Quadratic programming approach to reactive power optimization on the primary feeders

Contents In this paper we suggest the use of the quadratic programming technique to determine the optimum size and location of shunt capacitors on radial distribution feeders so as to maximize overall savings, including the cost of capacitors. The saving function which is of quadratic form is maximized for a set of linear inequality constraints by using quadratic programming. — For quadratic programming, efficient alogrithms have been developed which can easily be implemented on digital computers. — The approach is illustrated by an application to a typical distribution feeder of 23 kV.

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Blindleistungsoptimierung an primären Einspeisungen mit Hilfe quadratischer Programmierung

Übersicht Diese Arbeit stellt die Anwendung der quadratischen Programmierung zur Ermittlung optimaler Werte und Orte von Parallelkapazitäten an radialen Verteilungen mit dem Ziel der Kosteneinsparung vor. Die Methode ist an einer 23-kV-Verteilung entwickelt und überprüft worden.

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Nomenclature A M×N array of constraint coefficients - B M vector of constrain limits - C N×M array of quadratic coefficients, from objective function - E Energy loss caused by reactive current in the feeder - E Reduction in energy loss - I_ck Capacitor current injected at nodek - Î_k Maximum reactive load current at nodek - K_c Annual cost per unit of installed capacitor ($/A) - K_E Per unit energy production cost ($/kWh) - K_P Annual cost per unit of power loss ($/kW) - m_k Reactive load factor for loadk - M Number of constraints - N Number of structural variables - P N vector of linear term coefficients from objective function - P Peak power loss caused by reactive current in the feeder - P Reduction in peak power loss - R_k Line resistance for sectionk - S Net saving resulting from peak power and energy loss reduction - T Total period of the reactive load curve - X_k Line reactance for sectionk