Patrick M. Santos Fernando M. M. Panadés Thiago F. L. Milagres Alessandro F. Moreira Universidade Federal de Minas Gerais Departamento de Engenharia Elétrica Av. Antônio Carlos, 6627, Pampulha Belo Horizonte, MG, 327- Brazil Email: moreira@cpdee.ufmg.br Abstract Filter networks have been considered to solve the overvoltage problem at motor terminals in long cable drives. However, none research has been dedicated to analyze their influence in the drive control performance. In this paper, an assessment of an electric drive will be done to establish the real influence of this frequency filtering in the control performance. Results will be presented showing that RLC inverter output filter is a very good option to mitigate the overvoltage phenomena present in the long cable industrial electric drives with no drawbacks on the control performance. Index Terms Industrial Drives; Electrical Drive Systems Design and Applications; Control Systems Design and Performance; Over-voltage and dv/dt Filter Applications. I. INTRODUCTION With the semiconductor technology allowing the power devices to switch at high frequencies and high speeds, the bandwidth achieved by the power inverters has been increased and, with it, the control performance. So it s how special drives with unusual trajectories could be designed and implemented. But the main drawback of these improvements is the transmission line effect that appears in industrial drives, which concern drives with long cables connecting the inverters to the motors. Among the undesirable consequences is the overvoltage phenomenon. The over-voltage phenomenon in long cable PWM based drives is well known. Mainly there are two philosophies to minimize this kind of problem: one is to match the cable characteristic impedance to the motor input impedance and the other is to increase the pulse rise time at the inverter output, in such a way that the transmission line effect is controlled. The first philosophy concerns the filters placed at the motor terminals [], [2], [3], [4], [5], [6]. The other one, the filters at inverter output [6], [7], [8], [9], []. So the purpose of this paper is to introduce a simple analysis of the behavior of a PWM based inverter control system robustness when a RLC Filter is placed at the inverter output to mitigate the over-voltage at motor terminals [7]. In order to proceed with this analysis a drive will be designed and a controller tuned to a specified trajectory. Some points will be discussed then: A comparison between the simulation results with and without the filter in the drive, using the drive dynamic stiffness as the tool of analysis []; How filter presence and its parameters variation affect the drive dynamic stiffness; The difference between motor terminal voltage waveform with and without filter. II. THE ELECTRIC DRIVE AND CONTROL TUNING SPECIFICATION The general drive that will be analyzed is described bellow and it s control system block diagram can be seen at Figure 2. For the purpose of controller design and tuning the system considered is: ) A 2hp induction motor is fed by an PWM based Inverter. It is considered as the motor been driven in the rotor field oriented condition. So the machine model used is the one with rotor magnetic flux constant and aligned to the d-axis in its d-q model [2]. 2) A # 6 AWG 2m length cable connects the inverter to the motor; 3) A RLC Filter is placed at inverter output to increase the pulse rise time and perform a reduction in the overvoltage seen by the motor terminals; 4) The inverter control system consists of a proportional and an integral controller, where it s gains, respectively are b a, the virtual process stiffness, and K a, the virtual process damping []. The integrated position error is not considered since the inverter used didn t have this control option and the operation is set to the sensorless mode; 5) The break frequencies utilized to tune the controller are 5Hz and 5Hz for the velocity and position loops respectively, considering the cut frequency of inverter as been 5Hz; 6) The initial filter parameters are R f = 42Ω, L f =25µH and C f =76nF [7]. 7) The speed reference and the load torque are illustrated by Figure. The quantities are in p.u. and their basis are: 9rpm and 8.2N.m (the rated torque for the induction motor utilized). The speed error tolerance is ±5rpm (or.5%) for a /6Hz sinusoidal trajectory. III. DYNAMIC STIFFNESS OF THE ELECTRIC DRIVE WITH AND WITHOUT FILTER Based on the control system illustrated at Figure 2 and setting the speed reference to zero, the dynamic stiffness was found for the system without the RLC Filter (F (s) =). To this particular problem the dynamic stiffness is related to the speed, instead of position, since there is no position control loop.
Fig. 2: Control system considered for analysis TABLE I DRIVE PARAMETERS AND RLC FILTER PARAMETERS. Motor Parameters Mechanical Parameters Controller Gains R s R r λ r L m L s/l r J b R a b a K a 4.2Ω 5.5Ω.624Wb 358.8mH 378.52mH.66kg.m 2.334N.m.s 2Ω 24N.m.s 72N.m/rad Speed Ref. and Load Torque.8.6.4.2.2.4.6.8 Speed Reference and Load Torque (in p.u.) ω ref T L 2 4 6 8 2 4 6 8 2 Fig. : Speed trajectory for drive operation and load torque applied to the motor. K S = R r (6) L r λ r In the expression above the subscript n denotes normal system, that is, without filter and ˆK T is the estimated torque constant. In the dynamic stiffness for the system with the filter that is written bellow the subscript f is for denoting the system with filter. The expression is: DS f (s) = As5 + ˆK T γs 4 + Bs 3 + Cs 2 + Ds + K T R a K a ˆK T s[l sτ 2 r s 3 + Es 2 + Gs + H] (7) Where: A = ˆK T JL sτ 2 r (8) B = ˆK T (τ 2 r δ + τ sη + JL s ) (9) DS n (s) = T L(s) Ω(s) = J ˆK T L s s3 αs 2 βs K T R a K a ˆK T s(l ss + R a + R s + K V K S ) () Where: α = ˆK T [bl s + J(K V K S + R a + R s )] (2) β = ˆK T (K T K V + br s + bk V K S + br a )+K T R a b a (3) K T = 3PL mλ r 4L r (4) K V = L sλ r L m (5) C =(ˆK T τ s ζ + ˆK T η + K T R a b a τ s ) () D =(ˆK T ζ + K T R a b a τ s + K T R a b a ) () E = τr 2 (K V K S + R s )+L s τ s (2) G = τ s (K V K S + R s + R a )+L s (3) H = K V K S + R s + R a (4) γ = J(L s τ s + K V K S τr 2 + R sl f )+bl s τ r 2 (5)
δ = K T K V + b(k V K S + R s ) (6) η = J(K V K S + R s + R a )+bl s (7) 3 2.5 2 Speed Error Evolution for System without Filter ζ = δ + br a = K T K V + b(k V K S + R s )+br a (8) τ s = R f C f (9).5.5 τ 2 r = ω 2 r = L f C f (2) This dynamic stiffness was found utilizing: F (s) = Rs L + L f C f s 2 + Rs L + L f C f (2) It can be seen in Figure 3 that the dynamic stiffness doesn t vary when the filter is introduced. For details about the parameters values check the Table I. The lowest absolute value of the dynamic stiffness for both systems was 2.46 N.m/rad/s at about 6Hz. So, what is expected is that the speed error will be the same for both systems. This result, achieved through simulation, can be seen at Figures 4 and 5. 2 Comparison between the Dynamic Stiffness.5 2 4 6 8 2 4 6 8 2 Fig. 4: Speed error evolution for the system without filtering. 3 2.5 2.5.5 Speed Error Evolution for System with Filter Dynamic Stiffness (N.m/rad/s) 2 Frequency (Hz) Fig. 3: Comparison between the drive dynamic stiffness with and without the filter. This is easily explained by the fact that the poles introduced by the filter are in high frequencies. Frequencies much higher than the ones used by the inverter to promote the control over the induction motor. So the electrical dynamic of filter is much faster than the control effort dynamic promoted by the inverter. This inference is illustrated in the next section, where experimental results are presented, and permits one to foresee that the changing in filter parameters will not affect this performance. Any changes that could be made, in accordance to the filter designing philosophy introduced in previous works, would not take those poles near to the ones of the inverter controller loops [3], [7]..5 2 4 6 8 2 4 6 8 2 Fig. 5: Speed error evolution for the system with filtering. IV. EXPERIMENTAL RESULTS The load used in this case is a separately excited DC machine operating as a generator. This is an easy way of impose a load torque that always oppose to the trajectory desired. That is, the DC generator is a permanent disturbance applied to the motor operation. The DC machine torque constant was set to K φ =.7523Wb, so the current necessary to promote the load torque specified is I T =6.6A rms or I Tmax =9.35A. Obviously the rms value is due to the fact that the sinusoidal trajectory will produce alternating current at the generator. The tacometer used has this conversion function: V (ω) =.333 +.528ω (22) Where V is the voltage output from tacometer and ω is the mechanical speed in revolutions per minute. So the voltage generated to 9rpm is 45.8V. In Figures 6 and 7 one can see the speed (in Volts) developed by the motor and the current at the DC machine for both systems: with and without filter. None difference can be realized just looking at the figures. So
for really proving the results the Figures 8 and 9 are presented in the sequence. The speed error is the parameter of analysis in those figures. As expected there are no differences, regarding the control system response, when the filter is introduced in the electric drive circuit. This was also expected from the analysis of the dynamic stiffness comparison. There was no difference between then, indicating that the both drive dynamics should be equal. This was proved too. 5 5 5 Experimental Speed Error for System without Filter 2 25 3 2 4 6 8 2 4 6 8 2 Fig. 8: Experimental speed error evolution for the system without filtering. 3 Experimental Speed Error for System with Filter 25 2 Fig. 6: Induction motor speed (in Volts) and current at DC machine for system without filter. 5 5 5 2 4 6 8 2 4 6 8 2 Fig. 9: Experimental speed error evolution for the system with filtering. Fig. 7: Induction motor speed (in Volts) and current at DC machine for system without filter. However, the induction machine terminal voltage is drastically improved, as one can note at the Figures and. The overvoltage is about % of inverter bus voltage as calculated by the simulation program and the abacus used before [3]. The overvoltage at motor terminals and the multi-reflection phenomenon at the inverter output were controlled and the inverter control performance was maintained intact. It is good to emphasize that the multi-reflection phenomenon is very undesirable once it may cause semiconductor switches failure, since the power dissipated will increase with the about V more that appear at the inverter output every switching period. It is obvious that the overall electric drive power consumption will increase too, but in some systems a failure leads to a great spent of time and money, justifying the usage of the filter. The expenses with a break are more expressive than the energy additional costs introduced by the filter usage. V. CONCLUSIONS It could be seen in this paper that the control performance of an inverter is not affected by the filtering process introduced by filters used to mitigate the overvoltage present at long cable drives. The drive parameters are set to filter the very high frequencies, but not those ones responsible for the control of the induction machine. The filter acts in the inverter output pulses, making them more adequate to travel along the cable without causing all the overvoltage seen in the system without it. But the frequencies cut by the filter are much higher than the ones used to control the motor.
Voltage (V) 6 5 4 3 2 Inverter Output and Motor Terminal Voltages without Filtering much energy). So the recommendation of using the RLC Filter at the inverter output in an long cable electric drive is reinforced after the analysis that took place in this paper. Beyond producing a very good result in the overvoltage mitigation, it did not interfered in the inverter control performance. ACKNOWLEDGMENT This research work has been supported by the following entities: LAI (Laboratório de Aplicaçoes Industriais) at UFMG- DEE/Brazil and WEG Indústrias S/A - Automação...2.3.4.5.6.7.8.9 x 5 Fig. : Inverter output and induction machine terminal voltages without filtering. Voltage (V) 35 3 25 2 5 5 Inverter Output and Motor Terminal Voltages with Filtering..2.3.4.5.6.7.8.9 x 5 Fig. : Inverter output and induction machine terminal voltages with filtering. Regarding the dynamic stiffness boarding, the control performance behavior is explained by the fact that the poles introduced by the filter are in very high frequencies making its dynamics much faster than the drive control one. Although it was not showed, it is easy to see that the parameters variation, obeying the design process presented before, will not affect this last conclusion. If so, the filter have lost its desired characteristics and its purpose is any different one, but mitigate the overvoltage in an optimal way (remembering that several sets of filter parameters are able to produce significant overvoltage reduction, but consuming too REFERENCES [] R. Kerkman, D. Leggate, and G. Skibinski. Interaction of Drive Modulation & Cable Parameters on AC Motor Transients. In IEEE Industry Application Society Annual Meeting, volume, pages 43 52, San Diego, CA, USA, 996. [2] G. Skibinski, R. Kerkman, D. Leggate, J. Pankau, and D. Schlegel. Reflected Wave Modeling Techniques for PWM AC Motor Drives. In IEEE Applied Power Electronics Conference and Exposition, volume 2, pages 2 29, USA, 998. [3] M. T. Tsai. Efficient Technique for Suppression of Motor Transient Voltage. IEEE Transactions on Aerospace and Electronic Systems, 39(2):49 59, April 23. [4] Deng Wen, L. V. Chuan, Jiang Jianguo, Huang Lipei, and Tamai Shinzo. Filter Design of Restraining Over-Voltage and Bearing Current in Induction Motor Fed by PWM Inverter. In IEEE Industrial Electronics Society Annual Conference, USA, 22. [5] B. Bolsens, K. De Brabandere, J. Van den Keybus, J. Driesen, and R. Belmans. Filter Design of Restraining Over-Voltage and Bearing Current in Induction Motor Fed by PWM Inverter. In IEEE International Electric Machines and Drives Conference, volume 3, pages 866 872, USA, 23. [6] S. Lee and K. Nam. Overvoltage Suppression Filter Design Methods Based on Voltage Reflection Theory. IEEE Transactions on Power Electronics, 9(2):264 27, March 24. [7] 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. In IEEE Industrial Electronics Society Annual Conference, Roanoke, USA, 23. [8] T. G. Habetler, N. Rajendra, and T. A. Nondahl. Design and Implementation of and Inverter Output LC Filter Used for DV/DT Reduction. IEEE Transactions on Power Electronics, 7(3):327 33, May 22. [9] 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, 33(5):38 45, September/October 997. [] L. Palma and P. Enjeti. Reflected Wave Modeling Techniques for PWM AC Motor Drives. In IEEE Applied Power Electronics Conference and Exposition, volume, pages 55 556, USA, 22. [] R. D. Lorenz and P. B. Schmidt. Synchronized Motion Control for Process Automation. In IEEE Industry Applications Society Annual Meeting, 989. [2] D. W. Novotny and T. A. Lipo. Vector Control and Dynamics of AC Drives. Oxford Science Publications, New York, USA, 997. [3] A. F. Moreira, P. M. Santos, T. A. Lipo, and G. Venkataramanan. Design of Filter Networks for Long Cable Drives through Simulation and Analysis. In Congresso Brasileiro de Eletrônica de Potência, Fortaleza, Brazil, 23.