A Real-Time Alternating Direction Method of Multipliers Algorithm for Nonconvex Optimal Power Flow Problem

A two‐stage adaptive‐robust optimization model for active distribution network with high penetration wind power generation

“…The vanadium liquid flow battery storage is installed at node 11 with the rated power and rated capacity as 50 MW and 100 MWh. The battery degradation cost δ sp is 30$/MWh, and the charging/discharging cost δ sI is 100$ per time, other parameters are cited from [36]. In order to intuitively quantify the robustness of different optimization models with changed parameters, the robustness assessment is conducted based on the statistical underlying Risk Index (RI) defined from wind power generation probability densities as illustrated in Figure 1 of [22]., which is calculated as the percentage of the wind power generation fluctuations residing outside of the bounds W l w,t and W u w,t .…”

“…(1) The first one is the 69-bus radial distribution network [36] as shown in Figure 6a, which consists of 68 branches, 15 DERs, 3 battery units and 3 wind farms. The detailed network branch parameters and the hourly load demand are cited from Table A1 of the appendix in [36], and the fuel cost coefficients of 15 DERs in the bus set {1, 5,9,16,20,25,28,35,37,44,54,56,58,59, 69} are cited from the Table A2. Three battery units are connected at buses 41, 50 and 65 with the rated energy capacity of 300 kWh and charging/discharging power limit of 150 kW.…”

“…The network is formed by replicating the aforementioned 69-bus distribution network four times with extra feeders added between buses 69 and 1. The parameters of units and wind power generators are copied from the 69-bus network, while the data of distribution network feeders, the load demands and the fuel cost coefficients of 60 DERs are the same as those in [36]. Based on these parameters setting, regarding the efficiency of the proposed method for solving the aforementioned 18bus, the 69-bus and the extended 276-bus radial distribution networks, the key results in terms of iterations and the computation time cost are provided in Table 9.…”

“…The network is formed by replicating the aforementioned 69‐bus distribution network four times with extra feeders added between buses 69 and 1. The parameters of battery units and wind power generators are copied from the 69‐bus network, while the data of distribution network feeders, the load demands and the fuel cost coefficients of 60 DERs are the same as those in [36].…”

Distributed ADMM Using Private Blockchain for Power Flow Optimization in Distribution Network With Coupled and Mixed-Integer Constraints

“…If the algorithm reaches the iteration limit with no feasible binary solution, the values of ρ 1 and ρ 2 are updated by 5% and warm start the OPF subproblem. In the last step, all the binary variables are fixed based on the condition in (21), and the OPF problem is solved until it converges. The algorithm flowchart is shown in Fig.…”