The phenomenon of reflection of electromagnetic (em) waves on an electrical conductor is very
similar to a wave in water. At a given point, the magnitude of the water wave varies with time
and its phase is retarded. As one moves away from the origin of the wave, the amplitude
diminishes and eventually subsides. However, if there is a barrier to the wave movement, there is
reflection. Consequently, the amplitude of oscillation at a given point is the sum of the incident
and the reflected wave at that point. Similar results are observed when an em wave travels on a
transmission line. If a load on a transmission line is physically at infinite distance from the source,
there exists no reflection similar to a water wave originating in a pond with boundary at infinity.
One can electrically create an infinite transmission line (a line having no reflection) if the surge
impedance at the terminating end matches the cable surge impedance. However, in most cases the
motor and cable surge impedances are mismatched which causes voltage reflections; voltage
reflection further causes voltage amplification at the motor terminals since the motor and the ASD
are usually physically separated by long lead lengths.
Vx = v+ + v- (1)
Referring to Figure 1, it is evident the incident wave, v+, is equal to the sum of the receiving end
voltage and the drop across the surge impedance of the cable. Similarly, the reflected wave, v-, is
equal to the difference between the receiving end voltage and the drop across the surge
impedance. From these observations, one can rewrite the voltage at any given point on the
transmission line as follows:
Vx is voltage at a point x units away from the receiving end;
VR is voltage at receiving end;
IR is current at receiving end;
ZC is characteristic impedance of line; = L/C;
L is phase inductance per unit length;
C is line-ground capacitance per unit length;
y = + j;
is attenuation constant;
is phase constant;
The exponential terms are used in equation (2) to help explain the variations of the voltage
waveform as a function of the distance along the line. The first term in equation (2) denotes the
Incident wave while the latter term in equation (2) denotes the Reflected wave. Based on
equation (2), the following points are worth noting:
(a) x is zero at the receiving end and increases as one moves away from the receiving end
towards the point of interest on the transmission line. On moving away from the receiving end
(for increasing values of x), the incident wave increases in magnitude and advances in phase;
(b) On moving away from the receiving end (for increasing values of x), the reflected wave
diminishes in magnitude and retards in phase;
(c) If the terminating point is at infinite distance from the point of interest (i.e., x is at infinity),
then there exists no reflected wave;
(d) If the terminating impedance is equal to the characteristic impedance, i.e., ZR = ZC, there
exists no reflected wave. A line terminated in its characteristic impedance is known as a flat line or
an infinite line.
Bundled conductor lines have lower values of ZC as they have lower L and higher C than lines
with single conductors per phase;
(e) From equation (2), it is interesting to note that under no load conditions, IR = 0. This results
in the incident wave to be equal and in phase with the reflected wave at the point of termination,
i.e., at x = 0. Hence, the actual voltage at the point of termination which is given by equation (1),
equals 2 times the incident voltage wave. This shows the voltage doubling effect under open or
no load conditions;
Coefficient of Reflection
ZR is the terminating impedance;
vR+ is the incident voltage wave at termination;
vR- is the reflected voltage wave at termination;
iR+ is the incident current wave at termination;
iR- is the reflected current wave at termination;
Further, the incident and reflected current components can be expressed as:
iR+ = vR+/ ZC (4)
iR- = vR-/ ZC (5)
Substituting for iR+ and iR- in equation for ZR:
The ratio of the reflected wave to the incident wave is known as the coefficient of reflection
and is denoted as PR at receiving end. For voltage, the coefficient is:
The reflection phenomenon exists at the sending end as well. The coefficient of reflection at the
sending end is denoted by PS. For voltage, the coefficient is:
From equations (7) and (8), a few interesting remarks can be made:
(a) If at point of termination there is a short-circuit, then ZR = 0; and PR = -1; vR-= - vR+ and
so the sum of reflected and incident voltages at the point of termination is Zero, i.e., (vR- + vR+ =
0);
(b) If the point of termination is an open circuit, then ZR = ; PR = 1; and so the sum of reflected
and incident voltages at point of termination is 2vR+;
(c) If at the point of termination, ZR = ZC; then there exists no reflection since PR = 0;
(d) Mismatched impedance causes overvoltage when ZR >> ZC and PR approaches a value of
Unity; If ZR<< ZC, then PR is negative, and reflection exists but it does not result in voltage
amplification at termination;
(e) As mentioned earlier, coefficient of reflection for Source (PS) exists as well; typically, source
impedance ZS , is Zero and hence, PS is approximately -1; Note that under ideal conditions, the
rms value of sending end voltage does not change from its nominal value;
Applying the above theories to the case of a motor being fed via an ASD, one can come to a few
interesting conclusions. The mismatch between cable and motor surge impedance is the highest
for small motors; Also, in all cases, the coefficient of reflection is positive, which means that there
always exists amplification of the voltage at the motor terminals. Typical motor and cable surge
impedances for popular sizes of motors is given below [2]:
HP ZR ZC PR
25 1500 80 0.9
50 750 70 0.83
100 375 50 0.76
200 188 40 0.65
400 94 30 0.52
Smaller hp motors have larger inductance and less amount of slot insulation which results in a
higher surge impedance compared to larger hp motors.
Critical Cable Length
If the speed of propagation of the em wave is assumed to be v and the rise time of the PWM
wavefront (defined as the time taken for the output to go from 10 per cent to 90 per cent of its
peak value) is tr, then the distance traveled by the wavefront during its rise time is simply v x tr. If
the terminating point is at a position where the incident wave has just reached 50 percent of its
full value and if total reflection is assumed, i.e., PR = 1.0, then the sum of the incident and
reflected waves will yield 100% of the peak value of the incident wave. Any distance greater than
this critical length would allow the incident wave to build up to more than 50 per cent of its peak
value and if total reflection is considered, the effective wavefront at the terminating point will be
greater than 1.0 p.u. Thus the critical cable length is given by:
The speed of propagation of a wavefront over the conductor depends on the inductance and
capacitances per unit length of the conductor. Mathematically, it is given by:
Typical values for the speed of propagation, v, range from 100 to 150 m/ sec. The rise time of
typical IGBTs used in ASDs range from 0.4 to 0.6 sec. Using equation (10), the critical length is
calculated to vary from 20 to 45 meters.
Mitigation Techniques
3-Phase Load Reactors
Adding a 3-phase load reactor at the motor end will result in altering the surge impedance of the
motor. The line inductance component of the surge impedance of the motor is artificially made
high which causes the overall surge impedance of the motor to be higher than normal. The
mismatch between the surge impedances of the motor and the cable is aggravated thereby
resulting in a higher coefficient of reflection and a higher voltage at the terminating point. Since
the terminating point now has the 3-phase inductor first and then the motor terminals, the
overvoltage is experienced by the windings of the reactor instead of the motor. The reflected
voltage traveling along the conductor back to the sending end will have a higher amplitude
because of the larger degree of mismatch at the terminating point.
Adding a 3-phase load reactor at the ASD end will result in altering the surge impedance of the
cable. Typically, the surge impedance of the cable is lower than that of the motor. By increasing
the surge impedance of the cable artificially, the coefficient of reflection, PR is made lower which
reduces the magnitude of reflected wavefront. The reflected voltage travelling back on the
conductor towards the motor is reduced which reduces the stress on the cable.
RC Snubbers
Using the same drive/motor combination as above with the motor 1000 feet from the inverter, the
performance of the basic snubber network was satisfactory.
The snubber network will also extend the voltage rise time to several microseconds while
clamping the peak voltage. The snubber circuit (or impedance matching network) can effectively
minimize motor terminal voltage spikes and offer very good protection for the motor. Snubber
networks can cost less than $50 but must be located at the motor terminals as they are a cable
terminating device. In some cases it may be necessary to match the snubber impedance to the
actual line impedance in order to maximize its effect.
LC Filter
The beauty of this filter is that the motor sees a voltage waveform that is nearly sinusoidal. The
relative cost of this solution, based on a 5HP drive/motor combination is less than $250.
As the capacitor requirement (for tuning purposes) becomes greater, it is practical to add a
dampening resistor in series with the capacitor network. An alternative to this is the LC filter with
isolated capacitors.
LC Filter With Isolated Capacitor
The waveforms accomplished with this isolated capacitor technique are quite similar to the
waveforms captured with the basic LC filter as the concept is the same. Overall system
performance is optimized with this filter network because a sinusoidal waveform is provided for
the motor while voltage drop is minimized. Motor life is extended due to the improved waveform.
The relative cost of this network, based on 5HP drive/motor combination is about $450.
Mahesh Swamy, and John A. Houdek are with MTE Corporation
Let the voltage at any given point which is x meters away from the load end, be denoted by Vx.
This voltage is the sum of incident and reflected waves at that point. Let the incident wave be
denoted as v+ and the reflected wave be denoted as v-. Vx is given by:
As explained earlier, any em wave traveling on an electrical conductor exhibits the phenomenon of
reflection, exception being an infinite transmission line or a line terminated in its characteristic
impedance. Referring to Figure 1, the value of the terminating impedance, ZR, is given by the
ratio of the voltage and current at the point of termination. The voltage and current components
are made up of the incident and reflected waves. Mathematically, this can be represented as:
The phenomenon of reflection occurs irrespective of the distance between the motor and the ASD
as evidenced from the discussions in the preceding paragraphs. The magnitude of the voltage at a
given point on the transmission line is a function of the distance x from the terminating point as
shown by equation (2). The worst case of reflection at the terminating point occurs under open
circuit conditions. In order to estimate the critical length at which the magnitude of the sum of the
incident and reflected wave is higher than the peak value of the incident wave, one has to know
the speed of propagation of em waves on the transmission line.
As shown in the preceding paragraphs, in most long lead length cases involving induction motors
fed from ASDs, there exists voltage amplification. This overvoltage at the motor terminals can
deteriorate the insulation system of the motor thereby causing premature motor failures. Four
different techniques are discussed in this section which help alleviate the overvoltage problem
encountered by motors fed from ASDs at long distances. These four techniques are: the use of
3-phase load reactors; the use of RC snubbers at the motor terminals; applying low pass filter
section to wave shape the output from an ASD; and isolated form of the technique used above.
By using a 3-phase load reactor in between the motor and the ASD, one can change the
characteristic impedance of the motor or that of the source depending on where the inductor is
physically placed. Typical values of impedance used is 0.03 p.u (3 per cent impedance). A higher
value of impedance can cause a larger drop across the inductor thereby reducing the fundamental
component of the voltage at the motor terminals. This can result in torque reduction and in some
cases yield unsatisfactory operation at low speeds and high torque loads. For centrifugal load
applications, an inductance of 0.05 p.u. (5 per cent impedance) may also be used without
conspicuous deterioration in torque characteristics at practical operating points.
The RC snubber is the simplest and lowest cost of all methods employed. In its simplest form it
consists of resistors and capacitors configured as shown in Fig. 2. The RC snubber is typically
installed at the motor terminals and acts as an impedance matching network. The snubber
components are carefully selected to cause the load impedance to match the characteristic
impedance of the motor cables. When the motor surge impedance is equal to the line
characteristic impedance, then voltage reflection does not occur and excessive voltage will not be
experienced at the motor terminals.
The LC filter combines a load reactor and a capacitor network to form a low pass filter as
illustrated in Figure 3. The basic concept is that the filter network has a resonant frequency of
approximately 1 to 1.5 kHz and frequencies higher than that will be absorbed by the filter and not
passed on to the motor. Of course it is important that the inverter switching frequency be set to
about 1kHz higher than this resonant frequency to prevent excessive filter current and drive
malfunction. In fact, it has been found that the performance of this basic LC filter network, while
very good at 2.0 or 2.5 kHz, actually improves as the switching frequency is increased.
This network follows the same basic principles as the basic LC filter except it utilizes an isolation
transformer to feed the capacitors. Large values of capacitance can be used because the
transformer ratio reduces the capacitor current on the transformer primary side. We get the full
effect of the capacitor in conjunction with the series inductor, while minimizing the capacitor
current and capacitive reactance as seen by the inverter output circuit. The transformer impedance
offers the dampening which is desirable for large values of capacitance. The transformer also
offers some inductance which allows the use of a lower inductance value of series reactor thereby
reducing the voltage drop and improving motor torque.