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.