- Volume 12 Issue 6
In order to solve the AC optimal power flow (OPF) problem considering the generators' on/off status, it is necessary to model the problem as mixed-integer nonlinear programming (MINLP). Because the computation time to find the optimal solution to the mixed-integer AC OPF problem increases significantly as the system becomes larger, most of the existing solutions simplify the problem either by deciding the on/off status of generators using a separate unit commitment algorithm or by ignoring the minimum output of the generators. Even though this kind of simplification may make the overall computation time tractable, the results can be significantly erroneous. This paper proposes a novel algorithm for the mixed-integer AC OPF problem, which can provide a near-optimal solution quickly and efficiently. The proposed method is based on a combination of the outer approximation method and the relaxed AC OPF theory. The method is applied to a real-scale power system that has 457 generators and 2132 buses, and the result is compared to the branch-and-bound (B&B) method and the genetic algorithm. The results of the proposed method are almost identical to those of the compared methods, but computation time is significantly shorter.
Optimal power flow;MINLP;Unit commitment;Relaxed AC OPF;Outer approximation;Branch-and-bound
- J. Carpentier, "Contribution a l'etude du dispatching economique," Bull. Soc. Francaise Electr., vol. 3, no. 1, pp. 431-447, 1962.
- J. Zhu, Optimization of power system operation, Second edition. Hoboken, New Jersey: IEEE Press: Wiley; Piscataway, NJ, 2015.
- C. A. Floudas, Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press, USA, 1995.
- A. Schecter and R. P. O'Neill, "Optimal Power Flow Paper 6: Exploration of ACOPF Feasible Region for the Standard IEEE Test Set," 2013.
- H. Zhang, V. Vittal, G. T. Heydt, and J. Quintero, "A relaxed AC optimal power flow model based on a Taylor series," in 2013 IEEE Innovative Smart Grid Technologies-Asia (ISGT Asia), pp. 1-5, 2013.
- R. P. O'Neill, A. Castillo, and M. B. Cain, "Optimal Power Flow Paper 2: The IV formulation and linear approximations of the AC optimal power flow problem," Rap Tech Fed. Energy Regul. Comm., 2012.
- S. Lee, W. Kim, and B. H. Kim, "Performance Comparison of Optimal Power Flow Algorithms for LMP Calculations of the Full Scale Korean Power System," J. Electr. Eng. Technol., vol. 10, no. 1, pp. 109-117, 2015. https://doi.org/10.5370/JEET.2015.10.1.109
- W. H. E. (Empros S. I. Liu and A. D. (Pacific G. and E. C. Papa Iexopoulos, "Discrete Shunt Controls in a Newton Optimal Power Flow," IEEE Trans. Power Syst. Inst. Electr. Electron. Eng. U. S., vol. 7, no. 4, Nov. 1992.
- L. Chen, H. Suzuki, and K. Katou, "Mean field theory for optimal power flow," IEEE Trans. Power Syst., vol. 12, no. 4, pp. 1481-1486, 1997. https://doi.org/10.1109/59.627845
- T. Kulworawanichpong and S. Sujitjorn, "Optimal power flow using tabu search," IEEE Power Eng. Rev., vol. 22, no. 6, pp. 37-39, 2002. https://doi.org/10.1109/MPER.2002.4312341
- D. C. Walters and G. B. Sheble, "Genetic algorithm solution of economic dispatch with valve point loading," IEEE Trans. Power Syst., vol. 8, no. 3, pp. 1325-1332, Aug. 1993. https://doi.org/10.1109/59.260861
- Z.-L. Gaing, "Constrained optimal power flow by mixed-integer particle swarm optimization," in IEEE Power Engineering Society General Meeting, pp. 243-250, 2005.
- L. Liu, X. Wang, X. Ding, and H. Chen, "A Robust Approach to Optimal Power Flow With Discrete Variables," IEEE Trans. Power Syst., vol. 24, no. 3, pp. 1182-1190, Aug. 2009.
- M. A. Duran and I. E. Grossmann, "An outerapproximation algorithm for a class of mixed-integer nonlinear programs," Math. Program., vol. 36, no. 3, pp. 307-339, Oct. 1986. https://doi.org/10.1007/BF02592064
- M. B. Cain, R. P. O'neill, and A. Castillo, "Optimal Power Flow Paper 1: History of optimal power flow and formulations," Fed. Energy Regul. Comm., pp. 1-36, 2012.
- T. N. dos Santos and A. L. Diniz, "A Dynamic Piecewise Linear Model for DC Transmission Losses in Optimal Scheduling Problems," IEEE Trans. Power Syst., vol. 26, no. 2, pp. 508-519, May 2011. https://doi.org/10.1109/TPWRS.2010.2057263
- H. Kim and W. Kim, "Integrated Optimization of Combined Generation and Transmission Expansion Planning Considering Bus Voltage Limits," J. Electr. Eng. Technol., vol. 9, no. 4, pp. 1202-1209, 2014. https://doi.org/10.5370/JEET.2014.9.4.1202
- J. P. Ruiz, J. Wang, C. Liu, and G. Sun, "Outerapproximation method for security constrained unit commitment," Transm. Distrib. IET Gener., vol. 7, no. 11, pp. 1210-1218, Nov. 2013. https://doi.org/10.1049/iet-gtd.2012.0311
- J. Viswanathan and I. E. Grossmann, "A combined penalty function and outer-approximation method for MINLP optimization," Comput. Chem. Eng., vol. 14, no. 7, pp. 769-782, 1990. https://doi.org/10.1016/0098-1354(90)87085-4
- M. Hunting, "The AIMMS Outer Approximation Algorithm for MINLP," Paragon Decis. Technol. Haarlem, 2011.
- Richard E. Rosenthal, GAMS - A User's Guide. 2016.
- N. Andrei, Nonlinear Optimization Applications Using the GAMS Technology. Springer, 2013.
- "GAMS Solvers." [Online]. Available: http://www.gams.com/latest/docs/solvers/index.html. [Accessed: 17-Jan-2017].
- Harmonic and power loss minimization in power systems incorporating renewable energy sources and locational marginal pricing vol.10, pp.5, 2018, https://doi.org/10.1063/1.5041923
Supported by : National Research Foundation of Korea(NRF), Korea Institute of Energy Technology Evaluation and Planning(KETEP)