Tuning of FACTS Device Stabilizers
11.2 A ‘simplistic’ tuning procedure for a SVC
The application of a ‘simplistic’ procedure to the tuning of a SVC, BSVC_4, at bus number 410 in the fourteen-generator network in Figure 10.1 is now examined. As stated in Table 10.17, the maximum and minimum reactive power generation for BSVC_4 is 1100 and Mvar, respectively, giving a reactive range (Mbase) of 1430 Mvar. The operating condition selected is the heavy load condition of Case 1 (see Table 10.2). For all PSSs in ser- vice, with their damping gains set to 20 pu on machine MVA rating, the local and inter-area modes are shown in Table 10.11. For illustrative purposes we will consider the more lightly damped of the complex inter-area modes, M ( ).
The terminal voltage bus frequency, (pu of system frequency), which is the rate of change of the terminal-voltage angle, rad, is employed as the stabilizing signal. As shown in (8.9) the transfer function of the bus-frequency pre-filter is:
, (11.1)
where (rad/s) and is the system frequency (Hz). At = 50 Hz,
; TF is normally set so that high frequency noise above the selected cor- ner frequency (1/TF) is attenuated, say, TF= 0.005 s1.
The block diagram of the FACTS device controller and stabilizer is shown in Figure 11.2.
Let us assume that the transfer function of the FDS is , a real gain (i.e. omitting compensation, washout and low-pass filters). Let’s calculate the values of the mode M for a range of gain values (not knowing as yet what constitute high gain values). As noted in Figure 10.38, the value of Mbase is 1430 Mvar, Sbase = 100 Mvar.
1. The time constant TF (5 ms) is very short. Such time constants should typically be 3 or more times the cycle time of the PSS processor to reduce phase errors at higher frequen- cies.
330 –
0.52 – j1.80
freq
freq s
s
--- 10 s 1+sTF ---
=
0 = 2f0 f0 f0
10
= 0.003183
Vs Fs rq s = kfds
Figure 11.2 The controller and stabilizer, F(s), for SVC BSVC_4 showing terminal voltage control, the provision of droop, and the frequency stabilizing signal .
In Table 11.1 the mode shifts in mode M for Case 1 are shown as the stabilizer gain kfds is increased from zero with the stabilizer in service. The mode shift for a gain of 30 pu is shown in Figure 11.3. Ideally, to introduce pure damping to the mode, the mode shift should lie at . Phase lag compensation must therefore be provided for the multi-machine sys- tem in this example noting that the required lag compensation angle increases with increas- ing gain. Although the lag compensation which the stabilizer transfer function should provide is as much as for the selected gain range, let us derive the transfer function of the lag compensation with a lag angle of at (1.8 rad/s) for the stabilizer gain of 30 pu.
Table 11.1 Case 1. Shifts in inter-area mode M with increasing FDS transfer function gain kfdsa
kfds (pu) Mode M Mode Shift Angle b
0 - -
10 5.0
20 7.6
30 11.1
40 15.7
Note: (a) FDS is a pure gain transfer function.
(b) Required lag compensation angle
Vref
Vd 500
s
2.5 1+s0.005
Vt
0.01
B
Q/Vt]
Vs
Frq
F-T F-T: Frequency
Transducer FDSF(s)
KS
KS
1 KS = Mbase / Sbase
and are in
per-unit on Mbase
B Q Vt
Frq
180
16
11 s = 0+j1.8
0.522 – j1.797
0.649
– j1.786 –0.127j0.011 0.778
– j1.763 –0.256j0.034 0.905
– j1.722 –0.383j0.075 1.024
– j1.656 –0.502j0.141
Sec. 11.2 A ‘simplistic’ tuning procedure for a SVC 535
Figure 11.3 Shift in mode M both for Kfds=30 puand for FDS transfer function (11.2).
The calculation of the transfer function of the lag compensator is similar to that for lead compensation in the example in Section 2.12.1.4 and is based on frequency response analy- sis with . The simple compensator transfer function for the lag angle of at 1.8 rad/s is . When washout and low pass filters, with corner fre- quencies 0.17 and 30 rad/s respectively, are included the transfer function of the FDS is:
, with pu. (11.2)
With the FDS of BSVC_4 in service with the above transfer function the resulting value of
mode M is for pu compared to the value of for the
scalar transfer function in Table 11.1. While the FDS enhances the damping of mode M relative to the case when the FDS is out of service, the mode shift
is not quite that desired; moreover, its modal frequency is increased from that with the sta- bilizer off-line. There are therefore a number of observations that can be found in this ‘sim- plistic’ procedure.
• The agreement between the value of the targeted mode using the ‘simplistic’ proce- dure to evaluate the stabilizer transfer function is not as close as desirable. (Further iterations of the procedure could improve the result.)
• The lag compensation of the stabilizer transfer function is based on the frequency response calculation using rather than the complex value in the vicinity of the targeted mode, . This problem is compounded when the washout and low-pass filters are added. A more rigorous, iterative process is required to converge on a lag transfer function for the stabilizer - with the specified filters - in the vicinity of the targeted mode. (With the FDS out of service, mode M varies between and over the six operating conditions, see Tables 10.11, 10.15 and 10.16.)
0.91 – j1.72
= 11.1 –0.52j1.80
Imag
Real 0.86
– j1.84 –0.34j0.05 0.38
– j0.08 Kfds=0
Kfds=30 pu FDS transfer
function
F s
s = 0+j 11
1+s0.458
1+s0.674
F s Vs
Frq
--- kfds 6s 1 6s+
--- 1+s0.458 1+s0.674 --- 1
1+s0.033 ---
= = kfds = 30
0.86
– j1.84 kfds = 30 –0.91j1.72
kfds = 30
0.34 – j0.05
s = jf s = +jf
0.43
– j1.76 –0.59j2.51
• No cognizance has been given to the suitability of the stabilizer transfer function (11.2) over an encompassing range of operating conditions (including outages, etc.) in enhancing the damping of the targeted mode.
• Although the damping of the targeted mode may be enhanced over the range of oper- ating conditions, the damping of other modes may be degraded.
• Under some operating conditions the presence of zeros or modes (other than rotor modes), in the vicinity of the targeted mode may significantly affect the trajectory of the mode as the stabilizer gain is increased.
• From Figure 10.26 it is observed that the frequency of the inter-area mode M decreases with increasing PSS damping gains. To improve synchronizing torques it may be desirable to tune the FDS to enhance not only the damping of the targeted mode but also to increase its oscillatory frequency.
It is clear that a method for tuning the stabilizers is desirable that better takes account of the range of operating conditions, the filters and the complex value of the targeted mode.