**7. Interharmonic source determination case study #2**

84 Power Quality Harmonics Analysis and Real Measurements Data


The power direction method relies on the information about the difference between the interharmonic voltage and current angles. If this difference is close to 90 or 270 degrees, the cosine of this difference will be very close to zero. For interharmonics of very low magnitude, the power may oscillate around zero, because the angle displacement usually exhibit lots of fluctuation due to measurement inaccuracies. Therefore, caution is needed

In the present case study, such fluctuation happens for interharmonics 264 Hz and 348 Hz. Furthermore, the active power results shown in Fig. 13 and Fig. 14 reveal that the power level is very low. This was also shown in Table 1, which revealed that many snapshots contain data with very low energy level. For these frequencies, the conclusions drawn using the power direction method cannot be trusted. A final conclusion about these frequencies

Using the phase sequence characteristics of interharmonics, it can be verified that interharmonics 228 Hz and 348 Hz of this case study are one pair, and interharmonics 264 Hz and 384 Hz are another pair. From (12), it can be estimated that the drives' frequencies are 48 Hz and 54 Hz, and that the number of pulses of the inverter is *p2* = 6. From this equation, it was also identified that 228 Hz and 264 Hz are negative sequence, whereas 348 Hz and 384 Hz are positive sequence, as explained in (Zhang et al, 2005). Therefore, all

> 228 60 6 48, 364 60 6 54, 348 60 6 48, 384 60 6 54.

The same conclusion about the sequence is verified through analyzing the measurements: the symmetrical components of the interharmonic currents are calculated and one of them (positive-, negative- or zero-sequence) is observed to match the phase currents (the system is

Since it is clear that the source of two interharmonic frequencies of a pair is the same, it is confirmed that Table 4 shows some inconsistencies: Customer 3 cannot be the source of interharmonic 264 Hz unless it is also the source of interharmonic 384 Hz. It was, however, determined that Customer 2 is the source of interharmonic 384 Hz. This inconsistency for Customer 2 undermines the credibility of the conclusions taken at this frequency. It is not possible that interharmonic 264 Hz comes from both Customer 3 and Customer 2. Finally

 

when using the power direction method, since it is too sensitive to this angle.

will be provided in next subsection by using the theory of interharmonic pairing.

**P (W) Customer 2** 

**P (W) Customer 3** 

(14)

**P (W) Customer 1** 

**IH Freq (Hz)** 

**6.2 The** *VIH-IIH* **angle displacement** 

parameters in (12) can be estimated as

fairly balanced).

**P (W) Feeder** 

Table 4. Active Power Results for the Feeder and Customers

**6.3 The Interharmonic phase sequence characteristics** 

In a second case, interharmonic problems were experienced in another oilfield area of Alberta, Canada. Measurements were taken at three customers, codenamed Customer 1, Customer 2, and Customer 3, which were operating big oil extraction ASD drives and were suspected interharmonic sources. The system diagram is shown in Fig. 16. The measurements at the metering points revealed that the interharmonic detected frequencies were present throughout the system.

Fig. 16. Field measurement locations at system #2

Fig. 17 shows a sample contour plot of the spectrum calculated for the three Customers' currents in order to obtain the frequencies of the interharmonic components present in this system. Two main interharmonics are identified: 151 Hz and 271 Hz.

Figure 17. Contour plot of the interharmonic data recorded at the three Customers (phase A): (a) customer 1, (b) customer 2, (c) customer 3.

#### **7.1 Criteria for determining the reliability of the data**

Table 5 shows the percentage of reliable snapshots obtained by using the quantization error criterion. Only snapshots with an energy level higher than the quantization error could be

On the Reliability of Real Measurement Data for Assessing Power Quality Disturbances 87

For the network impedance estimation application, it has been found that the energy level for *ΔI(f)* is a useful data filtering, but for *ΔV(f)* it has been found that it does not really make any difference. The Coherence index does not reveal much information about unreliable measurements but clearly identifies the principal frequency components of the transient. Analyses carried out on the quantization error level demonstrated that quantization noise is substantial for high frequencies and that the measurements taken are not significantly affected by quantization noises. The suggested thresholds for data rejection used were determined through extensive experience with handling data and provided more accurate and dependable results. These thresholds can be further adjusted as new data are analyzed

For the interharmonic source detection, the power direction method is very sensitive to the typical low energy level of the interharmonic currents. It was observed that this low energy level affects the displacement angle between voltage and current, which may prevent using the method to conclude about some frequencies. Interharmonic pairing theory was used to draw a final conclusion for the smaller-magnitude interharmonics in the case study. For the higher magnitude interharmonics, the power direction method could be used with the

The author gratefully acknowledges the financial support provided by Hydro One to partially cover the publication of this chapter and also their encouragement into improving

The author also expresses his gratitude towards Mr. Edwin Enrique Nino from ATCO electric for providing the several data sets of the network harmonic impedance collected in many Canadian utility sites, for processing the data and providing the presented results. Thanks are also extended to Mr. Hooman Mazin for providing part of the statistical analysis

Finally, the author expresses his appreciation to Prof. Wilsun Xu for his supervision,

Anis, W. R. & Morcos, M. M. (2002). Artificial Intelligence and Advanced Mathematical Tools for Power Quality Applications: A Survey, *IEEE Trans. Power Delivery*, vol. 17, no. 2. Axelberg, P. G. V., Bollen, M. J., Gu, I. Y. (2008). Trace of Flicker Sources by Using the Quantity of Flicker Power, *IEEE Trans. Power Delivery*, vol. 23, no. 1, pp. 465-471. Ghartemani, M. K. & Iravani, M. R. (2005). Measurement of Harmonics/Interharmonics of Time-Varying Frequencies, *IEEE Trans. Power Delivery*, vol. 20, no. 1, pp. 23-31.

IEEE Std. 519-1992 (1993) *IEEE Recommended Practices and Requirements for Harmonic Control* 

IEEE Std. 1159-1995. (1995). *IEEE Recommended Practice for Monitoring Electric Power Quality*. IEEE Task Force on Harmonics Modeling and Simulation. (2007). Interharmonics: Theory

IEEE Interharmonic Task Force. (1997). *Cigre 36.05/CIRED 2 CC02 Voltage Quality Working* 

and experience is built to improve the engineering judgment.

used in the network harmonic impedance data filtering application.

Harnett, D. L. (1982). Statistical Methods, Third Edition, Addison Wesley.

and Measurement, *IEEE Trans. Power Delivery*, vol. 22, no. 4.

confidence provided by the reliability criteria.

technical contributions and high-level advices.

*in Electrical Power Systems*

*Group*, *Interharmonics in Power Systems*.

**9. Acknowledgments** 

this research work.

**10. References** 

used. All the data were reliable in this case due to the high magnitude of the interharmonic components.


Table 5. Reliable Snapshots [%] According to the Quantization Error Criterion for System #2

Table 6 shows the correlation results for the locations, revealing that the interharmonic voltage and current had a high degree of correlation at the three customer loads.


Table 6. Correlation Results for System #2

#### **7.2 Results**

The power direction results are shown in Table 7. In this case, the data was deemed reliable by all reliability criteria.


Table 7. Power Direction (at Interharmonic Frequencies) Results for System #2

The information for sign(*PIH*) reveals that the sign(*PIH*) of Customer 3 is negative, so that Customer 3 was the source. In this case, the angle displacement between the voltage and current was not observed to fluctuate at around ±π/2 radians. Therefore, the power direction method can be used with full confidence.
