On the Concept of an Optimal Portfolio of Uncertain Flexible Loads

RESUMO

Flexible loads can enhance power system stability by providing reserves, but their limited energy capacity and uncertain availability distinguish them from conventional generators. To accommodate these characteristics, the Danish Transmission System Operator (TSO) recently introduced new reserve market rules that incorporate energy constraints and relax reliability requirements. In this context, the optimal reserve quantification becomes a joint chance-constrained reserve quantification problem, which is difficult to solve. In this paper, we derive two analytical reformulations of this problem: an exact one when a reserve direction dominates and an approximate one, otherwise. Furthermore, when flexible loads must collectively satisfy a reliability requirement, we introduce the concept of an optimal portfolio of flexible loads: adding loads with similar expected values but different stochastic behaviors to an existing portfolio may change the total portfolio's reserves. To support this idea, we theoretically study the marginal increase in reserves resulting from adding a load. Numerical results show that our analytical reformulations closely match the exact formulation, with a mean absolute error of 2.5%. Case studies further demonstrate the existence of optimal load groupings and our ability to predict the portfolio in which a load's marginal value is highest, leveraging our theoretical analysis.