Abstract
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.
Highlights
Driven by the massive increase of renewable energy generations and energy-saving applications, the legacy power grids are evolving as power electronic based power systems, and a large number of harmonics with wide-frequency and high-order are emitted by power electronics [1]–[6]
This paper proposes the quantitative relationship between harmonic amplification and cable length, and the main conclusions are drawn as follows: 1)
The period, maximum value and cable length segments of harmonic amplification are determined by theoretical analysis, which is of great significance in cable length planning for avoiding harmonics exceeding the limit or in analyzing the cause of harmonic exceeding the limit
Summary
Driven by the massive increase of renewable energy generations and energy-saving applications, the legacy power grids are evolving as power electronic based power systems, and a large number of harmonics with wide-frequency and high-order are emitted by power electronics [1]–[6]. F. Xu et al.: Study on the Quantitative Relationship Between Harmonic Amplification and Cable Length. With the cosines law, HAF is calculated and the cable length segments where harmonic exceeds limit are figured out quantitatively. We can determine the HAF, harmonic amplification period and the length segment of harmonic exceeding the limit, etc. By calculating the value and the sign of the derivative of Tu while l = 0, the trend of harmonic voltage amplification at the beginning of cable can be determined. Where n is a integer, and n ≥ 0, lH−EL (n) and lH+EL (n) represent the beginning and ending length of harmonic exceeding limit respectively, and the cable length segments between lH−EL (n) and lH+EL (n) is defined as the segments where harmonic exceeds limit (SHEL). Trend at the beginning of cable, maximum and cable length segments of harmonic amplification, we can determine the amplification situation of harmonic voltage in the cable and intuitively
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