From a04c0c680136e52dd0262c6d34aca84fb929dd25 Mon Sep 17 00:00:00 2001
From: lukelowry <wyattluke.lowery@gmail.com>
Date: Sun, 31 May 2026 22:29:55 -0500
Subject: [PATCH 1/2] Add EXAC2 exciter documentation stub

---
 .../PhasorDynamics/Exciter/EXAC2/README.md    |  72 ++++++++++++++++++
 .../Model/PhasorDynamics/Exciter/README.md    |   1 +
 docs/Figures/PhasorDynamics/EXAC2_diagram.png | Bin 0 -> 46405 bytes
 3 files changed, 73 insertions(+)
 create mode 100644 GridKit/Model/PhasorDynamics/Exciter/EXAC2/README.md
 create mode 100644 docs/Figures/PhasorDynamics/EXAC2_diagram.png

diff --git a/GridKit/Model/PhasorDynamics/Exciter/EXAC2/README.md b/GridKit/Model/PhasorDynamics/Exciter/EXAC2/README.md
new file mode 100644
index 000000000..ed9f4ad54
--- /dev/null
+++ b/GridKit/Model/PhasorDynamics/Exciter/EXAC2/README.md
@@ -0,0 +1,72 @@
+# **Exciter Model (EXAC2)**
+
+> [!NOTE]
+> This README is a documentation stub/template for the EXAC2 exciter. Parameters, variables, equations, initialization details, and outputs are intentionally left unfilled until the model is derived from its source documentation.
+
+## Block Diagram
+
+Standard model of the EXAC2 Exciter.
+
+<div align="center">
+   <img align="center" src="../../../../../docs/Figures/PhasorDynamics/EXAC2_diagram.png">
+
+  Figure 1: Exciter EXAC2 model.
+</div>
+
+## Model Parameters
+
+Symbol | Units | Description | Typical Value | Note
+-------|-------|-------------|---------------|-----
+
+### Model Derived Parameters
+
+## Model Variables
+
+### Internal Variables
+
+#### Differential
+
+Symbol | Units | Description | Note
+-------|-------|-------------|-----
+
+#### Algebraic
+
+Symbol | Units | Description | Note
+-------|-------|-------------|-----
+
+### External Variables
+
+#### Differential
+
+Symbol | Units | Description | Note
+-------|-------|-------------|-----
+
+#### Algebraic
+
+Symbol | Units | Description | Note
+-------|-------|-------------|-----
+
+## Model Equations
+
+### Differential Equations
+
+```math
+\begin{aligned}
+\end{aligned}
+```
+
+### Algebraic Equations
+
+```math
+\begin{aligned}
+\end{aligned}
+```
+
+## Initialization
+
+```math
+\begin{aligned}
+\end{aligned}
+```
+
+## Model Outputs
diff --git a/GridKit/Model/PhasorDynamics/Exciter/README.md b/GridKit/Model/PhasorDynamics/Exciter/README.md
index 81144066b..cb4b12cfb 100644
--- a/GridKit/Model/PhasorDynamics/Exciter/README.md
+++ b/GridKit/Model/PhasorDynamics/Exciter/README.md
@@ -14,4 +14,5 @@ device internal voltage.
 There are a few standard Exciter models
 - IEEE Type 1 Excitation Model (See [IEEET1](IEEET1/README.md))
 - IEEE DC1 Excitation Model (See [EXDC1](EXDC1/README.md))
+- EXAC2 Excitation Model (See [EXAC2](EXAC2/README.md))
 - Simplified Excitation System Model (See [SEXS-PTI](SEXS-PTI/README.md))
diff --git a/docs/Figures/PhasorDynamics/EXAC2_diagram.png b/docs/Figures/PhasorDynamics/EXAC2_diagram.png
new file mode 100644
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From 0bd6fbe3f9c8365319352216acbdc6d7eadb5a00 Mon Sep 17 00:00:00 2001
From: lukelowry <wyattluke.lowery@gmail.com>
Date: Tue, 2 Jun 2026 16:53:18 -0500
Subject: [PATCH 2/2] docs: complete EXAC2 README [skip ci]

---
 .../PhasorDynamics/Exciter/EXAC2/README.md    | 199 ++++++++++++++++--
 1 file changed, 185 insertions(+), 14 deletions(-)

diff --git a/GridKit/Model/PhasorDynamics/Exciter/EXAC2/README.md b/GridKit/Model/PhasorDynamics/Exciter/EXAC2/README.md
index ed9f4ad54..3ec486d00 100644
--- a/GridKit/Model/PhasorDynamics/Exciter/EXAC2/README.md
+++ b/GridKit/Model/PhasorDynamics/Exciter/EXAC2/README.md
@@ -1,7 +1,16 @@
-# **Exciter Model (EXAC2)**
+# **IEEE Type AC2 Excitation System Model (EXAC2)**
 
-> [!NOTE]
-> This README is a documentation stub/template for the EXAC2 exciter. Parameters, variables, equations, initialization details, and outputs are intentionally left unfilled until the model is derived from its source documentation.
+EXAC2 is an IEEE Type AC excitation system with a voltage transducer, lead-lag
+input compensation, limited voltage-amplifier state, low-value gate, voltage
+regulator limits, exciter alternator state, stabilizing feedback, rectifier
+loading, saturation, and optional speed multiplier.
+
+Notes:
+- Internal voltage and current signals are on model base unless otherwise stated.
+- The rectifier loading block $F_{\mathrm{ex}}=f(I_N)$ is the source AC-exciter
+  loading curve from Fig. 1; it is not a CommonMath helper.
+- The source diagram labels the optional multiplier input as `Speed`; GridKit
+  uses machine speed deviation, so the enabled multiplier is $1+\omega$.
 
 ## Block Diagram
 
@@ -10,41 +19,116 @@ Standard model of the EXAC2 Exciter.
 <div align="center">
    <img align="center" src="../../../../../docs/Figures/PhasorDynamics/EXAC2_diagram.png">
 
-  Figure 1: Exciter EXAC2 model.
+  Figure 1: Exciter EXAC2 model. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/)
 </div>
 
 ## Model Parameters
 
-Symbol | Units | Description | Typical Value | Note
--------|-------|-------------|---------------|-----
+Symbol                              | Units    | JSON      | Description                                             | Typical Value | Note
+------------------------------------|----------|-----------|---------------------------------------------------------|---------------|------
+$T_R$                               | [sec]    | `Tr`      | Transducer time constant                                | 0.0           | Block name: `Tr`; if zero, $V_C$ is algebraic
+$T_B$                               | [sec]    | `Tb`      | Lag time constant for voltage-regulator input lead-lag  | 0.0           | Block name: `Tb`
+$T_C$                               | [sec]    | `Tc`      | Lead time constant for voltage-regulator input lead-lag | 0.0           | Block name: `Tc`
+$K_A$                               | [p.u.]   | `Ka`      | Voltage-amplifier gain                                  | 40.0          | Block name: `Ka`
+$T_A$                               | [sec]    | `Ta`      | Voltage-amplifier time constant                         | 0.1           | Block name: `Ta`
+$V_A^{\max}$                        | [p.u.]   | `VaMax`   | Maximum voltage-amplifier output                        | 1.0           | Block name: `VAMAX`
+$V_A^{\min}$                        | [p.u.]   | `VaMin`   | Minimum voltage-amplifier output                        | -1.0          | Block name: `VAMIN`
+$K_B$                               | [p.u.]   | `Kb`      | Regulator pre-limit gain after low-value gate           | 1.0           | Block name: `KB`
+$V_R^{\max}$                        | [p.u.]   | `Vrmax`   | Maximum voltage-regulator output                        | 1.0           | Block name: `Vrmax`
+$V_R^{\min}$                        | [p.u.]   | `Vrmin`   | Minimum voltage-regulator output                        | -1.0          | Block name: `Vrmin`
+$T_E$                               | [sec]    | `Te`      | Exciter alternator time constant                        | 0.5           | Block name: `Te`
+$K_L$                               | [p.u.]   | `Kl`      | Field-current limiter feedback gain                     | 0.0           | Block name: `KL`
+$K_H$                               | [p.u.]   | `Kh`      | Regulator feedback path gain                            | 0.0           | Block name: `KH`
+$K_F$                               | [p.u.]   | `Kf`      | Stabilizing feedback gain                               | 0.05          | Block name: `Kf`
+$T_F$                               | [sec]    | `Tf`      | Stabilizing feedback time constant                      | 0.7           | Block name: `Tf`; if zero, $V_F$ is algebraic
+$K_C$                               | [p.u.]   | `Kc`      | Rectifier loading current coefficient                   | 0.0           | Block name: `Kc`; forms $I_N$
+$K_D$                               | [p.u.]   | `Kd`      | Demagnetizing factor feedback gain                      | 0.0           | Block name: `Kd`
+$K_E$                               | [p.u.]   | `Ke`      | Exciter field-resistance line-slope margin              | 0.1           | Block name: `Ke`
+$V_{\mathrm{lr}}$                   | [p.u.]   | `VLr`     | Low-value gate lower reference                          | 0.0           | Source label: `VLR`
+$E_1$                               | [p.u.]   | `E1`      | First saturation voltage point                          | 2.8           | Block name: `E1`
+$S_E(E_1)$                          | [p.u.]   | `SE1`     | Saturation value at $E_1$                               | 0.08          | Block name: `Se1`
+$E_2$                               | [p.u.]   | `E2`      | Second saturation voltage point                         | 3.7           | Block name: `E2`
+$S_E(E_2)$                          | [p.u.]   | `SE2`     | Saturation value at $E_2$                               | 0.33          | Block name: `Se2`
+$s_{\mathrm{spd}}$                  | [binary] | `Spdmlt`  | Speed multiplier flag                                   | 0             | Block name: `Spdmlt`; 1 enables the speed multiplier
+
+### Parameter Validation
+
+Invalid EXAC2 parameter sets are rejected by the following checks.
+
+```math
+\begin{aligned}
+  &K_A > 0 \\
+  &T_R \ge 0,\quad T_A > 0,\quad T_B \ge 0,\quad T_C \ge 0,\quad T_E > 0,\quad T_F \ge 0 \\
+  &T_B > 0\quad\text{or}\quad(T_B = 0\ \text{and}\ T_C = 0) \\
+  &V_A^{\min} \le V_A^{\max},\quad V_R^{\min} \le V_R^{\max} \\
+  &s_{\mathrm{spd}} \in \{0,1\}
+\end{aligned}
+```
+
+The saturation points follow the same two-point validation used by other
+exciter READMEs: both saturation values are zero, or both points define a valid
+positive quadratic fit.
 
 ### Model Derived Parameters
 
+The saturation curve is fitted from the two supplied saturation points. If both
+saturation factors are zero, use $S_A=0$ and $S_B=0$. Otherwise:
+
+```math
+\begin{aligned}
+  C &= \sqrt{\dfrac{S_E(E_2)}{S_E(E_1)}} \\
+  S_A &= \dfrac{C E_1 - E_2}{C - 1} \\
+  S_B &= \dfrac{S_E(E_1)}{(E_1 - S_A)^2}
+\end{aligned}
+```
+
 ## Model Variables
 
 ### Internal Variables
 
 #### Differential
 
-Symbol | Units | Description | Note
--------|-------|-------------|-----
+Symbol                              | Units  | Description                                             | Note
+------------------------------------|--------|---------------------------------------------------------|------
+$V_E$                               | [p.u.] | Exciter alternator voltage state before output multipliers | State 1 in Fig. 1; source label: `VE`
+$V_C$                               | [p.u.] | Sensed compensated voltage                              | State 2 in Fig. 1; source label: `Sensed Vt`; algebraic when $T_R=0$
+$V_A$                               | [p.u.] | Limited voltage-amplifier output                        | State 3 in Fig. 1; source label: `VA`
+$x_{\mathrm{ll}}$                   | [p.u.] | Lead-lag block state                                    | State 4 in Fig. 1; source label: `VLL`
+$V_F$                               | [p.u.] | Stabilizing feedback washout output                     | State 5 in Fig. 1; source label: `VF`; algebraic when $T_F=0$
 
 #### Algebraic
 
-Symbol | Units | Description | Note
--------|-------|-------------|-----
+Symbol                              | Units  | Description                                             | Note
+------------------------------------|--------|---------------------------------------------------------|------
+$e_V$                               | [p.u.] | Voltage-regulator input error before lead-lag block     | Summing junction after sensed voltage
+$V_{\mathrm{ll}}$                   | [p.u.] | Lead-lag output                                         | Input to voltage amplifier
+$V_H$                               | [p.u.] | Regulator feedback path signal                          | Block name: `KH`
+$V_L$                               | [p.u.] | Field-current limiter low-value gate input              | Block name: `KL`; lower reference $V_{\mathrm{lr}}$
+$V_{\mathrm{lv}}$                   | [p.u.] | Low-value gate output                                   | Lesser of amplifier path and limiter path
+$V_R$                               | [p.u.] | Voltage-regulator output                                | Limited by $V_R^{\min}$ and $V_R^{\max}$
+$S_E$                               | [p.u.] | Saturation coefficient evaluated at $V_E$               | Uses derived saturation curve
+$I_N$                               | [p.u.] | Normalized exciter loading current                      | Source label: `IN`; satisfies $V_E I_N=K_C I_{\mathrm{fd}}$
+$F_{\mathrm{ex}}$                   | [p.u.] | Rectifier loading factor                                | Source label: `FEX`; source curve $F_{\mathrm{ex}}=f(I_N)$
+$V_{\mathrm{fe}}$                   | [p.u.] | Exciter feedback signal                                 | Sum of saturation/resistance and $K_D I_{\mathrm{fd}}$ paths
+$E_{\mathrm{fd}}$                   | [p.u.] | Field-voltage output                                    | Output after rectifier loading and optional speed multiplier
 
 ### External Variables
 
 #### Differential
 
-Symbol | Units | Description | Note
--------|-------|-------------|-----
+None.
 
 #### Algebraic
 
-Symbol | Units | Description | Note
--------|-------|-------------|-----
+Symbol                              | Units  | Description                                             | Note
+------------------------------------|--------|---------------------------------------------------------|------
+$E_C$                               | [p.u.] | Compensated terminal voltage magnitude                  | Source label: `EC`
+$V_{\mathrm{ref}}$                  | [p.u.] | Voltage-control reference                               | Source label: `VREF`
+$V_S$                               | [p.u.] | Stabilizer input signal                                 | Source label: `VS`; optional, defaults to zero
+$V_{\mathrm{uel}}$                  | [p.u.] | Under-excitation limiter input                          | Source label: `VUEL`; optional, defaults to zero
+$V_{\mathrm{oel}}$                  | [p.u.] | Over-excitation limiter input                           | Source label: `VOEL`; optional, defaults to zero
+$I_{\mathrm{fd}}$                   | [p.u.] | Machine field current                                   | Source label: `IFD`
+$\omega$                            | [p.u.] | Machine speed deviation                                 | Source label: `Speed`; optional when $s_{\mathrm{spd}}=0$
 
 ## Model Equations
 
@@ -52,21 +136,108 @@ Symbol | Units | Description | Note
 
 ```math
 \begin{aligned}
+  0 &= -T_R\dot V_C - V_C + E_C \\
+  0 &= -T_B\dot x_{\mathrm{ll}} - x_{\mathrm{ll}} + e_V \\
+  0 &= -T_A\dot V_A
+       + \text{antiwindup}\!\left(
+          V_A,
+          -V_A + K_A V_{\mathrm{ll}},
+          V_A^{\min},
+          V_A^{\max}
+       \right) \\
+  0 &= -T_E\dot V_E + V_R - V_{\mathrm{fe}} \\
+  0 &= -T_F\dot V_F - V_F + K_F\dot V_E
 \end{aligned}
 ```
 
+CommonMath defines the [Anti-Windup](../../../../CommonMath.md#anti-windup-indicator)
+target and smooth approximation.
+
 ### Algebraic Equations
 
 ```math
 \begin{aligned}
+  0 &= -e_V + V_{\mathrm{ref}} + V_S + V_{\mathrm{uel}} + V_{\mathrm{oel}} - V_C - V_F \\
+  0 &= -T_B(V_{\mathrm{ll}} - x_{\mathrm{ll}}) + T_C(e_V - x_{\mathrm{ll}}) \\
+  0 &= -V_H + K_H V_{\mathrm{fe}} \\
+  0 &= -V_L + V_{\mathrm{lr}} + K_L V_{\mathrm{fe}} \\
+  0 &= -V_{\mathrm{lv}} + \text{min}(V_A + V_H,\ V_L) \\
+  0 &= -V_R + \text{clamp}(K_B V_{\mathrm{lv}}, V_R^{\min}, V_R^{\max}) \\
+  0 &= -S_E + S_B\,q(V_E - S_A) \\
+  0 &= -V_E I_N + K_C I_{\mathrm{fd}} \\
+  0 &= -F_{\mathrm{ex}} + f(I_N) \\
+  0 &= -V_{\mathrm{fe}} + (K_E + S_E)V_E + K_D I_{\mathrm{fd}} \\
+  0 &= -E_{\mathrm{fd}}
+       + \left(1+s_{\mathrm{spd}}\omega\right)F_{\mathrm{ex}}V_E
 \end{aligned}
 ```
 
+CommonMath defines helper targets for [min and clamp](../../../../CommonMath.md#derived-functions)
+and the primitive [quadratic ramp](../../../../CommonMath.md#primitives) $q$.
+The rectifier loading function $f(I_N)$ is the source curve shown in Fig. 1.
+When $T_B=T_C=0$, the lead-lag block is bypassed so $V_{\mathrm{ll}}=e_V$.
+
 ## Initialization
 
+The machine initializes $E_{\mathrm{fd}}$ and $I_{\mathrm{fd}}$ first. For a
+standard unsaturated start, EXAC2 reads those values, sets all internal
+derivatives to zero, and first solves the coupled rectifier-loading equations:
+
+```math
+\begin{aligned}
+  0 &= -V_{E,0}I_{N,0} + K_C I_{\mathrm{fd},0} \\
+  0 &= -F_{\mathrm{ex},0} + f(I_{N,0}) \\
+  0 &= -E_{\mathrm{fd},0}
+       + \left(1+s_{\mathrm{spd}}\omega_0\right)F_{\mathrm{ex},0}V_{E,0}
+\end{aligned}
+```
+
+Then evaluate the feedback path:
+
 ```math
 \begin{aligned}
+  S_{E,0} &= S_B\,q(V_{E,0} - S_A) \\
+  V_{\mathrm{fe},0} &= (K_E + S_{E,0})V_{E,0} + K_D I_{\mathrm{fd},0}
 \end{aligned}
 ```
 
+Then solve the low-value gate and voltage-regulator chain:
+
+```math
+\begin{aligned}
+  V_{R,0} &= V_{\mathrm{fe},0} \\
+  V_{H,0} &= K_H V_{\mathrm{fe},0} \\
+  V_{L,0} &= V_{\mathrm{lr}} + K_L V_{\mathrm{fe},0} \\
+  V_{\mathrm{lv},0} &= \dfrac{V_{R,0}}{K_B} \\
+  V_{A,0} &= V_{\mathrm{lv},0} - V_{H,0} \\
+  V_{\mathrm{ll},0} &= \dfrac{V_{A,0}}{K_A} \\
+  V_{C,0} &= E_{C,0} \\
+  V_{F,0} &= 0 \\
+  x_{\mathrm{ll},0} &= e_{V,0} = V_{\mathrm{ll},0} \\
+  V_{\mathrm{ref},0}
+    &= e_{V,0} + V_{C,0} + V_{F,0}
+       - V_{S,0} - V_{\mathrm{uel},0} - V_{\mathrm{oel},0}
+\end{aligned}
+```
+
+This standard start requires $1+s_{\mathrm{spd}}\omega_0\ne 0$,
+$V_{E,0}\ne 0$, $K_A\ne 0$, $K_B\ne 0$, inactive $V_A$ and $V_R$ limits, and
+the low-value gate selecting the amplifier path. Starts with active low-value
+gate limiting or saturated regulator states are outside these closed-form
+equations.
+
 ## Model Outputs
+
+Output          | Units  | Description                         | Note
+----------------|--------|-------------------------------------|------
+`efd`           | [p.u.] | Field-voltage output                | $E_{\mathrm{fd}}$
+`ve`            | [p.u.] | Exciter alternator voltage state    | $V_E$
+`vc`            | [p.u.] | Sensed compensated voltage          | $V_C$
+`va`            | [p.u.] | Voltage-amplifier state             | $V_A$
+`vr`            | [p.u.] | Voltage-regulator output            | $V_R$
+`vll`           | [p.u.] | Lead-lag output                     | $V_{\mathrm{ll}}$
+`vf`            | [p.u.] | Stabilizing feedback state          | $V_F$
+`vlv`           | [p.u.] | Low-value gate output               | $V_{\mathrm{lv}}$
+`in`            | [p.u.] | Normalized exciter loading current  | $I_N$
+`fex`           | [p.u.] | Rectifier loading factor            | $F_{\mathrm{ex}}$
+`se`            | [p.u.] | Saturation coefficient              | $S_E$