Download Bi-directional switch

BI-DIRECTIONAL SWITCH-MODE CONVERTER
1.1 Introduction
A circuit capable of operation as a converter transferring average power over a cycle from dc
source to ac source and also capable of operation as an inverter transferring average power over a
cycle from ac source to dc source is called a bi-directional converter. The usually used three
phase PWM full- bridge inverters using controlled switches with inverse connected diode across
each of them as shown in Fig.1 can in fact be operated ac a bi-directional switch-mode power
converter.
Figure 1 Three-phase inverter.
1.2 Operation of the inverter
The full-bridge inverter consists of three legs, A, B and C. Each leg consists of two switches
and their antiparallel diodes. The two switches in each leg are switched in such a way that when
one of them is in its off state, the other switch is on. The two switches are never off
simultaneously. In practice they are both off for a short time interval, known as blanking time
that is negligible compared with the on/off intervals of switches, to avoid short circuiting of the
dc input.
If the converter switches in each leg are not off simultaneously, then the output current i o in
Fig 1 will flow continuously. The output voltage is solely dictated by the status of the switches.
For example, consider leg A. The output voltage vAo, with respect to the midpoint of the dc
source Vd, is dictated by the switch states: when TA+ is on, the output current will flow through
TA+ if io is positive or it will flow through DA+ if io is negative. In either case TA+ being on ensures
that point A is at the same potential as the positive terminal of the dc input and therefore
vAo = Vd /2 (if TA+ is on and TA- is off)
(1a)
Similarly, when TA- is on, io will flow through TA- if it is negative and io will flow through DA- if
it is positive. Therefore
vAo = - Vd /2
(if TA- is on and TA+ is off).
(1b)
Equations 1-a and 1-b show that vAo depends on the switch status and is independent of direction
of io.
1.2.1 Sinusoidal PWM operation of the inverter
In order to produce a sinusoidal output voltage waveform at a desired frequency f1, the
converter switches are pulse-width modulated by comparing a switching frequency triangular
waveform vtri with a sinusoidal control signal vcontrol at the desired frequency f1as shown in Fig.2
(a) for each phase.
1.2.1.1 PWM operation of one leg of the inverter
The frequency fs of the triangular waveform determines the frequency with which inverter
switches are switched and is kept constant along with its amplitude V. The control signal vc of
amplitude Vc is used to modulate the switch duty ratio. The amplitude modulation ratio m a is
defined as
ma=Vcontrol/Vtri
(2)
The frequency modulation ratio mf is defined as
mf = fs/f1
Comparing vcontrol and
Vtri,
(3)
the status of the switches and output voltages independent of the
direction of io, are:
vcontrol > vtri, TA+ is on,
vAo = Vd/2
(4a)
or
vcontrol  vtri, TA- is on,
vAo = -Vd/2
(4b)
Since the two switches are never off simultaneously, the output voltage v Ao (voltage at A
with reference to the mid point of dc supply) fluctuates between Vd/2 and –Vd/2. Voltage
Voltage vAo and its fundamental frequency component (dashed curve) are shown in Fig.2 (b) for
mf = 15 and ma=0.8 .The corresponding harmonic spectrum
is shown in Fig.2(c). This plot
shows three items of importance.
1. The peak amplitude of the fundamental-frequency component ( VA0)1 is ma times Vd/2
2.
The peak amplitude of the fundamental –frequency component ( VA0)1 can be shown to
be
VAO
= m a.
Vd/2
for vcontrol ≤ Vtri
(5)
Figure 2 Pulse-Width Modulation
For large mf, vcontrol is nearly constant over a switching period. vcontrol, vtri and
shown in Fig.3
vAo are
Figure 3
From Fig. 3(a), and 3(b), the average of vAo over a switching time period Ts, that can be
considered as the fundamental-frequency component (vAo)1 is
VAo
= Vd/2. [(Ts/2+2t1) -(Ts/2-2t1)]/Ts, where 4t1/Ts = vcontrol / Vtri
= (vcontrol/Vtri)Vd/2
for vcontrol ≤ Vtri
(6)
If the control voltage vcontrol varies sinusoidally at the frequency f1 = ω1/2π, which is the desired
(or the fundamental) frequency of the inverter output:
vcontrol = Vcontrol sin ω1t
(7)
where Vcontrol ≤ Vtri
Using Eqs. (6) and (7) and the foregoing arguments ,the fundamental frequency component
(vAo)1 is given by
(vAo)1 = (Vcontrol / Vtri) sin ω1t. Vd/2.
= ma sin ω1t. Vd/2, for ma≤ 1.0
Therefore,
(VAo)1 = ma Vd/2,
for ma ≤ 1.0
The range of ma from 0 to 1 is referred to as the linear range
(8)
2. 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 pattern holds good for all ma in the range 0-1.For a frequency modulation ratio ≥ 9, the
harmonic amplitudes are almost independent of mf, though mf defines the frequencies at which
they occur. 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 frequency modulation
ratio mf. The harmonic orders present are
h = (jmf ± k)
(9)
where the fundamental frequency corresponds to h=1. It is to be noted that only odd harmonics
will be present in the output voltage
In table 1-1, the normalized harmonics (VAO )h / (Vd/2) are tabulated as a function of the carrt
amplitude modulation ratio ma, assuming mf ≥ 9.Only those with significant amplitudes up to j =
4 in Eq. (9) are shown.
Table 1-1 Generalized Harmonics of vAO for a large mf
In the inverter circuit it may be noted
vAN = vAo+Vd/2
(10)
Therefore, the harmonic voltage components in vAN and vAo are the same.
(VAN)h = (VAO)h
(11)
Table 1-1 shows that that Eq.8 is followed almost exactly and the amplitude of the
fundamental component in the output voltage varies linearly with ma
3. The harmonic mf should be an odd integer. Choosing mf as odd integer results in odd
symmetry as well as even symmetry with the time origin shown in Fig. 2(b).Therefore only odd
sine terms are present in the Fourier series.
1.2.1.2 Sinusoidal PWM operation of all three legs of the inverter
To generate output voltages in leg B and leg C the same triangular waveform is compared with
sine wave vcontrol b and vcontrol c lagging vcontrol a by 120º and 240º respectively as shown in Fig
4(a). The wave form of the voltage at points A with reference to the negative dc bus of the threephase inverter are shown in Fig.4 as vAN. The wave form of the voltage at points B and C with
reference to the negative dc bus of the three-phase inverter will be same as vAN, but with a phase
lag of 120º and 240ºrespectively. It is noted that an identical amount of average dc component is
present in the output voltages vAN and vBN. These dc components are cancelled out in the line to
line voltages, as in vAB shown in Fig. 4(b).
,
Figure 4 Three-phase PWM waveforms and harmonic spectrum
In three phase inverters harmonics of the line-to-line voltages are of concern. The
harmonics in the output of any one of the legs, for example vAN in Fig.4 are identical to the
harmonics in vAo in Fig. 2., where only the odd harmonics exit as side bands, centered around mf
and its multiples, if mf is odd. Considering the harmonic at mf, (the same applies to its odd
multiples), the phase difference between the mf harmonic in vAN and vBN is (120mf) º.This phase
difference is equivalent to zero (a multiple of 360) if mf is odd and a multiple of 3.As a
consequence, the harmonics at mf is suppressed in the line to line voltage vAB. The same
argument applies in the suppression of harmonics at the odd multiples of m f if mf is chosen to be
an odd multiple of 3.
.
1.2.1.2.1 Linear Modulation (ma ≤ 1.0)
In the linear region (ma ≤ 1.0), the fundamental frequency component in the output voltage varies
linearly with the amplitude modulation ratio ma. From Eq. 8, the peak value of the fundamental
frequency component in one of the inverter legs is
(VAN)1 = ma Vd /2
(12)
Therefore the line to line rms voltage at the fundamental frequency due to 120º phase
displacement between phase voltages is
VLL1
= (√ 3 / √ 2) ma Vd /2
= 0.612 ma Vd
(ma ≤ 1.0)
(13)
The rms harmonic components of the line to line voltage can be calculated from Table 1-1,
recognizing that some of the harmonics are cancelled out in the line to line voltages. These
harmonic voltages are listed in Table 1-2
Table 1-2 Generalized Harmonics of vLL for a Large and odd mf that is a multiple of 3
1. 2.1.2.2 Over Modulation (ma ≥ 1.0)
If the peak of the control voltage is more than the peak of triangle waveform, ma becomes
≥ 1.0 and some of the switchings do not take place near the peak of the waveform v AO. The
waveform becomes flat topped. For sufficiently large values of ma, vAO becomes a square wave.
In the over modulation region compared to the region with ma ≤ 1.0, more sideband harmonics
appear centered around the frequencies of harmonics mf and its multiples. In this mode the line to
line voltage normalized with reference dc supply voltage does not increase proportionally with
ma. It increases linearly reaching a value of 0.612 at ma = 1. Beyond ma=1, it increases gradually
and reaches a value of 0.78 at ma=3.24 when the voltage vAN becomes a square wave as shown in
Fig 5
Figure 5 Three phase square wave inverter waveforms and line to line voltage.
1.2.2 CURRENT –REGULATED MODULATION
In applications like instantaneous var controller, ac servo drives and unity power factor ac- dc-ac
converters, it is necessary to control magnitude as well as phase relationship to the ac voltages
quickly. There are various ways to obtain the switching signals for the inverter switches.
Tolerance band control is one such method.
1.2.2.1 Tolerance band control
A scheme to force the inverter current follow a sinusoidal reference iA* is shown in Fig.6 The
actual phase current iA is compared with the tolerance band around the reference current for the
corresponding phase. If the actual current tries to go above the upper tolerance band T A_ is turned
on (TA+ is turned off). If the actual current tries to go below the lower tolerance band T A+ is
turned on. The switching frequency depends on how fast the current changes between the lower
and the upper limits.
Figure 6 Tolerance band control
1.3 RECTIFIER MODE OF OPERATION
The same bridge inverter can be used as an inverter as well as a converter (i.e. as dc - ac and ac dc). It can in general be called a converter. For ac-dc converters, braking of induction motor and
for interfacing power electronics equipments with power grid, rectifier mode of operation of the
switch-mode converter is used.
The inverter and rectifier modes of operation of the three phase bridge on a per phase basis are
shown in Fig. 7. eA can be one phase of an induction motor or line. In the phasor diagram for the
fundamental component motoring (inverting) mode is shown in Fig.7b. The converter voltage
VAn applied to the motor leads the back emf of the motor (line voltage) by an angle δ. The active
(real) component (IA)p of IA is in phase with EA, and therefore the converter is operating in the
inverter mode feeding power to the motor (lines).
The phase angle lead δ and the magnitude VAn of the ac voltage produced by the inverter
can be controlled by changing the phase angle and the magnitude of the reference sine-waves
applied to the pwm controller. If the converter voltage VAn is now made to lag EA by the same
angle δ as before, keeping its magnitude constant, the phasor diagram in Fig.7c shows that the
active (real) component (IA)p of IA is in phase opposition with EA, and therefore the converter is
operating in the converter mode feeding power from the motor (lines) to the dc source. From the
phasor diagram in Fig.7c, it can be shown that the real power per phase P and the reactive power
per phase Q supplied by the ac source to the converter are given by
P = (EA2/ωL) (VAn /EA) sinδ
(14)
Q = (EA2/ωL) [1-(VAn /EA) cosδ]
(15)
From the equations it is clear that for a given line voltage E A and the line inductance, desired
value P and Q can be obtained by controlling the magnitude and the phase of the converter
output voltage Van.
Figure 7 Operation modes: (a) circuit (b) inverter mode (c) converter mode
A three phase as dc ac switch mode converter is shown in Fig8.
Figure 8 Three phase switch mode ac dc ac converter
1.4
UPF SWITCH-MODE CONVERTERS
Rectification and inversion at unity power factor is of special importance. For example in doubly
fed induction generator system, rotor voltage at slip frequency or in a permanent magnet
generator system, the stator voltage is to be rectified to dc and the dc voltage is to be inverted
and fed to the grid. It is highly desirable that the rectification and inversion be done at unity
power factor. A phasor diagram for rectification and inversion ay unity power factor is shown in
Fig 9.
(a)
(b)
Figure 9 Rectification and inversion (a) rectification at unity power factor (b) inversion at
unity power factor
The front end ac to dc converter can be thought of as a pwm inverter producing an ac
fundamental rms voltage (from Eq. 12) at the input terminals An, Bn and Cn each equal to
VCONV1 = ma * Vd / (2 √2)
ma<1.0.
(16)
VCONV1 opposes the generator phase voltage. The power delivered against this opposing
voltage is the per phase power that is converted to dc. As per the phasor diagram, the
magnitude of the fundamental voltage VCONV1 at the input of the ac to dc converter opposing
the current IS1 is given by
VCONV1= (VS2+ω2L12 IS12)1/2,
(17)
where IS1 is the current supplied by the generator in phase with the phase rms voltage of the
generator VS, L1 is the source inductance of the generator and ω is the generator frequency.
If Vd is maintained as per Eq. 16 and 17 input current IS1 will be in phase with input
voltage and the power factor will be unity. In Fig.8, Vd is established by charging the
capacitor through the switch mode converter on the generator side. The value of Vd should be
of a sufficiently large value so that VCONV1 at the ac side of the converter is produced by a
PWM that corresponds to a PWM in a linear region. This is necessary to limit ripple in the
input current is.
The control circuit to regulate Vd at its reference value Vd* and to achieve a unity power
factor of operation is shown in Fig.10. The amplified error between Vd and Vd* is multiplied
with the signal proportional to the input voltage vs waveform to produce the reference current
signal is*.A current mode control such as a tolerance band control or a fixed frequency
control can be used to deliver is1 equal to is* and in phase or 180 degrees out of phase with
the line voltage vs. The magnitude and direction of power flow are automatically controlled
by regulating Vd at its desired value. It is possible to obtain a phase shift between vs and is1
and hence a finite reactive power flow by introducing the corresponding phase shift in the
signal proportional to vs in the control circuit of Fig 10. The steady state waveforms for a
unity power factor rectifier operation are shown in Fig 11.
Fig.10. Control of switch mode interface.
Fig 11. Wave forms at unity power factor operation (a)phasor diagrams;(b)circuit waveforms
It has been shown that the dc input current of a three phase PWM inverter operating
at high switching frequency and feeding a three phase load is given by
Id = 3 Vs Is cosφ1/Vd
Where Vs and Is are the sinusoidal per phase line quantities and cosφ1 is the angle by which
the phase current lags the phase voltage. However switching frequency currents flow through
dc filter capacitor. For rectification at unity power factor, φ1= 0 and
Id = 3 Vs Is / Vd
As only switching frequency currents flow through dc filter capacitor, only small filter
capacitor is needed. Ripple voltage on dc link voltage will also be small.
REFERENCE:
NED MOHAN, TORE M. UNDELAND and WILLIAM P.ROBBINS, POWER
ELECTRONICS. Converters, Applications and Design. JOHN WILEY & SONS, INC.2003.