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DOI: 10.23952/cot.2027.4
Received July 2, 2025; Accepted December 27, 2025; Published online July 7, 2026
Abstract. Differentiated energy services (DESs) have proven a promising solution to elicit load flexibility for the supply/demand balance in smart grids. This note explores energy services differentiated by duration requirements and service times, building upon existing models such as duration-differentiated energy services, duration-deadline jointly differentiated energy services, and multiple-arrival multiple-deadline differentiated energy services. A necessary and sufficient condition is derived to check the adequacy of a supply for a continuum of loads consuming the considered DESs. Moreover, to verify the economic feasibility of such DESs, we establish, in a forward market, the existence of an efficient competitive equilibrium, where self-interested DES consumers attain the maximum social welfare, even in the absence of a social planner.
How to Cite this Article:
Y. Mo, L. Qiu, A note on duration-service-time differentiated energy services, Commun. Optim. Theory 2027 (2027) 4.