A sediment Programming Approach for solving Multi-Objective Economic Dispatch Problems Incorporating Wind Power Units
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Date
2016
Authors
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Journal ISSN
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Publisher
Obafemi Awolowo University
Abstract
In practical applications of economic dispatch to power systems, stochastic variability is a vital issue as it is a means of ensuring optimal operation of power systems. Therefore, stochastic models are applicable in power dispatch problems as certain inaccurate and uncertain factors which naturally surface in system operations are readily addressed. A semidefinite programming (SDP) optimization approach for solving reformulated extended stochastic multi-objective model for economic dispatch (ED) that incorporates combined heat and power (CHP) units and wind power is presented in this research. This was achieved by converting the stochastic multi-objective model into their deterministic equivalents through their expectation, with the assumption that involved random variables are normally distributed. The multi-objective problem was recast in matrix form as a SDP relaxation problem and subsequently solved with a MATLAB programming suite. The system inequality and equality constraints uncertainty were entered into YALMIP, which is a linear matrix inequality parser. Simulations were performed on modified IEEE 6, 15 and 20 units’ networks with 2 CHP units and 20 wind parks for each of the networks. A comparative study was also conducted to demonstrate the effectiveness of the proposed method whereby the results of problem reformulations including stochastic and deterministic models of power dispatch were investigated and then compared with the results of the existing techniques reported in the literature. However, in the generation of the Pareto-front solutions, ideal minimum points were used in the determination of the maximum spread out of the Pareto solutions by the algorithm. This involves the use of standard weighted sum method in generating the Pareto-optimal solution between two objective functions. Different values of the control weight selection parameter k1 were used in the generation of Pareto points. Fifty one (51) runs were carried out for each parameter value to explore the effect of changes in control weight selection k1 and compared different cases. In the generation of the Pareto-optimal solution, different values of control weight selection k1= 1, 5, and 10 were examined.
At value of control weight selection k1=1, more points are missed from the lower point while a gradual progression in the spread out of the Pareto points were observed at the lower extreme point as the control weight selection k1 is further increased from 1. Simulation results have differentiated the costs of running power systems obtained by the system that includes both the cogeneration units and wind power penetration for various wind power prices while satisfying all the systems’ constraints. The optimization results are close within the order of magnitude 3.5% reductions in the case of modified IEEE six units, while SDP achieved lowest values of the optimized objective functions and Pareto set was formed faster in a single run compared to modified particle swarm optimization (MOPSO), genetic algorithm (GA) and weighted aggregated (WA) methods. The total costs obtained for running the power system that incorporates both the CHP units and the wind power units in the case of modified IEEE six units are 1218.5 $/hr, 1242.5 $/hr, 1266.2 $/hr taking the wind power price as 120$/pu, 150$/pu, 180$/pu respectively are lower compared to the total running cost obtained for the system that incorporates CHP units only which gives 1275.3 $/hr.
In conclusion, an optimal selection of control weight k1 parameter which gives a better convergence property and comparatively good extent of the algorithm was empirically determined. The proposed SDP technique has been employed in solving a stochastic power dispatch problem by minimizing the expectation of the multi-objective functions using the Gaussian probability distribution function and also Weibull probability distribution function is used in the characterization of a stochastic wind data, in an attempt to create suitable criteria to a better utilization of the wind power.
Description
xv,166 Pages
Keywords
MATLAB, YALMIP, MOPSO, Semidefinite programming,, Economic dispatch,
Citation
Alli,K.S(2016)A sediment Programming approach for solving multi-objective economic dispatch Problems incorporating Wind Power Units