Experimental verification of harmonic load models

Experimental Verification of Harmonic Load Models M. E. Balci, D. Ozturk, O. Karacasu and M. H. Hocaoglu Abstract--Present day power systems invariably have nonlinear loads, which inject harmonics into the system and give rise to nonsinusoidal voltages and currents. Power quality issues are a prime concern of the power industries as well as of customers. Thus under these conditions, it becomes imperative to study these nonlinear loads; their characteristics and effects. Accordingly, the harmonic analyses have become a regularly used tool in predicting the effects of harmonic producing loads on power systems. State of power system can be obtained in respect to the results of these analyses. The accuracy of these results depends on the modeling of harmonic producing loads. There are a large number of harmonic analysis methods that are in widespread use. In these analyses, the harmonic producing loads are widely modeled by various techniques namely; Constant Current Sources, Norton and Crossed Frequency Admittance Matrix. In this paper, the sensitivities of these models are evaluated for the system, which covers some of the harmonic producing loads, under the various waveform cases of supply voltages. Index Terms-- Harmonics; Harmonic analyses; Load modeling; Constant Current Source model; Norton model; Crossed Frequency Admittance Matrix model. I. INTRODUCTION I n the last decades, great interests have been focused on power quality concepts. This is mainly due to the fact that customer awareness on the subject has been gradually increased and also effective utilization of power network has become largely dependent on successful analysis of the power quality events. One of the most important quality factors for power systems is the harmonics, which are primarily caused by large proliferation of power electronic devices. Accordingly, harmonic analysis has become one of the most important studies of power system operation, planning and design [1]-[4]. Harmonics modeling and simulation is used in three main ways as follows: ƒ To estimate the harmonic impact of a new customer or load equipment, ƒ To evaluate the harmonic impact of existing equipment or customers and the supplying utility, ƒ And to evaluate effectiveness of various harmonic mitigation techniques. For power system harmonic analysis, there are largely and successfully employed number of techniques, which vary in This work is supported by Turkish Scientific Council under the project number of 106E132. M. E. Balci, D. Ozturk, O. Karcasu and M. H. Hocaoglu are with Department of Electronics Engineering, Gebze Institute of Technology, Gebze 41400 Turkey (e-mails: [email protected], [email protected], [email protected] and [email protected] ). terms of data requirements, modeling complexity, problem formulation and solution algorithms [1], [2], [5]-[8]. One of the most commonly used harmonic analysis technique is Frequency Scan [1], [3], which has comparatively simple structure and requires less data that make the frequency scan more preferable amongst various harmonic analysis techniques. In Frequency Scan, loads are generally modelled as a Constant Current Source (CCS) [1], [3], [9]. On the other hand, the main disadvantage of CCS model is that it may produce erroneous results in the cases of the voltage sensitive loads and for the networks, where large voltage variations are present. In addition, CCS model is enough to analyze cases involving typical operating conditions. For power system cases comprising non-typical spectrum, the accuracy of CCS model’s result becomes unacceptable. Thus, advanced harmonic analysis models and methods must be used to analyze the cases such as partial loading of harmonicproducing devices, excessive harmonic voltage distortions and unbalanced network conditions. In the cases, where the current harmonic spectrums of the harmonic producing loads are significantly changed by voltage, their voltage dependency must be considered to obtain accurate results. The requirement is the primary motivation for so-called Harmonic Iteration technique [5]-[8]. In this technique, a harmonic-producing device is modelled as supply voltage-dependent current sources. Some of the voltage dependent current source models, which are presented as several types in the literature, are Norton (N) and Crossed Frequency Admittance Matrix (CFAM) models [10]-[13]. It is also possible time domain models and transient solution programs such as EMTP be implemented for harmonic analysis [14], [15]. In the harmonic analysis based on time domain calculation, the loads are modeled by using differential state equations. Therefore, time domain models give much sensitive results than the frequency domain models, however; they must be implemented by extra computational efforts. In addition to above mentioned models, Transfer Function model, which are based on analytical calculations, exist in the literature [16]-[18]. Harmonic producing load models used for harmonic studies are usually a compromise between accuracy required and the data available. In this study, the sensitivity of Constant Current Source, Norton and Crossed Frequency Admittance Matrix models are evaluated for the system covers some of harmonic producing loads under the various waveforms of supply voltages. From the results, it could be concluded that Norton model is the best modeling approach for the considered loads and voltage cases. Furthermore, Constant Current Source model shows better performance than Crossed Frequency Admittance Matrix model. 1 Z N , h ∠δ h = Vh ∠ 1 α h − 2Vh ∠ 2 α h 2 I h ∠ 2 θh − 1I h ∠ 1 θh (1) II. OUTLINES OF THE ANALYZED MODELS In this section, the representations of analyzed models, which CCS, N and CFAM, are briefly summarized below: A. Constant Current Source Model In the cases of the loads, which are not much sensitive to voltage, and for the networks, where small voltage variations are present, harmonic producing loads are modeled as Constant Current Source. In addition, this model is usually placed in the analysis focused on resonance, which does not take into account the load dynamics. The representation of CCS model is given in Fig. 1. Fig. 1: The representation of CCS model. It can easily be understood from Fig. 1. that harmonic producing load is modeled as a fixed current source for each harmonic number. The advantage of this model is that the current harmonic spectra of numerous harmonic producing loads are already characterized in the literature; thus, it can be easily implemented in the harmonic analysis. However, it is not enough to analyze the interaction between network and harmonic producing loads for non-typical operating conditions. B. Norton Model For the accurate modeling of harmonic producing loads in the wider range of operating conditions, which is the lack of CCS model, N model is proposed in [10], [11]. The representation of N model is given in Fig. 2. 1 I N , h ∠ϕh = 1I h ∠ 1 θh + C. Crossed Frequency Admittance Matrix Model For the modeling of harmonic producing loads taking into account the voltage and current relation between different harmonic orders, CFAM model is proposed in [12], [13]. Fig. 3: The representation of CFAM model. It is shown from Fig. 3 that the harmonic producing load can be modeled as the admittances, which are calculated by considering not only the same orders but also different orders of voltage and current harmonics, in CFAM model. On the other hand, this model could be assumed as the voltage dependent current source expressed as where V1 ,V2 , voltage. Fig. 2: The representation of Norton model. (2) In (1) and (2), 1Vh ∠ 1 α h , 1I h ∠ 1 θh , 2Vh ∠ 2 α h and 2 I h ∠ 2 θh are the harmonic voltage and currents for two different cases, where one equipment of the network is connected and not connected to the network. On the other hand, it is an imperative issue for finding Norton impedance and Norton current sensitively that the voltage and current measurements must be referenced to the phase angle of a common bus voltage, which does not change with system condition. For the representative system, given in Fig. 2., the phase angle of VS,1 is a reference point for arranging the phase angles of voltage and current. However, this common bus may not exist for all cases; therefore, Thevenin equivalent voltage of the network side can be used as an alternative of common bus [10], [11]. Up to now, one can see from (1) and (2) that N Model is constructed by assuming superposition theorem. This matter means that load is modeled by ignoring the interaction between different order harmonics in the Model. I h = f (V1 ,V2 , In N model, harmonic producing load is modeled as the parallel connection of Norton impedance and Norton current source for each harmonic number. The components of N model, which are hth harmonic Norton impedance, ZN,h , and hth harmonic Norton current, IN,h , can be expressed as; 2 Vh ∠ 1 α h 2 V ∠ 2 αh = I h ∠ 2 θh + h Z N , h ∠δ h Z N , h ∠δ h , Vh ) , Vh (3) are the harmonic phasors of the supply CFAM model is experimentally constructed in two steps: • In the first step of the experiment, when the load is supplied by pure sinusoidal voltage, the terms of CFAM related to the fundamental frequency are calculated by means of the following expression: • Ik (4) ( k=1… n ) V1 In the second step of the experiment, when the load Yk 1 = • • is supplied by various voltage waveforms, which have constant fundamental component and superimposing one harmonic component at a time. Thus, the other terms of CFAM are calculated as; I k − Yk 1V1 Vj Ykj = j = 2… n In the first step of experimental verification, the exemplary power system is modeled as CCS, N and CFAM models. And then, the current is calculated by means of models under various voltage wave shapes with %5 THD. The harmonic contents of the source voltage wave shapes are synthesized by randomly selecting their magnitudes by keeping highest order harmonics of 11st and total harmonic distortion of %5 Finally, the current is measured in the case of considered voltage and the errors of the models are calculated as [13]: (5) • During the calculating process, using the same phase reference must be considered to obtain CFAM model accurately. ∫ (i (t ) − i (t )) t +T m III. EXPERIMENTAL RESULTS E= ∫ t 2 c dt (6) t +T The system used to identify the sensitivity of CCS, N and CFAM models is depicted in Fig. 4. 2 im ( t ) dt t Fig. 4: Experimental system. 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 3 5 7 Harmonic Numbers 9 11 15 20 10 18 5 16 14 i(t) (A) Magnitudes of Current Harmonics (% of Fundamental Harmonic Current) The experimental system consists of a computer, which is used for data processing, a data acquisition card and the exemplary power system, which comprises linear impedance load, a dimmer controlled impedance load (triac conduction angles: 90o-180o) and a number of computer at the same connection point. For sinusoidal voltage wave shape, the harmonic spectrums of the current drawn by the loads are given in Fig. 5. Magnitudes of Voltage Harmonics (% Values of Fundamental Harmonic Voltage) As a result of the steps, for one of the hundred test voltages, whose harmonic spectrum is given in Fig. 6 (a), the measured current and the estimated currents, obtained with the models, are given in Fig. 6 (b). 12 10 0 -5 8 -10 6 Measured CCS N CFAM 4 -15 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 t (sn) 2 3 5 7 Harmonic Numbers 9 11 Fig. 5: The harmonic spectrum of the load current under sinusoidal voltage. Fig. 5 shows that the load has 3rd, 5th, 9th and 11th harmonics. Furthermore, the THD of the load current is 25% under sinusoidal supply voltage. By using the test system above detailed, the experimental verification is done in three steps: Fig. 6: (a) The harmonic spectrum of one of the hundred test voltages and (b) the wave shapes of the measured current and the estimated currents, with the models. From Fig. 6 (b), one can see that the estimated currents, obtained by N and CFAM models, are much closer to the measured current than the estimated current with CCS for the voltage harmonic spectrum in Fig. 6 (a). Furthermore, error values of CCS, N and CFAM models respectively are 0.3264, 0.2620 and 0.2526. Therefore, in this case, it can be concluded that CFAM has the best approximation to the measured current. In addition, the approximation of N is better than CCS. However, the results in the several test voltage cases must be considered to give general conclusion about the performances of the models. As a result, for a hundred test voltage cases, the errors of models are calculated and they are given as histograms in Fig. 7. 50 CCS 40 30 20 10 fundamental voltage harmonic. And also, for all tests cases, the fundamental harmonic of voltage is kept constant. As a result, due to the fact that Norton and Constant Current Source models have constant current parts, they give much better results than Crossed Frequency Admittance Matrix model, identifies the loads as admittances. In the next study, the model performances will be analyzed by means of larger number test cases and load types. Also effects of voltage variation will be undertaken. Thus, the issue above mentioned will be discussed strictly. 0 30 V. REFERENCES Frequency N 20 [1] 10 0 30 [2] CFAM 25 20 15 [3] 10 5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Error [4] Fig. 7: The histograms of the models errors: (a) CCS, (b) N and (c) CFAM. [5] It is shown from Fig. 7 (a) that the error of CCS varies from 0.3 to 0.42 in 80% of test cases. In 15 % of test cases, its error is between 0.15 and 0.3. For the rest of the test, it has the errors between 0 and 0.08. On the other hand, Fig. 7 (b) shows that the error of N varies from 0.3 to 0.45 in 46% of the test cases. In the rest of test, its error is between 0.11 and 0.3. From the results of CFAM given in Fig. 7 (c), it can be concluded that its error varies between 0.3 and 0.45 in 59% of the test cases. In 31 % of the test cases, CFAM has the errors between 0.5 and 0.8. For the models, the values of mean, median and standard deviation are given in Table I. [6] TABLE I: The values of mean, median and standard deviation for the models. [11] CCS N CFAM Mean 0.3512 0.2909 0.4226 Median 0.3823 0.2843 0.4047 Standard Deviation 0.0855 0.0735 0.1211 Table I shows that expected error of the models is in between 0.4226 and 0.2909 for %5 THD. Even if the source voltage has small amount of harmonic distortion, the estimated model current varies significantly. IV. CONCLUSION In this paper, the sensitivity of Constant Current Source, Norton and Crossed Frequency Admittance Matrix models are evaluated for the system covers some of harmonic producing loads under the various waveform cases of supply voltages. 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