A hybrid optimal power flow model for transmission and distribution networks

• Proposing an efficient and low-computational burden model for the OPF problem. • A hybrid method based on the DCOPF concept and branch flow OPF model. • Developing an OPF model for both radial and meshed networks. This paper presents a fast and accurate optimization technique for optimal power flow (OPF) that can be conveniently applied to transmission and distribution systems. The method is based on the branch flow and DC optimal power flow (DCOPF) models. As the branch flow model is independent of the bus voltage angle, the model needs further development to enable use in meshed transmission systems. Thus, this paper adds the bus voltage angle constraint as a key constraint to the branch flow model so that the voltage angle can also be used in the power flow model in addition to the voltage magnitude control. The problem is based on second-order programming and modeled as a quadratically-constrained programming (QCP) problem solved using the CPLEX solver in GAMS. The functionality of the proposed model is tested utilizing four standard distribution systems, three transmission systems, a combined transmission-distribution network. The studied distribution systems include the 33-bus, 69-bus, 118-bus distribution (118-D) test systems, and 730-bus distribution system (730-D). Additionally, the studied transmission systems include 9-bus, 30-bus, and 118-bus transmission (118-T) test systems. The combined transmission-distribution system included the 9-bus transmission system with three connected distribution systems. The simulation results obtained from the developed technique are compared to those obtained from a conventional optimal flow model. The power losses and the absolute error of the solution are used as the two metrics to compare the methods’ performance for distribution networks. The absolute error of the solution derived from the proposed hybrid OPF compared to MATPOWER for the 33-bus system is 0.00198 %. For the 69-bus system, the error is 0.00044 %. In addition, for the 118-D and 730-D systems, the absolute errors are 0.0026 %, and 0.05 %, respectively. For the transmission network, the operating costs and the solution absolute error are the two metrics used for comparing the proposed hybrid OPF model and MATPOWER. The results indicate the superior performance of the hybrid OPF model to the Newton-Raphson method in MATPOWER in terms of operating cost. In this regard, cost reductions relative to values given by MATPOWER are 0.0005 %, 0.838 %, and 0.015 %, for the 9-bus, 30-bus, and 118-T systems, respectively. The simulation studies demonstrate the performance of the presented branch flow-based model in solving the OPF problem with accurate results.