Dynamic formulation and approximation methods to solve economic dispatch problems

• Published in: IET generation, transmission & distribution Vol. 7; no. 8; pp. 866 - 873
• Main Authors: Abouheaf, Mohammed I, Lee, Wei-Jen, Lewis, Frank L
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.08.2013; Institution of Engineering and Technology; The Institution of Engineering & Technology
• Subjects: active load demand; active load demand allocation; active load distribution optimality; Applied sciences; Approximation; base point method; concave programming; Cost function; costing; Demand; dynamic formulation‐approximation methods; economic dispatch problems; Economics; Electrical engineering. Electrical power engineering; Electrical power engineering; Exact sciences and technology; fuel generation cost function optimization; generating units; generation cost function models; gradient methods; gradient technique; Mathematical analysis; Mathematical models; Miscellaneous; Newton method; Newton technique; nonconvex ED problem; nonconvex generation cost function; Nonlinear dynamics; Operation. Load control. Reliability; operational constraints; optimal distribution; optimisation tool; Optimization; participation factor method; power generation dispatch; power generation economics; Power networks and lines; power system nonlinearity; transmission loss; valve point loading effect; participation factor method; active load distribution optimality; generation cost function models; costing; Newton technique; nonconvex ED problem; power generation economics; optimal distribution; optimisation tool; gradient technique; base point method; gradient methods; Newton method; concave programming; transmission loss; operational constraints; power system nonlinearity; valve point loading effect; power generation dispatch; nonconvex generation cost function; fuel generation cost function optimization; dynamic formulation-approximation methods; active load demand allocation; economic dispatch problems; active load demand; generating units; Dispatching problem; Load distribution; Approximate method; Optimization method; Non linear phenomenon; Optimization; Electrical network; Optimal allocation; Analytical method; Heuristic method; Cost function; Valve; Energy demand; Economic aspect; Economic impact; Non linear effect; Transmission loss; Comparative study
• DOI: 10.1049/iet-gtd.2012.0397
• ISSN: 1751-8687

Economic dispatch (ED) is an optimisation tool that is used to allocate active load demands to the generating units through optimising the fuel generation cost function subject to the different operational constraints. The high non-linearity of the power system imposes mathematical challenges in formulating the generation cost function models, which makes the ED problem hard to solve. This study introduces two ideas to solve issues related to the ED problem. First, a dynamic formulation technique is developed to optimally allocate the change in the total active load demand to the generating units. This technique is shown to be insensitive to the optimality of the initial active load distribution unlike the base point and participation factor method. Moreover, it guarantees an optimal distribution among the generating units due the change in the active load demand. Second, a novel approximation of the non-convex generation cost function is developed to solve non-convex ED problem with the transmission losses. This approximation enables the use of gradient and Newton techniques to solve the non-convex ED problem with valve point loading effect and transmission losses in an analytic approach. This approximation is compared with some heuristic optimisation techniques.