Modeling and simulation of dv/dt filters for AC drives with fast switching transients B.Basavaraja, Member, IEEE, and D.V.S.S.Siva Sarma, Member, IEEE
Abstract-- Many of today’s induction machines are operated using variable speed drives (VSD). VSDs are used for controlling the speed of induction machine by adjusting the amplitude and frequency of the AC voltage. These adjustments are made by advanced technology in semiconductors, which are faster switching devices. Faster switching reduces the switching power loss, requiring less heat sink, thus enabling drives to become more efficient and smaller, and this also helps to reduce cost. Along with the better performance enabled by the high switching speed and increased switching frequency, they have also raised several concerns related to the consequences of high speed switching. One of these concerns is the over-voltage that appears at the motor terminals due to the impedance mismatch between the power cable and the motor. In this paper, overvoltages at the motor terminal are analyzed and accurate simulation models of different filters are designed to reduce the overvoltage problems. The models can be readily implemented using computational tools like Matlab, thereby providing a convenient method to develop the best dv/dt filter solution for a particular drive to reduce the over voltage & hence increases the life of the motor. Index Terms- filter design, Induction motor, insulation failure, Matlab, mismatch impedance, overvoltages, PWM Inverter, transients.
I. INTRODUCTION A. Description of the system
T
common drive structure adopted by industry consists of an uncontrolled diode bridge rectifier, dc link, and PWM VSI inverter as shown in Fig. 1. Voltage source PWM inverter drive is the most common type of low voltage inverter drives, which is currently in use. The process of obtaining the required frequency involves converting the incoming alternating voltage to DC by means of a rectifier, smoothing the DC in an intermediate DC link with capacitive energy storage, and then inverting back to an alternating current. The pulsed output voltage is applied to the motor and the resultant voltage at motor terminal and its features of a
typical pulse waveform as shown in Fig. 2. The output of the PWM Inverter is of concern in this paper. Both frequency and magnitude of the output voltage are adjusted by controlling the inverter's operation. With IGBT devices, the inverter operates with a switching frequency ranging from tens of Hz to tens of thousands of Hz.
Fig. 1. Essential elements of PWM Inverter drive. 2Ud U
Completion of first reflection
Ud
0
Completion of third reflection Pulse first arrives at motor
t
HE
B.Basavaraja Research Scholar with Department of Electrical Engineering,NIT Warangal,INDIA & Associate Professor at SR Engg.College, Warangal,INDIA(e-mail:
[email protected]). D.V.S.S.Siva Sarma Asst.Professor with Department of Electrical Engineering,NIT Warangal,INDIA(e-mail:
[email protected]).
0-7803-9525-5/06/$20.00 ©2006 IEEE
Fig. 2. Features of a typical pulse waveform at the motor terminals.
However, this benefit can only be achieved under certain circuit conditions. Under some particular conditions, the fast changing voltage resulting from high frequency switching operation of IGBT PWM drive can create severe insulation problems for an induction motor. If a motor is exposed to high steep front surges then the breakdown strength of the insulation may be exceeded, causing turn insulation breakdown [1][2]. These results in large circulating current through the coil, precipitating motor ground insulation and precipitating a ground fault alarm. Although many motors, when new, have an excellent capability to resist turn insulation failure by surges, the turn insulation often gradually deteriorates from thermal and mechanical aging over the years [3].
II. ANALYSIS OF THE OVER VOLTAGE Using the high frequency models [4] of cable & Induction motor, a simulation program has been developed in Matlab to analyzes the over voltage considering different cable length & HP rating & finally design of best filter was modeled to reduce fast switching transients. A. High Frequency Model of the Induction Motor Another key factor for an accurate over-voltage analysis is the high frequency representation of the ac motor input impedance, which must be valid over a broad range of frequency. It is not necessary to verify how voltage will distribute inside the AC machine winding in order to calculate the over voltage at the terminals. It is important, rather, to know the value of the ac motor input impedance and how it varies as a function of frequency. The Fig. 3 shows the schematic of the proposed IM model that is implemented in the simulation program to evaluate the over-voltage analysis [3].
representations of the power cable. R1, R2, C3 are responsible to represent the low frequency and remaining for the high frequency phenomena. C. Transmission line representation of the power cable The power cable as a transmission line can be modeled either as a lumped-parameter network or as a distributedparameter circuit. Some of references in the literature favor the distributed-parameter representation over the lumped parameter representation [1]. Distributed-parameter representation provides more accurate results in the study of high frequency transients than the lumped-parameter models. However, distributed parameter representation typically leads to a heavy computational burden from the point of view of simulation. Indeed, the lumped parameter representation with an adequate choice of the number of segments can produce accurate results just as well, which will be demonstrated in this paper. The number of lumped segments that leads to an accurate characterization of the over-voltage can be determined from a consideration of the behavior of the electric field [2]. For instance, consider the electric field E at an arbitrary point x of the system written as
2π ⎞ ⎛ E=Emax sin⎜ωt − ⎟ λ⎠ ⎝
Fig. 3. High frequency model of an IM.
B. High frequency model of the power cable An adequate estimation of the power cable parameters is needed in order to have an accurate computation of the over voltage. Long cable lengths contribute to a damped high frequency ringing at the motor terminals due to the distributed nature of the power cable leakage inductance and coupling capacitance which results in over voltages and further stress the motor insulation. In addition, voltage reflection is a function of inverter output pulse rise time and the length of the motor cables, which behave as a transmission line for the inverter output pulses. So the cable representation resembles like lumped parameter model of the transmission line. The Fig. 4 shown below is the per phase representation of one lumped –segment of the power cable used in the Matlab simulation.
representing a wave with angular frequency ω and wavelength λ traveling in the +x direction. The variation of the electrical field δE over an increment of distance δx is given by: Therefore
2πE 2π ⎞ ∂E ⎛ δx = − max cos⎜ωt − ⎟δx (2) λ λ⎠ ∂x ⎝ δ E max δx = 2π (3) E max λ
δE =
wave Equation (3) can be used as a basis to calculate the number of lumped circuit elements necessary for accurate characterization of the voltage distribution. Knowing the desired value of the ratio |δE|max/Emax the length of each lumped segment across which there is negligible variation of E may be determined. This length is dependent on the value of the voltage pulse wavelength λ. Once this characteristic length is known, the entire length of the cable may be represented by an appropriate integral number of lumped parameter segments. The remaining task is to define the wavelength λ. From the electromagnetic theory the wavelength can be related to the phase constant β of the traveling by the expression:
λ= Fig. 4. High frequency model of an Cable.
The model conjugates low and high frequency
(1)
2π
β
(4)
The phase constant β can be calculated knowing the angular frequency ω and the electrical parameters of the
power cable per unit length as follows:
β = ℑ{ ( r + ω l ) ( g + ω c ) }
using MATLAB with different cable lengths and HP ratings of the machine.
( 5)
where r, l, g, and c are respectively the resistance, inductance, conductance, and capacitance of the line per unit length. The voltage pulse is a summation of many harmonic components that contribute to the formation of the electric field across the length of the cable. It is also known that the minimum frequency at which dv/dt related phenomenon of over voltage is related the rise time of the pulse.
f HG =
1
πτ rise
Therefore,
ω = 2π f HG
A. Cable Length Vs Peak Voltage
(6) (7 )
The next step is to define the maximum value of the ratio⎜δE⎜max/Emax, which represents a negligible variation of the electrical field. A reasonable value could be 1e-3, which will generally lead to quite short lengths of the lumped circuit as will be verified. However, this can become prohibitive, since it will increase too much the computational effort. Most of the simulation results, which will be shown later, have used a value of the lumped segment length that gives a ratio of 1e-2. For very fast rise time, such as τrise = 50 ns or τrise = 100 ns, even higher ratio value was used, being around 0.1 or 0.2. Using Equations (4) to (7), and fixing the ratio in Equation (3) at the values 1e-3, 1e-2, and 2e-1, various lengths of the lumped circuit were calculated for different voltage pulse rise times and for different AWG gauges for the conductor. Fig. 5 & 6 show the behavior of the critical length as a function of rise time for various ratios of ⎜δE⎜max/Emax. Performing curve fit in these plots, general equations to calculate the critical length of the lumped segment are obtained for each cable gauge as a function of rise time, as shown in Equations (8) to (11). These expressions can be promptly utilized to calculate the length of the lumped segment, or the number of lumped segments, that produces a sufficiently accurate calculation of the over voltage.
⎛ δE ⎞ #8AWG ⇒Lcrit=⎜ max⎟ ×[0.0679 ×τrise(ns) +0.1041 ] ⎜ Emax ⎟ ⎝ ⎠deired
(8)
⎛ δE ⎞ #10AWG⇒Lcrit=⎜ max⎟ ×[0.0501×τrise(ns) + 0.1483 ] ⎜ Emax ⎟ ⎠desird ⎝
(9)
Fig. 5. Line to Line Voltage Peak Vs Time for Rise time=350ns; cable=60m.
Fig. 6. Line Voltage Peak Vs Time for Rise time=1.2µs; cable=60m. TABLE I EFFECT OF CABLE LENGTH FOR 3 HP MOTOR: RISE TIME 350 N SEC. Cable Length (in meters) 10 20 30 60
Over Voltage (in Volts) 1100 1075 1060 1050
Output Pulse Rise Time (µs) 0.325 0.375 0.4 0.5
From the above waveforms & Table I, we can conclude that the voltage at the motor terminals becoming lower as the length of the cable increases for the same rise time and as the rise time increases the over voltage reduces for the same length of cable.
⎛δE ⎞ max ⎟ × [0.0796×τ rise(ns) + 0.007] (10) #12 AWG⇒ Lcrit = ⎜ ⎜ Emax ⎟ ⎝ ⎠deired
B. HP Rating Vs Peak Voltage
⎛δE ⎞ max ⎟ #16 AWG⇒ Lcrit = ⎜ × [0.0878×τ rise(ns) + 0.0671] (11) ⎜ Emax ⎟ ⎝ ⎠deired
Simulation is carried out for analyzing over voltage at the motor terminals for 3 hp and 15hp ratings of the motor for the same cable length and rise time, and the resulting waveforms are given below
III. SIMULATION RESULTS Using the above models simulation is carried out by
1200
V-T Curve at 3hp & 15hp IM terminal
-voltage at 15hp IM terminal
ge at 3hp IM terminal 1000 800 600 output of inverter 400 200 0 -200 -400 2
3
8
7
6 time-sec
5
4
10
9
-6
x 10
Fig. 7. Line to line voltage at motor and inverter terminals for 3hp, 15hp motor for a Cable Length 60m;rise Time 350ns.
Peak voltage(volts)
voll tag evolt s
10 9 8 7 6 5 4 3 2 1 0 0
20
40
60
80
100
50mt cable
100mt cable
200mt cable
(
120
HP Rating 25mt cable
voltage constraint of the motor, and Line Termination Network (LTN) watts loss dissipation. The function of Cf, is to "fool" the traveling wave pulse arriving at the motor into thinking it is optimally terminated in a Rf=Zo mode for just enough time to make Г=0 and then make the LTN network appear as an open circuit to prevent power dissipation. An uncharged capacitor is an equivalent short circuit to fast rising edges while an open circuit to dc bus values. Initially, line to line inverter output voltage is zero, since both phases are tied to either (+) or (-) bus. This insures Cf, is initially and automatically discharged. When one phase switches to the opposite bus, a full dc bus pulse with rise time trise is sent down the cable. When the traveling wave impinges on the motor terminals, the RC network charges. A design goal is to make Cf, voltage < 10% of Vdc bus at the end of trise, so as to effectively look like a line to line resistor termination while the pulse is propagating into the motor. Approximately full bus voltage is initially across Rf, and peak LTN current is (Vbus /Rf.). Cf, value is estimated using the simple RC charge equation given by
Fig. 8. HP vs. peak Voltage curve for different cable length connected between pwm inverter and motor.
From the above table and waveforms, it is observed that i). As the cable length increases the over voltage reduces. ii). As the rise time increases the over voltage reduces. iii). For large HP ratings over voltage is less.
VCf =(0.1) ∗Vbus=Vbus1−e rise
−t /(Rf Cf
)
(12)
Another constraint on Cf, selection, given a fixed Rf value, is to make the 3τ or 3*RfCf dis-charge time less than the inverter dwell time to ensure the capacitor is initially at zero before the next pulse. The schematic diagram of the RC filter at the motor is shown below,
IV. DESIGN OF DIFFERENT FILTERS In order to minimize the over voltage at the terminals of the motor, the filter component values are selected such that the equivalent impedance of the filter closely matches the surge impedance of the cable [5]. The operating frequency of the filter to minimize the voltage overshoot was chosen to be near the resonant frequency of the filter [6]. Circuit models of Fig. 9-11 shows the different filters at different points in circuit.
Fig. 9. RC filter.
B. Design of RLC-filter at motor terminals In this section a second order filter is proposed to reduce the over voltage at the terminals of the motor. The proposed second order shunt filer is shown in Fig. 10 below.
A. Design of RC filter at motor terminal In this method the cable is terminated by a first order filter consisting of a capacitor in series with the resistor to match with the cable and provide the proper level of damping to control the voltage overshoot. The optimum Rf value is equal to surge impedance Z0 i.e., Rf= Z0. Selection of optimum capacitor C, is a function of inverter pulse rise time, inverter dwell time, peak allowable
Fig. 10. proposed second order filter.
In order to minimize the over voltage at the terminals of the motor, the filter component values are selected such that the equivalent impedance of the filter closely matches the surge impedance of the cable.
Z eq =
=
=
jR f ω f L f j − R f + j ω fL f ω fC f
cutoff frequency.
jωfRL j f f ( Rf − jωfLf ) − ( Rf + jωfLf )( Rf − jωfLf ) ωfCf
Rfωf 2 Lf 2 jRf 2ωfLf j − − 2 2 2 2 ωfCf 2 2 Rf + ωf Lf Rf + ωf Lf
Fig. 11. Inverter Output Low-Pass Filter.
From Fig. 11, the transfer function H which defines the behavior of the network is
Magnitude of Zeq is given by
(13) Again, the resistor Rf is designed to result in an over damped circuit as given by,
(14)
The surge impedance parameters are given per unit length. So Zo will be constant for a given cable type. Therefore the filter design will be the same for a given cable regardless of the cable length. The resonant frequency of the filter was selected to be five times the switching frequency of the PWM inverter. The operating frequency of the filter to minimize the voltage overshoot was chosen to be near the resonant frequency of the filter. C. Design considerations for inverter output RLC filter In many applications, the motor terminals may not be accessible, as in drives for submersible pumps, where it may be more convenient to install a filter at the inverter terminals. A low-pass filter, as shown in Fig. 11, placed at the output terminals of the inverter can be specially designed to slow down the inverter output pulse rise time and, therefore, significantly reduce the over voltage and ringing at the motor terminals. There are several low pass polynomial filter configurations with different shapes of amplitude-versusfrequency responses. The topology in Fig. 11 was chosen since the series capacitor and resistor combination reduces the V2/R power losses across the damping resistor. The lower order (second-order) filter is desirable from the standpoint of the number of components, filter size, cost, and weight. In addition, the second-order filter is found to yield the necessary stopband attenuation characteristics and the maximum ripple values in the passband. Since a flat passband response is appropriate, as is exhibited in Butterworth filters, the selected attenuation is 3 dB at the
(15) Where the effective attenuation in decibels is (16) The filter resistor is designed for the filter component values to result in an over damped circuit. In addition, since the filter capacitor will represent a short circuit at high frequencies, is set equal to the characteristic impedance of the cable given in (2) to absorb the reflected energy. Therefore, (17) Thus, for 3-dB attenuation at a specified cutoff frequency, ωc, (14)–(16) can be solved for appropriate values of Lf and Cf. First, the cutoff frequency ( fc) should be determined. According to the Fourier series, the highest frequency component will determine the sharpness of a near square-wave pulse. Thus, the period Tc of the highest frequency component in the PWM inverter output pulse should be twice the critical rise time, or (18) (19) V. FILTER
PARAMETER CALCULATIONS
A. For RC filter As explained in RC filter design the equations are reduced to:
R f = Zsurge cable =
Cf =
τrise 0.1054 Rf
Ls Cp1
(20)
(21)
By solving above (20) and (21) equations for 280ns rise time, Rf = 41Ω and Cf = 64.8nF.
Fig. 15. Line to line voltage at motor and inverter terminals for RLC Filter at 3hp motor.
C. .RLC filter at inverter As explained in the RLC filter design at inverter the equations are reduced to,
Fig. 12. RC filter.
Rf =
Z surgecable 2
e(−ωn*τrise)(1+ωn*τrise) = 09 . Fig. 13. Line to line voltage at motor and inverter terminals for RC Filter at 3hp motor.
B. For RLC filter at motor
ωn 2 =
As explained in the RLC filter design at motor the equations are reduced to,
R f = Zsurge cable
(22)
e ( −ω n *τrise )(1+ω n*τrise ) = 0.9
(23)
1 = 2ω R fC f ω n2 =
1 L fC
n
2ωn =
2 Lf + Zsurgecable RfCf LfCf (2 Rf + Zsurgecable
Z surgecable L fC f ( 2 Rf + Z surgecable )
(26) (27)
(28)
(29)
By solving the above (26),(27),(28), and (29) equations for the rise time of 280ns, the values are, Rf=20.5Ω Lf= 3.0µH and Cf=130nF
(24)
(25) f
By solving above (22),(23),(24),and (25) equations for the rise time of 280ns, the values are Rf = 41Ω , Lf =192µH and Cf=28.55nF.
Fig. 14. Simulation circuit in Matlab.
Fig. 16. Simulation circuit in matlab.
Fig. 17. Line to line voltage at motor and inverter terminals for RLC Filter at inverter for 3hp motor.
D. Comparison of Different Filters Fig. 18 shows the simulation results for the circuits shown in Fig. 9-17.
conclusion from this analysis is that the solutions placed at the motor terminals are not able to reduce the dv/dt as much as the filters placed at the inverter terminals. This occurs because the filters at the motor terminals, which match the cable surge impedance, can only reduce the voltage to the dc bus level but are not capable of reducing the pulse rise time. VII. REFERENCES [1]
[2]
Fig. 18. Line to line voltage at motor and inverter terminals for each different Filter type inverter for 3hp motor; Cable Length 80m;rise Time 350ns.
Fig. 18 explains combined simulation results which gives how the peak voltage varies with time by adopting different filter circuits at different points in the circuit as well as without filter circuit. Hence by adopting filter circuit, peak voltage reduces at motor terminal & hence reduces insulation problems, which results, life span of the motor increases. TABLE II EFFECT OF FILTERS FOR INVERTER OUTPUT PULSE RISE TIME = 0.35 MICRO SEC; CABLE LENGTH=80M; 3 HP MOTOR Type of Filter Without filter RC@mtor RLC@motor RLC@inverter
Over Voltage (in Volts) 1030 500 500 450
Output Pulse Rise Time (in micro sec) 0.5 0.5 0.5 0.6
From the above table it is observed that RLC filter at inverter terminals reduces the over voltage and increases the output pulse rise time in comparison with RC and RLC filters placed at motor terminals. VI. CONCLUSION This paper has proposed first, the analysis of the overvoltage phenomena in long cable PWM drives. In next case, the over-voltage concepts were analyzed by taking different HP Rating of an Induction motor. It is observed that as cable length increases the over voltage reduces, as the rise time increases the over voltage reduces and for large HP ratings over voltage is less. Finally the most common dv/dt filter topologies for mitigating over voltage problems were analyzed. The main
[3]
[4]
[5]
[6]
[7]
[8]
F. Moreira, T. A. Lipo, G. Venkataramanan, and S. Bernet, “Modeling and Evaluation of dv/dt Filters for AC Drives with High Switching Speed,” Proceedings of 9th European Conference on Power Electronics and applications (EPE’01), Aug. 27-29, Graz, Austria, 2001. F. Moreira, T. A. Lipo, G. Venkataramanan, and S. Bernet, “High Frequency Modeling for Cable and Induction Motor Over-Voltage Studies in Long Cable Drives” IEEE Industrial Application Society 36th Annual Meeting Chicago, Illinois, USA, September 30 October 5, 2001. 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. 1138-1145, Sep/Oct 1997. von Jouanne, D. Rendusara, and P.N. Enjeti, “Filtering Techniques to Minimize the Effect of Long Motor Leads on PWM Inverter-Fed AC Motor Drive systems,” IEEE Transactions on Industry Applications, vol. 32, no. 4, pp. 919-926, July1996 G. Skibinski, “Design Methodology of a Cable Terminator to Reduce Reflected Voltage on AC Motors,” Proceedings of 31st IEEE Industry Applications Society Conference (IAS’96), San Diego, CA, USA, 1996. G. Skibinski, R. Kerkman, D. Leggate, J. Pankau, and D. Schlegel, “Reflected Wave Modeling Techniques for PWM AC Motor Drives,” Proceedings of 13th IEEE Annual Applied Power Electronics Conference and Exposition (APEC’98), vol. 2, pp. 10211029, Feb. 15- 19, Anaheim, CA, USA, 1998. SangCheol Lee and KwangHee Nam, Member, IEEE, “Over Voltage Suppression Filter Design Methods Based on Voltage reflection Theory” IEEE Transactions on Power Electronics, vol19, no.2, March 2004. R. Kerkman, D. Leggate and G. Skibinski. “Interaction of Drive Modulation & Cable Parameters on AC Motor Transients”, Proceedings of 31st IEEE Industry Applications Society Conference (IAS’96), vol. 1, pp. 143-152, San Diego, CA, USA, 1996.
VIII. BIBLIOGRAPHIES Mr. Basavaraja Banakar was born in 1970.He is IEEE Member since2005. He obtained his B.Tech(EEE) degree from Gulbarga University and M.Tech from Karantaka Unversity, India. He worked as a Lecturer in VEC, Bellary, Associate Professor at SSJ Engineering College, Mahaboobnagar. Presently he is pursuing a Doctoral program at National Institute of Technology, Warangal, India & working as Associate Professor at SR Engineering College, Ananthasagar,Waranagal. His areas of interest include power electronics and drives and EMTP applications. Dr.D.V.S.S.Siva Sarma was born in 1964. He is IEEE Member since2004. He obtained his B.Tech (EEE) and M.Tech(Power Systems) from JNTU College of Engineering, Anantapur in 1986 and 1988 respectively. He obtained his Doctorate degree from Indian Institute of Technology, Chennai in 1993. Since 1992, he is working as Faculty member of Department of Electrical Engineering at National Institute of Technology, Warangal, Andhra Pradesh
(Formerly Regional Engineering College, Warangal). His areas of interest include Power System Transients, Fault diagnostics, Protection and Condition Monitoring of Power Apparatus, High Voltage Engineering and
EMTP applications. Presently he is a chairman of Indian EMTP user group and counselor for IEEE student branch of NIT Warangal.
