Types of Power System Stabilizers
8.3 Performance of a PSS with electric power as the stabilizing sig- nal
mise with the increase in phase lead at the lower modal frequencies. In the case of a reduction in the time constant, say from 10 s to 5 s, the phase lead at the modal fre- quency of 2 rad/s is increased from to . If desired, the increased phase lead so introduced by the two washouts can be compensated for in the tuning of the PSS main compensation blocks.
4. If the inter-area modes are not of concern, the washout filter time constants can likewise be determined based on the relatively higher frequency of the local-area mode(s).
8.3 Performance of a PSS with electric power as the stabilizing sig-
Sec. 8.3 PSS with electrical power as the stabilizing signal 405
Figure 8.5 Structure of the PSS with electric power as the stabilizing signal. Note the negative sign of the PSS output signal at the summing junction to the AVR.
So that transfer function of the low-pass filter acts as an integrator over the range of modal frequencies it is required that its corner frequency at rad/
s should be a decade or more below the lowest (inter-area) modal frequency. With this choice of , the gain of the filter rolls off at -20 dB/decade over the range of modal fre- quencies and its associated phase angle is approximately -90 deg. This is the case for an ideal integrator (see Section 2.12.1.2).
For example, assume the lowest (inter-area) modal frequency is 2 rad/s; the corner frequen- cy should ideally be 0.2 rad/s or less. For a values of TH of 5.0 and 7.5 s the corner frequen- cies are respectively 0.2 and 0.133 rad/s; Table 8.3 shows that for these values of TH the frequency response of the associated pseudo-integrator agrees well with that of the ideal in- tegrator at and above 2 rad/s. While it is common to set TH = TW a higher value of TH (say TH = 7.5 s when TW = 5 s) is sometimes used in practice.
Table 8.3 Responses of the ideal integrator and the pseudo-integrator at lower frequencies.
Because a synthesized speed signal is derived from the electrical power output using the pre- filter of (8.5), the design of the compensating transfer function of the PSS follows the pro- cedure based on a speed-stabilizing signal as outlined in Section 5.10.6. The compensating transfer function is the same as for the speed PSS given in (5.49).
The rapid attenuation of the electric power signal with frequency is noted in Table 8.3.
A feature of the use of electric power perturbations as a stabilizing signal is that the torsional rad/s Ideal:
TH=5 s TH=7.5 s 1
2 4
S sTW
1+sTW k Compensation
transfer function VS Washout
Filter Damping
Gain
LP Filter TH/2H
1+sTH
Pe
AVR
Vr
Vt
Pre- filter PSS
VS
TH1+sTH 1s
fc = 1TH TH
f s 1
jf ---
= TH1+sTH
1.0–90 0.9806–78.69 0.9912–82.41
0.50–90 0.4975–84.29 0.4989–86.19
0.25–90 0.2497–87.14 0.2499–88.09
f
oscillations which occur on the shafts of generating units are heavily attenuated. This topic is discussed later in Section 8.5.3.
Several cautionary comments follow.
1. The electrical power output of the generator will closely follow any ramping of the mechanical power output of the turbine. Depending on the ramp rate and the time constant of the washout filter(s), there may be a significant deviation in the associ- ated PSS output. As a result of this signal being injected into the excitation system, there could be unacceptable variations in terminal voltage and hence in the reactive power output of the generator [13]. This problem is ameliorated by providing an appropriate pre-filter, such as in the Delta-P-omega stabilizer [14], or employing an
‘integral-of-accelerating-power’ PSS, to be discussed in Section 8.5.
2. Care should be taken to ensure that negative feedback of the PSS output signal is applied at the AVR summing junction.
3. Prior to purchase due care should be taken to ensure that the power input PSS pro- vides for the synthesis of a rotor-speed signal from the electrical-power input.
8.3.2 Dynamic performance of a speed-PSS with an electric power pre-filter.
A PSS designed for a speed-stabilizing signal used with an electric power pre-filter forms the basis for the assessment of the dynamic performance of the integrated stabilizer. Five oper- ating conditions for the sixth-order generator-SMIB system, shown in Table 5.6, are used to illustrate the performance of the PSS. Its performance is compared to that of the PSS which uses “true” rotor speed for the same fives cases.
A single washout filter with time constant of 5 s is selected in Section 5.10.6.2 for the five Cases. The associated corner frequency of 0.2 rad/s is more than a decade below the single rotor mode of oscillation (~ 9 rad/s)1. The inertia constant of the unit is 3 MWs/MVA. As revealed in Table 8.3 a suitable time constant for the pseudo-integrator is 7.5 s. The transfer function for the electric power pre-filter is thus
. (8.6)
A comparison of the modes resulting from the use of an electric power pre-filter that syn- thesizes a rotor speed signal with those produced by a true rotor speed PSS is shown in Table 8.4. Because there is close agreement in the values of the modes, it is concluded that the pre-filter accurately synthesizes rotor speed perturbation with the caveat that slow vari- ations in mechanical power may cause variations in the reactive output of the generator.
1. The corner frequency of 0.2 rad/s is a decade below any potential inter-area modal fre- quencies of 2 rad/s if the SMIB system represents a generator in a multi-machine system.
TH2H 1+sTH
--- 1.25 1 7.5s+ ---
=
Sec. 8.4 PSS with bus-frequency as the stabilizing signal 407 Table 8.4 Comparison of modes for Speed and Electric Power PSSs*