# SCRX _Source: `GridKit/Model/PhasorDynamics/Exciter/SCRX/README.md`_ ## **Bus Fed or Solid Fed Static Excitation System Model (SCRX)** SCRX is a static excitation system with a voltage-error lead-lag block, a limited exciter lag, and a source selector that scales the exciter output by either terminal voltage or a constant source. Notes: - Internal voltage signals are on model base unless otherwise stated. - The source diagram shows a shared SCRX/SCRX1-style selector. In the diagram, `C_SWITCH = 0` selects the bus-fed multiplier $E_T$, and `C_SWITCH = 1` selects the solid-fed multiplier 1. - Some source material labels the lead-lag numerator input as `TA/TB`; the model equations below use explicit time constants $T_A$ and $T_B$. - `Rc_Rfd` is a source-data parameter for input compatibility, but it is not an active block in Fig. 1 and is not used by the equations below. ### Block Diagram Standard model of the SCRX Exciter. ```{image} ../../../../../Figures/PhasorDynamics/SCRX_diagram.png :align: center ``` Figure 1: Exciter SCRX model. Figure courtesy of [PowerWorld](https://www.powerworld.com/WebHelp/) ### Model Parameters Symbol | Units | JSON | Description | Typical Value | Note ------------------------------------|----------|------------|---------------------------------------------------------|---------------|------ $T_A$ | [sec] | `Ta` | Lead-lag numerator time constant | 0.0 | Source label: `TA/TB` in some SCRX source data $T_B$ | [sec] | `Tb` | Lead-lag denominator time constant | 0.0 | Block name: `TB`; if zero, the lead-lag block is algebraic $K$ | [p.u.] | `K` | Exciter gain | 1.0 | Block name: `K` $T_E$ | [sec] | `Te` | Exciter lag time constant | 0.0 | Block name: `TE`; if zero, $E_{\mathrm{fd}}'$ is algebraic $E_{\mathrm{fd}}^{\max}$ | [p.u.] | `Efdmax` | Maximum limited exciter output before source multiplier | 5.0 | Block name: `EFDMAX` $E_{\mathrm{fd}}^{\min}$ | [p.u.] | `Efdmin` | Minimum limited exciter output before source multiplier | -5.0 | Block name: `EFDMIN` $C_{\mathrm{sw}}$ | [binary] | `Cswitch` | Source multiplier selector | 0 | Source label: `C_SWITCH`; 0 = bus-fed $E_T$, 1 = solid-fed constant 1 $R_c/R_{\mathrm{fd}}$ | [p.u.] | `Rc_Rfd` | Source-data compatibility parameter | 0.0 | Not active in Fig. 1 equations #### Parameter Validation Invalid SCRX parameter sets are rejected by the following checks. ```{math} \begin{aligned} &T_A \ge 0,\quad T_B \ge 0,\quad T_E \ge 0 \\ &T_B > 0\quad\text{or}\quad(T_B = 0\ \text{and}\ T_A = 0) \\ &E_{\mathrm{fd}}^{\min} \le E_{\mathrm{fd}}^{\max} \\ &C_{\mathrm{sw}} \in \{0,1\} \end{aligned} ``` #### Model Derived Parameters The source multiplier is: ```{math} \begin{aligned} M_{\mathrm{src}} &= (1 - C_{\mathrm{sw}})E_T + C_{\mathrm{sw}} \end{aligned} ``` When $T_B=0$, the lead-lag block is treated as a bypass with $V_{\mathrm{ll}}=e_V$. ### Model Variables #### Internal Variables ##### Differential Symbol | Units | Description | Note ------------------------------------|--------|---------------------------------------------------------|------ $x_{\mathrm{ll}}$ | [p.u.] | Lead-lag block state | State 1 in Fig. 1 $E_{\mathrm{fd}}'$ | [p.u.] | Limited exciter output before source multiplier | State 2 in Fig. 1; algebraic when $T_E=0$ ##### Algebraic Symbol | Units | Description | Note ------------------------------------|--------|---------------------------------------------------------|------ $e_V$ | [p.u.] | Voltage-error signal before lead-lag block | Summing junction in Fig. 1 $V_{\mathrm{ll}}$ | [p.u.] | Lead-lag output | Drives the limited exciter lag $M_{\mathrm{src}}$ | [p.u.] | Source multiplier | $E_T$ when $C_{\mathrm{sw}}=0$, 1 when $C_{\mathrm{sw}}=1$ $E_{\mathrm{fd}}$ | [p.u.] | Field-voltage output | Output after source multiplier #### External Variables ##### Differential None. ##### Algebraic Symbol | Units | Description | Note ------------------------------------|--------|---------------------------------------------------------|------ $E_C$ | [p.u.] | Compensated terminal voltage magnitude | Source label: `EC` $E_T$ | [p.u.] | Terminal-voltage source multiplier | Source label: `ET`; used only when $C_{\mathrm{sw}}=0$ $V_{\mathrm{ref}}$ | [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 zero ### Model Equations #### Differential Equations ```{math} \begin{aligned} 0 &= -T_B\dot x_{\mathrm{ll}} - x_{\mathrm{ll}} + e_V \\ 0 &= -T_E\dot E_{\mathrm{fd}}' + \text{antiwindup}\!\left( E_{\mathrm{fd}}', -E_{\mathrm{fd}}' + K V_{\mathrm{ll}}, E_{\mathrm{fd}}^{\min}, E_{\mathrm{fd}}^{\max} \right) \end{aligned} ``` CommonMath defines the [Anti-Windup](../../../common-math.md#derived-functions) target and smooth approximation. #### Algebraic Equations ```{math} \begin{aligned} 0 &= -e_V + V_{\mathrm{ref}} + V_{\mathrm{uel}} + V_S + V_{\mathrm{oel}} - E_C \\ 0 &= -T_B(V_{\mathrm{ll}} - x_{\mathrm{ll}}) + T_A(e_V - x_{\mathrm{ll}}) \\ 0 &= -M_{\mathrm{src}} + (1 - C_{\mathrm{sw}})E_T + C_{\mathrm{sw}} \\ 0 &= -E_{\mathrm{fd}} + M_{\mathrm{src}}E_{\mathrm{fd}}' \end{aligned} ``` When $T_B=0$, SCRX bypasses the lead-lag block so $V_{\mathrm{ll}}=e_V$. ### Initialization The machine initializes $E_{\mathrm{fd}}$ first. For a standard unsaturated start, SCRX reads that value along with $E_C$, $E_T$, and any attached limiter or stabilizer inputs, sets all internal derivatives to zero, and evaluates: ```{math} \begin{aligned} M_{\mathrm{src},0} &= (1 - C_{\mathrm{sw}})E_{T,0} + C_{\mathrm{sw}} \\ E_{\mathrm{fd},0}' &= \dfrac{E_{\mathrm{fd},0}}{M_{\mathrm{src},0}} \\ V_{\mathrm{ll},0} &= \dfrac{E_{\mathrm{fd},0}'}{K} \\ x_{\mathrm{ll},0} &= e_{V,0} = V_{\mathrm{ll},0} \\ V_{\mathrm{ref},0} &= e_{V,0} + E_{C,0} - V_{\mathrm{uel},0} - V_{S,0} - V_{\mathrm{oel},0} \end{aligned} ``` This closed-form start requires $M_{\mathrm{src},0}\ne 0$, $K\ne 0$, and $E_{\mathrm{fd}}^{\min}\le E_{\mathrm{fd},0}'\le E_{\mathrm{fd}}^{\max}$. Starts that bind the exciter limit are outside these closed-form equations. ### Model Outputs Output | Units | Description | Note ----------------|--------|-------------------------------------|------ `efd` | [p.u.] | Field-voltage output | $E_{\mathrm{fd}}$ `efd_pre` | [p.u.] | Limited exciter output before source multiplier | $E_{\mathrm{fd}}'$ `vll` | [p.u.] | Lead-lag output | $V_{\mathrm{ll}}$ `msrc` | [p.u.] | Source multiplier | $M_{\mathrm{src}}$