COMPENSATED LINE
8.2 Resonant Characteristics Of The Dual-Compensated System
Before attempting to apply supplementary control to damp out subsynchronous oscillations, this section first examines the resonant interactions between the transmission line and the generator
shaft dynamics when the line is compensated with both conventionai series capacitors and a three-level SSSC; this combined form of series compensation is hereafter referred to as dual-compensation. As in the previous chapter, all the investigations make use of the detailed PSCADIEMTDC model of the SSSC and the system under investigation is the IEEE First Benchmark Model.
Since an infinite number of possible combinations of conventional compensation (Xc) and SSSC compensation (Xq) could have been considered for the analyses in this chapter, some method of deciding upon a manageable number of interesting scenarios was required. The approach adopted was to consider three case studies: in two of these cases, a value of conventional series compensating reactance was chosen that, on its own (i.e. without added SSSC compensation), would result in a resonant frequency in the transmission line tuned exactly to one particular torsional mode in the IEEE First Benchmark Model; in the third case, a value of conventional series reactance was chosen that on its own would result in a resonant frequency tuned between two torsional modes in the IEEE First Benchmark Model. Finally, in all three cases, the amount of additional SSSC compensating reactance,Xq , was chosen such that the total compensationXc+ Xq would add up to 0.3707 pu. This value of total series compensation corresponds to that required to cause a resonant frequency in the line exactly tuned to Mode 2 when all the compensation is conventional. A summary of the three case studies, and the associated values of Xc and Xq*, is shown in Table 8.1.
Table 8.1: Capacitor and SSSC compensating reactance values for the three case studies considered in the IEEE First Benchmark Model.
Case Study Xc (pu) Xq*(pu) Xc +Xq*(pu)
1 0.178 0.1927 0.3707
2 0.224 0.1467 0.3707
3 0.275 0.0957 0.3707
As in previous chapters, when conducting simulation studies for each of these cases, the system initially operates at steady state; a three-phase fault of duration 0.075 seconds is then applied at the receiving-end of the transmission line at t
=
0.1 seconds. In each case, time-domain results are shown to predict the response of four system variables from the PSCADIEMTDC simulation, namely, generator speed deviation, the electrical torque, LPA-LPB turbine shaft torque and the GEN-EXC shaft torque. In addition, the frequency spectrum of each of these variables is determined, by performing Fast Fourier Transform analysis on the time domain results, in order to be able to better understand the resonant interactions occurring in each case.8.2.1 Case 1 - Without Supplementary Damping Control
In this case study, the individual compensating reactances of the conventional capacitor and SSSC are Xc
=
0.178 pu and Xq* =
0.1927 pu respectively, adding up to a total capacitive reactance of 0.3707 pu. Recall that in Chapter Six, it was shown that for Xc=
0.178 pu of conventional compensating capacitance (with no SSSC), the subsynchronous complementary frequency of the transmission line exactly matches the Mode 4 mechanical frequency of 32.285 Hz. Similarly, recall that when the transmission line is compensated solely by conventional capacitors, this total value of compensating reactance of 0.3707 pu is exactly tuned to the Mode 2 torsional frequency of 20.005 Hz.Fig. 8.1 shows the time-domain response of the selected system variables following the disturbance for the combination of conventional and SSSC compensation in Case 1. The system is clearly unstable as the generator speed, electrical torque and mechanical shaft torques all exhibit large, negatively damped oscillations. The frequency-domain results in Fig. 8.2
~}
(c) LPA-LPB Torque
(
(d) GEN-EXC Torque
(F
o0.5 1 1.5 2 2.5
Time(5)
Fig.8.l: Time domain simulation results for the Case 1 dual-compensated system with no supplementary damping control.
give a clearer indication of the specific mode frequencies present in the unstable response.
TheFFfresults in Fig. 8.2 show that the predominant subsynchronous frequency present in all of the variables' response is clearly that of Mode 3 (25.55 Hz). Although the dominance of Mode 3 seems to overshadow other modes, the effect of Mode 1 and Mode 4 is still present in both the generator speed deviation and the LPA-LPB torque, as well as Mode 2 being present in the GEN-EXC torque.
: :£:"1")
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(c) LPA-LPB Torque
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o _ _-I...._.b./,--l-=:::...c~I--"'I~_--L_ _-L-_ _...l..-_ _L - _ - - - l_ _---L._ _
(d)GEN-EXC Torque
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• :.-i--
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: Mode 2 ( 7) •
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10 20 30 40 50 60 70 80 90 100Frequency (Hz) S'0-
-;;; 500 ::Ea:l
Fig.8.2: FFTs of the time-domain responses shown in Fig. 8.1.
Interestingly, the frequency of Mode 4 (32.285 Hz) is not the dominant mode in this case study, despite the fact that, without the SSSC, the conventional compensation level in this case would be exactly tuned to Mode 4. Thus, the effect of adding SSSC compensation to the conventional compensation appears to be a complex resonant condition that is distinct from the interaction that occurs between the conventional capacitors and the generator shaft modes without the SSSC present.
8.2.2 Case 2 - Without Supplementary Damping Control
In this case study, the individual compensating reactances of the conventional capacitor and SSSC areXc
=
0.224 pu andXq=
0.1467 pu, respectively. The complementary frequency of a system compensated solely with Xc = 0.224 pu of conventional capacitance falls half way between the Mode 3 and Mode 4 frequencies.Fig. 8.3 shows the time-domain response of the selected system variables following the disturbance for the combination of conventional and SSSC compensation in Case 2. The response of the system for this combination of SSSC and conventional compensation is not negatively damped as in Case 1 (c.f. Fig. 8.1), but the oscillations are nevertheless of considerable amplitude and are sustained, and are therefore clearly of concern. The FFrs of each variable in Fig. 8.3 are shown in Fig. 8.4. The FFrs of generator speed and electrical torque show that the predominant frequency component present in the response of these variables is that of Mode 3 (25.55 Hz). However, the response of the LPA-LPB torque also shows significant components of Mode 1 and 4 whilst the GEN-EXC torque, as was observed in Case 1, shows Mode 2 being the dominant frequency.
(c)LPA-LPB Torque
1'1f.,U'IVIIlII/l
\f\f\f\(\IV0I"~~'W~]
, Wj
~ _:
o 0.5 1 1.5 2 2.5...Q) Q.
Time(5)
Fig.8.3: Time domain simulation results for the Case2dual-compensated system with no supplementary damping control.
(a) Generator Speed Deviation
J '::[(E£(f~.f:·EI.ctE~~"l·.···,· .. ·.··IJ=J
(c) LPA-LPB Torque
(d) GEN-EXC Torque
100
70 80 90
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: : Mode 3 (48) • •
...
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0L.-_---l.._"'-bc~=~...l_..1l~___l_ ___L_ _...l__ _. L __ ___l._ __ L_ ____.J
o 10 20 30 40 50 60
Frequency (Hz)
~Cl 50 S'100 .e,
Fig.8.4: FFTs of the time-domain responses shown in Fig. 8.3.
In a transmission line compensated solely by conventional capacitors, it is expected that at this value of compensation of Xc
=
0.224 pu the system should be relatively stable (at least in comparison with Case I and 3) since the natural frequency of the transmission line is not exactly tuned to any particular torsional mode. The results of Figs 8.3 and 8.4 show that for this particular case, the extra SSSC reactance inserted into the line to enhance the power flow does not have a significant destabilising effect on the system, but that the combined conventional and SSSC compensated system once again exhibits a complex, multi-modal response in which the amplitudes of the torsional oscillations following a disturbance are of concern.8.2.3 Case 3 - Without Supplementary Damping
In this case study, the compensating reactances of the conventional capacitor and SSSC areXc
=
0.275 pu andXq
=
0.0957 pu, respectively. Recall that in Chapter Six, it was shown that forXc=
0.275 pu of conventional reactance, the subsynchronous complementary frequency of the transmission line exactly matches the Mode 3 mechanical frequency of 25.55 Hz.Fig. 8.5 shows the time-domain response of the selected system variables following the disturbance for the combination of conventional and SSSC compensation in Case 3. The FFTs of each variable in Fig. 8.5 are shown in Fig. 8.6. The results in Fig. 8.5 show that for this case the system is clearly once again negatively damped, with the oscillations in the LPA-LPB and GEN-EXC mechanical torques, in particular, noticeably increasing in amplitude with time. Also of note is the high-frequency behaviour evident in the response of the electrical torque in Fig. 8.5(b). The FFT results in Fig. 8.6(b) show that these oscillations in the electrical torque are in fact at a supersynchronous frequency of 90 Hz. TheFFf results in Fig. 8.6 show that, with the exception of the GEN-EXC mechanical torque, the predominant subsynchronous frequency present in all of the variables' responses is that of Mode 1 (15.71 Hz).
As in both previous cases, Fig. 8.6 shows that the predominant frequency present in the response of the GEN-EXC torque for this case is again that of Mode 2, although the Mode 1 frequency is also strongly evident in the GEN-EXC torque as well for this case.
(a) Generator Speed Deviation
(b) Electrical Torque 3
'c 2 ::::>
:v 1 a. 0
-1L - ---l.. - L ..I....- - - . l --.J
(c) LPA-LPB Torque
2 2.5 1.5
Time(5)
~_:E:
(d) GEN-EXC Torque: : :~
Fig.8.5: Time domain simulation results for the Case3 dual-compensated system with no supplementary damping control.
(a) Generator Speed Deviation
(c) LPA-LPB Torque
~ ::: l··· • jJ- Mod. 1 ~J:::)3 17
19
'1" ' . 1 'I' "'," .'J
::i!: 500 ... . . . . . .
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(d) GEN-EXC Torque 200
S'B
Cl 100 ::i!:t'!I
00 10 20 30 40 50 60
Frequency (Hz)
70 80 90 100
Fig.8.6: FFTs of the time-domain responses shown in Fig. 8.5.
In a transmission line compensated solely by conventional capacitors at this value of compensation ofXc = 0.275 pu the complementary frequency of the transmission line is exactly tuned to the Mode 3 mechanical frequency of 25.55 Hz. However, with the added capacitive reactance provided by the SSSC, the Mode 3 frequency now no longer dominates in the system oscillations; instead, it is now Mode 1 that is being strongly destabilized. Thus, as in Case 1, where the conventional compensation was, on its own, also exactly tuned to destabilise a particular mode, the additional of the SSSC has noticeably altered the resonant interactions between the conventional capacitors and the generator shaft modes.
In a transmission line compensated solely with conventional series capacitors, as shown in Chapter Six, the torsional modes that will be destabilised by a certain value of capacitive reactance are predictable. Similarly, Chapter Six showed that in a transmission line compensated solely by an SSSC, the resonant frequency in the transmission line is also relatively easy to predict and explain. However, the results in this section demonstrate that the resonant characteristics that are observed when SSSC compensation is added in series with conventional series capacitors are complex, and noticeably different from those associated with the resonances caused by the series capacitors acting alone. In particular, one distinct characteristic of dual-compensation is that the resonance is no longer dominated by one mode alone, but rather that
strong, multi-modal resonances are typically observed. This is distinct from the multi-modal resonances that may occur in conventionally compensated radial systems, where the electrical resonance in the line may be tuned to a value close to two torsional modes and destabilize them both to some extent. However, the series combination of conventional and SSSC compensation appears, rather, to destabilize multiple modes over a wide frequency range. The reason for this phenomenon is not fully understood, but could be examined by conducting impedance versus frequency scans for the dual compensated system similar to those carried out in Chapter Six.
Furthermore, it can be observed that the subsynchronous characteristics of the dual-compensated system are highly dependent on the relative magnitudes of the different forms of compensation that make up the total compensating reactance.
Now that the particular resonant characteristics of the three dual-compensation cases chosen for study have been established, the following section considers the design of supplementary damping controllers for the SSSC, using the approach described in Chapter Seven, for each of these three cases.