Modified whale optimization algorithm for coordinated design of fuzzy lead‐lag structure‐based SSSC controller and power system stabilizer

Abstract

Summary In this paper, a new fuzzy lead‐lag controller for a coordinated structure combining static synchronous series compensator and power system stabilizer is designed to improve the power system stability. The controller parameters are optimized by using a modified whale optimization algorithm (MWOA). The newly proposed MWOA attains a suitable balance among exploration and exploitation phases of WOA. This potential of this MWOA is certified by means of utilizing the benchmark functions and by further comparing with that of a few heuristic algorithms such as whale optimization algorithm, fast evolutionary programming algorithm, gravitational search algorithm, differential evolution, and particle swarm optimization. Here, the MWOA technique is utilized to tune the parameters of the proposed controller. The controller is tested under various loading conditions as well as system configurations such as single‐machine infinite bus system and multimachine power system. Finally, the simulation results so obtained using the designed controller under different disturbance conditions are contrasted with that of the conventional lead‐lag structure controller.

Multi objective design of type II fuzzy based power system stabilizer for power system with wind farm turbine considering uncertainty

“…The stabilization of low frequency oscillations (LFOs) is one of the most important issues in multi-area power systems with weak tie-lines. 2 The Abbreviations: T m , mechanical torque; t f , time of occurrence of the fault; T e , electric torque; t p , time permitted to damp the oscillation; H m , constant inertia; OS ij and US ij , overshoot and undershoot of the speed deviation of generators i and j, respectively; X m , reactance; T s,ij , its damping time; i qr and i dr , the rotor current in the Park area; α, β, and γ, weighting factors; i qs and ids, stator current in the Park transformation area; f, w, weighting factor; r 1 and r 2 , random numbers that are distributed uniformly; ω b and ω m , base electrical and mechanical angular velocity of the system; c 1 and c 2 , personal best solution and the global best solution learning coefficients; ω b and ω m , base electrical and mechanical angular velocity of the system; k, w, weighting; υ t , velocity of the blade tip; V k [t + 1], velocity of particle; υ w , wind speed at the top of the rotor; P w , mechanical power; η GB , gearbox ratio; ρ, air density; p, number of generator poles; υ w , wind speed; R, rotor's radius; θ P , torque angle; α, represents Weibull scale parameter; A r , area enclosed by the rotor; β, parameter of Weibull Form; λ, relative velocity of the tip of the blade; P r , rated power of the wind farm; C P , coefficient of power efficiency; V ci , V co , and V r , specifications of a wind turbine; SLD, single line diagram; Δω ij , angular speed deviation of generators; MOPSO, multi objective particle swarm optimization; t sim , time of simulation; OT2F-PSS, optimized type II fuzzy power system stabilizer; ISEUS, integral of square error until settling; PDF, probability distribution function; FD, figure of demerit; PSO, particle swarm optimization; PSS, power system stabilizer; DFIG, doubly fed induction generator; HBB-BC, Hybrid Big Bang-Big Crunch; μ A (x), represents the membership; J x , initial member; PB, positive big; H, inertial constant; PS, positive short; OT1F-PSS, optimized type I fuzzy based PSS (OT1F-PSS); Z, zero; NB, is negative big; NS, negative short. continuation of these oscillations in a power system with wind farm can lead to both a reduction in the power of the transmission lines and instability in the power.…”

“…By increasing the penetration of wind resources, their impact on the dynamic stability of the power system has been increased. The stabilization of low frequency oscillations (LFOs) is one of the most important issues in multi‐area power systems with weak tie‐lines . The continuation of these oscillations in a power system with wind farm can lead to both a reduction in the power of the transmission lines and instability in the power .…”

“…The stabilization of low frequency oscillations (LFOs) is one of the most important issues in multi-area power systems with weak tie-lines. 2 The Abbreviations: T m , mechanical torque; t f , time of occurrence of the fault; T e , electric torque; t p , time permitted to damp the oscillation; H m , constant inertia; OS ij and US ij , overshoot and undershoot of the speed deviation of generators i and j, respectively; X m , reactance; T s,ij , its damping time; i qr and i dr , the rotor current in the Park area; α, β, and γ, weighting factors; i qs and ids, stator current in the Park transformation area; f, w, weighting factor; r 1 and r 2 , random numbers that are distributed uniformly; ω b and ω m , base electrical and mechanical angular velocity of the system; c 1 and c 2 , personal best solution and the global best solution learning coefficients; ω b and ω m , base electrical and mechanical angular velocity of the system; k, w, weighting; υ t , velocity of the blade tip; V k [t + 1], velocity of particle; υ w , wind speed at the top of the rotor; P w , mechanical power; η GB , gearbox ratio; ρ, air density; p, number of generator poles; υ w , wind speed; R, rotor's radius; θ P , torque angle; α, represents Weibull scale parameter; A r , area enclosed by the rotor; β, parameter of Weibull Form; λ, relative velocity of the tip of the blade; P r , rated power of the wind farm; C P , coefficient of power efficiency; V ci , V co , and V r…”

The nonlinear autoregressive network with exogenous inputs (NARX) neural network to damp power system oscillations

“…The commissioning of the controller must be finalized as quickly as possible and must also endorse adequate operation regarding different operating conditions of the electrical system 5 . Researchers developed a large quantity of PSS design techniques that performed quite well in stabilizing the system, such as adaptive control techniques, 6 fuzzy logic, 5 sliding mode control techniques, 7 robust control techniques, 8 optimization methods using LQR, 9 H∞ techniques, 10 artificial intelligence techniques 11‐13 and linear control techniques, such as pole placement 13 . Therefore, using conventional methods under inconstant operating conditions is a complex process 14 .…”

“…Several optimization algorithms are used for power system stabilization. Some examples of optimization algorithms applied to stabilizers and power systems are genetic algorithms (GAs), 15,16 the honeybee mating optimization, 8 swarm techniques, the Taguchi technique, 17 particle swarm, 4 and the whale optimization algorithm (WOA) 5,14,18 . GAs differ from the conventional search optimization methods because of their best solutions in several applications as described in 15,16 due to the following aspects: (a) GAs operate in a set of coded solutions and not in the solutions themselves; (b) GAs perform a search procedure from a set of solutions and not from a single solution; (c) GAs use only values of a nonderived suitability function or other auxiliary knowledge; and (d) GAs use probabilistic and not deterministic transition rules.…”