Study on the Quantitative Relationship Between Harmonic Amplification and Cable Length

With the large increase of the wide-frequency and high-order harmonic in power electronic based systems as well as the wide use of cables with large distributed capacitance in modern power grids especially renewable energy generations, the harmonic amplification in cables becomes a serious problem. Some researchers have paid attention to this problem, but the quantitative relationship between harmonic amplification and cable length has not been determined, which is studied in this paper to cover the shortage. First, the influence factors of harmonic amplification are converted into two rotation phasors. These factors, including cable parameters, harmonic frequency and equivalent harmonic impedance of power system, are converted into the initial amplitude, phase and angular frequency of the rotation phasors. Then, the solution of harmonic amplification factor (HAF) is converted to solve the reciprocal of the amplitude of the sum of the two rotation phasors. With the cosines law, HAF and the cable length segments where harmonic exceeds the limit can be figured out quantitatively. The analysis method and conclusions proposed can help to guide cable length planning for avoiding harmonic exceeding the limit or to analyze the cause of harmonic exceeding the limit. Correctness and effectiveness are verified by the simulation and field cases.