Action of the pre-filter, no washout filters

Types of Power System Stabilizers

8.6 Conceptual explanation of the action of the pre-filter in the IAP PSS

8.6.1 Action of the pre-filter, no washout filters

It is clear from the plots that a torsional mode, say the first at 15 Hz (~95 rad/s), is attenu- ated by 50 dB or more. The parameters commonly used for the RTF are ^N=1, ^M= 5 and T₉= 0.1. The value of the time constant T₉ more-or-less determines the corner frequency of the RTF. If for example, the variations in mechanical power output are slow, and the tor- sional modes possess low frequency components, it may be desirable to reduce the value of T₉, and/or set ^N=2.

While the RTF tracks a ramp input signal with zero tracking error, it tracks a signal which is the integral of a ramp, i.e. a parabola , with a constant track- ing error. The ramp-tracking characteristics of the filter are analysed in Appendix 8–I.2.

from which it can be shown that the steady-state tracking error to a parabolic input is finite,

i.e. when and N=1, M= 5.

8.6 Conceptual explanation of the action of the pre-filter in the IAP

Sec. 8.6 Action of the pre-filter in the IAP PSS 417

pu, (8.15)

where is the perturbation in mechanical power output of the turbine and includes a ramp change in turbine power. Rearranging (8.15) and integrating the resulting expression, we can express the integral of the electrical power signal, ^IPE, as:

. (8.16) Each term in (8.16) has the dimensions of speed (pu). Consequently, on the basis of (8.16), the output of the integration of the electrical power signal, , contains information not only on the mechanical power ramp and perturbations but also the ‘true’ rotor speed . As mentioned, if any torsional modes, which typically exceed 8 Hz (50 rad/s), are present in the electrical power signal they are heavily attenuated through the in- tegrator transfer function , i.e. 50 dB at 50 rad/s for H=3 MWs/MVA.

Let us combine the signal IPE with the input speed signal of (8.13), as shown dia- grammatically in Figure 8.11(i). A signal IPM results:

, (8.17)

i.e. . (8.18)

Note that IPM contains only the perturbations in mechanical power and the torsional modes, the true rotor speed signals in (8.17) having been cancelled out; this cancella- tion is an essential feature of the IAP pre-filter.

As shown in Figure 8.11(ii), the signal ^IPM is passed through the RTF. By judicious selection of the parameters of the RTF it will attenuate significantly the higher-frequency torsional modes and track the integral of the mechanical power ramp-changes with negligible tracking error¹. An analysis of these features of the RTF are given in Appendix 8–I. The output of the RTF therefore contains the integral of mechanical power, ², the levels of the torsional modes having been attenuated significantly.

1. Strictly-speaking, because of the ideal integrator in the basic pre-filter structure shown in Figures 8.10 and 8.11, the tracking error of the RTF to a ramp in mechanical power is non-zero. As explained in Section 8.6.2.2 this error is very small, and is zero when there are one or more washout filters ahead of the integrator.

2. Note that the slow changes in the integral of mechanical power are not attenuated by the RTF (see its frequency response in Figure 8.9).

P_m  Pt – _e t 2H t d

d_in t

=

P_m t

IPE 1

2H

---P_e t dt _2H^---1 ^Pm t dt–^in t

= =

IPE 1

2H

---P_e t dt

=

_in t

P_e s 2Hs

_C t

IPM IPE+_C t 1 2H

---P_m t dt–_in t

 

 

 

_in  t + _t t

 

+

= =

IPM 1

2H

---P_m t dt+^t t

=

_in t

V_rtf 1

2H---P_m t dt

=

Figure 8.11 The action of the pre-filter. (i) The implementation of (8.13) and (8.16).

(ii) The ramp tracking filter attenuates the torsional modes in the speed input and tracks the integral of the mechanical changes with negligible steady-state error.

(iii) The signals containing the integral of the mechanical changes are cancelled out at the summing junction and the true speed signal is synthesized.

Finally, as shown in Figure 8.11(iii), the negated signal IPE is combined with the output of the RTF at the summing junction. The component present in each signal is cancelled out resulting in the output of the pre-filter being the required ‘true’ rotor speed,

.

To compensate for a difference in the levels of the speed signal in the speed-signal path from that derived from electric power¹, the gain is provided as shown in Figure 8.12. (For ex- ample, this adjustment may be required if an attenuated speed signal is derived from bus fre- quency, see Section 8.4.2). Furthermore, to eliminate any steady-state levels in the electrical power and speed inputs, and , two washout filters are added to each input;

this completes the block diagram of the IAP pre-filter. (The effect on the synthesized speed signal , say, of having two washouts in the speed input and one in the electric power input path is discussed briefly in the later Section 8.6.4.2.)

We know that the RTF follows a ramp input at its terminals with zero steady-state error between its input and output. In practice there are washout filters and an integrator between the mechanical ramp input and the input to the RTF. The input to the RTF may no longer be a ramp, how does this affect the steady-state error?

1. The degradation in performance of the PSS in such a case is illustrated in Figure 8.20(i).

P_e

+

+ _out

IPE 1

2H---P_edt⁼ _2H^---1 ^Pmdt–_in

=

_C = _in+_t IPM 1

2H---P_mdt+_t

=

+ V_rtf 1

2H---P_mdt

=

(ii)

(i) (iii)

_in

= RTF

1 2H---

_t t

_out = _in

1

2H---P_m t dt

_in s

k_s

P_e t _C t

_out

e_fss

Sec. 8.6 Action of the pre-filter in the IAP PSS 419

Figure 8.12 Block diagram of the prefilter for the IAP PSS. The gain is set to unity in the following analysis.

8.6.2 Effect of the washout filters and integrators on the performance of the pre-