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针对一类含任意拓扑结构连接以及不可靠通信连接而引起的关联系统子系统间信息交换故障情况问题,提出了一种关联系统分析以及分散控制器设计方法。该方法首先把关联系统子系统间通信故障的随机变量看作是关联系统模型不确定性来源,并且用分式线性变换形式建立关联系统。然后,借助鲁棒控制理论推导出在最大通信连接故障情况下关联系统均方稳定的充分条件。在给定某一通信故障率下,基于线性矩阵不等式理论,通过设计分散状态反馈控制器来保证整个大系统是均方稳定的。最后,通过中国南方电网局部缩减模型作为仿真实例说明所提出模型和方法的有效性。仿真结果表明,当南方电网局部电力元件之间的通信发生故障时使用本文的方法能够很好地进行电网设计和广域控制,并使整个局部电网是均方稳定的。
Aiming at the problem of information exchange failures between related subsystems caused by arbitrary topological connections and unreliable communication connections, an associated system analysis and decentralized controller design method are proposed. The method first considers the stochastic variable that relates to the communication failure among the system subsystems as the source of the uncertainty of the associated system model, and establishes the correlation system by the form of fractional linear transformation. Then, the robust control theory is used to derive the sufficient conditions for the mean square stability of the associated system under the condition of the maximum communication connection failure. Given a certain communication failure rate, based on the theory of linear matrix inequality, decentralized state feedback controller is designed to ensure that the entire large-scale system is mean-square-stable. Finally, the effectiveness of the proposed model and method is illustrated by using the China Southern Grid partial reduction model as a simulation example. The simulation results show that the proposed method can be used to design the power grid and control the wide area well when the communication between the local power components of the China Southern Power Grid fails. Moreover, the whole local grid is mean-square-stable.