Capacitor allocation and sizing in distribution feeders using interval mathematics

The paper presents the application of Interval Mathematics as a new method to, rigorously, address uncertainties associated with capacitor installation in distribution feeders. While several methods exist to determine optimal capacitor sizes and locations in distribution feeders, these methods usually require data which may be uncertain in nature. To account for such uncertainties a heuristic method coupled with interval mathematics is developed with the aim of maximizing the cost saving by placing single node-located capacitors at a selected sequence of nodes. The method determines a set of nodes to be compensated with their associated interval capacitor sizes; followed by a local search loop, at any one node, to determine the final standard capacitor size at this node. While catering for uncertainties, the method also offers utilities with alternatives for selecting the standard capacitor sizes to be used and the associated costs to be saved. This should enable utilities to make informed decisions regarding installing capacitors for reactive power compensation in their distribution systems. A procedure is devised in order to produce sharp bounds of the interval outcomes. Successful implementation of the proposed method is described using a nine buses example distribution feeder.