Component Library

SimpleLag block

    ╭─────────╮
 in │    K    │ out
╶───┤╶───────╴├────╴
    │ 1 + s T │
    ╰─────────╯

Additional structural parameters:

• guess=0/default: initial guess/default for the internal state (equals output in steady state)
• allowzeroT: if true, the lag is bypassed when T=0 (this does not reduce the model order)

For a concrete list of variables and parameters please check the model source on GitHub.

SimpleLead block

    ╭─────────╮
 in │ 1 + s T │ out
╶───┤╶───────╴├────╴
    │    K    │
    ╰─────────╯

This block directly uses Dt(in), therefore it does not add additional states but may not be used in all scenarios!

For a concrete list of variables and parameters please check the model source on GitHub.

LeadLag block

    ╭──────────╮
 in │  1 + sT1 │ out
╶───┤K╶───────╴├────╴
    │  1 + sT2 │
    ╰──────────╯

Additional structural parameters:

• guess=0: initial guess for the internal state (equals input in steady state)
• allowzeroT: if true, the lead-lag is bypassed when T1=0 and T2=0 (this does not reduce the model order)

For a concrete list of variables and parameters please check the model source on GitHub.

Derivative approximation block. Modeled after Modelica.Blocks.Continuous.Derivative

    ╭─────────╮
 in │   s K   │ out
╶───┤╶───────╴├────╴
    │ 1 + s T │
    ╰─────────╯

Additional structural parameters:

• guess=0: initial guess for the internal state (equals input in steady state)

For a concrete list of variables and parameters please check the model source on GitHub.

Simple gain block

 in ╭───╮ out
╶───┤ K ├────╴
    ╰───╯

For a concrete list of variables and parameters please check the model source on GitHub.

SimpleLagLim block

              __ outMax
             /
      ╭─────────╮
   in │    K    │ out
  ╶───┤╶───────╴├────╴
      │ 1 + s T │
      ╰─────────╯
outMin __/

Additional structural parameters:

• guess=0: initial guess for the internal state (equals output in steady state)

For a concrete list of variables and parameters please check the model source on GitHub.

LimIntegrator block

              __ outMax
             /
        ╭─────╮
     in │  K  │ out
    ╶───┤╶───╴├────╴
        │ s T │
        ╰─────╯
outMin __/

Additional structural parameters:

• guess=0: initial guess for the internal state (equals output in steady state)

For a concrete list of variables and parameters please check the model source on GitHub.

DeadZone block, modeled after Modelica.Blocks.Nonlinear.DeadZone

        │    ╱
   uMin │   ╱
─────┼╼━┿━╾┼─────
    ╱   │ uMax
   ╱    │

A dead zone nonlinearity that outputs zero when the input is within the specified band [uMin, uMax].

• If in < uMin: out = in - uMin (negative linear)
• If uMin ≤ in ≤ uMax: out = 0 (dead zone)
• If in > uMax: out = in - uMax (positive linear)

Structural parameters:

• uMax: Upper dead zone limit
• uMin=-uMax: Lower dead zone limit (defaults to -uMax for symmetric dead zone)

For a concrete list of variables and parameters please check the model source on GitHub.

ss_to_mtkmodel(A, B, C, D; name=nothing, guesses=zeros(size(A,1)))

Convert a state-space representation to a ModelingToolkit model.

Matrices can be either of real numbers or symbolic parameters/terms.

Returns A System object with variables in (input), out (output), and x₁, x₂, ... (states).

siso_tf_to_ss(num, den)

Convert a SISO transfer function to state-space representation.

Takes polynomial coefficients for numerator and denominator and returns state-space matrices (A, B, C, D). The transfer function is represented as:

       num[1]sⁿ + num[2]sⁿ⁻¹ + ... + num[end]
G(s) = ─────────────────────────────────────
       den[1]sᵐ + den[2]sᵐ⁻¹ + ... + den[end]

Arguments

• num: Vector of numerator coefficients (highest degree first)
• den: Vector of denominator coefficients (highest degree first)

Returns

A tuple (A, B, C, D) of state-space matrices in controller canonical form.

Notes

• Leading zeros in num/den are automatically truncated
• Transfer function must be proper (numerator degree ≤ denominator degree)
• Adapted from SymbolicControlSystems.jl (Copyright (c) 2020 Fredrik Bagge Carlson, MIT License)

QUAD_SE(u, SE1, SE2, E1, E2)

Quadratic Saturation Function through two points (E1,SE1) and (E2,SE2).

EXP_SE(u, SE1, SE2, E1, E2)

Exponential Saturation Function through two points (E1,SE1) and (E2,SE2).

SlackAlgebraic

Algebraic slack bus that enforces constant real and imaginary voltage components.

For a concrete list of variables and parameters please check the model source on GitHub.

SlackDifferential

Slack bus with differential voltage states, holding voltage constant via zero derivatives.

For a concrete list of variables and parameters please check the model source on GitHub.

VariableFrequencySlack

Slack bus with a dynamic voltage angle driven by a configurable (possibly time-varying) frequency.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_GENCLS

This model is a port of the OpenIPSL Electrical.Machines.PSSE.GENCLS model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Machines.PSSE.GENCLS. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_GENROU

This model is a port of the OpenIPSL Electrical.Machines.PSSE.GENROU model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Machines.PSSE.GENROU. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_GENROE

This model is a port of the OpenIPSL Electrical.Machines.PSSE.GENROE model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Machines.PSSE.GENROE. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_GENSAL

This model is a port of the OpenIPSL Electrical.Machines.PSSE.GENSAL model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Machines.PSSE.GENSAL. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_GENSAE

This model is a port of the OpenIPSL Electrical.Machines.PSSE.GENSAE model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Machines.PSSE.GENSAE. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

SauerPaiMachine

Machine Model as described in the book of Sauer and Pai.

For a concrete list of variables and parameters please check the model source on GitHub.

Swing

Simplified swing-equation generator with constant voltage magnitude and active power balance.

For a concrete list of variables and parameters please check the model source on GitHub.

ClassicalMachine

Classical synchronous machine model with transient reactance and swing dynamics.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_EXST1

This model is a port of the OpenIPSL Electrical.Controls.PSSE.ES.EXST1 model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Controls.PSSE.ES.EXST1. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_ESST4B

This model is a port of the OpenIPSL Electrical.Controls.PSSE.ES.ESST4B model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Controls.PSSE.ES.ESST4B. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_ESST1A

This model is a port of the OpenIPSL Electrical.Controls.PSSE.ES.ESST1A model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Controls.PSSE.ES.ESST1A. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_SCRX

This model is a port of the OpenIPSL Electrical.Controls.PSSE.ES.SCRX model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Controls.PSSE.ES.SCRX. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_IEEET1

This model is a port of the OpenIPSL Electrical.Controls.PSSE.ES.IEEET1 model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Controls.PSSE.ES.IEEET1. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

AVRFixed

Trivial AVR that holds the field voltage at a fixed parameter value.

For a concrete list of variables and parameters please check the model source on GitHub.

AVRTypeI

IEEE Type I excitation system with amplifier, stabilizer feedback, field circuit, and ceiling function.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_IEEEG1

This model is a port of the OpenIPSL Electrical.Controls.PSSE.TG.IEEEG1 model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Controls.PSSE.TG.IEEEG1. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_HYGOV

This model is a port of the OpenIPSL Electrical.Controls.PSSE.TG.HYGOV model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Controls.PSSE.TG.HYGOV. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

GovFixed

Trivial governor that holds the mechanical torque at a fixed parameter value.

For a concrete list of variables and parameters please check the model source on GitHub.

TurbineGovTypeI

Type-I turbine governor with droop, servo, and transient gain reduction stages (Milano p. 359).

For a concrete list of variables and parameters please check the model source on GitHub.

TGOV1

TGOV1 steam turbine governor with droop, valve limiter, and reheater.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_GGOV1_EXPERIMENTAL

This model is a port of the OpenIPSL Electrical.Controls.PSSE.TG.GGOV1 model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_IEEEST

This model is a port of the OpenIPSL Electrical.Controls.PSSE.PSS.IEEEST model, maintaining the same mathematical formulation while adapting to PowerDynamics/ModelingToolkit conventions.

Validation

Validated against the OpenIPSL SMIB testcase Tests.Controls.PSSE.PSS.IEEEST. See validation plot generated by automatic validation script in /test/OpenIPSL_test.

For a concrete list of variables and parameters please check the model source on GitHub.

PQLoad

Constant-power load that draws fixed active and reactive power regardless of voltage.

For a concrete list of variables and parameters please check the model source on GitHub.

VoltageDependentLoad

Load whose active and reactive power scale as a polynomial function of voltage magnitude.

For a concrete list of variables and parameters please check the model source on GitHub.

ConstantYLoad

Constant-admittance (shunt Y) load drawing current proportional to the bus voltage.

For a concrete list of variables and parameters please check the model source on GitHub.

ZIPLoad

ZIP load combining constant-impedance, constant-current, and constant-power fractions.

For a concrete list of variables and parameters please check the model source on GitHub.

ConstantCurrentLoad

Constant-current load drawing a fixed current magnitude at a configurable phase offset relative to the bus voltage.

For a concrete list of variables and parameters please check the model source on GitHub.

PSSE_Load

PSS/E load model combining ZIP (constant-impedance/current/power) characteristics with voltage-dependent scaling.

For a concrete list of variables and parameters please check the model source on GitHub.

PiLine

Pi-section transmission branch with series impedance, shunt admittances, and optional transformer ratios.

For a concrete list of variables and parameters please check the model source on GitHub.

PiLine_fault

Pi-section branch with a configurable mid-point fault (short-circuit or impedance-to-ground).

For a concrete list of variables and parameters please check the model source on GitHub.

Breaker

Ideal circuit breaker: enforces equal terminal voltages when closed, zero current when open.

For a concrete list of variables and parameters please check the model source on GitHub.

DynamicSeriesRLBranch(; R, L, ω0, r_src=1, r_dst=1)

Dynamic transmission line modeled as a series R-L circuit with optional transformer ratios.

This model represents a series resistance and inductance connecting two buses. The line current is a differential state, suitable for:

• Transmission lines with significant inductive reactance
• Transformer models with leakage impedance
• Dynamic analysis requiring explicit current dynamics

Parameters

• R: Line resistance [pu]
• L: Line reactance [pu] at frequency ω0. Related to physical inductance by L = ω0 * L_actual.
• ω0: Frame angular frequency [rad/s]. Default: 2π*50 rad/s.
• r_src: Transformer voltage ratio at source. Default: 1.
• r_dst: Transformer voltage ratio at destination. Default: 1.

For a concrete list of variables and parameters please check the model source on GitHub.

StaticShunt(; G, B)

Static (algebraic) shunt element with constant admittance Y = G + jB.

This model represents a linear shunt connected to a bus, drawing current proportional to the bus voltage: I = Y * V. It has no dynamic states and is evaluated algebraically.

Parameters

• G: Shunt conductance [pu]. Positive values represent resistive losses (real power consumption).
• B: Shunt susceptance [pu]. Positive values represent capacitive behavior (leading current), negative values represent inductive behavior (lagging current).

For a concrete list of variables and parameters please check the model source on GitHub.

DynamicCShunt(; C, ω0=2π*50)

Dynamic shunt element modeled as a pure capacitor.

The capacitor voltage is a differential state, suitable for DAE index reduction at current-source buses and modelling shunt capacitor banks without resistive losses.

Parameters

• C: Shunt susceptance [pu] at frequency ω0. Related to physical capacitance by C = ω0 * C_actual.
• ω0: Frame angular frequency [rad/s]. Default: 2π*50 rad/s.

For a concrete list of variables and parameters please check the model source on GitHub.

DynamicParallelRCShunt(; R, C, ω0=2π*50)

Dynamic shunt element modeled as a parallel R ∥ C circuit.

This model represents a parallel combination of resistance and capacitance connected to a bus. The capacitor voltage is a differential state, suitable for:

• Shunt capacitor banks with resistive losses
• Dynamic susceptance for DAE index reduction at current-source buses
• Fast transient behavior of reactive compensation

Parameters

• R: Shunt resistance [pu]
• C: Shunt susceptance [pu] at frequency ω0. Related to physical capacitance by C = ω0 * C_actual.
• ω0: Frame angular frequency [rad/s]. Default: 2π*50 rad/s.

For a concrete list of variables and parameters please check the model source on GitHub.

IdealDroopInverter

Simplified droop-controlled inverter with first-order power filtering and ideal voltage source output.

For a concrete list of variables and parameters please check the model source on GitHub.

DroopInverter(; name=:droop_inv, filter_type, defaults...)

Grid-forming inverter with droop control for frequency and voltage regulation.

Wraps VoltageSource with DroopOuter controller implementing P-f and Q-V droop characteristics. Suitable for:

• Grid-forming inverters in microgrids
• Virtual synchronous machine (VSM) implementations
• Parallel inverter operation with power sharing

Parameters

• filter_type: :LC or :LCL filter topology (passed to VoltageSource)
• Droop controller parameters: Kp (P-f droop), Kq (Q-V droop), τ_p, τ_q (power filter time constants)
• Filter parameters inherited from VoltageSource: Lf, C, Lg, ω0
• defaults...: Additional parameter/variable defaults (e.g., Kp=0.5, τ_p=0.2)

For a concrete list of variables and parameters please check the model source on GitHub.

SimpleGFL(; name, iset_input=false, defaults...)

Simplified grid-following inverter with L-filter, current control, and PLL.

Implements single-loop current control (CC1) with PLL synchronization and simple L-filter. Suitable for:

• Basic grid-following inverter models
• Simplified renewable energy source representation
• Studies where detailed filter dynamics are not critical

Parameters

• iset_input: If true, current setpoint comes from RealInput ports. If false, uses internal isetd/isetq parameters.
• Lf: Filter reactance [pu]. Related to physical inductance by Lf = ω0 * Lf_actual.
• ω0: Frame angular frequency [rad/s]. Default: 2π*50 rad/s.
• PLL and CC1 controller gains
• defaults...: Additional parameter/variable defaults (e.g., Lf=0.05, PLL_Kp=50)

For a concrete list of variables and parameters please check the model source on GitHub.

SimpleGFLDC(; name, defaults...)

Grid-following inverter with DC-link dynamics and active power control.

Extends SimpleGFL with DC-link capacitor model and PI controller for DC voltage regulation. The DC voltage controller generates active current reference (q-axis). Suitable for:

• Inverters with significant DC-link capacitance
• Renewable sources with DC power input (solar PV, battery storage)
• Studies requiring DC-side transient analysis

Parameters

• Lf: Filter reactance [pu]. Related to physical inductance by Lf = ω0 * Lf_actual.
• ω0: Frame angular frequency [rad/s]. Default: 2π*50 rad/s.
• C_dc: DC-link capacitance [pu]
• V_dc: DC voltage reference [pu]
• kp_v_dc, ki_v_dc: DC voltage PI controller gains
• P_dc: External DC power draw [pu]
• PLL and CC1 controller gains
• defaults...: Additional parameter/variable defaults (e.g., Lf=0.03, V_dc=2.0)

For a concrete list of variables and parameters please check the model source on GitHub.

VoltageSource(; name, Vset_input=false, filter_type=:LC, defaults...)

Grid-forming voltage source inverter with cascaded voltage and current control.

Implements two-loop control with voltage controller (VC) commanding current references to inner current controller (CC1). Operates in a fixed dq-frame (no PLL). Suitable for:

• Grid-forming inverters establishing voltage and frequency
• Islanded or weak-grid operation
• Droop-controlled systems (via DroopInverter wrapper)

Parameters

• Vset_input: If true, voltage setpoint comes from RealInput ports. If false, uses internal Vset/δset parameters.
• filter_type: :LC for LC filter or :LCL for LCL filter.
• Lf: Inverter-side filter reactance [pu]. Related to physical inductance by Lf = ω0 * Lf_actual.
• C: Filter susceptance [pu]. Related to physical capacitance by C = ω0 * C_actual.
• Lg: Grid-side filter reactance [pu]. Related to physical inductance by Lg = ω0 * Lg_actual (LCL only).
• ω0: Frame angular frequency [rad/s]. Default: 2π*50 rad/s.
• Various PI controller gains (CC1KP, CC1KI, VCKP, VCKI)
• defaults...: Additional parameter/variable defaults (e.g., Lf=0.01, CC1_KP=0.1)

For a concrete list of variables and parameters please check the model source on GitHub.

DroopOuter

Power droop outer control loop implementing P-f and Q-V droop for grid-forming inverters.

For a concrete list of variables and parameters please check the model source on GitHub.

CurrentSource(; name, iset_input=false, defaults...)

Grid-following current source inverter with triple-loop cascaded control and PLL.

Implements three-loop control: outer current controller (CC2) → voltage controller (VC) → inner current controller (CC1). Uses PLL for grid synchronization. Suitable for:

• Grid-following inverters injecting controlled current
• Renewable energy sources (solar, wind) in grid-connected mode
• Active/reactive power control applications

Parameters

• iset_input: If true, current setpoint comes from RealInput ports. If false, uses internal isetd/isetq parameters.
• Lf: Inverter-side filter reactance [pu]. Related to physical inductance by Lf = ω0 * Lf_actual.
• C: Filter susceptance [pu]. Related to physical capacitance by C = ω0 * C_actual.
• Lg: Grid-side filter reactance [pu]. Related to physical inductance by Lg = ω0 * Lg_actual.
• ω0: Frame angular frequency [rad/s]. Default: 2π*50 rad/s.
• PLL and controller gains (PLLKp, PLLKi, CC1*, VC, CC2_)
• defaults...: Additional parameter/variable defaults (e.g., Lf=0.01, PLL_Kp=100)

For a concrete list of variables and parameters please check the model source on GitHub.

SimplePLL(; name, Kp, Ki, defaults...)

Basic PLL that tracks the grid voltage angle by driving the q-axis voltage to zero. Uses a PI controller on the angle error signal u_q.

Parameters

• Kp: Proportional gain
• Ki: Integral gain
• defaults...: Additional parameter/variable defaults

For a concrete list of variables and parameters please check the model source on GitHub.

PLL_LPF(; name, Kp, Ki, τ_lpf, defaults...)

PLL with an additional low-pass filter on the frequency output. Uses a PI controller on the angle error, followed by a first-order LPF on the estimated frequency ω.

Parameters

• Kp: Proportional gain
• Ki: Integral gain
• τ_lpf: Low-pass filter time constant [s]
• defaults...: Additional parameter/variable defaults

For a concrete list of variables and parameters please check the model source on GitHub.

VC

Voltage controller for the filter capacitor voltage, implementing PI control with optional current feedforward decoupling.

For a concrete list of variables and parameters please check the model source on GitHub.

CC1

Inner current controller for the inverter-side inductor current, implementing PI control with optional decoupling feedforward.

For a concrete list of variables and parameters please check the model source on GitHub.

CC2

Outer current controller for the grid-side inductor current, implementing PI control with optional voltage feedforward decoupling.

For a concrete list of variables and parameters please check the model source on GitHub.

LCLFilter

LCL output filter (inverter-side inductor, capacitor, grid-side inductor) for inverters, modeled in the global dq-frame.

For a concrete list of variables and parameters please check the model source on GitHub.

LCFilter

Inductor-capacitor (LC) output filter for inverters, modeled in the global dq-frame.

For a concrete list of variables and parameters please check the model source on GitHub.

LFilter

Single-inductor (L) output filter for inverters, modeled in the global dq-frame.

For a concrete list of variables and parameters please check the model source on GitHub.

RXGroundFault

Shunt RX impedance to ground representing a fault, switchable via the enable parameter.

For a concrete list of variables and parameters please check the model source on GitHub.