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In linear quadratic regulator (LQR), two different weighting matrices play an important role in presenting the performance of this controller. Instead of using classic common approach, which is trial and error method, this study proposes a particle swarm optimization (PSO) algorithm to track the best solution of the weighting matrices. The proposed algorithm is tested on shunt hybrid active power filter (APF) to mitigate the harmonic contents in voltage and current signals in a nonlinear load system. The modeling work of this proposed system is simulated using MATLAB/Simulink software. From the simulation, the obtained results proved that using PSO in tuning the LQR controller produce smoother nonlinear voltage and current signals. In fact, the amount of current to be injected into network can be reduced up to 95%. Besides, less time is consumed during searching the optimum weighting matrices using the proposed approach.

The replacement of a conventional synchronous generator (SG) with higher wind penetration greatly reduces the inertial support available for the system. Therefore, a new consideration-the dynamic frequency changes in a wind energy system using a super-capacitor (SC)-is proposed here to provide faster, limitless, inertial response during load disturbances. By considering the dynamic frequency change in defining the power exchange between SC and network, this proposed method not only provides inertial and primary frequency response but is also able to avoid a second frequency dip. To avoid deep charge and discharge of SC, a simple energy management system (EMS) which considers the system frequency deviation and the state of charge (SOC) of SC is adopted in this technique. The effectiveness of the proposed technique is modelled in MATLAB/Simulink software. Comparative analyses between the proposed virtual inertial support (VIS)-based SC and existing VIS control strategies are performed. The simulation results obtained prove that the proposed VIS greatly reduces the frequency nadir and peak frequency of the system during sudden load increase and decrease, respectively.

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