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Abstract-This paper introduces a technique for meter placement for the purpose of improving the quality of voltage and angle estimates across a network. The proposed technique is based on the sequential improvement of a bivariate probability index governing relative errors in voltage and angle at each bus. The meter placement problem is simplified by transforming it into a probability bound reduction problem, with the help of the two sided-Chebyshev inequality. A straightforward solution technique is proposed for the latter problem, based on the consideration of 2-error ellipses. The benefits of the proposed technique are revealed by Monte Carlo simulations on a 95-bus UKGDS network model. Index Terms-Bivariate Chebyshev bound, distribution management system, distribution system state estimation, error ellipse, measurement placement.

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Jo over a class of arcs x whose values at a and b have been specified. Existence theory provides rather weak conditions under which the problem has a solution in the class of absolutely continuous arcs, conditions which must be strengthened in order that the standard necessary conditions apply. The question arises: What necessary conditions hold merely under hypotheses of existence theory, say the classical Tonelli conditions? It is shown that, given a solution x, there exists a relatively open subset f! of [a,b], of full measure, on which x is locally Lipschitz and satisfies a form of the Euler-Lagrange equation. The main theorem, of which this is a corollary, can also be used in conjunction with various classes of additional hypotheses to deduce the global smoothness of solutions. Three such classes are identified, and results of Bernstein, Tonelli, and Morrey are extended. One of these classes is of a novel nature, and its study implies the new result that when L is independent of t, the solution has essentially bounded derivative. 'The support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.