Types of Power System Stabilizers
8.5 Performance of the “Integral-of-accelerating-power” PSS
Sec. 8.5 Integral-of-accelerating-power PSS 413 Note: In the event of significant transients that lead to sudden changes in bus-voltage angle, e.g. a line fault followed by the tripping of the circuit, the synthesized rotor speed derived from the bus-voltage angle will not necessarily be representative of the true rotor speed until the resulting large-amplitude oscillations have markedly decayed.
porates a ‘ramp tracking filter’ which tracks a ramp ideally with zero tracking error - and thereby offsets the ramp in the electrical power input; this is a second role of the IAP pre- filter.
Let us consider the influence of the torsional modes, the ramping of mechanical power, and the characteristics of the ramp tracking filter.
8.5.2 Torsional modes introduced by the speed stabilizing signal
A generating unit, in the case of a steam turbine, may consist of high pressure, intermediate and low-pressure stages, the generator and an exciter. The lumped masses are connected by shafts whose torsional stiffness is finite. As is illustrated in Chapter 9 for a linear spring-mass system, the rotating masses similarly exhibit modal frequencies and damping dependent on the inertia of the masses and the stiffness of the interconnecting shafts [5], [12].
Since the mechanical stiffness of the shaft components is at least an order of magnitude higher than the effective electro-mechanical coupling between the generator and the power system, the entire rotating mass of the mechanical shaft of a large turbo-generator is more- or-less uniformly subject to the power system’s inter- and local-area modes of frequency 1.5 to 15 rad/s. The first torsional mode for large steam turbine units can be as low as 8 Hz (50 rad/s) [5], [6]. Depending on the mode shape of the particular torsional mode, a shaft-speed transducer that is located in a region of the shaft that closely corresponds to a peak of the torsional oscillations (an anti-node of the mode shape) can result in a significant component of the torsional mode in the speed signal. One way to avoid this problem is to locate the speed transducer at a node of the modal shape [5]; this, however, is not always practical since in some cases the node may lie inside a turbine stage.
It will be assumed in the analysis that the input speed signal to the pre-filter, , com- prises the ‘true’ rotor speed component, , ‘corrupted’ by the first and higher torsion- al modes (as well as noise), , i.e.
. (8.13) 8.5.3 The electric power signal supplied to the pre-filter
The electric power signal input to the pre-filter is a filtered representation of the instantane- ous electric power. The filtering process typically introduces a very small phase shift over the range of electro-mechanical modal frequencies and consequently the input power signal closely follows the low frequency perturbations in power associated with the local- and in- ter-area modes. Furthermore, as mentioned earlier, if the mechanical power output of the turbine is ramped, say, in the relatively slow process of generation despatch, i.e. changing power output from one level to another, the electrical power output of the generator will closely follow the mechanical power.
C t
in t
t t
C t = in t + t t
Sec. 8.5 Integral-of-accelerating-power PSS 415 If there is any component of the torsional modes in the electric power signal, depending on how it is calculated, the component - being of significantly higher frequency than the rotor mode - will be significantly attenuated by the integration in the pre-filter.
8.5.4 The Ramp Tacking Filter (RTF) The RTF is a low-pass filter of the form,
, where . (8.14)
The RTF serves a number of purposes. Firstly, it tracks a ramp signal at its input with zero tracking error. Secondly, it significantly attenuates signals at frequencies above the corner frequency . Thirdly, as will be demonstrated, it passes the low frequency perturbations associated with mechanical power changes with negligible attenuation. The frequency re- sponses for two typical sets of parameter values for the RTF are shown in Figure 8.9. (It should be noted that the tracking feature of the RTF is defeated if deviates markedly
from , for example if ).
Figure 8.9 Frequency responses of the Ramp Tracking Filter for N=1, T9= 0.1, , M= 5 or M= 4.
F s 1+sT8 1+sT9
M
--- N
= T8 = M T 9
1T9
T8
T8 = M T 9 T8 = 0
100 101 102 103
−150
−100
−50 0
Magnitude (dB)
100 101 102 103
−350
−300
−250
−200
−150
−100
−50 0
Frequency (rad/s)
Phase (deg)
M=5 M=4
T8 = M T 9
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.