Economic Load Dispatch Using Linear Programming: A Comparative Study

Economic Load Dispatch Using Linear Programming: A Comparative Study

Ahmad A. Al-Subhi (King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia) and Hesham K. Alfares (King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia)
Copyright: © 2016 |Pages: 21
DOI: 10.4018/IJAIE.2016010102


This paper presents an optimum solution of the economic dispatch (ED) problem without considering transmission losses using linear programming (LP). In the ED problem, several on-line units (generators) are available, and it is needed to determine the power to produce by each unit in order to meet the required load at minimum total cost. To apply LP, the nonlinear cost functions of all generators are approximated by linear piecewise functions. To examine the effectiveness of this linearization method, a comprehensive set of benchmark test problems is used consisting of 3, 6, 18, 20, 38, and 40 generators. Using this set, LP solutions of linearized ED problems are compared with several other techniques available in the literature. The LP technique with piecewise linearization shows an overall competitive advantage in terms of total cost, solution time, and load satisfaction accuracy. The impact of varying the width of the linearized pieces (segments) is also discussed. All the computational analysis is performed using MATLAB software environment.
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The economic dispatch (ED) problem involves the determination of the operation of generation facilities to produce energy at the lowest cost to reliably serve consumers, recognizing any operational limits of generation and transmission facilities. Many techniques have been proposed in the literature to solve this problem. Ciornei and Kyriakides (2013) present a comprehensive review of ED models and techniques since 1991, and provide a database of ED test systems commonly used in the literature.

One type of these techniques is the classical techniques category that includes Lambda-Iteration Algorithm (LIA), Gradient method, Newton’s method and Lagrange multiplier method. In addition, heuristic approaches are becoming very popular in solving the ED problem. These techniques include Genetic Algorithms (GA), Tabu Search (TS), Simulated Annealing (SA), Differential Evolution (DE) and Particle Swarm Optimization (PSO). Other solution categories include Quadratic Programming (QP), cost composite function, sequential approach with matrix framework, and Dynamic Programming (DP). In addition, hybrid methods, which are combinations of more than one method to solve ED problem, are also used.

Currently, the ED problem is still under the investigation and attention by many researchers. A recent literature search has found several works published on ED optimization using both established and innovative methods. Some of the techniques used recently to solve ED problems include PSO (Lin et al., 2015), Grey Wolf Optimization (GWO) (Tung & Chakravorty, 2015), Mixed Integer Quadratic Programming (MIQP) (Absil et al., 2015), Fast Lambda Iteration (FLA) (Zhan et al., 2014), Artificial Neural Networks (ANN) (Momoh & Reddy, 2014), Flower Pollination Algorithm (FPA) (Vijayaraj & Santhi, 2016), Ant Lion Optimization (ALO) (Nischal & Mehta, 2015), and Gravitational Search Algorithm (GSA) (Hota & Sahu, 2015).

Advancements in smart grid and Distributed Generation (DG) have wide ED applications in optimizing power generation from several energy sources instead of only one conventional source. Examples of these sources include wind, solar, and battery storage. Combining these different sources, including their respective constraints, and trying to optimize the power generated from each source is not an easy task. The authors of Zhu (2014), Liu et al. (2014), Lorca and Sun (2015), Mudumbai and Dasgupta (2014), Su and Chuang (2014), Zhang and Giannakis (2014), Shen et al. (2014) and Jose (2014) show various approaches in smart grid environment to optimize the generated power from each DG.

In the area of LP applications on ED, Hoke et al. (2013) apply a fast and reliable LP approach to the ED of grid-tied micro-grids containing several DGs such as conventional generators, energy storage, and wind turbines. Their simulations have shown quick and reliable results. In Jabr et al. (2000), a simplified homogeneous and self-dual LP interior point algorithm is presented. The algorithm is applied to the security constrained economic dispatch (SCED) problem. A method for solving the economic power dispatch problem in the presence of renewable energy sources is described in Elsaiah et al. (2014). The proposed method uses LP because of flexibility, reliability and speed. Chamba and Ano (2013) propose an innovative hybrid methodology that integrates LP within a meta-heuristic algorithm to calculate the optimal power flow and the reserve assigned to each unit.

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