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In this paper, we propose an analytical framework to quantify the amount ofdata samples needed to obtain accurate state estimation in a power system - aproblem known as sample complexity analysis in computer science. Motivated bythe increasing adoption of distributed energy resources into thedistribution-level grids, it becomes imperative to estimate the state ofdistribution grids in order to ensure stable operation. Traditional powersystem state estimation techniques mainly focus on the transmission networkwhich involve solving an overdetermined system and eliminating bad data.However, distribution networks are typically underdetermined due to the largenumber of connection points and high cost of pervasive installation ofmeasurement devices. In this paper, we consider the recently proposedstate-estimation method for underdetermined systems that is based on matrixcompletion. In particular, a constrained matrix completion algorithm wasproposed, wherein the standard matrix completion problem is augmented withadditional equality constraints representing the physics (namely power-flowconstraints). We analyze the sample complexity of this general method byproving an upper bound on the sample complexity that depends directly on theproperties of these constraints that can lower number of needed samples ascompared to the unconstrained problem. To demonstrate the improvement that theconstraints add to distribution state estimation, we test the method on a141-bus distribution network case study and compare it to the traditional leastsquares minimization state estimation method.

Sample Complexity of Power System State Estimation using Matrix Completion