Optimal Control of the Cascaded Kainji-Jebba Hydroelectric Power Station Based on Conjugate Gradient
DOI:
https://doi.org/10.11113/elektrika.v18n3.148Keywords:
Conjugate gradient, Inflow, Operating head, Optimal control, Performance indexAbstract
Electricity supply in Nigeria has been far below the estimated demand and the installed capacity of the plants. Hence, there has been continuous research on improving the performance of the existing plants, but the government mainly focuses on increasing the installed capacity. This paper presents the determination of the optimal release of water to maximize the energy generation potential of the cascaded Kainji-Jebba hydroelectric power station in Nigeria. The problem was formulated as an optimal control problem with an objective of minimizing the deviation of the head of the Jebba reservoir within a set limit. A conjugate gradient algorithm was then used as a direct solution to the optimal control problem. The computed control law and the resulting state trajectories of 2% error affirm the solution to be genuine and reliable. The algorithm is recommended for use in the design of a real-time optimal controller for the system and a decision guide for the operators.References
O. Ogunbiyi, C. T. Thomas, I. A. O. Omeiza, J. Akanni, and B. J. Olufeagba, “Dynamical Control Model of the Cascaded Kainji-Jebba Hydropower Operating Head,†FUOYE J. Eng. Technol., vol. 4, no. 1, 2019.
A. S. Sambo, B. Garba, I. H. Zarma, and M. M. Gaji, “Electricity Generation and the Present Challenges in the Nigerian Power Sector.,†J. Energy Power Eng., vol. 6, no. 7, pp. 1–17, 2012.
T. S. Abdulkadir, A. W. Salami, A. R. Anwar, and A. G. Kareem, “Modelling of Hydropower Reservoir Variables for Energy Generation: Neural Network Approach,†Ethiop. J. Environ. Stud. Manag., vol. 6, no. 3, pp. 310–316, 2013.
T. O. Ale, K. E. Alowolodu, J. O. Babatola, and B. J. Olufeagba, “Inflow Forecasting for Kainji Dam Using Time Series Model,†Int. J. Math. Arch., vol. 2, no. 12, pp. 2844–2851, 2011.
O. D. Jimoh, “Optimized Operation of Kainji Reservoir,†AU J. Technol., vol. 12, no. 1, pp. 34–42, 2008.
C. T. Thomas, O. Ogunbiyi, M. F. Akorede, and B. J. Olufeagba, “Assessment of Failure and Repair Behaviors of the Jebba Hydroelectric Power Station,†ELEKTRIKA, vol. 17, no. 3, pp. 13–19, 2018.
I. A. O. Omeiza, H. A. Ojongbede, C. T. Thomas, and B. J. Olufeagba, “Assessment of Performance of Turbo-Alternators at The Jebba Hydroelectric Power Station in Nigeria from 2005 – 2014,†Niger. J. Technol., vol. 38, no. 1, pp. 134–141, 2019.
O. Von Stryk, “Numerical Solution of Optimal Control Problems by Direct Collocation,†Optim. Control - Calc. Var. Optim. Control Theory Numer. Methods, Int. Ser. Numer. Mathmatics, vol. 111, pp. 129–143, 1993.
M. Athans, “The status of Optimal Control Theory and Applications for Deterministic System,†IEEE Trans. Automat. Contr., vol. 11, no. 3, pp. 580–596, 1966.
J. T. Betts, A Direct Aprocach to Solving Optimal Control Problem. 1999, pp. 73–75.
S. Kek, “Nonlinear Programming Approach For Optimal Control Problems,†in 2nd International Conference On Global Optimization and Its Applications 2013 (ICoGOIA2013), 2013, pp. 22–27.
V. M. Becerra, S. Engineering, U. K. Optimal, and J. Bernoulli, “Optimal control,†Scholarpedia, 2018. .
C. K. Ghaddar, “Rapid Solution of Optimal Control Problems by a Functional Spreadsheet Paradigm: A Practical Method for the Non-Programmer,†Math. Comput. Appl., vol. 23, no. 6, pp. 1–23, 2018.
H. Rodrigues, M. Monteiro, and D. Torres, “Optimal control and numerical software: an overview,†2014. .
L. S. Lasdon, “The Conjugate Gradient Method for Optimal Control Problem,†IEEE Trans. Automat. Contr., vol. 12, no. 2, pp. 132–138, 1967.
R. W. H. Sargent, “Optimal Control,†J. Comput. Appl. Math., vol. 124, pp. 361–371, 2000.
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