Equitable Active-Reactive Power Envelopes for Distributed Energy Resources in Power Distribution Systems

The operating envelope (OE) provides an effective method to manage distributed energy resources (DERs) in power distribution systems (DSs) by offering allowable regions of nodal power injections. The active-reactive power envelope (P-Q envelope) is a desirable type of OE that would increase the allowable active power range and release the reactive power flexibility. However, existing OE studies have not established P-Q envelopes with guaranteed equitableness. This paper proposes an equitable P-Q envelope calculation and optimization method. First, we model the P-Q envelopes as convex polygons on active-reactive power planes of nodal power injections. Second, we define the proportional equitableness of P-Q envelopes and establish two equitable conditions, under which the equitableness of P-Q envelopes is proved mathematically. Third, we propose the P-Q envelope calculation method. Specifically, the P-Q envelopes are initially established considering the security constraints of DSs and then modified by a geometric method to satisfy two equitable conditions. Finally, we develop the optimization method to increase the maximum active power export and import provided by P-Q envelopes by coordinating the on-load tap changer, capacitor banks, and distributed generators. The proposed methods are tested on the 33-bus, real-world 135-bus and 455-bus DSs. Numerical results show that the proposed method efficiently obtains the P-Q envelopes with strict proportional equitableness and remarkably enlarges the size of P-Q envelopes by optimizing the control strategies of DS devices. Compared with existing OE calculation methods, the proposed method obtains the largest allowable power range using the shortest computation time.