Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering

13.1
13. WAVE NATURE OF THE MOTOR CABLE AND VOLTAGE STRESS OF THE MOTOR
IN INVERTER DRIVE ....................................................................................................................... 1
13.1 Cable Modelling .................................................................................................................. 1
13.2 Reflected Voltage at a Point of Discontinuity of the Characteristic Impedance ................. 2
13.3 Continuing Voltage at a Point of Discontinuity of the Characteristic Impedance .............. 3
13.4 Motor Overvoltage .............................................................................................................. 3
13.5 Limiting of Overvoltages .................................................................................................... 5
13. WAVE NATURE OF THE MOTOR CABLE AND VOLTAGE STRESS OF THE
MOTOR IN INVERTER DRIVE

Inverter pulse width modulation produces steep-edged voltage pulses by switching the DC-link
voltage to the motor windings. Beside the well-known economical and control benefits, this sets
certain requirements for the motor cables and the insulation of the motor windings and conductors.
Compared with a drive operating direct-on-line, a control of an inverter-fed electrical drive sets
special requirements for the cabling and insulation. The use of Insulated Gate Bipolar Transistors
(IGBTs) as switching semiconductor devices has led to approximately 50 ns pulse rise and fall
times. Due to short switching times, the switching losses of the drive decrease, and consequently,
also the required heat-exchange area is reduced. Short switching times allow a high switching
frequency, which in turn improves the waveform of the current fed to the motor and reduces the
noise caused by the motor, when the switching frequency of the motor is adjusted such that it does
not cause resonances in the motor system. On the other hand, the efficiency of the inverter is
reduced in any case as the switching frequency increases, and thus it is most profitable to apply low
frequencies.
13.1 Cable Modelling

In the cables commonly used in motor drive systems, the electromagnetic wave propagates 150 m
in a microsecond. Compared to this, the switching frequency of the modern inverters is high; the
current rise time in the IGBT is typically below 100 ns. Therefore, at frequencies notably higher
than the normal electric network frequency, the cable cannot be described with concentrated cable
parameters, but we have to employ distributed constants. Now the resistance, inductance,
conductance, and capacitance are spread along the entire length of the cable. Inductance and
capacitance per unit length determine the characteristic cable impedance individual for each cable

Z
l
c
0
= . (13.1)

c is the capacitance per unit length
l is the inductance per unit length
Z
0
is the characteristic impedance

Hence, the structure and sheathing of the cable determine the magnitude of the characteristic
impedance Z
0
, which is thus independent of the cable length. The value of the cable characteristic
impedance is typically of the scale of 100 O. The wave velocity in the cable depends on the cable
materials; materials refer here to the media surrounding the conductor, not the conductor itself. The
highest possible speed is the speed of light C, which can be reached in vacuum. The wave velocity v
can be determined by the cable characteristics

Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering

13.2

c l
C
v

= =
1
r r
c
(13.2)

C is the speed of light
c
r
is the relative permittivity

r
is the relative permeability

The relative permittivity c
r
of the sheathing of the motor cable can be for instance 4, in which case
the wave velocity in the cable is reduced to a half of the speed of light, that is, v = 150 m/s. When
a wave propagating in the cable reaches a point of discontinuity, that is, a junction point at which
the cable characteristic impedance changes, there occurs reflection. The reflection from the junction
of the larger cable impedance can be explained by the current decrease in the region of the larger
impedance. As a result, some extra charge starts to accumulate in the junction. This charge causes
an increase in voltage, and a new wave is created, which is split up into a reflected part and a
continuing (forward-travelling) part.
13.2 Reflected Voltage at a Point of Discontinuity of the Characteristic Impedance

The voltage reflection at the cable end can be divided into two extreme cases
- a cable shorted at the end; the amplitude of the reflected wave is equal in magnitude with the
incidence wave, but with a negative sign, in which case the voltage is zero at the motor terminals
- the cable is open at the end; the amplitude of the reflected wave is equal in magnitude with the
same sign, resulting in a voltage two times the magnitude of the incident voltage at the motor
terminals

In a normal case, the motor impedance is notably higher than the characteristic impedance of the
cable. In the case of incident (incoming) wave, that is, in the case of an inverter-fed electrical drive,
a pulse travelling from the cable to the motor terminal thus inevitably causes a reflection. The ratio
of the reflected pulse and the incident pulse is expressed by the reflection coefficient . This
coefficient depends on the characteristic impedance Z
0
of the motor cable and the characteristic
impedance Z
m
of the motor (winding) experienced by the wave

=

+
Z Z
Z Z
m 0
m 0
. (13.3)

As can be seen in Eq. (13.3), the value of the reflection coefficient varies between 0 s s 1, when
Z
m
> Z
0
. A common value for the reflection coefficient at the junction of the cable and motor is
between 0.6 and 0.9. The reflected voltage u
r
can be expressed with the incoming voltage u and the
reflection coefficient

u u =
r
. (13.4)

When the voltage pulse has reached the motor terminals, the reflected part of the wave returns to
the inverter. At the inverter, the wave encounters the large DC link capacitor. The characteristic
impedance of the capacitor is close to zero for the high-frequency returning wave, and thus the
wave is reflected back as negative (the reflection coefficient is approximately -1). Between the
motor and inverter, there travels a voltage surge that attenuates according to the reflection
coefficient. The attenuation depends also strongly on the losses occurring in the cable.
Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering

13.3
13.3 Continuing Voltage at a Point of Discontinuity of the Characteristic Impedance

At a point of discontinuity of the cable characteristic impedance, the continuing wave under two
extreme conditions are given below:
- the cable is shorted at the end; the amplitude of the continuing voltage surge is zero
- the cable is open at the end; the amplitude of the continuing voltage surge is two times the
amplitude of the incidence voltage

The ratio of the forward-travelling and incoming backward-travelling pulse is described by the
transmission coefficient t. This factor, like the reflection coefficient, is a function of the motor
cable characteristic impedance Z
0
and the motor (winding) characteristic impedance Z
m


t =
+
2Z
Z Z
m
m 0
(13.5)

As can be seen from Eq. (13.5), the value of transmission coefficient varies between 1 s t s 2,
when Z
m
> Z
0
. The forward-travelling voltage u
2
can be expressed with the incoming voltage u and
the transmission coefficient t

u u t =
2
. (13.6)
13.4 Motor Overvoltage

If the amplitude of the motor overvoltage is at maximum twice the pulse from the inverter, the
increase in voltage can be explained with the waveguide theory presented above. The magnitude of
the reflected voltage depends on the cable length as well as the impedance matching between the
motor and the cable. When we assume a total mismatching between the motor and the cable, the
motor can be expressed as an open cable end. Now, a perfect reflection from the motor terminals is
obtained, and the voltage may double.

Duplication of the voltage requires a cable length above the definite critical cable length, because
the negative wave returning from the inverter suppresses the overvoltage. If the pulse reaches its
peak value before the suppressing wave arrives, in other words, if the pulse rise time is shorter than
the time required for the wave to travel the distance to and from the inverter, the voltage is doubled.
Thus, the length of travel of the wave required for a perfect reflection, that is, the critical cable
length L
kr
is obtained from

L
t v
kr
r
=

2
. (13.7)

t
r
is the parallel rise time of the voltage pulse
v is the propagation speed of the voltage pulse

Assuming v = 150 m/s and t
r
= 100 ns (IGBT) for the wave, we obtain a critical cable length of 7.5
m.

Under certain conditions, the motor voltage may rise above the theoretical value of two times the
DC link voltage. If the oscillation of the latest pulse has not been attenuated by the time a new pulse
arrives, their combined effect may lead to overvoltages, the magnitude of which is three times or
even four times the pulse voltage. We may conclude from this that switching frequency and
Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering

13.4
modulation have a significant influence on the magnitude of this overvoltage, whereas the effect of
the rate of pulse rise is less important. The characteristic oscillation frequency f of the cable has a
significant effect on the damping of the cable, which in turn impacts on the magnitude of residual
charge in the cable. So far, no suitable material that would provide good damping has been found
for high-frequency waves.

The oscillation frequency at the motor terminals is determined with the wave velocity v and the
cable length L, and is thus independent of the characteristic values of the inverter and the motor,
such as the pulse edge rise time or the motor power. The wave velocity in turn is a function of the
characteristic values of the cable according to Eq. (13.2). During one period of oscillation, the wave
propagates the distance L four times (Figure 13.1).

Inverter
Motor
t
p
4t
p


Figure 13.1 Voltage response of the motor to the inverter pulse

The cycle time T is now four times the wave propagation time t
p
. Hence we may write for the
oscillation frequency f

f
T t
v
L L l c
= = = =

1 1
4 4
1
4
p
(13.8)

c is the capacitance per unit length
l is the inductance per unit length
L is the cable length
t
p
is the wave propagation time
T is the cycle time of the oscillation
v is the wave velocity

The characteristic oscillation frequency of the cable has thus an indirect effect on the attenuation of
the wave. The conductor resistance and thus the attenuation increase due to skin effect. Skin effect
in turn is a function of oscillation frequency. Hence an increase in oscillation frequency speeds up
the attenuation of the wave. The oscillation of the reflected wave has to be attenuated before the
next pulse arrives in order to avoid overvoltages that exceed the double DC link voltage.

Double Pulsing

Figure 13.2 illustrates the so-called double pulsing phenomenon, which causes large overvoltages.
The phenomenon occurs, if the transient (oscillation) caused by the pulse has not attenuated before
the next pulse arrives, in other words, the dwell time is not long enough. Initially, the voltages of
the inverter and the cable are equal. The fall edge of the pulse causes a reflection in the motor
terminals based on the progressive wave theory, and the reflected wave continues to the inverter,
where it is reflected back at the reflection coefficient -1. Simultaneously with the wave reflected
Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering

13.5
from the inverter, the rise edge of the inverter control pulse arrives at the motor. As a combined
effect of these two waves, there occurs a situation illustrated in Figure 13.2.
Inverter
Motor
t
p

Figure 13.2 Occurrence mechanism of the double pulsing

The magnitude of the voltage acting upon the motor terminals depends on the damping of the cable,
the uncharged time of the pulse, that is, the period for which the voltage of the pulse is zero, as well
as the cable length and the inverter switching frequency.

Double Switching

To achieve the required output frequency, the inverter switches the semiconductor switches of each
phase according to its program. When considering the case as a whole, we may end up in a
situation, in which the change in the voltage between different phases is double the DC link voltage
(Fig. 13.3). This may happen if the states of two inverter branches are switched simultaneously.

u
1
u
2
u
12


Figure 13.3 Change in the line voltage when two phase voltages change simultaneously.

Double switching causes overvoltages that are even higher than the overvoltages caused by double
pulsing. At worst, these overvoltages are higher than the calculated withstand voltages of the
machine designed for inverter drive. Double switching has to be prohibited in the design of the
modulator operation; double switching does not inherently belong to the properties of for instance a
space vector modulator.



13.5 Limiting of Overvoltages

Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering

13.6
Overvoltages can be reduced by filtering, or by means of inverter programming. The most common
method to implement filtering is to mount the series chokes to the motor cable. They suppress the
high-frequency components and thus round out the pulse edges. The solution naturally increases the
inductance and causes a voltage loss, which in turn reduces the motor voltage and the torque
obtained from the motor. The cable inductance and the inductance of the series inductors are
summed with the stator leakage inductance, and consequently, the breakdown torque of the machine
is reduced considerably.

With small machines (P < 20 kW), the characteristic impedance of the motor can, due to the
impedance of the winding, be 10 to 100-fold to the cable impedance. Therefore, the incident wave
is reflected back from the motor according to Eqs. (13.3) and (13.4). However, if the cable is
terminated with an impedance corresponding with the cable characteristic impedance, no reflection
takes place.

As the machine size increases, the characteristic impedance decreases, and thereby the machine and
cable impedances approach each other. Consequently, matching is improved without any extra
measures, and the reflection of waves decreases. This, however, does not imply that the voltage rise
would not be significant in large machines; as a matter of fact, the problems related to inverter drive
tend to be emphasized in large machines.

In the following, three methods for matching the impedances are presented. All the methods are
based on a filter constructed of passive components and mounted parallel to the motor. The
characteristic impedance of the cable Z
0
is notably lower than the characteristic impedance of the
motor Z
m
, and therefore Z
0
is decisive. Now we aim at bringing the impedance Z
s
equal to Z
0
. The
parallel connection of the filter and motor can be simplified according to the following equation.

=

+
~

+
(
(
s m 0
s m 0
s 0
s 0
Z Z Z
Z Z Z
Z Z
Z Z
|| )
|| )
(13.9)

Thus, we may neglect the characteristic impedance of the motor, and design the filter with the cable
characteristic impedance.

The cable can be terminated by a resistance R connected in parallel with the motor, the value of
which is determined based on the cable characteristic impedance; in other words, we write R = Z
0
.

R Z
l
c
= =
0
(13.10)

However, the power loss caused by the resistance alone is so significant that this method is not a
real alternative in eliminating the reflections. For instance, at 460 V, in a 30 m cable, the losses in
the resistance are of the scale of 1 kW, when the characteristic impedance of the cable is 190 O.

The series connection of the capacitor and the resistance constitutes a filter of Figure 13.4, which
could come into question in the impedance matching. The resonant frequency of the filter is
selected empirically at a frequency that is five times the inverter switching frequency. The angular
frequency is determined by the operating frequency, which is set close to the resonant frequency.
Now we obtain for the impedance Z
S01
of the filter

Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering

13.7
Z R
C
S01

= +
|
\

|
.
|
01
2
01
2
1
e
, (13.11)

where C
01
is the capacitance of the filter
R
01
is the resistance of the filter
Z
S01
is the impedance of the filter
e is the angular frequency

We aim at overdamping of the filtering circuit, and thus we may write the condition for R
01


R
l
C
01
>
4
01
(13.12)

C
01
is the capacitance of the filter
l is the inductance of the cable
R
01
is the resistance of the filter

C
01
R
01

Figure 13.4 RC filter.

Power losses with this structure and under the same conditions as in the previous case (460 V, 30
m, 190 O) remain at the level of 150 W.

As shown in Figure 13.5, a second-order filter comprises the capacitance C
02
, the inductance L
02
,
and the resistance R
02
.

C
02
R
02
L
02

Figure 13.5 Second-order filter.

We may now write for the impedance Z
S02
of the filter in question

Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering

13.8
Z
R L
R L
R L
R L C
S02
2
2 2

=
+
|
\

|
.
| +
+

|
\

|
.
|
02 02
2
02
2
02
2
2
02
2
02
02
2
02
2
02
2
1 e
e
e
e e
(13.13)

C
02
is the capacitance of the filter
L
02
is the inductance of the filter
R
02
is the resistance of the filter
Z
S02
is the impedance of the filter
e is the angular frequency

Again, we aim at overdamping the filtering circuit. Now we can write for R
02


R
L C
C
02
<
02 02
02
2
(13.14)

C
02
is the capacitance of the filter
L
02
is the inductance of the filter
R
02
is the resistance of the filter

The power losses are here of the same scale as for the RC filter, that is, about 150 W. In practice,
matching of the motor cable is not usually carried out for instance because of the losses shown
above. If filtering is applied, the target is chiefly to modify the steep pulse rise edges in order to
keep the filter size reasonable. In practice, small-size du/dt filters are applied quite extensively
particularly in industrial inverter drives.

The means to reduce overvoltages by programming come into question basically in the previously
discussed cases of double pulsing and double switching. Double pulsing can be prevented by
eliminating pulses that are below certain duration. The preset uncharged time is defined
individually for each system, and it can be determined by the cable damping, cable length, and the
inverter switching frequency. Double switching is prevented when designing the modulator.

The voltage fed by the inverter is comprised of almost rectangular pulses. Due to fast rise and fall
times, the pulse includes extremely high-frequency harmonics. These harmonics cause extra
currents in the windings, which in turn lead to increased losses and consequently to an increase in
the winding temperature. This temperature rise has to be compensated either by reducing the power
or it has to be taken into account as faster thermal aging when compared to a drive operated direct-
on-line. Based on the thermal resistance of the insulations, the insulation classes have been
determined and standardized for different insulators. Table 11.2 presented some insulation classes
and limit temperatures in compliance with the standards IEC 34-1 and IEC 85.

Previously, we discussed the effect of steep-edged voltage pulses of the inverter on the temperature
rise of the machine. An inverter control may cause problems in the cooling of the machine, even
though the control does not directly warm up the winding of the machine. The ventilating fans and
openings of the machine have been designed for normal direct-on-line operation. At low rotation
speeds, the cooling of the machine does not necessarily suffice, and therefore, external cooling is
required; this is typically arranged by a blower.

A normal low-frequency (50/60 Hz) supply voltage is evenly distributed in the winding, and the
voltage loss over both the winding and the consecutive turns remains constant. When applying
inverter control, the voltage distribution is no longer even; the steep-edged voltage pulses have been
shown to cause notably larger voltage stresses in the motor windings than the conventional
Electrical Drives Juha Pyrhnen, LUT, Department of Electrical Engineering

13.9
sinusoidal line voltage. It is possible that the first and last turns are located side by side in the
winding. Now the voltage acting upon the entire coil is also the voltage between these outmost coil
turns. The insulation of individual conductors in the coil has been designed to prevent an electric
contact between the conductors at normal-frequency line voltage. The uneven distribution of
voltage over the winding and between different turns leads to significant overvoltages both to
ground and between the conductors. The isolation of coils from the motor frame is notably stronger
than the insulation between the conductors, and thus the machine insulation fails most probably
inside the coils.

In the worst case, 80 % of the phase voltage stays in a multiple-turn winding in the distance of the
first turn. Thus, the field strengths in the insulation distances may rise to a level required by partial
discharges, even though the turns of the winding would be in proper order. Partial discharges have
conventionally been connected to high-voltage machines. However, the voltage over the winding
may increase in an inverter drive to a level that is high enough to cause partial discharges, which in
turn lead to premature aging of the insulations. Similarly as in the case of overvoltages, the
insulation between the conductors is proportionally weaker than the insulation of the coil, and
therefore a more critical issue when considering the durability of the insulations.

The waveguide theory explains, based on reflection, the overvoltage acting upon the motor
terminals. The effect of characteristic impedance is obvious. The overvoltages and their occurrence
mechanisms are discussed in brief; the overvoltages are categorized according to their magnitude
compared with the double incident voltage. For an overvoltage less than double the incident
voltage, the critical length of the cable is determined. There are two methods to reduce the
overvoltages: impedance matching implemented by passive components, and programming
methods.

References

Kerkman, R. J., Leggate, D., Skibinski, G. L. 1997. Interaction of Drive Modulation and Cable
Parameters on AC Motor Transients. IEEE Transactions on Industry Applications, Vol. 33, No. 3,
pp. 722731.

Liukko, T. 1998. Moottorikaapelin aaltoluonne ja eristeiden kestvyys invertterikytss. In
Pyrhnen, J. (ed.) Shknkytttekniikan erikoiskysymyksi 1998, Opetusmoniste 1 LTKK
(Lecture Notes), Department of Electrical Engineering, Lappeenranta University of Technology (in
Finnish).

Mbaye, A., Bellomo, J. P., Lebey, T., Oraison, J. M., Peltier, F. 1997. Electrical Stresses Applied to
Stator Insulation in Low voltage Induction Motors Fed by PWM Drives. IEE Proceedings -Electr.
Power Applications, Vol. 144, No. 3, pp. 191198.

Paloniemi, Keskinen: Shkkoneiden eristykset. Shkmekaniikan lisensiaattiseminaari, Otaniemi
1996. ISBN 951-22-3298-7 (in Finnish)

von Jouanne, A., Rendusara, D., Enjeti, P., and Gray, W. 1996. 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, Issue 4, pp. 919926.