From 3e66e3b7b8ccc8b16187e02d7f3062d800fd4ac1 Mon Sep 17 00:00:00 2001
From: lukelowry <wyattluke.lowery@gmail.com>
Date: Sun, 31 May 2026 22:29:54 -0500
Subject: [PATCH 1/2] Add ESAC6A exciter documentation stub

---
 .../PhasorDynamics/Exciter/ESAC6A/README.md   |  72 ++++++++++++++++++
 .../Model/PhasorDynamics/Exciter/README.md    |   1 +
 .../Figures/PhasorDynamics/ESAC6A_diagram.png | Bin 0 -> 48428 bytes
 3 files changed, 73 insertions(+)
 create mode 100644 GridKit/Model/PhasorDynamics/Exciter/ESAC6A/README.md
 create mode 100644 docs/Figures/PhasorDynamics/ESAC6A_diagram.png

diff --git a/GridKit/Model/PhasorDynamics/Exciter/ESAC6A/README.md b/GridKit/Model/PhasorDynamics/Exciter/ESAC6A/README.md
new file mode 100644
index 000000000..b8f5f2f81
--- /dev/null
+++ b/GridKit/Model/PhasorDynamics/Exciter/ESAC6A/README.md
@@ -0,0 +1,72 @@
+# **Exciter Model (ESAC6A)**
+
+> [!NOTE]
+> This README is a documentation stub/template for the ESAC6A 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 ESAC6A Exciter.
+
+<div align="center">
+   <img align="center" src="../../../../../docs/Figures/PhasorDynamics/ESAC6A_diagram.png">
+
+  Figure 1: Exciter ESAC6A 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..92eb10404 100644
--- a/GridKit/Model/PhasorDynamics/Exciter/README.md
+++ b/GridKit/Model/PhasorDynamics/Exciter/README.md
@@ -12,6 +12,7 @@ device internal voltage.
 
 ## Types
 There are a few standard Exciter models
+- ESAC6A Excitation Model (See [ESAC6A](ESAC6A/README.md))
 - IEEE Type 1 Excitation Model (See [IEEET1](IEEET1/README.md))
 - IEEE DC1 Excitation Model (See [EXDC1](EXDC1/README.md))
 - Simplified Excitation System Model (See [SEXS-PTI](SEXS-PTI/README.md))
diff --git a/docs/Figures/PhasorDynamics/ESAC6A_diagram.png b/docs/Figures/PhasorDynamics/ESAC6A_diagram.png
new file mode 100644
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From dad1ecdd3ab3f44ee0720a8c2f52c278d913b5b2 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 ESAC6A README [skip ci]

---
 .../PhasorDynamics/Exciter/ESAC6A/README.md   | 193 ++++++++++++++++--
 1 file changed, 179 insertions(+), 14 deletions(-)

diff --git a/GridKit/Model/PhasorDynamics/Exciter/ESAC6A/README.md b/GridKit/Model/PhasorDynamics/Exciter/ESAC6A/README.md
index b8f5f2f81..c2b556cd7 100644
--- a/GridKit/Model/PhasorDynamics/Exciter/ESAC6A/README.md
+++ b/GridKit/Model/PhasorDynamics/Exciter/ESAC6A/README.md
@@ -1,7 +1,16 @@
-# **Exciter Model (ESAC6A)**
+# **IEEE Type AC6A Excitation System Model (ESAC6A)**
 
-> [!NOTE]
-> This README is a documentation stub/template for the ESAC6A exciter. Parameters, variables, equations, initialization details, and outputs are intentionally left unfilled until the model is derived from its source documentation.
+ESAC6A is an IEEE Type AC excitation system with sensed terminal-voltage
+feedback, cascaded regulator lead-lag blocks, voltage-regulator limits, an
+exciter alternator state, field-current feedback limiting, 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 ESAC6A Exciter.
 <div align="center">
    <img align="center" src="../../../../../docs/Figures/PhasorDynamics/ESAC6A_diagram.png">
 
-  Figure 1: Exciter ESAC6A model.
+  Figure 1: Exciter ESAC6A 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
+$K_A$                               | [p.u.]   | `Ka`      | Voltage-regulator gain                                  | 40.0          | Block name: `Ka`
+$T_A$                               | [sec]    | `Ta`      | Regulator denominator time constant                     | 0.1           | Block name: `Ta`
+$T_K$                               | [sec]    | `Tk`      | Regulator numerator time constant                       | 0.0           | Block name: `Tk`
+$T_B$                               | [sec]    | `Tb`      | Lag time constant for second lead-lag block             | 0.0           | Block name: `Tb`
+$T_C$                               | [sec]    | `Tc`      | Lead time constant for second lead-lag block            | 0.0           | Block name: `Tc`
+$V_A^{\max}$                        | [p.u.]   | `VaMax`   | Maximum first regulator block output                    | 1.0           | Block name: `VAMAX`
+$V_A^{\min}$                        | [p.u.]   | `VaMin`   | Minimum first regulator block output                    | -1.0          | Block name: `VAMIN`
+$V_R^{\max}$                        | [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`
+$V_{\mathrm{fe}}^{\mathrm{lim}}$    | [p.u.]   | `Vfelim`  | Feedback-limiter summing-junction reference             | 0.0           | Source label: `VFELIM`
+$K_H$                               | [p.u.]   | `Kh`      | Feedback-limiter gain                                   | 1.0           | Block name: `KH`
+$V_H^{\max}$                        | [p.u.]   | `Vhmax`   | Maximum feedback-limiter lead-lag output                | 1.0           | Block name: `VHMAX`; lower limit is zero
+$T_H$                               | [sec]    | `Th`      | Feedback-limiter denominator time constant              | 0.0           | Block name: `TH`
+$T_J$                               | [sec]    | `Tj`      | Feedback-limiter numerator time constant                | 0.0           | Block name: `TJ`
+$K_C$                               | [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`
+$E_1$                               | [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 ESAC6A parameter sets are rejected by the following checks.
+
+```math
+\begin{aligned}
+  &K_A > 0 \\
+  &T_R \ge 0,\quad T_A > 0,\quad T_K \ge 0,\quad T_B \ge 0,\quad T_C \ge 0,\quad T_E > 0 \\
+  &T_H \ge 0,\quad T_J \ge 0 \\
+  &T_B > 0\quad\text{or}\quad(T_B = 0\ \text{and}\ T_C = 0) \\
+  &T_H > 0\quad\text{or}\quad(T_H = 0\ \text{and}\ T_J = 0) \\
+  &V_A^{\min} \le V_A^{\max},\quad V_R^{\min} \le V_R^{\max},\quad V_H^{\max} \ge 0 \\
+  &s_{\mathrm{spd}} \in \{0,1\}
+\end{aligned}
+```
+
+The saturation points are either disabled together or define a valid positive
+two-point 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 $T_R=0$
+$x_A$                               | [p.u.] | First regulator lead-lag denominator state              | State 3 in Fig. 1; source label: `TA Block`
+$x_{\mathrm{ll}}$                   | [p.u.] | Second lead-lag denominator state                       | State 4 in Fig. 1; source label: `VLL`
+$V_F$                               | [p.u.] | Stabilizing feedback signal                             | State 5 in Fig. 1; source label: `VF`
 
 #### Algebraic
 
-Symbol | Units | Description | Note
--------|-------|-------------|-----
+Symbol                              | Units  | Description                                             | Note
+------------------------------------|--------|---------------------------------------------------------|------
+$e_V$                               | [p.u.] | Voltage-regulator input error before first lead-lag     | Summing junction after sensed voltage
+$V_A$                               | [p.u.] | Limited first regulator lead-lag output                 | Limited by $V_A^{\min}$ and $V_A^{\max}$
+$V_{\mathrm{ll}}$                   | [p.u.] | Second lead-lag output                                  | Input to $V_R$ summing junction
+$V_H$                               | [p.u.] | Feedback-limiter lead-lag output before $K_H$           | Limited by 0 and $V_H^{\max}$
+$V_H^{\mathrm{pre}}$                | [p.u.] | Feedback-limiter lead-lag output before limits          | Bypasses to $V_F$ when $T_H=T_J=0$
+$V_R$                               | [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, $K_D I_{\mathrm{fd}}$, and feedback-limiter 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`
+$V_{\mathrm{uel}}$                  | [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
+$I_{\mathrm{fd}}$                   | [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
 
@@ -52,6 +136,11 @@ Symbol | Units | Description | Note
 
 ```math
 \begin{aligned}
+  0 &= -T_R\dot V_C - V_C + E_C \\
+  0 &= -T_A\dot x_A - x_A + K_A e_V \\
+  0 &= -T_B\dot x_{\mathrm{ll}} - x_{\mathrm{ll}} + V_A \\
+  0 &= -T_E\dot V_E + V_R - V_{\mathrm{fe}} \\
+  0 &= -T_H\dot V_F - V_F + V_{\mathrm{fe}}
 \end{aligned}
 ```
 
@@ -59,14 +148,90 @@ Symbol | Units | Description | Note
 
 ```math
 \begin{aligned}
+  0 &= -e_V + V_{\mathrm{ref}} + V_{\mathrm{uel}} + V_S - V_C - V_F \\
+  0 &= -V_A
+       + \text{clamp}\!\left(
+          x_A + \dfrac{T_K}{T_A}(K_A e_V - x_A),
+          V_A^{\min},
+          V_A^{\max}
+       \right) \\
+  0 &= -T_B(V_{\mathrm{ll}} - x_{\mathrm{ll}}) + T_C(V_A - x_{\mathrm{ll}}) \\
+  0 &= -V_H^{\mathrm{pre}}
+       +
+       \begin{cases}
+         V_F, & T_H = T_J = 0 \\
+         V_F + \dfrac{T_J}{T_H}(V_{\mathrm{fe}} - V_F), & T_H > 0
+       \end{cases} \\
+  0 &= -V_H + \text{clamp}\!\left(V_H^{\mathrm{pre}}, 0, V_H^{\max}\right) \\
+  0 &= -V_R + \text{clamp}(V_{\mathrm{ll}} - K_H V_H, 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}} + V_{\mathrm{fe}}^{\mathrm{lim}} \\
+  0 &= -E_{\mathrm{fd}}
+       + \left(1+s_{\mathrm{spd}}\omega\right)F_{\mathrm{ex}}V_E
 \end{aligned}
 ```
 
+CommonMath defines helper targets for [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 second lead-lag block is bypassed. When $T_H=T_J=0$, the
+feedback-limiter lead-lag block is bypassed before the 0-to-$V_H^{\max}$ clamp.
+
 ## Initialization
 
+The machine initializes $E_{\mathrm{fd}}$ and $I_{\mathrm{fd}}$ first. For a
+standard unsaturated start, ESAC6A reads those values and sets all internal
+derivatives to zero. First solve 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:
+
+```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} + V_{\mathrm{fe}}^{\mathrm{lim}} \\
+  V_{F,0} &= V_{\mathrm{fe},0} \\
+  V_{H,0}^{\mathrm{pre}} &= V_{F,0} \\
+  V_{H,0} &= \text{clamp}(V_{H,0}^{\mathrm{pre}}, 0, V_H^{\max}) \\
+  V_{R,0} &= V_{\mathrm{fe},0} \\
+  V_{\mathrm{ll},0} &= V_{R,0} + K_H V_{H,0} \\
+  V_{A,0} &= V_{\mathrm{ll},0} \\
+  x_{A,0} &= V_{A,0} \\
+  x_{\mathrm{ll},0} &= V_{\mathrm{ll},0} \\
+  V_{C,0} &= E_{C,0} \\
+  e_{V,0} &= \dfrac{x_{A,0}}{K_A} \\
+  V_{\mathrm{ref},0} &= e_{V,0} + V_{C,0} + V_{F,0} - V_{\mathrm{uel},0} - V_{S,0}
+\end{aligned}
+```
+
+This standard start requires $1+s_{\mathrm{spd}}\omega_0\ne 0$,
+$V_{E,0}\ne 0$, inactive $V_A$, $V_R$, and $V_H$ limits, and nonsingular
+regulator gains/time constants. Starts that bind those limits 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.] | First regulator output              | $V_A$
+`vll`           | [p.u.] | Second lead-lag output              | $V_{\mathrm{ll}}$
+`vf`            | [p.u.] | Feedback-limiter state              | $V_F$
+`vh`            | [p.u.] | Feedback-limiter output             | $V_H$
+`vr`            | [p.u.] | Voltage-regulator output            | $V_R$
+`in`            | [p.u.] | Normalized exciter loading current  | $I_N$
+`fex`           | [p.u.] | Rectifier loading factor            | $F_{\mathrm{ex}}$
+`se`            | [p.u.] | Saturation coefficient              | $S_E$