Table 3 The optimum parameters of the PI controllers used in the system control.

From: Optimizing control and management of hybrid power system, consisting PV-wind and battery-super capacitor, using COOT algorithm

Gains

\(\:{Kp}_{1}\)

\(\:{Ki}_{1}\)

\(\:{Kp}_{2}\)

\(\:{Ki}_{2}\)

\(\:{Kp}_{3}\)

\(\:{Ki}_{3}\)

\(\:{Kp}_{4}\)

\(\:{Ki}_{4}\)

\(\:{Kp}_{5}\)

\(\:{Ki}_{5}\)

\(\:{Kp}_{6}\)

\(\:{Ki}_{6}\)

\(\:{Kp}_{7}\)

\(\:{Ki}_{7}\)

GA -PI

95.2340

90.7677

99.5889

58.4372

99.8323

19.0675

39.8228

57.5075

11.3808

100

100

11.7834

100

59.3345

COOT-PI

100

24.0447

100

99.9565

99.9949

22.0796

7.1496

100

11.4498

100

99.7063

88.7763

99.9828

62.6826

  1. Following obtaining the results of the PI controller, we applied the COOT optimization algorithm with the objective function to determine the optimal parameters of the PI-PID controller, as presented in Table 4. Since their number is large, we increased the number of search agents to 140:
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