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Genetic Lagrangian Relaxation Selection Method for the Solution of Unit Commitment Problem

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The units' commitment problem is considered as the selection of units to be placed in operation, and the load distribution among them. The solution of these problems can be solved by using optimization problems, with a general objective of minimizing the system operating costs subject to demand and operating constraints. This optimization problem is formulated as mathematical programming problems. The commitment uses Lagrange multiplier method of the available units so as to limit the search range for economical and satisfactory commitment schedules based on an iterative technique used and the progression from one iteration to the next is based on an extrapolation technique in which the last two successive values of the incremental cost are employed to estimate the next value. This paper presents the solution of these problems by modifying Lagrange multiplier method to provide efficient solutions for formulating the unit commitment problem over periods of up to 24 hours. The unit commitment problem is solved by using the genetic algorithm tuning of the Lagrangian multiplier λ. The main function of the Unit Commitment takes into consideration the spinning reserve, start-up cost for each unit is dependent on the amount of time the unit has been shutdown prior to start-up. A variety of spinning reserve requirement is observed and the operation of individual units must satisfy the specified minimum up and minimum downtimes constraints. The proposed modification and presents the test results on a benchmark system comprising 10 generators. The solution method is applied to test power systems. The mathematical algorithm for the solution of the specified problem is presented and the results of the computed studies reflect the robustness of the modified algorithm in solving the unit commitment problem compared with the conventional method.
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Unit Commitment; Lagrangian Relaxation; Optimization Problems; Equality Constraints; Non-Equality Constraints; Incremental Cost; Spinning Reserve; Start-Up; Genetic Algorithm

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V. N. Dieu & W. Ongsakul, Ramp rate constrained unit commitment by improved priority list and augmented Lagrange Hopfield network, Electric Power Systems Research, vol. 78, 2008, 291-301.

Abouheaf, M. I.; Lee, W.-J.; Lewis, F. L. Dynamic formulation and approximation methods to solve economic dispatch problems. IET Gener. Transm. Distrib. 2013, 7, 866–873.

A. I. Cohen & M. Yoshimura, A branch-and-bound algorithm for unit commitment, IEEE Transactions on Power Apparatus and Systems, vol.102 n.20, 1983, 444–451.

S. Pan, J. Jian and L. Yang, A mixed integer linear programming method for dynamic economic dispatch with valve point effect. mathOC 2017.

X. S. Yang, S. S. S. Hosseini & H. G. Amir, Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect, Applied Soft Computing 12 1180–1186, 2012.

K. Chandrasekaran & S. P. Simon, Tuned fuzzy adapted firefly lambda algorithm for solving unit commitment problem, Journal of Electrical Systems, vol. 8 n.3, 2012, 132–150.

S. Pan, J. Jian and L. Yang, A Hybrid MILP and IPM for Dynamic Economic Dispatch with Valve Point Effect. math 2017.

S. Pan, J. Jian and L. Yang, Economic and environmental load dispatch using a genetic algorithm, in 2017 2nd International Conference Sustainable and Renewable Energy Engineering (ICSREE), 2017, pp. 53–57.

T. Sabo, A Survey on Environmental-Economic Load Dispatch using Lagrange Multiplier Method, IJECT Vol. 3, Issue 1, Jan. - March 2012.

H. Y. Yamin & S. M. Shahidehpour, Unit commitment using a hybrid model between lagrangian relaxation and genetic algorithm in competitive electricity markets, Electric Power System, vol. 68 n.2, 2004, 83–92.

A. Gupta, K. K. Swarnkar, and K. Wadhwani, Combined Economic Emission Dispatch Problem using Particle Swarm Optimization, International Journal of Computer Applications, vol. 49. 2012.

Gjorgiev, B., Cepin, M.:A multi-objective optimization based solution for the combined economic-environmental power dispatch problem, Engineering Applications of Artificial Intelligence, 2013, 26, pp. 417–429.

A. Amudha & C. C. A. Rajan, Integrating gradient search logistic regression and artificial neural network for profit based unit commitment, International Journal of Computational Intelligence Systems, vol.7 n.1, 2014, pp. 90-104.

M. N. Nwohu, and Osaremwinda Osarobo Paul, Evaluation of Economic Load Dispatch Problem in Power Generating Stations by the Use of Ant Colony Search Algorithms’, International Journal of Research Studies in Electrical and Electronics Engineering (IJRSEEE) vol.3 n.1, 2017, PP. 20-29

Sangwato, S., Oonsivilai, A., Optimal Power Flow with Interline Power Flow Controller Using Hybrid Genetic Algorithm, (2015) International Review of Electrical Engineering (IREE), 10 (6), pp. 727-733.

Y. Zhi-Min, W. Xu, & Z. Xian, Survey of genetic algorithm’s application in field of automatic control, Information and Control Journal, vol. 29, 2000, pp. 329-339.

C. C. A. Rajan & M. R. Mohan, An evolutionary programming-based tabu search method for solving the unit commitment problem, IEEE Transactions on Power Systems, vol. 19 n.1,2004, 577-585.

I. J. Raglend, C. Raghuveer, G.Avinash, N. P. Padhy & D. P. Kothari, Solution to profit based unit commitment problem using particle swarm optimization, Applied Soft Computing, vol. 10 n. 4, 2010, 1247-1256.

Al Hasibi, R., Hadi, S., Sarjiya, S., Integrated and Simultaneous Model of Power Expansion Planning with Distributed Generation, (2018) International Review of Electrical Engineering (IREE), 13 (2), pp. 116-127.

Rizk-Allah, R., Abdel Mageed, H., El-Sehiemy, R., Abdel Aleem, S., El Shahat, A., A New Sine Cosine Optimization Algorithm for Solving Combined Non-Convex Economic and Emission Power Dispatch Problems, (2017) International Journal on Energy Conversion (IRECON), 5 (6), pp. 180-192.

Krishnamurthy, S., Kriger, C., Deivakkannu, G., Development of a Data Acquisition, Storage and Retrieval System for the Real-Time Solution of the Economic Dispatch Problem, (2016) International Review of Electrical Engineering (IREE), 11 (4), pp. 399-410.

Alshammari, B., Dynamic Environmental/Economic Power Dispatch with Prohibited Zones Using Improved Multi-Objective PSO Algorithm, (2016) International Review of Electrical Engineering (IREE), 11 (4), pp. 411-419.

Toscano, L., Existence theorems for a general variational equation with non coercive main part, (2017) International Review on Modelling and Simulations (IREMOS), 10 (6), pp. 378-391.

Toscano, L., Toscano, S., On the solvability of a class of general systems of variational equations with nonmonotone operators, (2011) Journal of Interdisciplinary Mathematics, 14 (2), pp. 125-147.


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