Optimal planning and operation of moving target defense for detecting false data injection attacks in smart grids

Abstract

Moving target defense (MTD) in the power system is a promising defense strategy to detect false data injection (FDI) attacks against state estimation by using distributed flexible AC transmission system (D-FACTS) devices. Optimal planning and operation are two essential stages in the MTD application. MTD planning determines the optimal allocation of D-FACTS devices, while MTD operation decides the optimal D-FACTS setpoints under different load conditions in real-time. However, most MTD works focus on studying the MTD operation methods and neglect MTD planning. It is generally assumed that all lines are equipped with D-FACTS devices, which is the most expensive MTD planning solution. This dissertation separates MTD planning and MTD operation as two independent problems by distinguishing their roles in attack detection effectiveness, MTD application costs, and MTD hiddenness. The contributions of this work are three-fold as follows.

Firstly, this dissertation proves that MTD planning can determine the MTD detection effectiveness, regardless of D-FACTS device setpoints in MTD operation. This work designs max-rank MTD planning algorithms by using the minimum number of D-FACTS devices to ensure MTD detection effectiveness and minimize the MTD planning cost. It is proved that any MTDs under proposed planning algorithms have the maximum rank of its composite matrix, a widely used metric of the MTD detection effectiveness. In addition, this work further points out the maximum rank of the composite matrix is not strictly equivalent to maximal MTD detection effectiveness. Three types of unprotected buses in MTD are identified, and attack detecting probability (ADP) is introduced as a novel metric for measuring the detection effectiveness of MTD planning. It is proved that the rank of the composite matrix merely represents the lower bound of ADP, while the number of unprotected buses determines the upper bound of ADP. Then, a novel graph-theory-based planning algorithm is proposed to achieve maximal MTD detection effectiveness.

Secondly, this dissertation highlights that MTD operation ought to focus on reducing the MTD operation cost. This work proposes an AC optimal power flow (ACOPF) model considering D-FACTS devices as an MTD operation model, in which the reactance of D-FACTS equipped lines are introduced as decision variables to minimize system losses and generation costs. The proposed model can be used by system operators to achieve economic and cybersecure system operations. In addition, this dissertation rigorously derives the gradient and Hessian matrices of the objective function and constraints with respect to line reactance, which are further used to build an interior-point solver of the proposed ACOPF model.

Finally, this dissertation designs the optimal planning and operation of D-FACTS devices for hidden MTD (HMTD), which is a superior MTD method stealthy to sophisticated attackers. A depth-first-search-based MTD planning algorithm is proposed to guarantee the MTD hiddenness while maximizing the rank of its composite matrix and covering all necessary buses. Additionally, this work proposes DC- and AC-HMTD operation models to determine the setpoints of D-FACTS devices. The optimization-based DC-HMTD model outperforms the existing HMTD operation in terms of CPU time and detection effectiveness. The ACOPF-based HMTD operation model ensures the hiddenness and minimizes the generation cost to utilize the economic benefits of D-FACTS devices. Comparative numerical results on multiple systems show the efficacy of the proposed planning and operation approaches in achieving high detecting effectiveness and MTD hiddenness.