Innovative location research of multiple harmonic sources based on statistical data correlation

Hongzhi Zang Shandong Electric Power Research

Institute Jinan, China 250002

Xia Qian China Huadian Tendering Co.，Ltd

Beijing, China 100031

Xiaodong Yu Shandong Polytechnic University

Jinan, China 250353

Abstract—Harmonic voltages at PCC of a power grid are the combinations of voltage contributions of each harmonic source located in the same grid. In particular, quantifying harmonic contributions of the customers and the utility system is highly important for power quality management. This paper presents a new method of harmonic source identification problems: how to quantify the harmonic levels observed at a network location. The paper first defines the problem. It then presents a statistical correlation based method to estimate the index. The characteristics of the proposed method are investigated through case studies. Finally, the improvements of the proposed method are discussed.

Keywords—power quality; harmonic source indentification; hamonic contributions of multiple loads; statistical correlation analysis

I. INTRODUCTION In modern power system, lots of nonlinear and

electronically switched loads will distort steady state ac voltage and current waveforms, which poses a potential threat to the performance of power system. The harmonic problem has become increasingly significant. Developing methods to indentify harmonic sources is an important task. Extensive literature review has shown that much work has been done in this field. In the past, the research work is focused on identifying the major harmonic source and separating the harmonic contribution of a customer from that of the utility system. Especially, after the "reward and punishment program" being proposed, quantifying the individual harmonic impacts of the multiple harmonic producing loads is gaining more attention [1].

II. PROBELME DESCERIPTION AND ITS SOLUTION A noticeable trend in power systems nowadays is the

emergence of harmonic-producing loads. These loads typically have comparable sizes and are distributed all over the power system. In case that there is a reported harmonic problem in the system, identifying loads that actually causes the reported problem is a challenging issue for utility companies. Unfortunately, there are no viable techniques that can pinpoint which customers cause harmonic distortions at a specific location of a system. The problem can be explained by the following example. A harmonic problem is reported in Bus X of a power distribution or transmission system, we name this bus as observation point. The system is known to contain, for example, three major harmonic-producing customers A, B and

C as shown in Figure 1.We name this loads as suspicious loads. The problem to solve is to determine if these three suspicious loads are the cause of the problem. The harmonic voltages at point X are used as the quantitative indictor of the reported problem. A qualitative Yes or No answer is not sufficient in this case since all of them are likely to contribute to the voltage distortions at point X. It is clear that we need to quantify the contribution of each suspicious load to this indictor. Some methods try to establish an equivalent circuit of the system based on measured data [2-4]. But because of the load variations, it is difficult to establish an equivalent circuit with adequate accuracy.

Figure 1. A typical power distribution or transmission system.

The proposed idea uses field measurement data to solve this problem. Typically, utility companies can perform continuous harmonic monitoring at sites. The basic idea is to find a cause-and-effect relationship between the measurement data. This relationship itself is a convincing indicator of the impact of the customers. The project has been approached according to the following strategy:

• Establishing a technically sound formulation of the problem considering practical constraints of existing power quality instruments;

• Defining a special index to quantify the impact of harmonic-producing loads for the problem explained above

• Developing practically useful methods to solve the problem.

Implementing the methods in a software package for the consortium members and providing a technical tutorial on the project results to facilitate technology transfer.

978-1-4577-0547-2/12/$31.00 ©2012 IEEE

A. Statistical Correlation method An algorithm is proposed to estimate harmonic impact,

namely 1- Statistical Correlation method and 2- Least Square method.

hBIhAI

hxV

hCI

Figure 2. Schematic diagram of the power system

The basic idea of proposed method can be understood by an example (see Fig.2). Assume that the current of the suspicious loads (load A, B and C) are monitored. Simultaneously, the harmonic voltage is also measured at observation point (bus X). The basic idea is to correlate two sets of data to determine if there is a relationship between them. As an example, Fig.3 and Fig. 4 shows the correlation between the 5th harmonic currents of load A and 5th harmonic voltages of site X. This figure reveals that the harmonic voltage at Site X is strongly influenced by load A. They exhibit an almost linear relationship as follows:

V5Site X (%) = 0.5743 I5Site A (%) + 3.549 (1)

The equation suggests that if there is a 1% increase of the harmonic current of load A, the harmonic voltage at Bus X will increase by 0.57%. We can also see that if harmonic current of load A is disconnected (I5SiteA=0), the harmonic voltage at that location would be 3.549%. This voltage is the background harmonic voltage that would exist if customer A does not inject any harmonic currents. So the background voltage distortion is about 3.549%.

One important condition to use the above correlation analysis is that there must be only one harmonic load change at any given time. If, for example, both the harmonic loads A and B change simultaneously, it will be difficult to determine if a harmonic distortion change is caused by the load A or by the load B. If one can find a time interval that only harmonic load A varies, while other loads are roughly unchanged. Then it can be reasonable to assume Eh is constant in this time interval.

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1 301 601 901 1201 1501 1801 2101 2401 2701 3001 3301Tim e (seconds)

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VoltageCurrent

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Figure 3. The data of harmonic voltage and current

y = 0.5743x + 3.549

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0 2 4 6 8 10 12 14 16 18 20Current (%)

Volta

ge (%

)

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y = 0.5743x + 3.549

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y = 0.5743x + 3.549

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Figure 4. Correlation of harmonic voltage and current trend

( )

( )2

cos

cos

hAX hAX hhXhAX hAX

hXhX

hAX hAX h

hX

V V EVV V

VV

V V E

V

β

α

⋅ += ⋅ =

+=

(2)

So, the harmonic impact can be formulated as follows.

( )

2

2

cosImpact 100%

hAX hAX hAX

hX

V V E

V

α+= × (3)

we have 222 )cos(2 hXhhAXhhAX VEVEV =++ α (4)

Let’s assume the magnitude of hXAV increases, while hE remains fixed. So, we get

( ) ( )( )222 )cos(2

hXhX

hXhAXhAXhhAXhAX

VV

EVVEVV

Δ+

=Δ+++Δ+ α(5)

Neglecting ( )2hXVΔ and ( )2hXAVΔ , we get

hX

hhXA

hXA

hX

VEV

VV )cos(α+

=ΔΔ

(6)

For the projection of hXAV on the hXV , we have

hX

hhAXhAX

hX

hhAXhAX

hX

hXhAXhXA

VEVV

VEVV

V

VVV

)cos(

)(cos

2 α

β

+=

+⋅=⋅=

(7)

Finally, the harmonic impact of load A on Bus X can be estimated by following formula.

%100×ΔΔ

⋅=hA

hX

hX

hAX BusA load I

VVI

Impact Harmonic (8)

It is important to notice that only the measurement data associated with single load changes are used for correlation analysis. For example, the data that are shown in Fig. 5 time interval T1, are acceptable for finding the harmonic impact of load B. Load B varies in this time interval, whereas load A is roughly unchanged. So, it can be concluded that any variation of harmonic distortion in bus X is caused by load B. Similarly, data shown in Fig. 5 time interval T2, are acceptable for finding harmonic impact of load A on the observation point, bus X. This approach transforms the problem of harmonic impact determination to a problem of selecting a proper data set for correlation analysis.

Figure 5. variation of harmonic load A and B

B. Time series segmentation As previously discussed, both the suggested methods

transform the problem of harmonic impact determination to a problem of selecting a proper data set. Data selection algorithm seeks time intervals where only the harmonic current one of the suspicious loads varies while those of others remain roughly unchanged. The algorithm is proposed.

The key idea of the first proposed algorithm is to mark time intervals that a load is roughly unchanged for each suspicious load, independently. Thereafter, intersections of these time intervals will be selected for analysis. The idea is explained with an example for the case that there are three suspicious harmonic polluters in the studied system Fig. 1. To find the harmonic impact of load A on the observation bus, harmonic load B and C should be unchanged. First, time intervals where the variation of a load is low (for example less than 5%, normalized to the maximum load current) are selected for both load B and C independently. The intersection of these

time intervals, T1 and T2, shown in Fig. 6, will be selected for the correlation analysis. While this algorithm is straightforward in theory, it is not technically sound when applied to real field data. Working with field test data, we found that the intersection time intervals are usually short and do not provide conclusive data for the evaluation of the harmonic impact. In addition, when the number of suspicious loads increases, these intersection time intervals dramatically decrease both in number and duration. To overcome this technical issue, load segmentation method is proposed to merge these intersection time intervals. The idea and its implementation algorithm are explained in the next section.

Figure 6. Time series segmentation

III. EXPERIMENT RESULTS The circuit utilized for the experiment is shown in Fig. 7. It

consists of three harmonic loads including one PC, one laptop, and fluorescent lamps. Voltage probes measure harmonic voltage in bus 1 to 4. A current probe measures injected current from the load attached to bus 1 (Ih). During the experiment, the number of lamps is increased one by one. The harmonic voltages and currents are measured and recorded. Utilizing this recorded data, harmonic impacts of fluorescent lamps towards the observation points (bus 1 to 4) are estimated. The harmonic impact of harmonic load (fluorescent lamps) in the experiment case study is calculated as follows:

• Measure the harmonic voltages nlhXV − at each bus when lamps are not connected. The fundamental voltage at PCC is assumed as reference point.

• Measure the harmonic voltages hXV at each bus when lamps are connected. The fundamental voltage at PCC is assumed as reference point.

• Calculate the impact of lamps on the harmonic voltage of each bus nlhXhXlampshX VVV ,, −= .

• Calculate the harmonic impact of lamps on each bus

%100, ×= −

hX

plampshXlampsX V

VimpactHarmonic (9)

where plamphXV −, is the projection of lampshXV , into hXV .

Figure 7. Lab experiment scheme

Figure 8.Impact of number of lamps on the third order harmonic voltage

of buses

The harmonic voltages are monitored. Fig.8 shows harmonic voltages in buses. When no lamp is on, there is a background harmonic voltage in the system generated by other harmonic loads. The proposed method is utilized to assess average harmonic impacts of the lamps in each node.

Figure. 9 Harmonic voltage in bus 1 versus injected harmonic current

Using this method, the average harmonic impact of these lamps is evaluated. The same approach is done for other nodes. The results are shown in Table 1.

TABLE 1: ESTIMATED HARMONIC IMPACT OF LAMPS VERSUS EXACT HARMONIC IMPACTS

IV. CONCLUSION

This paper has presented s new class of practical harmonic source identification methods. The paper first proposes an index to quantify harmonic impact of several known harmonic-producing loads on the harmonic distortion level observed at a specific point of network.Thereafter, a method is proposed to estimate this index.The method proposed here has a gerneral application in power quality disturbance impact quantification. Also,this method can be applied in electric power quality monitoring platform which could act as senior application. Developing efficient data-selection algorithms can be considered as a further improvement of this paper.

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