IEEE Systems, Man and Cybernetics Magazine - July 2021 - 25

model has a PV module in area 1 and a reheater turbine
thermal power plant in area 2. The PV module shown in
Figure 1(a) consists of a PV panel, the maximum power
point tracking, an inverter, and filters [16], [17], [35]. Further
details and a block diagram of the PV module are
available in [38] and [39]. The state variables x1
and x2
describe the dynamic change in the PV module. The transfer
function of area 1 is given by
TF s
PV
() ()()
()
= ++
+
13
2
c
as as
Ka s
signifies the speed governor setting,
x4 represents the turbine output,
x5
output, and state x6
.
(1)
The components in area 2 are the speed governor, turbine,
reheater, generator, and load model. The state variable
x3
indicates the reheater
shows the area
2 frequency output. The tie-line
power deviation is represented
by state .x7
The transfer functions of those
components of area 2 are shown in
Figure 1(a). (, ,,KK Ksg tr
and (, ,,TT Tsg tr
and T )ps
and K )ps
are the
gains and time constants of the
speed governor, turbine, reheater,
and generator load models,
respectively. R is the speed regulation
parameter of the governor,
B is the frequency bias parameter,
and a12
T Pd2
where n is the total number of areas in the power systems,
area i refers to the ith area in the power systems, c(i) is
the index of the controller gain, and oj
is the system order
of the jth area. The system with the proposed controller is
shown in Figure 1(b). In the proposed method, each area
has a controller associated with it. Area 1 has a controller
[, ]
Kk k , and area 2 has a controller K ,area 2
area,11 2
=
[, , , ] .kkk k
3 456
and k2
state variables x1
troller component k3
In Figure 1(b), the area 1 controller components k1
affect the system response with respect to the
respectively. In area 2, conand
x ,2
ering the speed governor setting (),x3
affects the system response considk4
influences
the
system performance as it incorporates
the turbine output (),x4
k5
Since its introduction,
the GSA has been
applied to a wide
variety of problems,
such as power system
design and control,
pattern recognition,
and image
processing.
is a coefficient. T Pd1 and
are the disturbances of
areas 1 and 2, respectively. The dynamics of the system
shown in Figure 1(a) are given in (S1) (see " Additional
Information " ). Considering the parameter values from
the " Parameter Values for PV Integrated Thermal Power
Systems " section in " Additional Information, " the system
described by (S1) is unstable, as it has eigenvalues at
-99.347, -12.24, −3.28 + 0.52i, − 3.28 − 0.52i, 0.93 + 0.74i,
0.93 − 0.74i, and -0.24.
Proposed Controller
The main objective of this work is to incorporate the
dynamic variations of the key components of the load frequency
control model. To control each state, a controller in
the following form is proposed:
KK ,, ,,
area
=6
where
Kk ,, ,,
,( kk11 12)( )()
areaicicici
= 6
and
coi
i
=
=
() | ,
j 1
j
(4)
-+ -+
f
@
(3)
area,, ,KK @
12 area n
f
(2)
the values of Kps
influences the system performance
by considering the dynamic
variat ions of the reheater
module (),x5
and k6
influences
the system response as it incorporates
the frequency variations
().x6
The state equations of the
system are given in (S2) (see
" Additional Information " ).
The objective is to find a set of
and Tps
ditions) [7], [27]. The load disturbances ( Pd1
controller gains that will ensure
system stability as well as improve
system performance in the presence
of disturbances. The system
parameters in a power system
change with different operating
conditions or load demands (e.g.,
change in different loading conT
and TP )d2
can also vary with time, which will affect the frequency
and the tie-line power variations in the system. Therefore,
the controller should be sensitive to these parametric
uncertainties and load variations and act accordingly to
maintain the system output within the tolerance limits.
The stability of the system with the nominal or perturbed
parameters in (S2) can be found by obtaining the
eigenvalues of the system matrix. Furthermore, to improve
the performance of the system, a metaheuristic framework
based on the GSA is proposed.
Optimizing Controller Gains Through the GSA
The GSA was first proposed by Rashedi et al. [40]. It is
inspired by the Newtonian laws of gravity and interaction
of masses. In the GSA, the controller gains in (2) are represented
as the position of agents. These agents move
through a search space depending on the gravitational
attractions among them. The interactions help agents to
scan the search space for an optimal solution. Upon satisfaction
of some user-defined iterations, the process is
stopped, and the best solution is obtained depending
upon the optimal value of an objective function.
July 2021 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 25
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IEEE Systems, Man and Cybernetics Magazine - July 2021

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