Power Systems Glossary

A comprehensive glossary of terms used in power systems analysis and throughout GAT documentation.

A

AC (Alternating Current)

Electric current that periodically reverses direction. Power grids use AC because it can be easily transformed to different voltage levels. In North America, AC alternates at 60 Hz; in Europe, 50 Hz.

AC Power Flow

Analysis that solves the full nonlinear power flow equations, accounting for both real power (P) and reactive power (Q), voltage magnitudes and angles. More accurate than DC power flow but computationally harder. See Power Flow Guide.

Active Power

See Real Power.

Admittance (Y)

The inverse of impedance. Measures how easily current flows through a circuit element. Complex quantity: Y = G + jB, where G is conductance and B is susceptance. Units: Siemens (S). See Impedance & Admittance.

ADMS (Advanced Distribution Management System)

Software platform that integrates SCADA, outage management, and distribution automation. GAT's gat-adms crate provides FLISR and VVO algorithms. See ADMS Guide.

Angle

Voltage angle (θ) at a bus, measured in radians or degrees relative to a reference bus. Angle differences drive real power flow: larger Δθ means more MW flowing.

Apparent Power (S)

The magnitude of complex power: S = √(P² + Q²). Measured in volt-amperes (VA) or megavolt-amperes (MVA). Determines equipment sizing because conductors must carry both real and reactive current. See Complex Power.

Area

A geographic or administrative region of the power grid, often corresponding to a utility or balancing authority. Multi-area analysis considers power transfers between areas via tie-lines (corridors).

Arrow (Apache Arrow)

Columnar in-memory data format used by GAT for high-performance data interchange. GAT stores networks as Arrow directory datasets with separate tables for buses, branches, generators, and loads. See Arrow Schema.

B

Bad Data

Measurements in state estimation that are inconsistent with the physical model. Bad data detection identifies and removes erroneous measurements before estimating system state.

Balancing Authority

Entity responsible for maintaining load-generation balance in a control area. Must continuously adjust generation to match demand and maintain frequency.

Base MVA (Sbase)

Reference power used for per-unit calculations. Typical values: 100 MVA for transmission, 1-10 MVA for distribution. All per-unit quantities are ratios relative to this base.

Base Voltage (Vbase)

Reference voltage for per-unit calculations, typically the nominal voltage at each bus. Combined with base MVA, determines base impedance: Zbase = Vbase² / Sbase.

Branch

A transmission line or transformer connecting two buses. Characterized by impedance (R + jX), thermal rating, and optionally a tap ratio (for transformers). GAT stores branches in branches.arrow.

Branch Flow Model

OPF formulation using branch power flows as variables instead of bus injections. The Farivar-Low SOCP relaxation uses this model. Naturally handles radial networks.

Bus

A node in the power network where components connect. Buses have voltage magnitude and angle. Types include slack (reference), PV (generator), and PQ (load). GAT stores buses in buses.arrow.

Bus Type

Classification determining which quantities are known vs. solved:

Slack (Ref, Type 3): V and θ fixed; P and Q solved
PV (Type 2): P and V fixed; Q and θ solved
PQ (Type 1): P and Q fixed; V and θ solved

See Bus Types for a detailed explanation.

C

Capability Curve

A generator's operating envelope in the P-Q plane, showing feasible combinations of real and reactive power output. Limited by field current, armature current, and prime mover.

Capacitor Bank

Shunt device that injects reactive power to raise voltage. Switched capacitor banks provide discrete voltage control; static VAR compensators (SVCs) provide continuous control.

CAIFI (Customer Average Interruption Frequency Index)

Reliability metric: average number of interruptions per customer affected. CAIFI = (Total interruptions) / (Customers affected). Lower is better.

Charging (Line Charging)

Capacitive reactive power generated by transmission line shunt capacitance. Modeled as B/2 at each end in the π-model. Significant for long high-voltage lines.

Clarabel

Interior-point conic solver used by GAT for SOCP relaxation of OPF. Handles second-order cone constraints efficiently.

Conductance (G)

Real part of admittance. Represents resistive losses. G = R / (R² + X²).

Conductor

Physical wire carrying current. Conductor properties (resistance, ampacity) determine branch parameters and thermal limits.

Congestion

When power flow on a branch approaches or exceeds its thermal limit. Congestion creates price separation (different LMPs) between buses.

Contingency

A hypothetical failure event (e.g., loss of a generator or transmission line). Contingency analysis tests whether the system can survive such events. See N-1 and Contingency Analysis.

Convergence

When an iterative solver reaches a solution within acceptable tolerance. Power flow typically converges in 3-10 Newton-Raphson iterations. Non-convergence may indicate an infeasible operating point.

Corridor

In multi-area analysis, a tie-line connecting two areas with limited transfer capacity. GAT's Corridor type models inter-area power transfers.

Cost Model

Function relating generator output to operating cost. Common forms:

Quadratic: Cost = c₀ + c₁·P + c₂·P²
Piecewise linear: Segments with different slopes
No cost: For must-run units or renewables

D

DC Power Flow

Linearized approximation assuming: (1) voltage magnitudes ≈ 1.0 p.u., (2) angle differences are small, (3) resistance << reactance. Solves Bθ = P, a linear system. Fast but ignores reactive power and losses.

DC-OPF

Optimal power flow using DC power flow approximation. Results in a linear program (LP) that solves quickly. Good for screening studies but underestimates losses.

Demand

Electrical load that must be served. May be fixed (inelastic) or price-responsive (elastic). GAT stores demand in loads.arrow.

DER (Distributed Energy Resource)

Small-scale generation or storage connected at distribution level: rooftop solar, batteries, EVs, demand response. Managed by DERMS.

DERMS (Distributed Energy Resource Management System)

Software coordinating DER dispatch, aggregation, and grid services. See DERMS Guide.

Dispatch

The real-time allocation of generation to meet demand. Economic dispatch minimizes cost; security-constrained dispatch also respects transmission limits.

E

Economic Dispatch

Optimization to minimize generation cost while meeting demand. Ignores network constraints (copper-plate assumption). The simplest OPF variant.

ELCC (Effective Load Carrying Capability)

Capacity credit of a variable resource (wind, solar). The additional load the system can serve while maintaining the same reliability level. Accounts for resource variability.

ENS (Energy Not Served)

Reliability metric: total energy (MWh) that cannot be delivered due to capacity shortfalls. Also called Expected Unserved Energy (EUE).

EUE (Expected Unserved Energy)

See ENS.

Exciter

Generator component controlling field current and thus terminal voltage. Automatic voltage regulators (AVRs) adjust excitation to maintain voltage setpoint.

F

Fast Decoupled Power Flow

Newton-Raphson variant exploiting P-θ and Q-V decoupling. Uses constant Jacobian approximations (B' and B'') for faster iterations. Good for well-conditioned transmission networks.

Fault

An abnormal current path, usually a short circuit. Types include three-phase, line-to-line, line-to-ground. Protection systems detect and isolate faults.

Feasibility

A power flow or OPF solution is feasible if all constraints are satisfied: power balance, voltage limits, thermal limits, generator limits.

Flat Start

Initial guess for iterative solvers: V = 1.0 p.u., θ = 0 for all buses. Simple but may cause convergence issues for stressed systems. GAT's AC-OPF uses flat start by default.

FLISR (Fault Location, Isolation, Service Restoration)

Distribution automation sequence: locate fault, isolate faulted section, restore service to unaffected customers via alternate feeds. See ADMS Guide.

Flow Limit

See Thermal Limit.

FOR (Forced Outage Rate)

Probability that a unit is unavailable due to unplanned failure. Used in reliability calculations. Typical values: 2-10% for thermal units.

Frequency

System frequency (50 or 60 Hz) indicates generation-load balance. Frequency drops when load exceeds generation; rises when generation exceeds load.

G

Generation

Conversion of primary energy to electricity. Types: thermal (coal, gas, nuclear), hydro, wind, solar, storage discharge.

Generator

A machine converting mechanical or chemical energy to electricity. Characterized by capacity limits (Pmin, Pmax, Qmin, Qmax), cost curve, and voltage setpoint. GAT stores generators in generators.arrow.

Graph

Mathematical representation of network topology. Buses are nodes; branches are edges. GAT uses petgraph for graph algorithms. See Graph Reference.

Grid

The interconnected network of generation, transmission, and distribution facilities delivering electricity.

H

Hosting Capacity

Maximum DER penetration a distribution feeder can accommodate without violating voltage or thermal constraints. Key metric for interconnection studies.

Hessian

Matrix of second partial derivatives. Used by interior-point OPF solvers (IPOPT) for Newton steps. GAT computes sparse Hessians in hessian.rs.

HVDC (High Voltage Direct Current)

DC transmission for long distances or asynchronous interconnections. Modeled as controllable injections at converter buses.

I

IEEE Test Cases

Standard benchmark networks: IEEE 14, 30, 57, 118, 300 bus systems. Used for algorithm validation. GAT includes these in test_data/.

Impedance (Z)

Opposition to current flow. Complex quantity: Z = R + jX, where R is resistance and X is reactance. Units: ohms (Ω). See Impedance & Admittance.

Injection

Net power entering the network at a bus: P_inj = P_gen - P_load. Positive injection means generation exceeds local load.

Interior Point Method

Optimization algorithm that traverses the interior of the feasible region. IPOPT implements this for nonlinear programming. Efficient for large-scale OPF.

IPOPT (Interior Point Optimizer)

Industry-standard nonlinear optimization solver. GAT's solver-ipopt feature enables IPOPT backend for AC-OPF.

Island

A connected component of the network graph. Synchronous islands must each have a slack bus. GAT's gat graph islands detects islands.

J

Jacobian

Matrix of partial derivatives relating power injections to voltages and angles. Used in Newton-Raphson power flow. For n buses: 2n × 2n matrix with blocks ∂P/∂θ, ∂P/∂V, ∂Q/∂θ, ∂Q/∂V. See Newton-Raphson Method.

K

kV (Kilovolt)

Voltage unit: 1 kV = 1,000 volts. Transmission typically 115-765 kV; distribution 4-35 kV; residential 120/240 V.

kVA (Kilovolt-Ampere)

Apparent power unit: 1 kVA = 1,000 VA. Used for transformer and equipment ratings.

kW (Kilowatt)

Real power unit: 1 kW = 1,000 watts. Household loads typically 1-10 kW.

L

L-BFGS (Limited-memory BFGS)

Quasi-Newton optimization algorithm using limited Hessian history. GAT's default AC-OPF solver uses L-BFGS with penalty method via the argmin crate.

Line

A transmission or distribution conductor connecting buses. Characterized by R, X, and B (line charging). Distinguished from transformers by tap ratio = 1.0.

LMP (Locational Marginal Price)

The marginal cost of serving one additional MW at a specific bus. Includes energy, losses, and congestion components. Units: $/MWh. Key output of OPF for electricity markets. See LMP Pricing.

Load

Electrical demand at a bus. May be constant power (P, Q fixed), constant current, or constant impedance. GAT stores loads in loads.arrow.

Load Flow

See Power Flow.

LOLE (Loss of Load Expectation)

Reliability metric: expected hours per year when load exceeds available generation. Planning standard: often LOLE ≤ 0.1 days/year (2.4 hours/year). See Reliability Guide.

LODF (Line Outage Distribution Factor)

Sensitivity: if line k trips, how does flow redistribute to line l? Used for contingency screening without re-solving power flow.

Losses

Power dissipated in transmission (I²R losses). DC power flow ignores losses; AC power flow computes them. Typical transmission losses: 2-5% of generation.

M

Manifest

GAT's metadata file (manifest.json) in Arrow directories, storing source info, checksums, and conversion provenance.

MATPOWER

MATLAB-based power system simulation package. GAT imports MATPOWER .m case files. See Convert Guide.

Monte Carlo

Probabilistic simulation sampling random scenarios (generator outages, load variations). Used for reliability assessment. See Reliability Guide.

MVA (Megavolt-Ampere)

Apparent power unit: 1 MVA = 1,000 kVA = 1,000,000 VA. Standard for transmission equipment ratings.

MVAR (Megavolt-Ampere Reactive)

Reactive power unit: 1 MVAR = 1,000,000 VAR. Generators, capacitors, and reactors are rated in MVAR capability.

MW (Megawatt)

Real power unit: 1 MW = 1,000 kW = 1,000,000 W. Standard for generation capacity and load.

N

N-1 Criterion

Security standard requiring the system to survive any single contingency (one generator or line outage) without overloads or voltage violations. Foundation of transmission planning. See Contingency Analysis.

N-2

Security criterion for two simultaneous contingencies. Required for critical facilities.

Newton-Raphson

Iterative algorithm for nonlinear equations. Power flow uses Newton-Raphson: xₖ₊₁ = xₖ - J⁻¹·f(xₖ). Quadratic convergence near solution. See Newton-Raphson Method.

Node

See Bus.

NLP (Nonlinear Program)

Optimization with nonlinear objective or constraints. AC-OPF is an NLP due to power flow equations.

O

Observability

A system is observable if available measurements uniquely determine the state. State estimation requires observability; additional pseudo-measurements may be needed.

OPF (Optimal Power Flow)

Optimization minimizing generation cost (or losses) subject to power flow equations, generator limits, voltage limits, and thermal limits. Variants: DC-OPF, SOCP, AC-OPF. See OPF Guide.

Outage

Planned or forced disconnection of equipment. Outage scenarios are inputs to reliability and contingency analysis.

P

PandaPower

Python library for power system analysis. GAT imports pandapower networks via JSON format. See Convert Guide.

Penalty Method

Optimization technique converting constrained problems to unconstrained by adding penalty terms for constraint violations. GAT's L-BFGS solver uses quadratic penalty.

Per-Unit (p.u.)

Normalized units dividing actual values by base values. Simplifies calculations across voltage levels. V_pu = V_actual / V_base. Typical: V ≈ 1.0 p.u., Z << 1.0 p.u.

PGLib (Power Grid Library)

IEEE PES benchmark library with realistic OPF test cases. GAT benchmarks against PGLib-OPF. See Benchmarking Guide.

Phase Angle

See Angle.

Phase Shifter

Transformer with adjustable phase shift for power flow control. Creates asymmetric Y-bus entries.

Polar Coordinates

Representing complex voltage as magnitude and angle: V∠θ. GAT's AC-OPF uses polar formulation.

Power Factor

Ratio of real to apparent power: pf = P/S = cos(φ). Unity power factor (pf = 1) means no reactive power. Lagging pf indicates inductive load. See Complex Power.

Power Flow

Analysis computing steady-state voltages and flows given generation and load. Solves nonlinear algebraic equations (AC) or linear approximation (DC). Foundation of all grid analysis.

PSS/E

Siemens PTI power system simulator. Industry-standard format for transmission planning. GAT supports PSS/E RAW file import.

PTDF (Power Transfer Distribution Factor)

Sensitivity: 1 MW injection at bus i, withdrawal at bus j → flow change on each line. Linear for DC power flow. Used for transfer limits and congestion analysis.

PV Bus

Generator bus with specified real power P and voltage magnitude V. Reactive power Q and angle θ are solved. See Bus Types.

PQ Bus

Load bus with specified real power P and reactive power Q. Voltage magnitude V and angle θ are solved. See Bus Types.

Q

Q (Reactive Power)

See Reactive Power.

R

Ramp Rate

Maximum rate of change of generator output, typically MW/minute. Constrains how quickly generation can adjust. Important for renewable integration.

Rating

Maximum continuous operating limit. Thermal rating limits branch flow; generator rating limits output.

Reactance (X)

Imaginary part of impedance, representing energy storage in magnetic fields (inductors) or electric fields (capacitors). X = ωL for inductors, X = -1/(ωC) for capacitors.

Reactive Power (Q)

Power oscillating between source and load due to phase difference between voltage and current. Measured in VAR (volt-ampere reactive). Essential for voltage control but does not perform useful work. See Complex Power.

Real Power (P)

Power doing useful work, measured in watts (W). Also called active power. P = V·I·cos(φ). See Complex Power.

Reference Bus

See Slack Bus.

Reliability

Ability of the power system to deliver electricity to customers. Measured by indices like LOLE, EUE, SAIDI. See Reliability Guide.

Reserve

Generation capacity held back for contingencies. Types: spinning reserve (online, synchronized), non-spinning reserve (offline, quick-start).

Resistance (R)

Real part of impedance, representing energy dissipation. Causes I²R losses. Lower resistance means more efficient transmission.

S

SAIDI (System Average Interruption Duration Index)

Reliability metric: average outage duration per customer. SAIDI = (Sum of customer interruption durations) / (Total customers).

SCADA (Supervisory Control and Data Acquisition)

System for real-time monitoring and control of grid equipment. Provides measurements for state estimation.

Security

Ability to withstand disturbances without cascading failures. Security-constrained OPF ensures N-1 security.

Shunt

Element connected between bus and ground. Shunt capacitors inject reactive power; shunt reactors absorb it. Modeled as admittance to ground.

Slack Bus

Reference bus with fixed voltage angle (θ = 0) that absorbs power imbalance. Every synchronous island needs exactly one slack bus. Also supplies/absorbs losses. See Bus Types.

SOCP (Second-Order Cone Program)

Convex optimization with conic constraints. SOCP relaxation of OPF provides lower bounds and often tight solutions for radial networks. See OPF Guide.

State Estimation

Determining system state (voltage magnitudes and angles) from redundant measurements. Filters measurement noise and detects bad data. See State Estimation Guide.

Steady State

Operating condition where all quantities are constant (or periodic at system frequency). Power flow analyzes steady state; dynamic simulation analyzes transients.

Substation

Facility housing transformers, switches, and protection equipment. Buses often represent substation nodes.

Susceptance (B)

Imaginary part of admittance. B > 0 for capacitors (inject Q); B < 0 for inductors (absorb Q).

Swing Bus

See Slack Bus.

T

Tap Ratio

Transformer turns ratio, typically near 1.0 with ±10% adjustment range. Off-nominal taps provide voltage regulation. Modeled in Y-bus and branch equations.

TEP (Transmission Expansion Planning)

Optimization determining which new lines to build to serve future load while meeting reliability standards. See gat-algo TEP module.

Thermal Limit

Maximum power flow a branch can carry without overheating. Determined by conductor ampacity and ambient temperature. Enforced as |S| ≤ S_max in OPF.

Tie-Line

Transmission line connecting two control areas. Tie-line flows are scheduled and monitored for interchange accounting.

Topology

The structure of network connections: which buses connect via which branches. Graph analysis reveals islands, critical branches, and redundancy.

Transformer

Device changing voltage level via electromagnetic induction. Modeled with tap ratio and impedance. Step-up transformers connect generators; step-down serve loads.

Transmission

High-voltage bulk power transfer, typically 69 kV and above. Distinguished from distribution by voltage level and radial vs. networked topology.

U

Unit Commitment

Day-ahead optimization deciding which generators to start/stop. Considers startup costs, minimum up/down times, and forecast demand.

V

VAR (Volt-Ampere Reactive)

Unit of reactive power. See Reactive Power.

Voltage

Electric potential difference driving current. Transmission voltages: 115-765 kV. Distribution: 4-35 kV. Measured in volts (V) or per-unit.

Voltage Collapse

Cascading voltage decline when reactive power support is exhausted. Prevented by maintaining adequate reactive reserves and voltage margins.

Voltage Magnitude (|V|)

The absolute value of complex voltage, typically 0.95-1.05 p.u. for normal operation. Controlled by generator excitation, tap changers, and reactive devices.

VVO (Volt-VAR Optimization)

Distribution automation optimizing voltage regulator and capacitor bank settings to minimize losses while maintaining voltage quality.

W

Warm Start

Initial guess from a previous solution, accelerating convergence. Useful for contingency analysis where cases differ slightly.

Watt (W)

Unit of real power: 1 W = 1 J/s = 1 V·A·cos(φ).

WLS (Weighted Least Squares)

State estimation algorithm minimizing weighted sum of squared measurement residuals. Standard approach for transmission state estimation.

X

X (Reactance)

See Reactance.

Y

Y-Bus (Admittance Matrix)

Sparse matrix Y where Y_ij = -y_ij (off-diagonal) and Y_ii = Σy + shunts (diagonal). Fundamental to power flow: I = Y·V. GAT builds Y-bus in ybus.rs. See Y-Bus Matrix.

Z

Z-Bus (Impedance Matrix)

Inverse of Y-bus: Z = Y⁻¹. Dense matrix used for fault analysis. Rarely formed explicitly for large networks.

Zone

Subregion within an area for loss calculation or pricing. Zonal pricing aggregates buses into price zones.