# Multi-Point Time-Synchronized Waveform Recording for the Analysis of Wide-Area Harmonic Propagation
## 4 Results
### Multiple Harmonic Sources Energized by Public Grid  
The operation of the public grid is characterized by the presence of time-varying background harmonic voltages. This alters the harmonic behavior of the loads studied in this work and influences the final values of voltage distortion. To illustrate this case, the outcome of FFT analysis for selective harmonics collected in the form of synchronized time series is presented in Figure 11. A highly  
Figure 10: Currents of emulated harmonic source. fluctuating behavior of voltages at 250 Hz and 350 Hz can be observed with some periodic patterns visible at frequencies 550 Hz and 650 Hz. Furthermore, in Figures 12, and 13, synchronized time series of harmonic currents through distribution transformers are shown. It can be noted that these currents exhibit also time-varying behavior with levels of some of the harmonics changed in comparison with case A.4. Looking at the harmonic voltages at low-voltage test bays (Figures 14 and 15), we observe a remarkable difference between these two points. With harmonic voltage at 250 Hz at Substation A as high as 3.7 V against a maximum of 2.7 V at Substation G and significantly higher values of voltages at 550 Hz and 650 Hz. Moreover, the final value of voltage distortion at MV level is the complex sum of background distortion transferred from upstream network and voltage drop produced by combined harmonic current phasor flowing through harmonic system impedance. A direct comparison between cases represented by Figures 8, 12 and 13 can lead to inconsistent conclusions about the nature of harmonic processes occurring in the grid; therefore, a quantitative method to evaluate the undergoing phenomena is required. Figure 11: Isolation transformer harmonic voltages. Test sequence B.4—public grid supply. Figure 12: Harmonic currents through Substation G. Test sequence B.4—public grid supply. Figure 14: Harmonic voltages at LV side of Substation G. Test sequence B.4—public grid supply. Figure 13: Harmonic currents through Substation A. Test sequence B.4—public grid supply. Figure 15: Harmonic voltages at LV side of Substation A. Test sequence B.4—public grid supply. Synchronized harmonic phasors present a powerful tool for analyzing harmonic data. In this paper, an example is given on how to estimate LV harmonic contributions based on the Voltage Harmonic Vector Method [20]. For the sake of clarity, only harmonic components at 250 Hz and 350 Hz were considered in the calculations. The calculations according to the Voltage Harmonic Vector Method require employment of utility harmonic impedance. In this work, we assume the MV/LV transformers as components dominating the system LV harmonic impedance. Based on the datasheets, the fundamental frequency reactance was estimated to 0.05 \(\Omega\) and 0.0179 \(\Omega\) for Substation G and Substation A, respectively. The harmonic impedances at 250 Hz and 350 Hz were then recalculated based on simple theoretical derivations providing proportional linear approximations for the frequency-dependent inductance. According to the Voltage Harmonic Vector Method, the following applies:  
\[\underline{U}_{U-h}=\underline{U}_{\text{PCC}-h}-\underline{I}_{\text{PCC}-h} \cdot\underline{Z}_{U-h}, \tag{20}\]  
where \(\underline{U}_{U-h}\) is utility voltage representing background harmonic voltage source, \(\underline{U}_{\text{PCC}-h}\) is harmonic voltage measured at LV side of respective substation, \(\underline{I}_{\text{PCC}-h}\) vectorial sum of individual injection currents, and \(\underline{Z}_{U-h}\) is utility harmonic impedance. The harmonic impedance of transformer can be calculated as:  
\[\underline{Z}_{U-h}=h\cdot X_{f} \tag{21}\]  
where \(h\) is a harmonic order and \(X_{f}\) is a transformer reactance at fundamental frequency.