Multi-objective mean-variance-skewness model for nonconvex and stochastic optimal power flow considering wind power and load uncertainties. (English) Zbl 1380.90242
Summary: This paper presents a multi-objective mean-variance-skewness (MVS) model for reliably assessing the problem of nonconvex and stochastic optimal power flow (NSOPF), considering valve-point effect, stochastic load and uncertain integrated wind power. The MVS model aims to maximize both the expected return and skewness while simultaneously minimizing the risk, which is formulated as a competing and conflicting three-objective optimization problem. Based on such a model, we propose a multi-objective optimization algorithm, multiple preys based evolutionary predator and prey strategy (MPEPPS), to provide Pareto solutions, which show the trade-off relationship among the expected return, the skewness and the risk of the dispatching objective. Subsequently, a multi-criteria decision making method, the technique for order preference by similarity to an ideal solution (TOPSIS), is applied for determining the final dispatch solution. The objective of this paper is to develop a reliable model to assess the NSOPF from the perspective of economics and reliability of power system operation, and propose an efficient algorithm to obtain a solution that considers all of the possible load and wind power simultaneously. Simulation results based on a modified IEEE 30-bus power system demonstrate the reliability and effectiveness of the MVS and MPEPPS in solving NSOPF.
MSC:
| 90C29 | Multi-objective and goal programming |
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
| 90C15 | Stochastic programming |
| 90C26 | Nonconvex programming, global optimization |
| 90C59 | Approximation methods and heuristics in mathematical programming |
| 90C90 | Applications of mathematical programming |
Keywords:
evolutionary computations; mean-variance-skewness model; optimal power flow; uncertainties; multi-objective optimizationReferences:
| [1] | Ai, X.; Wen, J.; Wu, T.; Lee, W.-J., A discrete point estimate method for probabilistic load flow based on the measured data of wind power, IEEE Transactions on Industry Applications, 49, 5, 2244-2252 (2013) |
| [2] | Allen, L.; Fleming, P., Review of canid management in Australia for the protection of livestock and wildlife - Potential application to coyote management, Sheep and Goat Research Journal, 19, 97-104 (2004) |
| [3] | Bahmani-Firouzi, B.; Farjah, E.; Azizipanah-Abarghooee, R., An efficient scenario-based and fuzzy self-adaptive learning particle swarm optimization approach for dynamic economic emission dispatch considering load and wind power uncertainties, Energy, 50, 232-244 (2013) |
| [4] | Briec, W.; Kerstens, K., Portfolio selection in multidimensional general and partial moment space, Journal of Economic Dynamics and Control, 34, 4, 636-656 (2010) · Zbl 1202.91293 |
| [5] | Bruno, S.; Ahmed, S.; Shapiro, A.; Street, A., Risk neutral and risk averse approaches to multistage renewable investment planning under uncertainty, European Journal of Operational Research, 250, 3, 979-989 (2016) · Zbl 1346.90636 |
| [6] | Chen, K.; Yu, J., Short-term wind speed prediction using an unscented Kalman filter based state-space support vector regression approach, Applied Energy, 113, 690-705 (2014) |
| [7] | Cheng, R.; Jin, Y.; Narukawa, K.; Sendhoff, B., A multiobjective evolutionary algorithm using Gaussian process-based inverse modeling, IEEE Transactions on Evolutionary Computation, 19, 6, 838-856 (2015) |
| [8] | Chronopoulos, M.; Lumbreras, S., Optimal regime switching under risk aversion and uncertainty, European Journal of Operational Research, 256, 2, 543-555 (2017) · Zbl 1395.91485 |
| [9] | Collan, M.; Luukka, P., Evaluating R&D projects as investments by using an overall ranking from four new fuzzy similarity measure based TOPSIS variants, IEEE Transactions on Fuzzy Systems, 22, 3, 505-515 (2013) |
| [11] | Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T., A fastand elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6, 2, 182-197 (2002) |
| [12] | Dorvlo, A. S., Estimating wind speed distribution, Energy Conversion and Management, 43, 17, 2311-2318 (2002) |
| [13] | Durillo, J. J.; Nebro, A. J.; Coello, C. A.C.; García-Nieto, J.; Luna, F.; Alba, E., A study of multiobjective metaheuristics when solving parameter scalable problems, IEEE Transactions on Evolutionary Computation, 14, 4, 618-635 (2010) |
| [14] | Elberg, C.; Hagspiel, S., Spatial dependencies of wind power and interrelations with spot price dynamics, European Journal of Operational Research, 241, 1, 260-272 (2015) · Zbl 1338.91100 |
| [15] | Elton, E. J.; Gruber, M. J.; Brown, S. J.; Goetzmann, W. N., Modern portfolio theory and investment analysis (2009), John Wiley & Sons: John Wiley & Sons New York |
| [16] | Fisher, R. A., Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population, Biometrika, 10, 4, 507-521 (1915) |
| [17] | Gabrel, V.; Murat, C.; Thiele, A., Recent advances in robust optimization: An overview, European Journal of Operational Research, 235, 3, 471-483 (2014) · Zbl 1305.90390 |
| [18] | Gotoh, J. Y.; Takano, Y., Newsvendor solutions via conditional value-at-risk minimization, European Journal of Operational Research, 179, 1, 80-96 (2007) · Zbl 1275.90057 |
| [20] | Guo, C. X.; Zhan, J. P.; Wu, Q. H., Dynamic economic emission dispatch based on group search optimizer with multiple producers, Electric Power Systems Research, 86, 8-16 (2012) |
| [21] | Hajian, M.; Rosehart, W. D.; Zareipour, H., Probabilistic power flow by Monte Carlo simulation with Latin supercube sampling, IEEE Transactions on Power Systems, 28, 2, 1550-1559 (2013) |
| [22] | Hansen, N.; Müller, S.; Koumoutsakos, P., Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES), Evolutionary Computation, 11, 1, 1-18 (2003) |
| [23] | Harvey, C. R.; Siddique, A., Conditional skewness in asset pricing tests, Journal of Finance, 55, 3, 1263-1295 (2000) |
| [24] | He, S.; Wu, Q. H.; Saunders, J. R., Group search optimizer: an optimization algorithm inspired by animal searching behavior, IEEE Transactions on Evolutionary Computation, 13, 5, 973-990 (2009) |
| [25] | Huang, H.; Chung, C.; Chan, K. W.; Chen, H., Quasi-Monte Carlo based probabilistic small signal stability analysis for power systems with plug-in electric vehicle and wind power integration, IEEE Transactions on Power Systems, 28, 3, 3335-3343 (2013) |
| [26] | Jahanshahloo, G.; Hosseinzadeh, F. L.; Izadikhah, M., An algorithmic method to extend TOPSIS for decision-making problems with interval data, Applied Mathematics and Computation, 175, 2, 1375-1384 (2005) · Zbl 1131.90386 |
| [27] | Ji, B.; Yuan, X.; Chen, Z.; Tian, H., Improved gravitational search algorithm for unit commitment considering uncertainty of wind power, Energy, 67, 52-62 (2014) |
| [28] | Joro, T.; Na, P., Portfolio performance evaluation in a mean-variance-skewness framework, European Journal of Operational Research, 175, 1, 446-461 (2006) · Zbl 1137.91453 |
| [29] | Joshi, D.; Kumar, S., Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making, European Journal of Operational Research, 248, 1, 183-191 (2016) · Zbl 1346.91051 |
| [30] | K, D., Multi-objective optimization using evolutionary algorithms (2001), Wiley: Wiley New York · Zbl 0970.90091 |
| [31] | Kimball, M. S., Precautionary saving in the small and in the large, Econometrica: Journal of the Econometric Society, 58, 1, 53-73 (1990) |
| [32] | Kocuk, B.; Dey, S. S.; Sun, X. A., Strong SOCP relaxations for the optimal power flow problem, Operations Research, 64, 6, 1177-1196 (2016) · Zbl 1354.90154 |
| [33] | Konno, H.; Suzuki, K.-I., A mean-variance-skewness portfolio optimization model, Journal of the Operations Research Society of Japan, 38, 2, 173-187 (1995) · Zbl 0839.90012 |
| [34] | Li, M. S.; Wu, Q. H.; Ji, T. Y.; Rao, H., Stochastic multi-objective optimization for economic-emission dispatch with uncertain wind power and distributed loads, Electric Power Systems Research, 116, 367-373 (2014) |
| [35] | Li, Y. Z.; Wu, Q. H., Downside risk constrained probabilistic optimal power flow with wind power integrated, IEEE Transactions on Power Systems, 31, 2, 1649-1650 (2016) |
| [36] | Li, Y. Z.; Wu, Q. H.; Jiang, L.; Yang, J. B., Optimal power system dispatch with wind power integrated using nonlinear interval optimization and evidential reasoning approach, IEEE Transactions on Power Systems, 31, 3, 2246-2254 (2016) |
| [37] | Li, Y. Z.; Wu, Q. H.; Li, M. S.; Zhan, J. P., Mean-variance model for power system economic dispatch with wind power integrated, Energy, 72, 510-520 (2014) |
| [38] | Liao, H. L.; Wu, Q. H.; Li, Y. Z.; Jiang, L., Economic emission dispatching with variations of wind power and loads using multi-objective optimization by learning automata, Energy Conversion and Management, 87, 990-999 (2014) |
| [39] | Lin, Y.; Johnson, J. X.; Mathieu, J. L., Emissions impacts of using energy storage for power system reserves, Applied Energy, 168, 444-456 (2016) |
| [40] | Liu, X.; Wilsun, X., Minimum emission dispatch constrained by stochastic wind power availability and cost, IEEE Transactions on Power Systems, 25, 3, 1705-1713 (2010) |
| [41] | Markowitz, H., Mean-variance approximations to expected utility, European Journal of Operational Research, 234, 2, 346-355 (2014) · Zbl 1304.91203 |
| [42] | Miranda, V.; Hang, P. S., Economic dispatch model with fuzzy wind constraints and attitudes of dispatchers, IEEE Transactions on Power Systems, 20, 4, 2143-2145 (2005) |
| [43] | Mohandes, M.; Rehman, S.; Rahman, S., Estimation of wind speed profile using adaptive neuro-fuzzy inference system (ANFIS), Applied Energy, 88, 11, 4024-4032 (2011) |
| [44] | Morales, J. M.; Perez-Ruiz, J., Point estimate schemes to solve the probabilistic power flow, IEEE Transactions on Power Systems, 22, 4, 1594-1601 (2007) |
| [45] | Mustard, D., Numerical integration over the n-dimensional spherical shell, Mathematics of Computation, 18, 88, 578-589 (1964) · Zbl 0121.34202 |
| [46] | O’Brien, W. J.; Evans, B. I.; Howick, G. L., A new view of the predation cycle of a planktivorous fish, white crappie (pomoxis annularis), Canadian Journal of Fisheries and Aquatic Sciences, 43, 10, 1894-1899 (1986) |
| [47] | Papavasiliou, A.; Oren, S. S., Multiarea stochastic unit commitment for high wind penetration in a transmission constrained network, Operations Research, 61, 3, 578-592 (2013) · Zbl 1273.90035 |
| [48] | Pindoriya, N. M.; Singh, S. N.; Singh, S. K., Multi-objective mean-variance-skewness model for generation portfolio allocation in electricity markets, Electric Power Systems Research, 80, 10, 1314-1321 (2010) |
| [49] | Ruiz, C.; Conejo, A., Robust transmission expansion planning, European Journal of Operational Research, 242, 2, 390-401 (2015) |
| [50] | Samuelson, P. A., The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments, The Review of Economic Studies, 37, 4, 537-542 (1970) · Zbl 0212.52001 |
| [51] | Shi, L.; Wang, C.; Yao, L.; Ni, Y.; Bazargan, M., Optimal power flow solution incorporating wind power, IEEE Systems Journal, 6, 2, 233-241 (2012) |
| [52] | Su, C.-L., Probabilistic load-flow computation using point estimate method, IEEE Transactions on Power Systems, 20, 4, 1843-1851 (2005) |
| [53] | Thomson, P. C., The behavioural ecology of dingoes in North-Western Australia. II. Activity patterns, breeding season and pup rearing, Wildlife Research, 19, 5, 519-529 (1992) |
| [54] | Venkatesh, P.; Gnanadass, R.; Padhy, N. P., Comparison and application of evolutionary programming techniques to combined economic emission dispatch with line flow constraints, IEEE Transactions on Power Systems, 18, 2, 688-697 (2003) |
| [55] | Wang, L.; Yang, Y.; Dong, C.; Morosuk, T.; Tsatsaronis, G., Multi-objective optimization of coal-fired power plants using differential evolution, Applied Energy, 115, 4, 254-264 (2014) |
| [56] | Yang, J. B., Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties, European Journal of Operational Research, 131, 1, 31-61 (2001) · Zbl 0979.90081 |
| [57] | Yang, J. B.; Xu, D. L., On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty, IEEE Transactions on Systems Man & Cybernetics, Part A: Systems & Humans, 32, 3, 289-304 (2002) |
| [58] | Yang, Z.; Duan, Z.; Wang, J.; Wang, T.; Song, Y.; Zhang, J., Quadratic radical function better than Fisher Z transformation, Transactions of Tianjin University, 19, 381-384 (2013) |
| [59] | Yu, H.; Chung, C. Y.; Wong, K. P.; Lee, H. W.; Zhang, J. H., Probabilistic load flow evaluation with hybrid latin hypercube sampling and Cholesky decomposition, IEEE Transactions on Power Systems, 24, 2, 661-667 (2009) |
| [60] | Zaman, M.; Elsayed, S. M.; Ray, T.; Sarker, R. A., Evolutionary algorithms for dynamic economic dispatch problems, IEEE Transactions on Power Systems, 31, 2, 1486-1495 (2016) |
| [61] | Zhang, J.; Lam, W. H.; Chen, B. Y., On-time delivery probabilistic models for the vehicle routing problem with stochastic demands and time windows, European Journal of Operational Research, 249, 1, 144-154 (2016) · Zbl 1346.90198 |
| [62] | Zhao, M.; Chen, Z.; Blaabjerg, F., Probabilistic capacity of a grid connected wind farm based on optimization method, Renewable energy, 31, 13, 2171-2187 (2006) |
| [63] | Zhao, Z.; Yang, J.; Hu, Z.; Che, H., A differential evolution algorithm with self-adaptive strategy and control parameters based on symmetric Latin hypercube design for unconstrained optimization problems, European Journal of Operational Research, 250, 1, 110-122 (2016) |
| [64] | Zheng, J. H.; Chen, J. J.; Wu, Q. H.; Jing, Z. X., Multi-objective optimization and decision making for power dispatch of a large-scale integrated energy system with distributed dhcs embedded, Applied Energy, 154, 369-379 (2015) |
| [65] | Zhou, B.; Geng, G.; Jiang, Q., Hierarchical unit commitment with uncertain wind power generation, IEEE Transactions on Power Systems, 31, 1, 94-104 (2016) |
| [66] | Zhou, W.; Peng, Y.; Sun, H., Optimal wind-thermal coordination dispatch based on risk reserve constraints, European Transactions on Electrical Power, 21, 1, 740-756 (2011) |
| [67] | Zhu, S.; Fukushima, M., Worst-case conditional value-at-risk with application to robust portfolio management, Operations Research, 57, 5, 1155-1168 (2009) · Zbl 1233.91254 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
