Analysis of Overvoltage and its Mitigation in Long Cable PWM Drives using Distributed-Parameter Representation

Analysis of Overvoltage and its Mitigation in Long Cable PWM Drives using Distributed-Parameter Representation Thiago F. L. Milagres, Alessandro F. Moreira, Wallace C. Boaventura Departamento de Engenharia Elétrica, UFMG. Belo Horizonte - MG - Brasil Tel: +55 (3) 3499-484 Email: moreira@cpdee.ufmg.br Abstract This paper presents a power cable modeling using multi-conductor transmission line with distributedparameter representation, with frequency-dependent parameter, to be employed in the overvoltage phenomena analysis. The P SCAD/EMT DC c software is utilized to implement the simulation models. A distributed-parameter representation of the power cable is used to analyze the overvoltage phenomenon in PWM drives and its mitigation by the use of passive filters. Two types of filters are implemented at the inverter output: reactors and RLC filters. Both overvoltage and common-mode current transients are analyzed for a hp drive system with m power cable length. Analysis of the overvoltage in medium voltage drives and its mitigation are also included. Experimental results come along with the simulated ones showing the suitability of the models. Index Terms Industrial Drives; Electrical Drive Systems Design and Applications; Overvoltage and DV/DT Filter Design I. INTRODUCTION As the technology has progressed in the application of pulse width modulation (PWM) inverters over the past decade, the switched-power devices used in these inverters also have been greatly improved, resulting faster switching rates. Moreover, in several industrial plants the cable connecting the converter and the machine may have a length of some hundreds of meters, resulting in problems both in the converter and in the machines, such as the overvoltage phenomena [], [], [3], [4], [5]. This paper focus on the representation of the power cable to analyze the overvoltage phenomena in long cable PWM drives and their mitigation, using passive filters. In previous work, the multi-conductor transmission line using distributed parameter representation has successfully analyzed the overvoltage phenomena [6]. Herein, the power cable model implemented in P SCAD/EMT DC c package takes into account the frequency dependence of its parameters by the proper modeling of the characteristic admittance Y c (ω) and the propagation function A(ω) in the phase domain. The model is utilized to analyze the response of passive filters, such as RLC filter and reactors, placed at the inverter output to minimize the overvoltage at the motor terminals. This is a relevant aspect because allows one to study the overvoltage and its mitigation approaches through simulation. Another goal of this paper is to analyze the characteristics of the common-mode current, which generally circulates through grounding cables and may cause machine bearing failures and electromagnetic interference at the drive and at other equipments nearby. The simulation model is very useful to predict the amplitude of these types of currents and its attenuation by the application of the passive filters. This paper will present a detailed description of the computational model and simulation results of overvoltage and common-mode currents in a hp drive with m power cable length. Experimental results are also presented demonstrating the suitability of the multi-conductor transmission line using distributed parameter modeling. The overvoltage analysis and its mitigation are extended to a medium voltage drive (46V/3A) using the aforementioned computational model. Selected simulation results come along demonstrating the suitability of the models. II. DISTRIBUTED-PARAMETER REPRESENTATION OF THE CABLE An accurate cable line model must take frequencydependent parameters into account. In the frequency domain, a cable line is completely characterized by the characteristic admittance Y c (ω) and the propagation function A(ω), where ω is the natural frequency. A transformation matrix T (ω) derived from eigenvalue/ eigenvector theory is used to obtain Y c (ω) and A(ω) in the modal-domain or phase-domain. Thus, the study of overvoltage phenomena in long cable PWM drives is best done using multi-conductor transmission line with distributed (frequency-dependent) parameter representation. This model should be used whenever the studies require a very detailed representation of the cable over a wide frequency range. Frequency dependent models can be solved using modal techniques or using more advanced phase-domain model techniques [7], [8]. The modal-domain cable line models were implemented in many EMTP-type programs (ATP, EMTP and EMTDC) [9]. This class of models uses real-constant transformation matrices to avoid numerical convolutions in the phase-modal and modal-phase domain transitions, saving substantial computational time when computing electromagnetic transients in multiphase systems. This line model is suitable for symmetrical transmission line configuration. However, for asymmetrical lines and underground cables, the frequency dependence of the modal transformation matrix may be strong and should

be taken into account. The transformation matrix elements are approximated by rational functions in the frequency domain leading to additional convolutions in the time domain. These elements have to be entirely evaluated over a wide frequency range, which is best done avoiding the eigenvectors switchovers []. Most of the cable models used in the EMTP programs has its roots in the modeling of overhead transmission lines, and can be divided into two categories: Lumped-parameter models - consist of multiphase coupled pi-circuit, where R, L, C and G are calculated at a given frequency. Distributed-parameter models - take into account the intrinsic characteristics of the cable, and are based on traveling wave theory. For the drive systems analyzed in this paper(low and Medium Voltages Drives, LVD and MVD respectively), the power cables connecting the inverter-motor have a length of meters and the voltage pulse has a rise time equal to τ = 7 ns (LVD) and τ =.7 µs (MVD). Thus, the model should represent frequencies up to /τ = 5.9 MHz (LVD) and /τ =,59 MHz (MVD). The signal wavelength is λ 5 meters (LVD) and λ 5 meters (MVD). Considering lumpedparameter models, in order to represent with good accuracy the voltage transients, the cable length should be smaller than ten times the wavelength []. In addition, in Power Electronics applications, due to the harmonic produced by the inverter, a model which takes into account the frequency dependence of its per-unit length parameters is preferable for modeling such applications. Figure shows the voltage pulse waveforms at the inverter and motor terminals measured for the low voltage drive. It can be noticed the travel time between the two voltage pulses and also the damping and distortion effects in the motor terminal voltage. In such cases, lumped parameters model is not suitable to represent the voltage pulse propagation effect and then distributed-parameter model is chosen. 9 8 7 6 5 4 3 Line to Line inverter and motor terminal No Filter Line to Line Inverter Terminal Line to Line Motor Terminal 3 4 5 6 7 8 Fig.. Voltage at the inverter and motor terminals for hp drive with m cable length. Voltage pulse rise time: 7 ns. DC bus voltage: 53 V. x 6 III. ANALYSIS OF THE OVERVOLTAGE AND ITS MITIGATION IN LOW VOLTAGE DRIVES The distributed-parameter representation of the power cable to study the overvoltage phenomena is implemented using the P SCAD/EMT DC c. This package is primarily used for simulating the electromagnetic transients in electrical systems, including the study of overvoltage problems in long cable PWM drives. The following describes the implementation of the hp motor drive system to study the overvoltage phenomena at the motor terminals: The voltage source is modeled as three phase-to-ground voltage steps, with a rise time of 7 nanoseconds, to generate a line-to-line voltage of 53 V. The power cable is modeled as a four non-shielded (.5mm )coupled cables. Inner conductor electrical characteristics and cable geometry are as following: External diameter of each wire:.5 cm; Thickness of the wire insulation:.7 cm; Conductor resistivity:.7 x 8 Ωm; Conductor relative permeability: ; Wire insulator relative permittivity:.; Wire insulator relative permeability: ; Ground resistivity: Ωm; The motor input impedance is modeled using the same lumped-parameter model from previous works [], [3], [4]. Figure presents a schematic of the system simulated using the P SCAD/EMT DC c, showing the three-phase voltage source, the four wire power cable and the high frequency model of the motor input impedance. Several simulations were conducted and selected results are presented here. Figure 3 shows the overvoltage waveforms for a hp drive with m power cable length. Line-toline motor terminal voltages are shown for both simulation and experimental results. Figure 4 shows the common-mode currents waveforms for both simulation and experimental results. One can verify that almost double DC bus peak voltage appears at the motor terminals as expected and close to A common-mode current peak flows in the system. The simulation results has reasonable accuracy comparing with the experimental ones. The discrepancies between them appears mainly because of inaccuracies in the motor input impedance representation. The following figures show the results obtained when the passive filters are utilized. One approach is to place a RLC filter at the inverter output (Figure 5). This type of filter has demonstrated to be a successful solution for both overvoltage and common-mode currents problems in long cable PWM drives [5], [6]. Figure 6 shows overvoltage waveforms at the motor terminals when a RLC filter is applied. One may notice that the overvoltage is reduced from 8 to % of the DC bus voltage. Figure 7 shows both simulated and experimental results for the common-mode currents. It can be verified that about 5%

. Eag Eabf C sim-cabo C sim-cabo Eal Eab 55.. C C R=. Ebg Ebcf Ecaf C3 C3 Ebl Ebc Eca 55. R=. Ecg I_cm C4 C4 Ecl..e-5 R= 55. sim-cabo. 7.73. 3..74 3..74 3..74 Fig.. Schematic of the motor drive system simulated in PSCAD / EMTDC c. 8 Line to line motor terminal voltages No Filter FROM INVERTER L L TO CABLE TERMINALS 6 4 L R R R C C C..4.6.8..4.6.8 x 5 Fig. 5. Schematic of the RLC filter placed at the inverter output. 8 6 4..4.6.8..4.6.8 x 5 Fig. 3. Overvoltage waveforms for a hp drive with m cable length. Voltage pulse rise time: 7 ns. DC bus voltage: 53 V. Upper plot: simulation. Bottom plot: experimental. Common Mode Current No Filter Simultaion Results..4.6.8..4.6.8 x 5..4.6.8..4.6.8 x 5 Fig. 4. Common-mode currents waveforms for a hp drive with m cable length. Voltage pulse rise time: 7 ns. DC bus voltage: 53 V. Upper plot: simulation. Bottom plot: experimental. attenuation in the magnitudes of the common-mode currents are obtained. Figure 8 and 9 show respectively the overvoltage and common-mode currents waveforms when pu reactors are connected at the inverter output. One may verify that the dynamic response of the line-to-line voltage is much better with the use of RLC filters comparing to reactors, although the amplitudes of the common-mode currents are lower when reactors are used. IV. ANALYSIS OF THE OVERVOLTAGE AND ITS MITIGATION IN MEDIUM VOLTAGE DRIVES The analysis of the overvoltage was also conducted for a Medium Voltage Drive using the P SCAD/EMT DC c software. The system configuration is the following: A 5 cv PWM drive, IGBT with rise time of.7 µsec; A three-phase power cable F icapep DRY, x95 mm, 6/ kv, Copper HWPR ST NBR 785 3, length of 5 meters; 5 cv induction motor (46V/88A). The simulation results were obtained for the following conditions: i) without any type of filter; ii) using reactors at the inverter output; iii) using RLC filters at the inverter output. The computation model was very useful to predict both overvoltage and DV/DT at the motor as well as to get a first approach of the DV/DT filter. The medium voltage system was modeled following the same procedure of the low voltage drive modeling of the previous section with the following modifications: The voltage source is modeled as three phase-to-ground voltage steps, with a rise time of.7 µsec, to generate a phase-to-ground voltage of 3 kv. The cable cross section representation is shown in Figure, where the dimensions are in millimeters. Table I

TABLE I ELECTRICAL CHARACTERISTICS OF THE POWER CABLE. Radius (m) Resistivity (Ωm) Relative Permeability (µ r) Relative Permitivity (ɛ r) Conductor.67.7x 8 Insulation.49.8 Armour.59.7x 8 Insulation.785.6 8 Line to line motor terminal voltages RLC Filter 8 Line to line motor terminal voltages Reactor Filter 6 6 4 4..4.6.8..4.6.8 x 5.5.5.5 3 3.5 4 4.5 5 x 5 8 8 6 6 4 4..4.6.8..4.6.8 x 5.5.5.5 3 3.5 4 4.5 5 x 5 Fig. 6. Overvoltage waveforms for a hp drive with m cable length. RLC filter at the inverter output: R filter = 4 Ω; L filter = µh; C filter = 8 nf. Voltage pulse rise time: 7 ns. DC bus voltage: 53 V. Upper plot: simulation. Bottom plot: experimental. Common Mode Current RLC Filter Fig. 8. Overvoltage waveforms for a hp drive with m cable length. pu reactor at the inverter output. Voltage pulse rise time: 7 ns. DC bus voltage: 53 V. Upper plot: simulation. Bottom plot: experimental..5 Common Mode Current Reactor Filter.5.5..4.6.8..4.6.8 x 5.5.5.5.5 3 3.5 4 4.5 5 x 5.5.5.5..4.6.8..4.6.8 x 5.5.5.5.5 3 3.5 4 4.5 5 x 5 Fig. 7. Common-mode currents waveforms for a hp drive with m cable length. RLC filter at the inverter output: R filter = 4 Ω; L filter = µh; C filter = 8 nf. Voltage pulse rise time: 7 ns. DC bus voltage: 53 V. Upper plot: simulation. Bottom plot: experimental. Fig. 9. Common-mode currents waveforms for a hp drive with m cable length. pu reactor at the inverter output. Voltage pulse rise time: 7 ns. DC bus voltage: 53 V. Upper plot: simulation. Bottom plot: experimental. shows the power cable electrical characteristics. The motor input impedance is modeled using the same lumped-parameter model that was utilized in previous works and also for the low voltage analysis. The model parameters were adjusted to represent the 5 cv induction motor, which schematic is shown in Figure. Selected simulation results are presented as follows. Figures and 3 shows respectively the overvoltage and the DV/DT at the motor as a function of the cable length. One can verify the necessity of the DV/DT filter to reduce such stress in the motor. Two types of DV/DT filter, with the same configuration as in low voltage analysis, were analyzed and selected simulation results are presented in the following figures. Figures 4 and 5 shows respectively the overvoltage and the DV/DT at the motor when a three-phase reactor is placed at the drive output. One can observe that it is possible to reduce the overvoltage to.5 pu ( pu =.85 kv) and the DV/DT to V/µsec. However, a considerable reactor is necessary to accomplish

3 DV/DT in a 3kV / 3A Drive 95 9 85 8 DV/DT [V/µs] 75 7 65 6 55 Fig.. Cross section representation of the power cable FICAP EP- DRY x95 mm, 6/ kv, Copper HWPR ST NBR 785 3. Dimensions are in millimeters. Fig. 3. 5 5 5 5 3 35 4 45 5 55 Length [m] DV/DT in the motor as a function of cable length...9 Overvoltage x Lf Cable m Cable m Cable 3m Cable 4m Cable 5m Overvoltage [pu].8.7.6.5.4 3 4 5 6 7 8 9 Lf [µh] Fig.. Schematic diagram of the 5 cv induction motor. Legend: R=54Ω; R=4Ω; R3=5Ω; C=4 nf; C=4 nf; L= mh. Overvoltage in a 3kV / 3A Drive. Fig. 4. Overvoltage at the motor as a function of reactor numbers for various lengths of power cable. DV/DTt x Lf 8 Cable m Cable m 6 Cable 3m. 4 Cable 4m Cable 5m Overvoltage [pu].9.8.7 DV/DT [V/µs] 8 6 4.6 3 4 5 6 7 8 9 Lf [µh] Fig...5 5 5 5 3 35 4 45 5 55 Length [m] Overvoltage at the motor as a function of cable length. Fig. 5. DV/DT at the motor as a function of reactor numbers for various lengths of power cable. this task. Better results can be obtained by the use of the RLC filter. Similar simulation results are presented in Figures 6 and 7 when a RLC filter is used at the drive output. These figures shows respectively the reduction of the overvoltage and DV/DT stresses at the motor for various numbers of filter capacitors and power cable lengths, with fixed resistor and reactor filter elements. One can verify that much better results are attained with smaller reactive elements. V. CONCLUSIONS Analysis of the overvoltage phenomena was performed using a distributed-parameter representation of the power cable with the P SCAD/EMT DC c software, which is a better choice than the lumped-parameter representation when the

Overvoltage x Cf (R f =Ω L f =µh) DV/DT x Cf (R f =Ω L f =µh).65 Cable m 6 Cable m.6 Cable m Cable 3m 59 Cable m Cable 3m.55 Cable 4m 58 Cable 4m Cable 5m Cable 5m.5 57 Overvoltage [pu].45.4 DV/DT [V/µ] 56 55.35 54.3 53.5 5. 8 4 6 8 Cf [nf] 5 8 4 6 8 Cf [nf] Fig. 6. Overvoltage at the motor as a function of filter capacitor C f for various lengths of cable. R f = Ω and L f = µh. Fig. 7. DV/DT at the motor as a function of filter capacitor C f for various lengths of cable. R f = Ω and L f = µh. analysis includes very fast voltage pulse rise times and long cable drivers. The model was able to represent the overvoltage and common-mode current with good accuracy. The behavior of passive filters placed at the inverter output (Reactor and RLC filters) were also analyzed, demonstrating their suitability in the overvoltage mitigation and common-mode current attenuation. In all studied cases, low and medium voltage drives, the RLC filters have given better results in the overvoltage mitigation than the reactors. Some discrepancies still exist in the voltage and current waveforms comparing simulation and experimental results. The main reason is related to the model of the motor input impedance that was used in the computational program. In fact, the measurement of the motor input impedance is not straightforward, specially for medium voltage motors. The authors still work on this subject. A experimental analysis of passive filters in mitigation the overvoltage is being extended to medium voltage drives and the results will be published in the future. ACKNOWLEDGMENT The authors would like to thank the Laboratório de Aplicações Industriais of the Departamento de Engenharia Elétrica, UFMG, and WEG Automação S/A, which have supported this work. REFERENCES [] E. Persson, Transient effects in applications of pwm inverters to induction motors, IEEE Transactions on Industry Applications, vol. 8, no. 5, pp. 95, Sep/Oct 99. [] A. Bonnett, Analysis of the impact of pulse-width modulated inverter voltage waveforms on ac induction motors, IEEE Transactions on Industry Applications, vol. 3, no., pp. 386 39, March/April 996. [3] G. Skibinski, D. Leggate, and R. Kerkman, Cable characteristics and their influence on motor over-voltage, in IEEE Applied Power Electronics Conference and Exposition, vol., Atlanta, GA, USA, 997, pp. 4. [4] R. Kerkman, D. Leggate, D. Schlegel, and G. Skibinski, Pwm inverters and their influence on motor over-voltage, in IEEE Applied Power Electronics Conference and Exposition, vol., Atlanta, GA, USA, 997, pp. 3 3. [5] J. M. Bentley and P. L. Link, Evaluation of motor power cables for pwm ac drives, IEEE Transactions on Industry Applications, vol. 33, no., pp. 34 358, March/April 997. [6] T. F. L. Milagres, P. M. Santos, F. M. M. Panadés, and A. F. Moreira, Over-voltage analysis using multi-conductor transmission line with distributed parameter representation, in VI Induscon Conferência Internacional de Aplicações Industriais, Joinville, SC, Brasil, 4. [7] A. Morched, B. Gustavesen, and M. Tartibi, A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables, IEEE Transactions on Power Delivery, vol. 4, no. 3, pp. 3 38, July 999. [8] B. Gustavsen, Frequency-dependent transmission line modeling utilizing transposed conditions, IEEE Transactions on Power Delivery, vol. 7, no. 3, pp. 834 839, july. [9], Validation of frequency-dependent transmission line models, IEEE Transactions on Power Delivery, vol., no., pp. 95 933, April 5. [] A. B. Fenandes and W. L. A. Neves, Frequency-dependent transformation matrices for phase-domain transmission line models, IEEE Power Engineering Society Summer Meeting, vol. 3, pp. 78 787, July. [] A. E. A. de Araújo and W. L. A. Neves, Cálculo de Transitórios Eletromagnéticos em Sistemas de Energia. Editora UFMG, 5. [] A. Boglietti and E. Carpaneto, Induction motor high frequency model, in IEEE Industry Application Society Annual Meeting, vol., Phoenix, AZ, USA, 999, pp. 53 6. [3] A. F. Moreira, T. A. Lipo, G. Venkataramanan, and S. Bernet, Modeling and evaluation of dv/dt filters for ac drives with high switching speed, in 9th European Conference on Power Electronics and Applications (EPE ), Graz, Austria,. [4], High frequency modeling for cable and induction motor: Overvoltage studies in long cable drives, IEEE Transactions on Industry Applications, vol. 38, no. 5, pp. 97 36, Sep./Oct.. [5] A. von Jouanne and P. N. Enjeti, Design considerations for an inverter output filter to mitigate the effects of long motor leads in asd applications, IEEE Transactions on Industry Applications, vol. 33, no. 5, pp. 38 45, September/October 997. [6] A. F. Moreira, P. M. Santos, T. A. Lipo, and G. Venkataramanan, Filter networks for long cable drives and their influence on motor voltage distribution and common-mode currents, IEEE Transactions on Industrial Electronics, vol. 5, no., pp. 55 5, April 5.