IEEE Systems, Man and Cybernetics Magazine - July 2021 - 30

Additional Information (Continued)
and b are 30 and 10,
kk kk k
and k ..33 5931
12 34 5
G ()0c
respectively; and the
maximum number of iterations is 100. The optimal
controller gains obtained by the proposed method are
., ., ., ., .,
=- == ==6
5330810952
17 9836 15 99787948
=
The performance of the system with the objective
function as per (S3) is given in Table S2. Here, the
maximum peak (),Mp
settling time (),ts
load disturbance is added at t 15 s=
= at time t 45 s=
is decreased to 0.02 p.u. MW at time t 30 s=
T P 0d2
. Afterward, the load
, and, finally,
. The performances of the system are
obtained considering the nominal and !25 % variations in the
parameters ,, ,,KT TTps ps
t sg and R along with the variable load
and objective
value are considered to demonstrate the results. It is
observed from Table S2 that the undershoot of the
frequency responses for area 1 has reduced in
comparison to the system response considering ISE
[refer to (13) and the nominal data in Table S1] as an
objective function; however, the settling time of the area
1 frequency response has increased. Improvements in
the undershoot and settling time are observed for area 2
responses. Similar observations are also noted for the tieline
responses.
A variable load disturbance is considered in area 2 of the
two-area PV integrated thermal power system as shown in
Figure S2 [19]. Initially, the value of Pd2
, the value of Pd2
zero. At time t 5s=
T is considered as KT ss== =
T is increased to 0.015
rt sg
03303008
B = 0.8 p.u. MW/Hz, T2 12
per unit (p.u.) MW. A further increment of 0.015 p.u. MW in
disturbance. These performances are tabulated in Table S3.
Four-Area Power Systems
The nominal parameters of four-area power systems
are given in the sidebar section " Parameter Values for
Interconnected Four-Area Power Systems. " The fourarea
system with the proposed feedback controller is
shown in Figure S3. The performance obtained by the
proposed method for the four-area interconnected
power system considering the nominal and perturbed
system parameters is tabulated in Table S4. The frequency
responses and tie-line power deviations of the considered
system are shown in Figure S4(a)-(f).
Parameter Values for PV Integrated
Thermal Power Systems
See [27] and [35]. K 120Hz/p.u.MW,
., ., .,T
ps =
T 20 s , K ,1t
ps =
=
99.4974747, a2 =−50, a3 = 0.502525317, an a 1= .
r = .0545 p.u. MW/Hz, Kc = −18, a1
d 12
Tr = 10 s. R = 0.4 p.u. MW/Hz.
=
Table S4. The performance of interconnected four-area power systems by the
proposed method considering nominal and perturbed system parameters.
Parameters % Change Performance
Mp (−ve)
(×10−4)
( fT in Hz;
T P in
Nominal
p.u. MW)
ts (s)
+25
KK
KK
TT
ps ps
ps ps
ps ps
12
,,
34
12
,,
,,
TT ,andps34
ps
-25
(×10−4) ( fT
in Hz; PT in
p.u. MW)
ISE (×10−7)
Mp (−ve)
ts (s)
(×10−4) ( fT
in Hz; PT in
p.u. MW)
ISE (×10−7)
Mp (−ve)
ts (s)
ISE (×10−7)
116.29 130.96 144.61 151.58
3.2642 0.4066 0.00047 0.6999
137.65
1.022
140.11
4.0039
151.58
0.1786
142.18
0.9947
(Continued)
116.29 130.95 144.59 151.56
3.265
0.4068 0.00047 0.7003
4.1472 0.8302 0.0192 0.6583
137.63
1.0221
0.3402
140.09
4.0042
0.6803
151.55
0.1785
0.3322
142.16
0.9947
0.3401
116.29 130.96 144.59 151.56
3.2647 0.4067 0.00047 0.7002
4.1479 0.8306 0.0192 0.6586
137.64
1.0221
0.3402
140.1
4.0039
0.6803
151.55
0.1785
0.3322
142.16
0.9947
0.3401
Tf1
Tf2
Tf3
Tf4
4.1476 0.8305 0.0192 0.6585
TP12
0.3402
T P13
0.6803
T P14
0.3322
T P23
0.3401
30 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE July 2021
IEEE Systems, Man and Cybernetics Magazine - July 2021

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