SEXS-PTI

Source: GridKit/Model/PhasorDynamics/Exciter/SEXS-PTI/README.md

Simplified Excitation System Model (SEXS-PTI)

Block Diagram

Simplified excitation system model.

Figure 1: Exciter SEXS-PTI model. Figure courtesy of PowerWorld

Model Parameters

Symbol	Units	Description	Typical Value	Note
\(T_A\)	[sec]	Numerator time constant of lag-lead block
\(T_B\)	[sec]	Denominator time constant of lag-lead block
\(T_E\)	[sec]	Exciter field time constant
\(K\)	[p.u.]	Voltage regulator gain
\(E_{fd}^{\max}\)	[p.u.]	Maximum excitation output
\(E_{fd}^{\min}\)	[p.u.]	Minimum excitation output

PowerWorld/PSS/E SEXS_PTI data often gives \(T_A/T_B\) as a ratio. GridKit stores \(T_A\) and \(T_B\) separately, so convert ratio-format data with \(T_A = (T_A/T_B)T_B\) before passing parameters to the model.

Model Variables

Internal Variables

Differential

Symbol	Units	Description	Note
\(V_R\)	[p.u.]	Lag-lead block state
\(E_{fd}\)	[p.u.]	Exciter field voltage output

Algebraic

Symbol	Units	Description	Note
\(V_{tr}\)	[p.u.]	Terminal voltage error signal

External Variables

Differential

None.

Algebraic

Symbol	Units	Description	Note
\(E_C\)	[p.u.]	Compensated machine terminal voltage magnitude	Computed from bus voltage
\(V_{ref}\)	[p.u.]	Reference voltage	Set during initialization
\(V_S\)	[p.u.]	Stabilizer output	Optional, defaults to zero
\(V_{OEL}\)	[p.u.]	Over-excitation limiter signal	Constant zero until modeled
\(V_{UEL}\)	[p.u.]	Under-excitation limiter signal	Constant zero until modeled

Model Equations

Differential Equations

The SEXS-PTI differential equations, as derived from the model diagram. Define the pre-limit derivative of \(E_{fd}\)

\[f = \dfrac{1}{T_E}\left[-E_{fd} + \dfrac{K}{T_B}(-V_R + T_A V_{tr})\right]\]

so that \(\dot E_{fd}\) can be written in piecewise form compactly.

\[\begin{split}\begin{aligned} \dot V_R &= -V_{tr} + \dfrac{1}{T_B}(-V_R + T_A V_{tr}) \\ \dot E_{fd} &= \begin{cases} f & \text{if } (E_{fd}^{\min} < E_{fd} < E_{fd}^{\max}) & \lor \\ & \quad (E_{fd} \leq E_{fd}^{\min} \land f > 0) & \lor \\ & \quad (E_{fd} \geq E_{fd}^{\max} \land f < 0) \\ 0 & \text{else} \end{cases} \end{aligned}\end{split}\]

In simulation the piecewise form above is replaced with a smooth approximation where \(\phi\) is GridKit’s smooth anti-windup indicator. See CommonMath: Anti-Windup Indicator for its definition, behavior, and design rationale.

Algebraic Equations

\[\begin{aligned} 0&=-V_{tr}-E_C+V_{ref}+V_S+V_{OEL}+V_{UEL} \end{aligned}\]

Initialization

The generator initializes the EFD signal first. SEXS-PTI then reads that value as \(E_{fd,0}\) and assumes steady state with \(V_S=V_{OEL}=V_{UEL}=0\):

\[\begin{split}\begin{aligned} E_C &= \sqrt{V_r^2+V_i^2} \\ V_{tr,0} &= \dfrac{E_{fd,0}}{K} \\ V_{R,0} &= (T_A - T_B)V_{tr,0} \\ V_{ref} &= E_C + V_{tr,0} \end{aligned}\end{split}\]

All derivatives initialize to zero.