mathematics-11-01796 (1)

Mathematics 2023, 11, 1796 20 of 32
Table 5. Results for Case 2.
Controller
parameters
Algorithm Proposed ESMOA GSO CO
K P1 3 3 3
K i 2.712281 3 3
K P2 Area 1
0.019315 3 3
K d 1.315795 1.217712 2.178291
n 336.0855 282.2859 500
K P1 3 3 3
K i 1.174453 1.893716 1.244513
K P2 Area 2
3 3 3
K d 1.644572 1.373006 1.585313
n 489.4933 183.442 471.6436
ITAE Value 0.023653 0.026281 0.023821
ITAE improvement percent compared to the
proposed ESMOA
- 9.99 0.7057
Mathematics 2023, 11, x FOR PEER REVIEW 20 of 32
Figure 9 also shows the dynamic responses for frequency variations in each region
and tie-line transfer power. As seen in Figure 9, the suggested ESMOA outperforms the
Figure 9 also shows the dynamic responses for frequency variations in each region
CO and GSO and in tie-line reducing transfer power. the objective As seen in Figure function. 9, the suggested It provides ESMOA the outperforms lowestthe
settling times of
3.0999, 0.92, CO and 3.6663 GSO in reducing s for the deviations objective function. in frequency It provides the inlowest areasettling 1, frequency times of in area 2, and
3.0999, 0.92, and 3.6663 s for the deviations in frequency area 1, frequency in area 2, and
transfer power,
transfer
respectively.
power, respectively.
The
The
CO
CO
algorithm
algorithm obtains
obtains
settling
settling
times of
times
3.1744,
of
1.3345,
3.1744, 1.3345, and
3.7474 s, while and 3.7474 the GSO s, while algorithm the GSO algorithm attains settling times of 3.5335, of 3.5335, 1.5755, and 1.5755, 4.2202 s and 4.2202 s for
for the deviations in frequency in area 1, frequency in area 2, and transfer power, respec-
the deviations in frequency in area 1, 2, and transfer power, respectively.
tively.
(a)
Figure 9. Cont.
(b)