Multi-period power flow analysis in distribution systems with distributed generation using the nonlinear programming model
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https://doi.org/10.54939/1859-1043.j.mst.104.2025.49-58Keywords:
Multi-period power flow (MPF); Nonlinear programming (NLP); Distributed generation (DG).Abstract
The traditional power flow analysis of power systems is usually conducted over a single time period. However, many problems in the power systems, such as determining energy loss and optimizing the location and capacity of shunt capacitors, require performing power flow analysis over multiple time periods. This paper presents a method based on nonlinear programming (NLP) to calculate multi-period power flow (MPF) for a distribution grid with distributed generation (DG). This nonlinear optimization model features a constant objective function, with constraints defined by a system of power balance equations and predetermined values for the voltage magnitude and phase angle at the slack bus. The NLP model is programmed using the GAMS language, and the solution is computed using the KNITRO optimization solver. The proposed multi-time period power flow analysis method was evaluated on the distribution grid in Luc Ngan district, Bac Giang province, with 54 nodes and 96 time periods. The calculation results show that the solution of the proposed approach has a very small error compared to the traditional Newton-Raphson technique. At the same time, distributed generation units have a significant impact on energy loss and voltage profile in the power distribution network.
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