A mixed-integer linear programming approach for robust state estimation

Yanbo CHEN 0 1 Jin MA 0 1 0 Received: 22 August 2014 / Accepted: 12 November 2014 The Author(s) 2014. This article is published with open access at Springerlink.com Y. CHEN, State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University , Beijing 102206, China J. MA , School of Electrical and Information Engineering, University of Sydney , Sydney, NSW 2006 , Australia (&) 1 CrossCheck date: 12 November 2014 In this paper, a mixed integer linear programming (MILP) formulation for robust state estimation (RSE) is proposed. By using the exactly linearized measurement equations instead of the original nonlinear ones, the existing mixed integer nonlinear programming formulation for RSE is converted to a MILP problem. The proposed approach not only guarantees to find the global optimum, but also does not have convergence problems. Simulation results on a rudimentary 3-bus system and several IEEE standard test systems fully illustrate that the proposed methodology is effective with high efficiency. 1 Introduction Power system state estimation (SE) is a core function of energy management system (EMS) [1]. As a data filter, SE can provide reliable data to EMS, thereby improve the safety of power network operation. With the development of smart grid, SE will play an increasingly important role in power system operation and control. The model and implementation of SE were firstly proposed by Schweppe and Wildes in [24] in 1970. From then on, various SE models have been proposed, among which the weighted least square (WLS) approach and the fast-decoupled SE (FDSE) approach [5] are the most popular SE methods; but WLS and FDSE are very sensitive to bad measurements, i.e. bad data (BD). To suppress the effect of bad measurements on the estimation value of WLS or FDSE, the largest normal residual (LNR) test [1] or other BD identification approaches based on residual [6, 7] are always used to detect and identify any existing bad measurements, but these methods cannot effectively identify conforming bad measurements and leverage bad measurements [1]. For retaining unbiased estimation despite the existence of different types of bad measurements, many robust state estimation (RSE) approaches have also been proposed, including the weighted least absolute value (WLAV) estimation [812], the quadratic-linear (QL) estimator [13, 14], and the quadratic-constant (QC) estimator [15, 16], etc. Recently, the maximum normal measurement rate (MNMR) estimator, the maximum exponential square (MES) estimator and the maximum exponential absolute value (MEAV) estimator have been suggested in [17], [18] and [19], respectively, showing good performance in suppressing the effect of bad measurements. Mathematically, traditional SE models boil down to solve an optimization problem that is nonlinear and nonconvex in general. Thus, several issues are inevitably concerned: The global optimum cannot be guaranteed theoretically, whereas a local optimum is meaningless for SE; ` Iterative algorithms are generally required for solving the nonlinear programs, the process may become time-consuming as the number of iterations increases and in certain severe circumstances, the iterative algorithms may fail to converge; Leverage bad measurements will affect the estimation performance at certain extent. In literature, some research work has been devoted to address these issues. For example, a backtracking and trust region based method is proposed to enhance the convergence properties of SE in [20]. In [21], a novel RSE approach using mixed integer nonlinear programming (MINP) formulation is proposed. Since it is not susceptible to leverage bad measurements, this approach shows strong robustness even in pathological cases. However, the above three problems have not yet been comprehensively solved due to the intrinsic non-convexity and nonlinearity of traditional SE models. Reference [22] proposes a factorized approach for WLS, further giving rise to a bilinear state estimation approach [23]. Both of the approaches actually imply an exact linearization scheme of measurement equations. Motivated by this, we propose a mixed integer linear programming (MILP) formulation for RSE. The main idea is to use the exactly linearized measurement equations instead of the original nonlinear ones in the MINP model. Since the global optimum of MILP can be efficiently obtained by employing mature solvers, such as CPLEX, this approach has a very good prospect of online application. Main contributions of our paper are twofold: A methodology for obtaining the global optimum of SE is proposed, and a MILP model for RSE is presented; ` A mixed integer quadratic programming (MIQP) formulation for comprehensive SE is proposed. The rest of this paper is organized as follows: traditional SE models are shortly reviewed in Section 2. Section 3 proposes a MILP formulation for RSE and a MIQP formulation for comprehensive (...truncated)