**6.1 Applying the reliability criteria**

82 Power Quality Harmonics Analysis and Real Measurements Data

**264 Hz**

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67

Customer 3 Customer 2 Customer 1

Customer 3 Customer 2 Customer 1

> Customer 3 Customer 2 Customer 1

**Time Step**

**348 Hz**

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67

**Time Step**

**384 Hz**

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67

**Time Step**




**Pa (W)**

**Pa (W)**

Fig. 13. Active power at the loads for *fIH = 264Hz* 

Fig. 14. Active power at the loads for *fIH = 348Hz* 

Fig. 15. Active power at the loads for *fIH = 384Hz* 

**Pa (W)**

The first step to utilize the reliability criteria is to obtain the percentage of snapshots containing measurements with energy levels above the quantization error. This result for the case study is shown in Table 1. According to this criterion, the interharmonic currents measured at the feeder may be unreliable because they are too low as compared to the current fundamental component. This fact does not mean that the measured interharmonics are harmless, but simply that 12 bits of the data acquisition device are not enough to accurately measure their magnitudes. As for the loads, all data are reliable, except those of Customer 3 at 348 Hz.


Table 1. Percentage of Snapshots with Energy Level Higher than Quantization Step

The interharmonic voltage-current correlation for all the locations is calculated as well, and shown in Table 2. The results obtained for the feeder show that its measurements may not reliable. For the loads, it can be seen that the correlation is generally high, except for that of Customer 2 at 264 Hz.


Table 2. *V-I* Correlation Coefficient (%)

The other reliability criteria are also used but do not add much information to the conclusions to be drawn in Table 3, which summarizes the reliability at each frequency for each location.


Table 3. Reliability Summary

Table 4 shows the average of calculated active power at the feeder and at the loads (phase A). Note that the shaded cells are the ones that should not be trusted.

On the Reliability of Real Measurement Data for Assessing Power Quality Disturbances 85

the possibility that Customer 3 is the source of the interharmonic 264 Hz can be ruled out

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

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

**Frequency [Hz]**

(a) (b) (c) Figure 17. Contour plot of the interharmonic data recorded at the three Customers (phase

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

200 400 600

**Frequency [Hz]**

200 400 600

**Time [hours]**

0.4 0.6 0.8 1 1.2 1.4 1.6 10:49 10:59 11:09 11:17 11:27

because this frequency is a pair of 384 Hz, which was generated from Customer 2.

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

were present throughout the system.

Fig. 16. Field measurement locations at system #2

**Frequency [Hz]**

200 400 600

**Time [hours]**

12:26

12:36

12:46

system. Two main interharmonics are identified: 151 Hz and 271 Hz.

**Time [hours]**

1 1.5 2 2.5 3

A): (a) customer 1, (b) customer 2, (c) customer 3.

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

16:21 16:31 16:41 16:51


Table 4. Active Power Results for the Feeder and Customers

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

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

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

#### **6.3 The Interharmonic phase sequence characteristics**

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 parameters in (12) can be estimated as

$$\begin{aligned} & -228 = 60 - 6 \times 48, \\ & -364 = 60 - 6 \times 54, \\ & +348 = 60 + 6 \times 48, \\ & +384 = 60 + 6 \times 54. \end{aligned} \tag{14}$$

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 fairly balanced).

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 the possibility that Customer 3 is the source of the interharmonic 264 Hz can be ruled out because this frequency is a pair of 384 Hz, which was generated from Customer 2.
