Download Switch_Mode_Inverters

Switch-Mode DC-AC Inverters
Applications:
• ac motor drives
• Uninterruptible ac power supplies
• Where a sinusoidal ac output is required whose
magnitude and frequency both have to be controlled
Terminal voltage is adjustable
in its magnitude and frequency
8-1
Switch-Mode DC-AC Inverter: Bi-directional power flow
8-2
Switch-Mode DC-AC Inverter: Basic concepts
•
•
•
•
•
•
•
•
Inverters with single- and three-phase
ac outputs will be discussed
Input is dc voltage source
Such inverters are called voltage-source
inverters (VSI)
The other type of inverter is a currentsource inverter (CSI) where the input is
a dc current source
Discussion will be limited to VSI
Four-quadrant operation
Rectifier mode: quadrants 2 and 4
Inverter mode: quadrants 1 and 3
8-3
Switch-Mode DC-AC Inverter: Basic concepts (cont’d)
•
•
•
•
•
•
vo can be assumed to be sinusoidal
io will lag vo since the inverter will drive an
inductive load such as a motor
In interval 1, both vo and io are positive and
interval 3, both vo and io are negative
Therefore during intervals, 1 and 3, po=voio will
be positive, and power will flow from the dc to ac
side which is the inverter mode of operation
During the intervals 2 and 4, vo and io will be
opposite signs, and power will flow from the ac
side to the dc side which is the rectifier mode of
operation
Thus, switch-mode inverters are capable of
operating in all four quadrants
8-4
Synthesis of a Sinusoidal Output by PWM
One-leg inverter
•
•
•
•
Inverter output to be sinusoidal with
voltage and frequency controllable
Vd/2
Inverter switching frequency is
determined by
- Sinusoidal control signal – which is
used to modulate the switch duty ratio and
-Vd/2
has a frequency f1.
- Triangular waveform
Output voltage magnitude fluctuates
between Vd /2 and –Vd /2
Output voltage frequency is determined
by the control signal frequency
Frequency modulation ratio, mf=fs/f1
8-5
Single Phase Half-Bridge Inverter
•
•
•
Two equal capacitors are connected in series across the dc input
Vd /2 is the voltage across each capacitor
Items of importance:
- peak amplitude of the fundamental frequency component Vo1 is
ma (=Vcontrol /Vtri) times Vd /2
- harmonics in the inverter output voltage waveforms
8-6
Single Phase Half-Bridge Inverter (cont’d)
•
•
•
•
The switches T+ and T- are controlled based on the comparison of vcontrol and vtri
When vcontrol > vtri , T+ is on and vAo=Vd /2
When vcontrol < vtri , T- is on and vAo=-Vd /2
Since the two switches are never off simultaneously, the output voltage vAo fluctuates
between Vd /2 and -Vd /2.
8-7
Harmonic Spectrum of VAo
•
•
The normalized harmonic voltages
with significant amplitudes are
plotted
This plot shows three items of
importance:
– The peak value of the fundamental
frequency component is ma times
Vd/2.
– Harmonics appear as side bands,
cantered around the switching
frequency
– The harmonic mf should be an odd
integer.
8-8
Fundamental Frequency Component of VAo
• The peak amplitude of the fundamental-frequency component (VAo)1 is
ma times Vd/2. This can be explained by first considering a constant
vcontrol as shown in the following figure.
• The average output voltage (or more specifically, the output voltage
averaged over one switching time period Ts = 1/fs) VAo depends on the
ratio of Vcontrol to Vtri for a given Vd
V Ao
V
Vd
 control

2
V tri

Vcontrol  V tri
8-9
Fundamental Frequency Component of VAo (Cont’d)
• Let us assume that Vcontrol varies very little during a switching time
period, that is, mf is large.
• Therefore, assuming Vcontrol to be constant over a switching time
period, following figure indicates how the "instantaneous average"
value of vAo (averaged over one switching time period Ts) varies from
one switching time period to the next. This "instantaneous average" is
the same as the fundamental-frequency component of vAo.
8-10
Fundamental Frequency Component of VAo (Cont’d)
• The average output voltage (or more specifically, the output voltage
averaged over one switching time period Ts = 1/fs) VAo depends on the
ratio of Vcontrol to Vtri for a given Vd
v control  Vcontrol sin 1t

Vcontrol  V tri

Vcontrol sin 1t Vd
  v Ao 1 
Vcontrol  V tri

2
V tri
V
 m a sin 1t d
for m a  1.0
2
Therefore,
 V Ao 1  ma
Vd
2
• which shows that in a sinusoidal PWM, the amplitude of the
fundamental-frequency component of the output voltage varies linearly
with ma. Therefore, the range of ma from 0 to 1 is the linear range.
8-11
Harmonics in the Inverter Output Voltage VAo
The harmonics in the inverter output voltage waveform appear as sidebands,
centered around the switching frequency and its multiples, that is, around
harmonics mf, 2mf, 3mf, and so on. This general pattern holds true for all
values of ma in the range 0-1.
the harmonic amplitudes are almost independent of mf, though mf defines the
frequencies at which they occur. Theoretically, the frequencies at which
voltage harmonics occur can be indicated as
fh = (jmf ± k)f1
that is, the harmonic order h corresponds to the kth sideband of j times the
frequecy modulation ratio mf.
h = j(mf) ± k
where the fundamental frequency corresponds to h = 1. For odd values of j,
the harmonics exist only for even values of k. For even values of j, the
harmonics exist only for odd values of k.
8-12
Harmonics in the Inverter Output Voltage VAo
8-13
Single-Phase Full-Bridge Inverter
•
•
•
Consists of two one-leg inverters
Preferred over other arrangements in higher power ratings
With the same dc input voltage, output voltage is twice that of the half-bridge inverter
8-14
PWM to Synthesize Sinusoidal Output
•
•
•
•
When TA+ is ON, vAo=Vd/2
When TB- is ON, vBo= - Vd/2
vBo(t)= - vAo(t)
vo(t)= vAo(t) - vBo(t) = 2 vAo(t)
•
Peak of the fundamental frequency
component:
V o1  ma Vd
where the amplitude modulation ratio
ma 
•
Vcontrol
 1.0
Vtri
Output voltage switches between Vd
and - Vd
8-15
Example 1: Switch-mode inverter (one phase-leg, half bridge)
A general analysis of the switch-mode inverter (shown in the figure below) is to be
done. The switching frequency fs, which is also the frequency of the triangular signal
is 1450 Hz. The DC voltage, Vd, is 600 V. Output voltage is sinusoidal voltage with a
frequency equal to 50 Hz. The load is connected between the inverter leg A and the dc
voltage midpoint o.
+
Vd
-
+
Vd /
2+
Vd /
2-
TA+
o
DA+
A
io
TA-
+
DA-
vA
N-
N
•
•
•
•
Find the frequency modulation ratio, mf.
Calculate the output voltage (rms value of 1. harmonic), when the amplitude
modulation ratio, ma, is equal to 0.8?
Prove that (Vo1)peak = ma (Vd / 2 ).
Compute the rms value of the 5 most dominant harmonics of vAo (at ma=0,8), by
using Table 8-1, page 207. Also indicate the frequencies at which these
harmonics appear.
8-16
Example 2: Bipolar single phase half bridge inverter
8-17
Single-Phase Push-Pull Inverters
• requires a transformer with a center-tapped
primary
• T1 is ON (and T2 is OFF):
vo=Vd/n, where n is the transformer
turns ratio.
• T2 is ON (and T1 is OFF):
vo= - Vd/n
• The peak value of the fundamental
component of the output voltage:
Vo1= ma (Vd/n)
8-18
• No more than one switch in series conducts at any instant of time
• Less switching voltage drops
• Thus, this results in a significant improvement in energy efficiency
8-19
Three-Phase Inverter
• Used to supply three-phase loads
• Three single-phase inverters could be used, however, 12 switches are
necessary, as a result, less efficient
• Consists of three legs, one for each phase
• One of the two switches in a leg is always ON at any instant
• Output of each leg depends on Vd and the switching status
8-20
8-21
Summary
• dc-to-ac converters are known as inverters
• The function of an inverter is to change the dc input voltage to an ac output
voltage of desired magnitude and frequency
• The output voltage waveforms of ideal inverters should be sinusoidal
• However, the output of practical inverters contains harmonics
• For high power applications, low distorted sinusoidal waveforms are required
• Harmonic contents could be minimized by the use of high-speed
semiconductor switching techniques
• Inverters are widely used in industrial applications
- motor drives, UPS, induction heating, standby power supplies, etc.
- input may be a battery, fuel cell, solar cell, or there dc source
• dc-to-ac inverters can make smooth transition into the rectification mode,
where the flow of power reverses from the ac side to the dc side
• Two types of inverters: single-phase inverters and three-phase inverters
8-22