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Optimal robust disturbance observer based sliding mode controller using multi-objective grasshopper optimization algorithm to enhance power system stability

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Abstract

Power system stabilizer (PSS) has operated as an auxiliary controller for the synchronous generator excitation system to suppress the power system low frequency oscillations. This paper aims to design an optimal robust disturbance observer based sliding mode controller (RDO-SMC) acting as PSS to enhance the power system dynamic stability through the nonlinear control of excitation system. Indeed, the sliding disturbance observer has expeditiously estimated the accumulated consequence of unknown nonlinearities, parameter uncertainties, non-ideal dynamic models and exterior time-varying interferences in support of sliding mode controller. The sliding surface trajectory has been mathematically derived using Lyapunov theory. RDO-SMC has investigated the low frequency suppression of both the terminal voltage and angular speed. Due to multi-objective nature of the designed control problem, multi-objective grasshopper optimization algorithm (MOGOA) has been implemented to optimally tune the parameters of RDO-SMC and other understudy controllers. To verify and validate the performance of proposed controller, the analyses have been performed in single-machine infinite-bus and multi-machine power systems under different disturbance conditions. At last, the comprehensive simulation results have certainly confirmed the dynamic capability of the optimal RPO-SMC.

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  1. Department of Electrical Engineering, Shadegan Branch, Islamic Azad University, Shadegan, Iran

    Ali Darvish Falehi

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  1. Ali Darvish Falehi
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Correspondence to Ali Darvish Falehi.

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Appendix

Appendix

1.1 Single-machine infinite-bus power system

Generator: SB = 2100MVA, H = 3.7 s, VB = 13.8 kV, RS = 2.8544e−3, f = 60 Hz, \( X_{d} \) = 1.305 p.u.,\( X^{\prime}_{d} \) = 0.296 p.u \( X^{\prime\prime}_{d} \) = 0.252 p.u.,\( X_{q} \) = 0.474 p.u.,\( X^{\prime}_{q} \) = 0.243 p.u.,\( X^{\prime\prime}_{q} \) = 0.18 p.u., \( T_{d} \) = 1.01 s, \( T^{\prime}_{d} \) = 0.053 s, \( T^{\prime\prime}_{qo} \) = 0.1 s.

Load at Bus-2 250 MW.

Transformer 2100 MVA, 13.8/500 kV, 60 Hz, R1 = R2 = 0.002 p.u., L1 = 0, L2 = 0.12 p.u., D1/Yg connection, Rm = 500 p.u., Lm = 500 p.u.

Transmission line 3-Ph, 60 Hz, Length = 300 km each, R1 = 0.02546 Ω/km, R0 = 0.3864 Ω/km, L1 = 0.9337e−3 H/km, L0 = 4.1264e−3 H/km, C1 = 12.74e−9 F/km, C0 = 7.751e−9 F/km.

Hydraulic Turbine and Governor Ka = 3.33, Ta = 0.07, Gmin = 0.01, Gmax = 0.97518, Vgmin = − 0.1 p.u./s, Td = 0.01 s, β = 0 Tw = 2.67 s Vgmax = 0.1 p.u./s, Rp = 0.05, Kp = 1.163, Ki = 0.10

1.2 Four-machine eleven-bus power system

Generators SB = SB2 = SB3 = SB4 = 900MVA, VB = 20 kV, f = 60 Hz, \( {\text{X}}_{\text{d}} \) = 1.8, \( X^{\prime}_{d} \) = 0.3, \( X^{\prime\prime}_{d} \) = 0.25 pu, \( X_{q} \) = 1.7 pu, \( X^{\prime}_{q} \) = 0.55, \( X^{\prime\prime}_{q} \) = 0.25 pu, \( T_{d} \) = 8 s; \( T^{\prime}_{d} \) = 0.03 s, \( T^{\prime\prime}_{qo} \) = 0.05 s, RS = 2.5e−3, H = 6.5 s, p = 4.

Transformers SB1 = SB2 = SB3 = SB4 = 900 MVA, D1/Yg, V1 = 20 kV, V2 = 230 kV, R1 = R2 = 1e−6 pu, L1 = 0, L2 = 0.15 pu, Rm = 500 pu, Lm = 500 pu.

Transmission lines 3-Ph, R1 = 0.0529 Ω/km, R0 = 1.61 Ω/km, L1 = 1.403e−3H/km, L0 = 6.1e−3 H/km, C1 = 8.775e−9 F/km, C0 = 5.249e−9 F/km.

Loads Load 9 = 967 MW − 987 MVAR, Load 7 = 1767 MW − 437 MVAR.

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Darvish Falehi, A. Optimal robust disturbance observer based sliding mode controller using multi-objective grasshopper optimization algorithm to enhance power system stability. J Ambient Intell Human Comput 11, 5045–5063 (2020). https://doi.org/10.1007/s12652-020-01811-8

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