From 2d69db40bc8280730d8f26408b6b507d64fa9fd7 Mon Sep 17 00:00:00 2001
From: lukelowry <wyattluke.lowery@gmail.com>
Date: Sun, 31 May 2026 16:50:13 -0500
Subject: [PATCH 1/2] Add ESST4B exciter documentation stub

---
 .../PhasorDynamics/Exciter/ESST4B/README.md   |  69 ++++++++++++++++++
 .../Model/PhasorDynamics/Exciter/README.md    |   1 +
 .../Figures/PhasorDynamics/ESST4B_diagram.png | Bin 0 -> 47228 bytes
 3 files changed, 70 insertions(+)
 create mode 100644 GridKit/Model/PhasorDynamics/Exciter/ESST4B/README.md
 create mode 100644 docs/Figures/PhasorDynamics/ESST4B_diagram.png

diff --git a/GridKit/Model/PhasorDynamics/Exciter/ESST4B/README.md b/GridKit/Model/PhasorDynamics/Exciter/ESST4B/README.md
new file mode 100644
index 000000000..bcb0d24cc
--- /dev/null
+++ b/GridKit/Model/PhasorDynamics/Exciter/ESST4B/README.md
@@ -0,0 +1,69 @@
+# **Exciter Model (ESST4B)**
+
+## Block Diagram
+
+Standard model of the ESST4B Exciter.
+
+<div align="center">
+   <img align="center" src="../../../../../docs/Figures/PhasorDynamics/ESST4B_diagram.png">
+
+  Figure 1: Exciter ESST4B 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 03428d4be..16008155d 100644
--- a/GridKit/Model/PhasorDynamics/Exciter/README.md
+++ b/GridKit/Model/PhasorDynamics/Exciter/README.md
@@ -17,4 +17,5 @@ There are a few standard Exciter models
 - IEEE DC1 Excitation Model (See [EXDC1](EXDC1/README.md))
 - ESDC2A Excitation Model (See [ESDC2A](ESDC2A/README.md))
 - EXAC1 Excitation Model (See [EXAC1](EXAC1/README.md))
+- IEEE ST4B Excitation Model (See [ESST4B](ESST4B/README.md))
 - Simplified Excitation System Model (See [SEXS-PTI](SEXS-PTI/README.md))
diff --git a/docs/Figures/PhasorDynamics/ESST4B_diagram.png b/docs/Figures/PhasorDynamics/ESST4B_diagram.png
new file mode 100644
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literal 0
HcmV?d00001


From c44a6d203efd2ae21836aecbd092dadb6a468bd1 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 ESST4B README [skip ci]

---
 .../PhasorDynamics/Exciter/ESST4B/README.md   | 198 ++++++++++++++++--
 1 file changed, 186 insertions(+), 12 deletions(-)

diff --git a/GridKit/Model/PhasorDynamics/Exciter/ESST4B/README.md b/GridKit/Model/PhasorDynamics/Exciter/ESST4B/README.md
index bcb0d24cc..fa77d9030 100644
--- a/GridKit/Model/PhasorDynamics/Exciter/ESST4B/README.md
+++ b/GridKit/Model/PhasorDynamics/Exciter/ESST4B/README.md
@@ -1,4 +1,18 @@
-# **Exciter Model (ESST4B)**
+# **IEEE Type ST4B Potential- or Compound-Source Controlled-Rectifier Exciter Model (ESST4B)**
+
+ESST4B is a static excitation system with compensated-voltage sensing, an outer
+proportional/integral voltage regulator, a lag block, an inner
+proportional/integral regulator with exciter-output feedback, low-value
+over-excitation limiter gating, and potential- or compound-source rectifier
+scaling.
+
+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
+  controlled-rectifier loading curve from Fig. 1; it is not a CommonMath helper.
+- The potential-source calculation uses explicit real and imaginary terminal
+  voltage/current components; the diagram's complex expression is not used as
+  model-equation notation below.
 
 ## Block Diagram
 
@@ -7,41 +21,108 @@ Standard model of the ESST4B Exciter.
 <div align="center">
    <img align="center" src="../../../../../docs/Figures/PhasorDynamics/ESST4B_diagram.png">
 
-  Figure 1: Exciter ESST4B model.
+  Figure 1: Exciter ESST4B 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`        | Compensated-voltage transducer time constant            | 0.0           | Block name: `Tr`; if zero, sensed voltage is algebraic
+$K_{\mathrm{pr}}$                   | [p.u.] | `Kpr`       | Outer regulator proportional gain                       | 1.0           | Block name: `KPR`
+$K_{\mathrm{ir}}$                   | [p.u./s] | `Kir`     | Outer regulator integral gain                           | 0.0           | Block name: `KIR`
+$V_R^{\max}$                        | [p.u.] | `Vrmax`     | Maximum outer regulator output                          | 1.0           | Block name: `VRMAX`
+$V_R^{\min}$                        | [p.u.] | `Vrmin`     | Minimum outer regulator output                          | -1.0          | Block name: `VRMIN`
+$T_A$                               | [sec]  | `Ta`        | Regulator lag time constant                             | 0.0           | Block name: `Ta`; if zero, $V_A$ is algebraic
+$K_{\mathrm{pm}}$                   | [p.u.] | `Kpm`       | Inner regulator proportional gain                       | 1.0           | Block name: `KPM`
+$K_{\mathrm{im}}$                   | [p.u./s] | `Kim`     | Inner regulator integral gain                           | 0.0           | Block name: `KIM`
+$V_M^{\max}$                        | [p.u.] | `VmMax`     | Maximum inner regulator output                          | 1.0           | Block name: `VMMAX`
+$V_M^{\min}$                        | [p.u.] | `VmMin`     | Minimum inner regulator output                          | 0.0           | Block name: `VMMIN`
+$K_G$                               | [p.u.] | `Kg`        | Exciter-output feedback gain into inner regulator       | 0.0           | Block name: `KG`
+$K_P$                               | [p.u.] | `Kp`        | Potential-source voltage coefficient magnitude          | 0.0           | Source label: `KP`
+$K_I$                               | [p.u.] | `Ki`        | Potential-source current coefficient                    | 0.0           | Source label: `KI`
+$V_B^{\max}$                        | [p.u.] | `VbMax`     | Maximum rectifier source multiplier                     | 999.0         | Block name: `VBMAX`
+$K_C$                               | [p.u.] | `Kc`        | Rectifier loading current coefficient                   | 0.0           | Block name: `Kc`; forms $I_N$
+$X_L$                               | [p.u.] | `Xl`        | Source reactance term in potential-source calculation   | 0.0           | Source label: `XL`
+$\theta_P$                          | [deg]  | `ThetaPDeg` | Potential-source coefficient angle                      | 0.0           | Source label: `thetaP`; forms $K_P^{\mathrm{r}}$ and $K_P^{\mathrm{i}}$
+$V_G^{\max}$                        | [p.u.] | `VgMax`     | Maximum exciter-output feedback signal                  | 999.0         | Block name: `VGMAX`; ceiling on $K_G E_{\mathrm{fd}}$
+
+### Parameter Validation
+
+Invalid ESST4B parameter sets are rejected by the following checks.
+
+```math
+\begin{aligned}
+  &T_R \ge 0,\quad T_A \ge 0 \\
+  &V_R^{\min} \le V_R^{\max},\quad V_M^{\min} \le V_M^{\max} \\
+  &V_B^{\max} > 0,\quad V_G^{\max} \ge 0
+\end{aligned}
+```
 
 ### Model Derived Parameters
 
+The potential-source coefficient is resolved into real scalar components:
+
+```math
+\begin{aligned}
+  K_P^{\mathrm{r}} &= K_P\cos\theta_P \\
+  K_P^{\mathrm{i}} &= K_P\sin\theta_P
+\end{aligned}
+```
+
+Here $\theta_P$ is converted from degrees before evaluating the trigonometric
+functions.
+
 ## Model Variables
 
 ### Internal Variables
 
 #### Differential
 
-Symbol | Units | Description | Note
--------|-------|-------------|-----
+Symbol                              | Units  | Description                                             | Note
+------------------------------------|--------|---------------------------------------------------------|------
+$V_M$                               | [p.u.] | Inner regulator output                                  | State 1 in Fig. 1
+$V_C$                               | [p.u.] | Sensed compensated voltage                              | State 2 in Fig. 1; source label: `Sensed Vt`; algebraic when $T_R=0$
+$V_A$                               | [p.u.] | Lagged outer-regulator output                           | State 3 in Fig. 1; algebraic when $T_A=0$
+$x_R$                               | [p.u.] | Outer regulator integral state                          | State 4 in Fig. 1; source label: `VR`
 
 #### Algebraic
 
-Symbol | Units | Description | Note
--------|-------|-------------|-----
+Symbol                              | Units  | Description                                             | Note
+------------------------------------|--------|---------------------------------------------------------|------
+$e_V$                               | [p.u.] | Voltage-error signal into outer regulator               | Summing junction after sensed voltage
+$V_R$                               | [p.u.] | Limited outer regulator output                          | Limited by $V_R^{\min}$ and $V_R^{\max}$
+$V_G$                               | [p.u.] | Limited exciter-output feedback signal                  | $K_G E_{\mathrm{fd}}$ limited by $V_G^{\max}$
+$e_M$                               | [p.u.] | Inner regulator error                                   | $V_A$ minus $V_G$
+$V_{\mathrm{lv}}$                   | [p.u.] | Low-value gate output                                   | Lesser of $V_M$ and $V_{\mathrm{oel}}$
+$V_{\mathrm{src}}^{\mathrm{r}}$     | [p.u.] | Real component of the potential-source expression       | From terminal voltage/current components
+$V_{\mathrm{src}}^{\mathrm{i}}$     | [p.u.] | Imaginary component of the potential-source expression  | From terminal voltage/current components
+$V_E$                               | [p.u.] | Potential- or compound-source voltage magnitude         | Nonnegative source magnitude
+$I_N$                               | [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 $F_{\mathrm{ex}}=f(I_N)$
+$V_B$                               | [p.u.] | Rectifier source multiplier                             | Limited by $V_B^{\max}$
+$E_{\mathrm{fd}}$                   | [p.u.] | Field-voltage output                                    | Product of low-value gate and $V_B$
 
 ### External Variables
 
 #### Differential
 
-Symbol | Units | Description | Note
--------|-------|-------------|-----
+None.
 
 #### Algebraic
 
-Symbol | Units | Description | Note
--------|-------|-------------|-----
+Symbol                              | Units  | Description                                             | Note
+------------------------------------|--------|---------------------------------------------------------|------
+$V_{\mathrm{comp}}$                 | [p.u.] | Compensated voltage input                               | Source label: `VCOMP`
+$V_{\mathrm{ref}}$                  | [p.u.] | Voltage-control reference                               | Source label: `VREF`
+$V_{\mathrm{uel}}$                  | [p.u.] | Under-excitation limiter input                          | Source label: `VUEL`; optional, defaults to zero
+$V_S$                               | [p.u.] | Stabilizer input signal                                 | Source label: `VS`; optional, defaults to zero
+$V_{\mathrm{oel}}$                  | [p.u.] | Over-excitation limiter input                           | Source label: `VOEL`; optional, defaults to a high value when omitted
+$V_{\mathrm{r}}$                    | [p.u.] | Terminal-voltage real component                         | Source label: `VT`
+$V_{\mathrm{i}}$                    | [p.u.] | Terminal-voltage imaginary component                    | Source label: `VT`
+$I_{\mathrm{r}}$                    | [p.u.] | Terminal-current real component                         | Source label: `IT`
+$I_{\mathrm{i}}$                    | [p.u.] | Terminal-current imaginary component                    | Source label: `IT`
+$I_{\mathrm{fd}}$                   | [p.u.] | Machine field current                                   | Source label: `IFD`
 
 ## Model Equations
 
@@ -49,21 +130,114 @@ Symbol | Units | Description | Note
 
 ```math
 \begin{aligned}
+  0 &= -T_R\dot V_C - V_C + V_{\mathrm{comp}} \\
+  0 &=
+    -\dot x_R
+    + \text{antiwindup}\!\left(
+        V_R,
+        K_{\mathrm{ir}}e_V,
+        V_R^{\min},
+        V_R^{\max}
+      \right) \\
+  0 &= -T_A\dot V_A - V_A + V_R \\
+  0 &=
+    -\dot V_M
+    + \text{antiwindup}\!\left(
+        V_M,
+        K_{\mathrm{im}}e_M,
+        V_M^{\min},
+        V_M^{\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_V + V_{\mathrm{ref}} + V_{\mathrm{uel}} + V_S - V_C \\
+  0 &= -V_R + \text{clamp}(K_{\mathrm{pr}}e_V + x_R, V_R^{\min}, V_R^{\max}) \\
+  0 &= -V_G + \text{min}(K_G E_{\mathrm{fd}}, V_G^{\max}) \\
+  0 &= -e_M + V_A - V_G \\
+  0 &= -V_{\mathrm{lv}} + \text{min}(V_M, V_{\mathrm{oel}}) \\
+  0 &= -V_{\mathrm{src}}^{\mathrm{r}}
+       + K_P V_{\mathrm{r}}
+       - X_L K_P^{\mathrm{i}} I_{\mathrm{r}}
+       - \left(K_I + X_L K_P^{\mathrm{r}}\right)I_{\mathrm{i}} \\
+  0 &= -V_{\mathrm{src}}^{\mathrm{i}}
+       + K_P V_{\mathrm{i}}
+       + \left(K_I + X_L K_P^{\mathrm{r}}\right)I_{\mathrm{r}}
+       - X_L K_P^{\mathrm{i}} I_{\mathrm{i}} \\
+  0 &= -V_E^2
+       + \left(V_{\mathrm{src}}^{\mathrm{r}}\right)^2
+       + \left(V_{\mathrm{src}}^{\mathrm{i}}\right)^2 \\
+  0 &= -V_E I_N + K_C I_{\mathrm{fd}} \\
+  0 &= -F_{\mathrm{ex}} + f(I_N) \\
+  0 &= -V_B + \text{min}(V_E F_{\mathrm{ex}}, V_B^{\max}) \\
+  0 &= -E_{\mathrm{fd}} + V_{\mathrm{lv}}V_B
 \end{aligned}
 ```
 
+CommonMath defines helper targets for [min and clamp](../../../../CommonMath.md#derived-functions).
+The rectifier loading function $f(I_N)$ is the source curve shown in Fig. 1.
+
 ## Initialization
 
+For a standard unsaturated start, the machine initializes
+$E_{\mathrm{fd},0}$ and $I_{\mathrm{fd},0}$ first. ESST4B reads those values,
+sets all internal derivatives to zero, and evaluates:
+
 ```math
 \begin{aligned}
+  V_{C,0} &= V_{\mathrm{comp},0} \\
+  V_{\mathrm{src},0}^{\mathrm{r}}
+    &= K_P V_{\mathrm{r},0}
+       - X_L K_P^{\mathrm{i}} I_{\mathrm{r},0}
+       - \left(K_I + X_L K_P^{\mathrm{r}}\right)I_{\mathrm{i},0} \\
+  V_{\mathrm{src},0}^{\mathrm{i}}
+    &= K_P V_{\mathrm{i},0}
+       + \left(K_I + X_L K_P^{\mathrm{r}}\right)I_{\mathrm{r},0}
+       - X_L K_P^{\mathrm{i}} I_{\mathrm{i},0} \\
+  V_{E,0} &=
+    \sqrt{
+      \left(V_{\mathrm{src},0}^{\mathrm{r}}\right)^2
+      + \left(V_{\mathrm{src},0}^{\mathrm{i}}\right)^2
+    } \\
+  0 &= -V_{E,0}I_{N,0} + K_C I_{\mathrm{fd},0} \\
+  F_{\mathrm{ex},0} &= f(I_{N,0}) \\
+  V_{B,0} &= \text{min}(V_{E,0}F_{\mathrm{ex},0}, V_B^{\max}) \\
+  V_{\mathrm{lv},0} &= \dfrac{E_{\mathrm{fd},0}}{V_{B,0}} \\
+  V_{M,0} &= V_{\mathrm{lv},0} \\
+  V_{G,0} &= \text{min}(K_G E_{\mathrm{fd},0}, V_G^{\max}) \\
+  e_{M,0} &= 0 \\
+  V_{A,0} &= V_{G,0} \\
+  V_{R,0} &= V_{A,0} \\
+  x_{R,0} &= V_{R,0} \\
+  e_{V,0} &= 0 \\
+  V_{\mathrm{ref},0} &= V_{C,0} - V_{\mathrm{uel},0} - V_{S,0}
 \end{aligned}
 ```
 
+This closed-form start requires $V_{E,0}\ne 0$, $V_{B,0}\ne 0$, inactive
+$V_R$, $V_M$, $V_G$, and $V_B$ limits, and the low-value gate selecting $V_M$.
+Starts with active low-value gate limiting or saturated PI states are outside
+these closed-form equations.
+
 ## Model Outputs
+
+Output          | Units  | Description                         | Note
+----------------|--------|-------------------------------------|------
+`efd`           | [p.u.] | Field-voltage output                | $E_{\mathrm{fd}}$
+`vm`            | [p.u.] | Inner regulator output              | $V_M$
+`vc`            | [p.u.] | Sensed compensated voltage          | $V_C$
+`va`            | [p.u.] | Lagged outer-regulator output       | $V_A$
+`vr`            | [p.u.] | Outer regulator output              | $V_R$
+`vg`            | [p.u.] | Exciter-output feedback signal      | $V_G$
+`vlv`           | [p.u.] | Low-value gate output               | $V_{\mathrm{lv}}$
+`ve`            | [p.u.] | Potential-source voltage magnitude  | $V_E$
+`vb`            | [p.u.] | Rectifier source multiplier         | $V_B$
+`in`            | [p.u.] | Normalized exciter loading current  | $I_N$
+`fex`           | [p.u.] | Rectifier loading factor            | $F_{\mathrm{ex}}$