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Bi-objective mixed integer linear programming for managing building clusters with a shared electrical energy storage. (English) Zbl 1458.91153
Summary: Emerging smart grid infrastructures are allowing buildings to connect to components in other buildings and utilize them in different ways. Clearly, these interconnected building clusters provide new opportunities for building operators to collaborate and help reduce their operational costs over a planning horizon. Nevertheless, since each building can be treated as an independent decision maker here, related fairness concerns have to be addressed in these collaborative environments. We address these issues on building clusters when a single electrical energy storage is shared between two buildings with deterministic demand. We introduce three energy storage sharing strategies, and develop a bi-objective mathematical formulation for each strategy. Several techniques such as piecewise McCormick relaxation are employed for linearizing non-linear terms in the proposed formulations. An extensive computational study demonstrates the efficacy of our proposed linearization techniques, and compares all three strategies in terms of fairness and freedom.

##### MSC:
 91B74 Economic models of real-world systems (e.g., electricity markets, etc.) 90C11 Mixed integer programming 90C29 Multi-objective and goal programming
##### Software:
weightedHypervolume
Full Text:
##### References:
 [1] AlSkaif, T.; Zapata, M. G.; Bellalta, B., A reputation-based centralized energy allocation mechanism for microgrids, 2015 IEEE International Conference on Smart Grid Communications (SmartGridComm), 416-421, (2015) [2] Bathurst, G.; Strbac, G., Value of combining energy storage and wind in short-term energy and balancing markets, Electr. Power Syst. Res., 67, 1, 1-8, (2003) [3] Belotti, P.; Soylu, B.; Wiecek, M. M., Fathoming rules for biobjective mixed integer linear programs: review and extensions, Discrete Optim., 22, Part B, 341-363, (2016) · Zbl 1387.90152 [4] Bianchi, M.; Pascale, A. D.; Melino, F., Performance analysis of an integrated CHP system with thermal and electric energy storage for residential application, Appl. Energy, 112, 928-938, (2013) [5] Bischi, A.; Taccari, L.; Martelli, E.; Amaldi, E.; Manzolini, G.; Silva, P.; Campanari, S.; Macchi, E., A detailed MILP optimization model for combined cooling, heat and power system operation planning, Energy, 74, 12-26, (2014) [6] Boland, N.; Charkhgard, H.; Savelsbergh, M., A criterion space search algorithm for biobjective mixed integer programming: the triangle splitting method, INFORMS J. Comput., 27, 4, 597-618, (2015) · Zbl 1338.90364 [7] Castro, P. M., Tightening piecewise mccormick relaxations for bilinear problems, Comput. Chem. Eng., 72, 300-311, (2015) [8] Chen, H.; Cong, T. N.; Yang, W.; Tan, C.; Li, Y.; Ding, Y., Progress in electrical energy storage system: a critical review, Prog. Nat. Sci., 19, 3, 291-312, (2009) [9] Dächert, K., Adaptive Parametric Scalarizationsin Multicriteria Optimization, (2014), The University of Wuppertal, PhD thesis [10] Dai, R.; Hu, M.; Yang, D.; Chen, Y., A collaborative operation decision model for distributed building clusters, Energy, 84, 759-773, (2015) [11] Ehrgott, M., A discussion of scalarization technique for multiple objective integer programming, Ann. Oper. Res., 147, 343-360, (2006) · Zbl 1188.90236 [12] Hu, M.; Cho, H., A probability constrained multi-objective optimization model for CCHP system operation decision support, Appl. Energy, 116, 230-242, (2014) [13] Hu, M.; Weir, J. D.; Wu, T., Decentralized operation strategies for an integrated building energy system using a memetic algorithm, Eur. J. Oper. Res., 217, 1, 185-197, (2012) · Zbl 1244.90142 [14] Hu, M.; Weir, J. D.; Wu, T., An augmented multi-objective particle swarm optimizer for building cluster operation decisions, Appl. Soft Comput., 25, 347-359, (2014) [15] Isermann, H., The enumeration of the set of all efficient solutions for a linear multiple objective program, Oper. Res. Q., 28(3), 711-725, (1977) · Zbl 0372.90086 [16] Lee, W.-S.; Chen, Y.; Wu, T.-H., Optimization for ice-storage air-conditioning system using particle swarm algorithm, Appl. Energy, 86, 9, 1589-1595, (2009) [17] Li, C.-Z.; Shi, Y.-M.; Liu, S.; ling Zheng, Z.; chen Liu, Y., Uncertain programming of building cooling heating and power (bchp) system based on Monte-Carlo method, Energy Build., 42, 9, 1369-1375, (2010) [18] Liu, S.; Henze, G. P., Experimental analysis of simulated reinforcement learning control for active and passive building thermal storage inventory: part 1. theoretical foundation, Energy Build., 38, 2, 142-147, (2006) [19] Liu, S.; Henze, G. P., Experimental analysis of simulated reinforcement learning control for active and passive building thermal storage inventory: part 2: results and analysis, Energy Build, 38, 2, 148-161, (2006) [20] McCormick, G. P., Computability of global solutions to factorable nonconvex programs: part i — convex underestimating problems, Math Program., 10, 1, 147-175, (1976) · Zbl 0349.90100 [21] Sobieski, D. W.; Bhavaraju, M. P., An economic assessment of battery storage in electric utility systems, IEEE Trans. Power Apparatus Syst., PAS-104, 12, 3453-3459, (1985) [22] Stidsen, T.; Andersen, K. A.; Dammann, B., A branch and bound algorithm for a class of biobjective mixed integer programs, Manage. Sci., 60, 4, 1009-1032, (2014) [23] Vincent, T.; Seipp, F.; Ruzika, S.; Przybylski, A.; Gandibleux, X., Multiple objective branch and bound for mixed 0-1 linear programming: corrections and improvements for biobjective case, Comput. Oper. Res., 40, 1, 498-509, (2013) · Zbl 1349.90006 [24] Walawalkar, R.; Apt, J.; Mancini, R., Economics of electric energy storage for energy arbitrage and regulation in New York, Energy Policy, 35, 4, 2558-2568, (2007) [25] Wang, H.; Varman, P., Balancing fairness and efficiency in tiered storage systems with bottleneck-aware allocation, Proceedings of the 12th USENIX Conference on File and Storage Technologies (FAST 14), 229-242, (2014) [26] Zitzler, E.; Brockhoff, D.; Thiele, L., The hypervolume indicator revisited: on the design of Pareto-compliant indicators via weighted integration, (Obayashi, S.; Deb, K.; Poloni, C.; Hiroyasu, T.; Murata, T., Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science, vol. 4403, (2007)), 862-876 [27] Zitzler, E.; Thiele, L.; Laumanns, M.; Fonseca, C.; Grunert da Fonseca, V., Performance assessment of multiobjective optimizers: an analysis and review, Evol. Comput. IEEE Trans., 7, 2, 117-132, (2003)
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