PSS1A

Source: GridKit/Model/PhasorDynamics/Stabilizer/PSS1A/README.md

[!NOTE] This is not yet implemented

[!NOTE] The Parameters, variables, and equations need to be formatted and verified - this is WIP.

../../../../../_images/PSS1A.JPG

Figure 1: Power system stabilizer PSS1A model. Figure courtesy of PowerWorld

Model Parameters

  • \(I_{cs}\) - stabilizer input code, (2)

  • \(A_{1}\) - notch filter parameters, (0)

  • \(A_{2}\) - notch filter parameters, (0)

  • \(T_{1}\) - lead/lag time constant, sec (0.25)

  • \(T_{2}\) - lead/lag time constant, sec (0.03)

  • \(T_{3}\) - lead/lag time constant, sec (0.25)

  • \(T_{4}\) - lead/lag time constant, sec (0.03)

  • \(T_{5}\) - washout numerator time constant, sec (20)

  • \(T_{6}\) - washout denomirator time constant/transducer time constant, sec (0.02)

  • \(K_{S}\) - stabilizer gains, (10)

  • \(L_{smax}\) - maximum stabilizer output, pu (0.1)

  • \(L_{smin}\) - minimum stabilizer output, pu (-0.1)

  • \(V_{cu}\) - stabilizer input cutoff threshold, pu (0)

  • \(V_{cl}\) - stabilizer input cutoff threshold, pu (0)

Model Variables

These were the variables listed in the old documentation.

  1. rotor speed deviation (p.u.)

  2. bus frequency deviation (p.u.) - default

  3. generator electrical power in Gen MVA Base (p.u.)

  4. generator accelerating power (p.u.)

  5. bus voltage (p.u.)

  6. derivative of p.u. bus voltage

Internal Variables

Differential

TBD

Algebraic

TBD

External Variables

Differential

None.

Algebraic

Symbol

Units

Description

Note

\(u\)

[p.u.]

Stabilizer input signal

\(V_{ct}\)

[p.u.]

Cutout signal (compared to \(V_{cl},V_{cu}\))

from the block diagram

Differential Equations

\[ \begin{align}\begin{aligned}\begin{split}\begin{aligned} \dot{V_{1}} &= \dfrac{1}{ T_{6} }( V_{SI}-V_{1} ) \\ \dot{x_{1}} &= -\dfrac{ V_{2} }{ T_{5} } \\ \dfrac{d^{2}V_{3}}{dt^{2}}+\dfrac{A_{1}}{A_{2}}\dfrac{dV_{3}}{dt}&=\dfrac{1}{A_{2}}(V_{2}-1) \\ \dfrac{dx_{2}}{dt}&=\dfrac{1}{T_{2}}(V_{3}-V_{4}) \\ \dfrac{dx_{3}}{dt}&=\dfrac{1}{T_{4}}(V_{4}-V_{5})\end{split}\\\end{aligned}\end{aligned}\end{align} \]

Algebraic Equations

\[\begin{split}\begin{aligned} V_{2} &= x_{1} + K_{S} V_{1} \\ V_{4}&=x_{2}+\dfrac{T_{1}}{T_{2}}V_{3} \\ V_{5}&=x_{3}+\dfrac{T_{3}}{T_{4}}V_{4} \\ V_{llout} &= \begin{cases} L_{SMAX} &\text{if } V_{5}>V_{SMAX} \\ L_{SMIN} &\text{if } V_{5}<V_{SMIN} \\ V_{5} \end{cases} \end{aligned}\end{split}\]