# Real power-system economic dispatch using a variable weights linear programming method

### Abstract

This paper presents an ecient method to solve an economic load dispatch problem with load flow type network securityconstraints: the active generation limits and line active power flows limits. A new form of linear programming methodis proposed: a variable weights linear programming. The nonlinear dispatch problem is transformed into a linearone through variable weights linear programming. To achieve good linear, representation the nonlinear cost functionsbetween the active generation limits are approximated by the sum of products of cost values multiplied by the variableweights. The nonlinear equality network constraint containing the losses expressed by the specially formulated andcalculated function of generated powers is transformed into a linear one, the same manner as above. The set of nonlinearinequality constraints on line active power flows is linearly expressed in terms of active bus generation powers withupper limits on the active power flow to each violating lines. The dispatch problem transformed this manner with orwithout solving the load flow problem is demonstrated that the proposed method has practical application for real-timecontrol/dispatch.### References

1-Mostefa Rahli: " Répartition Optimale des Puissances Actives par la Programmation Linéaire " These de Magister, U.S.T.O, Oran, Algeria, July 1985.

2- G.W. Stagg, A.H. El Abiad: " Computer Methods in Power System Analysis "

Mc Graw Hill Int, Book Company Japan, 1983.

3- K.R.C. Mamandur, G.J. Berg: " Economic Shift in Electric Power Generation with Line Flow Constraints "I.E.E.E Trans on P.A.S, Vol PAS-97, n° 5, Sep-Oct 1978.

4- S.C. Tripathy: " Real Time Monitoring of Power System Using Fast Decoupled Load Flow " Proc I.E.E, Vol 124, n° 7, July 1977.

5- Li Wenywan: " An On Line Economic Power System Dispatch Method with Security Electric Power System Research "

I.E.E.E Trans on P.A.S, n° 9, 1985, 173-181.

6- M.E. Hawary, S.Y. Mansour: "Performance Evaluation of Parameter Estimation Algorithms for Economic Operations of Powers Systems "

I.E.E.E Trans on P.A.S, Vol 101, n° 3, march 1982, 574-579.

7- L.L. Freris, A.M. Sasson: " Investigations of the Load Flow Problems "

Proc. I.E.E, Vol 115, n° 10, October 1968.

8- Y. Wallach: " Calculations and programs for power system analysis "

Prentice-Hall, Englewood Cliffs, 1986.

9- M. Rahli : “Economic dispatching using linear and non linear programming”

PhD thesis, USTO-MB, Oran, Algeria, January 1996.

10- L. Benasla, “Contribution to the study of the stability and the optimal economic dispatch,” Ph.D. dissertation, University of Science and Technology, ORAN, Algeria, 2004.

11- Younes M et M. Rahli, La répartition optimale des puissances en utilisant l’algorithme génétique, ICEEE ’2004, Laghouat, april, 24-25-26, 2004, pp 354-358.

12- Rahli M. Pirotte P: Optimal load flow using sequential unconstrained minimization technique (SUMT) method under power transmission losses minimization. Electric Power Systems Research 52: pp 61-64. (1999).

13- A. S. Deepak Mishra and K. Kalra, “Or-neuro based hopfield neural network for solving economic load dispatch problem,” Neural information processing – letters and reviews., vol. 10, 2006.

14- A. Belmadani, L. Benasla, M. Rahli: Etude d’un dispatching economique-environnemental par la méthode Harmony Search ; Acta Electrotehnica ; Volume50 ; N°1 ; 2009, pp 44-49

15- A. Belamadani, L. Benasla, M. Rahli: Etude d’un Dispatching Economique par l’Algorithme Harmony Search: Application au Réseau Ouest Algérien; 1er Séminaire National sur le Génie Electrique Appliqué aux Energies Renouvelables ; 27-28 Janvier 2010 ; Chleff, Algérie

16- Abderrahim Belmadani, Lahouaria Benasla and Mostefa Rahli : "A Fast Harmony Search Algorithm for solving Economic Dispatch Problem";

Book "Search Algorithms",ISBN 978-953-7619-X-X published by INTECH., June 2010., http://www.intechweb.org/

17- Abderrahim Belmadani, Lahouaria Benasla, Mostefa Rahli : A Fast Harmony Search Algorithm for solving Economic Dispatch Problem;

Przeglad Elektrotechniczny (Electrical Review); ISSSN 0033-2097; R.86; NR 3/2010, pp 274-278, http://pe.org.pl/

18- F.Z. Benayed, M. Rahli et L. Abdelhakem-Koridak: Optimisation du dispatching économique par l’algorithme Search Harmony,

Acta Electrotehnica Journal, Volume 52, N°1, 2011, Mediamira Sciences Publishers

2- G.W. Stagg, A.H. El Abiad: " Computer Methods in Power System Analysis "

Mc Graw Hill Int, Book Company Japan, 1983.

3- K.R.C. Mamandur, G.J. Berg: " Economic Shift in Electric Power Generation with Line Flow Constraints "I.E.E.E Trans on P.A.S, Vol PAS-97, n° 5, Sep-Oct 1978.

4- S.C. Tripathy: " Real Time Monitoring of Power System Using Fast Decoupled Load Flow " Proc I.E.E, Vol 124, n° 7, July 1977.

5- Li Wenywan: " An On Line Economic Power System Dispatch Method with Security Electric Power System Research "

I.E.E.E Trans on P.A.S, n° 9, 1985, 173-181.

6- M.E. Hawary, S.Y. Mansour: "Performance Evaluation of Parameter Estimation Algorithms for Economic Operations of Powers Systems "

I.E.E.E Trans on P.A.S, Vol 101, n° 3, march 1982, 574-579.

7- L.L. Freris, A.M. Sasson: " Investigations of the Load Flow Problems "

Proc. I.E.E, Vol 115, n° 10, October 1968.

8- Y. Wallach: " Calculations and programs for power system analysis "

Prentice-Hall, Englewood Cliffs, 1986.

9- M. Rahli : “Economic dispatching using linear and non linear programming”

PhD thesis, USTO-MB, Oran, Algeria, January 1996.

10- L. Benasla, “Contribution to the study of the stability and the optimal economic dispatch,” Ph.D. dissertation, University of Science and Technology, ORAN, Algeria, 2004.

11- Younes M et M. Rahli, La répartition optimale des puissances en utilisant l’algorithme génétique, ICEEE ’2004, Laghouat, april, 24-25-26, 2004, pp 354-358.

12- Rahli M. Pirotte P: Optimal load flow using sequential unconstrained minimization technique (SUMT) method under power transmission losses minimization. Electric Power Systems Research 52: pp 61-64. (1999).

13- A. S. Deepak Mishra and K. Kalra, “Or-neuro based hopfield neural network for solving economic load dispatch problem,” Neural information processing – letters and reviews., vol. 10, 2006.

14- A. Belmadani, L. Benasla, M. Rahli: Etude d’un dispatching economique-environnemental par la méthode Harmony Search ; Acta Electrotehnica ; Volume50 ; N°1 ; 2009, pp 44-49

15- A. Belamadani, L. Benasla, M. Rahli: Etude d’un Dispatching Economique par l’Algorithme Harmony Search: Application au Réseau Ouest Algérien; 1er Séminaire National sur le Génie Electrique Appliqué aux Energies Renouvelables ; 27-28 Janvier 2010 ; Chleff, Algérie

16- Abderrahim Belmadani, Lahouaria Benasla and Mostefa Rahli : "A Fast Harmony Search Algorithm for solving Economic Dispatch Problem";

Book "Search Algorithms",ISBN 978-953-7619-X-X published by INTECH., June 2010., http://www.intechweb.org/

17- Abderrahim Belmadani, Lahouaria Benasla, Mostefa Rahli : A Fast Harmony Search Algorithm for solving Economic Dispatch Problem;

Przeglad Elektrotechniczny (Electrical Review); ISSSN 0033-2097; R.86; NR 3/2010, pp 274-278, http://pe.org.pl/

18- F.Z. Benayed, M. Rahli et L. Abdelhakem-Koridak: Optimisation du dispatching économique par l’algorithme Search Harmony,

Acta Electrotehnica Journal, Volume 52, N°1, 2011, Mediamira Sciences Publishers

Published

2014-11-29

How to Cite

RAHLI, Mostefa et al.
Real power-system economic dispatch using a variable weights linear programming method.

**Journal of Power Technologies**, [S.l.], v. 95, n. 1, p. 34--39, nov. 2014. ISSN 2083-4195. Available at: <https://papers.itc.pw.edu.pl/index.php/JPT/article/view/518>. Date accessed: 25 apr. 2024.
Issue

Section

Power Plant

### Keywords

power systems, economic dispatching, load flow

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