Types of Power System Stabilizers
8.6 Conceptual explanation of the action of the pre-filter in the IAP PSS
8.6.4 Potential causes of degradation in performance of the pre-filter of the IAP PSS
Sec. 8.6 Action of the pre-filter in the IAP PSS 429
Figure 8.18
8.6.4 Potential causes of degradation in performance of the pre-filter of the IAP
In Section 8.5.1 it is pointed out that the speed signal may be derived from a number of sources, including the true rotor speed which itself may be subject to some form of process- ing prior to injection to the pre-filter of the PSS. In the case of a ‘speed’ signal derived from bus-frequency the signal may be subject to attenuation as established in Section 8.4.2 For illustrative purposes it will now be assumed that the true rotor speed signal is pro- cessed through a first-order pre-processing filter prior to input to the PSS pre-filter.
Let the transfer function of the speed pre-processing filter of the true rotor speed signal be
. (8.19)
With this transfer function the effects of attenuation - or gain - and phase shift on the output speed signal of the PSS pre-filter, are to be analysed. The output of the speed pre-processing filter is , A and TA are the gain and time constant. The relevant elements of the PSS pre-filter which includes the speed pre-processing filter are shown in Figure 8.19. Perturbations in mechanical power output and the torsional mode are assumed to be absent; according to (8.4) the true rotor speed is
. (8.20)
Figure 8.19 Signals in the IAP pre-filter assuming non-ideal pre-processing of the speed input signal through a transfer function ( = 0).
Based on (8.19) and Figure 8.19 it can be shown that the output of the pre-filter is:
. (8.21)
Clearly, at low frequencies and at high frequencies . Over the frequency range typically of interest the responses, or distortion factors
in the true speed, are shown in Figure 8.20 for a range of values of A and time constants TA. The parameters of the RTF of (8.14) are N= 1, M= 5 and T9=0.1 s.
in
GA s
GA s = Ain = A1+sTA
S= out
A
–in 1
2Hs---Pe
=
+ +
out
A
RTF +
in
GA s
– in
A–in
– in
r
Pe s 1 2Hs---
GA Ps m
out A–1–sTA 1+sTA
---RTF s +1 in
=
outAin outin
outin
Sec. 8.6 Action of the pre-filter in the IAP PSS 431
Figure 8.20 Distortion factors, , due non-ideal pre-processing of the true speed input signal to the pre-filter. Values A: 0.8 to 1.2; (i) TA= 0, (ii) TA= 0.05 s.
Of concern in the figure are the effects of the amplitude and the phase shift on the pre-pro- cessed speed signal over the range of frequencies of the rotor modes, 1.5 to 15 rad/s, and their deviation from the ideal response of . Although the range of values of A and TA employed in Figure 8.20 may be considered somewhat extreme, the results imply that ap- propriate care is required in the pre-processing of the speed input signal to the pre-filter.
These results show that depending on how the speed-input signal to the pre-filter is derived in practice, significant distortion in both gain and phase of the synthesised speed signal can occur.
Various methods can be employed for calculating the electric power. Any pre-processing fil- ters which are employed in the electric power input signals paths may also result in incom- plete cancellation of the speed signal at the input to the RTF. This would likewise result in distortion of the speed output of the PSS pre-filter. The effects of any pre-processing of in- put signals to the PSS pre-filter should therefore be examined to assess if they degrade the performance of the PSS.
100 101
0.4 0.6 0.8 1 1.2 1.4
Distortion Factor
100 101
−30
−20
−10 0 10 20 30
Frequency (rad/s)
Phase (deg)
A=1.2 A=1.1 A=1.0 A=0.9 A=0.8
100 101
0.4 0.6 0.8 1 1.2 1.4
Distortion Factor
100 101
−30
−20
−10 0 10 20 30
Frequency (rad/s)
Phase (deg)
A=1.2 A=1.1 A=1.0 A=0.9 A=0.8
(i) A, TA=0 s (ii) A, TA=0.05 s
outin
A
1 0
Consider the case of a bus-frequency stabilizing input, the associated pseudo-speed signal being derived from the rate of change of terminal voltage angle as in (8.9). The deg- radation in the amplitude of this signal is discussed in Section 8.4.2. The effect of such deg- radation on the output of prefilter is illustrated in Figure 8.20(i). Not only is the amplitude of modified but also is its phase- which could introduce an additional phase lag in the PSS over the modal frequency range of interest.
8.6.4.2 One or two washout filters in the electrical-power and speed paths?
Recall that a washout filter is introduced with the purpose of eliminating any steady-state offsets, or DC levels, in the input signal, as well as blocking very slow changes in the input.
It is thus necessary to include at least one washout filter in each path of the pre-filter.
The effect on the response of the RTF of one or two washout filters in the electrical-power path has been examined in Section 8.6.2. The performance requirements for the pre-filter may thus determine the number of washout filters in this path.
What are the effects of choosing a different number of washout filters in the speed and elec- tric power paths? The following requirements must be satisfied:
• When considering the presence of the local- and inter-area modes in each of the two signal paths, the frequency response of both one or two washout filters should be ide- ally, or close to, over the range of modal frequencies. This requirement dictates the value of the washout time constant, Tw.
• The frequency response of a pseudo-integrator in the electrical-power path should be ideally, or close to, over the range of modal frequencies. This requirement determines the time constant of the pseudo-integrator.
If there are different numbers of washout filters in the speed and power paths an imprecise cancellation of the true rotor-speed at the input to the RTF occurs under perturbed condi- tions. It is therefore desirable that the same number of washouts be employed in both input paths.
8.6.4.3 Effect on the synthesized speed signal of setting the RTF time constant T8 to zero.
As in earlier sections, the SMIB system Case C, described in Section 5.10 will be used to in- vestigate the performance of the pre-filter when the time constant is set to zero.
In order for the RTF to follow a ramp with zero steady-state error a requirement is that in the RTF transfer function of (8.14). Setting to zero turns the RTF into a simple low-pass filter of order M if N = 1. With this setting and for a ramp in mechanical power the output of the RTF follows the input signal IPM with non-zero error. In Figure 8.21, and comparing it with Figure 8.18(a)-(ii), this error is seen to manifest itself not
freq
out
out
1 0
1 2H f
–90
T8
T8 = MT9 T8
Sec. 8.7 The Multi-Band Power System Stabilizer 433 only in the synthesized speed signal at the output of the pre-filter, but also in the PSS output.
Consequently there is an associated undesirable swing of the generator terminal voltage and reactive power output during ramping of the mechanical power.
Figure 8.21 Deviation in the synthesized speed output ( ) from the speed input ( ), and the consequent effect on the PSS output signal ( ), due to setting
in the RTF. (Compare these responses with those in Figure 8.18(a)-(ii).)