IEEE Systems, Man and Cybernetics Magazine - July 2021 - 28

Additional Information (Continued)
Table S2. The performance of two-area PV integrated thermal power systems
with the proposed method considering (S3) as an objective function.
Mp
Tfve1
()(Hz)
-
0.00196
Tfv Hze2
0.0028
()()
-
TP (p.u.MW)
0.00065
tie
The authors in [28] proposed an ACO-based PID controller
for a single-area nuclear power plant in different loading
conditions. In [29], the authors proposed a direct synthesis
process, and, in [30], the authors used the Laurent series for
the design of PID controllers for frequency control in singleand
multiarea power systems.
In [31], the authors used a robust PI controller for a
multiarea interconnected power system for the LFC using
population extremal optimization (PEO) and LMI techniques
considering different objective functions. In [32], a tuning
method for a PI controller using the crazy PSO algorithm for
the LFC in a two-area nonreheater thermal plant with the
GDB was proposed.
In [33], a differential evolution-based PI controller was
proposed for the LFC in an interconnected power system
using ITAE and author-defined objective function. The
authors in [34] proposed a hybrid PSO and BFO algorithmbased
PI controller for an interconnected power system
for frequency control using ITAE and an author-defined
objective function. In [35], the authors proposed a PEObased
adaptive PI controller for frequency control in a PV
integrated thermal power system considering IAE, ITAE, ISE,
and ITSE as objectives.
Additional Methodology
The dynamics of a two-area PV integrated thermal power
system [Figure 1(a)] are given by
0.04
0.03
0.02
0.01
-0.01
010203040
Time (s)
T f1
11.1
o
o
o
o
o
o
o
ts (s)
Tf2
7.94
.
.
1
2
=- 11 + c
()
3 36 x7
Tsg
x T
K x T x
.
4
x
t
1
t
rt
x T
K
xT xx xP h.
6
7
2r 12 26 71
56 Tps
^
ps
T d
ps
ps
x T x
1
5 34 5
Tt
=- -+
=- +- -
==+
-=-
+=
--21
13 27
c
1
sg
sg
sg
()
BR x
Ka12
sg
T x T
K
34
t
KK x TT
K
c11r mx T x
Ka12
rt
ps
r
x T
K
72
ps
ps
TPd
(S1)
The state equation of the two-area PV integrated thermal power
system with the proposed controller [Figure 1(b)] is given by
o
o
o
o
o
o
xaxK x
xa ax ax Kx
x
1
2
=- 11 + c
()
1
sg
t
1
7
3 36 7
Tsg
T x T
K
sg
sg
()
BR x
x
x T
K x T x
4
x5
x6
t
rt
Tt
Kk
Tps
ps
ps
x3
34
t
xT kx1 () 26 71
o 21 k xxx P h.
7
=- -+
=- +- -
==+
-=-
-+ -
-+ +=-
+- -- -
21 13 27
c
Ka12
sg
KK x TT
K
Kk
Tps
ps
Kk
ps
r 12
^
6
d 1
TTps
1
nx6
34 5
3
c11r mx T x
d
rt
4
x4
ps
r
T
K
2
ps
ps
Ka12
Tps
Kk
Tps
ps
x T
K
5
nx5
72
ps
ps
TPd
T d
(S2)
Additional Results
Two-Area PV Integrated Thermal Power Systems
The nominal system parameters of a two-area PV integrated
thermal power system are given in the sidebar section
" Parameter Values for PV Integrated Thermal Power Systems. "
The comparative responses of the area 2 frequency and
tie-line power deviations with the nominal and perturbed
system parameters are shown in Figure S1(a) and (b). The
performance of the proposed method under parametric
uncertainty is tabulated in Table S1.
Furthermore, in the proposed analysis, the L3
error is
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