmission Reliability Margin reserved for system uncertainties.
cbm_mw	CBM	float	MW	5.0	Capacity Benefit Margin reserved for load service entities.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_ttc.exe IEEE14_case.db --from-area 1 --to-area 2

2. Advanced Parameterized Execution:

run_ttc.exe IEEE14_case.db --from-bus 2 --to-bus 5 --trm 15 --cbm 10 --n-1-check

# Calculates NERC TTC and ATC between Bus 2 and Bus 5, considering line thermal limits and all N-1 contingencies.

Output Data Tables & Results in SQLite Database:

res_ttc_atc Inter-Area Transfer Capability Results

source_area sink_area ttc_mw trm_mw cbm_mw atc_mw limiting_element

run_cpf.exe

Continuation Power Flow & Voltage Stability (CPF)

P-V / Q-V Curves · Saddle-Node Bifurcation · Maximum Loading Margin

Traces the full P-V nose curve past the saddle-node bifurcation critical point using tangent predictor and orthogonal corrector algorithms with automatic step-size adaptation. Accurately determines the critical voltage collapse point and system loading margin $\lambda_{max}$.

What Happens When Executed? (Internal Solver Workflow)

1. Establishes base load flow operating point at lambda = 0.
2. Defines load and generation directional expansion vector: P_d(lambda) = P_d0 * (1 + lambda * K_d).
3. Computes tangent predictor vector [dx, dlambda] using augmented Jacobian J_aug.
4. Applies perpendicular or pseudo-arclength corrector iterations to project back onto the solution manifold.
5. Adapts continuation step size dynamically around the high-curvature nose point (saddle-node bifurcation).
6. Records the complete upper and lower voltage curve into 'res_cpf_curves' and outputs critical margin lambda_max.

Input Parameters & CLI Flags

Table 13.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to SQLite database.
target_buses	Buses	str	—	all	Comma-separated list of critical load buses to trace.
step_size	σ	float	—	0.05	Initial continuation arclength step size.
lambda_max_limit	λ_lim	float	—	3.0	Maximum system loading parameter to simulate.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_cpf.exe IEEE14_case.db --target-buses 4,9,14

2. Advanced Parameterized Execution:

run_cpf.exe IEEE14_case.db --load-increase-dir uniform --step 0.05 --plot-pv

# Traces full P-V nose curve for IEEE 14-bus network, identifying the exact voltage collapse loading margin lambda_max.

Output Data Tables & Results in SQLite Database:

res_cpf_curves P-V Curve Voltage Trajectory

lambda bus vm_pu loading_margin_mw

res_cpf_summary Critical Bifurcation Point Summary

critical_lambda bifurcation_type weakest_bus critical_voltage_pu

run_motor_starting.exe

Dynamic Motor Starting Analysis (MS)

Large Induction Motors · Voltage Sag · Acceleration Time & Torque

Simulates dynamic motor starting transients for large squirrel-cage and wound-rotor induction motors. Solves coupled electromechanical differential-algebraic equations: $J \frac{d\omega}{dt} = T_e - T_L$. Computes bus voltage dips, starting currents (500%-700%), and thermal ride-through limits.

What Happens When Executed? (Internal Solver Workflow)

1. Initializes steady-state pre-start system power flow condition.
2. Connects stopped motor model at slip s = 1.0 with locked-rotor impedance Z_LR.
3. Evaluates severe instantaneous voltage drop at connection busbar and adjacent feeders.
4. Numerically integrates motor mechanical acceleration equation: J * d_omega/dt = T_e(omega, V) - T_L(omega).
5. Accounts for reduced motor torque due to voltage sag (T_e proportional to V^2).
6. Stores transient speed, torque, current, and voltage profiles into 'res_motor_starting'.

Input Parameters & CLI Flags

Table 14.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to database containing motor parameters.
motor_id	Motor	int	—	1	Unique motor identification index.
start_method	Method	str	—	direct_online	'direct_online', 'star_delta', 'autotransformer', or 'soft_starter'.
inertia	J	float	kg·m²	15.0	Combined motor and coupled mechanical load moment of inertia.
v_dip_threshold	V_dip	float	%	15.0	Maximum acceptable bus voltage dip percentage during start.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_motor_starting.exe IEEE14_case.db --motor 1

2. Advanced Parameterized Execution:

run_motor_starting.exe IEEE14_case.db --bus 4 --hp 500 --method autotransformer --tap 0.65

# Simulates dynamic acceleration of 500 HP induction motor at Bus 4 using 65% autotransformer tap starting.

Output Data Tables & Results in SQLite Database:

res_motor_starting Dynamic Acceleration Profiles

time_sec speed_rpm slip torque_nm current_a bus_voltage_pu

run_grounding.exe

Substation Ground Grid Design (GND - IEEE 80)

IEEE 80-2013 / 2021 · Mesh & Step Potentials · Ground Resistance

Engineers substation earthing systems in accordance with IEEE 80-2013/2021. Calculates ground grid resistance $R_g$ using Schwarz equations, touch voltage ($E_{touch}$), step voltage ($E_{step}$), and Ground Potential Rise ($GPR$) based on soil resistivity profiles and fault current levels.

What Happens When Executed? (Internal Solver Workflow)

1. Reads multi-layer soil resistivity parameters (rho_1, rho_2, h_1) from Wenner 4-pin test data.
2. Calculates surface crushed rock layer derating factor C_s.
3. Computes tolerable touch and step voltage safety criteria for 50 kg and 70 kg human body models.
4. Evaluates total conductor length L_C, ground rod length L_R, and total buried length L_T.
5. Calculates Ground Potential Rise: GPR = I_G * R_g, mesh voltage E_m, and corner step voltage E_s.
6. Exports safety verification flags and earthing conductor schedules into 'res_ground_grid'.

Input Parameters & CLI Flags

Table 15.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to substation grid database.
grid_area	A	float	m²	2500	Total substation ground grid footprint area.
soil_resistivity	ρ	float	Ω·m	100.0	Apparent uniform or upper-layer soil resistivity.
fault_current	I_f	float	kA	25.0	Maximum symmetrical grid fault current.
burial_depth	h	float	m	0.50	Conductor installation burial depth beneath grade.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_grounding.exe substation_grid.db

2. Advanced Parameterized Execution:

run_grounding.exe substation_grid.db --area 2500 --rho 100 --depth 0.5 --conductors 12 --fault-ka 25

# Computes IEEE 80 mesh and step voltages for 2,500 m2 substation grounding grid with 25 kA fault current.

Output Data Tables & Results in SQLite Database:

res_ground_grid Ground Grid Safety Evaluation

grid_resistance_ohm gpr_volts mesh_voltage_v tolerable_touch_v safety_status

run_reliability.exe

Distribution System Reliability Evaluation (REL - IEEE 1366)

IEEE 1366-2022 · SAIFI / SAIDI / CAIDI / EENS · Customer Outage Metrics

Computes radial and looped distribution feeder reliability indices according to IEEE 1366. Calculates system average interruption frequency index ($SAIFI$), system average interruption duration index ($SAIDI$), customer average interruption duration ($CAIDI$), and expected energy not supplied ($EENS$).

What Happens When Executed? (Internal Solver Workflow)

1. Reads component failure rates lambda (failures/km-year) and repair times r (hours).
2. Identifies feeder sectionalizing switches, reclosers, fuses, and alternative tie feeds.
3. Evaluates customer interruption frequency and duration for each feeder section outage.
4. Simulates automated switching and fault isolation restoring unfaulted upstream/downstream zones.
5. Aggregates system indices: SAIFI = sum(lambda_i * N_i) / sum(N_i) and SAIDI = sum(r_i * lambda_i * N_i) / sum(N_i).
6. Writes feeder and customer reliability rankings into 'res_reliability'.

Input Parameters & CLI Flags

Table 16.1 — Execution Flags

Flag / Argument	Symbol	Type	Unit	Default	Description & Range
case_file	File	str	—	required	Path to distribution network database.
eval_period	T	int	hours	8760	Reliability evaluation period (default 1 calendar year = 8760 h).
switch_automation	Auto	int	—	1	1=Model automated sectionalizing switches and FLISR restoration.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_reliability.exe IEEE14_case.db --rel-all

2. Advanced Parameterized Execution:

run_reliability.exe IEEE14_case.db --feeder 1 --switch-automation --eval-period 8760

# Evaluates IEEE 1366 reliability indices for Feeder 1 with automated switching, computing SAIFI, SAIDI, CAIDI, and EENS.

Output Data Tables & Results in SQLite Database:

res_reliability_indices System Reliability Indices

saifi_occ_yr saidi_hr_yr caidi_hr asai eens_mwh_yr

res_feeder_outages Feeder Section Outage Breakdown

section failure_rate_yr outage_duration_hr customers_affected

run_py2sqlite.exe

Python Script to SQLite Database Converter

Parses human-readable Python power grid case definitions (.py) and converts them into high-performance binary SQLite databases (.db).

What Happens When Executed? (Internal Solver Workflow)

1. Reads Python dictionary structures from .py file (bus, line, trafo, gen, load arrays).
2. Validates physical data types, bus index consistency, and impedance values.
3. Creates relational schema inside target .db file and commits records via indexed SQL transactions.
4. Returns exit code 0 on successful compilation.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_py2sqlite.exe case14.py case14.db

2. Advanced Parameterized Execution:

run_py2sqlite.exe case14.py case14.db --validate --force-overwrite

# Converts case14.py into case14.db with schema validation and automatic table replacement.

run_sqlite2py.exe

SQLite Database to Python Script Exporter

Exports binary SQLite grid containers (.db) back into clean, formatted Python scripts (.py) for version control and scripting.

What Happens When Executed? (Internal Solver Workflow)

1. Connects to SQLite database and queries all component definition tables.
2. Extracts engineering parameters and simulation results.
3. Writes beautifully formatted, syntactically valid Python dictionary source file.
4. Returns exit code 0.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

run_sqlite2py.exe case14.db case14_exported.py

2. Advanced Parameterized Execution:

run_sqlite2py.exe case14.db case14_exported.py --include-results

# Dumps SQLite database case14.db back into Python code including latest simulation result matrices.

DevEN.exe

Commercial Desktop GUI & Graphical CAD

The complete interactive workstation application providing vector CAD single-line schematics, docking inspectors, and solver controls.

What Happens When Executed? (Internal Solver Workflow)

1. Launches high-performance 60 FPS hardware-accelerated CAD canvas.
2. Provides multi-window workspace with component palettes, inspector grids, and real-time result visualizers.
3. Orchestrates backend solver DLLs and standalone executables with background worker threads.
4. Supports live undo/redo, automatic bus numbering, and multi-format export.

Ready-to-Run CLI Command Examples (Click Copy to Clipboard):

1. Default / Basic Execution:

DevEN.exe

2. Advanced Parameterized Execution:

DevEN.exe case14.db --study lfa --fullscreen

# Launches DevEN desktop CAD, immediately loading case14.db and opening the Load Flow solver dashboard.

22-Slot Compact Hyphen-Delimited CLI Format

DevEN supports a deterministic, positional slot string syntax that allows headless servers and automated orchestrators to configure every solver parameter in a single command argument without configuration files.

# 22-Slot Format Blueprint:
# <engine>-<vinit>-<tol>-<maxiter>-<qlim>-<charging>-<tap>-<shunt>-<vmin>-<vmax>-<vref>-<sbase>-<freq>-<rate>-<isl>-<pf>-<scalep>-<scaleq>-<dcloss>-<trace>-<dump>-<sparse>

# Production Command:
run_loadflow.exe case14.db 0-0-0.000001-20-1-1-1-0-0.90-1.10-1.0-100.0-50.0-1-1-1-1.0-1.0-0-0-1-1
                        

Batch Automation & Scripting (.bat / PowerShell)

Use this template to automatically run multiple cases in sequence, convert databases, and log results into an audit directory:

@echo off
echo === BATCH RUNNING DEV-EN POWER FLOWS ===
for %%f in (*.db) do (
    echo Solving %%f...
    run_loadflow.exe "%%f" 0-0-0.000001-20
    if errorlevel 1 echo ERROR: Diverged on %%f
)
echo === ALL CASES COMPLETED ===
                        

DevEN Universal Python Automation API

deven_api

Enterprise-grade headless automation layer for Python 3.10–3.14. Zero GUI dependencies, dynamic network CRUD, 10 industrial calculation engines, and live Outbar logging.

Download API PDF Manual

4.0

0. Architecture & Quick Start

The deven_api module is located in the root of DevEN . It operates purely in memory using standard Python dictionaries and optimized NumPy sparse matrix arrays, allowing seamless deployment in batch scripts, automation loops, and continuous integration pipelines.

Standard Quick Start Script

import deven_api as deven

# 1. Load your network database (.db, .py, .raw, .json)
deven.load_case(r"E:\cases\IEEE118BUS.py")

# 2. Run Newton-Raphson Load Flow
res = deven.run_lfa(method="nr", tol=1e-6, max_iter=20)

# 3. Query bus voltages & branch flows
v_pu, angle = deven.get_bus_voltage(1)
print(f"Bus 1 Voltage: {v_pu:.4f} p.u. | Angle: {angle:.2f}°")

Multi-Session Support

Instantiate deven.DevENSession() to create multiple isolated in-memory networks. Perfect for comparing Base Case vs. Contingency / Expansion cases side-by-side.

Outbar Logger Integration

Emits timestamped, color-coded logging records ([HH:MM:SS] DevEN/info - ...) matching standard enterprise Outbar format. Custom log callbacks can be attached via deven.set_log_callback().

4.1

1. Case Lifecycle & Database I/O

Method Signature	Parameters	Returns	Functionality
`deven.load_case(path)`	`path`: File path (.db, .py, .raw, .json)	`PowerGridData`	Loads case into memory, builds bus/branch indices, and validates topology.
`deven.save_case(path=None)`	`path`: Target output path (optional)	`str`	Serializes the active grid back to disk in native SQLite or Python format.
`deven.export_case(path, format)`	`format`: "raw", "py", "db"	`str`	Exports case to PSS/E RAW format or Python network database.
`deven.new_case(name, base_mva)`	`base_mva`: System base MVA (default 100.0)	`PowerGridData`	Initializes a new empty network ready for programmatic element population.
`deven.validate_network()`	None	`List[str]`	Checks for unenergized islands, missing swing bus, and impedance bounds.

4.2

2. Element CRUD & Grid Manipulation

Programmatically create, modify, clone, and remove substations, transmission circuits, and generation assets on the fly:

Element Manipulation API Examples

# 1. Modify Element Parameters
deven.set_bus(101, base_kv=138.0, name="Substation_North")
deven.set_line(12, rateA=300.0, status=1)
deven.set_generator(1, P_out=85.0, V_set=1.03)

# 2. Add New Grid Elements
deven.add_bus(205, name="Solar_Farm_POI", base_kv=34.5, type=2)
deven.add_line(line_id=88, from_bus=101, to_bus=205, r=0.015, x=0.08, rateA=120.0)
deven.add_generator(gen_id=30, bus=205, P_out=50.0, Qmax=25.0, Qmin=-15.0)

# 3. Clone Transmission Line (Duplicate parallel circuit)
deven.clone_element("line", src_id=88, new_id=89)

# 4. Remove Outaged Element
deven.delete_element("line", 89)

4.3

3. Study Solvers (LFA, SCS...)

LFA Engine

Load Flow Analysis (LFA)

Newton-Raphson (NR), Fast Decoupled (FDLF), and Gauss-Seidel (GS) power flow.

res = deven.run_lfa(method="nr", tol=1e-6, max_iter=20)
# res['converged']  -> True/False
# res['buses']      -> dict of bus voltages
# res['branches']   -> dict of power flows
# res['summary']    -> generation/demand/losses

SCS Engine

Short Circuit (IEC 60909)

Computes symmetrical breaking currents (Ik"), peak currents (ip), and breaking powers (Sk").

res = deven.run_scs(fault_bus=101, method="iec", fault_type="3phase")
# Returns exact VDE 0102 / IEC table results

CA Engine

N-1 Contingency Analysis

Simulates transmission line and transformer single outages, ranking post-contingency overloads.

res = deven.run_ca(criteria="n-1", max_loading=100.0)

HC Engine

Hosting Capacity (HC)

Determines maximum renewable generation capacity connectable before thermal/voltage violations occur.

res = deven.run_hc(target_buses=[10, 12], max_kw=50000.0)

4.4

4. Bus Voltages & Results Querying

Querying Results and Screening Overloads

# 1. Direct Bus Voltage Query
v_pu, angle = deven.get_bus_voltage(1)

# 2. Transmission Line Power Flows
flows = deven.get_line_flows(1)
# Returns: {'p_fwd': 268.3, 'q_fwd': 155.2, 'losses_mw': 0.0, 'loading_pct': 31.0, ...}

# 3. Automatic Violation Screening
viols = deven.get_violations(v_min=0.95, v_max=1.05, max_loading=100.0)
for v in viols["thermal_violations"]:
    print(f"Overloaded Branch {v['branch']}: Loading={v['loading_pct']:.2f}%")

4.5

5. Industrial Automation Recipes

Recipe: Print All Bus Voltages and Filter Lines Loaded Over 50%

import deven_api as deven

# 1. Load case
deven.load_case(r"E:\cases\IEEE118BUS.py")

# 2. Run AC Load Flow
res = deven.run_lfa(method="nr", tol=1e-6, max_iter=20)

# 3. Print Bus Voltages Table
print("=" * 60)
print(f"{'Bus ID':<10} {'Voltage (p.u.)':<18} {'Angle (deg)':<15}")
print("=" * 60)
for bus_id, data in res["buses"].items():
    print(f"{bus_id:<10} {data['v_pu']:<18.4f} {data['angle_deg']:<15.2f}")

# 4. Print Transmission Lines Loaded > 50%
print("\n" + "=" * 80)
print(f"{'Branch ID':<15} {'From Bus':<10} {'To Bus':<10} {'Active Flow (MW)':<18} {'Loading (%)':<15}")
print("=" * 80)
for br_id, br in res["branches"].items():
    loading = br.get("loading_pct", 0.0)
    if loading > 50.0:
        print(f"{str(br_id):<15} {br['from_bus']:<10} {br['to_bus']:<10} {br['p_fwd']:<18.2f} {loading:<15.2f}")

4.6

6. In-GUI Interactive Command Bar Reference

At the bottom of the DevEN Outbar window, engineers can type immediate text commands into the DevEN CMD > prompt:

Command Syntax	Description	Example
`load <path>`	Loads network database into current session.	`load IEEE118BUS.py`
`run lfa [nr\|fdlf\|gs]`	Executes Load Flow Analysis and streams iteration log.	`run lfa nr`
`run scs <bus_id>`	Calculates IEC 60909 short circuit fault currents.	`run scs 101`
`set bus <id> <key>=<val>`	Updates bus parameter.	`set bus 101 base_kv=138.0`
`set line <id> status=0`	Takes transmission line out of service.	`set line 12 status=0`
`get voltage <bus_id>`	Prints solved voltage magnitude and angle in Outbar.	`get voltage 101`
`get violations`	Prints table of all voltage and thermal violations.	`get violations`
`cls / clear`	Clears Outbar text history.	`cls`

About DevEN (Develop Electric Network) & Licensing

Commercial Software Specification

The next-generation, high-performance power system planning and simulation workstation. Built for electrical engineers, utilities, EPC contractors, and universities.

What is DevEN? (Develop Electric Network)

DevEN stands for Develop Electric Network. It is an industrial-grade, commercial power system simulation and computer-aided design (CAD) platform engineered to model, analyze, and optimize electric power transmission grids, distribution networks, industrial facilities, and microgrids.

Native C/C++ Compute Engine

Pre-compiled native solvers deliver 10x to 50x faster execution than interpreted Python tools, solving 10,000-bus networks in milliseconds.

Modern High-DPI Vector CAD

Fluid 60 FPS single-line schematic editor with real-time voltage heatmaps, animated flow arrows, and multi-monitor docking workspaces.

Universal Tri-Format Database

Native SQLite (.db), Python script (.py), and SQL dumps (.sql) interoperability with zero proprietary file lock-in.

Platform Features & Technical Capabilities

Capability Area	DevEN Implementation	Industrial Benefit
Grid Components	10 fundamental elements (Bus, Line, 2W/3W Trafo, Gen, Slack, Load, Shunt, SVC, BESS)	Complete coverage of transmission, distribution, industrial, and microgrid assets.
Solver	9 core studies (LFA, SCS IEC 60909, CA N-1, TS Dynamics, HC Solar, SEN, BESS, AF IEEE 1584, HAR IEEE 519) (LFA, SCS IEC 60909, CA N-1, TS Dynamics, HC Solar, SEN, BESS, AF IEEE 1584)	All engineering studies unified in one workstation without buying add-on modules.
Execution Modes	Full Graphical CAD GUI + 32 Standalone Headless CLI Executables + Python SDK	Interactive design on desktop or automated batch scripting on cloud servers.
Compliance Standards	IEC 60909, IEEE 399, IEEE 1584-2018, NFPA 70E, NERC TPL-001, IEEE 1547-2018	Ready for utility interconnection filings and OSHA regulatory safety audits.
Safety Engineering	Integrated Arc Flash Hazard Calculator & Printable Label Designer	Directly generates switchgear warning stickers with exact cal/cm2 and PPE categories.

Why Choose DevEN Over Other Power System Softwares?

Comparison of DevEN against legacy commercial platforms (ETAP, PSS/E, DIgSILENT PowerFactory) and open-source Python packages (pandapower, PyPSA):

Feature / Dimension	DevEN	Legacy Commercial (ETAP / PSS/E)	PowerFactory	Open Source (pandapower / PyPSA)
Solver Speed	Pre-compiled C/C++ Sparse (Sub-millisecond)	Fast compiled Fortran / C++	Fast compiled C++	Interpreted Python overhead (Slower)
Licensing Cost	Transparent, Perpetual / Affordable Tiers	Extremely Expensive ($15k - $35k per seat)	High Enterprise Cost ($20k+)	Free Open-Source (No GUI/CAD)
Hardware Dongles	Zero Dongles (Software Key / Floating LAN)	Physical USB Dongles (Hasp keys)	License Server / USB	None
Database Schema	Open SQLite (.db) + Python (.py)	Proprietary closed binary format	Proprietary database	Python dataframes in RAM
CLI Headless Execution	32 Standalone .exe (Zero Python needed)	Complex COM / API wrappers	Python engine API	Python scripts only
Arc Flash & BESS	Included Built-In Standard	Expensive separate add-on modules	Separate module options	Not natively supported

Commercial Licensing Editions

Academic & Research

Universities & Non-Profit

Full CAD GUI & all 8 solvers
Up to 1,000 buses per case
Student thesis & research use
Community forum support

Academic Grant / Discount

Professional Consultant

POPULAR

Consultants, EPCs & Design Firms

Unlimited buses & grid scale
All 8 solvers + IEEE 1584 Arc Flash
32 standalone CLI executables
Perpetual or Annual Seat License
Priority email & patch support

Single-Seat Workstation

Enterprise Utility & Site

Transmission & Distribution Utilities

Floating LAN server license daemon
Unlimited network seats across company
High-performance cloud cluster nodes
Custom solver DLL integration & API
Dedicated 24/7 technical hotline

Site Floating Network

How to Buy License & Activation Process

Step 1: Request Quote

Submit your required license edition and number of seats to the DevEN commercial sales desk.

Step 2: 30-Day Trial Key

Receive a fully functional 30-day evaluation license key to test on your internal network models.

Step 3: Commercial License

Upon purchase, receive your permanent digital license file or floating network server certificate.

Step 4: Instant Activation

Activate in one click inside 'DevEN.exe -> Help -> License Manager' or via CLI: 'DevEN.exe --activate KEY'.

Commercial Inquiries & Licensing Desk

Devaraj E & team Bengaluru (ಬೆಂಗಳೂರು), India devarajedeva2002@gmail.com

Official DevEN Distribution