Optimal Period Partitioning and Time-of-Use Electricity Pricing for Residential Customers Using Moving Boundary Technique and Multi-Objective Differential Evolution
Keywords:
moving boundary technique, multi-objective differential evolution, optimal period partitioning, price elasticity, time-of-use rateAbstract
The widespread adoption of Electric Vehicles (EVs) has significantly altered residential electricity consumption patterns, with most EV charging concentrated during evening peak hours, thereby intensifying stress on power grids and operational costs. While Time-of-Use (TOU) pricing is widely used for demand response, many prior studies rely on single-objective or weighted-sum methods, and multi-objective approaches provide limited quantitative evaluation of Pareto front quality. This study addresses these challenges by employing Multi-Objective Differential Evolution (MODE) to optimize TOU electricity pricing for simultaneously minimizing peak demand and total customer energy costs, incorporating price elasticity of demand to reflect realistic consumer response behavior. The quality and diversity of Pareto-optimal solutions are evaluated using the Hypervolume Indicator (HV), ensuring a well-distributed and high-performing set of pricing strategies across the entire trade-off surface, and using the Moving Boundary Technique (MBT) to determine optimal time boundaries for off-peak, mid-peak, and peak periods based on actual hourly load characteristics. The load data utilizes a real residential dataset from Thailand’s Provincial Electricity Authority (PEA), demonstrates the superiority of the optimized TOU three rates compared with the conventional TOU two rates, the proposed approach yields three distinct solution categories: a minimum-peak solution achieving 11.4% peak demand reduction, a minimum-cost solution delivering 34.7% total customer cost savings, and a balanced solution offering 9.5% peak reduction alongside 29% cost savings. Additionally, the minimum-peak solution reduces CO2 emissions by 745 tons daily through strategic load shifting to solar-rich hours.
References
A. Tayri and X. Ma, “Grid Impacts of Electric Vehicle Charging: A Review of Challenges and Mitigation Strategies,” Jul.
, 2025, Multidisciplinary Digital Publishing Institute (MDPI). doi: 10.3390/en18143807.
M. Muratori and G. Rizzoni, “Residential Demand Response: Dynamic Energy Management and Time-Varying Electricity
Pricing,” IEEE Transactions on Power Systems, vol. 31, no. 2, pp. 1108–1117, Mar. 2016, doi:10.1109/TPWRS.2015.2414880.
J. S. Vardakas, N. Zorba, and C. V. Verikoukis, “A Survey on Demand Response Programs in Smart Grids: Pricing Methods
and Optimization Algorithms,” IEEE Communications Surveys and Tutorials, vol. 17, no. 1, pp. 152–178, Jan. 2015, doi:
1109/COMST.2014.2341586.
Q. Wu, L. Wang, and H. Cheng, ”Research of TOU power price based on multi-objective optimization of DSM and costs of
power consumers,” in Proc. IEEE Int. Conf. Electric Utility Deregulation, Restructuring Power Technol., 2004, pp. 343–348.
N. Yu and J. Yu, ”Optimal TOU decision considering demand response model,” in Proc. International Conference on Power
System Technology., Chongqing, 2006, pp. 1–5.
Z. F. Tan, M. Bin Wang, J. X. Qi, J. C. Hou, and X. Li, “Time-of-use price optimizing model and fuzzy solving method,”
Xitong Gongcheng Lilun yu Shijian/System Engineering Theory and Practice, vol. 28, no. 9, pp. 145–151, 2008, doi:
1016/s1874-8651(09)60039-9.
V. Venizelou, N. Philippou, M. Hadjipanayi, G. Makrides, V. Efthymiou, and G. E. Georghiou, “Development of a novel
time-of-use tariff algorithm for residential prosumer price-based demand side management,” Energy, vol. 142, pp. 633–646,
Jan. 2018, doi: 10.1016/j.energy.2017.10.068.
W. Hu, Z. Chen and B. Bak-Jensen, ”Optimal load response to time-of-use power price for demand side management in
Denmark,” in Proc. IEEE PES Gen. Meet., 2010, pp. 1–6.
H. Aalami, G. R. Yousefi, and M. P. Moghadam, ”Demand response model considering EDRP and TOU programs,” in Proc.
IEEE/PES Transmiss. Distrib. Conf. Expo., Chicago, IL, USA, 2008, pp. 1–6.
C. Taihua, L. Hong, H. Yang, and G. Junlin, ”Research on seasonal power load characteristics and modeling of TOU price,”
in Proc. 29th Chin. Control Decis. Conf. (CCDC), 2017, pp. 1415–1420.
L. Dengfeng, L. Zhonghao, L. Xiaoju, Y. Juan, Y. Mincai, and L. Xinyu, “Optimization method of time-of-use electricity
price for the cost savings of power grid investment,” Front. Energy Res., vol. 12, 2024, doi: 10.3389/fenrg.2024.1361116.
H. Jang, S. Moon, and J. Kim, “Effects of time-of-use pricing for residential customers and wholesale market consequences
in South Korea,” Energy Econ., vol. 134, p. 107557, Jun. 2024, doi: 10.1016/j.eneco.2024.107557.
W. Xue et al., “Research on the Optimal Design of Seasonal Time-of-Use Tariff Based on the Price Elasticity of Electricity
Demand,” Energies (Basel), vol. 16, no. 4, Feb. 2023, doi: 10.3390/en16041625.
P. You et al., “Price-Based Demand Response: A Three-Stage Monthly Time-of-Use Tariff Optimization Model,”Energies
(Basel), vol. 16, no. 23, Dec. 2023, doi: 10.3390/en16237858.
P. Wang, Y. Ma, Z. Ling, and G. Luo, “Peak-valley period partition and abnormal time correction for time-of-use tariffs
under daily load curves based on improved fuzzy c-means,” IET Generation, Transmission and Distribution, vol. 17, no. 24,
pp. 5396–5409, Dec. 2023, doi: 10.1049/gtd2.13052.
H. Yang, L. Wang, Y. Zhang, H. M. Tai, Y. Ma, and M. Zhou, “Reliability evaluation of power system considering time of use electricity pricing,” IEEE Transactions on Power Systems, vol. 34, no. 3, pp. 1991–2002, May 2019,
doi:10.1109/TPWRS.2018.2879953.
H. Yang, L. Wang, Y. Ma, D. Zhang, and W. U. Hongbin, “Optimization strategy of price-based demand response considering the bidirectional feedback effect,” IET Generation, Transmission and Distribution, vol. 15, no. 11, pp. 1752–1762, Jun.
, doi: 10.1049/gtd2.12131.
H. Yang, L. Wang, and Y. Ma, “Optimal time of use electricity pricing model and its application to electrical distribution
system,” IEEE Access, vol. 7, pp. 123558–123568, 2019, doi: 10.1109/ACCESS.2019.2938415.
S. Li, C. Sun, and Z. Li, “Improved TOU Tariff Design for Facilitating Peak-Cutting and Valley-filling in Power Systems,”
in IEEE 7th Conference on Energy Internet and Energy System Integration, Institute of Electrical and Electronics Engineers
Inc., 2023, pp. 2986–2991. doi: 10.1109/EI259745.2023.10512918.
S. Das and P. N. Suganthan, “Differential evolution: A survey of the state-of-the-art,” IEEE Transactions on Evolutionary
Computation, vol. 15, no. 1, pp. 4–31, Feb. 2011, doi: 10.1109/TEVC.2010.2059031.
H. A. Abbass, R. Sarker, and C. Newton, ”PDE: A Pareto-frontier differential evolution approach for multi-objective optimization problems,” in Proc. Congr. Evol. Comput., vol. 2, 2001, pp. 971–978.
L. Zhao, D. Li, X. Huang, and B. Zhou, ”Modified non-dominated sorted differential evolution for multi-objective optimization,” in Proc. Chin. Control Conf. (CCC), 2017, pp. 2830–2834.
E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, and V. G. Da Fonseca, “Performance assessment of multiobjective
optimizers: An analysis and review,” Apr. 2003. doi: 10.1109/TEVC.2003.810758.
A. Faruqui, R. Hledik, and N. Newell, “Arcturus 2.0: A Meta-Analysis of Time-Varying Pricing Programs,” The Brattle
Group, Boston, MA, USA, Rep., 2017. [Online]. Available: https://www.brattle.com
A. Sukawattanapornkul, A. Siritaratiwat, P. Khunkitti, C. Surawanitkun, and R. Chatthaworn, ”The novel price elasticity of
demand model for time of use electricity rates determination,” Int. J. Eng. Res. Technol., vol. 12, no. 10, pp. 1799–1807, 2019.
“Load profile: Load Research of PEA.” 2024. [Online]. Available: http://peaoc.pea.co.th/loadprofile/en/.
Provincial Electricity Authority, Thailand. Electricity Tariffs (May 2023), 2023. Available: https://pea.co.th/en/electricitytariffs.
“Thailand Carbon Dioxide Emission per Electricity Generation Economic Indicators CEIC.”. [Online]. Available: https://www.ceicdata.com/en/thailand/carbon-dioxide-emissions-statistics/carbon-dioxide-emission-per-electricitygeneration.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
