Closure to "state estimation distributed processing"

Abstract

The authors are to be commended on presenting an interesting and well written paper 1 to address distributed state estimation processing. Their approach is based on decomposition techniques; the power network is divided into geographical areas and the solution of each area subproblem is iteratively coordinated until the optimal integrated solution is achieved. The authors have also presented test results applied to actual large-scale power systems. We would appreciate authors' comments on the following points.We recently presented preliminary results using a similar approach where we address the multi-area state estimation problem [1]. We found that the efficiency of the proposed augmented Lagrangian highly depends on a fine tuning of the , and parameters. However, the authors used identical values for all the test systems presented in the paper. 1 Have the authors explored any strategy for choosing those parameters as a problem-dependent data function? How sensitive is the proposed approach to the starting point 0 ?We find useful to share our experiences in comparing the proposed approach against a standard Lagrangian relaxation technique. The use of the auxiliary principle problem as presented by the authors yielded a fairly efficient approach in terms of number of iterations (six iterations at most). However, the introduction of the quadratic term =2kf a (x) 0f b (y)k 2 (see Section 2.2.1) may lead to slightly different solutions as compared to the ones obtained in a centralized approach. On the other hand, a standard Lagrangian relaxation technique, which usually takes larger number of iterations to converge, may outperform the proposed approach in terms of accuracy. The quadratic term, which is introduced to improve convergence, "convexifies" the dual function associated with problems (1-2) and thus, it leads to slightly different results.In Section 2.3, the authors make reference to communication issues where they state that "only the computed border variables are exchanged between adjacent areas." It should be noted that Lagrange multipliers associated with "f a (x) 0 f b (y) = 0" constraints should also be exchanged between control areas, at least at the first iteration of the algorithm. In the case a central computer controlling the coordination is in charge of not only checking for convergence but also variable updating, Lagrange multipliers should be exchanged at each iteration. In any case, we agree with the authors that the amount of information to be exchanged is quite small.In our experiments, we have found that the number of iterations of the decomposition scheme is related to the following index I:where s t is the apparent power flow through tie-line t, and n t is the total number of tie-lines. This ratio give a measure of the coupling between areas. In our tested systems, it showed to be a good index to get an idea of the rate of convergence of the decomposition approach. The larger the index, the lower the number of iterations to achieve convergence. Could this result be extended to the test sy...

A taxonomy of multi-area state estimation methods

“…Ebrahimian and Baldick [23] applied in 2000 the so-called "Auxiliary Problem Principle", a well-known technique in large-scale optimization, to develop a two-step procedure based on border-bus overlapping areas. The overall WLS objective function is expressed as the sum of partial functions, each one corresponding to a subsystem.…”

Simulation and evaluation of optimization problem solutions in distributed energy management systems

“…Each subsystem is described by its own constraints and its own part of the objective function (if any): optimization subproblems thus correspond to physical subsystems. It is the case, for example, of the state estimation problem split into state estimation subproblems [5], [16], or the optimal power flow problem divided into optimal power flow subproblems [17].…”

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Distributed State Estimation of Multi-region Power System based on Consensus Theory

“…Authors of [8] presented an effective and accurate method for multi-area power system state estimation, which could improve the bad data detection capability and the convergence speed by using well-tuned measurement weights. In [9], an overlapped sub-region partitioning was proposed for the distributed state estimation problem, and a parallel algorithm based on the principle of virtual boundary measurement was designed to solve the problem. Authors of [10] proposed a multi-area paralleled state estimation method on the basis of sub-regions independently performing the local state estimation and the control center coordinately calculating the global optimal solution with the boundary variables.…”