Multi-area state estimation using distributed SDP for nonlinear power systems

State estimation (SE) is an important task allowing power networks to monitor accurately the underlying system state, while multi-area SE is becoming increasingly popular as the power grid comprises multiple interconnected “subgrids.” For nonlinear AC power systems, SE per subgrid amounts to minimizing a nonlinear least-squares cost that is inherently nonconvex, thus giving rise to many local optima. Despite the non-convexity, a recent SE approach based on semidefinite programming (SDP) has been effective in approaching globally optimal performance at the price of higher computational cost. A novel reduced-complexity algorithm is developed in this paper for local control areas to solve the centralized SDP-based SE problem in a distributed fashion. It leverages results on positive semidefinite matrix completion to split a global state matrix constraint into local ones, which further allows for parallel implementation using the alternating-direction method of multipliers (ADMM). With minimal data exchanges among neighboring areas, each control center can efficiently perform local updates that scale with each area's size (number of buses). Numerical simulations using the IEEE 14-bus system demonstrate the asymptotic convergence of local state matrices, and desirable estimation accuracy attainable with a limited number of exchanges.

[1]  A. Monticelli,et al.  Electric power system state estimation , 2000, Proceedings of the IEEE.

[2]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[3]  Georgios B. Giannakis,et al.  Distributed Robust Power System State Estimation , 2012, IEEE Transactions on Power Systems.

[4]  Charles R. Johnson,et al.  Positive definite completions of partial Hermitian matrices , 1984 .

[5]  Soummya Kar,et al.  Cooperative distributed state estimation: Local observability relaxed , 2011, 2011 IEEE Power and Energy Society General Meeting.

[6]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[7]  Antonio Gómez Expósito,et al.  A Multilevel State Estimation Paradigm for Smart Grids , 2011, Proceedings of the IEEE.

[8]  Dick Duffey,et al.  Power Generation , 1932, Transactions of the American Institute of Electrical Engineers.

[9]  Zhi-Quan Luo,et al.  Semidefinite Relaxation of Quadratic Optimization Problems , 2010, IEEE Signal Processing Magazine.

[10]  Georgios B. Giannakis,et al.  Robust power system state estimation for the nonlinear AC flow model , 2012, 2012 North American Power Symposium (NAPS).

[11]  G.B. Giannakis,et al.  Consensus-Based Distributed MIMO Decoding Using Semidefinite Relaxation , 2007, 2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing.

[12]  Georgios B. Giannakis,et al.  Estimating the state of AC power systems using semidefinite programming , 2011, 2011 North American Power Symposium.

[13]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[14]  David Tse,et al.  Distributed algorithms for optimal power flow problem , 2011, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[15]  A. G. Expósito,et al.  Power system state estimation : theory and implementation , 2004 .

[16]  Ali Abur,et al.  On the use of PMUs in power system state estimation , 2011 .

[17]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[18]  Hadi Saadat,et al.  Power System Analysis , 1998 .