Two three-phase linear power flow models for distribution power system under polar coordinates

Purpose The purpose of this study is to provide a non-iterative linear method to solve the power flow equations of alternating current (AC) power grid. Traditional iterative power flow calculation is limited in speed and reliability, and it is unsuitable for the real-time and online applications of the modern distribution power system (DPS). Thus, it would be of great significance if a fast and flexible linear power flow (LPF) solution could be introduced particularly necessary for the robust and fast control of DPS, especially when the system consists of star and delta connections ZIP load (a constant impedance, Z, load, a constant current, I, load and a constant power, P, load) and the high penetration of distributed solar and wind power generators. Design/methodology/approach Based on the features of DPS and considering the approximate balance of three-phase DPS, several approximations corresponding to the three-phase power flow equations have been discussed and analyzed. Then, based on those approximations, two three-phase LPF models have been developed under the polar coordinates. One model has been formulated with the voltage magnitudes [referred to the voltage magniudes based linear power flow method (VMLPF)], and another model has been formulated with the logarithmic transform of voltage magnitudes [referred to the logarithmic transform of voltage based linear power flow method LGLPF)]. Findings The institute of electrical and electronic engineers (IEEE) 13-bus, 37-bus, 123-bus and an improved 615-bus unbalanced DPSs are used to test the performances of the methods considering star and delta connections ZIP load and PV buses (voltage-controlled buses). The test results validate the effectiveness and accuracy of the proposed two models. Especially when considering the PV buses and delta connection ZIP load, the proposed two models perform much well. Moreover, the results show that VMLPF performs a bit better than LGLPF. Research limitations/implications Except for the transformer with Yg–Yg connection winding can be dealt with directly, the transformers with other connections are not discussed in this proposed paper and need to be further studied. Originality/value These proposed two models can deal with ZIP load with star and delta connections as well as multi slack buses and PV buses. The single-phase, two-phase and three-phase hybrid networks can be directly included too. The proposed two models are capable of offering enough accuracy level, and they are therefore suitable for online applications that require a large number of repeated power flow calculations.

Efficient Reduction in the Annual Investment Costs in AC Distribution Networks via Optimal Integration of Solar PV Sources Using the Newton Metaheuristic Algorithm

This research addresses the problem of the optimal placement and sizing of (PV) sources in medium voltage distribution grids through the application of the recently developed Newton metaheuristic optimization algorithm (NMA). The studied problem is formulated through a mixed-integer nonlinear programming model where the binary variables regard the installation of a PV source in a particular node, and the continuous variables are associated with power generations as well as the voltage magnitudes and angles, among others. To improve the performance of the NMA, we propose the implementation of a discrete–continuous codification where the discrete component deals with the location problem and the continuous component works with the sizing problem of the PV sources. The main advantage of the NMA is that it works based on the first and second derivatives of the fitness function considering an evolution formula that contains its current solution (xit) and the best current solution (xbest), where the former one allows location exploitation and the latter allows the global exploration of the solution space. To evaluate the fitness function and its derivatives, the successive approximation power flow method was implemented, which became the proposed solution strategy in a master–slave optimizer, where the master stage is governed by the NMA and the slave stage corresponds to the power flow method. Numerical results in the IEEE 34- and IEEE 85-bus systems show the effectiveness of the proposed optimization approach to minimize the total annual operative costs of the network when compared to the classical Chu and Beasley genetic algorithm and the MINLP solvers available in the general algebraic modeling system with reductions of 26.89% and 27.60% for each test feeder with respect to the benchmark cases.