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.

Figure 1: Exciter SCRX model. Figure courtesy of PowerWorld

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.

\[\begin{split}\begin{aligned} &T_A \ge 0,\quad T_B \ge 0,\quad T_E \ge 0 \\ &T_B > 0\quad\text{or}\quad(T_B = 0\ \text{and}\ T_A = 0) \\ &E_{\mathrm{fd}}^{\min} \le E_{\mathrm{fd}}^{\max} \\ &C_{\mathrm{sw}} \in \{0,1\} \end{aligned}\end{split}\]

Model Derived Parameters

The source multiplier is:

\[\begin{aligned} M_{\mathrm{src}} &= (1 - C_{\mathrm{sw}})E_T + C_{\mathrm{sw}} \end{aligned}\]

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

\[\begin{split}\begin{aligned} 0 &= -T_B\dot x_{\mathrm{ll}} - x_{\mathrm{ll}} + e_V \\ 0 &= -T_E\dot E_{\mathrm{fd}}' + \text{antiwindup}\!\left( E_{\mathrm{fd}}', -E_{\mathrm{fd}}' + K V_{\mathrm{ll}}, E_{\mathrm{fd}}^{\min}, E_{\mathrm{fd}}^{\max} \right) \end{aligned}\end{split}\]

CommonMath defines the Anti-Windup target and smooth approximation.

Algebraic Equations

\[\begin{split}\begin{aligned} 0 &= -e_V + V_{\mathrm{ref}} + V_{\mathrm{uel}} + V_S + V_{\mathrm{oel}} - E_C \\ 0 &= -T_B(V_{\mathrm{ll}} - x_{\mathrm{ll}}) + T_A(e_V - x_{\mathrm{ll}}) \\ 0 &= -M_{\mathrm{src}} + (1 - C_{\mathrm{sw}})E_T + C_{\mathrm{sw}} \\ 0 &= -E_{\mathrm{fd}} + M_{\mathrm{src}}E_{\mathrm{fd}}' \end{aligned}\end{split}\]

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:

\[\begin{split}\begin{aligned} M_{\mathrm{src},0} &= (1 - C_{\mathrm{sw}})E_{T,0} + C_{\mathrm{sw}} \\ E_{\mathrm{fd},0}' &= \dfrac{E_{\mathrm{fd},0}}{M_{\mathrm{src},0}} \\ V_{\mathrm{ll},0} &= \dfrac{E_{\mathrm{fd},0}'}{K} \\ x_{\mathrm{ll},0} &= e_{V,0} = V_{\mathrm{ll},0} \\ V_{\mathrm{ref},0} &= e_{V,0} + E_{C,0} - V_{\mathrm{uel},0} - V_{S,0} - V_{\mathrm{oel},0} \end{aligned}\end{split}\]

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	\(M_{\mathrm{src}}\)