Applications of Semidefinite Programming Techineques for solving some Non-Convex Power Dispatch problems
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Date
2016
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Obafemi Awolowo University
Abstract
This study formulated the non-convex economic dispatch (ED) problems as convex ones. The formulation was then extended to handle the multi-objective economic emission dispatch problem, and the resulting convex problems were solved using semidefinite programming (SDP) techniques. The performance of the SDP techniques in solving the problems was also evaluated. This was done with a view to obtaining globally optimal solutions of the real-world non-convex power dispatch problems.
Non-convex ED problems which consider the effects of valve point loading (VPL), multiple fuel options (MFO), and combined cycle co-generation power plants (CCCP) in the operation of modern power plants were formulated as convex problems by performing decomposition of the fuel cost function, followed by convex relaxation of the decomposed ED problems. Two formulations were considered. In the first formulation (called sSDP), the non-convex ED problem was represented as an optimization problem having polynomial fuel cost objective function and constraints with vector variables. In the second formulation (called qmSDP), the problem was reformulated as a quadratic matrix programming problem. In order to extend the problem formulation to the multi-objective case, minimization of pollutant emissions from the power plants was considered as an additional objective function. Both objectives were aggregated using the adaptive weighted sum method. The resulting convex ED problems were modelled in MATLAB/CVX/YALMIP environments and solved using the SDPT3 and SEDUMI SDP solvers. Datasets used included the modified IEEE 30-bus, six generator test system incorporating CCCP and MFO units, the MFO ten unit system, the three unit, thirteen unit and forty-unit systems with VPL effects, and the multi-objective forty-unit system with VPL and emission coefficients. The solutions obtained for the different systems were evaluated by comparing them with the results reported in the literature.
The results showed that for the CCCP problem, both sSDP and qmSDP techniques returned better fuel costs of 946.6858 and 946.6851 $/h, respectively compared to 949.1428 $/h which is the best reported value in the literature. For the modified IEEE 30-bus MFO problem, sSDP and qmSDP techniques obtained better fuel costs of 647.5894 and 647.5341 $/h, respectively compared to the best reported value of 647.7900 $/h. In solving the ten unit MFO problem, qmSDP gave the best minimum solution of 481.7226 $/h. sSDP however returned a fuel cost of 481.8281 $/h. Results for the VPL problem showed that sSDP and qmSDP obtained best minimum fuel costs of 8234.0717, 17963.9848 and 121412.5355 $/h for the three, thirteen and forty-unit test systems, respectively. For the multiobjective economic emission dispatch problem, the SDP techniques obtained a set of Pareto-optimal solutions that completely dominated those obtained by the Non-dominated Sorting Genetic Algorithm (NSGA-II). The spacing and extent metric values for the SDP solution set were 2.0321 × 103 and 1.8320 × 105 while the corresponding values for NSGA-II were 85.4675 and 5.0408×104, respectively.
This study concluded that SDP techniques can obtain globally optimal solutions of non-convex power dispatch problems. This would help power system operators to make better decisions regarding the economical cost and environmentallyfriendly operation of power system networks.
Description
xix,170 Pages
Keywords
Semidefinite programming, Non-convex Power, Dispatch Problems, CCP, MATLAB
Citation
Alawode,K.O(2016).Applications of Semidefinite Programming Techniques for solving some non-convex power dispatch problems.Obafemi Awolowo University.