[Paper Review] Dispatchable Region for Active Distribution Networks Using Approximate Second-Order Cone Relaxation

Zhigang Li, Wenjing Huang+2 more|arXiv (Cornell University)|Jul 1, 2021

Optimal Power Flow Distribution4 citations

TL;DR

This paper proposes a convex optimization-based dispatchable region framework for active distribution networks using approximate second-order cone relaxation of AC power flow equations. By reformulating the AC power flow via second-order cone relaxation and approximating it with a polyhedron, the method enables computationally efficient and accurate assessment of renewable integration capacity, validated on systems of varying scale with high accuracy and low solution time.

ABSTRACT

Uncertainty in distributed renewable generation threatens the security of power distribution systems. The concept of the dispatchable region was developed to assess the ability of power systems to accommodate renewable generation at a given operating point. Although DC and linearized AC power flow equations are typically used to model dispatchable regions for transmission systems, these equations are rarely suitable for distribution networks. To achieve a suitable trade-off between accuracy and efficiency, this paper proposes a dispatchable region formulation for distribution networks using tight convex relaxation. Second-order cone relaxation is adopted to reformulate the AC power flow equations, which are then approximated by a polyhedron to improve tractability. Further, an efficient adaptive constraint generation algorithm is employed to construct the proposed dispatchable region. Case studies on distribution systems of various scales validate the computational efficiency and accuracy of the proposed method.

Motivation & Objective

• To address the challenge of assessing renewable integration capacity in active distribution networks under uncertainty.
• To develop a computationally efficient and accurate method for determining the dispatchable region in distribution systems.
• To overcome the limitations of DC and linearized AC models in distribution networks by using convex relaxation techniques.
• To ensure tractability while maintaining high accuracy through polyhedral approximation of second-order cone relaxations.
• To validate the method on distribution systems of varying sizes with respect to computational efficiency and solution accuracy.

Proposed method

• The paper employs second-order cone relaxation (SOCP) to convexify the non-convex AC power flow equations in distribution networks.
• The relaxed SOCP formulation is then approximated by a polyhedron to improve computational tractability.
• An adaptive constraint generation algorithm is used to iteratively refine the dispatchable region representation.
• The method leverages tight convex relaxation to balance accuracy and computational efficiency.
• The formulation is designed to be scalable and applicable to distribution networks with high penetration of distributed renewable sources.
• The approach is implemented and validated on test systems of various sizes to evaluate performance.

Experimental results

Research questions

• RQ1 How can the dispatchable region be accurately and efficiently determined in active distribution networks with high renewable penetration?
• RQ2 What is the trade-off between accuracy and computational efficiency when using second-order cone relaxation for distribution network dispatchable regions?
• RQ3 Can polyhedral approximation of the SOCP relaxation maintain solution accuracy while improving tractability?
• RQ4 How does the proposed method compare to traditional DC and linearized AC models in terms of accuracy and computational speed?
• RQ5 What is the scalability of the proposed dispatchable region framework across distribution systems of different sizes?

Key findings

• The proposed method achieves high accuracy in determining the dispatchable region, with solution quality close to the true AC power flow results.
• The use of polyhedral approximation significantly improves computational tractability without sacrificing solution fidelity.
• The adaptive constraint generation algorithm efficiently converges to a tight representation of the dispatchable region.
• Case studies on distribution systems of various scales confirm the method's computational efficiency and scalability.
• The method outperforms traditional DC and linearized AC models in accuracy for distribution network applications.
• The framework is validated as a reliable tool for assessing renewable hosting capacity in active distribution networks.