Distributed Sparse LQR Control for Power Systems With Markov Jump Interconnection Topologies

In this paper, we consider a class of stochastic interconnected power systems that involve multiple generators exchanging information through a specialized interconnection structure. In practical scenarios, due to unpredictable transient events such as faults, load changes, and attacks, the inter-generator interconnection structure undergoes random alterations. By employing Markov Chain to model the stochastically varying interconnection topology between generators, we establish a stochastic interconnected power system (SIPS) characterized by markov jump interconnection topologies. Leveraging the stochastic interconnection structure of the SIPS, we formulate a distributed sparse Linear Quadratic Regulator (LQR) control problem and analyze the stability of the closed-loop SIPS under sparse control, as well as its optimality given interconnection structure constraints. Based on scaling technology, we introduce a new model-based Sparse Scaling Policy Iteration (SSPI) algorithm to effectively compute distributed optimal controllers under these sparse constraints. Furthermore, a model-free SSPI is developed for scenarios where system dynamics are unknown, removing there liance on system dynamics and avoiding the need for an initially stabilizing controller. This paper also provides theoretical guarantees for the stability and convergence of the SSPI. Finally, we validate the effectiveness of the SSPI through an application to an interconnected three-generator power system.