Reactive-Power Compensators
3.9 THE THYRISTOR-SWITCHED CAPACITOR–THYRISTOR- CONTROLLED REACTOR (TSC–TCR)
3.9.1 Configuration
The TSC–TCR compensator shown in Fig. 3.35 usually comprisesnTSC banks and a single TCR that are connected in parallel. The rating of the TCR is chosen to be 1
/
n of the total SVC rating. The capacitors can be switched in discrete steps, whereas continuous control within the reactive-power span of each step is provided by the TCR. Thus the maximum inductive range of the SVC cor- responds to the rating of the relatively small interpolating TCR.As the size of TCR is small, the harmonic generation is also substantially reduced. The TSC branches are tuned with the series reactor to different domi- nant harmonic frequencies. To avoid a situation in which all TSCs and, conse- quently, the associated filters are switched off (with only the TCR in operation), an additional nonswitchable capacitive-filter branch is provided.
The main motivations in developing TSC–TCRs was for enhancing the oper- ational flexibility of the compensator during large disturbances and for reducing the steady-state losses. A fixed capacitor–thyristor-controlled reactor (FC–TCR) behaves like a parallel LC circuit that tends to set up a resonance with the ac system impedance during large disturbances. What particularly aggravates the problem is when severe voltage swings are experienced and followed by load rejection. In this event, a TSC–TCR can quickly operate to disconnect all the capacitors from the compensator, precluding the resonant oscillations. This fea- ture of disconnecting the capacitor in exigencies is not available with FC–TCRs.
SVC HV Bus
Filter
L L C C
Figure 3.35 A general TSC–TCR SVC.
THE TSC–TCR 83
BLC
−6.86 pu BL
BC 1 = BC + BLC BCBLC BC 2 = 2BC1 BC 3 = 3BC1 IL
ISVC Bj
IC
BC 1 = 0.286 pu BC 2 = 0.572 pu BC 3 = 0.857 pu
−0.316 pu BC
−0.274 pu
V2
−6 pu
Vsyst
(TSCs Tuned for n = 5) Figure 3.36 A practical example of a 6-pulse TCR–TSC compensator with three TSCs.
3.9.2 Operating Characteristic
3.9.2.1 A Practical Example A TSC–TCR scheme can be considered as a fixed capacitor TCR scheme, where the capacitor may have a number of differ- ent values. Thus an understanding of the TSC–TCR can be obtained by applying the theory of an FC–TCR SVC developed in Section 3.6 to a practical example of TSC–TCR.
An example configuration is given in Fig. 3.36. The SVC consists of three TSCs and one TCR in a 6-pulse arrangement and has the same ratings as the example for a fixed-capacitor scheme in Fig. 3.22. It is assumed that the TSC branches are tuned tonc5and, furthermore, that all TSC branches are identical.
Calculation of the Operating-Range Limits Equations (3.28) and (3.29) can be used to determine the susceptance of the SVC at the limits of the operat- ing range. In Eq. (3.28), BC is replaced by BC3 of the TSC scheme to get the susceptance at the production limit. Figure 3.36 definesBC3 as the susceptance of all three TSC branches in parallel and considers the influence of the damp- ing reactors. In Eq. (3.29), BC is considered zero for the TSC scheme at the absorption limit, for all capacitors are switched off. With the given data, the susceptance at production limit is
84 PRINCIPLES OF CONVENTIONAL REACTIVE-POWER COMPENSATORS
BSVC max c BjBC3
Bj+BC3 c1pu (3.49)
and the susceptance at the absorption limit is BSVC min c BjBC3
Bj+BC3 c−0.3pu (3.50) This shows that the rating of the TSC scheme discussed here is the same as that for the previously discussed FC–TCR scheme. (See Section 3.6.2.)
The overall operating characteristic of the TSC–TCR scheme can be assem- bled by applying the equations for FC–TCR schemes, assuming that there is one, two, three, or no capacitors connected. Here, the total operating range con- sists of four subranges. Equations (3.25), (3.27), and (3.29) are used to deter- mine the characteristics.
Subrange With Three TSCs Turned On The total compensator current is ISVCc−V Bj(BC3+BTCR)
Bj+BC3+BTCR (3.51)
The negative sign indicates a capacitive current. The currents at the two limits are
ISVC capc−V BjBC3
Bj+BC3 c−1pu (3.52) and
ISVC ind c−V Bj(BC3+BL)
Bj+BC3+BL c−0.595pu (3.53) The current at the inductive limit of the subrange with three TSCs is still capac- itive.
Other Subranges The subranges with one, two, or no TSCs are determined in an analogous manner as the subrange with three TSCs. Figure 3.37 gives the results; it can be seen that the subranges overlap, which is required for contin- uous, stable control. The figure also shows the transformer-secondary voltage calculated with Eq. (3.33) and the capacitor voltage calculated with Eq. (3.42).
3.9.3 Current Characteristic
It is interesting to visualize how the TSCs and the TCR share the current and contribute to the total SVC current. This is, however, difficult to observe from
THE TSC–TCR 85
3 TSC
2 TSC
1 TSC
0 TSC
Production Limit a = 180° 3 TSC
Absorption Limit a = 90° 0 TSC
−1 pu −0.5 pu 1.22 pu
1.17 pu 1 pu
0.3 pu ISVC 0.95 pu 1.04 pu
VSVC VC
V2
Inductive Capacitive
Vsyst
Figure 3.37 The voltage–current characteristic of the example TSC–TCR SVC.
the operating characteristics derived above. Generally, the TSC and TCR cur- rents add to give the total current as follows:
ISVCcIC+IL (3.54)
where
ICc−V2nBCn, ILcV2nBTCR (3.55) The subscriptnindicates the number of TSC branches turned on and, therefore, can have values 0, 1, 2, . . . ,nmax, wherenmax is the total number of TSCs—in this case, three. In the preceding two equations, V2n can be substituted from Eq. (3.33) to give
ICc−V BjBCn
Bj+BCn+BTCR (3.56)
ILc−V BjBTCR
Bj+BCn+BTCR (3.57)
where nc1, 2, . . . is the number of TSC circuits in operation andBCn is the total susceptance of n TSC branches. Substituting BTCR c 0 and BTCR c BL in the foregoing equations, respectively, results in the currents at the absorp- tion limit and at the production limit of each subrange for different numbers of TSCs. The results for the scheme analyzed here are presented in Fig. 3.38. It is
86 PRINCIPLES OF CONVENTIONAL REACTIVE-POWER COMPENSATORS
a = 180° a = 90°
Production
0 TSC
Absorption ISVC pu IL I pu
Vsyst= 1pu (constant)
ISVC= IC + IL
−1.0 3 TSC 2 TSC
1 TSC
−0.941
−0.598
−0.4
−0.285
−0.6
−0.8
−1.0 IC
−1.0 −0.8−0.6−0.4−0.2
Figure 3.38 The current characteristic of the example TSC–TCR SVC.
emphasized that the variation of the transformer-secondary voltage influences these characteristics. The highest steady-state current in the TCR is with three connected TSCs, because the transformer-secondary voltage is high when three TSCs are on (assuming the system voltage is constant over the entire range).
3.9.4 Susceptance Characteristic
Equation (3.27) can be used to calculate the SVC susceptance in the TSC–TCR scheme as follows:
BSVCc Bj(BCn+BTCR)
Bj+BCn+BTCR (3.58)
wherenc1, 2, . . . is the number of TSC branches in operation andBCn is the total susceptance of nTSC branches. With a linear approximation, Eq. (3.58) reduces to
BSVCc冢1− BBCnj 冣 BCn+冢1− 2BCnBj+BL冣 BTCR (3.59)
Figure 3.39 gives the total susceptanceBSVC as a function of the susceptance of the controlled reactor BTCR for the example data. These characteristics are of importance for control design, for the controls vary BTCR and the effect on the system is caused byBSVC.
THE TSC–TCR 87
0 TSC 3 TSC
2 TSC
1 TSC
−0.2 0.2 0.4 0.6 0.8 1.0
−0.3
−0.3 −0.2
BTCR BSVC
−0.03 0.27 0.59
−0.1
Figure 3.39 The susceptance characteristic of the example TSC–TCR SVC.
3.9.5 Mismatched TSC–TCR
A TSC–TCR scheme in which the TCR cannot compensate for one TSC step because its rating is too small, is shown in Fig. 3.40. Each subrange shows the typical operating characteristic of an FC scheme. However, instead of overlap areas, there are now gaps, and no operation is possible within these dead zones.
To illustrate the problems arising from such a scheme, a typical system charac- teristic is given in the Fig. 3.40. The compensator cannot stabilize the system voltage to 1 pu. The operating points with voltages closest to nominal voltage areAorB. Operating pointAis with two TSCs switched on and results in some overvoltage, whereas operating point Bis with only one TSC but shows some undervoltage. This is a discontinuous system and creates problems in control.
The standard design for TSC–TCR schemes is therefore to include a finite overlap. However, discontinuous operation may sometimes occur under degraded operating conditions; for example, in a 12-pulse scheme, one TCR is shut down and the remaining 6-pulse TCR is too small to compensate for one TSC.
TheV-Icharacteristic of TSC–TCR SVC shown in Fig. 3.40 is a simple case when the bus voltage is regulated strictly at the specified reference level. Prac- tical SVCs incorporate a slight slope in theV-Icharacteristics to obtain certain advantages, as discussed in Chapter 5 (Section 5.1.3). The problem of coordi- nation between the TSC and TCR for an SVC having a droop in the operating characteristics is illustrated in Fig. 3.41. A careful examination reveals that to obtain a smooth characteristic, it is necessary to vary slightly the TCR knee
88 PRINCIPLES OF CONVENTIONAL REACTIVE-POWER COMPENSATORS
2 TSC 1 TSC
0 TSC Production Limit
ISVC Absorption Limit
VSVC A
B
Inductive Capacitive
Figure 3.40 The operating characteristic of a TSC–TCR SVC with mismatched ratings of TSCs and TCRs.
voltage and current slope at every TSC switching [3]. An overlap or hysteresis, as discussed previously, is always desirable to avoid chattering of TSCs. In this scheme, a TSC is turned on at a lower system voltage but turned off at a higher voltage level.
2 TSC + TCR
1 TSC
+ TCR 0 TSC; TCR only
Desired Smooth Characteristic
ISVC VSVC
System Load Line
Inductive Capacitive
Figure 3.41 Coordination issues in a TSC–TCR SVC.
A COMPARISON OF DIFFERENT SVCS 89 3.10 A COMPARISON OF DIFFERENT SVCS
3.10.1 Losses
The real-power losses are an important factor during the selection of a specific SVC configuration. Because these losses are constantly present, the capitalized cost of these losses keep accruing to significantly high levels.
A comparison of losses of three main SVC configurations, namely, FC–TCR, TSC–TCR, and MSC–TCR, is presented in Fig. 3.42. In each of these cases, the losses associated with the step-down transformer are neglected; however, the losses are expressed as the percent of rated MVA of SVC. The following losses are contributed by different components:
1. Small, resistive losses are in the permanently connected filter branches in the TSC–TCR and MSC–TCR.
2. Losses in the main capacitors in all three SVCs.
3. Valve-conduction losses and switching losses in the thyristor power cir- cuit.
4. Resistive losses in the inductor of the TCR, which increases substantially with the TCR current.
Maximum losses occur with FC–TCR in the floating state, that is, when the SVC is not exchanging any reactive power with the power system. This condi- tion is a prime disadvantage with this type of SVC, as for an extended period of time, the SVC largely remains in the floating state with its reactive power margins in standby to meet any system exigency.
The TSC–TCR losses are the least in the floating state, just as with MSC–TCR. However, these losses increase as more TSCs are switched into service. The TCR losses in a TSC–TCR are lower because of the smaller reac-
TCR TSC 2
TSC 1
C1 C2
Total Total
Total 1%
Power Losses
1%
Power Losses
1%
Power Losses
Fixed-Capacitor and Filter Losses
(a) FC -TCR (b) TSC -TCR (c) MSC -TCR
Filter-Capacitor Losses
Figure 3.42 A comparison of losses for different SVC configurations.
90
SVC No.FeatureSynchronous CondenserSR/FCFC–TCR/FC–TCTTSCTSC–TCRMSC–TCR 1Control rangeInductive and capacitiveInductive and capacitive (with FC)Inductive and capacitiveCapacitiveInductive and capacitiveInductive and capacitive 2Nature of controlContinuous, activeContinuous, inherentContinuous, activeDiscrete, activeContinuous, activeContinuous, active 3Response timeSlowFast: system-, slope-, correction-capacitor-, and filter-dependent
Fast: system- and control dependentFast: control- dependentFast: system- dependentMedium: system- dependent 4Control capability: Voltage control Auxiliary-stabilizing signals Individual-phase control
Good Limited Limited
Limited No Limited
Good Good Good
Limited No Limited
Good Good Good
Good Good Good 5Harmonic generationNoneVery low: lowest harmonic (17th)Low: filters neededNoneLow: filters neededLow: filters needed 6Overvoltage limitation; overload capabilityVery goodVery good: limited by slope-correction capacitor
ModerateNoneLimitedLimited 7Rotating inertiaYesNoNoNoNoNo 8Sensitive to frequency deviationsYesNoNoNoNoNo 9LossesModerate; rotating losses as wellModerate: increase with lagging currentMedium: increase with lagging currentSmall: increase with leading currentSmall: configuration- dependent
Small 10Direct EHV connectionNoSR: no; FC: yesTCR: no; TCT, FC: yesNoNoTCR: no; MSC: yes 11EnergizationSlowFast and direct; some transientsFast with control action; minimal transients
Fast with control action; some transients Fast with control action; some transients Fast with control action; some transients
TABLE 3.1 Comparison of Different Reactive Compensators
REFERENCES 91 tor rating. This SVC generates higher losses only for short duration when it is involved in system stabilization in case of a contingency. The MSC–TCR losses show a similar trend as those of the TSC–TCR, but they have a much lower magnitude in comparison, for the losses associated with thyristor valves are absent. Losses in each of the three SVCs are dependent on the operating point, so the preference of one SVC configuration over another must be based on the operating point at which the SVC will generally reside for most of the time in a given application.
3.10.2 Performance
A performance comparison of different SVC configurations is presented in Table 3.1 [1]. It is evident that there is no single SVC that acts as a panacea for all reactive-power compensation requirements. The choice of a specific SVC is based on several considerations—the application requirement, speed of response, frequency of operation, losses, capital cost, and so forth. Neverthe- less, the TSC–TCR is by far the most versatile among all SVC configurations, athough with a cost premium.