Abstract—Considering the guidelines contained in documents

such as the IEEE Standard 519 and IEC 61000-3-6 that includes, among other indexes of power quality, the thematic of the harmonic distortion, the mentioned text refers to issues associated with definitions, measuring procedures, reference values, etc. Taking under consideration these determinations, and recognizing that the mitigating solutions for the adequacy of performance indexes involve significant financial costs, the proposition of finding ways to determine the responsibility for possible violations of pre-established limits for harmonic distortion arises. Among the proposals found to detect the contribution portions coming from the supplier and the customer, it is noteworthy that, in general, the methodologies based on principles use the frequency domain harmonized with the superposition of effects. Despite the simplicity of this procedure, it is emphasized that it relies on measuring information and on the previous knowledge of the equivalent harmonic impedances of the utility and customer, whose information are of difficult access. In this context, this paper is focused on a feasibility proposition to solve the above mentioned difficulties in obtaining the percentage of responsibility between the parties.

Index Terms—Harmonic, harmonic source detection, sharing responsibilities, superposition principle.

I. INTRODUCTION CCORDING to the international recommendations [1,2] toward the definition of the reference values of the power

quality indicators, where the presence of harmonic distortion is considered, it becomes important to have available means that lead to an identification of the origin of the phenomena responsible for the deterioration of electrical supplies. In fact, standards and recommendations have attempted to establish limits on the quantities that characterize voltage deviations, aiming to maintain the standards of power quality at acceptable levels. In a particular manner, the harmonic distortions have occupied an important position in the global scenery of power quality indicators.

In general, the rules and guidelines established by

Manuscript received June01, 2011. This work was supported in part by the Federal University of Uberlandia and FAPEMIG.

I. N. Santos is with the Federal University of Uberlandia, Uberlandia, MG, Brazil (e-mail: ivan@ieee.org).

J. C. Oliveira is with the Federal University of Uberlandia, Uberlandia, MG, Brazil (e-mail: jcoliveira@ieee.org).

J. R. Macedo Jr. is with the Federal University of Uberlandia, Uberlandia, MG, Brazil (e-mail: jrubens@ieee.org).

regulatory agencies settle reference values for total and individual voltage distortions. Despite this classical procedure, it is worth remembering that some recommendations also include limiting values for harmonic currents.

Although the existing documents contemplate issues related to values, measuring procedures, protocols, etc., there is virtually no mention of any mechanisms for the identification of the source of distortions, i.e., the contribution percentage to be attributed to the utility and the customer. This issue assumes importance as the mitigating solutions imply in implementation costs and the financial responsibility of such procedures could lead to disputes between the involved parties. In fact, once found a violation of the limits approved for a certain assessment at the Point of Common Coupling (PCC) between the parties, it is of utmost relevance the employment of a systematic procedure for the identification of the responsibility rates for each agent.

Recognizing the importance of the nature, value and origin of the phenomena, it is thus evident the need for the availability of safe and reliable methods that lead to a consensus concerning the discussed issues.

Among the possibilities mentioned in the literature for the identification of responsibilities, one of the most familiar proposals is based on the concept of analysis of electrical circuits, namely the superposition principle. The use of such procedure can be identified in the studies [3,4] initially conducted under the coordination of researcher Wilsun Xu from Canada, which were discussed, considered and evaluated by the authors of this paper [5,6].

Within this context and using the above mentioned basis, this paper aims to explore the traditionally established procedure, which employs the principle of currents superposition and, additionally, describes the principle of voltage superposition. Despite the simplicity of the methods under analysis, it is worth mentioning that one of the most complex points for the practical application of the process lies on the need of pre-knowledge of the equivalent harmonic impedances of the utility and, in particular, the customer’s one. Once showed the applicative limitations of the procedure, this work proceeds so that to propose a methodology that enables the practical application of the superposition process, highlighting a proposal to solve difficulties inherent to the uncertainties associated with the mentioned equivalent impedances.

Therefore, this article is directed to the following focal points:

Modified Superposition Method for Assignment of Responsibilities on Harmonic Distortions

Ivan Nunes Santos, Member, IEEE, José Carlos de Oliveira, Member, IEEE José Rubens Macedo Jr, Senior Member, IEEE

A

978-1-4673-0378-1/11/$26.00 ©2011 IEEE

• Considerations on the original methods that use the principle of superposition of harmonic currents and voltages at the PCC, in accordance with [3];

• Proposition of a procedure that enables the application of the superposition methodology without the need of prior knowledge of the equivalent impedances of the supplied system and/or the customer.

II. SUPERPOSITION METHOD The Fig. 1 is a representative and generic configuration of

an electrical system seen from the point of common coupling between the supplier and the customer. In this figure, the customer is represented by linear and nonlinear loads, while the utility system is simplistically shown through a non-detailed complex that includes its basic constituent parts, namely: generation, transmission, distribution, other customers, etc.

The physical arrangement shown may be better observed from its Norton equivalent circuit as shown in Fig. 2. This must be understood as a representation that uses the modeling technique in frequency domain. It is worth noting that the equivalent circuit should be considered for each focused harmonic order, which is generally represented by h. Both the representative source of the utility and the combination of the linear and nonlinear load are shown in this equivalent.

In this Fig. 2, is equivalent harmonic impedance of utility at order h and is equivalent harmonic impedance of customer. and are the harmonic current at order hof the each system. and are, respectively, harmonic voltage and harmonic current at order h at the PCC.

The equations (1) and (2), derived from the Norton equivalent circuit, give the harmonic currents generated by each one of the representative current sources of the nonlinear loads present in the circuit of the supplier and costumer, respectively.

pcc hu h pcc h

u h

VI I

Z−

− −−

= + (1)

pcc hc h pcc h

c h

VI I

Z−

− −−

= − (2)

The contributions of each of the involved parties, for the total current ( and for total voltage ( at the PCC, can be found, as already pointed out, by means of the superposition principle. The circuits associated with this analysis strategy can be visualized in Fig. 3. The first one elucidates the configuration directed for the determination of the contributions coming from the utility circuit (for total current and total voltage) and the second one is associated with the contributions deriving from the customer.

In the Fig. 3, is the contribution of harmonic current at order h from utility to the total current and

is the contribution of customer to the total current at PCC. and are, respectively, the contribution of harmonic voltage at order h from utility and from customer to the total voltage .

The contributions of the harmonic currents can be found

Fig. 1. Representation of an electrical system from PCC.

UTILITY

PCC

NON-LINEARLOAD

LINEARLOAD

Fig. 2. Norton equivalent circuit of the electrical system for a givenharmonic order h.

PCC

u hZ −

c hZ −

u hI −

c hI −

pcc hV −pcc hI −

Fig. 3. Equivalent circuits for determining the individual harmonic contributions of current and voltage at the PCC for the harmonic order h.

(a) (b)

PCC PCC

u hZ − u hZ −

c hZ − c hZ −

u hI −

c hI −

u pcc hI − − c pcc hI − −c pcc hV − −u pcc hV − −

through the application of traditional principles of circuit analysis and, concerning the voltages, similar procedures may be used, as explained hereafter.

A. Current Superposition Method The contributions for the total harmonic currents at the PCC

may be determined by the equations (3) and (4).

u hu pcc h u h

u h c h

ZI IZ Z

−− − −

− −

=+

(3)

c hc pcc h c h

u h c h

ZI IZ Z

−− − −

− −

=+

(4)

Therefore, the total current at the PCC may be obtained trough the superposition of these components, i.e.: ( )pcc h u pcc h c pcc hI I I− − − − −= + − (5)

The currents superposition method suggested in [3,4] establishes that the sharing of responsibilities between the parties should be effected by means of the projections values of the representative phasors of the individual current contribution ( and over total current phasor ( . These projections are highlighted in Fig. 4.

In the Fig. 4, and are, respectively, the projection of and over .

It is noteworthy that the procedure herein presented accomplishes, by itself, the separation of responsibilities of the current harmonic distortions present at the PCC. A similar procedure will be presented hereafter, but focused on the sharing of harmonic voltage distortions.

B. Voltage Superposition Method The contributions for the total harmonic voltage at the PCC

can be determined by the equations (6) and (7).

u h c hu pcc h u h

u h c h

Z ZV IZ Z

− −− − −

− −

=+

(6)

u h c hc pcc h c h

u h c h

Z ZV IZ Z

− −− − −

− −

=+

(7)

Then, the total voltage at the PCC can be obtained as follows:

pcc h u pcc h c pcc hV V V− − − − −= + (8)

The method of voltages superposition follows the same strategy presented for currents superposition. Therefore, the principle for the sharing of responsibilities between the agents should be accomplished through the projections values of the representative phasor of the individual contributions of voltage ( and ) over the total voltage phasor ( , as shown in Fig. 5.

In this previous Fig. 5, and are, respectively, the projection of and over

. Considering that the main rules and recommendations,

national and international, use reference values for the harmonic voltages, instead of harmonic currents, this implies that, for the moment, the establishment of a procedure addressed to the proposal supported by the voltages superposition method seems to be more attractive. Meanwhile, despite of the simplicity of the mentioned method here presented, it is worth saying that one of the more complex points to achieve a good accuracy in the results, is linked with the need of pre-knowing the equivalent harmonic impedances of both utility and customer. This difficulty, as demonstrated in [7] leads to sharing results that may present numerical and even inconsistent discrepancies regarding the parties contribution. Before this conjuncture, additional researches were conducted with the main purpose centered in a strategy for solving the above mentioned difficulties.

III. MODIFIED SUPERPOSITION METHOD BY INSERTION OF DOMINANT IMPEDANCE

The methodology here proposed is based, as already told, in the voltages superposition principle, as determined by the equations (6) and (7), which point out the importance of knowing the impedances of both utility and customer. The relation between the impedances, in the terms indicated by the equations, originates the complex constant hereunder.

u h c hh

u h c h

Z ZKZ Z

− −

− −

=+

(9)

Introducing this magnitude in the expressions previously referred:

u pcc h h u hV K I− − −= (10)

Fig. 4. Decomposition of the current at the PCC in two scalars accrued fromthe projections.

u proj hI − −

u pcc hI − −

c pcc hI − −−

c proj hI − −pcc hI −

Fig. 5. Decomposition of the voltage at the PCC in two scalars accrued from the projections.

u proj hV − −

u pcc hV − −

c pcc hV − −

c proj hV − −pcc hV −

c pcc h h c hV K I− − −= (11)

It can be noticed, from the above expressions, that the contribution portion of each one of the involved agents for the total harmonic distortion at PCC, for a determined operational situation, depends exclusively on the complex currents values

and . Therefore, to generate the sharing of responsibilities it will be sufficient the knowledge of these currents, or even the proportionality relation between them. Thus and considering this statement, the procedure herein proposed consists of a quite simple strategy, which is configured with the inclusion, at the PCC, of a passive component that presents as a harmonic impedance known and dominant over those previously described ( and ). This leads to the use of an arrangement in the form of a tuned filter, which fulfills the required properties.

The Fig. 6 illustrates the new configuration of the system with the insertion of the harmonic impedance of the selected harmonic filter. In this figure, is equivalent harmonic impedance from the filter to the order h, is harmonic current at order h drained by the harmonic filter, and and are, respectively, harmonic current at order h to the upstream and to the downstream of PCC.

In sequence, the applicable formulation to the new circuit proceeds, using the superposition principle. This can be

evidenced in Fig. 7. In the Fig. 7, and are, respectively, the

contribution of harmonic current atorder h from utility and from customer to total current of filter .

Whereas it is a filter, the new harmonic voltage at order h in the PCC will be presented with a very low value, the following observations are valid:

• The filter impedance is predominant over the remaining impedances of the system;

• Before this situation the current – Fig. 7a – is practically equal to ;

• Additionally, the current – Fig. 7b – is nearly equal to .

• Considering these facts, the following can then be written:

fu h u h pcc in hI I I− − − −= = (12)

fc h c h pcc out hI I I− − − −= = − (13)

Finally, using the superposition principle, the total current at order h in the filter will be:

f h fu h fc h

u h c h

pcc in h pcc out h

I I I

I II I

− − −

− −

− − − −

= +

= +

= −

(14)

Once obtained and , considering the application of the methodology of voltages superposition, the projections of these phasors over the representative one for the total current should be conducted, generating the projections

and , respectively. These projections are, as already stated, proportional to those linked with the method of voltages superposition – Fig. 8.

From the above mentioned it may be said that the sharing of responsibilities on the harmonic distortion at order h at the PCC, and in accordance with the presented steps, must follow the sequence of procedures set forth below to achieve the desired focal point of this study:

1) Insert a harmonic filter at order h near the PCC, with tuning frequencies compatible with the harmonic components of interest;

2) Determine the magnitude: and ,

fu proj hI − −

fu hI −

fc hI −

fc proj hI − −f hI −

Fig. 8. Decomposition of the current at the filter in two scalars accrued from the projections.

Fig. 6. Physical arrangement related to the modified superposition method.

Fig. 7. Determination of the harmonic contributions of current at order h for the total current of the filter.

PCC

c hZ − c hI −

Utility Side

u hZ −u hI −

Customer Side

f hZ −

Filter

f hI −

pcc in hI − − pcc out hI − −

PCC

c hZ −u hZ −u hI −f hZ −

fu hI −

(a)

(b)

PCC

c hZ − c hI −u hZ −f hZ −

fc hI −

as illustrated in Fig. 6; 3) Find the , and using (12), (13) and

(14), respectively; 4) Project the phasors and over the , in

agreement with Fig. 8; 5) Finally, determine the percentage that will define the

parcels of responsibilities, employing for both, the numerical results of the projections above referenced.

It is worth noting that the results from the application of the

Modified Superposition Method should be considered together with equations (10) and (11). Since these equations show that the percentages of the currents are directly linked with the responsibilities of the voltage distortions by the complex constant . This fact determines that although the values shown in Fig. 8 are expressed in current, these percentages are representative of portions of the supplier and consumer contributions to the voltage distortion at PCC.

IV. CONCLUSIONS This paper examined an issue of great importance

nowadays, which is linked with the sharing of responsibilities between the supplier agent and the customer regarding the harmonic distortions. This subject meets great repercussion due to current and future expectations related to the compliance of the requirements of the basic network procedures and also of the electric-power distribution. In this environment, the main points were synthesized and associated with the proposals found in the literature, which are generally based on the principles of superposition of effects. As highlighted in the text, despite the practicality and simplicity of the established procedures, their accomplishment meet great barriers when characterizing and obtaining the representative parameters of the equivalent harmonic impedances of the involved agents. As shown in other studies, the uncertainties linked to the equivalent impedances lead to very significant errors for the sharing results, whose fact determine the ineffectiveness of the process for the desired purposes, under the current terms. Before these evidences, this study was focused in the searching of an alternative to solve the problems pointed out here, and consequently was directed to a systematic that would lead to a calculus mechanism in which the impedance of the supplier and customer played a secondary role in the process. With this in mind, it arose the idea of using near the coupling point between the source and the load, a dominant impedance, over the remaining ones, thus resulting in the inclusion of a tuned filter, which, once attached to the arrangement under analysis, provided means of reaching the proportions of responsibilities between the parties.

ACKNOWLEDGMENT The authors express their thanks to FAPEMIG for financial

support conceded through scholarships and others, and the Federal University of Uberlandia, for providing the structure for the accomplishment of this research.

REFERENCES [1] IEEE Recommended Practice and Requirements for Harmonic Control

in Electric Power Systems, IEEE Standard 519-1992. [2] Electromagnetic Compatibility (EMC) - Part 3: Limits - Section 6:

Assessment of emission limits for distorting loads in MV and HV power systems - Basic EMC publication, IEC 61000-3-6, 1996.

[3] W. Xu, and Y. Liu, “A method for determining customer and utility harmonic contributions at the point of common coupling”, IEEE Transactions on Power Delivery, vol. 15, no. 2, pp 804-811, April 2000.

[4] W. Xu, and Y. Liu, “A method to determine customer harmonic contributions for incentive-based harmonic control applications”, IEEE Panel on Harmonic Measurements and Allocation, pp 361-366, 1999.

[5] S. F. P. Silva, and J. C. Oliveira, “The Sharing of Responsibility between the Supplier and the Consumer for Harmonic Voltage Distortion: A Case Study”, Electric Power Systems Research, v. 78, p. 1959-1964, 2008.

[6] J. C. Oliveira, S. F. P. Silva, I. N. Santos, and F. H. Costa, “A Case Study of Sharing the Harmonic Voltage Distortion Responsibility Between the Utility and the Consumer”, International Conference on Renewable Energies and Power Quality, Valencia (Spain), April 2009.

[7] F. H. Costa, J. C. Oliveira, and I. N. Santos, “Avaliação do Desempenho das Metodologias para a Representação de Consumidores Visando o Compartilhamento das Distorções Harmônicas”, VIII Congresso Brasileiro sobre Qualidade da Energia Elétrica, Blumenau/SC, agosto 2009.

Ivan Nunes Santos (M’10) Received B.Sc. and M.Sc. from the Federal University of Uberlândia, Brazil. He has taught and is currently working toward a D.Sc. in Electrical Engineering at the Federal University of Uberlândia. His research interests include electrical power systems and power quality. José Carlos de Oliveira (M’10) Received B.Sc. and M.Sc. from the Federal University of Itajubá, Brazil, and a Ph.D. from the University of Manchester, Institute of Science Technology, Manchester, U.K.He is currently a Professor anda Researcher atthe Faculty of Electrical Engineering, Federal Universityof Uberlândia, Minas Gerais, Brazil. He is also thePresident of the Power Quality Brazilian Society. His research interests include electrical power systems and power quality. José Rubens Macedo Jr (M’05–SM’08) Received B.Sc. and M.Sc. from the Federal University of Uberlândia, Brazil, and D.Sc. from the Federal University of Espírito Santo, Vitória, Brazil. At present, he is a Professor of Electrical Engineering at the Federal University of Uberlândia and Vice-President of the Power Quality Brazilian Society. His research interests include power quality, system modeling and simulation.