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Table 1 Optimum parameters for PID, PD-PID, PI-PD and PIDD-PI controller under bilateral transactions

From: Cascade controller based modeling of a four area thermal: gas AGC system with dependency of wind turbine generator and PEVs under restructured environment

Controller gains

PID

PD-PID

PI-PD

PIDD-PI

Area 1 (outer loop)

    

 KP1*

0.7623

0.6428

0.2526

0.8654

 KI1*

0.8317

–

0.7773

0.1727

 KDD1*

0.6369

0.5850

–

0.4620

 N1*

34.141

–

–

27.036

Area 2 (outer loop)

    

 KP2*

0.4871

0.6232

0.5930

0.6698

 KI2*

0.6783

–

0.9759

0.2318

 KDD2*

0.5669

0.4161

–

0.1919

 N2*

75.944

–

–

54.385

Area 3 (outer loop)

    

 KP3*

0.6656

0.8079

0.7394

0.6161

 KI3*

0.8552

–

0.7035

0.3981

 KDD3*

0.5600

0.4773

–

0.2848

 N3*

60.358

–

–

10.075

Area 4 (outer loop)

    

 KP4*

0.1966

0.7248

0.5771

0.8909

 KI4*

0.9992

–

0.9986

0.2990

 KDD4*

0.2077

0.6629

–

0.8387

 N4*

69.177

–

–

39.685

Area 1 (inner loop)

    

 KPP1*

–

0.6779

0.7904

0.9638

 KIP1*

–

0.9358

–

0.9330

 KD1*

–

0.4908

0.3783

–

 NC5*

–

41.764

87.572

–

Area 2 (inner loop)

    

 KPP2*

–

0.5718

0.4939

0.9776

 KII2*

–

0.6510

–

0.2645

 KD2*

–

0.6627

0.4525

–

 NC2*

–

42.756

41.856

–

Area 3 (inner loop)

    

 KPP3*

–

0.5201

0.7459

0.9140

 KII3*

–

0.7932

–

0.1336

 KD3*

–

0.3259

0.5719

–

 NC3*

–

76.152

57.746

–

Area 4 (inner loop)

    

 KPP4*

–

0.3118

0.9363

0.3332

 KIP4*

–

0.9998

–

0.9837

 KD4*

–

0.2759

0.2216

–

 NC4*

–

38.186

44.396

–

  1. * represents optimum values for the PIDD - PI controller using Harris Hawk Algorithm