**A Modified Harmony Search Algorithm for the**

Economic Dispatch Problem

Economic Dispatch Problem

**Dinu Călin SECUI, Simona DZITAC, Gabriel BENDEA,
Codruţa BENDEA, Cristina HORA**

University of Oradea

University Street, Oradea, 410087, Romania

csecui@uoradea.ro, gbendea@uoradea.ro, simona.dzitac@gmail.com, cbendea@uoradea.ro, chora@uoradea.ro

**Abstract**: The paper presents a modified harmony search algorithm (MHS), useful for solving the economic dispatch (ED) problem assuming a non-linear cost function and various technical restrictions. The ED problem is a very important optimization problem for power systems, and technical restrictions must be considered: prohibited operating zones and ramp rate limits of power generating units, as well as transmission line losses. The MHS algorithm is based on harmony search (HS) algorithm, but a new harmony is obtained by inserting some features from artificial bee colony algorithm. The efficiency of MHS algorithm is tested against two systems consisting of 6 and 38 thermal power generating units. Results are compared with those obtained by applying other optimization techniques.

**Keywords**: economic dispatch; harmony search; transmission losses.

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**CITE THIS PAPER AS**:

Dinu Călin SECUI, Simona DZITAC, Gabriel BENDEA, Codruta BENDEA, Cristina HORA, **A Modified Harmony Search Algorithm for the Economic Dispatch Problem**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 23 (2), pp. 143-152, 2014.

**Introduction**

Economic dispatch (ED) is an optimization problem of power systems that aims to determine the output power of thermal power generating units in order to have a minimal fuel cost for the entire system and, in the meantime, to satisfy some technical restrictions while operating the units.

The mathematical model of ED problem is non-linear, where both objective function and restrictions system may be non-linear. Classical methods were used for solving the ED problem: linear programming [1], non-linear programming [2], quadratic programming [3], Lagrangian relaxation algorithm [4] and dynamic programming [5]. Usually, these methods have got difficulties in finding a global optimum, they being able to offer only a local optimum point. Moreover, classical methods need a calculation of derivatives and some checking on continuity and derivability conditions of functions belonging to optimization model. To cover these drawbacks several artificial intelligence-based optimization techniques were applied. One of the most frequently used methods is based on the particle swarm optimization (PSO) applied in classical, enhanced or hybrid versions: PSO, PSO with time varying acceleration coefficients (PSO-TVAC) [6-8], new PSO (NPSO, NPSO-LSR) [9, 10], improved PSO [11], distributed Sobol PSO with tabu search algorithm (DSPSO-TSA) [12]. Other methods used for solving ED problems are: evolutionary programming (EPs) [13], biogeography-based optimization (BBO) [14], tabu search and multiple tabu search (TS, MTS) [15], differential evolution (DE) [16, 17], hybrid DE (DEPSO) [18], artificial bee colony algorithm (ABC) [19], incremental ABC with local search (IABC-LS) [20], harmony search (HS) [21], differential HS (DHS) [22].

Harmony search is a meta-heuristic algorithm inspired from a musical process of searching for a perfect state of harmony. The HS is an easy to implement algorithm, having good convergence characteristics and may be easily adapt to work with other algorithms [23, 24]. Thus, the HS algorithm or its versions were successfully used for solving mathematical [25-27] and engineering problems with continuous variables: reliability optimization [28], automatic parameter configuration [29], design of water distribution networks [30] etc.

In this paper, the HS classical algorithm is enhanced with some features specific to artificial bee colony algorithm in order to solve the economic dispatch problem. The new algorithm is called modified harmony search (MHS) algorithm. Its results are compared with others obtained by applying different optimization techniques.

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