access icon free Kullback–Leibler divergence-based distributionally robust optimisation model for heat pump day-ahead operational schedule to improve PV integration

© The Institution of Engineering and Technology
Received 23/12/2017, Accepted 15/03/2018, Revised 04/03/2018, Published 23/03/2018

For its high coefficient of performance and zero local emissions, the heat pump (HP) has recently become popular in North Europe and China, which shows potential in absorbing local photovoltaic (PV) generation. In this study, the authors describe a distributionally robust optimisation (DRO)-based HP day-ahead operational schedule model (HP-DOSM) to match the PV power generation, which can well capture the uncertainties of weather, PV, and load prediction errors. Moreover, this DRO-based HP-DOSM can be transformed into a tractable deterministic model. The DRO method they proposed is suitable for linear expectation constrained optimisation whose ambiguity set is constructed using Kullback–Leibler divergence, which could be further transformed into deterministic conic/linear constraints. Compared with robust optimisation (RO) models, the authors’ model is less conservative since more statistical information on the uncertainties is utilised. Numerical tests were conducted to demonstrate its performance, compared with the RO model via Monte Carlo simulations.

Inspec keywords: optimisation; heat pumps; power generation scheduling; load forecasting; statistical analysis; photovoltaic power systems

Other keywords: PV power generation; heat pump day-ahead operational scheduling; China; linear expectation constrained optimisation; Kullback-Leibler divergence-based distributional robust optimisation model; tractable deterministic model; statistical information; North Europe; DRO model; load prediction; HP-DOSM; deterministic conic-linear constraint; zero local emission; Monte Carlo simulation; photovoltaic generation

Subjects: Other topics in statistics; Air conditioning; Optimisation techniques; Power system planning and layout; Solar power stations and photovoltaic power systems

References

    1. 1)
      • 7. Howlader, H.O.R., Matayoshi, H., Senjyu, T.: ‘Distributed generation incorporated with the thermal generation for optimum operation of a smart grid considering forecast error’, Energy Convers. Manage., 2015, 96, pp. 303–314.
    2. 2)
      • 12. Zhang, Y., Shen, S., Mathieu, J.: ‘Distributionally robust chance-constrained optimal power flow with uncertain renewables and uncertain reserves provided by loads’, IEEE Trans. Power Syst., 2017, 32, (2), pp. 1378–1388.
    3. 3)
      • 21. Hu, Z., Hong, L.J.: ‘Kullback-leibler divergence constrained distributionally robust optimization’. 2012, http://www.optimization-online.org/DB_FILE/2012/11/3677.pdf..
    4. 4)
      • 3. Arteconi, A., Hewitt, N.J., Polonara, F.: ‘Domestic demand-side management (DSM): role of heat pumps and thermal energy storage (TES) systems’, Appl. Therm. Eng., 2013, 51, (1–2), pp. 155–165.
    5. 5)
      • 8. Vanhoudt, D., Geysen, D., Claessens, B., et al: ‘An actively controlled residential heat pump: potential on peak shaving and maximization of self-consumption of renewable energy’, Renew. Energy, 2014, 63, pp. 531–543.
    6. 6)
      • 11. Wiesemann, W., Kuhn, D., Sim, M.: ‘Distributionally robust convex optimization’, Oper. Res., 2014, 62, (6), pp. 1358–1376.
    7. 7)
      • 15. Delage, E., Ye, Y.: ‘Distributionally robust optimization under moment uncertainty with application to data-driven problems’, Oper. Res., 2008, 58, (3), pp. 595–612.
    8. 8)
      • 4. Gao, Z., Chen, D.-M., Yang, J.-H., et al: ‘Study on rural low-voltage distribution network planning with coal-to-electricity project’, Electr. Electron., 2015.
    9. 9)
      • 23. Li, X., Natarajan, K., Teo, C.-P., et al: ‘Distributionally robust mixed integer linear programs: persistency models with applications’, Eur. J. Oper. Res., 2014, 233, (3), pp. 459–473.
    10. 10)
      • 17. Kuhn, D., Esfahani, P.M.: ‘Data-driven distributionally robust optimization using the Wasserstein metric Performance guarantees and tractable reformulations’, Optim. Control, 2016, 24, (9), pp. 1–52.
    11. 11)
      • 14. Xiong, P., Jirutitijaroen, P., Singh, C.: ‘A distributionally robust optimization model for unit commitment considering uncertain wind power generation’, IEEE Trans. Power Syst., 2017, 32, (1), pp. 39–49.
    12. 12)
      • 22. Huang, K.-L., Mehrotra, S., Bansal, M.: ‘Decomposition algorithms for two-stage distributionally robust mixed binary programs’, 2017.
    13. 13)
      • 5. Xinhua, available at http://news.xinhuanet.com/local/2017-01/25/c_1120381959.htm.
    14. 14)
      • 25. Peng, J.W., Li, H., Zhang, C.L.: ‘Performance comparison of air-source heat pump water heater with different expansion devices’, Appl. Therm. Eng., 2016, 99, pp. 1190–1200.
    15. 15)
      • 24. Chen, X., Wu, W., Zhang, B., et al: ‘Data-driven DG capacity assessment method for active distribution networks’, IEEE Trans. Power Syst., 2017, 32, (5), pp. 3946–3957.
    16. 16)
      • 2. EHPA: ‘European heat pump association’, Outlook European Heat Pump Statistics, 2011.
    17. 17)
      • 26. Jiang, S., Wang, S., Jin, X., et al: ‘Optimum compressor cylinder volume ratio for two-stage compression air source heat pump systems’, Int. J. Refrig., 2016, 67, pp. 77–89.
    18. 18)
      • 29. http://data.cma.cn/site/index.html. ‘China Meteorological Administration’.
    19. 19)
      • 20. Ben-Tal, A., Hertog, D.D., Waegenaere, A.D., et al: ‘Robust solutions of optimization problems affected by uncertain probabilities’, Manage. Sci., 2013, 59, (2), pp. 341–357.
    20. 20)
      • 31. Li, C., Xu, Y., Yu, X., et al: ‘Risk-averse energy trading in multienergy microgrids: a two-stage stochastic game approach’, IEEE Trans. Ind. Inf., 2017, 13, (5), pp. 2620–2630.
    21. 21)
      • 1. Ibañez-Puy, M., Bermejo-Busto, J., Martín-Gómez, C., et al: ‘Thermoelectric cooling heating unit performance under real conditions’, Appl. Energy, 2017, 200, pp. 303–314.
    22. 22)
      • 28. den Hertog, D., Ben-Tal, A., De Waegenaere, A., et al: ‘Robust solutions of optimization problems affected by uncertain probabilities’, 2011.
    23. 23)
      • 18. Jiang, R., Guan, Y.: ‘Data-driven chance constrained stochastic program’, Math. Program., 2016, 158, (1), pp. 291–327.
    24. 24)
      • 19. Chen, X., Zhang, Y.: ‘Uncertain linear programs: extended affinely adjustable robust counterparts’, Oper. Res., 2009, 57, (6), pp. 1469–1482.
    25. 25)
      • 13. Zymler, S., Kuhn, D., Rustem, B.: ‘Distributionally robust joint chance constraints with second-order moment information’, Math. Program., 2011, 137, (1–2), pp. 167–198.
    26. 26)
      • 27. Tant, J., Geth, F., Six, D., et al: ‘Multiobjective battery storage to improve PV integration in residential distribution grids’, IEEE Trans. Sustain. Energy, 2013, 4, (1), pp. 182–191.
    27. 27)
      • 30. Botev, Z.I., Grotowski, J.F., Kroese, D.P.: ‘Kernel density estimation via diffusion’, Ann. Stat., 2010, 38, (5), pp. 2916–2957.
    28. 28)
      • 16. Loizou, N.: ‘Distributionally robust game theory’, 2015, arXiv:1512.03253.
    29. 29)
      • 6. Wanjiru, E.M., Sichilalu, S.M., Xia, X.: ‘Optimal control of heat pump water heater-instantaneous shower using integrated renewable-grid energy systems’, Appl. Energy, 2017, 201, pp. 332–342.
    30. 30)
      • 10. Klein, K., Herkel, S., Henning, H.M., et al: ‘Load shifting using the heating and cooling system of an office building: quantitative potential evaluation for different flexibility and storage options’, Appl. Energy, 2017, 203, pp. 917–937.
    31. 31)
      • 9. Wang, D., Ge, S., Jia, H., et al: ‘A demand response and battery storage coordination algorithm for providing microgrid tie-line smoothing services’, IEEE Trans. Sustain. Energy, 2014, 5, (2), pp. 476–486.
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