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Harmonic Calculation Toolbox in Industry Application for Adjustable Speed Drive Lucian Asiminoaei, Frede Blaabjerg, Steffan Hansen, Institute of Energy Technology, Danfoss Drives A/S, Aalborg University, DK-6300, Graasten, Denmark, DK-9220, Aalborg SE, Denmark, s.hansen@danfoss.com las@iet.auc.dk, fbl@iet.auc.dk Abstract–Previous to electrical installation of large power non- estimated, and this approach provides an easy and fast linear loads, a comprehensive design-study is often required in software implementation. order to determine if the overall installation complies with This paper describes the development of calculation tools for international regulations in respect to harmonics. Current THD, estimation the six-pulse diode rectifier harmonics. The focus is voltage distortion and power factor are just few parameters to be placed on estimation of line-side harmonic distortion when aware off. This paper focuses on estimation of line-side harmonic distortion when connecting one or multiple six-pulse diode connecting one or multiple six-pulse diode rectifiers to any rectifiers to any supply transformer. Results are put into a supply transformer. practical PC software toolbox for harmonic estimation on real Results are put into a practical PC software toolbox for applications. Through a combination of an off-line database and harmonic estimation on real applications. Using a combination new interpolation techniques very good results have been of offline database and interpolation techniques very good achieved. The final results obtained are very close to the results can be achieved. Comparisons between the toolbox measurements on real applications and the toolbox can be used results and real measurement validate the implementation. for future ASD designs and installations. Keywords – variable speed drive; harmonics analysis; load flow II. SIX-PULSE RECTIFIER MODELS analysis; power system harmonic; software tools. Four state of the art methods have been analyzed in [15] for I. INTRODUCTION modeling the six-pulse diode rectifier: ideal, table-based, Lately, end users of non-linear 3-phase equipment, such as analytical and numerical. It is shown that a close correlation Adjustable Speed Drives (ASD), require a detailed harmonic exists between the number of required parameters and the calculation report for their application. Both harmonic voltage accuracy of the result. And as expected, the more parameters and current spectrum up to the 50th harmonic are requested. are known, the more accurate results are obtained. Fig. 1 This involves both knowledge on the power system and the shows a comparison of measured and simulated line-currents equipment level. of a six-pulse diode rectifier when the system parameters are For ASD’s the most used front-end topology is still the 6- well determined. pulse diode rectifier, due to well-known advantages such as, 10 high efficiency, low cost, robustness and reliability. 8 measured Unfortunately, even though the six-pulse diode rectifier has a simulated very simple circuit topology, calculation of the (harmonic) 6 I sa [A] currents is not a trivial task. It is for example well known that 4 the harmonic currents of the six-pulse diode rectifier are heavily depending on the supply impedance and supply 2 voltage quality (i.e. pre-distortion and unbalance) [1] – [7]. Furthermore, as this paper will show, the harmonic current 0 0.01 0.012 0.014 0.016 0.018 0.02 Time [s] emission is also depending on the numbers and rating of the Fig. 1. Comparisons of measured and simulated line-current of the three-phase connected rectifiers. Besides these aspects there is always a rectifier (2.2 kW). Time-domain and frequency-domain representation. little lack of knowledge with respect to the system. Thus, the estimation of the harmonic current emission in a certain point In a context of practical use, to estimate the harmonic is far beyond a simple engineering problem. distortion in a given industrial application, the table-based There are different approaches to calculate the harmonic model has the advantages of easy implementation in a currents, some from the practical [10], others from the spreadsheet format, where the amount of data is highly analytical point of view [12] or even combinations of both. depending on the accuracy required. The achievement of this paper is to prove that using an The availability of a numerical simulator or programs like empirical method correlated with analytical expressions the Matlab “in the field” is a significant limitation for the harmonic model of the rectifier part of ASD's can be analytical and numerical models. However, the analytical model may be compiled into a stand-alone PC-software 0-7803-8269-2/04/$17.00 (C) 2004 IEEE. 1628 application, where after the analytical model can provide Ultimately, harmonic data and all analytical expressions are accurate harmonic estimation without prior table generation compiled using the Matlab programming into a graphical even “in the field”. interface application where the user provides the input The circuit-based simulators have significant advantages parameters. Thus, for a given case the input parameters are under non-ideal voltage conditions, as it must be recognized used to search the database retrieving for the best-fitted that the current of a diode rectifier is highly depending on the information and estimating the harmonic currents based on a supply voltage quality. Thus, it is recommended to use linear interpolation algorithm. numerical simulators to predict the harmonic current distortion of the diode rectifier at significant non-ideal conditions. B. Analyzing the basic circuit However, this requires more detailed knowledge of the system Initially, a correlation between the toolbox diagram and the parameters such as phase-angle of the harmonic voltage system should be established for simulation. This will help distortion, harmonic impedance, resonance frequency, etc. In choosing the right parameters in the simulation to meet certain the case that these parameters are not available, the table- requirements, i.e. acceptable data size and simulation time. based or analytical models might be just as exact. The ASD is a typical three-phase capacitive smoothed Supported by the conclusions and experience of [15] it is rectifier containing an ac-inductance, a dc-reactance and a chosen to let the harmonic calculation toolbox be based on a resistive load. Fig. 3 presents a Spice schematic used for table-based model. Harmonic data (collected by simulating the simulations. six-pulse diode rectifier) are pre-processed and saved in The relationship between the simulated circuit and the databases. Furthermore, analytical expressions are used to toolbox circuit is done as following. The voltage ac-sources reduce data size where applicable. represent the secondary side of the transformer (see Fig. 2). In this way, the developed tools keep the goal of accurate, The Lac and Rac components identify the cable and the practical and easy to be implemented in PC software. transformer short-circuit impedance and the Rload component identifies the power rating of the rectifier. III. PRINCIPLE OF TOOLBOX DEVELOPMENT As these parameters can vary from case to case, eg. A. General description transformer inductance, transformer rating, cable length, ASD rating, etc., it is necessary to establish a practical number of The toolbox is developed around a general power system parameters to express the line-side harmonic current since it is diagram as shown in Fig. 2a. It includes a transformer, two sets known that all these have impact on the emission level. of cables, a linear load and multiple connected drives. The Therefore, the harmonic current emission should be drives consist of six-pulse front-end diode rectifiers. In real expressed as a function of multiple arguments as: cases, the ASD could be supplied alone or most likely, i h = f ( x1 , x 2 , x3 ...x n ) (1) connected together with other ASDs at panel point, therefore the toolbox allows parallel connection of different types of drives. where: ih represents the characteristic harmonic currents of the Since the number of drives and their characteristic may vary six-pulse diode rectifier, (i.e. nominal power, load, internal dc-link inductance, x1… xn are the arguments of the function. supplementary ac-inductance) it is difficult to analyze the Having too many arguments (equivalent to as running the system in a one-step iteration. simulations in "all possible cases" with "all possible values") Instead of using a large and laborious harmonic analysis, a new creates large memory storage requirements and excessive time approach has been found in this paper by "splitting" the original spent on simulation. diagram into multiple simple diagrams, as shown in Fig. 2b. On the other hand, if the number of arguments is too small or Each system contains an equivalent model of the power system not properly chosen, the consequence will be a lack of and one single ASD. The ASD is separately analyzed using knowledge when the harmonic currents are required for a circuit simulators and data are minimized and stored in given case. databases for offline estimations later in the developed toolbox. Therefore, previous to simulate the system, some The last step is to use the superposition principle and a assumptions should be made, like: compensation factor (due to a reciprocal influence when the • the line voltage is balanced and sinusoidal, drives are connected in parallel) in order to regroup the • the grid is purely inductive (Rac=0), original diagram. • all passive components are linear, i.e. the resistance and Panel Drive 1 ac-impedance ih Grid Drive 1 inductance are constant at all frequencies. Transformer Drive 2 ih ac-impedance D1 D3 D5 PCC Vsa Ldc Cable Cable ih ih Grid Drive 2 Lac Rac Grid Drive 3 ih ih … Vsb Lac Rac Cdc Rload ac-impedance Other Lac Rac Grid Drive n Vsc Loads Drive n ih ih D4 D6 D2 (a) (b) Fig. 2. System diagrams used in a) harmonic toolbox analyzes, b) individual study approach. Fig. 3. Basic circuit layout of the simulated six-pulse rectifier. 1629 Furthermore, it is assumed that the diode rectifier is of the Therefore, even the harmonic currents are expressed as a voltage-stiff type. This means that the dc-link capacitor is function of only three arguments, the simulation data are still sufficient large to maintain a constant dc-link voltage. This is high. The consequences are the need of a large storage and a fair assumption since most of the diode rectifiers used in difficult data handling. today’s power electronic converters are of this type. The amount of data can be minimized by using an By investigating common applications it can be concluded interpolation algorithm and analytical expressions in the that three arguments practically cover the requirements for toolbox. calculating the harmonics. The 5th and the 7th harmonic currents are typically the weightiest ih = f ( Lac , Ldc , Rload ) (2) harmonics in the current distortion. An approximation of these The arguments are expressed on a per unit basis of an with analytical expressions will bring significant errors. initially established nominal power. Then simulations have Therefore, the 5th and the 7th harmonic currents are stored without been run independently on the circuit in Fig. 3, varying one further minimization. parameter and keeping the other constant: Instead, higher harmonics are suitable for an analytical • ac-reactance Lac, between 0% to 25% p.u., approach, because they have lower values and from the 11th harmonic, the currents will have similar shapes. • dc-link inductance Ldc, between 0 to 10% p.u., Fig. 5 presents as an example the 11th harmonic current. • load, between 10% to 160% of nominal load. These harmonic currents are depicted with respect to ac- and The results are the harmonic currents up to the 50th harmonic. dc-link inductance at a load of 100%. Thus, based on the specified assumptions the harmonic One can note the existence of 2 zones, namely the common- currents can be expressed depending on these three input and the spreading-zone. In the common-zone the currents are parameters. following the same curve and can be well fitted by an analytical expression, based on an average method, a least IV. DATA ANALYSIS square method or even using polynomial coefficients. As initially mentioned the toolbox uses for estimating the The spreading-zone is due to the low values of the ac- and current harmonics a look-up table method. Therefore all dc-inductance, highly dependent on the value of the dc-link harmonic data have to be achieved in advance. This can be inductance when the phenomenon of discontinuous done in two steps, an individual ASD analysis followed by a conduction mode appears. Fig. 7 details the spreading-zone system aggregation analysis. when the values of the ac- and the dc-inductance are smaller than 1%. The currents cannot be fitted anymore with one A. Individual analysis single curve, instead each current may be linearized and simple expressions can be used for each. This section evaluates the line-side harmonic current 40 emission of single ASD, as a function of the prior established 35 Spreading input parameters. The study is initially made with the load zone 30 value set to 100%, expressing the harmonic currents as a function of Lac and Ldc. Then the load variation is considered 25 Ldc=0% i11/i1 [%] and further harmonic dependencies are investigated. 20 Ldc=1% An example is shown in Fig. 4, which gives the level of the 15 Ldc=2% 5th harmonic current (expressed in percentage of the 10 fundamental current). Since this only shows the harmonic with Common a load value of 100% the amount of data will be significant 5 Ldc=10% zone when the load varies within the span from 10% to 160%. 0 0 5 10 15 20 25 Lac [%] Fig. 5. Simulated 11th harmonic current dependence on ac- and dc-link inductance at 100% load. 90 80[%] 80 60 70 50 Ldc=0% 60 i5/i1 [%] i5/i1 i11/i1 [%] 40[%] 40 50 Ldc=0.2 35[%] Levels [%] 30[%] 30 40 Ldc=0.4 25[%] 20[%] % 30 20 Ldc=0.6 15[%] % 20 Ldc=0.8 0 10 % ] Ldc=1% [% 10 5 c 0 0.2 0.4 0.6 0.8 1 Ld 0 5 10 10 15 20 25 Lac [%] Lac [%] Fig. 6. Simulated 11th harmonic current when Lac and Ldc are smaller than 1% Fig. 4. Three-dimensional view of the 5th harmonic current at 100% load. versus Lac and Ldc in the ASD at 100% load. 1630 14 Ih [%] Legend: Ih max Simulated harmonic currents Maximum value of 12 Estimated harmonic currents the harmonic current k 10 Load Ldc=0% 10% i5/i1 [%] 8 I(0,Ldc) 20% Average vector 6 I(Lac, Ldc) (1-k) Iavg (0) 40% 4 60% α 100% 80% Iavg (1) Load 180% Iavg (2) 2 0 Lac 1 2 Lac [%] Fig. 7. Analytical expression found for the higher harmonic current, 0 0 5 10 15 20 25 Lac [%] starting with the 11th harmonic. Fig. 8. Simulated and estimated 5th harmonic current This paper has found a convenient way to combine the with respect to the load variation. analytical approaches for both the spreading- and common- Even the harmonic currents are still expressed as a three- zone. Fig. 7 depicts the analytical representation. For Lac dimensional function (3), the database is reduced by storing higher than 1%, the 11th harmonic currents are fitted by the only two dependencies (Lac and Ldc) while the third one (the average curve (referred to as the average vector). load) being analytically reconstructed using (4) and (5). For Lac smaller than 1%, the dc-link inductance (Ldc) comes Fig. 8 provides a comparison of the simulated and estimated into an equation. Eq. (3) gives the value of 11th harmonic 5th harmonic currents. Solid lines represent the 5th harmonic currents when both Lac and Ldc are smaller than 1%. currents as a function of Lac and Load. Dashed lines represent I11 = I avg (1) + (1 − Lac )(1 − Ldc )(I h max − I avg (1) ) (3) the current estimation using (5) and the function of the current where: Iavg(1) is the first value of the average vector, depending on Lac at 100% load. The comparison reveals a Ih max is the maximum value among all currents, good approximation if the load is between 20% and 160% of Lac and Ldc are the ac- and dc-inductance. the nominal power which are values that practically cover Thus, the entire set of 11th harmonic currents is reduced to most cases. one point (the maximum value of the current) and one curve. In this way, the initial desire to keep minimum data for A simple estimate gives that the database was reduced up to storage and a simple implementation for analytical expressions 90% of the initial amount (ten curves are fitted only by the can be fulfilled, and simultaneously having the harmonic average vector curve). estimation at an acceptable accuracy. Even further minimization can be done using polynomial coefficients. The presented approach has the advantage of being compiled into one function. Then the function is identical for all B. Aggregation of the system higher harmonic currents due to the similarity of the shape. After estimating the harmonic currents in the individual Until now the load has had a value of 100%. As initially cases, the initial approach must be reconsidered. The initial established, the load also influence on (3) and consequently, intention of simply adding the harmonic currents from every the simulations should also include the load variation as well. ASD can not solve the problem, because the results obtained This will lead to a further increase of the database. only consider the drive connected alone to the power supply. For that reason, further effort has been done to compress (3) Typically, many ASD's are connected to the same line. even more. This can be achieved if studying the effect of the Therefore, a correction factor should be considered due to the load variation on the harmonic levels. parallel connection. The correction factor is related to the It was noted that the load variation has the same effect as common section of the inductance (Lac) situated in front of the changing the Lac value into a new value, correlated with the ASD's. new load. Changing the per-unit base calculation of Lac will The investigation is done considering one drive as the give this correlation by calculating the base impedance and Lac analyzed drive, and then simulations are performed to record as (4), (5). the harmonic evolution of this, when another drive is Z base ( nom ) (4) connected in parallel. U2 2 U nom Z base ( new) = nom = = A simplified toolbox diagram of parallel-connected drives is Pnew Pnom ⋅ Load Load shown in Fig. 9. Under the assumption that the linear load Lac ( new) = Lac ( nom ) ⋅ Load (5) does not contribute to the harmonic content, it is eliminated where: Unom is the nominal voltage of the drive, from the diagram leaving the drives alone to share the cable Load is the new load of the drive, in percentage, and transformer impedance. Pnom and Pnew are the nominal power and the new power, The drive analyzed for harmonics is denoted by P1, while Pn-1 Zbase(nom), Zbase(new) are base of the impedance at Pnom, Pnew stands for all other parallel drives. They both share the same Lac(nom), Lac(new) are per-unit ac-inductances. ac-inductances in front (transformer and cable). 1631 Drives 10 ASD 1 Panel P1 9 Lac=0.5% ih 8 Transformer ASD 2 ih ex , er Cable ih 7 Grid ASD 3 6 KLac Lac=1% ih Pn-1 5 Lac=2% ASD n 4 Lac=3% ih 3 Fig. 9. Diagram of the parallel connection of ASD. P1 is the drive under 2 investigation and P2, P3… Pn are grouped into a generic drive Pn-1. Lac=8% 1 The diagram presented in Fig. 9 can be reduced to a new -1.5 -1 -0.5 0 0.5 1 log10(Pn-1/P1) 1.5 2 2.5 3 3.5 equivalent diagram, by grouping the drives into a generic Pn-1 Fig. 11. Compensation characteristics for Lac due to the parallel connection of drive, as suggested by the dashed line. ASD's. This paper investigates the harmonic changes of the analyzed drive P1 when the power drawn by Pn-1 varies. By conducting a • The THDi of the P1 in the stand-alone case (referred to as series of simulations, the study concludes that the rating of the standalone-THDi) was obtained with respect to the ac- Pn-1 influences the P1 harmonic emission. inductance (Lac). Simulations have been run, independently changing: • Then, the focus is to get the value of the ac-inductance, • ac-reactance Lac, between 0% to 25% p.u., which gives the same effect in harmonic distortion as the • Pn-1 power, between 0.1 to 2000 times the power of P1. parallel connection. This can be done using both It is worth to mention, that for all simulated cases, the P1 characteristics, stand-alone-THDi and parallel-THDi, to drive had no change in parameter values (load, nominal obtain a function of Lac vs. Pn-1/P1. power, component values, etc.). • The last step is to normalize this function in order to obtain a The simulations gave the value of the harmonic currents. multiplication (compensation) factor for the ac-inductance. Furthermore, as an overall index on the harmonic changes, the The compensation factor is shown in Fig. 11. Total current Harmonic Distortion (THDi) has been computed. To find the compensation factor for a given case it is just as The results are displayed in Fig. 10, and represent the THDi of simple as establishing the power ratio of the considered drive the drive P1, with respect to the power ratio (the ratio of Pn-1/P1 and the value of the ac-inductance situated in front of the drive. powers). By using the curves in Fig. 11, the correction factor is found, Even no changes have been done in the P1 parameters, the which then is multiplied with the value of the ac-inductance results show that the harmonic content of the P1 changes (Lac) to obtain the new value of the Lac. The new value is then because of the influence of the parallel drive. This conclusion used to retrieve the harmonic currents from the databases leads to the idea of reevaluating the harmonic values obtained stored in the individual simulations. in the stand-alone simulations with a compensation factor due The conclusion of this study is that when several drives are to the parallel connection. The compensation factor is connected in parallel, a reciprocal influence appears between correlated with the value of the Lac-inductance. each other because of sharing the same transformer and line The development of the compensation factor is done by: impedance. This influence decreases the harmonic currents • The THDi from P1 in the parallel connection (referred to as compared to those calculated in the stand-alone case. parallel-THDi) was obtained with respect to the power ratio However, a compensation factor can be found to correct the Pn-1/P1. current values, allowing a superposition principle finally to be 45 Lac=0.5% applied. 40 35 V. TOOLBOX IMPLEMENTATION Lac=1% 30 The goal is to obtain a practical harmonic toolbox. Based on THDi [%] Lac=2% 25 Lac=3% the selected simulation parameters, the implementation only Lac=4% cares about choosing the right inputs for the toolbox to have a 20 practical relation (i.e. nameplate numbers rather than catalog 15 datasheets). Lac=8% 10 The inputs to the toolbox are: • the transformer data consists of nominal power, short- 5 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 circuit impedance and secondary voltage, • cables are characterized by length, material and number of pairs, log10(Pn-1/P1) Fig. 10. Simulated THDi of the P1 drive • the linear load is defined by linear power and cos(ϕ), as a function of power ratio and ac-inductance. 1632 • drives are characterized by the nominal power, load and B. Harmonic calculation harmonic mitigation solution (ac-inductors, dc-coils, The harmonic calculation starts by calculating the harmonic filters, etc.). currents from each drive, then by summing all specific The electrical diagram used for toolbox implementation is harmonic currents at the panel point, the calculation is shown in Fig. 12. Linear Load extended upstream to the transformer towards grid connection. PCC The harmonic currents calculation are performed as: Plin • the total ac-inductance is evaluated by summing the cable Transformer cos(ϕ) Drives and transformer inductances, Cable Trafo-Bus Grid ex, er Qsvc Panel Drive 1 • the ac-inductance (Lac) is expressed in per-unit basis of ih ΣPLoad ih ih each drive, vh vh Drive 2 Cable Bus-Panel ih • based on the power ratio (the ratio between powers of the ih Drive 3 current drive and the sum of the others) a correction factor vh vh ih is applied to the Lac value due to the parallel influence, • based on the value of Lac and other ASD’s parameters, an Drive n individual harmonic current assessment is performed by ih Fig. 12. Electrical diagram used for harmonic toolbox implementation. retrieving the currents from internal databases, • the harmonic currents at the PCC are calculated by In the implementation, there are two calculation flows, one to summing the individual currents coming from the drives, compute the fundamental current and one to compute the • different harmonic related indices are evaluated, i.e. THDi, relative harmonic currents at different points. For the TDD, PWHD, etc. fundamental current the calculation flow is from the Knowing the harmonic currents and cable impedance, next transformer to the drives. For the harmonics the calculation steps are to compute voltage drop and total harmonic voltage flow has the opposite direction, meaning from the drives to the distortion, which can easily be done [7], [8]. transformer. VI. TOOLBOX VERIFICATION A. Fundamental current In the final toolbox - Danfoss VLT MCT 31 harmonic A load-flow calculation can do the determination of the calculation - the Matlab code has been compiled into a voltages and currents in a power system network. The basic dynamic link library (DLL) and is called by a user friendly schematic is displayed in Fig. 13. graphical interface as shown in Fig. 14. It should be P LIN mentioned that despite that the toolbox is designed for Power flow P1, Q1 cos( ϕ ) calculation with Danfoss ASD's only (both with 6-pulse and harmonic filters) it is also possible to make the calculations I2 PCC with non-Danfoss ASD's as long the drive parameters are Q SVC Cable known. Furthermore, all internal results are written out to a R1 X1 harmonic analysis report in Rich Text Format. ΣP DRIVES V1 V2 In order to determine the accuracy of the approach, the ΣQ DRIVES toolbox has to assure similar results as real measurements. Good validations have been shown when comparing Fig. 13. Load-flow electrical diagram for harmonic toolbox calculation. simulated and a real case current in the time-domain. Knowing the active and reactive power (denoted by P1 However, since the target is to validate both, the acquired respective Q1 in Fig. 13) and also the cable impedance database and the implemented algorithm, validation with real (denoted by R1 and X1), the problem is reduced to a simple applications are a must. equation. The equation of voltage drop is given by: R ⋅ P + X 1 ⋅ Q1 (6) ∆V = V2 − V1 = 1 1 V2 This turns to be a quadric equation that has a solution as: 1 (7) V2 = V1 + V1 − 4(R1 ⋅ P + X 1 ⋅ Q1 ) 2 2 1 The current drawn can then easily be computed as: S (8) I2 = 1 3V2 The algorithm for the fundamental voltages and currents is continued sequentially up to the drives connection point (panel point in Fig. 12). Fig. 14. Graphical interface from the harmonic toolbox. 1633 The first tests were conducted with a programmable power VII. CONCLUSIONS supply (in order to get pure sinusoidal voltage) and a Danfoss This paper presents a new harmonic calculation toolbox, VLT 5032 (32 kVA). The drive were connected to the power which can be used for designing new and existing installations supply through a 30 m cable (100 mm2) and a 256 µH with ASD's. inductance simulating a 122 kVA transformer with 6.1% short The main focus has been on a table-based method that can be circuit impedance. The supply was set to 400 V nominal put into a toolbox. In a context of practical use to estimate the voltage and 50 Hz frequency. harmonic distortion in a given industrial application by e.g. a In this particular case all relevant data are exactly known and sales engineer, the table-based model has the advantages of the supply voltage is programmed to be a pure sinusoidal easy implementation into a spreadsheet format. voltage. The toolbox calculations are therefore as expected However, several analytical expressions can reduce the "table very close to the actual measurements as shown in Table I. dimension" and can provide an efficient way to be compiled Another test is on a real application, which is a water into a stand-alone PC-software application. pumping station with only a single ASD, as it can be seen in Finally, the approach is validated by real measurements with Fig. 15. Typical for an application like this, only limited data satisfactory results. are available. The supply transformer has a nominal power of 200 kVA with an impedance of 5%. The cable between the REFERENCES transformer and the ASD is approximately 10 m. The input power of the ASD is measured to 48 kW. The dc-link [1] W. F. Ray, “The Effect of Supply Reactance on Regulation and Power Factor for an Uncontrolled 3-Phase Bridge Rectifier with a Capacitive inductance is approximately 3%, while the value of the dc-link Load”, IEE Conf. Publ. No. 273, 1986, pp. 523-526. capacitor is 26.5%. [2] W. F. Ray, R. M. Davis, I. D. Weatherhogg, “The Three-Phase Bridge Table II compares the actual measurements with the results Rectifier with Capacitive Load”, IEE Conf. Publ. No. 291, 1988, pp. of the toolbox. Furthermore harmonic currents and voltages 153-156. are displayed, as results of toolbox calculation, in Fig. 16. [3] M. Grötzbach, “Line Side Behavior of Uncontrolled Rectifier Bridges with Capacitive dc Smoothing”, Proc. of EPE Conf., 1989, pp. 761 – 764. [4] M. Grötzbach, T. Strasser, L. Lorenz, “Line Side Harmonics of Three- phase Current Controlled Rectifiers in Continuous and Discontinuous Operation Mode”, Proc. of EPE Conf., 1993, pp. 707-712. [5] S. Hansen, P. Nielsen, F. Blaabjerg, ”Harmonic Cancellation by Mixing Non-linear Single-phase and Three-phase Loads”, IEEE Trans. on Industry Applications, Vol. 36, No. 1, 2000, pp. 152 - 159. [6] S. Jeong, J. Choi, “Line Curent Characteristics of the Three-Phase Uncontrolled Rectifiers under Line Voltage Unbalance Conditions”, IEEE Trans. On Power Electronics, Vol. 17, No. 6, 2002, pp. 935 – 945. Fig. 15. Circuit diagram of the water pumping station with ASD. [7] S. Hansen, “Harmonic Distortion of Rectifier Topologies for Adjustable Speed Drives“ Ph.D. dissertation, Aalborg University, Institute of Energy Technology, 2000, ISBN 87-89179-37-4. Table I. Comparisons of Table II. Comparisons of measurements and toolbox results measurements and toolbox results [8] S. Hansen, P. Nielsen, P. Thøgersen, “Harmonic Distortion and in laboratory conditions. in the water pumping station case. Reduction Techniques of PWM Adjustable Speed Drives – A Cost Benefit Analysis”, Proc. of NORpie Conf., 2000, Aalborg, Denmark, Harmonic Measured Toolbox Harmonic Measured Toolbox pp. 271-277. order h [%] [%] order h [%] [%] i5 35.4 33.6 i5 32 29.3 [9] D. E. Rice, “A Detailed Analyze of Six-Pulse Converter Harmonic i7 14.2 14.3 i7 13.8 12.6 Current”, IEEE Trans. on Industry Applications, Vol. 30, No. 2, 1994, THDi 39.6 38.3 THDi 37 33.6 pp. 294-304. v5 2.4 2.3 v5 2.1 1.9 [10] IEEE Std 519-1992 “IEEE Recommended Practice and Requirement for v7 1.3 1.4 v7 1.2 1.1 Harmonic Control in Electrical Power Systems“, IEEE, 1993, ISBN 1- THDv 3.9 3.8 THDv 4.2 3.3 55937-239-7. [11] N. Mohan, T. M. Undeland, W. P. Robbins, ”Power Electronics”, John Willey & Sons, 1995, ISBN 0-471-30576-6. [12] M. Sakui, H. Fujita, “An Analytical Method for Calculating Harmonic Currents of a Three-Phase Diode-Bridge Rectifier with dc Filter”, IEEE Trans. on Power Electronics, Vol. 9, No. 6, 1994, pp. 631-637. [13] Y. Baghzouz, “An Accurate Solution to Line Harmonic Distortion Produced by ac/dc Converters with overlap and dc-ripple”, IEEE Trans. on Industry Applications, Vol. 29, No. 3, 1993, pp. 536 - 540. [14] M. Grötzbach, M. Bauta, R. Redmann, “Line Side Behavior of Six- Pulse Diode Bridge Rectifiers with AC-side Reactance and Capacitive load”, Proc. of Power Quality Conf., 1995, pp. 525-534. [15] S. Hansen, L. Asiminoaei, F. Blaabjerg, ”Simple and Advanced a) b) Methods for Calculating Six-Pulse Diode Rectifier Line-Side Fig. 16. Toolbox harmonic results in water pumping station case. Harmonics”, Proc. of IAS'03, 2003, Vol. 3, pp. 2056-2062. a) Harmonic currents. b) Harmonic voltages. 1634

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