Skip to main content
SpringerLink
Log in

Quadratic programming approach to reactive power optimization on the primary feeders

Blindleistungsoptimierung an primären Einspeisungen mit Hilfe quadratischer Programmierung

  • Published:
Archiv für Elektrotechnik Aims and scope Submit manuscript

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.

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

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

ΔE :

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

ΔP :

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

References

  1. Kuester, J. L.; Mize, J. H.: Optimization techniques with fortran. New York: McGraw-Hill 1973

    Google Scholar 

  2. Garver, L. L.: Transmission planning — an application of optimization methods in power system engineering. IEEE Tutorial Course Text 76 CH 1107-2-PWR (1976) 77–84

  3. Duran, H.: Optimum number, Location, and size of shunt capacitors in radial distribution feeders. A dynamic programming approach. IEEE Trans. Pas-87, No. 9 (1968) 1769–1774

    Google Scholar 

  4. Hano, I.; Tamura, Y.; Narita, S.; Matsumoto, K.: Real time control of system voltage and reactive power. IEEE Trans. Pas-88, No. 10 (1969) 1544–1559

    Google Scholar 

  5. Grainger, J. J.; Lee, S. H.: Optimum Size and Location of shunt capacitors for reduction of losses on distribution feeders. IEEE Trans., Pas-100, No. 3 (1981) 1105–1118

    Google Scholar 

  6. Cook, R. F.: Calculating loss reduction afforded by shunt capacitor application. IEEE Trans., Pas-83 (1964) 1227 bis 1230

    Google Scholar 

  7. Ibrahim, E. S.; El-Shibini, M. A.; Azzous, E. M.: Optimum reactive power control in distribution system. faculty of engineering and technology, Helwan University 1982

Download references

Author information

Authors and Affiliations

  1. Electrical Engineering Dept. Faculty of Engineering, Cairo University, Cairo

    M. A. El-Shibini

  2. Electrical Engineering Department, Helwan University, Helwan, Egypt

    E. S. Ibrahim

Authors
  1. M. A. El-Shibini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. S. Ibrahim
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

El-Shibini, M.A., Ibrahim, E.S. Quadratic programming approach to reactive power optimization on the primary feeders. Archiv f. Elektrotechnik 68, 267–271 (1985). https://doi.org/10.1007/BF01845938

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01845938

Keywords

Search

Navigation