From 04592daf83c892cadd34c8ed4a1653825dc6a0df Mon Sep 17 00:00:00 2001 From: lukelowry Date: Fri, 26 Jun 2026 20:43:20 -0500 Subject: [PATCH 1/4] Type 4 Wind Docs --- GridKit/Model/PhasorDynamics/Wind/README.md | 15 + .../Model/PhasorDynamics/Wind/WT4E/README.md | 384 ++++++++++++++++++ .../Model/PhasorDynamics/Wind/WT4G/README.md | 298 ++++++++++++++ .../Model/PhasorDynamics/Wind/WT4T/README.md | 214 ++++++++++ .../PhasorDynamics/Wind/WTGPTA/README.md | 233 +++++++++++ .../PhasorDynamics/Wind/WT4E/diagram.png | Bin 0 -> 74603 bytes .../PhasorDynamics/Wind/WT4G/diagram.png | Bin 0 -> 71291 bytes .../PhasorDynamics/Wind/WT4T/diagram.png | Bin 0 -> 19906 bytes .../PhasorDynamics/Wind/WTGPTA/diagram.png | Bin 0 -> 44048 bytes docs/GridKit/Model/PhasorDynamics/README.md | 1 + .../Model/PhasorDynamics/Wind/README.md | 17 + .../Model/PhasorDynamics/Wind/WT4E/README.md | 6 + .../Model/PhasorDynamics/Wind/WT4G/README.md | 6 + .../Model/PhasorDynamics/Wind/WT4T/README.md | 6 + .../PhasorDynamics/Wind/WTGPTA/README.md | 6 + 15 files changed, 1186 insertions(+) create mode 100644 GridKit/Model/PhasorDynamics/Wind/README.md create mode 100644 GridKit/Model/PhasorDynamics/Wind/WT4E/README.md create mode 100644 GridKit/Model/PhasorDynamics/Wind/WT4G/README.md create mode 100644 GridKit/Model/PhasorDynamics/Wind/WT4T/README.md create mode 100644 GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md create mode 100644 docs/Figures/PhasorDynamics/Wind/WT4E/diagram.png create mode 100644 docs/Figures/PhasorDynamics/Wind/WT4G/diagram.png create mode 100644 docs/Figures/PhasorDynamics/Wind/WT4T/diagram.png create mode 100644 docs/Figures/PhasorDynamics/Wind/WTGPTA/diagram.png create mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/README.md create mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md create mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md create mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md create mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md diff --git a/GridKit/Model/PhasorDynamics/Wind/README.md b/GridKit/Model/PhasorDynamics/Wind/README.md new file mode 100644 index 000000000..fc5ad33f2 --- /dev/null +++ b/GridKit/Model/PhasorDynamics/Wind/README.md @@ -0,0 +1,15 @@ +# **Wind Models** + +## Introduction + +Wind models represent wind-turbine generator and converter components in the +phasor dynamics model. + +## Types + +The GridKit wind documentation includes: + +- Type 4 Wind Electrical Control Model WT4E (See [WT4E](WT4E/README.md)) +- Type 4 Wind Generator/Converter Model WT4G (See [WT4G](WT4G/README.md)) +- Type 4 Wind Turbine Model WT4T (See [WT4T](WT4T/README.md)) +- Wind Turbine Generator Pitch-Control Model WTGPTA (See [WTGPTA](WTGPTA/README.md)) diff --git a/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md b/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md new file mode 100644 index 000000000..fdef6c143 --- /dev/null +++ b/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md @@ -0,0 +1,384 @@ +# **Type 4 Wind Electrical Control Model (WT4E)** + +WT4E is a WECC electrical-control model for full-converter wind-turbine +generators. In GridKit it is represented as a signal-control model that +computes active- and reactive-current commands for a downstream converter +interface model. + +## Notes + +- When used with WT4G, connect WT4E `iqcmd` and `ipcmd` to the downstream converter current-command ports. +- The separate-model `varflg = -1` mode is not included in the equations below. + +## Block Diagram + +Standard WT4E electrical-control model. + +![](../../../../../docs/Figures/PhasorDynamics/Wind/WT4E/diagram.png) + +Figure 1: WT4E block diagram. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) + +## Model Parameters + +Symbol | Units | JSON | Description | Typical Value | Note +------------------------------------|----------|------------|---------------------------------------------------------|---------------|------ +$S^\mathrm{base}$ | [MVA] | `mva` | WT4E component power base | 100.0 | Required positive value +$s_{\mathrm{var}}$ | [binary] | `varflg` | Reactive-control mode flag | - | 1 = WindCONTROL emulation, 0 = local reactive-power or power-factor control +$K_{\mathrm{qi}}$ | [p.u./s] | `Kqi` | Reactive-power control integral gain | - | Block name: `Kqi` +$K_{\mathrm{vi}}$ | [p.u./s] | `Kvi` | Voltage-control integral gain | - | Block name: `Kvi` +$V^{\max}$ | [p.u.] | `Vmax` | Maximum regulated-voltage reference | - | Block name: `Vmax` +$V^{\min}$ | [p.u.] | `Vmin` | Minimum regulated-voltage reference | - | Block name: `Vmin` +$Q^{\max}$ | [p.u.] | `Qmax` | Maximum reactive-power command | - | Block name: `Qmax` +$Q^{\min}$ | [p.u.] | `Qmin` | Minimum reactive-power command | - | Block name: `Qmin` +$T_R$ | [sec] | `Tr` | WindCONTROL voltage-measurement lag time constant | - | State 4 +$T_C$ | [sec] | `Tc` | WindCONTROL output lag time constant | - | State 6 +$K_{\mathrm{pv}}$ | [p.u.] | `Kpv` | WindCONTROL proportional gain | - | State 3 path +$K_{\mathrm{iv}}$ | [p.u./s] | `Kiv` | WindCONTROL integral gain | - | State 5 path +$s_{\mathrm{pfa}}$ | [binary] | `pfaflg` | Power-factor angle control flag | - | 1 = power-factor angle control, 0 = reactive-power control +$F_N$ | [-] | `Fn` | Fraction of online wind-turbine generators | - | Block name: `Fn` +$T_V$ | [sec] | `Tv` | WindCONTROL proportional-path lag time constant | - | State 3 +$T_{\mathrm{pwr}}$ | [sec] | `Tpwr` | Active-power measurement filter time constant | - | State 7 +$I_p^\mathrm{hl}$ | [p.u.] | `Iphl` | Active-current hard limit | - | Block name: `Iphl` +$I_q^\mathrm{hl}$ | [p.u.] | `Iqhl` | Reactive-current hard limit | - | Block name: `Iqhl` +$s_{PQ}$ | [binary] | `Pqflag` | P/Q priority flag for converter current limit | - | 0 = Q priority, 1 = P priority +$I_{TD}^{\max}$ | [p.u.] | `ImaxTD` | Temperature-dependent maximum converter current | - | Block name: `ImaxTD` +$V_{iq}^{\lim}$ | [p.u.] | `Viqlim` | Voltage-dependent reactive-current limit | - | Block name: `Viqlim` + +### Parameter Validation + +Invalid WT4E parameter sets are rejected by the following checks. Let $\epsilon_T=10^{-3}$. + +```math +\begin{aligned} + T &\leftarrow \max\!\left(T, \epsilon_T\right) + \quad T\in\{T_R,T_C,T_V,T_{\mathrm{pwr}}\} \\ + S^\mathrm{base} + &> 0 \\ + s_{\mathrm{var}}, s_{\mathrm{pfa}}, s_{PQ} + &\in \{0,1\} \\ + F_N + &> 0 \\ + V^{\min} + &\le V^{\max} \\ + Q^{\min} + &\le Q^{\max} \\ + I_p^\mathrm{hl}, I_q^\mathrm{hl}, I_{TD}^{\max}, V_{iq}^{\lim} + &\ge 0 +\end{aligned} +``` + +### Model Derived Parameters + +```math +\begin{aligned} + s_{\mathrm{var}}^\mathrm{off} + &= 1 - s_{\mathrm{var}} \\ + s_{\mathrm{pfa}}^\mathrm{off} + &= 1 - s_{\mathrm{pfa}} \\ + k_{\mathrm{base}} + &= \dfrac{S^\mathrm{sys}}{S^\mathrm{base}} +\end{aligned} +``` + +## Model Variables + +### Internal Variables + +#### Differential + +Symbol | Units | Description | Note +------------------------|--------|-------------------------------------|------ +$V^\mathrm{ref}$ | [p.u.] | Regulated-voltage reference state | State 1 in Fig. 1 +$x_q^\mathrm{cmd}$ | [p.u.] | Reactive-current command state | State 2 in Fig. 1; source label: `Iqcmd`; component base +$x_V^\mathrm{P}$ | [p.u.] | WindCONTROL proportional-path state | State 3 in Fig. 1; source label: `Kpv` +$V^\mathrm{meas}$ | [p.u.] | Filtered WindCONTROL voltage input | State 4 in Fig. 1; source label: `VregMeas` +$x_V^\mathrm{I}$ | [p.u.] | WindCONTROL integral-path state | State 5 in Fig. 1; source label: `Kiv` +$Q^\mathrm{ord}$ | [p.u.] | Filtered reactive-power order | State 6 in Fig. 1; source label: `Qord`; component base +$P^\mathrm{meas}$ | [p.u.] | Filtered electrical active power | State 7 in Fig. 1; source label: `Pmeas`; component base + +#### Algebraic + +Symbol | Units | Description | Note +------------------------------------|----------|-------------------------------------|------ +$Q^\mathrm{pf}$ | [p.u.] | Power-factor-angle reactive-power command candidate | Component base +$Q^\mathrm{sel}$ | [p.u.] | Selected reactive-power command | Component base +$Q^\mathrm{ctrl}$ | [p.u.] | Selected reactive-control output before final reactive-power limit | Component base +$Q^\mathrm{cmd}$ | [p.u.] | Limited reactive-power command | Component base +$e_Q$ | [p.u.] | Reactive-power control error | +$e_V$ | [p.u.] | Voltage-control error | +$I_q^\mathrm{cap}$ | [p.u.] | Reactive-current hard-limit cap | Component base +$I_p^\mathrm{cap}$ | [p.u.] | Active-current hard-limit cap | Component base +$I_q^\mathrm{circ}$ | [p.u.] | Reactive-current limit from converter current circle | +$I_p^\mathrm{circ}$ | [p.u.] | Active-current limit from converter current circle | +$I_q^{\max}$ | [p.u.] | Final reactive-current upper limit | Component base +$I_q^{\min}$ | [p.u.] | Final reactive-current lower limit | Component base +$I_p^{\max}$ | [p.u.] | Final active-current upper limit | Component base +$I_q^\mathrm{cmd}$ | [p.u.] | Reactive-current command output | System base +$I_p^\mathrm{cmd}$ | [p.u.] | Active-current command output | System base + +### External Variables + +#### Differential +None. + +#### Algebraic + +Symbol | Units | Type | Description | Note +-------------------------------------|--------|---------|-----------------------------------|------ +$V_C$ | [p.u.] | Known | WindCONTROL voltage input | Source label: `Vc` +$P_e$ | [p.u.] | Known | Electrical active-power feedback | Signal port `pelec`; system base +$Q_e$ | [p.u.] | Known | Electrical reactive-power feedback | Signal port `qelec`; system base +$V_T$ | [p.u.] | Known | Terminal voltage magnitude | Signal port `vterm` +$P^\mathrm{ord}$ | [p.u.] | Known | Active-power order from turbine/governor model | Signal port `pord`; system base +$V_{\mathrm{RFQ}}$ | [p.u.] | Unknown | Voltage/reactive-control reference | Optional signal port `vrfq` +$Q^\mathrm{ref}$ | [p.u.] | Unknown | Reactive-power reference | Optional signal port `qref`; system base +$\phi^\mathrm{ref}$ | [rad] | Unknown | Power-factor angle reference | Optional signal port `pfaref` + +## Model Equations + +### Differential Equations + +```math +\begin{aligned} + 0 &= + -\dot{V}^\mathrm{ref} + + \text{antiwindup} + \left(V^\mathrm{ref}, K_{\mathrm{qi}}e_Q;\, V^{\min}, V^{\max}\right) \\ + 0 &= + -\dot{x}_q^\mathrm{cmd} + + \text{antiwindup} + \left(x_q^\mathrm{cmd}, K_{\mathrm{vi}}e_V;\, I_q^{\min}, I_q^{\max}\right) \\ + 0 &= + -\dot{x}_V^\mathrm{P} + + \dfrac{1}{T_V} + \left( + \dfrac{K_{\mathrm{pv}}}{F_N}\left(V_{\mathrm{RFQ}} - V^\mathrm{meas}\right) + - x_V^\mathrm{P} + \right) \\ + 0 &= + -\dot{V}^\mathrm{meas} + + \dfrac{1}{T_R} + \left(V_C - V^\mathrm{meas}\right) \\ + 0 &= + -\dot{x}_V^\mathrm{I} + + \dfrac{K_{\mathrm{iv}}}{F_N} + \left(V_{\mathrm{RFQ}} - V^\mathrm{meas}\right) \\ + 0 &= + -\dot{Q}^\mathrm{ord} + + \dfrac{1}{T_C} + \left( + \text{clamp} + \left(x_V^\mathrm{P} + x_V^\mathrm{I};\, Q^{\min}, Q^{\max}\right) + - Q^\mathrm{ord} + \right) \\ + 0 &= + -\dot{P}^\mathrm{meas} + + \dfrac{1}{T_{\mathrm{pwr}}} + \left(k_{\mathrm{base}}P_e - P^\mathrm{meas}\right) +\end{aligned} +``` + +CommonMath defines the [Anti-Windup](../../../../CommonMath.md#anti-windup-indicator) +target and smooth approximation, and +[clamp](../../../../CommonMath.md#derived-functions). + +### Algebraic Equations + +```math +\begin{aligned} + 0 &= + -Q^\mathrm{pf} + + P^\mathrm{meas}\tan\!\left(\phi^\mathrm{ref}\right) \\ + 0 &= + -Q^\mathrm{sel} + + s_{\mathrm{pfa}}Q^\mathrm{pf} + + s_{\mathrm{pfa}}^\mathrm{off}k_{\mathrm{base}}Q^\mathrm{ref} \\ + 0 &= + -Q^\mathrm{ctrl} + + s_{\mathrm{var}}Q^\mathrm{ord} + + s_{\mathrm{var}}^\mathrm{off}Q^\mathrm{sel} \\ + 0 &= + -Q^\mathrm{cmd} + + \text{clamp} + \left(Q^\mathrm{ctrl};\, Q^{\min}, Q^{\max}\right) \\ + 0 &= + -e_Q + + Q^\mathrm{cmd} + - k_{\mathrm{base}}Q_e \\ + 0 &= + -e_V + + V^\mathrm{ref} + - V_T \\ + 0 &= + -I_q^\mathrm{cap} + + \text{min} + \left(\text{min}\left(I_q^\mathrm{hl}, V_{iq}^{\lim}\right), I_{TD}^{\max}\right) \\ + 0 &= + -I_p^\mathrm{cap} + + \text{min} + \left(I_p^\mathrm{hl}, I_{TD}^{\max}\right) \\ + 0 &= + -\left(I_q^\mathrm{circ}\right)^2 + + \left(I_{TD}^{\max}\right)^2 + - s_{PQ}\left(k_{\mathrm{base}}I_p^\mathrm{cmd}\right)^2 \\ + 0 &= + -\left(I_p^\mathrm{circ}\right)^2 + + \left(I_{TD}^{\max}\right)^2 + - \left(1-s_{PQ}\right)\left(x_q^\mathrm{cmd}\right)^2 \\ + 0 &= + -I_q^{\max} + + \left(1-s_{PQ}\right)I_q^\mathrm{cap} + + s_{PQ}\text{min} + \left(I_q^\mathrm{cap}, I_q^\mathrm{circ}\right) \\ + 0 &= + -I_q^{\min} + - I_q^{\max} \\ + 0 &= + -I_p^{\max} + + s_{PQ}I_p^\mathrm{cap} + + \left(1-s_{PQ}\right)\text{min} + \left(I_p^\mathrm{cap}, I_p^\mathrm{circ}\right) \\ + 0 &= + -k_{\mathrm{base}}I_q^\mathrm{cmd} + + x_q^\mathrm{cmd} \\ + 0 &= + -k_{\mathrm{base}}I_p^\mathrm{cmd} + + \text{clamp} + \left( + \dfrac{k_{\mathrm{base}}P^\mathrm{ord}}{V_T};\, + 0,\, + I_p^{\max} + \right) +\end{aligned} +``` + +CommonMath defines [clamp and min](../../../../CommonMath.md#derived-functions). + +## Initialization + +### External Priors + +```math +\begin{aligned} + V_{C,0} + &\leftarrow \text{WindCONTROL voltage input} \\ + P_{e,0}, Q_{e,0} + &\leftarrow \text{electrical-power feedback on system base} \\ + V_{T,0} + &\leftarrow \text{terminal voltage magnitude} \\ + P_0^\mathrm{ord} + &\leftarrow \text{active-power order start} +\end{aligned} +``` + +### Internal Initialization + +Initialization is performed by evaluating the steady-state residuals in +dependency order. Let subscript $0$ denote initial values and set all internal +derivatives to zero: + +```math +\begin{aligned} + P_0^\mathrm{meas} + &= k_{\mathrm{base}}P_{e,0} \\ + V_0^\mathrm{meas} + &= V_{C,0} \\ + Q_0^\mathrm{cmd} + &= + \text{clamp} + \left(k_{\mathrm{base}}Q_{e,0};\, Q^{\min}, Q^{\max}\right) \\ + x_{V,0}^\mathrm{P} + &= 0 \\ + x_{V,0}^\mathrm{I} + &= Q_0^\mathrm{cmd} \\ + Q_0^\mathrm{ord} + &= Q_0^\mathrm{cmd} \\ + Q_0^\mathrm{pf} + &= Q_0^\mathrm{cmd} \\ + Q_0^\mathrm{sel} + &= Q_0^\mathrm{cmd} \\ + Q_0^\mathrm{ctrl} + &= Q_0^\mathrm{cmd} \\ + e_{Q,0} + &= Q_0^\mathrm{cmd} - k_{\mathrm{base}}Q_{e,0} \\ + V_0^\mathrm{ref} + &= V_{T,0} \\ + e_{V,0} + &= 0 \\ + x_{q,0}^\mathrm{cmd} + &= \dfrac{Q_0^\mathrm{cmd}}{V_{T,0}} \\ + I_{q,0}^\mathrm{cap} + &= + \text{min} + \left(\text{min}\left(I_q^\mathrm{hl}, V_{iq}^{\lim}\right), I_{TD}^{\max}\right) \\ + I_{p,0}^\mathrm{cap} + &= + \text{min} + \left(I_p^\mathrm{hl}, I_{TD}^{\max}\right) \\ + I_{p,0}^\mathrm{circ} + &= + \sqrt{ + \left(I_{TD}^{\max}\right)^2 + - \left(1-s_{PQ}\right)\left(x_{q,0}^\mathrm{cmd}\right)^2 + } \\ + I_{p,0}^{\max} + &= + s_{PQ}I_{p,0}^\mathrm{cap} + + \left(1-s_{PQ}\right)\text{min} + \left(I_{p,0}^\mathrm{cap}, I_{p,0}^\mathrm{circ}\right) \\ + I_{p,0}^\mathrm{cmd} + &= + \dfrac{1}{k_{\mathrm{base}}} + \text{clamp} + \left( + \dfrac{k_{\mathrm{base}}P_0^\mathrm{ord}}{V_{T,0}};\, + 0,\, + I_{p,0}^{\max} + \right) \\ + I_{q,0}^\mathrm{circ} + &= + \sqrt{ + \left(I_{TD}^{\max}\right)^2 + - s_{PQ}\left(k_{\mathrm{base}}I_{p,0}^\mathrm{cmd}\right)^2 + } \\ + I_{q,0}^{\max} + &= + \left(1-s_{PQ}\right)I_{q,0}^\mathrm{cap} + + s_{PQ}\text{min} + \left(I_{q,0}^\mathrm{cap}, I_{q,0}^\mathrm{circ}\right) \\ + I_{q,0}^{\min} + &= -I_{q,0}^{\max} \\ + I_{q,0}^\mathrm{cmd} + &= \dfrac{x_{q,0}^\mathrm{cmd}}{k_{\mathrm{base}}} +\end{aligned} +``` + +### External Solved + +```math +\begin{aligned} + V_{\mathrm{RFQ},0} + &\leftarrow V_0^\mathrm{meas} \\ + Q_0^\mathrm{ref} + &\leftarrow \dfrac{Q_0^\mathrm{cmd}}{k_{\mathrm{base}}} \\ + \phi_0^\mathrm{ref} + &\leftarrow + \begin{cases} + \tan^{-1}\!\left(Q_0^\mathrm{cmd}/P_0^\mathrm{meas}\right) & P_0^\mathrm{meas} \ne 0 \\ + 0 & P_0^\mathrm{meas} = 0 + \end{cases} +\end{aligned} +``` + +Initialization rejects nonpositive terminal voltage, negative current-circle +radicands, and nonzero WT4E antiwindup rates. + +## Monitorable Outputs + +Output | Units | Description | Note +----------------|--------|-------------------------------------|------ +`iqcmd` | [p.u.] | Reactive-current command output | $I_q^\mathrm{cmd}$ (system base) +`ipcmd` | [p.u.] | Active-current command output | $I_p^\mathrm{cmd}$ (system base) +`vmeas` | [p.u.] | Filtered WindCONTROL voltage input | $V^\mathrm{meas}$ +`pmeas` | [p.u.] | Filtered electrical active power | $P^\mathrm{meas}$ (component base) +`qord` | [p.u.] | Filtered reactive-power order | $Q^\mathrm{ord}$ (component base) diff --git a/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md b/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md new file mode 100644 index 000000000..fb042bbe0 --- /dev/null +++ b/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md @@ -0,0 +1,298 @@ +# **Type 4 Wind Generator/Converter Model (WT4G)** + +WT4G is a first-generation WECC type 4 wind generator/converter model for +full-converter wind plants. In GridKit it is represented as a controlled current +source at the network interface. + +## Notes + +- Internal current states and limiter quantities are on component base. +- Signal ports, monitor outputs, branch currents, and branch powers are on system base. +- LVACM uses $V_T$; LVPL uses $V^\mathrm{meas}$. +- HVRCM is represented by algebraic current $I_q^\mathrm{extra}$. +- PowerWorld fields `Iolim` and `Khv` are not parameters of this GridKit implementation. + +## Block Diagram + +Standard WT4G converter-interface model. + +![](../../../../../docs/Figures/PhasorDynamics/Wind/WT4G/diagram.png) + +Figure 1: Type 4 Wind Generator/Converter WT4G model. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) + +## Model Parameters + +Symbol | Units | JSON | Description | Typical Value | Note +---------------------------------|----------|-----------|-------------------------------------------------------|---------------|------ +$P_0$ | [p.u.] | `P0` | Initial active power injection | 1.0 | System base; required initialization source +$Q_0$ | [p.u.] | `Q0` | Initial reactive power injection | 0.0 | System base; required initialization source +$S^\mathrm{base}$ | [MVA] | `mva` | WT4G component power base | 100.0 | +$T_d$ | [sec] | `Td` | Current-control lag time constant | 0.02 | States 1 and 2 in Fig. 1; block name: `Td` +$T_{\mathrm{LVPL}}$ | [sec] | `T_LVPL` | LVPL voltage sensor time constant | 0.02 | State 3 in Fig. 1; block name: `T_LVPL` +$R_p^{\max}$ | [p.u./s] | `rrpwr` | Active-current magnitude recovery rate limit | 999.0 | Block name: `rrpwr` +$s_L$ | [binary] | `LVPLSW` | LVPL switch | 1 | Block name: `LPVLSW` +$I_{L1}$ | [p.u.] | `LVPL1` | LVPL upper-current ceiling | 1.1 | Block name: `Lvpl1` +$V_{L0}$ | [p.u.] | `zerox` | LVPL zero-crossing voltage | 0.4 | Block name: `zerox` +$V_{L1}$ | [p.u.] | `brkpt` | LVPL upper breakpoint voltage | 0.9 | Block name: `brkpt` +$V_{A0}$ | [p.u.] | `LVPnt0` | LVACM lower breakpoint voltage | 0.4 | Block name: `Lvpnt0` +$V_{A1}$ | [p.u.] | `LVPnt1` | LVACM upper breakpoint voltage | 0.9 | Block name: `Lvpnt1` +$V_{\mathrm{hv}}^{\max}$ | [p.u.] | `VLim` | Terminal-voltage ceiling for HV reactive management | 1.2 | Block name: `VLim` + +### Parameter Validation + +Invalid WT4G parameter sets are rejected by the following checks. Let $\epsilon_T=10^{-3}$. + +```math +\begin{aligned} + T &\leftarrow \max\!\left(T, \epsilon_T\right) + \quad T\in\{T_d,T_{\mathrm{LVPL}}\} \\ + S^\mathrm{base} + &> 0 \\ + R_p^{\max} + &> 0 \\ + s_L + &\in \{0,1\} \\ + I_{L1} + &\ge 0 \\ + 0 + &\le V_{L0} < V_{L1} \\ + 0 + &\le V_{A0} < V_{A1} \\ + V_{\mathrm{hv}}^{\max} + &> 0 +\end{aligned} +``` + +### Model Derived Parameters + +```math +\begin{aligned} + s_L^\mathrm{off} + &= 1 - s_L \\ + k_{\mathrm{base}} + &= \dfrac{S^\mathrm{sys}}{S^\mathrm{base}} \\ + M_p + &= 100 R_p^{\max} +\end{aligned} +``` + +$M_p$ is a finite surrogate for inactive active-current rate limits, +not a physical WT4G parameter. + +## Model Variables + +### Internal Variables + +#### Differential + +Symbol | Units | Description | Note +----------------------|--------|---------------------------|------ +$E_q$ | [p.u.] | Reactive-current lag state | State 1 in Fig. 1 before the `-1` block; component base +$I_p$ | [p.u.] | Active-current state | State 2 in Fig. 1; component base +$V^\mathrm{meas}$ | [p.u.] | Filtered terminal voltage | State 3 in Fig. 1 + +#### Algebraic + +Symbol | Units | Description | Note +---------------------------|----------|-------------------------------------------------------------|------ +$V_T$ | [p.u.] | Terminal voltage magnitude | +$I_{\mathrm{r}}$ | [p.u.] | Branch-current real component | System base +$I_{\mathrm{i}}$ | [p.u.] | Branch-current imaginary component | System base +$I_q^\mathrm{extra}$ | [p.u.] | Extra inductive current from high-voltage reactive current management | Component base +$I_L$ | [p.u.] | LVPL upper-limit current curve | Component base; function of $V^\mathrm{meas}$ +$A^\mathrm{LVACM}$ | [p.u.] | Low-voltage active-current management gain | Function of $V_T$ +$\ell_p$ | [p.u./s] | Smooth active-current lower rate bound | Component base; equivalent to diagram `Rdown` +$u_p$ | [p.u./s] | Smooth active-current upper rate bound | Component base; effective `Rup` +$P^\mathrm{br}$ | [p.u.] | Branch active power | System base +$Q^\mathrm{br}$ | [p.u.] | Branch reactive power | System base + +### External Variables + +#### Differential +None. + +#### Algebraic + +Symbol | Units | Type | Description | Note +--------------------------------|--------|---------|------------------------------------------------------------------|------ +$V_{\mathrm{r}}$ | [p.u.] | Known | Terminal voltage, real component | Bus input +$V_{\mathrm{i}}$ | [p.u.] | Known | Terminal voltage, imaginary component | Bus input +$I_p^\mathrm{cmd}$ | [p.u.] | Unknown | Active-current command in the terminal-voltage reference frame | Optional signal port `ipcmd`; system base +$E_q^\mathrm{cmd}$ | [p.u.] | Unknown | Reactive-current command before the diagram `-1` block | Optional signal port `eqcmd`; system base + +WT4G initializes the current-command ports from the required `P0`/`Q0` +power-flow injection. If no controller is connected, the resolved initialization +commands are held constant during residual evaluation. + +## Model Equations + +### Differential Equations + +The state equations use CommonMath helper notation. + +```math +\begin{aligned} + 0 &= -\dot E_q + + \dfrac{1}{T_d}\left(k_{\mathrm{base}}E_q^\mathrm{cmd} - E_q\right) \\ + 0 &= -\dot I_p + + \ell_p + + \dfrac{1}{T_d} + \rho\left(k_{\mathrm{base}}I_p^\mathrm{cmd} - I_p - T_d\ell_p\right) + - \dfrac{1}{T_d} + \rho\left(k_{\mathrm{base}}I_p^\mathrm{cmd} - I_p - T_d u_p\right) \\ + 0 &= -\dot V^\mathrm{meas} + + \dfrac{1}{T_{\mathrm{LVPL}}}\left(V_T - V^\mathrm{meas}\right) +\end{aligned} +``` + +Here $\rho$ is GridKit's [ramp](../../../../CommonMath.md#primitives). + +### Algebraic Equations + +```math +\begin{aligned} + 0 &= -V_T^2 + V_{\mathrm{r}}^2 + V_{\mathrm{i}}^2 \\ + 0 &= -V_T I_{\mathrm{r}} + + \dfrac{1}{k_{\mathrm{base}}} + \left[ + V_{\mathrm{i}}\left(E_q - I_q^\mathrm{extra}\right) + + V_{\mathrm{r}}I_p A^\mathrm{LVACM} + \right] \\ + 0 &= -V_T I_{\mathrm{i}} + + \dfrac{1}{k_{\mathrm{base}}} + \left[ + -V_{\mathrm{r}}\left(E_q - I_q^\mathrm{extra}\right) + + V_{\mathrm{i}}I_p A^\mathrm{LVACM} + \right] \\ + 0 &= -I_q^\mathrm{extra} + + \rho(V_T - V_{\mathrm{hv}}^{\max}) \\ + 0 &= -I_L + + \text{linseg}(V^\mathrm{meas};\ V_{L0},\ V_{L1},\ I_{L1}) \\ + 0 &= -A^\mathrm{LVACM} + + \text{linseg}(V_T;\ V_{A0},\ V_{A1},\ 1) \\ + 0 &= -\ell_p + - R_p^{\max} + - \left(M_p - R_p^{\max}\right)\sigma(I_p) \\ + 0 &= -u_p + + M_p\left(1-\sigma(I_p)\right) + + R_p^{\max}\sigma(I_p) + \left(s_L^\mathrm{off} + s_L\sigma(I_L - I_p)\right) \\ + 0 &= -P^\mathrm{br} + + V_{\mathrm{r}} I_{\mathrm{r}} + V_{\mathrm{i}} I_{\mathrm{i}} \\ + 0 &= -Q^\mathrm{br} + + V_{\mathrm{i}} I_{\mathrm{r}} - V_{\mathrm{r}} I_{\mathrm{i}} +\end{aligned} +``` + +Here $\text{linseg}$ is GridKit's +[linear segment](../../../../CommonMath.md#derived-functions), $\rho$ is the +[ramp](../../../../CommonMath.md#primitives), and $\sigma$ is the +[step function](../../../../CommonMath.md#primitives). + +## Network Interface + +The bus receives the WT4G branch-current variables directly: + +```math +\begin{aligned} + I_{\mathrm{r}}^\mathrm{inj} &:= I_{\mathrm{r}} \\ + I_{\mathrm{i}}^\mathrm{inj} &:= I_{\mathrm{i}} +\end{aligned} +``` + +## Initialization + +### External Priors + +```math +\begin{aligned} + V_{\mathrm{r},0}, V_{\mathrm{i},0} + &\leftarrow \text{terminal-bus voltage} \\ + P_0, Q_0 + &\leftarrow \text{power-flow injection on system base} +\end{aligned} +``` + +### Internal Initialization + +Initialization is performed by evaluating the steady-state residuals in +dependency order. Let subscript $0$ denote initial values and set all internal +derivatives to zero: + +```math +\begin{aligned} + V_{T,0} + &= \sqrt{V_{\mathrm{r},0}^2 + V_{\mathrm{i},0}^2} \\ + V_0^\mathrm{meas} + &= V_{T,0} \\ + A_0^\mathrm{LVACM} + &= \text{linseg}\left(V_{T,0};\ V_{A0},\ V_{A1},\ 1\right) \\ + I_{p,0}^\mathrm{cmd} + &= + \begin{cases} + \dfrac{P_0}{V_{T,0}A_0^\mathrm{LVACM}} & P_0 \ne 0 \\ + 0 & P_0 = 0 + \end{cases} \\ + E_{q,0}^\mathrm{cmd} + &= \dfrac{Q_0}{V_{T,0}} \\ + I_{p,0} + &= k_{\mathrm{base}}I_{p,0}^\mathrm{cmd} \\ + E_{q,0} + &= k_{\mathrm{base}}E_{q,0}^\mathrm{cmd} \\ + I_{q,0}^\mathrm{extra} + &= 0 \\ + I_{L,0} + &= \text{linseg}\left(V_0^\mathrm{meas};\ V_{L0},\ V_{L1},\ I_{L1}\right) \\ + \ell_{p,0} + &= -R_p^{\max} + - \left(M_p - R_p^{\max}\right)\sigma(I_{p,0}) \\ + u_{p,0} + &= M_p\left(1-\sigma(I_{p,0})\right) + + R_p^{\max}\sigma(I_{p,0}) + \left(s_L^\mathrm{off} + s_L\sigma(I_{L,0} - I_{p,0})\right) \\ + I_{\mathrm{r},0} + &= \dfrac{1}{k_{\mathrm{base}}V_{T,0}} + \left[ + V_{\mathrm{i},0}\left(E_{q,0} - I_{q,0}^\mathrm{extra}\right) + + V_{\mathrm{r},0}I_{p,0}A_0^\mathrm{LVACM} + \right] \\ + I_{\mathrm{i},0} + &= \dfrac{1}{k_{\mathrm{base}}V_{T,0}} + \left[ + -V_{\mathrm{r},0}\left(E_{q,0} - I_{q,0}^\mathrm{extra}\right) + + V_{\mathrm{i},0}I_{p,0}A_0^\mathrm{LVACM} + \right] \\ + P_0^\mathrm{br} + &= V_{\mathrm{r},0}I_{\mathrm{r},0} + V_{\mathrm{i},0}I_{\mathrm{i},0} \\ + Q_0^\mathrm{br} + &= V_{\mathrm{i},0}I_{\mathrm{r},0} - V_{\mathrm{r},0}I_{\mathrm{i},0} +\end{aligned} +``` + +Here $\text{linseg}$ is GridKit's +[linear segment](../../../../CommonMath.md#derived-functions), and $\sigma$ is +the [step function](../../../../CommonMath.md#primitives). + +### External Solved + +```math +\begin{aligned} + I_p^\mathrm{cmd} + &\leftarrow I_{p,0}^\mathrm{cmd} \\ + E_q^\mathrm{cmd} + &\leftarrow E_{q,0}^\mathrm{cmd} +\end{aligned} +``` + +WT4G writes the resolved current commands to attached `ipcmd` and `eqcmd` +ports. If no controller is attached, those values are used as constant command +inputs. + +## Monitorable Outputs + +Output | Units | Description | Note +-------|--------|-----------------------------|------ +`ir` | [p.u.] | Real current injection | System base; exported through `ibranchr` when assigned +`ii` | [p.u.] | Imaginary current injection | System base; exported through `ibranchi` when assigned +`p` | [p.u.] | Active-power output | System base; exported through `pbranch` when assigned +`q` | [p.u.] | Reactive-power output | System base; exported through `qbranch` when assigned diff --git a/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md b/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md new file mode 100644 index 000000000..f8db98cfd --- /dev/null +++ b/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md @@ -0,0 +1,214 @@ +# **Type 4 Wind Turbine Model (WT4T)** + +WT4T is a WECC simplified wind-turbine active-power control model for +full-converter wind-turbine generators. In GridKit it is represented as a +signal-control model that computes an active-power order for a downstream +electrical-control model. + +## Notes + +- When used with WT4E, connect WT4T `pord` to WT4E `pord`. +- Signal ports and active-power order are on system base. +- Internal measured, PI, and washout quantities are on component base. + +## Block Diagram + +Standard WT4T simplified wind-turbine model. + +![](../../../../../docs/Figures/PhasorDynamics/Wind/WT4T/diagram.png) + +Figure 1: WT4T block diagram. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) + +## Model Parameters + +Symbol | Units | JSON | Description | Typical Value | Note +------------------------------------|----------|------------|---------------------------------------------------------|---------------|------ +$P^\mathrm{rate}$ | [MW] | `MWCap` | WT4T turbine rating | - | Required positive value +$T_{\mathrm{pw}}$ | [sec] | `Tpw` | Electrical-power measurement filter time constant | - | State 1 in Fig. 1 +$K_{\mathrm{pp}}$ | [p.u.] | `Kpp` | Pitch-control proportional gain | - | Block name: `Kpp` +$K_{\mathrm{ip}}$ | [p.u./s] | `Kip` | Pitch-control integral gain | - | State 2 path +$T_f$ | [sec] | `Tf` | Washout time constant | - | State 3 in Fig. 1 +$K_f$ | [p.u.] | `Kf` | Washout gain | - | Block name: `Kf` +$\Delta P^{\max}$ | [p.u.] | `dPmx` | Maximum PI output limit | - | Block name: `dPmax` +$\Delta P^{\min}$ | [p.u.] | `dPmn` | Minimum PI output limit | - | Block name: `dPmin` + +### Parameter Validation + +Invalid WT4T parameter sets are rejected by the following checks. Let $\epsilon_T=10^{-3}$. + +```math +\begin{aligned} + T &\leftarrow \max\!\left(T, \epsilon_T\right) + \quad T\in\{T_{\mathrm{pw}},T_f\} \\ + P^\mathrm{rate} + &> 0 \\ + \Delta P^{\min} + &\le 0 \le \Delta P^{\max} +\end{aligned} +``` + +### Model Derived Parameters + +```math +\begin{aligned} + k_{\mathrm{base}} + &= \dfrac{S^\mathrm{sys}}{P^\mathrm{rate}} +\end{aligned} +``` + +## Model Variables + +### Internal Variables + +#### Differential + +Symbol | Units | Description | Note +------------------------|--------|-------------------------------------|------ +$P^\mathrm{meas}$ | [p.u.] | Filtered electrical active power | State 1 in Fig. 1; component base +$x_P^\mathrm{I}$ | [p.u.] | Pitch-control integral state | State 2 path; component base +$x_f$ | [p.u.] | Washout lag state | State 3 in Fig. 1; component base + +#### Algebraic + +Symbol | Units | Description | Note +------------------------------------|----------|-------------------------------------|------ +$P^\mathrm{iin}$ | [p.u.] | Pitch-control input error | Component base +$P^\mathrm{iou}$ | [p.u.] | Limited pitch-control output | Component base +$P_f$ | [p.u.] | Washout feedback signal | Component base +$P^\mathrm{ord}$ | [p.u.] | Active-power order output | System base + +### External Variables + +#### Differential +None. + +#### Algebraic + +Symbol | Units | Type | Description | Note +-------------------------------------|--------|---------|-----------------------------------|------ +$P_e$ | [p.u.] | Known | Electrical active-power feedback | Signal port `pelec`; system base +$P^\mathrm{aux}$ | [p.u.] | Known | Auxiliary power input | Optional signal port `paux`; system base; defaults to zero +$P^\mathrm{ref}$ | [p.u.] | Unknown | Active-power reference | Optional signal port `pref`; system base + +## Model Equations + +### Differential Equations + +```math +\begin{aligned} + 0 &= + -\dot{P}^\mathrm{meas} + + \dfrac{1}{T_{\mathrm{pw}}} + \left(k_{\mathrm{base}}P_e - P^\mathrm{meas}\right) \\ + 0 &= + -\dot{x}_P^\mathrm{I} + + \text{antiwindup} + \left( + K_{\mathrm{pp}}P^\mathrm{iin} + x_P^\mathrm{I},\, + K_{\mathrm{ip}}P^\mathrm{iin};\, + \Delta P^{\min}, \Delta P^{\max} + \right) \\ + 0 &= + -\dot{x}_f + + \dfrac{1}{T_f} + \left(k_{\mathrm{base}}P^\mathrm{ord} - x_f\right) +\end{aligned} +``` + +CommonMath defines the [Anti-Windup](../../../../CommonMath.md#anti-windup-indicator) +target and smooth approximation. + +### Algebraic Equations + +```math +\begin{aligned} + 0 &= + -P_f + + \dfrac{K_f}{T_f} + \left(k_{\mathrm{base}}P^\mathrm{ord} - x_f\right) \\ + 0 &= + -P^\mathrm{iin} + + k_{\mathrm{base}}P^\mathrm{ref} + + k_{\mathrm{base}}P^\mathrm{aux} + - P^\mathrm{meas} + - P_f \\ + 0 &= + -P^\mathrm{iou} + + \text{clamp} + \left( + K_{\mathrm{pp}}P^\mathrm{iin} + x_P^\mathrm{I};\, + \Delta P^{\min},\, + \Delta P^{\max} + \right) \\ + 0 &= + -k_{\mathrm{base}}P^\mathrm{ord} + + k_{\mathrm{base}}P^\mathrm{ref} + + P^\mathrm{iou} + - P_f +\end{aligned} +``` + +CommonMath defines [clamp](../../../../CommonMath.md#derived-functions). + +## Initialization + +### External Priors + +```math +\begin{aligned} + P_{e,0} + &\leftarrow \text{electrical active-power feedback on system base} \\ + P_0^\mathrm{aux} + &\leftarrow \text{auxiliary power input on system base} \\ + P_0^\mathrm{ord} + &\leftarrow \text{active-power order start on system base} +\end{aligned} +``` + +### Internal Initialization + +Initialization is performed by evaluating the steady-state residuals in +dependency order. Let subscript $0$ denote initial values and set all internal +derivatives to zero: + +```math +\begin{aligned} + P_0^\mathrm{meas} + &= k_{\mathrm{base}}P_{e,0} \\ + x_{f,0} + &= k_{\mathrm{base}}P_0^\mathrm{ord} \\ + P_{f,0} + &= 0 \\ + P_0^\mathrm{iin} + &= 0 \\ + P_0^\mathrm{iou} + &= + k_{\mathrm{base}}P_0^\mathrm{ord} + - k_{\mathrm{base}}P_{e,0} + + k_{\mathrm{base}}P_0^\mathrm{aux} + + P_{f,0} \\ + x_{P,0}^\mathrm{I} + &= P_0^\mathrm{iou} +\end{aligned} +``` + +### External Solved + +```math +\begin{aligned} + P_0^\mathrm{ref} + &\leftarrow P_{e,0} - P_0^\mathrm{aux} +\end{aligned} +``` + +Initialization rejects nonzero WT4T antiwindup rates. + +## Monitorable Outputs + +Output | Units | Description | Note +----------------|--------|-------------------------------------|------ +`pord` | [p.u.] | Active-power order output | $P^\mathrm{ord}$ (system base) +`pmeas` | [p.u.] | Filtered electrical active power | $P^\mathrm{meas}$ (component base) +`piin` | [p.u.] | Pitch-control input error | $P^\mathrm{iin}$ (component base) +`piou` | [p.u.] | Limited pitch-control output | $P^\mathrm{iou}$ (component base) +`pf` | [p.u.] | Washout feedback signal | $P_f$ (component base) diff --git a/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md b/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md new file mode 100644 index 000000000..65165063a --- /dev/null +++ b/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md @@ -0,0 +1,233 @@ +# **Wind Turbine Generator Pitch-Control Model (WTGPTA)** + +WTGPTA is a WECC wind-turbine generator pitch-control model. In GridKit it is +represented as a signal-control model that computes a blade-pitch angle from +rotor-speed and active-power command feedback. + +## Notes + +- WTGPTA corresponds to the source model `WTGPT_A`. +- The equivalent `WTPTA1` source model names $K_{\mathrm{ip}}$ and + $K_{\mathrm{pp}}$ as `Kiw` and `Kpw`. +- Signal ports and active-power commands are on system base. +- Pitch-control states and outputs are in degrees. + +## Block Diagram + +Standard WTGPTA pitch-control model. + +![](../../../../../docs/Figures/PhasorDynamics/Wind/WTGPTA/diagram.png) + +Figure 1: WTGPTA block diagram. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) + +## Model Parameters + +Symbol | Units | JSON | Description | Typical Value | Note +------------------------------------|---------------|-------------|---------------------------------------------------------|---------------|------ +$S^\mathrm{base}$ | [MVA] | `mva` | WTGPTA component power base | 100.0 | Required positive value; source label: `MVABase` +$T_\theta$ | [sec] | `Tp` | Blade-pitch response time constant | - | State 1 in Fig. 1 +$K_{\mathrm{pp}}$ | [deg/p.u.] | `Kpp` | Speed-control proportional gain | - | `WTPTA1` source label: `Kpw` +$K_{\mathrm{ip}}$ | [deg/p.u./s] | `Kip` | Speed-control integral gain | - | State 2 path; `WTPTA1` source label: `Kiw` +$K_{\mathrm{pc}}$ | [deg/p.u.] | `Kpc` | Pitch-compensator proportional gain | - | Block name: `Kpc` +$K_{\mathrm{ic}}$ | [deg/p.u./s] | `Kic` | Pitch-compensator integral gain | - | State 3 path +$\theta^{\min}$ | [deg] | `ThetaMin` | Minimum pitch angle | - | Block name: `ThetaMin` +$\theta^{\max}$ | [deg] | `ThetaMax` | Maximum pitch angle | - | Block name: `ThetaMax` +$R_\theta^{\min}$ | [deg/s] | `RThetaMin` | Minimum pitch-rate limit | - | Block name: `RThetaMin` +$R_\theta^{\max}$ | [deg/s] | `RThetaMax` | Maximum pitch-rate limit | - | Block name: `RThetaMax` +$K_{\mathrm{cc}}$ | [-] | `Kcc` | Cross-coupling gain from active-power error to speed-error path | - | Block name: `Kcc` + +### Parameter Validation + +Invalid WTGPTA parameter sets are rejected by the following checks. Let $\epsilon_T=10^{-3}$. + +```math +\begin{aligned} + T_\theta + &\leftarrow \max\!\left(T_\theta, \epsilon_T\right) \\ + S^\mathrm{base} + &> 0 \\ + \theta^{\min} + &\le \theta^{\max} \\ + R_\theta^{\min} + &\le 0 \le R_\theta^{\max} +\end{aligned} +``` + +### Model Derived Parameters + +```math +\begin{aligned} + k_{\mathrm{base}} + &= \dfrac{S^\mathrm{sys}}{S^\mathrm{base}} +\end{aligned} +``` + +## Model Variables + +### Internal Variables + +#### Differential + +Symbol | Units | Description | Note +------------------------------------|-------|-------------------------------------|------ +$\theta$ | [deg] | Blade-pitch angle | State 1 in Fig. 1 +$x_\omega^\mathrm{I}$ | [deg] | Speed-control integral state | State 2 in Fig. 1; source label: `PitchControl` +$x_P^\mathrm{I}$ | [deg] | Pitch-compensator integral state | State 3 in Fig. 1; source label: `PitchComp` + +#### Algebraic + +Symbol | Units | Description | Note +------------------------------------|----------|-------------------------------------|------ +$e_\omega$ | [p.u.] | Speed-control error | +$e_P$ | [p.u.] | Active-power command error | Component base +$\theta_\omega$ | [deg] | Limited speed-control pitch command | +$\theta_P$ | [deg] | Limited active-power pitch-compensator command | +$\theta^\mathrm{cmd}$ | [deg] | Combined pitch command before blade response | +$r_\theta$ | [deg/s] | Rate-limited pitch derivative target | + +### External Variables + +#### Differential +None. + +#### Algebraic + +Symbol | Units | Type | Description | Note +-------------------------------------|--------|---------|-----------------------------------|------ +$\omega_t$ | [p.u.] | Known | Turbine rotor speed | Signal port `omegat` +$P^\mathrm{ord}$ | [p.u.] | Known | Active-power order feedback | Signal port `pord`; system base +$\omega^\mathrm{ref}$ | [p.u.] | Unknown | Rotor-speed reference | Optional signal port `wref` +$P^\mathrm{ref}$ | [p.u.] | Unknown | Active-power reference | Optional signal port `pref`; system base + +## Model Equations + +### Differential Equations + +```math +\begin{aligned} + 0 &= + -\dot{\theta} + + \text{antiwindup} + \left(\theta, r_\theta;\, \theta^{\min}, \theta^{\max}\right) \\ + 0 &= + -\dot{x}_\omega^\mathrm{I} + + \text{antiwindup} + \left(x_\omega^\mathrm{I}, K_{\mathrm{ip}}e_\omega;\, + \theta^{\min}, \theta^{\max}\right) \\ + 0 &= + -\dot{x}_P^\mathrm{I} + + \text{antiwindup} + \left(x_P^\mathrm{I}, K_{\mathrm{ic}}e_P;\, + \theta^{\min}, \theta^{\max}\right) +\end{aligned} +``` + +CommonMath defines the [Anti-Windup](../../../../CommonMath.md#anti-windup-indicator) +target and smooth approximation. + +### Algebraic Equations + +```math +\begin{aligned} + 0 &= + -e_P + + k_{\mathrm{base}} + \left(P^\mathrm{ord} - P^\mathrm{ref}\right) \\ + 0 &= + -e_\omega + + \omega_t + - \omega^\mathrm{ref} + + K_{\mathrm{cc}}e_P \\ + 0 &= + -\theta_\omega + + \text{clamp} + \left(K_{\mathrm{pp}}e_\omega + x_\omega^\mathrm{I};\, + \theta^{\min}, \theta^{\max}\right) \\ + 0 &= + -\theta_P + + \text{clamp} + \left(K_{\mathrm{pc}}e_P + x_P^\mathrm{I};\, + \theta^{\min}, \theta^{\max}\right) \\ + 0 &= + -\theta^\mathrm{cmd} + + \theta_\omega + + \theta_P \\ + 0 &= + -r_\theta + + \text{clamp} + \left( + \dfrac{\theta^\mathrm{cmd} - \theta}{T_\theta};\, + R_\theta^{\min},\, + R_\theta^{\max} + \right) +\end{aligned} +``` + +CommonMath defines [clamp](../../../../CommonMath.md#derived-functions). + +## Initialization + +### External Priors + +```math +\begin{aligned} + \omega_{t,0} + &\leftarrow \text{turbine rotor-speed start} \\ + P_0^\mathrm{ord} + &\leftarrow \text{active-power order start on system base} \\ + \theta_0 + &\leftarrow \text{blade-pitch angle start} +\end{aligned} +``` + +### Internal Initialization + +Initialization is performed by evaluating the steady-state residuals in +dependency order. Let subscript $0$ denote initial values and set all internal +derivatives to zero: + +```math +\begin{aligned} + e_{P,0} + &= 0 \\ + e_{\omega,0} + &= 0 \\ + x_{P,0}^\mathrm{I} + &= 0 \\ + \theta_{P,0} + &= 0 \\ + x_{\omega,0}^\mathrm{I} + &= \theta_0 \\ + \theta_{\omega,0} + &= \theta_0 \\ + \theta_0^\mathrm{cmd} + &= \theta_0 \\ + r_{\theta,0} + &= 0 +\end{aligned} +``` + +### External Solved + +```math +\begin{aligned} + \omega_0^\mathrm{ref} + &\leftarrow \omega_{t,0} \\ + P_0^\mathrm{ref} + &\leftarrow P_0^\mathrm{ord} +\end{aligned} +``` + +Initialization rejects pitch starts outside +$[\theta^{\min},\theta^{\max}]$ and nonzero WTGPTA antiwindup rates. + +## Monitorable Outputs + +Output | Units | Description | Note +----------------|---------|-------------------------------------|------ +`theta` | [deg] | Blade-pitch angle | $\theta$ +`theta_cmd` | [deg] | Combined pitch command before blade response | $\theta^\mathrm{cmd}$ +`theta_speed` | [deg] | Limited speed-control pitch command | $\theta_\omega$ +`theta_power` | [deg] | Limited active-power pitch-compensator command | $\theta_P$ +`eomega` | [p.u.] | Speed-control error | $e_\omega$ +`ep` | [p.u.] | Active-power command error | $e_P$ (component base) diff --git a/docs/Figures/PhasorDynamics/Wind/WT4E/diagram.png b/docs/Figures/PhasorDynamics/Wind/WT4E/diagram.png new file mode 100644 index 0000000000000000000000000000000000000000..d71b2a6b78536676e6589c141b5fb29ba4c2a73b GIT binary patch literal 74603 zcmb4r2{@Er*tac3q_m(#{go6lvXxy?vS*JNWZ%oa%}|O;*_Q}|vW#tH%`&5sgc!>( zmY50+V>dGK+WXsS7x+KV-5WN6 zY;1x-tiSBjZYRUo*mjEbbgo#0L6@c?qYllXHP=kos%)>A>Ns*{H$dMVIh?_7snGh^ z^1YQ_m5}t3%)IBLfeue~-lD0g;n*vY9fA$STRBE$S%F?p&>q+B8y>pNbJ*WEWfSlA zK)Rsn+PYbr7CibgK^d#2+B$xwwcBqayd6q@peC=Xs!Cf8ys$VwKhJjH@0F2$C4%GM z-w$hYQ*{1b;*Z(Y|GsLga;1(`>}%BtCRqLo6P+56er;bvnwx3o@8bo zVbij-JpAB&0p^BjcfA05GfVoVZ+?#~AC}S|R^{MolUWBvF(*e>mzEfh|6JU)ZM!Lj zH}{lylDhLByg!xm@+Ecl!Q<<%Zk$bHiwRRpyd_-%F;htGJ|p-<$CmB*6P=q54y*d+ zw9wnPUrO!Sv^5C~lrI|em}pUT7UrIqn4q}CyV|TVnEeE3X$D~xyA_FsOZ}ZQ6VYbf z?CU_ zrc!PH&!2Aiix>Gil%dU{6&?!Z62*h^$8oFYe+I_>SxA}ioO(gLuH}NG?7ZQdTa_mI zT^-+LNsEi74h~7><&rQZum;0n!@W-#`qD=X_QHet`T48ci}mgcb;zp8+lr;!uvJNS zE^!wN(>o)myn2ZlI!}ztPr33}^wYe81EJUT6VV*qS9!Q&McS>)e+V5@{H17AH%uap z|6IIZ>m=;?z9Gv|_C>IAZ|#O{t;`j)b;;iUTzXSs{3!H<$b@-?T*jKxrAr+OMrQ*^GHJTcBXF% z!Cjd9!}l5~$IRfKox;k}!ov4F{i;&zCT9d6cg^$@A~LA8wQ|HAv0=Hq6PyjO)(V1m&3*FUw%7 zL8GS>2{o#^y%xT=Im{c(FY){okI4v!E|cplkKqlzIpNuo^)yN|r7vB&qzYsI>|V^T zk!}{5L8&BU2ztU=N51UdYM&m3`szY@=i4DC4Tp8qM0M3fR|n~HUz77`)PL3FaT`@% zYn8_MPGi`QbOpyby)CaY&}+2l!bf^!l`jrV#2*X6E>o#g&nv;9$oDF0Dj^5GhS^}* z;3(WU^TP!?+X5r`TN!K`4L@`W4Jw6a*=|6L_P5C?M|`N2et5M|6g62J-{Rb@_Gf{n zcrYBKBX!|K-2w&LU#x<*K7Y4Sa?$JrRG^%ErF^J2{rrnjOACw3I|36YC=2b~3D9NH zP1+0FI<9}NwEGyiGul*NhhK5GT)xn{pk2Zg%Rbhed+e`H&W=j4!)}Uj^vUvB->n!{ zZQJWsb{%2xBpg#VGG;U!^r=GN(bZiLo6+c(w)zkgsJRe8zvsXWInDMJaD=Y&14-9$|xWXxo>V5w6~B@2!b+qvZg2ut)UnM(e}0 zwY6>Cqv>*Ha(*6t!W&oQcvHJwMxXI38e!8vpUL`<$7zf%vZIqz?eknilS{bouZO8! zh_NO{R!Jamt8(?CYgFWZiX;^}gQDuXWA8=Nn?Pa zoNCUUIELoRl^j-3T}GlMI^Hb2S5<4YS-nU&rxncbp%Cy>eEXCW>COKFgx@Znc`9k> ziOz@Y*Tjenu5Try-fg0|&Y61>9{adstEnGn?)_rI(=#&OuhLX|-$C13j7o;y98dS6 zh#lfp?m%`cA=O(X()8TnHZ~$x3-><=!BRW@AFvwjfX{q{2@RE9z* zb;ImoUcPbtnW266!@o!Q=zNa~xF{dx*PoFBIeuRh|YAKj{85yec%2ZnqB5W5j;9r}i^Qbc> z|F8VZxGok*{JmN73g7&bzpv`=SM8KyUv1yf(4fzsR?q&6=HC)8|JVbBwa{(BB|MN7 zLnB0=JQ=liKi}}r7#4SRMZ?c<(#1L@Y5xxTUl!Aq@--0qJ;NG0n1+JA0O7r;X!s}@(Ypb

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zV;wldA?g^}OXkg=AxD_u04bg_eB6B5J7C1dX;RvMQ5w=s^&TsqTiraj?HrXt;~p{jIRMh&R%pgi~7h z;h?C$#F;1I;=c%TB6HI3Mtx zat?tohp46$80pto6Y7>GklFSo`wre+VG&@2>Hr_h-Ms>ecg|RqeDVHGoH^t5@(`O# zq$@Y8Wozz)m(QqSr^R3lu&9r2qBxxyO+H{5{l8av}FDuhA7q8yBH*uvO3WAMWwWb7G?;2XqS2hb}Xa)ki zZ24*%OCKRDH+9fex@$n4<$o5ntOy8CQ0dNalf z1S!mB=XUGi{C~f54Zb2@r))qg?zzs2 zKlDi+lT;lxj`bJGHnOh`XkEgT-9NN;y0g?+UnCYEWiEEGmx=^aKK zVdF@wQhTLgx3xt|;kTXc18RCSAN3m-UGRff5=}0G@IP(PHPCYDkd)Q0XFF7{|jA(3;O^GdNIV@Mbl*O@Cd(t>qjJ}HquUgy?) z0cHg{-(?>;%e|b-Y)LS={z6n6A@qiv*(*8nzQ5t>m`_FL8oz>z4|I{yyu@YbZbiYJ zI+Y1_w049GHt+gr?r7anOrlw*|16OieH<~}SlDa`QA>p)wrpi>#Ni6FUT1wh{nez^ zdDxs{^pS!qc?l86N15U~oW1NOW!www9KM)XxOctg%o!J>=k-y9_8fhwn!?}8*Dp0D z3u~KP>g((Kp=lEE-^XHPS9f>!bc@nU!_1NrJzzz2cc;cmC7vRYNYXaBvf^|TSM>m#Kco|@m2WecYfJLqaQ!M1GgIGa=S{9l#L00KfiXGoIv+` z9V_C#V5%mGA@*qU7s1s%aBOKy1+Tv88)z2=0r%F z=?2(>rx_lO!2wH>u?kk-t3oos_VySk0 SignalNode Stabilizer SynchronousMachine +Wind ``` ```{include} ../../../../GridKit/Model/PhasorDynamics/README.md diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/README.md new file mode 100644 index 000000000..6d5bde024 --- /dev/null +++ b/docs/GridKit/Model/PhasorDynamics/Wind/README.md @@ -0,0 +1,17 @@ +# Wind + +```{toctree} +:maxdepth: 4 +:titlesonly: +:hidden: + +WT4E +WT4G +WT4T +WTGPTA +``` + +```{include} ../../../../../GridKit/Model/PhasorDynamics/Wind/README.md +:start-line: 1 +:relative-images: +``` diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md new file mode 100644 index 000000000..c8fcaa21e --- /dev/null +++ b/docs/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md @@ -0,0 +1,6 @@ +# WT4E + +```{include} ../../../../../../GridKit/Model/PhasorDynamics/Wind/WT4E/README.md +:start-line: 1 +:relative-images: +``` diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md new file mode 100644 index 000000000..638435fdc --- /dev/null +++ b/docs/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md @@ -0,0 +1,6 @@ +# WT4G + +```{include} ../../../../../../GridKit/Model/PhasorDynamics/Wind/WT4G/README.md +:start-line: 1 +:relative-images: +``` diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md new file mode 100644 index 000000000..51a7ca122 --- /dev/null +++ b/docs/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md @@ -0,0 +1,6 @@ +# WT4T + +```{include} ../../../../../../GridKit/Model/PhasorDynamics/Wind/WT4T/README.md +:start-line: 1 +:relative-images: +``` diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md new file mode 100644 index 000000000..1b3320f87 --- /dev/null +++ b/docs/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md @@ -0,0 +1,6 @@ +# WTGPTA + +```{include} ../../../../../../GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md +:start-line: 1 +:relative-images: +``` From 69cfde351fa93e7286e047473228fc3b08007c8b Mon Sep 17 00:00:00 2001 From: lukelowry Date: Fri, 26 Jun 2026 22:42:02 -0500 Subject: [PATCH 2/4] Other wind models --- GridKit/Model/PhasorDynamics/Wind/README.md | 3 + .../PhasorDynamics/Wind/WTGARA/README.md | 139 +++++++++ .../Model/PhasorDynamics/Wind/WTGTA/README.md | 203 +++++++++++++ .../PhasorDynamics/Wind/WTGTRQA/README.md | 275 ++++++++++++++++++ .../PhasorDynamics/Wind/WTGARA/diagram.png | Bin 0 -> 6906 bytes .../PhasorDynamics/Wind/WTGTA/diagram.png | Bin 0 -> 51228 bytes .../PhasorDynamics/Wind/WTGTRQA/diagram.png | Bin 0 -> 50596 bytes .../Model/PhasorDynamics/Wind/README.md | 3 + .../PhasorDynamics/Wind/WTGARA/README.md | 6 + .../Model/PhasorDynamics/Wind/WTGTA/README.md | 6 + .../PhasorDynamics/Wind/WTGTRQA/README.md | 6 + 11 files changed, 641 insertions(+) create mode 100644 GridKit/Model/PhasorDynamics/Wind/WTGARA/README.md create mode 100644 GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md create mode 100644 GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md create mode 100644 docs/Figures/PhasorDynamics/Wind/WTGARA/diagram.png create mode 100644 docs/Figures/PhasorDynamics/Wind/WTGTA/diagram.png create mode 100644 docs/Figures/PhasorDynamics/Wind/WTGTRQA/diagram.png create mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/WTGARA/README.md create mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md create mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md diff --git a/GridKit/Model/PhasorDynamics/Wind/README.md b/GridKit/Model/PhasorDynamics/Wind/README.md index fc5ad33f2..43999554b 100644 --- a/GridKit/Model/PhasorDynamics/Wind/README.md +++ b/GridKit/Model/PhasorDynamics/Wind/README.md @@ -12,4 +12,7 @@ The GridKit wind documentation includes: - Type 4 Wind Electrical Control Model WT4E (See [WT4E](WT4E/README.md)) - Type 4 Wind Generator/Converter Model WT4G (See [WT4G](WT4G/README.md)) - Type 4 Wind Turbine Model WT4T (See [WT4T](WT4T/README.md)) +- Wind Turbine Generator Aerodynamic Model WTGARA (See [WTGARA](WTGARA/README.md)) - Wind Turbine Generator Pitch-Control Model WTGPTA (See [WTGPTA](WTGPTA/README.md)) +- Wind Turbine Generator Drive-Train Model WTGTA (See [WTGTA](WTGTA/README.md)) +- Wind Turbine Generator Torque-Control Model WTGTRQA (See [WTGTRQA](WTGTRQA/README.md)) diff --git a/GridKit/Model/PhasorDynamics/Wind/WTGARA/README.md b/GridKit/Model/PhasorDynamics/Wind/WTGARA/README.md new file mode 100644 index 000000000..4c91f4c12 --- /dev/null +++ b/GridKit/Model/PhasorDynamics/Wind/WTGARA/README.md @@ -0,0 +1,139 @@ +# **Wind Turbine Generator Aerodynamic Model (WTGARA)** + +WTGARA is a WECC wind-turbine generator aerodynamic model. In GridKit it is +represented as a signal-control model that computes mechanical power from +blade-pitch angle feedback. + +## Notes + +- WTGARA corresponds to the source model `WTGAR_A`. +- The equivalent PTI source model name is `WTARA1`. +- When used with WTGTA, connect WTGARA `pm` to WTGTA `pm`. +- Mechanical-power signal output is on system base. +- Internal aerodynamic power quantities are on component base. + +## Block Diagram + +Standard WTGARA aerodynamic model. + +![](../../../../../docs/Figures/PhasorDynamics/Wind/WTGARA/diagram.png) + +Figure 1: WTGARA block diagram. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) + +## Model Parameters + +Symbol | Units | JSON | Description | Typical Value | Note +------------------------------------|--------------|---------|---------------------------------------------------------|---------------|------ +$S^\mathrm{base}$ | [MVA] | `mva` | WTGARA component power base | 100.0 | Required positive value; source label: `MVABase` +$K_a$ | [p.u./deg^2] | `Ka` | Aerodynamic gain factor | - | Block name: `Ka` +$P_{\text{m},0}$ | [p.u.] | `Pm0` | Prior mechanical power | - | System base; block name: `Pm0` +$\theta_0$ | [deg] | `Theta` | Prior initial blade pitch angle | - | Block name: `Theta` + +### Parameter Validation + +Invalid WTGARA parameter sets are rejected by the following checks. + +```math +\begin{aligned} + S^\mathrm{base} + &> 0 +\end{aligned} +``` + +### Model Derived Parameters + +```math +\begin{aligned} + k_{\mathrm{base}} + &= \dfrac{S^\mathrm{sys}}{S^\mathrm{base}} +\end{aligned} +``` + +## Model Variables + +### Internal Variables + +#### Differential + +None. + +#### Algebraic + +Symbol | Units | Description | Note +------------------------------------|--------|-------------------------------------|------ +$P_\text{m}$ | [p.u.] | Mechanical-power output | System base; signal port `pm` + +### External Variables + +#### Differential + +None. + +#### Algebraic + +Symbol | Units | Type | Description | Note +------------------------------------|--------|---------|-------------------------------------|------ +$\theta$ | [deg] | Unknown | Blade-pitch angle | Signal port `theta` + +## Model Equations + +### Differential Equations + +None. + +### Algebraic Equations + +```math +\begin{aligned} + 0 &= + -k_{\mathrm{base}}\left(P_\text{m} - P_{\text{m},0}\right) + - K_a\theta\left(\theta - \theta_0\right) +\end{aligned} +``` + +## Initialization + +### External Priors + +```math +\begin{aligned} + P_\text{m} + &\leftarrow \text{mechanical-power start on system base} +\end{aligned} +``` + +### Internal Initialization + +None. + +### External Solved + +```math +\begin{aligned} + \theta + &\leftarrow + \begin{cases} + \dfrac{1}{2} + \left[ + \theta_0 + + \sqrt{ + \theta_0^2 + - \dfrac{4k_{\mathrm{base}}}{K_a} + \left(P_\text{m} - P_{\text{m},0}\right) + } + \right] & K_a\ne 0 \\ + \theta_0 & K_a = 0 + \end{cases} +\end{aligned} +``` + +Initialization requires $\theta_0\ge 0$, a nonnegative pitch radicand when +$K_a\ne 0$, and $P_\text{m} = P_{\text{m},0}$ when +$K_a=0$. + +## Monitorable Outputs + +Output | Units | Description | Note +----------------|--------|-------------------------------------|------ +`pm` | [p.u.] | Mechanical-power output | $P_\text{m}$ (system base) +`dtheta` | [deg] | Pitch-angle deviation | $\theta-\theta_0$ diff --git a/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md b/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md new file mode 100644 index 000000000..cb8136dd5 --- /dev/null +++ b/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md @@ -0,0 +1,203 @@ +# **Wind Turbine Generator Drive-Train Model (WTGTA)** + +WTGTA is a WECC wind-turbine generator two-mass drive-train model. In GridKit it +is represented as a signal-control model that computes turbine and generator +speed states from mechanical and electrical power feedback. + +## Notes + +- WTGTA corresponds to the source model `WTGT_A`. +- When used with WTGARA, connect WTGARA `pm` to WTGTA `pm`. +- When used with WTGPTA, connect WTGTA `omegat` to WTGPTA `omegat`. +- When used with WTGTRQA, connect WTGTA `omegag` to WTGTRQA `omegag`. +- Power signal inputs are on system base. +- Internal torque quantities are on component base. +- $\omega_g$ is an internal model variable and does not necessarily represent a + physical generator speed measurement. + +## Block Diagram + +Standard WTGTA drive-train model. + +![](../../../../../docs/Figures/PhasorDynamics/Wind/WTGTA/diagram.png) + +Figure 1: WTGTA block diagram. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) + +## Model Parameters + +Symbol | Units | JSON | Description | Typical Value | Note +------------------------------------|--------------|-----------|---------------------------------------------------------|---------------|------ +$H_t$ | [MW sec/MVA] | `Ht` | Turbine inertia | - | State 1 path +$H_g$ | [MW sec/MVA] | `Hg` | Generator inertia | - | State 3 path +$D^\mathrm{shaft}$ | [p.u.] | `DShaft` | Shaft damping coefficient | - | Block name: `Dshaft` +$K^\mathrm{shaft}$ | [p.u.] | `KShaft` | Shaft spring constant | - | Block name: `Kshaft` +$S^\mathrm{base}$ | [MVA] | `mva` | WTGTA component power base | 100.0 | Required positive value; source label: `MWCap` +$\omega_0$ | [p.u.] | `W0` | Initial speed | - | Diagram label: `W0` + +### Parameter Validation + +Invalid WTGTA parameter sets are rejected by the following checks. + +```math +\begin{aligned} + H_t, H_g + &> 0 \\ + D^\mathrm{shaft} + &\ge 0 \\ + K^\mathrm{shaft} + &> 0 \\ + S^\mathrm{base} + &> 0 \\ + \omega_0 + &> 0 +\end{aligned} +``` + +### Model Derived Parameters + +```math +\begin{aligned} + k_{\mathrm{base}} + &= \dfrac{S^\mathrm{sys}}{S^\mathrm{base}} \\ + \omega_s + &= 2\pi f_{\mathrm{nom}} +\end{aligned} +``` + +Here $f_{\mathrm{nom}}$ is the nominal system frequency. + +## Model Variables + +### Internal Variables + +#### Differential + +Symbol | Units | Description | Note +------------------------------------|-------|-------------------------------------|------ +$\omega_t$ | [p.u.] | Turbine speed output | State 1 in Fig. 1; signal port `omegat` +$\delta^\mathrm{shaft}$ | [rad] | Shaft angle | State 2 in Fig. 1 +$\omega_g$ | [p.u.] | Generator speed output | State 3 in Fig. 1; signal port `omegag` +$\delta_g$ | [rad] | Generator delta angle | State 4 in Fig. 1 + +#### Algebraic + +Symbol | Units | Description | Note +------------------------------------|--------|-------------------------------------|------ +$T_m$ | [p.u.] | Mechanical torque | Component base +$T_e$ | [p.u.] | Electrical torque | Component base +$T_{\mathrm{d}}$ | [p.u.] | Shaft damping torque | Component base +$T_{\mathrm{s}}$ | [p.u.] | Shaft spring torque | Component base + +### External Variables + +#### Differential + +None. + +#### Algebraic + +Symbol | Units | Type | Description | Note +------------------------------------|--------|-------|-------------------------------------|------ +$P_\text{m}$ | [p.u.] | Known | Mechanical power | Signal port `pm`; system base +$P_e$ | [p.u.] | Known | Electrical active-power feedback | Signal port `pelec`; system base + +## Model Equations + +### Differential Equations + +```math +\begin{aligned} + 0 &= + -\dot{\omega}_t + + \dfrac{1}{2H_t} + \left(T_m - T_{\mathrm{s}} - T_{\mathrm{d}}\right) \\ + 0 &= + -\dot{\delta}^\mathrm{shaft} + + \omega_s\left(\omega_t - \omega_g\right) \\ + 0 &= + -\dot{\omega}_g + + \dfrac{1}{2H_g} + \left(T_{\mathrm{s}} + T_{\mathrm{d}} - T_e\right) \\ + 0 &= + -\dot{\delta}_g + + \omega_s\left(\omega_g - \omega_0\right) +\end{aligned} +``` + +### Algebraic Equations + +```math +\begin{aligned} + 0 &= + -\omega_t T_m + + k_{\mathrm{base}}P_\text{m} \\ + 0 &= + -\omega_g T_e + + k_{\mathrm{base}}P_e \\ + 0 &= + -T_{\mathrm{d}} + + D^\mathrm{shaft}\left(\omega_t - \omega_g\right) \\ + 0 &= + -\omega_s T_{\mathrm{s}} + + K^\mathrm{shaft}\delta^\mathrm{shaft} +\end{aligned} +``` + +## Initialization + +### External Priors + +```math +\begin{aligned} + \omega_{t,0}, \omega_{g,0} + &\leftarrow \text{initial speeds} +\end{aligned} +``` + +### Internal Initialization + +Initialization is performed by evaluating the steady-state residuals in +dependency order. Let subscript $0$ denote initial values and set all internal +derivatives to zero: + +```math +\begin{aligned} + T_{\mathrm{d},0} + &= D^\mathrm{shaft}\left(\omega_{t,0} - \omega_{g,0}\right) \\ + T_{\mathrm{s},0} + &= 0 \\ + T_{m,0} + &= T_{\mathrm{s},0} + T_{\mathrm{d},0} \\ + T_{e,0} + &= T_{\mathrm{s},0} + T_{\mathrm{d},0} \\ + \delta_0^\mathrm{shaft} + &= 0 \\ + \delta_{g,0} + &= 0 +\end{aligned} +``` + +### External Solved + +```math +\begin{aligned} + P_{\text{m},0} + &\leftarrow \dfrac{\omega_{t,0}T_{m,0}}{k_{\mathrm{base}}} \\ + P_{e,0} + &\leftarrow \dfrac{\omega_{g,0}T_{e,0}}{k_{\mathrm{base}}} +\end{aligned} +``` + +Initialization rejects starts with $\omega_{t,0}\ne \omega_{g,0}$ or +$\omega_{g,0}\ne \omega_0$. + +## Monitorable Outputs + +Output | Units | Description | Note +------------------|--------|-------------------------------------|------ +`omegat` | [p.u.] | Turbine speed | $\omega_t$ +`omegag` | [p.u.] | Generator speed | $\omega_g$ +`shaft_angle` | [rad] | Shaft angle | $\delta^\mathrm{shaft}$ +`gen_delta_angle` | [rad] | Generator delta angle | $\delta_g$ +`tm` | [p.u.] | Mechanical torque | $T_m$ (component base) +`te` | [p.u.] | Electrical torque | $T_e$ (component base) diff --git a/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md b/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md new file mode 100644 index 000000000..73ce5c24d --- /dev/null +++ b/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md @@ -0,0 +1,275 @@ +# **Wind Turbine Generator Torque-Control Model (WTGTRQA)** + +WTGTRQA is a WECC wind-turbine generator torque-control model. In GridKit it is +represented as a signal-control model that computes speed and active-power +references for downstream wind-turbine controls. + +## Notes + +- WTGTRQA corresponds to the source model `WTGTRQ_A`. +- The equivalent PTI source model name is `WTTQA1`. +- When used with REECA, connect WTGTRQA `pref` to REECA `pref`. +- When used with WTGPTA, connect WTGTRQA `wref` to WTGPTA `wref`. +- Active-power signal ports are on system base. +- Internal measured power and torque-controller quantities are on component base. + +## Block Diagram + +Standard WTGTRQA wind-turbine generator torque-control model. + +![](../../../../../docs/Figures/PhasorDynamics/Wind/WTGTRQA/diagram.png) + +Figure 1: WTGTRQA block diagram. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) + +## Model Parameters + +Symbol | Units | JSON | Description | Typical Value | Note +------------------------------------|----------|-----------|---------------------------------------------------------|---------------|------ +$S^\mathrm{base}$ | [MVA] | `mva` | WTGTRQA component power base | 100.0 | Required positive value; source label: `MVABase` +$s_T$ | [index] | `Flag` | Torque-controller mode flag | - | 0 = torque control, 1 = speed control, 2 = torque control with $P^\mathrm{ref}_0$ upper torque limit +$K_{\mathrm{ip}}$ | [p.u./s] | `Kip` | Integral gain | - | State 3 path +$K_{\mathrm{pp}}$ | [p.u.] | `Kpp` | Proportional gain | - | Block name: `Kpp` +$T_p$ | [sec] | `Tp` | Electrical-power measurement lag time constant | - | State 2 in Fig. 1 +$T_{\omega}^{\mathrm{ref}}$ | [sec] | `Twref` | Speed-reference lag time constant | - | State 1 in Fig. 1 +$T_e^{\max}$ | [p.u.] | `Temax` | Maximum torque limit | - | Block name: `Temax` +$T_e^{\min}$ | [p.u.] | `Temin` | Minimum torque limit | - | Block name: `Temin` +$P_1$ | [p.u.] | `P1` | Power point 1 for speed-reference curve | - | Component base +$\omega_1$ | [p.u.] | `Speed1` | Speed point 1 for speed-reference curve | - | +$P_2$ | [p.u.] | `P2` | Power point 2 for speed-reference curve | - | Component base +$\omega_2$ | [p.u.] | `Speed2` | Speed point 2 for speed-reference curve | - | +$P_3$ | [p.u.] | `P3` | Power point 3 for speed-reference curve | - | Component base +$\omega_3$ | [p.u.] | `Speed3` | Speed point 3 for speed-reference curve | - | +$P_4$ | [p.u.] | `P4` | Power point 4 for speed-reference curve | - | Component base +$\omega_4$ | [p.u.] | `Speed4` | Speed point 4 for speed-reference curve | - | + +### Parameter Validation + +Invalid WTGTRQA parameter sets are rejected by the following checks. Let $\epsilon_T=10^{-3}$. + +```math +\begin{aligned} + T &\leftarrow \max\!\left(T, \epsilon_T\right) + \quad T\in\{T_p,T_{\omega}^{\mathrm{ref}}\} \\ + S^\mathrm{base} + &> 0 \\ + s_T + &\in \{0,1,2\} \\ + T_e^{\min} + &\le 0 \le T_e^{\max} \\ + 0 + &\le P_1 < P_2 < P_3 < P_4 \\ + \omega_1,\omega_2,\omega_3,\omega_4 + &> 0 +\end{aligned} +``` + +### Model Derived Parameters + +```math +\begin{aligned} + k_{\mathrm{base}} + &= \dfrac{S^\mathrm{sys}}{S^\mathrm{base}} \\ + \omega^\mathrm{sch}(P) + &= \omega_1 + + \text{linseg}\left(P;\, P_1, P_2, \omega_2-\omega_1\right) + + \text{linseg}\left(P;\, P_2, P_3, \omega_3-\omega_2\right) + + \text{linseg}\left(P;\, P_3, P_4, \omega_4-\omega_3\right) +\end{aligned} +``` + +CommonMath defines [linseg](../../../../CommonMath.md#derived-functions). + +## Model Variables + +### Internal Variables + +#### Differential + +Symbol | Units | Description | Note +------------------------------------|--------|-------------------------------------|------ +$\omega^\mathrm{ref}$ | [p.u.] | Filtered speed reference | State 1 in Fig. 1; signal port `wref` +$P^\mathrm{meas}$ | [p.u.] | Filtered electrical active power | State 2 in Fig. 1; component base +$x_T^\mathrm{I}$ | [p.u.] | Torque-control integral state | State 3 in Fig. 1; component base + +#### Algebraic + +Symbol | Units | Description | Note +------------------------------------|--------|-------------------------------------|------ +$\omega^\mathrm{cmd}$ | [p.u.] | Scheduled speed reference | From $\omega^\mathrm{sch}(P^\mathrm{meas})$ +$e_P$ | [p.u.] | Active-power reference error | Component base +$e_\omega$ | [p.u.] | Speed-control error | +$e_T$ | [p.u.] | Selected torque-controller error | +$T_e^{\max,\mathrm{eff}}$ | [p.u.] | Effective maximum torque limit | +$T_e^\mathrm{raw}$ | [p.u.] | Unlimited torque command | +$T_e^\mathrm{cmd}$ | [p.u.] | Limited torque command | +$P^\mathrm{ref}$ | [p.u.] | Active-power reference output | System base; signal port `pref` + +### External Variables + +#### Differential + +None. + +#### Algebraic + +Symbol | Units | Type | Description | Note +------------------------------------|----------|---------|-------------------------------------|------ +$P_e$ | [p.u.] | Known | Electrical active-power feedback | Signal port `pelec`; system base +$\omega_g$ | [p.u.] | Known | Generator speed from drive-train model | Signal port `omegag` +$s_{\mathrm{frz}}$ | [binary] | Known | Voltage-dip freeze signal | 1 freezes $x_T^\mathrm{I}$ +$P^\mathrm{ref}_0$ | [p.u.] | Known | Active-power reference input | Optional signal port `pref0`; system base + +## Model Equations + +### Differential Equations + +```math +\begin{aligned} + 0 &= + -\dot{\omega}^\mathrm{ref} + + \dfrac{1}{T_{\omega}^{\mathrm{ref}}} + \left(\omega^\mathrm{cmd} - \omega^\mathrm{ref}\right) \\ + 0 &= + -\dot{P}^\mathrm{meas} + + \dfrac{1}{T_p} + \left(k_{\mathrm{base}}P_e - P^\mathrm{meas}\right) \\ + 0 &= + -\dot{x}_T^\mathrm{I} + + \left(1-s_{\mathrm{frz}}\right) + \text{antiwindup} + \left( + T_e^\mathrm{raw}, K_{\mathrm{ip}}e_T;\, + T_e^{\min}, T_e^{\max,\mathrm{eff}} + \right) +\end{aligned} +``` + +CommonMath defines the [Anti-Windup](../../../../CommonMath.md#anti-windup-indicator) +target and smooth approximation. + +### Algebraic Equations + +```math +\begin{aligned} + 0 &= + -\omega^\mathrm{cmd} + + \omega^\mathrm{sch}\left(P^\mathrm{meas}\right) \\ + 0 &= + -e_P + + k_{\mathrm{base}}P^\mathrm{ref}_0 + - P^\mathrm{meas} \\ + 0 &= + -e_\omega + + \omega_g + - \omega^\mathrm{ref} \\ + 0 &= + -e_T + + \begin{cases} + \dfrac{e_P}{\omega_g} + & s_T\in\{0,2\} \\ + e_\omega + & s_T = 1 + \end{cases} \\ + 0 &= + -T_e^{\max,\mathrm{eff}} + + \begin{cases} + T_e^{\max} + & s_T\in\{0,1\} \\ + \dfrac{k_{\mathrm{base}}P^\mathrm{ref}_0}{\omega_g} + & s_T = 2 + \end{cases} \\ + 0 &= + -T_e^\mathrm{raw} + + K_{\mathrm{pp}}e_T + + x_T^\mathrm{I} \\ + 0 &= + -T_e^\mathrm{cmd} + + \text{clamp} + \left(T_e^\mathrm{raw};\, T_e^{\min}, T_e^{\max,\mathrm{eff}}\right) \\ + 0 &= + -k_{\mathrm{base}}P^\mathrm{ref} + + \omega_g T_e^\mathrm{cmd} +\end{aligned} +``` + +CommonMath defines [clamp](../../../../CommonMath.md#derived-functions). + +## Initialization + +### External Priors + +```math +\begin{aligned} + P^\mathrm{ref}_0 + &\leftarrow \text{active-power reference start} \\ + s_{\mathrm{frz}} + &\leftarrow \text{voltage-dip freeze signal} +\end{aligned} +``` + +### Internal Initialization + +Initialization is performed by evaluating the steady-state residuals in +dependency order. Let subscript $0$ denote initial values and set all internal +derivatives to zero: + +```math +\begin{aligned} + P_0^\mathrm{meas} + &= k_{\mathrm{base}}P^\mathrm{ref}_0 \\ + \omega_0^\mathrm{cmd} + &= \omega^\mathrm{sch}\left(P_0^\mathrm{meas}\right) \\ + \omega_0^\mathrm{ref} + &= \omega_0^\mathrm{cmd} \\ + e_{\omega,0} + &= 0 \\ + e_{P,0} + &= 0 \\ + e_{T,0} + &= + \begin{cases} + \dfrac{e_{P,0}}{\omega_0^\mathrm{ref}} + & s_T\in\{0,2\} \\ + e_{\omega,0} + & s_T = 1 + \end{cases} \\ + T_{e,0}^{\max,\mathrm{eff}} + &= + \begin{cases} + T_e^{\max} + & s_T\in\{0,1\} \\ + \dfrac{k_{\mathrm{base}}P^\mathrm{ref}_0}{\omega_0^\mathrm{ref}} + & s_T = 2 + \end{cases} \\ + T_{e,0}^\mathrm{cmd} + &= \dfrac{k_{\mathrm{base}}P^\mathrm{ref}_0}{\omega_0^\mathrm{ref}} \\ + x_{T,0}^\mathrm{I} + &= T_{e,0}^\mathrm{cmd} - K_{\mathrm{pp}}e_{T,0} \\ + T_{e,0}^\mathrm{raw} + &= K_{\mathrm{pp}}e_{T,0} + x_{T,0}^\mathrm{I} +\end{aligned} +``` + +### External Solved + +```math +\begin{aligned} + \omega_{g,0} + &\leftarrow \omega_0^\mathrm{ref} \\ + P_{e,0} + &\leftarrow P^\mathrm{ref}_0 +\end{aligned} +``` + +Initialization rejects nonpositive solved generator-speed starts, initialized +torque commands outside their limits, and nonzero WTGTRQA antiwindup rates. + +## Monitorable Outputs + +Output | Units | Description | Note +----------------|--------|-------------------------------------|------ +`pref` | [p.u.] | Active-power reference output | $P^\mathrm{ref}$ (system base) +`pmeas` | [p.u.] | Filtered electrical active power | $P^\mathrm{meas}$ (component base) +`wref` | [p.u.] | Filtered speed reference | $\omega^\mathrm{ref}$ +`tecmd` | [p.u.] | Limited torque command | $T_e^\mathrm{cmd}$ (component base) +`et` | [p.u.] | Selected torque-controller error | $e_T$ diff --git a/docs/Figures/PhasorDynamics/Wind/WTGARA/diagram.png b/docs/Figures/PhasorDynamics/Wind/WTGARA/diagram.png new file mode 100644 index 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zdUPZb?<>H65lb$EJdRfS-K$&l9N0`uC#vane+E5hPCz-Jnb2ooi>>x*?*TzjP*v?i zPlPgl>Cc}7f?`95yxQY31V6oFr2GrC9s!|w9XXD21a@HSmRjU`i%i!Bi^TYQlO`-ra|8$O|td=_YJSJT{TBr_f}!Sxek zL+G(E(?>hbu1o?=rz;w1I|>T&MqJ0o+y9R-sc7d!G}SyYYN85+dVeK7icd_S(u5lP zb)qNpPTs@B#6&vAU&wpjyczfzNMMp3f_nq+$>);A*k8mGwZlE&vrz?~3tS$1p@ms| zP5RIw3()tz?(poDW-qX*bP4q1BrK_+mehz0a1Oz7^pZRvFJ^q;#c($q&;5FrD3}t# zOdw2XHSL(n@K3?2sGW}~eJl^y0--761>l7Y76(cji#z1drRpiT{X)!y{lXol1MGdk zvy|5TLqPm=z<^K5eT&Nf91!%RLvS3}b&zT-I6s(l|7S WT4G WT4T +WTGARA WTGPTA +WTGTA +WTGTRQA ``` ```{include} ../../../../../GridKit/Model/PhasorDynamics/Wind/README.md diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/WTGARA/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/WTGARA/README.md new file mode 100644 index 000000000..e0bca6c5b --- /dev/null +++ b/docs/GridKit/Model/PhasorDynamics/Wind/WTGARA/README.md @@ -0,0 +1,6 @@ +# WTGARA + +```{include} ../../../../../../GridKit/Model/PhasorDynamics/Wind/WTGARA/README.md +:start-line: 1 +:relative-images: +``` diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md new file mode 100644 index 000000000..31d28f7b7 --- /dev/null +++ b/docs/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md @@ -0,0 +1,6 @@ +# WTGTA + +```{include} ../../../../../../GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md +:start-line: 1 +:relative-images: +``` diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md new file mode 100644 index 000000000..a39c323c4 --- /dev/null +++ b/docs/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md @@ -0,0 +1,6 @@ +# WTGTRQA + +```{include} ../../../../../../GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md +:start-line: 1 +:relative-images: +``` From b0072e7bd22f7e0e4f30fb8b753a927478102c2c Mon Sep 17 00:00:00 2001 From: lukelowry Date: Fri, 26 Jun 2026 22:59:08 -0500 Subject: [PATCH 3/4] Remove legacy and retain only second generation --- GridKit/Model/PhasorDynamics/Wind/README.md | 3 - .../Model/PhasorDynamics/Wind/WT4E/README.md | 384 ------------------ .../Model/PhasorDynamics/Wind/WT4G/README.md | 298 -------------- .../Model/PhasorDynamics/Wind/WT4T/README.md | 214 ---------- .../PhasorDynamics/Wind/WTGPTA/README.md | 10 +- .../Model/PhasorDynamics/Wind/WTGTA/README.md | 6 +- .../PhasorDynamics/Wind/WTGTRQA/README.md | 6 +- .../PhasorDynamics/Wind/WT4E/diagram.png | Bin 74603 -> 0 bytes .../PhasorDynamics/Wind/WT4G/diagram.png | Bin 71291 -> 0 bytes .../PhasorDynamics/Wind/WT4T/diagram.png | Bin 19906 -> 0 bytes .../Model/PhasorDynamics/Wind/README.md | 3 - .../Model/PhasorDynamics/Wind/WT4E/README.md | 6 - .../Model/PhasorDynamics/Wind/WT4G/README.md | 6 - .../Model/PhasorDynamics/Wind/WT4T/README.md | 6 - 14 files changed, 11 insertions(+), 931 deletions(-) delete mode 100644 GridKit/Model/PhasorDynamics/Wind/WT4E/README.md delete mode 100644 GridKit/Model/PhasorDynamics/Wind/WT4G/README.md delete mode 100644 GridKit/Model/PhasorDynamics/Wind/WT4T/README.md delete mode 100644 docs/Figures/PhasorDynamics/Wind/WT4E/diagram.png delete mode 100644 docs/Figures/PhasorDynamics/Wind/WT4G/diagram.png delete mode 100644 docs/Figures/PhasorDynamics/Wind/WT4T/diagram.png delete mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md delete mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md delete mode 100644 docs/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md diff --git a/GridKit/Model/PhasorDynamics/Wind/README.md b/GridKit/Model/PhasorDynamics/Wind/README.md index 43999554b..a5f5e9cdb 100644 --- a/GridKit/Model/PhasorDynamics/Wind/README.md +++ b/GridKit/Model/PhasorDynamics/Wind/README.md @@ -9,9 +9,6 @@ phasor dynamics model. The GridKit wind documentation includes: -- Type 4 Wind Electrical Control Model WT4E (See [WT4E](WT4E/README.md)) -- Type 4 Wind Generator/Converter Model WT4G (See [WT4G](WT4G/README.md)) -- Type 4 Wind Turbine Model WT4T (See [WT4T](WT4T/README.md)) - Wind Turbine Generator Aerodynamic Model WTGARA (See [WTGARA](WTGARA/README.md)) - Wind Turbine Generator Pitch-Control Model WTGPTA (See [WTGPTA](WTGPTA/README.md)) - Wind Turbine Generator Drive-Train Model WTGTA (See [WTGTA](WTGTA/README.md)) diff --git a/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md b/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md deleted file mode 100644 index fdef6c143..000000000 --- a/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md +++ /dev/null @@ -1,384 +0,0 @@ -# **Type 4 Wind Electrical Control Model (WT4E)** - -WT4E is a WECC electrical-control model for full-converter wind-turbine -generators. In GridKit it is represented as a signal-control model that -computes active- and reactive-current commands for a downstream converter -interface model. - -## Notes - -- When used with WT4G, connect WT4E `iqcmd` and `ipcmd` to the downstream converter current-command ports. -- The separate-model `varflg = -1` mode is not included in the equations below. - -## Block Diagram - -Standard WT4E electrical-control model. - -![](../../../../../docs/Figures/PhasorDynamics/Wind/WT4E/diagram.png) - -Figure 1: WT4E block diagram. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) - -## Model Parameters - -Symbol | Units | JSON | Description | Typical Value | Note -------------------------------------|----------|------------|---------------------------------------------------------|---------------|------ -$S^\mathrm{base}$ | [MVA] | `mva` | WT4E component power base | 100.0 | Required positive value -$s_{\mathrm{var}}$ | [binary] | `varflg` | Reactive-control mode flag | - | 1 = WindCONTROL emulation, 0 = local reactive-power or power-factor control -$K_{\mathrm{qi}}$ | [p.u./s] | `Kqi` | Reactive-power control integral gain | - | Block name: `Kqi` -$K_{\mathrm{vi}}$ | [p.u./s] | `Kvi` | Voltage-control integral gain | - | Block name: `Kvi` -$V^{\max}$ | [p.u.] | `Vmax` | Maximum regulated-voltage reference | - | Block name: `Vmax` -$V^{\min}$ | [p.u.] | `Vmin` | Minimum regulated-voltage reference | - | Block name: `Vmin` -$Q^{\max}$ | [p.u.] | `Qmax` | Maximum reactive-power command | - | Block name: `Qmax` -$Q^{\min}$ | [p.u.] | `Qmin` | Minimum reactive-power command | - | Block name: `Qmin` -$T_R$ | [sec] | `Tr` | WindCONTROL voltage-measurement lag time constant | - | State 4 -$T_C$ | [sec] | `Tc` | WindCONTROL output lag time constant | - | State 6 -$K_{\mathrm{pv}}$ | [p.u.] | `Kpv` | WindCONTROL proportional gain | - | State 3 path -$K_{\mathrm{iv}}$ | [p.u./s] | `Kiv` | WindCONTROL integral gain | - | State 5 path -$s_{\mathrm{pfa}}$ | [binary] | `pfaflg` | Power-factor angle control flag | - | 1 = power-factor angle control, 0 = reactive-power control -$F_N$ | [-] | `Fn` | Fraction of online wind-turbine generators | - | Block name: `Fn` -$T_V$ | [sec] | `Tv` | WindCONTROL proportional-path lag time constant | - | State 3 -$T_{\mathrm{pwr}}$ | [sec] | `Tpwr` | Active-power measurement filter time constant | - | State 7 -$I_p^\mathrm{hl}$ | [p.u.] | `Iphl` | Active-current hard limit | - | Block name: `Iphl` -$I_q^\mathrm{hl}$ | [p.u.] | `Iqhl` | Reactive-current hard limit | - | Block name: `Iqhl` -$s_{PQ}$ | [binary] | `Pqflag` | P/Q priority flag for converter current limit | - | 0 = Q priority, 1 = P priority -$I_{TD}^{\max}$ | [p.u.] | `ImaxTD` | Temperature-dependent maximum converter current | - | Block name: `ImaxTD` -$V_{iq}^{\lim}$ | [p.u.] | `Viqlim` | Voltage-dependent reactive-current limit | - | Block name: `Viqlim` - -### Parameter Validation - -Invalid WT4E parameter sets are rejected by the following checks. Let $\epsilon_T=10^{-3}$. - -```math -\begin{aligned} - T &\leftarrow \max\!\left(T, \epsilon_T\right) - \quad T\in\{T_R,T_C,T_V,T_{\mathrm{pwr}}\} \\ - S^\mathrm{base} - &> 0 \\ - s_{\mathrm{var}}, s_{\mathrm{pfa}}, s_{PQ} - &\in \{0,1\} \\ - F_N - &> 0 \\ - V^{\min} - &\le V^{\max} \\ - Q^{\min} - &\le Q^{\max} \\ - I_p^\mathrm{hl}, I_q^\mathrm{hl}, I_{TD}^{\max}, V_{iq}^{\lim} - &\ge 0 -\end{aligned} -``` - -### Model Derived Parameters - -```math -\begin{aligned} - s_{\mathrm{var}}^\mathrm{off} - &= 1 - s_{\mathrm{var}} \\ - s_{\mathrm{pfa}}^\mathrm{off} - &= 1 - s_{\mathrm{pfa}} \\ - k_{\mathrm{base}} - &= \dfrac{S^\mathrm{sys}}{S^\mathrm{base}} -\end{aligned} -``` - -## Model Variables - -### Internal Variables - -#### Differential - -Symbol | Units | Description | Note -------------------------|--------|-------------------------------------|------ -$V^\mathrm{ref}$ | [p.u.] | Regulated-voltage reference state | State 1 in Fig. 1 -$x_q^\mathrm{cmd}$ | [p.u.] | Reactive-current command state | State 2 in Fig. 1; source label: `Iqcmd`; component base -$x_V^\mathrm{P}$ | [p.u.] | WindCONTROL proportional-path state | State 3 in Fig. 1; source label: `Kpv` -$V^\mathrm{meas}$ | [p.u.] | Filtered WindCONTROL voltage input | State 4 in Fig. 1; source label: `VregMeas` -$x_V^\mathrm{I}$ | [p.u.] | WindCONTROL integral-path state | State 5 in Fig. 1; source label: `Kiv` -$Q^\mathrm{ord}$ | [p.u.] | Filtered reactive-power order | State 6 in Fig. 1; source label: `Qord`; component base -$P^\mathrm{meas}$ | [p.u.] | Filtered electrical active power | State 7 in Fig. 1; source label: `Pmeas`; component base - -#### Algebraic - -Symbol | Units | Description | Note -------------------------------------|----------|-------------------------------------|------ -$Q^\mathrm{pf}$ | [p.u.] | Power-factor-angle reactive-power command candidate | Component base -$Q^\mathrm{sel}$ | [p.u.] | Selected reactive-power command | Component base -$Q^\mathrm{ctrl}$ | [p.u.] | Selected reactive-control output before final reactive-power limit | Component base -$Q^\mathrm{cmd}$ | [p.u.] | Limited reactive-power command | Component base -$e_Q$ | [p.u.] | Reactive-power control error | -$e_V$ | [p.u.] | Voltage-control error | -$I_q^\mathrm{cap}$ | [p.u.] | Reactive-current hard-limit cap | Component base -$I_p^\mathrm{cap}$ | [p.u.] | Active-current hard-limit cap | Component base -$I_q^\mathrm{circ}$ | [p.u.] | Reactive-current limit from converter current circle | -$I_p^\mathrm{circ}$ | [p.u.] | Active-current limit from converter current circle | -$I_q^{\max}$ | [p.u.] | Final reactive-current upper limit | Component base -$I_q^{\min}$ | [p.u.] | Final reactive-current lower limit | Component base -$I_p^{\max}$ | [p.u.] | Final active-current upper limit | Component base -$I_q^\mathrm{cmd}$ | [p.u.] | Reactive-current command output | System base -$I_p^\mathrm{cmd}$ | [p.u.] | Active-current command output | System base - -### External Variables - -#### Differential -None. - -#### Algebraic - -Symbol | Units | Type | Description | Note --------------------------------------|--------|---------|-----------------------------------|------ -$V_C$ | [p.u.] | Known | WindCONTROL voltage input | Source label: `Vc` -$P_e$ | [p.u.] | Known | Electrical active-power feedback | Signal port `pelec`; system base -$Q_e$ | [p.u.] | Known | Electrical reactive-power feedback | Signal port `qelec`; system base -$V_T$ | [p.u.] | Known | Terminal voltage magnitude | Signal port `vterm` -$P^\mathrm{ord}$ | [p.u.] | Known | Active-power order from turbine/governor model | Signal port `pord`; system base -$V_{\mathrm{RFQ}}$ | [p.u.] | Unknown | Voltage/reactive-control reference | Optional signal port `vrfq` -$Q^\mathrm{ref}$ | [p.u.] | Unknown | Reactive-power reference | Optional signal port `qref`; system base -$\phi^\mathrm{ref}$ | [rad] | Unknown | Power-factor angle reference | Optional signal port `pfaref` - -## Model Equations - -### Differential Equations - -```math -\begin{aligned} - 0 &= - -\dot{V}^\mathrm{ref} - + \text{antiwindup} - \left(V^\mathrm{ref}, K_{\mathrm{qi}}e_Q;\, V^{\min}, V^{\max}\right) \\ - 0 &= - -\dot{x}_q^\mathrm{cmd} - + \text{antiwindup} - \left(x_q^\mathrm{cmd}, K_{\mathrm{vi}}e_V;\, I_q^{\min}, I_q^{\max}\right) \\ - 0 &= - -\dot{x}_V^\mathrm{P} - + \dfrac{1}{T_V} - \left( - \dfrac{K_{\mathrm{pv}}}{F_N}\left(V_{\mathrm{RFQ}} - V^\mathrm{meas}\right) - - x_V^\mathrm{P} - \right) \\ - 0 &= - -\dot{V}^\mathrm{meas} - + \dfrac{1}{T_R} - \left(V_C - V^\mathrm{meas}\right) \\ - 0 &= - -\dot{x}_V^\mathrm{I} - + \dfrac{K_{\mathrm{iv}}}{F_N} - \left(V_{\mathrm{RFQ}} - V^\mathrm{meas}\right) \\ - 0 &= - -\dot{Q}^\mathrm{ord} - + \dfrac{1}{T_C} - \left( - \text{clamp} - \left(x_V^\mathrm{P} + x_V^\mathrm{I};\, Q^{\min}, Q^{\max}\right) - - Q^\mathrm{ord} - \right) \\ - 0 &= - -\dot{P}^\mathrm{meas} - + \dfrac{1}{T_{\mathrm{pwr}}} - \left(k_{\mathrm{base}}P_e - P^\mathrm{meas}\right) -\end{aligned} -``` - -CommonMath defines the [Anti-Windup](../../../../CommonMath.md#anti-windup-indicator) -target and smooth approximation, and -[clamp](../../../../CommonMath.md#derived-functions). - -### Algebraic Equations - -```math -\begin{aligned} - 0 &= - -Q^\mathrm{pf} - + P^\mathrm{meas}\tan\!\left(\phi^\mathrm{ref}\right) \\ - 0 &= - -Q^\mathrm{sel} - + s_{\mathrm{pfa}}Q^\mathrm{pf} - + s_{\mathrm{pfa}}^\mathrm{off}k_{\mathrm{base}}Q^\mathrm{ref} \\ - 0 &= - -Q^\mathrm{ctrl} - + s_{\mathrm{var}}Q^\mathrm{ord} - + s_{\mathrm{var}}^\mathrm{off}Q^\mathrm{sel} \\ - 0 &= - -Q^\mathrm{cmd} - + \text{clamp} - \left(Q^\mathrm{ctrl};\, Q^{\min}, Q^{\max}\right) \\ - 0 &= - -e_Q - + Q^\mathrm{cmd} - - k_{\mathrm{base}}Q_e \\ - 0 &= - -e_V - + V^\mathrm{ref} - - V_T \\ - 0 &= - -I_q^\mathrm{cap} - + \text{min} - \left(\text{min}\left(I_q^\mathrm{hl}, V_{iq}^{\lim}\right), I_{TD}^{\max}\right) \\ - 0 &= - -I_p^\mathrm{cap} - + \text{min} - \left(I_p^\mathrm{hl}, I_{TD}^{\max}\right) \\ - 0 &= - -\left(I_q^\mathrm{circ}\right)^2 - + \left(I_{TD}^{\max}\right)^2 - - s_{PQ}\left(k_{\mathrm{base}}I_p^\mathrm{cmd}\right)^2 \\ - 0 &= - -\left(I_p^\mathrm{circ}\right)^2 - + \left(I_{TD}^{\max}\right)^2 - - \left(1-s_{PQ}\right)\left(x_q^\mathrm{cmd}\right)^2 \\ - 0 &= - -I_q^{\max} - + \left(1-s_{PQ}\right)I_q^\mathrm{cap} - + s_{PQ}\text{min} - \left(I_q^\mathrm{cap}, I_q^\mathrm{circ}\right) \\ - 0 &= - -I_q^{\min} - - I_q^{\max} \\ - 0 &= - -I_p^{\max} - + s_{PQ}I_p^\mathrm{cap} - + \left(1-s_{PQ}\right)\text{min} - \left(I_p^\mathrm{cap}, I_p^\mathrm{circ}\right) \\ - 0 &= - -k_{\mathrm{base}}I_q^\mathrm{cmd} - + x_q^\mathrm{cmd} \\ - 0 &= - -k_{\mathrm{base}}I_p^\mathrm{cmd} - + \text{clamp} - \left( - \dfrac{k_{\mathrm{base}}P^\mathrm{ord}}{V_T};\, - 0,\, - I_p^{\max} - \right) -\end{aligned} -``` - -CommonMath defines [clamp and min](../../../../CommonMath.md#derived-functions). - -## Initialization - -### External Priors - -```math -\begin{aligned} - V_{C,0} - &\leftarrow \text{WindCONTROL voltage input} \\ - P_{e,0}, Q_{e,0} - &\leftarrow \text{electrical-power feedback on system base} \\ - V_{T,0} - &\leftarrow \text{terminal voltage magnitude} \\ - P_0^\mathrm{ord} - &\leftarrow \text{active-power order start} -\end{aligned} -``` - -### Internal Initialization - -Initialization is performed by evaluating the steady-state residuals in -dependency order. Let subscript $0$ denote initial values and set all internal -derivatives to zero: - -```math -\begin{aligned} - P_0^\mathrm{meas} - &= k_{\mathrm{base}}P_{e,0} \\ - V_0^\mathrm{meas} - &= V_{C,0} \\ - Q_0^\mathrm{cmd} - &= - \text{clamp} - \left(k_{\mathrm{base}}Q_{e,0};\, Q^{\min}, Q^{\max}\right) \\ - x_{V,0}^\mathrm{P} - &= 0 \\ - x_{V,0}^\mathrm{I} - &= Q_0^\mathrm{cmd} \\ - Q_0^\mathrm{ord} - &= Q_0^\mathrm{cmd} \\ - Q_0^\mathrm{pf} - &= Q_0^\mathrm{cmd} \\ - Q_0^\mathrm{sel} - &= Q_0^\mathrm{cmd} \\ - Q_0^\mathrm{ctrl} - &= Q_0^\mathrm{cmd} \\ - e_{Q,0} - &= Q_0^\mathrm{cmd} - k_{\mathrm{base}}Q_{e,0} \\ - V_0^\mathrm{ref} - &= V_{T,0} \\ - e_{V,0} - &= 0 \\ - x_{q,0}^\mathrm{cmd} - &= \dfrac{Q_0^\mathrm{cmd}}{V_{T,0}} \\ - I_{q,0}^\mathrm{cap} - &= - \text{min} - \left(\text{min}\left(I_q^\mathrm{hl}, V_{iq}^{\lim}\right), I_{TD}^{\max}\right) \\ - I_{p,0}^\mathrm{cap} - &= - \text{min} - \left(I_p^\mathrm{hl}, I_{TD}^{\max}\right) \\ - I_{p,0}^\mathrm{circ} - &= - \sqrt{ - \left(I_{TD}^{\max}\right)^2 - - \left(1-s_{PQ}\right)\left(x_{q,0}^\mathrm{cmd}\right)^2 - } \\ - I_{p,0}^{\max} - &= - s_{PQ}I_{p,0}^\mathrm{cap} - + \left(1-s_{PQ}\right)\text{min} - \left(I_{p,0}^\mathrm{cap}, I_{p,0}^\mathrm{circ}\right) \\ - I_{p,0}^\mathrm{cmd} - &= - \dfrac{1}{k_{\mathrm{base}}} - \text{clamp} - \left( - \dfrac{k_{\mathrm{base}}P_0^\mathrm{ord}}{V_{T,0}};\, - 0,\, - I_{p,0}^{\max} - \right) \\ - I_{q,0}^\mathrm{circ} - &= - \sqrt{ - \left(I_{TD}^{\max}\right)^2 - - s_{PQ}\left(k_{\mathrm{base}}I_{p,0}^\mathrm{cmd}\right)^2 - } \\ - I_{q,0}^{\max} - &= - \left(1-s_{PQ}\right)I_{q,0}^\mathrm{cap} - + s_{PQ}\text{min} - \left(I_{q,0}^\mathrm{cap}, I_{q,0}^\mathrm{circ}\right) \\ - I_{q,0}^{\min} - &= -I_{q,0}^{\max} \\ - I_{q,0}^\mathrm{cmd} - &= \dfrac{x_{q,0}^\mathrm{cmd}}{k_{\mathrm{base}}} -\end{aligned} -``` - -### External Solved - -```math -\begin{aligned} - V_{\mathrm{RFQ},0} - &\leftarrow V_0^\mathrm{meas} \\ - Q_0^\mathrm{ref} - &\leftarrow \dfrac{Q_0^\mathrm{cmd}}{k_{\mathrm{base}}} \\ - \phi_0^\mathrm{ref} - &\leftarrow - \begin{cases} - \tan^{-1}\!\left(Q_0^\mathrm{cmd}/P_0^\mathrm{meas}\right) & P_0^\mathrm{meas} \ne 0 \\ - 0 & P_0^\mathrm{meas} = 0 - \end{cases} -\end{aligned} -``` - -Initialization rejects nonpositive terminal voltage, negative current-circle -radicands, and nonzero WT4E antiwindup rates. - -## Monitorable Outputs - -Output | Units | Description | Note -----------------|--------|-------------------------------------|------ -`iqcmd` | [p.u.] | Reactive-current command output | $I_q^\mathrm{cmd}$ (system base) -`ipcmd` | [p.u.] | Active-current command output | $I_p^\mathrm{cmd}$ (system base) -`vmeas` | [p.u.] | Filtered WindCONTROL voltage input | $V^\mathrm{meas}$ -`pmeas` | [p.u.] | Filtered electrical active power | $P^\mathrm{meas}$ (component base) -`qord` | [p.u.] | Filtered reactive-power order | $Q^\mathrm{ord}$ (component base) diff --git a/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md b/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md deleted file mode 100644 index fb042bbe0..000000000 --- a/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md +++ /dev/null @@ -1,298 +0,0 @@ -# **Type 4 Wind Generator/Converter Model (WT4G)** - -WT4G is a first-generation WECC type 4 wind generator/converter model for -full-converter wind plants. In GridKit it is represented as a controlled current -source at the network interface. - -## Notes - -- Internal current states and limiter quantities are on component base. -- Signal ports, monitor outputs, branch currents, and branch powers are on system base. -- LVACM uses $V_T$; LVPL uses $V^\mathrm{meas}$. -- HVRCM is represented by algebraic current $I_q^\mathrm{extra}$. -- PowerWorld fields `Iolim` and `Khv` are not parameters of this GridKit implementation. - -## Block Diagram - -Standard WT4G converter-interface model. - -![](../../../../../docs/Figures/PhasorDynamics/Wind/WT4G/diagram.png) - -Figure 1: Type 4 Wind Generator/Converter WT4G model. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) - -## Model Parameters - -Symbol | Units | JSON | Description | Typical Value | Note ----------------------------------|----------|-----------|-------------------------------------------------------|---------------|------ -$P_0$ | [p.u.] | `P0` | Initial active power injection | 1.0 | System base; required initialization source -$Q_0$ | [p.u.] | `Q0` | Initial reactive power injection | 0.0 | System base; required initialization source -$S^\mathrm{base}$ | [MVA] | `mva` | WT4G component power base | 100.0 | -$T_d$ | [sec] | `Td` | Current-control lag time constant | 0.02 | States 1 and 2 in Fig. 1; block name: `Td` -$T_{\mathrm{LVPL}}$ | [sec] | `T_LVPL` | LVPL voltage sensor time constant | 0.02 | State 3 in Fig. 1; block name: `T_LVPL` -$R_p^{\max}$ | [p.u./s] | `rrpwr` | Active-current magnitude recovery rate limit | 999.0 | Block name: `rrpwr` -$s_L$ | [binary] | `LVPLSW` | LVPL switch | 1 | Block name: `LPVLSW` -$I_{L1}$ | [p.u.] | `LVPL1` | LVPL upper-current ceiling | 1.1 | Block name: `Lvpl1` -$V_{L0}$ | [p.u.] | `zerox` | LVPL zero-crossing voltage | 0.4 | Block name: `zerox` -$V_{L1}$ | [p.u.] | `brkpt` | LVPL upper breakpoint voltage | 0.9 | Block name: `brkpt` -$V_{A0}$ | [p.u.] | `LVPnt0` | LVACM lower breakpoint voltage | 0.4 | Block name: `Lvpnt0` -$V_{A1}$ | [p.u.] | `LVPnt1` | LVACM upper breakpoint voltage | 0.9 | Block name: `Lvpnt1` -$V_{\mathrm{hv}}^{\max}$ | [p.u.] | `VLim` | Terminal-voltage ceiling for HV reactive management | 1.2 | Block name: `VLim` - -### Parameter Validation - -Invalid WT4G parameter sets are rejected by the following checks. Let $\epsilon_T=10^{-3}$. - -```math -\begin{aligned} - T &\leftarrow \max\!\left(T, \epsilon_T\right) - \quad T\in\{T_d,T_{\mathrm{LVPL}}\} \\ - S^\mathrm{base} - &> 0 \\ - R_p^{\max} - &> 0 \\ - s_L - &\in \{0,1\} \\ - I_{L1} - &\ge 0 \\ - 0 - &\le V_{L0} < V_{L1} \\ - 0 - &\le V_{A0} < V_{A1} \\ - V_{\mathrm{hv}}^{\max} - &> 0 -\end{aligned} -``` - -### Model Derived Parameters - -```math -\begin{aligned} - s_L^\mathrm{off} - &= 1 - s_L \\ - k_{\mathrm{base}} - &= \dfrac{S^\mathrm{sys}}{S^\mathrm{base}} \\ - M_p - &= 100 R_p^{\max} -\end{aligned} -``` - -$M_p$ is a finite surrogate for inactive active-current rate limits, -not a physical WT4G parameter. - -## Model Variables - -### Internal Variables - -#### Differential - -Symbol | Units | Description | Note -----------------------|--------|---------------------------|------ -$E_q$ | [p.u.] | Reactive-current lag state | State 1 in Fig. 1 before the `-1` block; component base -$I_p$ | [p.u.] | Active-current state | State 2 in Fig. 1; component base -$V^\mathrm{meas}$ | [p.u.] | Filtered terminal voltage | State 3 in Fig. 1 - -#### Algebraic - -Symbol | Units | Description | Note ----------------------------|----------|-------------------------------------------------------------|------ -$V_T$ | [p.u.] | Terminal voltage magnitude | -$I_{\mathrm{r}}$ | [p.u.] | Branch-current real component | System base -$I_{\mathrm{i}}$ | [p.u.] | Branch-current imaginary component | System base -$I_q^\mathrm{extra}$ | [p.u.] | Extra inductive current from high-voltage reactive current management | Component base -$I_L$ | [p.u.] | LVPL upper-limit current curve | Component base; function of $V^\mathrm{meas}$ -$A^\mathrm{LVACM}$ | [p.u.] | Low-voltage active-current management gain | Function of $V_T$ -$\ell_p$ | [p.u./s] | Smooth active-current lower rate bound | Component base; equivalent to diagram `Rdown` -$u_p$ | [p.u./s] | Smooth active-current upper rate bound | Component base; effective `Rup` -$P^\mathrm{br}$ | [p.u.] | Branch active power | System base -$Q^\mathrm{br}$ | [p.u.] | Branch reactive power | System base - -### External Variables - -#### Differential -None. - -#### Algebraic - -Symbol | Units | Type | Description | Note ---------------------------------|--------|---------|------------------------------------------------------------------|------ -$V_{\mathrm{r}}$ | [p.u.] | Known | Terminal voltage, real component | Bus input -$V_{\mathrm{i}}$ | [p.u.] | Known | Terminal voltage, imaginary component | Bus input -$I_p^\mathrm{cmd}$ | [p.u.] | Unknown | Active-current command in the terminal-voltage reference frame | Optional signal port `ipcmd`; system base -$E_q^\mathrm{cmd}$ | [p.u.] | Unknown | Reactive-current command before the diagram `-1` block | Optional signal port `eqcmd`; system base - -WT4G initializes the current-command ports from the required `P0`/`Q0` -power-flow injection. If no controller is connected, the resolved initialization -commands are held constant during residual evaluation. - -## Model Equations - -### Differential Equations - -The state equations use CommonMath helper notation. - -```math -\begin{aligned} - 0 &= -\dot E_q - + \dfrac{1}{T_d}\left(k_{\mathrm{base}}E_q^\mathrm{cmd} - E_q\right) \\ - 0 &= -\dot I_p - + \ell_p - + \dfrac{1}{T_d} - \rho\left(k_{\mathrm{base}}I_p^\mathrm{cmd} - I_p - T_d\ell_p\right) - - \dfrac{1}{T_d} - \rho\left(k_{\mathrm{base}}I_p^\mathrm{cmd} - I_p - T_d u_p\right) \\ - 0 &= -\dot V^\mathrm{meas} - + \dfrac{1}{T_{\mathrm{LVPL}}}\left(V_T - V^\mathrm{meas}\right) -\end{aligned} -``` - -Here $\rho$ is GridKit's [ramp](../../../../CommonMath.md#primitives). - -### Algebraic Equations - -```math -\begin{aligned} - 0 &= -V_T^2 + V_{\mathrm{r}}^2 + V_{\mathrm{i}}^2 \\ - 0 &= -V_T I_{\mathrm{r}} - + \dfrac{1}{k_{\mathrm{base}}} - \left[ - V_{\mathrm{i}}\left(E_q - I_q^\mathrm{extra}\right) - + V_{\mathrm{r}}I_p A^\mathrm{LVACM} - \right] \\ - 0 &= -V_T I_{\mathrm{i}} - + \dfrac{1}{k_{\mathrm{base}}} - \left[ - -V_{\mathrm{r}}\left(E_q - I_q^\mathrm{extra}\right) - + V_{\mathrm{i}}I_p A^\mathrm{LVACM} - \right] \\ - 0 &= -I_q^\mathrm{extra} - + \rho(V_T - V_{\mathrm{hv}}^{\max}) \\ - 0 &= -I_L - + \text{linseg}(V^\mathrm{meas};\ V_{L0},\ V_{L1},\ I_{L1}) \\ - 0 &= -A^\mathrm{LVACM} - + \text{linseg}(V_T;\ V_{A0},\ V_{A1},\ 1) \\ - 0 &= -\ell_p - - R_p^{\max} - - \left(M_p - R_p^{\max}\right)\sigma(I_p) \\ - 0 &= -u_p - + M_p\left(1-\sigma(I_p)\right) - + R_p^{\max}\sigma(I_p) - \left(s_L^\mathrm{off} + s_L\sigma(I_L - I_p)\right) \\ - 0 &= -P^\mathrm{br} - + V_{\mathrm{r}} I_{\mathrm{r}} + V_{\mathrm{i}} I_{\mathrm{i}} \\ - 0 &= -Q^\mathrm{br} - + V_{\mathrm{i}} I_{\mathrm{r}} - V_{\mathrm{r}} I_{\mathrm{i}} -\end{aligned} -``` - -Here $\text{linseg}$ is GridKit's -[linear segment](../../../../CommonMath.md#derived-functions), $\rho$ is the -[ramp](../../../../CommonMath.md#primitives), and $\sigma$ is the -[step function](../../../../CommonMath.md#primitives). - -## Network Interface - -The bus receives the WT4G branch-current variables directly: - -```math -\begin{aligned} - I_{\mathrm{r}}^\mathrm{inj} &:= I_{\mathrm{r}} \\ - I_{\mathrm{i}}^\mathrm{inj} &:= I_{\mathrm{i}} -\end{aligned} -``` - -## Initialization - -### External Priors - -```math -\begin{aligned} - V_{\mathrm{r},0}, V_{\mathrm{i},0} - &\leftarrow \text{terminal-bus voltage} \\ - P_0, Q_0 - &\leftarrow \text{power-flow injection on system base} -\end{aligned} -``` - -### Internal Initialization - -Initialization is performed by evaluating the steady-state residuals in -dependency order. Let subscript $0$ denote initial values and set all internal -derivatives to zero: - -```math -\begin{aligned} - V_{T,0} - &= \sqrt{V_{\mathrm{r},0}^2 + V_{\mathrm{i},0}^2} \\ - V_0^\mathrm{meas} - &= V_{T,0} \\ - A_0^\mathrm{LVACM} - &= \text{linseg}\left(V_{T,0};\ V_{A0},\ V_{A1},\ 1\right) \\ - I_{p,0}^\mathrm{cmd} - &= - \begin{cases} - \dfrac{P_0}{V_{T,0}A_0^\mathrm{LVACM}} & P_0 \ne 0 \\ - 0 & P_0 = 0 - \end{cases} \\ - E_{q,0}^\mathrm{cmd} - &= \dfrac{Q_0}{V_{T,0}} \\ - I_{p,0} - &= k_{\mathrm{base}}I_{p,0}^\mathrm{cmd} \\ - E_{q,0} - &= k_{\mathrm{base}}E_{q,0}^\mathrm{cmd} \\ - I_{q,0}^\mathrm{extra} - &= 0 \\ - I_{L,0} - &= \text{linseg}\left(V_0^\mathrm{meas};\ V_{L0},\ V_{L1},\ I_{L1}\right) \\ - \ell_{p,0} - &= -R_p^{\max} - - \left(M_p - R_p^{\max}\right)\sigma(I_{p,0}) \\ - u_{p,0} - &= M_p\left(1-\sigma(I_{p,0})\right) - + R_p^{\max}\sigma(I_{p,0}) - \left(s_L^\mathrm{off} + s_L\sigma(I_{L,0} - I_{p,0})\right) \\ - I_{\mathrm{r},0} - &= \dfrac{1}{k_{\mathrm{base}}V_{T,0}} - \left[ - V_{\mathrm{i},0}\left(E_{q,0} - I_{q,0}^\mathrm{extra}\right) - + V_{\mathrm{r},0}I_{p,0}A_0^\mathrm{LVACM} - \right] \\ - I_{\mathrm{i},0} - &= \dfrac{1}{k_{\mathrm{base}}V_{T,0}} - \left[ - -V_{\mathrm{r},0}\left(E_{q,0} - I_{q,0}^\mathrm{extra}\right) - + V_{\mathrm{i},0}I_{p,0}A_0^\mathrm{LVACM} - \right] \\ - P_0^\mathrm{br} - &= V_{\mathrm{r},0}I_{\mathrm{r},0} + V_{\mathrm{i},0}I_{\mathrm{i},0} \\ - Q_0^\mathrm{br} - &= V_{\mathrm{i},0}I_{\mathrm{r},0} - V_{\mathrm{r},0}I_{\mathrm{i},0} -\end{aligned} -``` - -Here $\text{linseg}$ is GridKit's -[linear segment](../../../../CommonMath.md#derived-functions), and $\sigma$ is -the [step function](../../../../CommonMath.md#primitives). - -### External Solved - -```math -\begin{aligned} - I_p^\mathrm{cmd} - &\leftarrow I_{p,0}^\mathrm{cmd} \\ - E_q^\mathrm{cmd} - &\leftarrow E_{q,0}^\mathrm{cmd} -\end{aligned} -``` - -WT4G writes the resolved current commands to attached `ipcmd` and `eqcmd` -ports. If no controller is attached, those values are used as constant command -inputs. - -## Monitorable Outputs - -Output | Units | Description | Note --------|--------|-----------------------------|------ -`ir` | [p.u.] | Real current injection | System base; exported through `ibranchr` when assigned -`ii` | [p.u.] | Imaginary current injection | System base; exported through `ibranchi` when assigned -`p` | [p.u.] | Active-power output | System base; exported through `pbranch` when assigned -`q` | [p.u.] | Reactive-power output | System base; exported through `qbranch` when assigned diff --git a/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md b/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md deleted file mode 100644 index f8db98cfd..000000000 --- a/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md +++ /dev/null @@ -1,214 +0,0 @@ -# **Type 4 Wind Turbine Model (WT4T)** - -WT4T is a WECC simplified wind-turbine active-power control model for -full-converter wind-turbine generators. In GridKit it is represented as a -signal-control model that computes an active-power order for a downstream -electrical-control model. - -## Notes - -- When used with WT4E, connect WT4T `pord` to WT4E `pord`. -- Signal ports and active-power order are on system base. -- Internal measured, PI, and washout quantities are on component base. - -## Block Diagram - -Standard WT4T simplified wind-turbine model. - -![](../../../../../docs/Figures/PhasorDynamics/Wind/WT4T/diagram.png) - -Figure 1: WT4T block diagram. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) - -## Model Parameters - -Symbol | Units | JSON | Description | Typical Value | Note -------------------------------------|----------|------------|---------------------------------------------------------|---------------|------ -$P^\mathrm{rate}$ | [MW] | `MWCap` | WT4T turbine rating | - | Required positive value -$T_{\mathrm{pw}}$ | [sec] | `Tpw` | Electrical-power measurement filter time constant | - | State 1 in Fig. 1 -$K_{\mathrm{pp}}$ | [p.u.] | `Kpp` | Pitch-control proportional gain | - | Block name: `Kpp` -$K_{\mathrm{ip}}$ | [p.u./s] | `Kip` | Pitch-control integral gain | - | State 2 path -$T_f$ | [sec] | `Tf` | Washout time constant | - | State 3 in Fig. 1 -$K_f$ | [p.u.] | `Kf` | Washout gain | - | Block name: `Kf` -$\Delta P^{\max}$ | [p.u.] | `dPmx` | Maximum PI output limit | - | Block name: `dPmax` -$\Delta P^{\min}$ | [p.u.] | `dPmn` | Minimum PI output limit | - | Block name: `dPmin` - -### Parameter Validation - -Invalid WT4T parameter sets are rejected by the following checks. Let $\epsilon_T=10^{-3}$. - -```math -\begin{aligned} - T &\leftarrow \max\!\left(T, \epsilon_T\right) - \quad T\in\{T_{\mathrm{pw}},T_f\} \\ - P^\mathrm{rate} - &> 0 \\ - \Delta P^{\min} - &\le 0 \le \Delta P^{\max} -\end{aligned} -``` - -### Model Derived Parameters - -```math -\begin{aligned} - k_{\mathrm{base}} - &= \dfrac{S^\mathrm{sys}}{P^\mathrm{rate}} -\end{aligned} -``` - -## Model Variables - -### Internal Variables - -#### Differential - -Symbol | Units | Description | Note -------------------------|--------|-------------------------------------|------ -$P^\mathrm{meas}$ | [p.u.] | Filtered electrical active power | State 1 in Fig. 1; component base -$x_P^\mathrm{I}$ | [p.u.] | Pitch-control integral state | State 2 path; component base -$x_f$ | [p.u.] | Washout lag state | State 3 in Fig. 1; component base - -#### Algebraic - -Symbol | Units | Description | Note -------------------------------------|----------|-------------------------------------|------ -$P^\mathrm{iin}$ | [p.u.] | Pitch-control input error | Component base -$P^\mathrm{iou}$ | [p.u.] | Limited pitch-control output | Component base -$P_f$ | [p.u.] | Washout feedback signal | Component base -$P^\mathrm{ord}$ | [p.u.] | Active-power order output | System base - -### External Variables - -#### Differential -None. - -#### Algebraic - -Symbol | Units | Type | Description | Note --------------------------------------|--------|---------|-----------------------------------|------ -$P_e$ | [p.u.] | Known | Electrical active-power feedback | Signal port `pelec`; system base -$P^\mathrm{aux}$ | [p.u.] | Known | Auxiliary power input | Optional signal port `paux`; system base; defaults to zero -$P^\mathrm{ref}$ | [p.u.] | Unknown | Active-power reference | Optional signal port `pref`; system base - -## Model Equations - -### Differential Equations - -```math -\begin{aligned} - 0 &= - -\dot{P}^\mathrm{meas} - + \dfrac{1}{T_{\mathrm{pw}}} - \left(k_{\mathrm{base}}P_e - P^\mathrm{meas}\right) \\ - 0 &= - -\dot{x}_P^\mathrm{I} - + \text{antiwindup} - \left( - K_{\mathrm{pp}}P^\mathrm{iin} + x_P^\mathrm{I},\, - K_{\mathrm{ip}}P^\mathrm{iin};\, - \Delta P^{\min}, \Delta P^{\max} - \right) \\ - 0 &= - -\dot{x}_f - + \dfrac{1}{T_f} - \left(k_{\mathrm{base}}P^\mathrm{ord} - x_f\right) -\end{aligned} -``` - -CommonMath defines the [Anti-Windup](../../../../CommonMath.md#anti-windup-indicator) -target and smooth approximation. - -### Algebraic Equations - -```math -\begin{aligned} - 0 &= - -P_f - + \dfrac{K_f}{T_f} - \left(k_{\mathrm{base}}P^\mathrm{ord} - x_f\right) \\ - 0 &= - -P^\mathrm{iin} - + k_{\mathrm{base}}P^\mathrm{ref} - + k_{\mathrm{base}}P^\mathrm{aux} - - P^\mathrm{meas} - - P_f \\ - 0 &= - -P^\mathrm{iou} - + \text{clamp} - \left( - K_{\mathrm{pp}}P^\mathrm{iin} + x_P^\mathrm{I};\, - \Delta P^{\min},\, - \Delta P^{\max} - \right) \\ - 0 &= - -k_{\mathrm{base}}P^\mathrm{ord} - + k_{\mathrm{base}}P^\mathrm{ref} - + P^\mathrm{iou} - - P_f -\end{aligned} -``` - -CommonMath defines [clamp](../../../../CommonMath.md#derived-functions). - -## Initialization - -### External Priors - -```math -\begin{aligned} - P_{e,0} - &\leftarrow \text{electrical active-power feedback on system base} \\ - P_0^\mathrm{aux} - &\leftarrow \text{auxiliary power input on system base} \\ - P_0^\mathrm{ord} - &\leftarrow \text{active-power order start on system base} -\end{aligned} -``` - -### Internal Initialization - -Initialization is performed by evaluating the steady-state residuals in -dependency order. Let subscript $0$ denote initial values and set all internal -derivatives to zero: - -```math -\begin{aligned} - P_0^\mathrm{meas} - &= k_{\mathrm{base}}P_{e,0} \\ - x_{f,0} - &= k_{\mathrm{base}}P_0^\mathrm{ord} \\ - P_{f,0} - &= 0 \\ - P_0^\mathrm{iin} - &= 0 \\ - P_0^\mathrm{iou} - &= - k_{\mathrm{base}}P_0^\mathrm{ord} - - k_{\mathrm{base}}P_{e,0} - + k_{\mathrm{base}}P_0^\mathrm{aux} - + P_{f,0} \\ - x_{P,0}^\mathrm{I} - &= P_0^\mathrm{iou} -\end{aligned} -``` - -### External Solved - -```math -\begin{aligned} - P_0^\mathrm{ref} - &\leftarrow P_{e,0} - P_0^\mathrm{aux} -\end{aligned} -``` - -Initialization rejects nonzero WT4T antiwindup rates. - -## Monitorable Outputs - -Output | Units | Description | Note -----------------|--------|-------------------------------------|------ -`pord` | [p.u.] | Active-power order output | $P^\mathrm{ord}$ (system base) -`pmeas` | [p.u.] | Filtered electrical active power | $P^\mathrm{meas}$ (component base) -`piin` | [p.u.] | Pitch-control input error | $P^\mathrm{iin}$ (component base) -`piou` | [p.u.] | Limited pitch-control output | $P^\mathrm{iou}$ (component base) -`pf` | [p.u.] | Washout feedback signal | $P_f$ (component base) diff --git a/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md b/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md index 65165063a..56784bc76 100644 --- a/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md +++ b/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md @@ -171,11 +171,11 @@ CommonMath defines [clamp](../../../../CommonMath.md#derived-functions). ```math \begin{aligned} - \omega_{t,0} + \omega_t &\leftarrow \text{turbine rotor-speed start} \\ - P_0^\mathrm{ord} + P^\mathrm{ord} &\leftarrow \text{active-power order start on system base} \\ - \theta_0 + \theta &\leftarrow \text{blade-pitch angle start} \end{aligned} ``` @@ -211,9 +211,9 @@ derivatives to zero: ```math \begin{aligned} - \omega_0^\mathrm{ref} + \omega^\mathrm{ref} &\leftarrow \omega_{t,0} \\ - P_0^\mathrm{ref} + P^\mathrm{ref} &\leftarrow P_0^\mathrm{ord} \end{aligned} ``` diff --git a/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md b/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md index cb8136dd5..084e743f4 100644 --- a/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md +++ b/GridKit/Model/PhasorDynamics/Wind/WTGTA/README.md @@ -149,7 +149,7 @@ $P_e$ | [p.u.] | Known | Electrical active-power ```math \begin{aligned} - \omega_{t,0}, \omega_{g,0} + \omega_t, \omega_g &\leftarrow \text{initial speeds} \end{aligned} ``` @@ -181,9 +181,9 @@ derivatives to zero: ```math \begin{aligned} - P_{\text{m},0} + P_\text{m} &\leftarrow \dfrac{\omega_{t,0}T_{m,0}}{k_{\mathrm{base}}} \\ - P_{e,0} + P_e &\leftarrow \dfrac{\omega_{g,0}T_{e,0}}{k_{\mathrm{base}}} \end{aligned} ``` diff --git a/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md b/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md index 73ce5c24d..3d7210165 100644 --- a/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md +++ b/GridKit/Model/PhasorDynamics/Wind/WTGTRQA/README.md @@ -200,7 +200,7 @@ CommonMath defines [clamp](../../../../CommonMath.md#derived-functions). ```math \begin{aligned} - P^\mathrm{ref}_0 + P^\mathrm{ref} &\leftarrow \text{active-power reference start} \\ s_{\mathrm{frz}} &\leftarrow \text{voltage-dip freeze signal} @@ -254,9 +254,9 @@ derivatives to zero: ```math \begin{aligned} - \omega_{g,0} + \omega_g &\leftarrow \omega_0^\mathrm{ref} \\ - P_{e,0} + P_e &\leftarrow P^\mathrm{ref}_0 \end{aligned} ``` diff --git a/docs/Figures/PhasorDynamics/Wind/WT4E/diagram.png b/docs/Figures/PhasorDynamics/Wind/WT4E/diagram.png deleted file mode 100644 index d71b2a6b78536676e6589c141b5fb29ba4c2a73b..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 74603 zcmb4r2{@Er*tac3q_m(#{go6lvXxy?vS*JNWZ%oa%}|O;*_Q}|vW#tH%`&5sgc!>( zmY50+V>dGK+WXsS7x+KV-5WN6 zY;1x-tiSBjZYRUo*mjEbbgo#0L6@c?qYllXHP=kos%)>A>Ns*{H$dMVIh?_7snGh^ z^1YQ_m5}t3%)IBLfeue~-lD0g;n*vY9fA$STRBE$S%F?p&>q+B8y>pNbJ*WEWfSlA zK)Rsn+PYbr7CibgK^d#2+B$xwwcBqayd6q@peC=Xs!Cf8ys$VwKhJjH@0F2$C4%GM z-w$hYQ*{1b;*Z(Y|GsLga;1(`>}%BtCRqLo6P+56er;bvnwx3o@8bo zVbij-JpAB&0p^BjcfA05GfVoVZ+?#~AC}S|R^{MolUWBvF(*e>mzEfh|6JU)ZM!Lj zH}{lylDhLByg!xm@+Ecl!Q<<%Zk$bHiwRRpyd_-%F;htGJ|p-<$CmB*6P=q54y*d+ zw9wnPUrO!Sv^5C~lrI|em}pUT7UrIqn4q}CyV|TVnEeE3X$D~xyA_FsOZ}ZQ6VYbf z?CU_ zrc!PH&!2Aiix>Gil%dU{6&?!Z62*h^$8oFYe+I_>SxA}ioO(gLuH}NG?7ZQdTa_mI zT^-+LNsEi74h~7><&rQZum;0n!@W-#`qD=X_QHet`T48ci}mgcb;zp8+lr;!uvJNS zE^!wN(>o)myn2ZlI!}ztPr33}^wYe81EJUT6VV*qS9!Q&McS>)e+V5@{H17AH%uap z|6IIZ>m=;?z9Gv|_C>IAZ|#O{t;`j)b;;iUTzXSs{3!H<$b@-?T*jKxrAr+OMrQ*^GHJTcBXF% z!Cjd9!}l5~$IRfKox;k}!ov4F{i;&zCT9d6cg^$@A~LA8wQ|HAv0=Hq6PyjO)(V1m&3*FUw%7 zL8GS>2{o#^y%xT=Im{c(FY){okI4v!E|cplkKqlzIpNuo^)yN|r7vB&qzYsI>|V^T zk!}{5L8&BU2ztU=N51UdYM&m3`szY@=i4DC4Tp8qM0M3fR|n~HUz77`)PL3FaT`@% zYn8_MPGi`QbOpyby)CaY&}+2l!bf^!l`jrV#2*X6E>o#g&nv;9$oDF0Dj^5GhS^}* z;3(WU^TP!?+X5r`TN!K`4L@`W4Jw6a*=|6L_P5C?M|`N2et5M|6g62J-{Rb@_Gf{n zcrYBKBX!|K-2w&LU#x<*K7Y4Sa?$JrRG^%ErF^J2{rrnjOACw3I|36YC=2b~3D9NH zP1+0FI<9}NwEGyiGul*NhhK5GT)xn{pk2Zg%Rbhed+e`H&W=j4!)}Uj^vUvB->n!{ zZQJWsb{%2xBpg#VGG;U!^r=GN(bZiLo6+c(w)zkgsJRe8zvsXWInDMJaD=Y&14-9$|xWXxo>V5w6~B@2!b+qvZg2ut)UnM(e}0 zwY6>Cqv>*Ha(*6t!W&oQcvHJwMxXI38e!8vpUL`<$7zf%vZIqz?eknilS{bouZO8! zh_NO{R!Jamt8(?CYgFWZiX;^}gQDuXWA8=Nn?Pa zoNCUUIELoRl^j-3T}GlMI^Hb2S5<4YS-nU&rxncbp%Cy>eEXCW>COKFgx@Znc`9k> ziOz@Y*Tjenu5Try-fg0|&Y61>9{adstEnGn?)_rI(=#&OuhLX|-$C13j7o;y98dS6 zh#lfp?m%`cA=O(X()8TnHZ~$x3-><=!BRW@AFvwjfX{q{2@RE9z* zb;ImoUcPbtnW266!@o!Q=zNa~xF{dx*PoFBIeuRh|YAKj{85yec%2ZnqB5W5j;9r}i^Qbc> z|F8VZxGok*{JmN73g7&bzpv`=SM8KyUv1yf(4fzsR?q&6=HC)8|JVbBwa{(BB|MN7 zLnB0=JQ=liKi}}r7#4SRMZ?c<(#1L@Y5xxTUl!Aq@--0qJ;NG0n1+JA0O7r;X!s}@(Ypb

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z&`1H6-Jr2)po5jP&%CSq#rb>P9zMAjXRNPR0`1uKQLTTkq#1DZvTpx;xeA5@9pDsd z1l+dhZvIc_xy%#b;LNT+i;TAb2Xs!RE)ILLwrwx4uM1qjaAoIni?_RhyU98?oC6kS zu4!vOS_4;buJt+WGyPR6rvOR_|k$*NMy5++0xDsk-fZ+{{qcoNbU@!qklE1w;6!>6u2}t2%&~YgYJxqrU zQnqbhy?1Xca7L!S@ag>5Uplu|z2x^_m6 -WT4G -WT4T WTGARA WTGPTA WTGTA diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md deleted file mode 100644 index c8fcaa21e..000000000 --- a/docs/GridKit/Model/PhasorDynamics/Wind/WT4E/README.md +++ /dev/null @@ -1,6 +0,0 @@ -# WT4E - -```{include} ../../../../../../GridKit/Model/PhasorDynamics/Wind/WT4E/README.md -:start-line: 1 -:relative-images: -``` diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md deleted file mode 100644 index 638435fdc..000000000 --- a/docs/GridKit/Model/PhasorDynamics/Wind/WT4G/README.md +++ /dev/null @@ -1,6 +0,0 @@ -# WT4G - -```{include} ../../../../../../GridKit/Model/PhasorDynamics/Wind/WT4G/README.md -:start-line: 1 -:relative-images: -``` diff --git a/docs/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md b/docs/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md deleted file mode 100644 index 51a7ca122..000000000 --- a/docs/GridKit/Model/PhasorDynamics/Wind/WT4T/README.md +++ /dev/null @@ -1,6 +0,0 @@ -# WT4T - -```{include} ../../../../../../GridKit/Model/PhasorDynamics/Wind/WT4T/README.md -:start-line: 1 -:relative-images: -``` From ec8c5464468c9b199f868814a6012c7a323c48a9 Mon Sep 17 00:00:00 2001 From: lukelowry Date: Fri, 26 Jun 2026 23:30:25 -0500 Subject: [PATCH 4/4] Minor Corrections --- .../PhasorDynamics/Wind/WTGPTA/README.md | 26 +++++++++---------- 1 file changed, 13 insertions(+), 13 deletions(-) diff --git a/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md b/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md index 56784bc76..60d813a56 100644 --- a/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md +++ b/GridKit/Model/PhasorDynamics/Wind/WTGPTA/README.md @@ -94,10 +94,10 @@ None. Symbol | Units | Type | Description | Note -------------------------------------|--------|---------|-----------------------------------|------ -$\omega_t$ | [p.u.] | Known | Turbine rotor speed | Signal port `omegat` -$P^\mathrm{ord}$ | [p.u.] | Known | Active-power order feedback | Signal port `pord`; system base -$\omega^\mathrm{ref}$ | [p.u.] | Unknown | Rotor-speed reference | Optional signal port `wref` -$P^\mathrm{ref}$ | [p.u.] | Unknown | Active-power reference | Optional signal port `pref`; system base +$\omega_t$ | [p.u.] | Unknown | Turbine rotor speed | Signal port `omegat` +$P^\mathrm{ord}$ | [p.u.] | Unknown | Active-power order feedback | Signal port `pord`; system base +$\omega^\mathrm{ref}$ | [p.u.] | Known | Rotor-speed reference | Optional signal port `wref` +$P^\mathrm{ref}$ | [p.u.] | Known | Active-power reference | Optional signal port `pref`; system base ## Model Equations @@ -171,12 +171,12 @@ CommonMath defines [clamp](../../../../CommonMath.md#derived-functions). ```math \begin{aligned} - \omega_t - &\leftarrow \text{turbine rotor-speed start} \\ - P^\mathrm{ord} - &\leftarrow \text{active-power order start on system base} \\ \theta - &\leftarrow \text{blade-pitch angle start} + &\leftarrow \text{blade-pitch angle start} \\ + \omega^\mathrm{ref} + &\leftarrow \text{rotor-speed reference start} \\ + P^\mathrm{ref} + &\leftarrow \text{active-power reference start on system base} \end{aligned} ``` @@ -211,10 +211,10 @@ derivatives to zero: ```math \begin{aligned} - \omega^\mathrm{ref} - &\leftarrow \omega_{t,0} \\ - P^\mathrm{ref} - &\leftarrow P_0^\mathrm{ord} + \omega_t + &\leftarrow \omega_0^\mathrm{ref} \\ + P^\mathrm{ord} + &\leftarrow P_0^\mathrm{ref} \end{aligned} ```