Investigation the Success of Semidefinite Programming for the Estimating of Fuel Cost Curves in Thermal Power Plants

Year 2021, Volume: 24 Issue: 1, 247 - 254, 01.03.2021

Uğur Güvenç , Hüseyin Bakır , Serhat Duman

https://doi.org/10.2339/politeknik.645827

Cited By: 2

Abstract

Accurate estimation of fuel cost curve parameters in thermal
power plants (TPP) has great importance because these parameters directly influence
the economic dispatch calculations. In this paper, a semidefinite programming
(SDP) approach was proposed for the estimation of fuel cost functions'
parameters in TPP. The parameter estimation problem was designed as a
minimization problem, where the objective function was accepted as the total
absolute error (TAE) in the study. Also, linear, quadratic, and cubic fuel cost
functions were used to estimate the fuel cost parameters. Coal, oil and gas
were preferred as the fuel types for the study. The results achieved from the
SDP method were compared with that of particle swarm optimization (PSO), artificial
bee colony (ABC), crow search algorithm (CSA) and least error square (LES) methods,
respectively. TAE parameter was taken into consideration when comparing the
performance of the methods. In the results, the SDP method gave better results
with respect to TAE. Clearly, the present paper showed that SDP has a high
potential to solve parameter estimation problems.

Keywords

Fuel cost function, Parameter estimation problem, Semidefinite programming

Investigation the Success of Semidefinite Programming for the Estimating of Fuel Cost Curves in Thermal Power Plants

Abstract

Accurate estimation of fuel cost curve parameters in thermal power plants is of great importance because these parameters directly influence the economic dispatch calculations. In this paper, a semidefinite programming (SDP) approach was proposed for the estimation of fuel cost functions' parameters in thermal power plants. The parameter estimation problem was designed as a minimization problem, where the objective function was accepted as the total absolute error (TAE) in the study. Also, linear, quadratic, and cubic fuel cost functions were used to estimate the fuel cost parameters. Different fuel types such as coal, oil and gas were preferred for simulation studies. The results achieved from the semidefinite programming method were compared with that of particle swarm optimization (PSO), artificial bee colony (ABC), crow search algorithm (CSA) and least error square (LES) methods, respectively. The performance of the methods were compared according to the TAE parameter. Simulation results showed that SDP method is more successful than other methods considered in this paper. Clearly, the present paper showed that SDP has a higher potential to solve parameter estimation problems.  

Keywords

Fuel cost function, parameter estimation problem, semidefinite programming

References

• Güvenç U., Sönmez Y., Duman S., and Yörükeren N.,’’Combined economic and emission dispatch solution using gravitational search algorithm’’, Scientia Iranica, 6: 1754-1762, (2012).
• Daycock C., DesJardins R., and Fennell S., “Generation cost forecasting using on-line thermodynamics models”, Electric Power , 5–7, (2004).
• El-Naggar K. M., AlRashidi M. R., and Al-Othman A. K., “ Estimating the input–output parameters of TPP using PSO”, Energy Conversion and Management, 7: 1767-1772, (2009).
• Sayah S., and Hamouda A., “Novel application of differential evolution algorithm for estimating fuel cost function of thermal generating units,” In 2015 Third World Conference on Complex Systems (WCCS), 1-6, (2015).
• Sayah S., and Hamouda A., “ Efficient method for estimation of smooth and nonsmooth fuel cost curves for TPP,” International Transactions on Electrical Energy Systems, 3:1-14, (2018).
• Sönmez Y., “Estimation of fuel cost curve parameters for TPP using the ABC algorithm,” Turkish Journal of Electrical Engineering & Computer Sciences, 21: 1827-1841, (2013).
• Askarzadeh A., and Gharibi M., “ Accurate estimation of cost function parameters for TPP using a novel optimization approach,” Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 24: 2986-2999, (2018).
• AlRashidi M. R., El-Naggar K. M., and AlHajri M. F., “ Estimation of fuel cost function characteristics using Cuckoo search,” In International Conference on Computer Science, Data Mining & Mechanical Engineering, Bangkok, Thailand, (2015).
• Durai S., S.Subramanian, and S. Ganesan, “ Preferred Economic Dispatch of Thermal Power Units,” Journal of Power and Energy Engineering, 11: 47-69, (2015).
• El-Hawary M. E., and Mansour S. Y., “Performance evaluation of parameter estimation algorithms for economic operation of power systems,” IEEE Transactions on Power Apparatus and Systems, 3: 574-582,1982.
• AlRashidi M. R., El-Naggar K. M., and AlHajri M. F., “Convex and non-convex heat curve parameters estimation using cuckoo search,” Arabian Journal for Science and Engineering, 3:873-882, (2015).
• Alawode K. O., Jubril A. M., Kehinde L. O., and Ogunbona P. O., ‘’Semidefinite programming solution of economic dispatch problem with non-smooth, non-convex cost functions,’’ Electric Power Systems Research, 164: 178-187, (2018).
• Jubril A. M., Olaniyan O. A., Komolafe O. A., and Ogunbona P. O., ‘’Economic-emission dispatch problem: A semi-definite programming approach’’, Applied Energy, 134: 446-455, (2014).
• Bai X., Wei H., Fujisawa K., and Wang Y., ‘’Semidefinite programming for optimal power flow problems,’’ International Journal of Electrical Power & Energy Systems, 30: 383-392, (2008).
• Rana M. M., Li L., and Su S. W., ‘’Controlling the renewable microgrid using semidefinite programming technique,’’ International Journal of Electrical Power & Energy Systems, 84,: 225-231, (2017).
• Davoodi E., Babaei E., and Mohammadi-ivatloo B., ‘’An efficient covexified SDP model for multi-objective optimal power flow’’, International Journal of Electrical Power & Energy Systems102: 254-264, (2018).
• Boyd S., and Vandenberghe L., “Semidefinite programming relaxations of non-convex problems in control and combinatorial optimization,” In Communications, Computation, Control, and Signal Processing, 279-287. Springer, Boston, (1997).
• Jubril A. M., Adediji A. O., and Olaniyan O. A., “Solving the combined heat and power dispatch problem: A semi-definite programming approach,” Electric Power Components And Systems, 12: 1362-1376, (2012).
• Molzahn D. K., Lesieutre B. C., and DeMarco C. L., “A sufficient condition for global optimality of solutions to the optimal power flow problem”, IEEE Transactions on Power Systems, 2: 978-979, (2013).
• Zhu Y., Jian J., Wu J., and Yang L., “Global optimization of non-convex hydro-thermal coordination based on semidefinite programming”, IEEE Transactions on Power Systems, 4: 3720-3728, (2013).
• Vandenberghe L., and Boyd S., “Semidefinite programming”, SIAM review, 1: 49-95, (1996).
• Overton M. and Wolkowicz H., “Semidefinite programming”, Mathematical Programming, 1: 105-109, (1997).
• CVX Research Incorporated, CVX: Matlab Software for Disciplined Convex Programming, version 2.1, (2019 July).