Constrained state estimation with partial measurements in unobservable distribution network

We developed a constrained state estimation method that clarifies the range of the feeder voltage in an unobservable distribution network in which the number of telemetric sensors is smaller than the number of state variables to be estimated. Instead of using pseudo-measurements, whose reliability is affected by unexpected power flow conditions, the method uses constant nominal boundaries as inequality constraints in the least squares problem. The ranged estimation is the maximum likelihood solution that satisfies the least squares criterion against the sensor measurements and satisfies the given inequality constraints at the same time. We evaluated the method in a case study simulation on a 30-node benchmark network with partial measurements. The evaluation result showed that the method clarified the feeder voltage ranges including or close to unmeasured exact values and that the size of the estimation range and error were sufficiently smaller compared with the allowable voltage fluctuation.