CAPACITOR PLACEMENT AND REAL-TIME CONTROL IN LARGE-SCALE UNBALANCED DISTRIBUTION-SYSTEMS - LOSS REDUCTION FORMULA, PROBLEM FORMULATION, SOLUTION METHODOLOGY AND MATHEMATICAL JUSTIFICATION

A comprehensive study of capacitor placements and real-time control in general unbalanced distribution systems is undertaken. New developmen ts in a loss reduction formula, problem formulations, solution methodo logy and mathematical justification are presented. The problem is deco upled into two subproblems: the capacitor placement subproblem and the real-time control subproblem. An effective solution algorithm for pla cing capacitors and determining their real-time control schemes for ge neral unbalanced distribution systems is proposed. To meet the need fo r efficient implementation in real-time environments, a fast pseudo gr adient type mechanism for deriving capacitor control settings is incor porated into the solution algorithms. A quadratic integer programming based approach is proposed to determine the number, locations and sizi ng of capacitors to be placed in the distribution systems. The subprob lem of determining capacitor control settings under varying loading co nditions is formulated as another quadratic integer programming proble m. Mathematical justification is provided to show that the proposed al gorithms are guaranteed to yield local optimal solutions. Numerical st udies on the determination of capacitor number, size, location and rea l-time control schemes on large-scale unbalanced distribution systems under nonlinear load variations are presented in great detail in the c ompanion paper [17].