H∞ voltage control of islanded microgrid three-phase inverter: a model-free integral reinforcement learning approach

In this paper, an inner-loop control method based on the integral reinforcement learning (IRL) algorithm is proposed to address the challenges of uncertain inverter model parameters and strong disturbances caused by nonlinear and unbalanced loads. Firstly, the mathematical model of an LC-type off-grid inverter is established in the d-q axis, and the off-grid inverter voltage control problem is transformed into an H
∞
tracking problem by introducing the augmented system. The reference signal of the inverter output voltage, together with the original state, are defined as the state of the augmented system. An initial control gain along with exploration noises are conducted on the inverter to collect augmented state data and disturbance data (output current). Then, by utilizing the principles of zero-sum game theory, the tracking Hamilton-Jacobi-Isaacs (HJI) equation is derived, and the IRL algorithm is proposed to solve this equation. The Kronecker products containing state values, control inputs, and disturbance values are calculated based on the measurement data, and the iterative inverter voltage control strategy is derived. Next, it is proven that the proposed control policy ensures the asymptotic stability of the augmented system and satisfies the L
2
gain condition. Finally, the effectiveness of the proposed algorithm is verified through simulation.