Linearized Analysis of the Synchronous Machine for PSS Chapter 6 ...

(One can alternatively use digital signal processing techniques.)
In the phase lead network above, we get that
G lead
V
( s)
=
V
( s)
=
( s)
2
1
R
2
⎧
⎨R
+ ⎩
1
R
2
1 ⎫
⎬
Cs ⎭
where
R
1
+ R2
R1R2
α =
R
, τ = C
R + R
2
1
2
{ R + 1/ Cs}
1
1 + ατs
= α (1 + τ s)
Dorf shows that the maximum value of phase lead given by the
above network occurs at a frequency of
1
ω =
m
τ
α
and the corresponding phase lead you get at this frequency is given
by
sin
φ m
α −1
= α + 1
So the idea is that you can know the frequency ω m that you want to
provide the maximum phase lead. This is the frequency of your
most troublesome electromechanical mode and is considered to be
the PSS tuning mode.
Note from the above diagram that the supplementary signal ∆T PSS
is actually lagging Δω, so one might think that we should provide
phase lag, not phase lead, to the input signal (which is actuated by
∆ω). This would in fact be the case if we could introduce the
“shaped” signal (the output of G lead ) directly at the machine shaft.
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