Effective saturation parameter

Author: lukelowry

GridKit/Model/PhasorDynamics/Exciter/ESDC1A/Esdc1a.hpp

@@ -38,7 +38,7 @@ namespace GridKit
         EV,      ///< \f$e_V\f$ Algebraic voltage-error summing output [p.u.]
         VLL,     ///< \f$V_{\mathrm{LL}}\f$ Algebraic input lead-lag output [p.u.]
         VHV,     ///< \f$V_{\mathrm{HV}}\f$ Algebraic high-value gate output [p.u.]
-        SE,      ///< \f$E_{\mathrm{fd}}'S_E(E_{\mathrm{fd}}')\f$ Scaled-quadratic saturation contribution [p.u.]
+        SE,      ///< \f$s_e\f$ Scaled-quadratic saturation contribution [p.u.]
         VFE,     ///< \f$V_{\mathrm{FE}}\f$ Algebraic exciter feedback drive [p.u.]
         EFD,     ///< \f$E_{\mathrm{fd}}\f$ Algebraic field-voltage output [p.u.]
         MAXIMUM, ///< Number of ESDC1A internal variables
@@ -166,6 +166,7 @@ namespace GridKit
         RealT lim_on_{1};
         RealT SA_{0};
         RealT SB_{0};
+        RealT Ke_eff_{Ke_};
 
         IdxT parameter_error_count_{0};
 

GridKit/Model/PhasorDynamics/Exciter/ESDC1A/Esdc1aData.hpp

@@ -69,7 +69,7 @@ namespace GridKit
         vc,  ///< \f$V_C\f$ Filtered terminal-voltage magnitude [p.u.]
         vr,  ///< \f$V_R\f$ Voltage-regulator output [p.u.]
         vf,  ///< \f$V_F\f$ Stabilizing feedback state [p.u.]
-        se,  ///< \f$E_{\mathrm{fd}}'S_E(E_{\mathrm{fd}}')\f$ Scaled-quadratic saturation contribution [p.u.]
+        se,  ///< \f$s_e\f$ Scaled-quadratic saturation contribution [p.u.]
         vfe  ///< \f$V_{\mathrm{FE}}\f$ Exciter feedback drive [p.u.]
       };
 

GridKit/Model/PhasorDynamics/Exciter/ESDC1A/Esdc1aImpl.hpp

@@ -351,7 +351,7 @@ namespace GridKit
         const ScalarT xll0  = ev0;
         const ScalarT vref0 = ev0 + vc0 - vs0 - uel_on_ * vuel0;
 
-        Ke_ = ke0;
+        Ke_eff_ = ke0;
 
         y[EFDP] = efdp0;
         y[VC]   = vc0;
@@ -564,7 +564,7 @@ namespace GridKit
 
         const ScalarT ec                = std::sqrt(wb[0] * wb[0] + wb[1] * wb[1]);
         const ScalarT ev_target         = vref + vs + uel_on_ * vuel - vc - vf;
-        const ScalarT vfe_target        = Ke_ * efdp + se;
+        const ScalarT vfe_target        = Ke_eff_ * efdp + se;
         const ScalarT efdp_rate         = (vr - vfe) / Te_;
         const ScalarT limited_efdp_rate = awmin(efdp, efdp_rate, ZERO<RealT>);
 
@@ -762,6 +762,8 @@ namespace GridKit
       template <typename scalar_type, typename index_type>
       void Esdc1a<scalar_type, index_type>::setDerivedParameters()
       {
+        Ke_eff_ = Ke_;
+
         // The lags are raised to the floor in place, so a negative value is
         // rejected here while the value as read is still available. verify()
         // reports the count.

GridKit/Model/PhasorDynamics/Exciter/ESDC1A/README.md

@@ -166,7 +166,7 @@ Symbol                              | Units  | Description
 $e_V$                               | [p.u.] | Voltage-error summing output      |
 $V_{\mathrm{LL}}$                   | [p.u.] | Input lead-lag output             |
 $V_{\mathrm{HV}}$                   | [p.u.] | High-value gate output            |
-$E_{\mathrm{fd}}'S_E(E_{\mathrm{fd}}')$ | [p.u.] | Scaled-quadratic saturation contribution |
+$s_e$                               | [p.u.] | Scaled-quadratic saturation contribution | $E_{\mathrm{fd}}'S_E(E_{\mathrm{fd}}')$
 $V_{\mathrm{FE}}$                   | [p.u.] | Exciter feedback drive            |
 $E_{\mathrm{fd}}$                   | [p.u.] | Field-voltage output              | Published through `efd`
 
@@ -263,12 +263,12 @@ of [Appendix A](#appendix-a-awmin).
           & s_{\mathrm{UEL}} = 1
       \end{cases} \\
   0 &=
-    -E_{\mathrm{fd}}'S_E(E_{\mathrm{fd}}')
+    -s_e
     + S_B q\left(E_{\mathrm{fd}}' - S_A\right) \\
   0 &=
     -V_{\mathrm{FE}}
-    + K_E E_{\mathrm{fd}}'
-    + E_{\mathrm{fd}}'S_E(E_{\mathrm{fd}}') \\
+    + K_E^{\mathrm{eff}} E_{\mathrm{fd}}'
+    + s_e \\
   0 &=
     -E_{\mathrm{fd}}
     + \left(1 + s_{\mathrm{spd}}\omega\right)E_{\mathrm{fd}}'
@@ -315,17 +315,16 @@ routed through the gate:
   E_{\mathrm{fd}}'
     &\leftarrow
       \dfrac{E_{\mathrm{fd}}}{1 + s_{\mathrm{spd}}\omega} \\
-  E_{\mathrm{fd}}'S_E(E_{\mathrm{fd}}')
+  s_e
     &\leftarrow S_B q\left(E_{\mathrm{fd}}' - S_A\right) \\
-  K_E
+  K_E^{\mathrm{eff}}
     &\leftarrow
       \begin{cases}
-        \dfrac{V_R^{\max}/10-E_{\mathrm{fd}}'S_E(E_{\mathrm{fd}}')}{E_{\mathrm{fd}}'} & K_E=0 \\
+        \dfrac{V_R^{\max}/10-s_e}{E_{\mathrm{fd}}'} & K_E=0 \\
         K_E & K_E\ne 0
       \end{cases} \\
   V_{\mathrm{FE}}
-    &\leftarrow K_E E_{\mathrm{fd}}'
-      + E_{\mathrm{fd}}'S_E(E_{\mathrm{fd}}') \\
+    &\leftarrow K_E^{\mathrm{eff}} E_{\mathrm{fd}}' + s_e \\
   V_R
     &\leftarrow V_{\mathrm{FE}} \\
   V_{\mathrm{HV}}
@@ -386,7 +385,7 @@ Output          | Units  | Description                         | Note
 `vc`            | [p.u.] | Filtered terminal-voltage magnitude | $V_C$
 `vr`            | [p.u.] | Voltage-regulator output            | $V_R$
 `vf`            | [p.u.] | Stabilizing feedback state          | $V_F$
-`se`            | [p.u.] | Scaled-quadratic saturation contribution | $E_{\mathrm{fd}}'S_E(E_{\mathrm{fd}}')$
+`se`            | [p.u.] | Scaled-quadratic saturation contribution | $s_e$
 `vfe`           | [p.u.] | Exciter feedback drive              | $V_{\mathrm{FE}}$
 
 ## Testing

GridKit/Model/PhasorDynamics/Exciter/IEEET1/Ieeet1.hpp

@@ -146,6 +146,8 @@ namespace GridKit
         RealT Ispdlim_{0.0}; ///< Speed limit flag indicator
 
         // Model Derived parameters
+        RealT Ke_eff_{Ke_};
+
         // Saturation coefficients derived from E1, E2, Se1, and Se2.
         RealT SA_{0};
         RealT SB_{0};

GridKit/Model/PhasorDynamics/Exciter/IEEET1/Ieeet1Impl.hpp

@@ -233,13 +233,14 @@ namespace GridKit
 
         ScalarT efdp = efd0 / (ONE<RealT> + omega * Ispdlim_);
         ScalarT ksat = SB_ * Math::qramp(efdp - SA_);
+        Ke_eff_      = Ke_;
         if (Ke_ == ZERO<RealT>)
         {
-          Ke_ = (Vrmax_ / 10.0 - static_cast<RealT>(ksat)) / static_cast<RealT>(efdp);
+          Ke_eff_ = (Vrmax_ / 10.0 - static_cast<RealT>(ksat)) / static_cast<RealT>(efdp);
         }
 
         ScalarT ve  = ksat;
-        ScalarT vr  = Ke_ * efdp + ve;
+        ScalarT vr  = Ke_eff_ * efdp + ve;
         ScalarT vtr = vr / Ka_;
         ScalarT vf{0};
         ScalarT vfx = (Kf_ / Tf_) * efdp;
@@ -351,7 +352,7 @@ namespace GridKit
         // Internal Differential Equations
         f[0] = -vts_dot + (Ec - vts) / Tr_;
         f[1] = -vr_dot + Math::antiwindup(vr, func, Vrmin_, Vrmax_);
-        f[2] = -efdp_dot + (vr - ve - Ke_ * efdp) / Te_;
+        f[2] = -efdp_dot + (vr - ve - Ke_eff_ * efdp) / Te_;
         f[3] = -vfx_dot + vf / Tf_;
 
         // Internal Algebraic Equations
@@ -467,6 +468,8 @@ namespace GridKit
           Ispdlim_ = std::get<RealT>(data.parameters.at(Parameter::Ispdlim));
         }
 
+        Ke_eff_ = Ke_;
+
         Tr_ = std::max(Tr_, TIME_CONSTANT_MINIMUM);
         Ta_ = std::max(Ta_, TIME_CONSTANT_MINIMUM);
         Te_ = std::max(Te_, TIME_CONSTANT_MINIMUM);

GridKit/Model/PhasorDynamics/Exciter/IEEET1/README.md

@@ -161,7 +161,7 @@ The IEEET1 differential equations, as derived from the model diagram, are:
    0 &= -\dot V_R
       + \text{antiwindup}
         \left(V_R, f_R; V_R^{\min}, V_R^{\max}\right) \\
-   0 &= -\dot E_{fd}' + \dfrac{1}{T_E}\left(V_R - V_E - K_E E_{fd}'\right) \\
+   0 &= -\dot E_{fd}' + \dfrac{1}{T_E}\left(V_R - V_E - K_E^{\mathrm{eff}} E_{fd}'\right) \\
    0 &= -\dot V_{fx} + \dfrac{1}{T_F}\left(V_f\right)
 \end{aligned}
 ```
@@ -201,13 +201,13 @@ with the current input values.
    E_{C,0}  &:= \sqrt{V_r^2 + V_i^2} \\
    E_{fd}'  &= \dfrac{E_{fd,0}}{1 + I_{\mathrm{spdlim}}\,\omega} \\
    k_\text{sat}  &= S_B\, q(E_{fd}' - S_A) \\
-   K_E &\leftarrow
+   K_E^{\mathrm{eff}} &\leftarrow
       \begin{cases}
         \dfrac{V_R^{\max}/10-k_\text{sat}}{E_{fd}'} & K_E=0 \\
         K_E & K_E\ne 0
       \end{cases} \\
    V_E      &= k_\text{sat} \\
-   V_R      &= K_E\, E_{fd}' + V_E \\
+   V_R      &= K_E^{\mathrm{eff}} E_{fd}' + V_E \\
    V_{tr}   &= \dfrac{V_R}{K_A} \\
    V_{fx}   &= \dfrac{K_F}{T_F}\, E_{fd}' \\
    V_{ts}   &= E_{C,0} \\

GridKit/Model/PhasorDynamics/Governor/Tgov1/README.md

@@ -102,7 +102,7 @@ The TGOV1 differential equations, as derived from the model diagram, are
 \end{aligned}
 ```
 
-CommonMath defines the [anti-windup](../../../../CommonMath.md#antiwindup)
+CommonMath defines the [Antiwindup](../../../../CommonMath.md#antiwindup)
 target and smooth approximation.
 
 ### Algebraic Equations