Three-phase Four-wire Harmonic Power-flow By Direct ZBUS Method For Distribution Networks

Three-phase four-wire distribution networks(DNs)is widely utilized in low-voltage DNs in Mainland China,the same as in medium-low voltage DNs in the U.S and Taiwan China.Three-phase four-wire DNs are at the end of the power system networks,with three-phase imbalance and harmonic pollution issues.Neutral current will flow back to the system and neutral voltage arises,because of the zero-sequence current resulting from unbalance system and the harmonic current caused by the proliferation of power electronic devices.These will destroy power equipment and increase power loss.Therefore,it's necessary to develop three-phase four-wire harmonic power flow analysis technology for DNs which could consider the effects of neutral wires and grounding.The developed technology is available for analyzing harmonics distribution and line loss accurately in the whole network,especially in neutral wires.This paper summarizes the advantages and disadvantages of the three-phase four-wire power flow models and algorithms in the previous literature.After that,the harmonic power flow analysis technique by direct ZBUS method is proposed and its application value is studied.Firstly,the fundamental models and harmonic models of three-phase four-wire DNs considering the neutral wires and the grounding are developed,including in the equivalent models of overhead lines and cable lines considering neutral,conductor mutual couplings and ground admittance branches,the transformer models with different connection modes,the three-phase load models with different types,the shunt capacitor models and the grid-connected models of distributed generation.Based on circuit decoupling and current injection principle,the series part of the distribution components is used as the node impedance matrix,and the parallel part is equivalent to the injection current sources.Secondly,the direct ZBUS method for harmonic power flow solution of three-phase four-wire DNs is deduced.The networks can be divided into radial networks and non-radial networks.The injection currents and formulas of bus impedance matrix for two types of networks are directly obtained by integrating the principles of graph theory and the network models,which can eliminate the inverse procedure of the full bus admittance matrix by the implicit ZBUS method to improve the computational efficiency.The accuracy of the direct ZBUS method and network models is verified through three IEEE test systems.At the same time,the convergence of the direct ZBUS method is tested by random grounding impedance.In addition,the performance of the method is compared with the forward-backward sweep method and Newton method based on the current injection principle.The iteration number of the proposed method is not be affected by the number of grounding points and grounding impedance,and the convergence performance is better than the above mentioned two methods.Finally,the influences of system grounding characteristics,load conditions,capacitor switching and distributed generation grid on the harmonic power flow distribution and power quality are discussed,especially neutral harmonic power flow and power loss ignored in the previous analysis.The analysis tool is the harmonic power flow analysis technology of the three-phase four-wire DNs proposed in this paper.The evaluation indicators include in the neutral voltages,neutral currents,harmonic distortions,line losses and voltage unbalances.The IEEE test systems and the actual power distribution system of Taiwan Power Company are utilized for testing.The proposed analysis technology can help researchers to implement the corresponding measures for three-phase imbalance and harmonic pollution in DNs,to restrain power loss effectively and ensure the power system runs economically and reliably.