PSS1A

Specification draft; not implemented. The equations and initialization remain unverified.

Block Diagram

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

Model Parameters

Symbol	Units	JSON	Description	Typical Value
\(I_{\mathrm{cs}}\)	[-]	TBD	Stabilizer input code	2
\(A_1\)	[s]	TBD	Notch denominator coefficient	0
\(A_2\)	[s²]	TBD	Notch denominator coefficient	0
\(T_1\)	[s]	TBD	Lead–lag 1 numerator time constant	0.25
\(T_2\)	[s]	TBD	Lead–lag 1 denominator time constant	0.03
\(T_3\)	[s]	TBD	Lead–lag 2 numerator time constant	0.25
\(T_4\)	[s]	TBD	Lead–lag 2 denominator time constant	0.03
\(T_5\)	[s]	TBD	Washout numerator time constant	20
\(T_6\)	[s]	TBD	Transducer time constant	0.02
\(K_\mathrm{s}\)	[p.u.]	TBD	Stabilizer gain	10
\(L_\mathrm{s}^{\max}\)	[p.u.]	TBD	Maximum stabilizer output	0.1
\(L_\mathrm{s}^{\min}\)	[p.u.]	TBD	Minimum stabilizer output	-0.1
\(V_\mathrm{cu}\)	[p.u.]	TBD	Upper cutout threshold	0
\(V_\mathrm{cl}\)	[p.u.]	TBD	Lower cutout threshold	0

Parameter Validation

TBD.

Model Derived Parameters

TBD.

Model Ports

Name	Port	Init	Description
`input`	Input	TBD	Stabilizer input \(u\) selected by \(I_{\mathrm{cs}}\)
`vct`	Input	TBD	Cutout signal \(V_{\mathrm{ct}}\)
`output`	Output	TBD	Limited stabilizer output \(V_{\mathrm{ss}}\)

Model Variables

These were the variables listed in the old documentation.

rotor speed deviation (p.u.)
bus frequency deviation (p.u.) - default
generator electrical power in Gen MVA Base (p.u.)
generator accelerating power (p.u.)
bus voltage (p.u.)
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
\(V_{\mathrm{ct}}\)	[p.u.]	Cutout signal (compared to \(V_\mathrm{cl},V_\mathrm{cu}\))	from the block diagram

Model Equations

Internal Equations

Differential

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

Algebraic

\[\begin{split}\begin{aligned} V_{2} &= x_{1} + K_\mathrm{s} V_{1} \\ V_{4}&=x_{2}+\dfrac{T_{1}}{T_{2}}V_{3} \\ V_{5}&=x_{3}+\dfrac{T_{3}}{T_{4}}V_{4} \\ V_{\mathrm{ss}} &= \begin{cases} L_\mathrm{s}^{\max} &\text{if } V_{5}>L_\mathrm{s}^{\max} \\ L_\mathrm{s}^{\min} &\text{if } V_{5}<L_\mathrm{s}^{\min} \\ V_{5} \end{cases} \end{aligned}\end{split}\]

External Equations

None.

Initialization

TBD.

Monitors

TBD.