基于平方和方法的H_∞最优励磁控制

H_∞ Optimal Excitation Control for Power System Based on Sum of Squares Programming

为了改善电力系统在干扰信号下的稳定性,在单机无穷大电力系统的基础上,提出了一种基于平方和方法的H_∞最优励磁控制设计方法。本文电力系统属于非多项式系统,而所提方法利用泰勒公式将非多项式系统等效转化为多项式系统,并保留高阶无穷小项。在给定扰动抑制率,以及利用平方和方法构造Lyapunov函数、控制器参数优化方面的优势前提下,可以将哈密顿-雅克比-伊萨克等式问题松弛为不等式约束表示的最优问题,最终结合策略迭代方法,实现了H_∞最优励磁控制器设计,提高了仿真的真实度。仿真结果表明所设计最优控制器可以有效改善系统性能,增强系统抗干扰能力。

To improve the stability of the power system under the disturbance signal,the paper proposes an H∞ optimal excitation control method based on sum of squares method of the single machine infinite power system.The power system is a kind of non-polynomial system,while the proposed method uses the Taylor formula of non-polynomial systems transformed into polynomial system which keeps the high order infinitely small.The methods transform the non-polynomial systems using the Talor method and keep the high order infinitely small.Under a given attenuation coefficient and taking the advantages of sum of squares in the construction of Lyapunov function and parameter optimization,the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities constraints.After applying the policy iteration technique,the method is able to design the H∞optimal excitation controller and enhance the reality of simulations.Experimental results prove that the method can not only effectively improve the system performance but also enhance the anti-interference ability of the system.