EXDC1

Source: GridKit/Model/PhasorDynamics/Exciter/EXDC1/README.md

[!NOTE]
This documentation is not in the standard format and EXDC1 is not scheduled to be developed as of 06/26/2025.

../../../../../_images/EXDC1.JPG

Figure 1: Exciter EXDC1 model. Figure courtesy of PoweWorld.

Nomenclature

Inputs

  • \(V_{REF}\) - voltage reference set point

  • \(E_{C}\) - output from the terminal voltage transducer

  • \(V_{S}\) - power system stabilizer output signal (if present)

  • \(V_{UEL}\) and \(V_{OEL}\) - limiters

Differential Variables

  • \(V_{t}\) - terminal voltage (2 is sensed \(V_{t}\))

  • \(V_{B}\) - input to a voltage regulator (3)

  • \(V_{R}\) - voltage regulator output also know as exciter field voltage (4)

  • \(V_{F}\) - stabilizing feedback signal (5)

Parameters

  • \(T_{R}\) - filter time constant, sec (0)

  • \(K_{A}\) - voltage regulator gain (40)

  • \(T_{A}\) - time constant, sec (0.1)

  • \(T_{B}\) - lag time constant, sec (0)

  • \(T_{C}\) - lead time constant, sec (0)

  • \(V_{RMAX}\) - maximum control element output, pu (1)

  • \(V_{RMIN}\) - minimum control element output, pu (-1)

  • \(K_{E}\) - exciter field resistance line slope margine, pu (0.1)

  • \(T_{E}\) - exciter time constant, sec (0.5)

  • \(K_{F}\) - rate feedback gain, pu (0.05)

  • \(T_{F1}\) - rate feedback time constant, sec (0.7)

  • \(E1\) - field voltage value, 1 (2.8)

  • \(SE1\) - saturation factor at E1, (3.7)

  • \(E2\) - field voltage value, 2 (3.7)

  • \(SE2\) - saturation factor at E2, (0.33)

Equations

First block

\[\dfrac{dV_{t}}{dt}=\dfrac{1}{T_{R}}(E_{C}-V_{t})\]

Second block

\[\dfrac{dx_{1}}{dt}=\dfrac{1}{T_{B}}((V_{REF}-V_{t}-V_{F}+V_{S}+V_{UEL}+V_{OEL})-V_{B})\]
\[V_{B}=x_{1}+\dfrac{T_{C}}{T_{B}}(V_{REF}-V_{t}-V_{F}+V_{S}+V_{UEL}+V_{OEL})\]

Third block

\[\begin{split}\dfrac{dV_{R}}{dt} = \begin{cases} \dfrac{1}{T_{A}}(K_{A}V_{B}-V_{R}) &\text{if } V_{RMIN}<=V_{R}<= V_{RMAX}\\ 0 &\text{if } V_{B}>0 \text{ and } V_{R}>=V_{RMAX} &\text{ also then } V_{R}=V_{RMAX}\\ 0 &\text{if } V_{B}<0 \text{ and } V_{R}<=V_{RMIN} &\text{ also then } V_{R}=V_{RMIN}\\ \end{cases}\end{split}\]

Fourth block

\[\dfrac{d\dfrac{E_{FD}}{\omega}}{dt}=\dfrac{1}{T_{E}}(V_{R}-\dfrac{(K_{E}+S_{E})E_{FD}}{\omega})\]

Feedback loop

\[\dfrac{dx_{2}}{dt}=-\dfrac{V_{F}}{T_{F1}}\]
\[V_{F}=x_{2}+\dfrac{K_{F}}{T_{F1}}\dfrac{E_{FD}}{\omega}\]

Saturation is modeled using an alternative quadratic function, with the value of Se specified at two points :

\[\begin{split}Sat(x) = \begin{cases} \dfrac{B(x-A)^2}{x} &\text{if } x>A \\ 0 &\text{if } x<=A \end{cases}\end{split}\]

same as with the synchronous machines. There are two solutions, and one where \(A<1\) should be chosen.

Initialization

\[V_{t}=V_{t_{0}}\]
\[E_{C}=V_{t_{0}}\]
\[(V_{REF}-V_{t}-V_{F}+V_{S}+V_{UEL}+V_{OEL})=V_{B}\]
\[V_{R}=V{R_{0}}\]
\[V_{B}=\dfrac{V{R_{0}}}{K_{A}}\]
\[\dfrac{E_{FD}}{\omega}=\dfrac{E_{FD_{0}}}{\omega}\]
\[V_{R}-\dfrac{(K_{E}+S_{E})E_{FD}}{\omega}=0\]
\[V_{F}=0\]
\[x_{2_{0}}=-\dfrac{K_{F}}{T_{F1}}\dfrac{E_{FD}}{\omega}\]