A Critical Impedance-based Method For Identifying Harmonic Sources

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 2, APRIL 2004

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A “Critical Impedance”-Based Method for Identifying Harmonic Sources Chun Li, Member, IEEE, Wilsun Xu, Senior Member, IEEE, and Thavatchai Tayjasanant, Student Member, IEEE

Abstract—This paper proposes a new method to determine whether the utility or the customer side has more contribution to the harmonic currents measured at the point of common coupling. The method is inspired by the observation that the direction of harmonic reactive power, instead of active power, is a more reliable indicator on the location of dominant harmonic sources. The method needs approximate impedance information to operate. Mathematical analysis, simulation studies, and field measurements have shown that this is a useful, reliable, and practical solution for the harmonic source detection problem. Index Terms—Harmonic source detection, harmonics, power quality.

I. INTRODUCTION

I

DENTIFICATION of harmonic sources in a power system has been a challenging task for many years. The most common tool to solve this problem is the harmonic power direction-based method [1]–[3]. In this method, if harmonic active power flows from utility to customer, the utility is considered as the dominant harmonic generator, and vice versa. Unfortunately, [4] and [5] have proven that this qualitative method is theoretically unreliable. Another group of practical methods for harmonic source detection is to measure the utility and customer harmonic impedances and then calculate the harmonic sources behind the impedances. There are a number of variations of this method [6]–[9]. Although this type of method is theoretically sound, it is very difficult to implement. The main problem is that the impedances can only be determined with the help of disturbances. Such disturbances are not readily available from the system or are expensive to generate with intrusive means. During the course of investigating the problems of the active power direction method, the authors have found that the reactive power direction is actually a more reliable indicator on the location of dominant harmonic source. But the inductive or capacitive characteristic of the combined utility and customer impedance affects the direction of reactive power. If one knows the approximate range of the impedance, however, it is possible to develop a practical and reliable method for harmonic source detection. The objective of this paper is to present such a method. The key idea of this method can be summarized as

Manuscript received October 4, 2001; revised May 10, 2002. This work was supported by a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors are with the Electrical and Computer Engineering Department, University of Alberta, Edmonton, AB T6G 2G7 Canada. Digital Object Identifier 10.1109/TPWRD.2004.825302

follows. The harmonic reactive power generated by the utility source is estimated first. An equivalent impedance (or admittance) that absorbs that reactive power is then determined. This impedance (or admittance) is termed as critical impedance (or admittance) (CI or CA). By comparing the CI (or CA) with the known range of the combined utility and customer impedance (or admittance), the location of the dominant harmonic source can be found. The method, therefore, takes advantage of both the power direction-based and the impedance-based methods. In this paper, the validity of the method is demonstrated with theoretical analysis. The method is also verified using computer simulations and field test results. This paper is organized as follows: Section II describes the principle of the method, Section III presents simulation as well as error analysis results, and Section IV applies the method to a real power system. Section V discusses an extension of the method. The paper concludes with Section VI. II. PRINCIPLE OF THE PROPOSED METHOD If the current harmonic pollution is mainly concerned, the problem of harmonic source detection is to determine which side–utility or customer–is the dominant contributor to the harmonic current measured at the point of common coupling (PCC). For this problem, it is common to assume that the utility and customer sides are represented by their respective Norton equivalent circuits as shown in Fig. 1 [8], [9]. In this are the customer and utility harmonic current figure, and sources, and and are the customer and utility harmonic impedances, respectively. The problem of harmonic source or has a larger contribution detection is to determine if . As analyzed in [4], this is to the PCC harmonic current theoretically equivalent to examining the magnitude of and . If is greater than , it can be shown , and vice that the utility side source contributes more to versa. Therefore, we can transform the Norton circuit into the Thevenin equivalent circuit as shown in Fig. 2. In this figure, , , and . The phase is set to zero and that of is denoted as . The angle of harmonic source detection problem now becomes to identify or has a higher magnitude. which voltage source A. Problems of Power Direction Method Since the proposed method is inspired by the active power direction method, it is worthwhile to examine the problems associated with the method. For simplicity, the case of is used. Following the classic power-angle equation, for two

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 2, APRIL 2004

direction method. In the next section, we will propose a method . to address the case of It should be noted that an important prerequisite for the above and . This reactive power direction method is condition is generally true at the fundamental frequency, but it is unlikely true at the harmonic frequencies. A solution to this problem will be presented in Section II–D. Fig. 1.

Norton equivalent circuit.

B. Proposed Reactive Power-Based Method

Fig. 2.

Thevenin equivalent circuit.

source ac circuits, the power flowing into source termined as

can be de-

(1) Note that is the phase angle difference between customer and utility side voltage sources. The significance of this equation is that the direction of active power is a function of instead of the magnitudes of the voltage sources. As a result, the active power direction-based harmonic source detection method is incorrect theoretically, as it cannot reveal the difference between the magnitudes of the two sources. It is common knowledge for power engineers that the phase angles of bus voltages mainly affect the flow of active power while the magnitudes of bus voltages mainly affect the flow of reactive power. One would therefore wonder if the direction of reactive power could indicate the relative magnitudes of two harmonic sources. This can be analyzed by examining the reactive power flowing into source (2) It shows that the direction of reactive power is indeed related to the voltage magnitudes. From the equation, if the utility side absorbs reactive power ( ), must be smaller than . In other words, one can conclude that the customer side has a . An intuitive explanation of this conlarger contribution to clusion is the following: the reactive power absorbed by must come from . Since the impedance is reactive, must have a sufficiently high magnitude in order to “push” the reac. If the utility side generates reactive tive power into source ), however, it does not necessarily imply that the power ( utility side is the dominant source. This is because the generated reactive power may not reach the customer side since the line absorbs reactive power. In any case, anyhow, at least one direction of reactive power can give a theoretically correct conclusion, which is an improvement over the unfounded active power

The proposed new method is based on the concept of reactive power flow and is conceived to address the case of . The method relies on the following two assumptions. • The utility side impedance is approximately known. This requirement is relatively easier to meet since the impedance of the step-down transformer generally dominates the system impedance and the system impedance varies little for distribution systems. The fact that low-order harmonics (5th to 13th) are those encountered in most troubleshooting studies also helps to estimate the range of the system impedance. Our experiences show that frequency scan studies on a properly developed system model will generally yield an acceptable range of the impedance. It should be noted, however, the above conclusion may not be applicable to transmission systems. The impedance could also be measured [6]–[8]. • The approximate range of the customer side impedance is known. The customer loads may change a lot and there are difficulties to determine their representative harmonic impedances. It is possible, however, to estimate the range of the impedance using frequency scan analysis on a simulation model of the customer plant. For a plant dominated with motors and drives, the frequency scan results could be sufficient. Field measurements could also be conducted to determine the typical values of the impedance. The objective here is to develop a robust method to determine and given the above conditions. the relative magnitude of The method should be able to provide correct answers even if the range of the combined utility and customer impedance ( ) is very large. Since correct conclusions can be drawn ), we for the case of utility side absorbing reactive power ( need to focus on the cases where reactive power is generated by and utility source only. Based on the condition of a known , the starting with the simplest case of can be determined as utility source (3) error will be analyzed later. The key idea The impact of of the proposed method is to find how far the reactive power can travel along the impedance , if generated by source we imagine that the impedance is uniformly distributed between and as an “impedance line.” With this consideration, the voltage at an arbitrary point along the “impedance line” can be determined as (Fig. 3) (4)

LI et al.: A “CRITICAL IMPEDANCE”-BASED METHOD FOR IDENTIFYING HARMONIC SOURCES

where . By letting find the point with the lowest voltage as

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, we can

(5) where is the reactance from we consider (2) and

to the lowest voltage point. If

(6) Fig. 3. Determination of voltage at one point along

Equation (5) can be rewritten as (7) Since the reactive power absorbed by is , which is equal according to (7), one can conclude that all reactive power to is absorbed by reactance . In other words, produced by is the furthest location where the reactive power output of can flow to. This location also has the lowest voltage along the and . “impedance line” between It is our postulation that if is located closer to the customer ), the utility source is expected to have a larger side ( magnitude since the source can “push” its reactive power output ) of the “impedance line.” Similarly, if beyond halfway ( or is located closer to the utility side, the customer source is expected to have a large magnitude. A method to determine the relative magnitude of the two sources can, therefore, be established on the basis of comparing the magnitudes of and . Mathematical analysis has shown that this postulation is or will correct. In the following, the criterion be proven to be the necessary and sufficient condition on which . one can conclude To prove the above postulation, let us assume where . By considering (5), the new expression for can be established as (8) The minimum value of

is obtained when

(9) , all possible The above equation indicates that if values of will be greater than . That is, is the to hold. On the other hand, if necessary condition for , one will get given (10) Straightforwardly, the condition for the above equation to hold is . Therefore, we have proven (11) Since the sign of the reactive power absorbed by source and are two important parameters for the proposed the quantity method, we introduce a signed fictitious impedance to combine

jX .

them into a single index. The new index is called CI and is defined as (12) is the reactive power absorbed by , as shown in where , Fig. 2. Note that CI and have the same signs. So if which implies the utility absorbs reactive power, we can conclude directly that the customer side is the dominant harmonic , the utility side generates reactive power. In source. If this case, the range of needs to be compared with the absolute value of CI for determining the dominant source. In summary, , the proposed method can be implefor the case of mented as follows. 1. Calculate the utility side voltage source by using , where is known. 2. Calculate the reactive power absorbed by , , where is the phase by which leads . . 3. Calculate 4. If , the utility source absorbs reactive power, the customer side is the main harmonic contributor. , the utility generates reactive power, the fol5. If lowing substeps are to be taken: If , where is the maximum of all possible values, the utility side is the main harmonic contributor. This is because the utility side, due to its high source voltage, can “push” its generated reactive power far deep into the customer side; If , where is the minimum of all possible values, the customer side is the main harmonic contributor. This case implies that the customer side source “pushes” its reactive power deep into the utility side. If , no definite conclusion can be drawn. But our study results show that such a condition generally implies that the utility and customer have comparable contributions to the PCC current. As a result, the exercise to determine precisely which side has more contribution may just have academic significance. C. Error Analysis The practical applicability of the CI method depends on its robustness. Since the customer impedance may have large variations, our knowledge about may have large errors. The method is expected to have a good tolerance to such errors. or , a conclusion can be For example, if

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 2, APRIL 2004

obtained reliably. If , however, it will be difficult to judge which side is the main harmonic contributor. To quantify the impact of impedance errors, we define an impedance error tolerance index (IET) as

(13) where is the true value of . A larger IET implies a more reliable answer. The index IET is found to depend on the system and . Fig. 4 shows operation condition characterized by the voltage magnitude and the reactive power flowing along the , , and “impedance line” for the case of . is positive if reactive power flows from customer to utility. is in phase with , the utility side It can be seen that when generates reactive power while the customer side absorbs. The and lowest voltage point, shown by the dotted line, is at . Accordingly, is 15 ( is beyond the total reactance ) and IET reaches 200%. This means that we can identify the harmonic source correctly even if our knowledge on has leads by 150 , both the an error up to 200%. When customer and utility sides generate reactive power. The lowest , which is between the utility and voltage point is at customer but is still greater than half of . Accordingly, and IET decrease to 56%. But we can still make correct prediction if the tolerance for impedance error is tightened. In conclusion, the robustness of the method can be described by the following. 1) If one side generates reactive power while the other side absorbs, the method has a large impedance error tolerance and, therefore, is highly reliable. 2) If both sides generate reactive power, the error tolerance will be smaller. However, the harmonic source can still be detected correctly as long as our knowledge about the total impedance has no larger errors than IET. D. Generalized CI Method Our discussion so far has assumed that the impedance between utility and customer is purely reactive. In real power systems, the impedance is usually in the form of . For this realistic case, we introduce a phase rotation to precondition the problem. The general equation for the power received by the utility source is as follows (Fig. 2):

Fig. 4. Voltage and reactive power profiles.

The transformed power has the form of (16) The above equation is identical to the pure reactance case. Consequently, all conclusions derived for the later case can be applied to the general case if , , and are used. Note that a new parameter is introduced here. The effect of its error will be studied in the next section. In summary, the harmonic source detection steps for general cases are as follows: and 1. calculate utility voltage ; , the customer side is the major harmonic 2. if contributor; , the following substeps are taken: 3. if if , the utility side is the main harmonic contributor. if , the customer side is the main harmonic contributor; if , no definite conclusion can be drawn. It is interesting to consider two special cases. One case is that . This case may the impedance is capacitive, namely occur if the customer side is under light load condition or has sufficient reactive power compensation. For this situation, the reactive power absorbed by the utility source is

(14)

(17)

where . Comparing (14) with those for the case of pure reactance [(1) and (2)], one can see the difference is only a rotation of degrees. Therefore, we introduce the following rotation transformation matrix:

The above equation shows that if the utility side delivers reactive power ( ), will hold. Hence, the conclusions for the capacitive impedance case are just opposite to those of the . In this case, inductive case. The second special case is is equal to the active power and the transformed reactive has the form of

(15)

(18)

LI et al.: A “CRITICAL IMPEDANCE”-BASED METHOD FOR IDENTIFYING HARMONIC SOURCES

Fig. 5. Performance of the CI method.

Fig. 6.

Impact of error on CI (inductive Z case).

Fig. 7.

Impact of error on CI (capacitive Z case).

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In other words, the active power is a technically sound indictor for harmonic source location for the cases where customer and utility are connected with a resistive element. It should be noted, however, that such a case rarely exists in a real power system. III. SIMULATION STUDY RESULTS The proposed method is verified in this section with a representative fictitious circuit given in [10]. The circuit parameters are

A. Performance of the Method Fig. 5 shows calculated CI while changes from 0 to 360 . The active and reactive power received at utility side, the current from by applying superposition law contribution to and from , , are all plotted [4], in the figure. CI is found to be between and when is is selected as the actual value. It can be seen that , which means the cusalways much greater than tomer side is the major harmonic contributor. The figure shows neither active nor reactive power direction can give the right answer for all operating conditions. However, if we know the impedance is reactive and its minimum magnitude is greater than 6.1, we can get correct answer for all possible operation is 43.4, the proposed method conditions. Since the actual has an IET of 86%. It means a correct answer can be obtained has errors as high as 86%. This even if our knowledge of requirement is easy to meet for dominant harmonics. B. Impact of Impedance Phase Variations The accuracy of the method is also affected by the impedance phase angle . Fig. 6 plots the CIs while has error from to at a step of 5 per curve. It is found that the minimum and the method still has IET up to 84%. CI changes to These simulations have demonstrated that the method is robust with respect to impedance errors.

The method can give a correct answer too when the total impedance is capacitive. Fig. 7 shows the simulation results for and when the error of varies the case of to 90 . Note that we need to check the range of from only when CI is positive. The maximum CI is calculated as 4.3. for this case is 27.7, the method can tolerate As the actual error up to 84% even if the phase of has an error of . C. Robustness of the Method With Respect to Ratio of

to

In the above examples, (106.1) is much greater than (8.1). It is natural to deduce that the robustness of the method could be aggravated while the harmonic current contributions from utility and customer become comparable. Table I shows the worst tolerance level on impedance error (IET) with respect when decreases from 3 to 0.6. It can to the error of be seen that even if is reduced by 80% (from 3 to 0.6), the method can still give right answers as long as our knowledge and a magnitude about has a phase angle error less then error less than 40%. Alternatively, if we are confident that the

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 19, NO. 2, APRIL 2004

TABLE I IMPACT OF HARMONIC MAGNITUDE ON ACCURACY OF CI METHOD

magnitude error of is less than 20%, the tolerance on phase . In angle error can be raised to 75 for the case of conclusion, the proposed method is quite robust with respect to impedance errors. In other words, the method can be implemented with very limited knowledge on the impedance data. D. Robustness of the Method With Respect to Accuracy of The last factor that may degrade the robustness of the CI . This impedance method is the error of the utility impedance and can influence the range of . It should is used to estimate be noted that first of all, the error of is generally small since the supply transformer dominates the utility impedance. Even if there are some errors in , the error can be regarded as changes of and . Since results have shown that the method can tolerate large impedance and source current variations, it is reasonvariation is insignificant. able to consider that the impact of IV. VERIFICATION USING FIELD MEASUREMENTS The proposed method is further assessed with field measurement data. The system, shown in Fig. 8, exhibits 5th harmonic distortions at the metering point. Extensive investigations were conducted to determine which side is the main contributor to the harmonic distortion. Due to a lack of other viable harmonic source detection techniques at the time of the project, the expensive impedance-based method was used. The utility and customer impedances were determined from a series of field measurements when disturbances such as line and capacitor switching were introduced to either side. At the utility side, eight operations were performed within several hours to find the customer-side harmonic impedance. The calculated average . Another 5th harmonic impedance is around two capacitor switching operations were performed at the , the result customer side to find the utility side impedance . The system was also modeled for frequency is scan studies. The scanned and are found to be very close to the measured ones. Eventually, the utility system was identified as the main harmonic contributor with an average 5th of 2160 V. The customer side source is about harmonic 858 V. The proposed method is applied to the ten snapshots . The with the assumption of calculated CI and other key parameters are listed in Table II. The following conclusions can be drawn from the table. 1) The CI is always negative, so the utility generates reactive power (after rotation of degrees) in all snapshots. The harmonic source location needs to be detected by com. paring CI with impedance 2) The main harmonic source is located at the utility side since is always larger than which is about 563 . This impedance value is derived from the measured data.

Fig. 8.

One-line diagram of the field test system.

3) The smallest IET has a value of 58%. It means that one can still detect the source correctly even if our knowledge differs from the actual (i.e., measured) value by about 58%. 4) The first three snapshots have smaller IET than others. This is because both the utility and customer sides generate reactive power in these cases. For the other seven cases, the utility side generates reactive power and the customer side absorbs; consequently, the tolerance on impedance error can go as high as 258%. 5) The active power produced by the utility source is equal to that received by the customer source. This is because, after the rotation transform, the power is assumed to . There is no transmit through a pure reactance of active power consumption is the rotated case. 6) Further studies show that even if has an error from to , the location of the main harmonic source can still be correctly detected. This practical case further proves the robustness of the proposed method. It is shown that the method requires only approximate harmonic impedance data and can tolerate large impedance errors. Another advantage of the method is that once we find one side absorbs reactive power (for example, the customer side of snapshots 4 to 10), one can conclude that the main harmonic source is located at the other side immediately without examining the magnitude of . V. DISCUSSIONS Our focus so far has been on determining which side has a larger contribution to the PCC current distortion. It is equally important to find out which source has more contribution to the PCC voltage distortion. In fact, limiting the voltage distortions has become more important in recent developments of harmonic standards. In this section, the subject of applying the proposed method to detect dominant source from the perspective of voltage distortion is discussed. The circuit for voltage distortion analysis is shown in Fig. 9. The problem here is to find the larger contributor to the voltage . According to the principle harmonic measured at PCC, of superposition, this is equivalent to finding which source or has a larger magnitude. If we still assume that the utility side is known, the utility side harmonic current admittance can be calculated from the PCC measurements. Consequently,

LI et al.: A “CRITICAL IMPEDANCE”-BASED METHOD FOR IDENTIFYING HARMONIC SOURCES

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TABLE II CALCULATION RESULTS OF THE TEN SNAPSHOTS

Note: the power direction is assumed to be sending for the utility . So the rotation transform developed where in Section II can be used directly. The transforming matrix is still (15). In conclusion, the reactive power consumption concept developed in this paper can be used to detect major harmonic source from the perspective of either PCC voltage distortion or PCC current distortion. VI. CONCLUSION Fig. 9.

Equivalent circuit for voltage harmonic analysis.

the reactive power absorbed by the utility current source can be determined as (19) where . Referring to (2), we can see that if , the utility current source receives reactive power, one can conclude that the customer side has more contribution to . If or the utility current source generates reactive power, we need to check how much admittance will completely absorb that reactive power. Similarly, imagine the admittance is uniformly and , follow the procedure (4)–(7) and distributed between consider: (20) the point where

is the smallest can be determined as (21)

where can be defined as the CA. The reactive power generated by the utility current source will be absorbed by . It can be seen that (21) has a similar structure as (7). By comparing with , we can determine the dominant harmonic contributor to . distortion. In other words, the conclusions developed the in the previous sections can be applied to detect the main voltage harmonic contributor by replacing with and with . When the conductance cannot be ignored, that is , it is easy to find

(22)

The widely known active power direction method for harmonic source detection is unfounded. A new reactive powerbased method is proposed in this paper. The method assumes that the utility side impedance and the range of the customer impedance are approximately known. A fictitious impedance (or admittance) named CI (or CA) is calculated from voltage and current measured at the PCC. The result is compared with the range of the combined utility and customer impedance (or admittance) to determine which side is the dominant contributor to the harmonic distortion measured at the PCC. The main contributions of this work can be summarized as follows. • Mathematical analysis has been presented to demonstrate the pros and cons of the power direction-based methods. The reactive power direction-based method is found to be technically sound and is reliable when one source absorbs reactive power. • The reactive power-based method is expanded with the concept of critical impedance (or admittance), which forms the core idea of the proposed method. Rigorous theoretical analysis has proven that the concept presents a powerful alternative solution for the harmonic source detection problem. • A rotation transform is introduced to deal with general cases. This transform has greatly simplified the analysis and understanding of the harmonic source detection problem. The combination of these three contributions has resulted in a useful, practical, and reasonably reliable method for locating dominant harmonic sources in a power system. • The paper has done extensive investigations on the error characteristics of the proposed method. The method is further checked using field measurements. All results have shown that the method is robust and practical. It has the potential to become a viable and easy-to-use tool for the harmonic source detection problem.

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REFERENCES [1] T. Tanaka and H. Akagi, “A new method of harmonic power detection based on the instantaneous active power in three-phase circuits,” IEEE Trans. Power Delivery, vol. 10, pp. 1737–1742, Oct. 1995. [2] P. H. Swart, M. J. Case, and J. D. Van Wyk, “On techniques for localization of sources producing distortion in three-phase networks,” The Eur. Trans. Elect. Power Eng., vol. 6, no. 6, pp. 391–396, Nov./Dec. 1996. [3] L. Cristaldi and A. Ferrero, “Harmonic power flow analysis for the measurement of the electric power quality,” IEEE Trans. Instrum. Meas., vol. 44, pp. 683–685, June 1995. [4] W. Xu, “On the validity of the power direction method of identifying harmonic source locations,” IEEE Power Eng. Rev., vol. 20, pp. 48–49, Jan. 2000. [5] A. E. Emanuel, “On the assessment of harmonic pollution,” IEEE Trans. Power Delivery, vol. 10, pp. 1693–1698, July 1995. [6] M. Tsukamoto, I. Kouda, Y. Natsuda, Y. Minowa, and S. Nishimura, “Advanced method to identify harmonic characteristic between utility grid and harmonic current sources,” in Proc. 8th Int. Conf. Harmonics Quality Power, Athens, Greece, Oct. 1998, pp. 419–425. [7] A. de Oliveira, J. C. de Oliveira, J. W. Resende, and M. S. Miskulin, “Practical approaches for AC system harmonic impedance measurements,” IEEE Trans. Power Delivery, vol. 6, pp. 1721–1726, Oct. 1991. [8] H. Yang, P. Pirotte, and A. Robert, “Assessing the harmonic emission level from one particular customer,” in Proc. 3rd Int. Conf. Power Quality: End-Use Applicat. Perspectives, Amsterdam, The Netherlands, 1994, B-2.08. [9] E. Thunberg and L. Soder, “A Norton approach to distribution network modeling for harmonic studies,” IEEE Trans. Power Delivery, vol. 14, pp. 272–277, Jan. 1999. [10] W. Xu and Y. Liu, “A method for determining customer and utility harmonic contributions at the point of common coupling,” IEEE Trans. Power Delivery, vol. 15, pp. 804–811, Apr. 2000.

Chun Li (S’99–M’01) received the B.E. and Ph.D. degrees in electrical engineering from Tsinghua University, Beijing, China, in 1996 and 2000, respectively. Currently, he is a Post-doctoral Fellow in the Electrical and Computer Engineering Department at the University of Alberta, Edmonton, AB, Canada. His current interests are harmonics and power quality.

Wilsun Xu (M’90–SM’95) received the Ph.D. degree from the University of British Columbia, Vancouver, BC, Canada, in 1989. Currently, he is a Professor with the University of Alberta, Edmonton, AB, Canada, and chairs the Harmonics Modeling and Simulation Task Force of the IEEE Power Engineering Society. He was an Engineer with BC Hydro, BC, Canada, from 1990 to 1996. His main research interests are power quality and harmonics.

Thavatchai Tayjasanant (S’01) received the B.Eng. degree in electrical power engineering from Chulalongkorn University, Bangkok, Thailand, in 1994, and the M.Sc. degree from the University of Manchester Institute of Science and Technology (UMIST), Manchester, U.K., in 1996. He is currently pursuing the Ph.D. degree at the University of Alberta, Edmonton, AB, Canada.