A Flexible Envelope Method for the Operation Domain of Distribution Networks Based on “Degree of Squareness” Adjustable Superellipsoid

Abstract

The operation envelope of distribution networks can obtain the independent p-q controllable range of each active node, providing an effective means to address the issues of different ownership and control objectives between distribution networks and distributed energy resources (DERs). Existing research mainly focuses on deterministic operation envelopes, neglecting the operational status of the system. To ensure the maximization of the envelope operation domain and the feasibility of decomposition, this paper proposes a modified hyperellipsoidal dynamic operation envelopes (MHDOEs) method for distribution networks based on adjustable “Degree of Squareness” hyperellipsoids. Firstly, an improved convex inner approximation method is applied to the non-convex and nonlinear model of traditional distribution networks to obtain a convex solution space strictly contained within the original feasible region of the system, ensuring the feasibility of flexible operation domain decomposition. Secondly, the embedding of the adjustable “Degree of Squareness” maximum hyperellipsoid is used to obtain the total p-q operation domain of the distribution network, facilitating the overall planning of the distribution network. Furthermore, the calculation of the maximum inscribed hyperrectangle of the hyperellipsoid is performed to achieve p-q decoupled operation among the active nodes of the distribution network. Subsequently, a correction coefficient is introduced to penalize “unknown states” during the operation domain calculation process, effectively enhancing the adaptability of the proposed method to complex stochastic scenarios. Finally, Monte Carlo methods are employed to construct various stochastic scenarios for the IEEE 33-node and IEEE 69-node systems, verifying the accuracy and decomposition feasibility of the obtained p-q operation domains.