# Optimal Power Flow in Stand-alone DC Microgrids

arXiv: https://arxiv.org/abs/1708.05140 · HTML: https://mlsanity.com/paper/1708.05140/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2017.

## Built on by (most cited first, 2 of 2)

- [You Shall Pass: Dealing with the Zero-Gradient Problem in Predict and Optimize for Convex Optimization](https://mlsanity.com/paper/2307.16304/) (2023)
- [From Inverse Optimization to Feasibility to ERM](https://mlsanity.com/paper/2402.17890/) (2024)

## Abstract (arXiv)

Direct-current microgrids (DC-MGs) can operate in either grid-connected or stand-alone mode. In particular, stand-alone DC-MG has many distinct applications. However, the optimal power flow problem of a stand-alone DC-MG is inherently non-convex. In this paper, the optimal power flow (OPF) problem of DC-MG is investigated considering convex relaxation based on second-order cone programming (SOCP). Mild assumptions are proposed to guarantee the exactness of relaxation, which only require uniform nodal voltage upper bounds and positive network loss. Furthermore, it is revealed that the exactness of SOCP relaxation of DC-MGs does not rely on either topology or operating mode of DC-MGs, and an optimal solution must be unique if it exists. If line constraints are considered, the exactness of SOCP relaxation may not hold. In this regard, two heuristic methods are proposed to give approximate solutions. Simulations are conducted to confirm the theoretic results.