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To address the scalability limitations of traditional centralized optimal power flow algorithms， a fully distributed algorithm for solving optimal power flow in DC systems with large-scale distributed energy sources is proposed. Firstly， the non-convex optimal power flow model of DC systems is transformed into a second-order cone programming （SOCP） model using convex relaxation methods. Subsequently， a distributed algorithm based on the alternating direction method of multipliers （ADMM） is established to solve this model. The algorithm is then transformed by eliminating consensus variables into an improved fully distributed algorithm for optimal power flow in DC systems. Finally， in simulation tests on enhanced IEEE 13-node and 118-node systems， the algorithm proved capable of achieving a globally optimal solution for optimal power flow in radial and ring DC systems. Notably， this was accomplished without the necessity of a central coordinating unit to synchronize boundary consistency information across regions. Instead， the algorithm relies on parallel optimization within each region and the exchange of minimal boundary node information between adjacent regions.

In order to improve the operating benefits of the distribution network (DN) and reduce the energy consumption costs of small-micro industrial parks (SMIPs), a two-layer optimal electricity trading method for DN with SMIPs is proposed. First, based on the Stackelberg game, a multi-objective two-layer optimal trading model for DN and SMIP is established. In the upper layer, the DN agent is regarded as the leader, and a trading model is established with the goal of maximizing the profits of agents. In the lower layer, an energy optimization model is proposed for the SMIP operators, which are regarded as the followers, with the goal of minimizing the operating costs. According to the buying and selling electricity prices at the upper and lower layers, a dynamic pricing strategy is formulated. The Karush-Kuhn-Tucker condition (KKT) is introduced to transform the two-layer model into a single-layer model, and based on linear transformations, the model is further converted into a mixed-integer linear programming model. The transformations aim to address the non-linear issues arising from multivariable coupling between the upper and lower-layer trading models. The simulation results show that the trading strategy proposed in this paper can effectively increase the profit of DNs while reducing the operating costs of SMIPs and can provide a reference for decision-making in the electricity market (EM) with the participation of SMIP. [ABSTRACT FROM AUTHOR]