OPTIMAL CAPACITOR PLACEMENT, REPLACEMENT AND CONTROL IN LARGE-SCALE UNBALANCED DISTRIBUTION-SYSTEMS - SYSTEM MODELING AND A NEW FORMULATION

This paper undertakes the problem of optimal capacitor placement, repl acement and control in large-scale unbalanced, radial or loop distribu tion networks. The problem is how to optimally determine the locations to install (or replace, or remove) capacitors, the types and sizes of capacitors to be installed (or replaced) and, during each load level, the control schemes for each capacitor in tile nodes of a general thr ee-phase unbalanced distribution system such that a desired objective function is minimized while the load constraints, network constraints and operational constraints (e.g. the voltage profile) at different lo ad levels are satisfied. The objective function considered consists of two terms: cost for energy loss and cost related to capacitor purchas e, capacitor installation, capacitor replacement and capacitor removal . Comprehensive modelings of different components are presented which include primary power networks, three-phase transformers (different wi nding connections, off-nominal tap ratio, core and copper losses), co- generators, voltage sensitive load models for single-phase, two-phase and three-phase loads, shunt apacitors and reactors. The new problem i s formulated as a combinatorial optimization problem with a non-differ entiable objective function. The configuration space essential in the design of a annealing-based solution methodology for tile new problem is derived. An effective solution methodology for solving the new prob lem and numerical studies on a realistic, unbalanced distribution netw ork, a 291-bus with 305 distribution lines and 6 transformers, with va rying loading conditions, will be presented in a companion paper [19].