**1. Introduction**

68 Power Quality Harmonics Analysis and Real Measurements Data

Gary W. Chang*,* Shin-Kuan Chen*,* Huai-Jhe Su*,* and Ping-Kuei Wang," Accurate

Abner Ramirez," The Modified Harmonic Domain: Inter-harmonics" IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 26, NO. 1, JANUARY 2011 Hooman E. Mazin*,* Wilsun Xu*,* and Biao Huang," Determining the Harmonic Impacts of

DELIVERY, VOL. 26, NO. 2, APRIL 2011

DELIVERY, VOL. 26, NO. 2, APRIL 2011.

Assessment of Harmonic and Interharmonic Currents Generated by VSI-Fed Drives Under Unbalanced Supply Voltages" IEEE TRANSACTIONS ON POWER

Multiple Harmonic-Producing Loads" IEEE TRANSACTIONS ON POWER

Power quality assessment is a power engineering field that is first and foremost driven by real data measurements. All the power quality assessment applications rely on results from real data processing. Take as an example the art of harmonic filter design, which is an engineering field notoriously known for relying on simulation-based planning; in this technical assessment, data recordings are indirectly used for finding the frequency response (or *R-X* plots) of the system impedance that is/are in turn used to determine the filters' tuning frequencies (Kimbark, 1971).

With so much reliance on the acquired data, the quality of such has become a very sensitive issue in power quality. An imperative action is to always employ high-resolution recording equipment in any instance of power quality analysis. Nevertheless, high-resolution equipment does not guarantee data usefulness because the measured data may be inherently of very low energy in a variety of ways. Therefore, to investigate such cases and to propose methods to identify useful data were the motivations for this research. This chapter proposes methods for data selection to be used in two applications where the reliability issue is crucial: the power system impedance estimation and the interharmonic source determination.

#### **1.1 The network harmonic impedance estimation**

Network impedance is power system parameter of great importance, and its accurate estimation is essential for power system analysis at fundamental and harmonic frequencies. This parameter is deemed of being of great importance for a variety of power system applications, such as evaluating the system short-circuit capacity, or defining the customer harmonic limits (Kimbark, 1971)-(IEEE Std. 519-1992). Several methods have been proposed to measure the network harmonic impedance and are available in literature. In this chapter, the transient-based approach is used to demonstrate the data selection methods. In the transient-based approach, the network impedance is conventionally calculated by using (Robert & Deflandre, 1997)

, *Z h Vh Ih eq* (1)

On the Reliability of Real Measurement Data for Assessing Power Quality Disturbances 71

the concern is the value of *I(f)* and *V(f)*. The reason for this will be explained in more detail in sections 3 and 4, and at this point it is just important to keep in mind that the introduced

As shown in (1), the network impedance determination is heavily reliant on *ΔI(f)*, which is the denominator of the expression. Any inaccuracy on this parameter can result in great numerical deviance of the harmonic impedance accurate estimation. Therefore, the *ΔI(f)* energy level is of great concern. For this application, a threshold was suggested in (Xu et al, 2002) and is present in (2). If the calculated index is lower than the threshold level, the

> 1%.

(2)

20 40

Number of cases

*I Hz* 

Fig. 1 shows an example on how this criterion can be used. The energy level for *ΔI(f)* is compared with the threshold. For this case, frequencies around the 25th harmonic order

60 *threshold I f <sup>I</sup>*

0 5 10 <sup>15</sup> <sup>20</sup> <sup>25</sup> <sup>30</sup> <sup>35</sup> <sup>40</sup> <sup>45</sup> <sup>0</sup>

Harmonic order

Fig. 1. Energy level of *ΔI(f)* seen in a three-dimensional plot

<sup>60</sup> <sup>0</sup>

This index is used in the problem of the network impedance estimation, which relies on the transient portion of the recorded voltages and currents (section 3 presents the method in detail). The random nature of a transient makes it a suitable application for using the power density spectrum (Morched & Kundur, 1987). The autocorrelation function of a random process is the appropriate statistical average, and the Fourier transform of the autocorrelation function provides the transformation from time domain to frequency

criteria is applied in both cases, but with this slight difference.

results obtained using these values are considered unreliable.

(1500Hz) are unreliable according to this criterion.

0.2

**2.2 Frequency-domain coherence index** 

domain, resulting in the power density spectrum.

0.4

0.6

Energy Level [%]

0.8

1

**2.1 The energy level index** 

where *ΔV(h)* and *ΔI(h)* are the subtraction in frequency domain of one or more cycles previous to the transient occurrence from the corresponding cycles containing the transient disturbance. The objective of this chapter is not to promote the use of the transient-based approach for determining the network harmonic impedance, nor is it to explain the method in detail. The reader is encouraged to consult (Robert & Deflandre, 1997) for details. In this application, the level of accuracy of such estimation can be supported by a set of indices, which are (but not limited to) the quantization noise in the data acquisition, the frequency resolution, the energy levels, and the scattering of the results obtained from the data.

### **1.2 The Interharmonics measurement**

Interharmonics are spectral components which frequencies are non-integer multiples of the supply fundamental frequency. This power quality event represents the target of the second application of the proposed reliability criteria. Diagnosing interharmonic problems is a difficult task for a number of reasons: (1) interharmonics do not manifest themselves in known and/or fixed frequencies, as they vary with the operating conditions of the interharmonic-producing load; (2) interharmonics can cause flicker in addition to distorting the waveforms, which makes them more harmful than harmonics; (3) they are hard to analyze, as they are related to the problem of waveform modulation (IEEE Task Force, 2007). The most common effects of interharmonics have been well documented in literature (IEEE Task Force, 2007), (Ghartemani & Iravani, 2005)-(IEEE Interhamonic Task Force, 1997), (Yacamini, 1996). Much of the published material on interharmonics has identified the importance of determining the interharmonic source (Nassif et al, 2009, 2010a, 2010b). Only after the interharmonic source is identified, it is possible to assess the rate of responsibility and take suitable measures to design mitigation schemes. Interharmonic current spectral bins, which are typically of very low magnitude, are prone to suffer from their inherently low energy level. Due to this difficulty, the motivation of the proposed reliability criteria is to strengthen existing methods for determining the source of interharmonics and flicker which rely on the active power index (Kim et al, 2005), (Axelberg et al, 2008).

### **1.3 Objectives and outline**

The objective of this research is to present a set of reliability criteria to evaluate recorded data used to assess power quality disturbances. The targets of the proposed methods are the data used in the determination of the network harmonic impedance and the identification of interharmonic sources. This chapter is structured as follows. Section 2 presents the data reliability criteria to be applied to both challenges. Section 3 presents the harmonic impedance determination problem and section 4 presents a network determination case study. Section 5 presents the interharmonic source determination problem and sections 6 and 7 present two case studies. Section 8 presents general conclusions and recommendations.
