Types of Power System Stabilizers
8.7 The Multi-Band Power System Stabilizer
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).)
Figure 8.22 Multi-Band PSS. SD: Speed Transducer. (See [16], [17] for details).
In particular, the low frequency band is introduced to provide damping for very low fre- quency phenomena encountered on isolated systems1, particularly the so-called global mode in such a system. It is stated in [17] that the MB-PSS and the integral-of-accelerating- power PSS “... can be tuned to achieve quite similar performance in the local, intra-unit and torsional modes ... since they both use an electric power signal to capture the high frequency dynamics. However, having many more degrees of freedom available to modulate its phase lead over a wide frequency range allows the MB-PSS to better balance its performance in inter-area modes from 0.1 to 0.8 Hz” (0.6 to 5 rad/s).
Low frequency oscillations have been observed, for example in hydro-systems: 0.63 rad/s between the Northwest and Southwest power systems in the US [18]; 0.31 to 0.50 rad/s on the Colombian system [19]. Oscillations lying in the intermediate range, associated with vor- tex instability in hydro machines, are reported to be less than 0.5 Hz (3 rad/s) [20], and about 1 Hz (6 rad/s) [21].
The speed signal , input to the high frequency band, is derived from the measured gen- erator electrical power output. A separate internal frequency transducer supplies a speed sig- nal to the low and intermediate frequency bands. Washout filters are provided in the intermediate and high frequency bands; torsional (notch) filters may be incorporated in the PSS structure. In each of the three bands is a differential filter arrangement; it is of interest to understand the characteristics of such a filter. An analysis of a simplified form of the filter, shown in Figure 8.23, is conducted in Appendix 8–I.3.
1. Systems may be isolated because there are no synchronous links to neighbouring systems.
KL11+sTL1 1+sTL2
1+sTL/R 1+sTL 1+sTL 1+sTL*R
1+sTI 1+sTI*R KL11+sTL7
1+sTL8 sTwI
1+sTwI sTwI 1+sTwI
1+sTI/R 1+sTI
sTwH 1+sTwH sTwH
1+sTwH
1+sTH/R 1+sTH
1+sTH*R
1+sTL5 1+sTL6 1+sTL11 1+sTL12 1+sTI5 1+sTI6 1+sTI11 1+sTI12 1+sTH5 1+sTH6 1+sTH11 1+sTH12 1+sTH
KL KL2
KI1 KI2
KH1
KH2
KL1 +
_
KI + _
KH +
_
+ + + SD
SD
L-I
Pe v
v
H
L I–
Sec. 8.7 The Multi-Band Power System Stabilizer 435
Figure 8.23 Filter G(s)
The analysis reveals the filter takes the form of the well-known Q-filter,
, (8.22)
where rad/s is the frequency at which the frequency response is at its maximum value K2. The frequency response of (8.22) with variation in damping ratio is given Figure 2.21.
It is of interest to examine the nature of the frequency response of the MB-PSS omitting washout filters, speed transducers, and torsional (notch) filters. Let the gains and centre fre- quencies of the three bands, evaluated in Figure 5 of [16] be KL= 5.0 pu, FL= 0.04 Hz;
KI= 25.0 pu, FI= 0.70 Hz; KH= 120 pu, FH= 8.0 Hz; respectively. The frequency re- sponses of three bands and the output of the MB-PSS are shown in Figure 8.24; they agree closely with Figures 5 and 6 in [16].
In [17], a detailed comparison is provided on a test system between the designs of the MB- PSS (PSS4B) and the integral-of-accelerating-power PSS (PSS2B). For the MB-PSS it is found that, by separating out the low frequency and the higher frequency bands (each of which have their own limits and wash-out filters), the lower-frequency band limits and wash- out can be adjusted independently of the higher frequency bands to account for islanding and large frequency deviations.
Figure 8.24 reveals that, for the selected parameter values, the phase response varies be- tween 35 and 60 degrees leading. That is, the phase response is relatively level over the range of 0.1 to 25 rad/s (0.02 to 4 Hz) in this case. However, the MB-PSS gain varies over a wide range. Interestingly, this approach contrasts with that of the P-Vr method (Section 5.8.1) in which the PSS transfer function attempts to account for the inherent gain and phase char- acteristic of the particular generator - on which the PSS is installed - over a relevant range of modal frequencies (e.g. see Figure 5.16) and an encompassing set of operating conditions.
1+sT/R 1+sT 1+sT 1+sT*R K1
K2 + _ K1
Differential filter Gdf(s)
G s K22 ms 1+2 ms+sm2 ---
=
m
Figure 8.24 Frequency responses of the MB-PSS assuming a common speed signal input to the three differential filters in Figure 8.22
A number of methods for the tuning the MB-PSS has been offered. For example, the pa- rameters of the MB-PSS are selected by adjusting the centre frequency and gain of each band so as to achieve the nearly flat phase response between 30 and 50 degrees over the range of frequencies, say, 0.05 Hz and 3 Hz (0.3 to 20 rad/s) in order to cover the global and intra- station modes. Other approaches, including optimization techniques, are proposed in [22], [23], [24] and [25].