Modeling and Nonlinear Optimal Control of WeakIslanded Grids Using FACTS Device in a Game Theoretic Approach

Modeling and Nonlinear Optimal Control of Weak/Islanded Grids Using FACTS Device in a Game Theoretic Approach


A nonlinear discrete-time model along with an optimal stabilizing controller using a unified power quality conditioner (UPQC) is proposed for weak/islanded grids in this paper. An advanced stabilizing controller greatly benefits islanded medium-sized grid and microgrid due to their relatively small stored energy levels, which adversely affect their stability, as opposed to larger grids. In addition, a discrete-time grid model and controller are preferred for digital implementation. Here, the discrete-time Hamilton-Jacobi-Isaacs optimal control method is employed to design an optimal grid stabilizer. While UPQC is conventionally utilized for power quality improvement in distribution systems in the presence of renewable energy, here, the stabilizing control is added and applied to the UPQC series voltage in order to mitigate the grid’s oscillations besides UPQC’s power conditioning tasks. Consequently, the UPQC can be employed to stabilize a grid-tie inverter (GTI) or a synchronous generator (SG) with minimum control effort. When controlling the GTI associated with renewable energy sources, a reduced UPQC structure is proposed that only employs the series compensator. Next, a successive approximation method along with neural networks is utilized to approximate a cost function of the grid dynamical states, the UPQC control parameters, and disturbance, in a two-player zero-sum game with the players being UPQC control and grid disturbances. Subsequently, the cost function is used to obtain the nonlinear optimal controller that is applied to the UPQC. Simulation results show effective damping behavior of the proposed nonlinear controller in controlling both GTI and SG in weak and islanded grids.


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