Identification of harmonic source location in power distribution network

Mohd Hatta Jopri, Aleksandr Skamyin, Mustafa Manap, Tole Sutikno, Mohd Riduan Mohd Shariff, Aleksey Belsky Faculty of Electrical and Electronic Engineering Technology, Universiti Teknikal Malaysia Melaka, Melaka, Malaysia Department of Electric Power and Electromechanics, Saint Petersburg Mining University, Saint Petersburg, Russia Department of Electrical Engineering, Universitas Ahmad Dahlan, Yogyakarta, Indonesia Electrical Section, Engineering Department, Malaysian Refining Company Sdn. Bhd., Malaka, Malaysia Electromechanical Department, Saint Petersburg Mining University, Saint Petersburg, Russia


INTRODUCTION
Due to the rise of harmonic-producing loads, harmonic distortion has become one of the primary power quality concerns [1], [2]. Harmonic distortion, which causes voltage and current waveforms to be distorted and contain various harmonic orders, is one of the most common types of disturbances [3]- [6]. The power system is impacted by the disturbances; therefore, monitoring is required to limit the impacts, which may include equipment failures due to overheating, reduced transformer life expectancy due to deterioration of insulation levels, nuisance tripping, and increased equipment power losses [7]- [10]. Moreover, harmonics can cause overheating and damage to end-user equipment, as well as have unfavorable effects on the power system. As a result, it is critical for a power system operator to understand the system's harmonic behavior [11]- [13]. As mentioned in [14]- [18], harmonic sources, on the other hand, have complicated properties such as nonlinearity and abrupt variations that are difficult to forecast using standard methods the foremost common circumstance that needs harmonic source location is to settle the disputes over who is responsible for harmonic distortions, whether it comes upstream or downstream of the point of common coupling (PCC) [19]- [21].

METHOD 2.1. Proposed method
The identification of harmonic source location is divided into five steps, as indicated in Figure 1. The signals are first measured for both voltage and current at the PCC of the network system. Second, four specific instances were explored for recognising harmonic sources on IEEE 4-bus test feeders [44]. The timefrequency representation (TFR) analysis was done on the PCC's voltage and current measurements in the third step (VPCC and IPCC). This analysis yielded the impedance TFR (ZTFR), which was then used to calculate the impedance spectral (ZS) components by calculating the values of the ZTFR components. Finally, the significant association between the fundamental impedance (Z1) and harmonic impedance (Zh) components of impedance spectrum (ZS) components was observed and employed for harmonic source detection. In this experiment, a harmonic generating load was chosen with an amplitude modulation index (ma) of 1.0, a frequency modulation index (mf) of 90, and an input frequency (fi) of 50 Hz [70]- [73]. The IEEE 4-bus test feeder is chosen and illustrated in Figures 2 and 3 in order to detect the harmonic source location in the power distribution network in consideration of upstream and downstream of the PCC. Where N is a non-harmonic source which is the resistor load and H is the harmonic producing load. In order to test and evaluate the proposed method, an experimental setup was built up in an advanced digital signal processing (ADSP) research facility, as illustrated in Figure 4.

S-transform
The S-transform (ST) is hybrid of wavelet transform (WT) and the STFT, which inherits the advantages of both in signal processing [74], [75]. In the transformation process, ST uses a moving and scalable localising Gaussian window in particular. ST can be defined as shown in: is the scalable Gaussian window, and σ(t) is a parameter that controls the position of the Gaussian window.

Signal parameters
The TFR is used to determine the signal parameters of power quality. Furthermore, the instantaneous value is used in the analysis to obtain real-time parameters [76]. − Instantaneous root-mean square voltage The root-mean square (RMS) voltage of signal (Vrms(t)) can be obtained from the sampled waveform, and written as [77], [78], − Instantaneous root-mean square fundamental voltage The instantaneous RMS fundamental voltage (V1rms(t)) can be computed as [79], where is the power spectrum obtained from the TFR of signal and 0 is the fundamental frequency corresponding to the power system frequency.

Impedance time-frequency representation analysis
The impedance TFR (ZTFR) offered useful information about the frequency response of the system, as well as harmonic points and possible issues caused by harmonic distortions. The desired current harmonic data and the difference in voltage harmonic data at the location of interest have to be measured in order to determine the impedance TFR. The ZTFR at each harmonic frequency was calculated using this data, and the results were shown [80]. The ZTFR equation can be expressed as, where SV(t,f) signifies the TFR of voltage and SI(t,f) signifies the TFR of current.

Spectral impedance
The spectral impedance (ZS) comprises the fundamental impedance (Z1) and harmonic impedance (Zh) that is obtained from ZTFR [81]. The fundamental impedance (Z1) was an impedance at 50 Hz, which was the frequency of the power source. In the meantime, harmonic impedance (Zh) was a harmonic impedance with an order of harmonics.

RESULTS AND DISCUSSION
The implementation of the proposed technique initially done by measuring the voltage and current signals at PCC with consideration of 4 specific cases as discussed in 2.1. The linear time-frequency distribution method namely S-transform is applied in the analysis. The location of harmonic sources can be distinguished by analyzing the significant relationship between Z1 and Zh, accordingly.

Case 1: no harmonic source
Only the linear loads were placed upstream and downstream of the PCC in case 1. The voltage signal in the time domain, as well as its voltage TFR, are shown in Figures 5(a) and (b). The maximum voltage was 342.5 V, while the maximum current was 66.5 A. Meanwhile, Figures 5 (c) and (d) illustrate the TFR of voltage and current signals derived from S-transform analysis. The higher the magnitude, the redder the colour bar, the lower the magnitude, and the bluer the colour bar. There were no other components in the signals and the largest magnitude was only seen at 50 Hz. The results showed that there were no harmonic components in the signal. The Z1 existed at 50 Hz with a resistance of 4.8 ohm and no harmonic components in the signal, as shown in Figure 5 (d). Thus, in case 1, the significant relationship between Z1 and Zh in the power system network at no harmonic producing load can be expressed as, where for harmonic component, h is any positive integer, whereas for interharmonic, h is any positive noninteger.

Case 2: harmonic source located at point of common coupling's downstream
The linear load is positioned upstream of the PCC in case 2, while the harmonic load is located downstream. The TFR of voltage and current signals derived from the S-transform analysis is shown in Figure 6(a) and (b). It can be seen that the harmonic and interharmonic components exist between 200 and 1000 Hz, whereas the fundamental components of voltage and current have the maximum magnitudes at 50 Hz. The ZTFR is calculated using (5) in Figure 6(c), and the figure demonstrates that impedance components occur at frequencies of 50 Hz, 275 Hz, 375 Hz, 600 Hz, 700 Hz, and 900 Hz, respectively. The ZS is then derived by calculating the parameters of the ZTFR, as shown in Figure 6(d). Table 1 summarises the ZS characteristics shown in Figure 6(d). The Z1 value is always higher than any Zh components, as can be seen. The relationship between the ZS components can be used to identify the location of harmonic sources, according to the findings. As a result, in instance 2, the significant relationship between Z1 and Zh at the condition of the harmonic source downstream of the PCC can be stated as, where for harmonic component, h is any positive integer whereas, for interharmonic, h is any positive noninteger.  Figure 6. Case 2 (a) voltage signal in TFR using S-transform, (b) current signal in TFR using S-transform, (c) TFR impedance using S-transform, and (d) spectral impedance

Case 3: harmonic sources located at point of common coupling's upstream and downstream
The TFR of voltage and current signals derived from the S-transform analysis for case 3 is shown in Figures 7(a) and 7(b). It can be seen that the harmonic and interharmonic components occur in the frequency range of 200 Hz to 1000 Hz, whereas the fundamental components of voltage and current, respectively, have the maximum magnitudes at 50 Hz. The voltage and current waveforms can be seen to be distorted due to the harmonic load located upstream and downstream of the PCC. The ZTFR is calculated using (5) in Figure 7(c), and the figure demonstrates that impedance components occur at frequencies of 50 Hz, 275 Hz, 375 Hz, 600 Hz, 700 Hz, and 900 Hz, respectively. The ZS is then calculated by estimating the parameters of the ZTFR, as shown in Figure 7 Table 2 summarises the ZS characteristics shown in Figure 7(d). The Z1 value is always lower than any Zh components, as can be shown. The relationship between the ZS components can be utilised to pinpoint the location of harmonic sources, according to the findings. As a result, in case 3, the significant relationship between Z1 and Zh at the condition of the harmonic source positioned upstream and downstream of the PCC may be expressed as shown in: where for harmonic component, h is any positive integer whereas, for interharmonic, h is any positive noninteger.   Table 3 summarizes the ZS characteristics shown in Figure 8(d). The Z1 value is the same for all Zh components, as can be observed. At the condition of the harmonic source positioned upstream of the PCC, the significant relationship between Z1 and Z1 can be stated as,

Case 4: harmonic source located at point of common coupling's upstream
where for harmonic component, h is any positive integer whereas, for interharmonic, h is any positive non-integer. Furthermore, the proposed method was tried and verified on an experimental setup in October, November, and December 2021, with the harmonic producing load in the linear area (amplitude modulation index is 0 ≤ ≤ 1 and inverter switching frequency range is between 2 kHz and 15 kHz) [82]. Surprisingly, as demonstrated in Figure 9, the proposed method offers 100 percent accurate harmonic source location detection. According to Table 4, the proposed method is 100 percent correct in each scenario, and the significant relationship of ZS for harmonic source location identification is summarised as shown in:

CONCLUSION
Time-frequency distribution analysis namely S-transform has shown tremendous result in this analysis. The major contribution of this study is the discovery of a significant relationship between ZS components that acquired from S-transform analysis in locating harmonic source location. As a result of the proposed method's results, the harmonic source site can be identified using the significant relationship of spectral impedances in a fast, cost-effective, and accurate manner.