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```PWM inverters Cont.
Unipolar Switching of the Bridge inverter.
Previously we have discussed Bipolar Voltage switching in which Leg A and Leg B are
switched in exact Anti-phase. We have seen that this produces an output voltage ripple at
the triangle wave frequency with peak to peak ripple voltage amplitude = 2xVd. An
alternative scheme known as uni-polar voltage switching offers significant advantages.
(Vcontrol)
+
TA+, TB-
Bipolar Switching
Carrier (Vtri)
Pulse Width
Modulated
Output
TA-, TB+
Unipolar Switching
Modulation (Vcontrol)
+
Carrier (Vtri)
-1
Inverse
Modulation
( -Vcontrol)
Pulse Width
Modulated
Output
+
Carrier (Vtri)
TA+
TA-
TB+
Pulse Width
Modulated
Output
TB-
Unipolar Switching cont.
Unipolar Switching has 2 major advantages:
1) The lowest ripple frequency has doubled to 2 x ftri
2) The peak to peak ripple voltage is now only Vd rather than 2Vd.
This frequency doubling will greatly reduce the size of inductor required to smooth the
output current.
Is it a harmonic or is it ripple?
The terminology can be slightly confused here. In general the term hamonics is used to
refer to unwanted low frequency components which are at integer multiples of the
reference frequency. Low frequency components at non integer components of the
reference frequency are known as interharmonics. If asynchronous modulation is
employed and mf is small then a PWM inverter can generate low frequency
interharmonics. It is rare to consider harmonics or interharmonics of more than 40 times
the reference frequency (eg 2kHz for a 50Hz system).
Ripple is the term usually used to refer to unwanted high frequency components
(typically more than 40 x the reference frequency). It is quite common for a pwm inverter
to have an mf of 100 or more. In this case it matters little whether or not the carrier is
synchronous with the reference and we consider the frequencies centred around the
triangle wave carrier to be ripple frequencies.
Peak to Peak Current Ripple Calculation for Bipolar and unipolar operation
fa = 50Hz
ftri = 20kHz
ma = 0.5
Vd = 300V
Output Inductor = 200uH
In both cases the worst case ripple will occur when the duty cycle of the output voltage
waveform is to 50%. For bipolar operation this occurs at 0 output voltage. In unipolar
operation this occurs at the instant when the carrier is 50% of the peak of the triangle
wave.
For the purpose of the calculation we assume that the inductor blocks all of the ripple.
Example done in class.
Peak to peak ripple current for Bipolar operation = (0.5*Vd)/(ftri.L)
Peak to Peak Ripple for Unipolar operation= (0.125*Vd)/(ftri.L)
Three Phase Bridge Inverter
The capacitor midpoint is ficticious.
Each leg uses the same triangle wave and produces an output voltage that swings
between –Vd/2 and +Vd/2 with respect to the fictitious midpoint.
The clever bit is that the reference voltagesfor leg a, b and c are all phase shifted by 120°
from each other so the resulting outputs on leg A,B and C are three phase shifted sine
wave – a proper 3 phase set. The fictitious midpoint actually represents the neutral pfor
each phase.
At maximum linear modulation (ma<1) the output voltage on any leg has a peak value
equal to Vd/2. Thus the maximu rms phase voltage (for linear modulation) is Vd/(2√2).
The line to line voltage is then √3.Vd/(2√2).
For a modulation index of less than 1 then the output voltage magnitude is
√3.ma.Vd/(2√2) = 0.612 ma.Vd (NB for ma <= 1.0)
Three Phase inverter Waveforms
It is important to note that the neutral is fictitious and cannot take any real current. This
implies that the three phase inverter should always be used with a delta connected load
where a neutral is not required. This has the added advantage that the harmonics (or
ripple) at the triangle carrier frequency largely canacels out in the line to line voltage
allowing us to benefit from the same frequency doubling effect we got with unipolar
operation of a single phase inverter. If the frequency modulation index mf is low then
perfect cancellation of the frequency component at ftri can be achieved if mf is an odd
multiple of three. For high values of moulation index this is less significant and the
dominant ripple frequency occurs at 2*ftri
Over Modulation
Just as in the Single phase inverter overmodulation can achieve a higher output voltage at
the expense of (i) linearity and (ii) increased dstortion. In the extrem overmodulation will
result in square wave output voltages. The maximu achievable line to line output voltage
is (√6/π).Vd = 0.78*Vd.
```
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