Constrained state estimation with applications in water distribution network monitoring

Abstract

This paper investigates the effects of imposing bounds on the measurements used in weighted least-squares (WLS) state estimation. The active limits for such bounds are derived and algorithms based on linear and quadratic programming kernels are presented. Using the lower limit for the bounds, the constrained WLS scheme becomes an adaptive maximally constrained scheme: M-WLS. For some networks, the poor prior knowledge of the global error characteristic results in some measurements having less influence than would be expected from the local error characteristics of their transducers. By using M-WLS estimation, the influence of such measurements on state estimation may be improved. Analysis of the adaptive bounding of the scheme can also lead to identification of critical measurement discrepancies. For the purpose of illustration, results are presented using simulated measurements; the head measurements (pressures) are consistent with nominal demands (nodal flows) and the demand measurements are generated by superimposing random errors of 2.5ls-1 rms on the nominal demands.