Line loss calculation model of low-voltage distribution network under harmonic and three-phase unbalance disturbances and its experimental validation

With the grid integration of distributed power sources and traction loads, the power quality problem of the power system has become more and more serious, aggravating the distribution network line losses, so it is important to study the calculation model of distribution network line loss under power quality disturbance in order to find loss reduction measures. This paper first theoretically derives the calculation model of line loss of low-voltage distribution network under separate disturbance of 2 common power quality problems, namely, harmonics and three-phase unbalance. Then, using the composite power quality disturbance decoupling method, the calculation model of line loss of low-voltage distribution network under the disturbance of harmonics and three-phase unbalance is derived, which improves the accuracy of line loss calculations. Finally, experiments are conducted for each part by Matlab/Simulink simulation tool to verify the correctness of the theoretical derivation.


Introduction
Distribution network loss is an important economic indicator in the power sector, and low-voltage distribution network loss accounts for more than half of the total loss of the power system.With the distributed power supply, traction power supply system and other electronic devices on the grid, the power quality of the power system is becoming more and more serious and aggravates the distribution network loss.Currently, most of the domestic and foreign studies focus on the impact of single power quality on the line loss.Literatures [1][2][3] studied the impact of harmonics on distribution network losses, and Literatures [4][5][6] analyzed the impact of three-phase unbalance on distribution network losses.However, the actual distribution network may contain multiple power quality problems at the same time, and the quantitative calculation of the power distribution network line loss under multiple power quality disturbances has not been carried out yet.Therefore, this paper first theoretically derives the calculation model of line loss of low-voltage distribution network under separate disturbance of 2 common power quality problems, namely, harmonics and three-phase unbalance.Then, using the composite power quality disturbance decoupling method, the calculation model of line loss of lowvoltage distribution network under the disturbance of harmonics and three-phase unbalance is derived, which improves the accuracy of line loss calculations.Finally, experiments are conducted for each part by Matlab/Simulink simulation tool to verify the correctness of the theoretical derivation.where: h -order of harmonics; h I -hth harmonic current RMS value; 1 I -fundamental current RMS value.Due to the existence of harmonic skin effect, so that the line impedance value changes, the current domestic and foreign recognized each harmonic impedance is: where: R -base wave resistance value of the wire.
Assuming no power quality disturbance, the phase and neutral line resistance are R, and the line current is I, the line loss is: For a three-wire, three-phase line, the line loss under harmonic disturbance is: where: hA I -hth harmonic current RMS value of phase A of the line; hB I -hth harmonic current RMS value of phase B of the line; hC I -hth harmonic current RMS value of phase C of the line.
For a three-wire, four-phase line, the line loss under harmonic disturbance is: where: hN I -neutral line hth harmonic current RMS value; hN R -neutral line hth harmonic resistance value.
Then the harmonic additional loss rate of the line is: where: for three-wire three-phase lines, 1  i ; for three-wire four-phase lines, 2  i .

Distribution network line loss calculation model under three-phase imbalance
In order to avoid the problem of double counting when calculating the line loss caused by power quality disturbances, only the fundamental current is considered without the effect of harmonic currents when analyzing the additional loss rate caused by three-phase current imbalance.
The negative sequence current imbalance and zero sequence current imbalance are defined, the expressions are: For a three-wire, three-phase line, the distribution network line loss under a three-phase unbalance disturbance is: For a three-wire, four-phase line, the distribution network line loss under a three-phase unbalance disturbance is: then the additional loss rate of the three-phase unbalance of the line is: where: for three-wire three-phase lines, 1  i ; for three-wire four-phase lines, 2  i .From Equation (10), it follows that: 1) For three-phase three-wire line, because there is no neutral line, so there is no zero-sequence current, three-phase unbalance additional loss rate is only proportional to the square of the negativesequence fundamental current unbalance.
2) For the three-phase four-wire line, three-phase unbalance additional loss rate is proportional to the negative sequence, zero sequence fundamental current unbalance square, due to zero sequence fundamental current in the neutral line will produce additional loss, so the impact of zero sequence current on the line loss is much greater than the impact of negative sequence current on the line loss.

Distribution network line loss calculation model under compound power quality disturbance
Multiple power quality disturbances may occur in the actual distribution network, so the impact of each power quality disturbance on line losses needs to be evaluated separately and combined to calculate the total line loss caused by the composite power quality disturbance.When calculating the distribution network line loss, the two factors of harmonics and three-phase unbalance need to be decoupled to avoid omission and double calculation.
In the calculation of harmonics, three-phase imbalance caused by the additional loss rate, should be the base value of the line loss under the action of the fundamental positive sequence current.Harmonics and three-phase imbalance changes when the fundamental positive sequence current is unchanged, the two reference values are the same, so the additional loss rate can be directly added.
The distribution network line loss under harmonic and three-phase unbalance disturbance is: where: for three-wire three-phase lines, 1  i ; for three-wire four-phase lines, 2  i .In summary, the steps for calculating the line loss of low-voltage distribution network under composite power quality disturbance are: extracting the current signal of each phase in the line; decomposing the current signal into fast Fourier levels to get the fundamental phase and each harmonic phase; using the effective value of each harmonic current to calculate the harmonic content rate of each harmonic to calculate the harmonic additional loss rate; using the fundamental current to obtain the negative sequence current unbalance degree and zero sequence current unbalance degree and the additional loss rate of three-phase unbalance can be calculated; the additional loss rate calculation formula can be used to find the distribution network line loss under compound power quality disturbance.

Experimentation
In this paper, we will use Matlab/Simulink simulation software to simulate the simplified distribution network and verify the correctness of the theoretical analysis.The distribution of three-phase load is changed to adjust the three-phase unbalance, and the harmonic content and number of harmonics are adjusted by controlling the harmonic current source.Establish a simple model in Matlab/Simulink simulation software as shown in Figure 1 to verify the correctness of the theoretical derivation mentioned above.
The parameters in the simulation model are set as follows: the voltage source is rated at 220V; three-phase line impedance and neutral line impedance are set to 1  ; balanced three-phase load power is 10kVA and power factor is 0.9.

Simulation of harmonic line loss
First, set the three-phase load to balanced state, while nulling the three-phase voltage source short circuit.Then an equivalent current source with adjustable amplitude and frequency is added to the load side as a simulated harmonic source.First, the effect of harmonic content on line loss is considered.The third harmonic is added to each phase with an amplitude of 10 A. The measurements are taken after changing the amplitude, and Table 1 shows the measurement data.It can be seen that the as the harmonic content increases, the line loss also increases, and is proportional to the square of harmonic content.
Second, the effect of the number of harmonics on the line loss is studied.As the number of harmonics increases, the skin response is enhanced and the line resistance increases.Table 2 shows the measurement data.From the data in Table 2, when the harmonics are positive sequence, negative sequence, line loss increases with the increase in the number of harmonics; when the harmonics are zero sequence, due to the existence of additional losses in the neutral line, the line loss may be greater than the line loss caused by the higher harmonics.

Simulation of three-phase unbalanced line loss
In this paper, three different kinds of light and heavy load cases of each phase that may occur in the actual distribution network are studied, and three representative three-phase load imbalance situations are listed, as shown in Table 3. Setting the three-phase voltage source as the ideal voltage source, the voltage RMS value of 220 and three-phase phase angle difference of 120, while all harmonic sources are set to zero.The load is adjusted to the balanced state and the three three-phase unbalance cases respectively, and Table 4 shows the measured data and calculation results.Table 4 shows the line losses for different imbalance cases.when the three-phase circuit reaches a balanced state, the line loss will be minimized.And when the circuit is unbalanced, the line loss will increase, and as the degree of unbalance increases, the line loss will also increase accordingly.

Simulation of line loss under the compound power quality problems
To ensure that the problem of compound power quality problems in the line is verified, adjusting the three-phase load power distribution and the amplitude and frequency of the equivalent current source.The experiment is divided into three groups, group 1: superimposed 9th and 11th harmonic currents are 10A, the three-phase load is 25kVA, 25kVA, 10kVA.group 2: superimposed 9th and 11th harmonic currents are 10A, the three-phase load is 30kVA, 30kVA, 0kVA.group 3: superimposed 9th and 11th harmonic currents are 20A, the three-phase load is 25kVA, 25kVA, 10kVA.Table 5 for the simulated and actual values of line loss.As can be seen from Table 5, the line is disturbed by compound power quality problems, and the error calculated by the method presented in this paper is very small.This shows the high practicality of the proposed method in practical applications.

Conclusions
A distribution network line loss calculation model under power quality disturbance is proposed.First, this paper derives the line loss calculation model when harmonics and three-phase imbalance are considered separately.Subsequently, the line loss calculation model considering both acting simultaneously on the line is derived using the superposition and decoupling principles.Finally, the experimental verification using Matlab/Simulink proves that the theoretical calculation model proposed is highly accurate.

Table 1 .
Relationship between harmonic content and line loss.

Table 2 .
Relationship between the number of harmonics and line loss.

Table 4 .
Line losses under different scenarios.

Table 5 .
Simulated and actual values of line loss under compound power quality disturbance.