IEEE Systems, Man and Cybernetics Magazine - July 2021 - 31

Additional Information (Continued)
1 × 10-4
-1
050 100
Time (s)
(a)
2 × 10-5
-2
-4
-6
050 100
Time (s)
(d)
150 200
150 200
3 × 10-6
2
1
-1
-2
-3
050 100
Time (s)
(b)
4 × 10-5
2
-2
-4
050 100
Time (s)
(e)
150 200
Nominal Parameters
+25% of Nominal Kps and Tps
-25% of Nominal Kps and Tps
Figure S4. The output responses of the four-area power system considering the nominal and perturbed
system parameters: the frequency variations in areas (a) 2, (b) 3, and (c) 4 as well as the tie-line power
deviations between areas (d) 1 and 3, (e) 1 and 4, and (f) 2 and 3.
Parameter Values for Interconnected
Four-Area Power Systems
See [29]. KKK K 120Hz/p.u.
ps23 ps4
ps1 234
ps
ps
ps
ps
tttt
=== =
sg rr rt tt t
sg
12 3
sg34
TT T== = KKKKK KKsg1234 123
4 123 1 2341035KKK TT TT
20 s, ==== == =
MW, Tps1
sg
sg
K ,.,. ,03 s 12sg ==
TT ., TTT .,=== RRRR
1234
24. Hz/p.u.MW, ====b bbb 0 .4251234 p.u.MW/Hz, 12
2220TTT .0707p.u.MW/Hz, and aa13
14==
13
14
23
23
rr r===
aa .1
12==
= === = === TTsg
==008s rrr 42s === =
2rT =
=
Parameter Values for Interconnected
Two-Area Power Systems With GDB
See [7]. KK 120 Hz/p.u.MW,
sg12
ps12
ps
KT T103stt t21 2
bb .0425 p.u.MW/Hz, 20T .,r 12 =
a12 =-1 .
12
== =
==
sg
==
150 200
9 × 10-5
6
3
-3
-6
-9
050 100
Time (s)
(c)
2 × 10-5
1
-1
-2
-3
050 100
Time (s)
(f)
150 200
150 200
TT ,20 s== Kt1
ps12
ps
,. ,TT ., ==
==02s RR .20 Hz/p.u.12
MW,
0707p.u.MW/Hz and
=
Since its introduction, the GSA has been applied to
Kk kk iN1==6
i (, , ..., )
12 d
ii
i
a wide variety of problems, such as power system
design and control, pattern recognition, and image
processing [41]. In [41], a detailed review elaborating
its applications into different engineering and science
domains is provided.
Consider a d-dimensional search space
do ,, ,in1
n
==
=
i 1
where n is the total number of areas in the power systems.
The controller gains
with states xx ,12 ,, ,xd
agent i is
kk , ,, kd
12
f
f are associated
respectively. The position of
FG
ij
m
() ()#aa R () +
= c
i aaj
#
MM m
() ()
ij ae kkm
- i
(( )( )),
j aa (8)
July 2021 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 31
| 6f
i
(5)
, ..., ,
(6)
where N is the total number of agents in the search space.
The initial values of the controller gains can be drawn
from a range satisfying the system stability as
kk km di N01 1 , ..., ,
m
m () (, )
m
l
u
i
,, and
! 6f 6== (7)
where l and u are the lower and upper limits of the respective
controller gains. Now, at a specific iteration
force acting on agent i from agent j in dimension m can be
written as
a , the
∆Ptie13 (p.u. MW)
∆f2 (Hz)
∆Ptie14 (p.u. MW)
∆f3 (Hz)
∆Ptie23 (p.u. MW)
∆f4 (Hz)

IEEE Systems, Man and Cybernetics Magazine - July 2021

Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - July 2021

contents
IEEE Systems, Man and Cybernetics Magazine - July 2021 - Cover1
IEEE Systems, Man and Cybernetics Magazine - July 2021 - Cover2
IEEE Systems, Man and Cybernetics Magazine - July 2021 - contents
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 2
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 3
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 4
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 5
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 6
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 7
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 8
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 9
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 10
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 11
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 12
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 13
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 14
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 15
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 16
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 17
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 18
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 19
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 20
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 21
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 22
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 23
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 24
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 25
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 26
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 27
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 28
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 29
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 30
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 31
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 32
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 33
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 34
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 35
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 36
IEEE Systems, Man and Cybernetics Magazine - July 2021 - 37
IEEE Systems, Man and Cybernetics Magazine - July 2021 - Cover3
IEEE Systems, Man and Cybernetics Magazine - July 2021 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/smc_202310
https://www.nxtbook.com/nxtbooks/ieee/smc_202307
https://www.nxtbook.com/nxtbooks/ieee/smc_202304
https://www.nxtbook.com/nxtbooks/ieee/smc_202301
https://www.nxtbook.com/nxtbooks/ieee/smc_202210
https://www.nxtbook.com/nxtbooks/ieee/smc_202207
https://www.nxtbook.com/nxtbooks/ieee/smc_202204
https://www.nxtbook.com/nxtbooks/ieee/smc_202201
https://www.nxtbook.com/nxtbooks/ieee/smc_202110
https://www.nxtbook.com/nxtbooks/ieee/smc_202107
https://www.nxtbook.com/nxtbooks/ieee/smc_202104
https://www.nxtbook.com/nxtbooks/ieee/smc_202101
https://www.nxtbook.com/nxtbooks/ieee/smc_202010
https://www.nxtbook.com/nxtbooks/ieee/smc_202007
https://www.nxtbook.com/nxtbooks/ieee/smc_202004
https://www.nxtbook.com/nxtbooks/ieee/smc_202001
https://www.nxtbook.com/nxtbooks/ieee/smc_201910
https://www.nxtbook.com/nxtbooks/ieee/smc_201907
https://www.nxtbook.com/nxtbooks/ieee/smc_201904
https://www.nxtbook.com/nxtbooks/ieee/smc_201901
https://www.nxtbook.com/nxtbooks/ieee/smc_201810
https://www.nxtbook.com/nxtbooks/ieee/smc_201807
https://www.nxtbook.com/nxtbooks/ieee/smc_201804
https://www.nxtbook.com/nxtbooks/ieee/smc_201801
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1017
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0717
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0417
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0117
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1016
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0716
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0416
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0116
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_1015
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0715
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0415
https://www.nxtbook.com/nxtbooks/ieee/systems_man_cybernetics_0115
https://www.nxtbookmedia.com