INTERNATIONAL JOURNAL
OF PROFESSIONAL ENGINEERING STUDIES
Volume V /Issue 5 /SEP 2015
SPACE VECTOR PULSEWIDTH AMPLITUDE MODULATION FOR A BUCK–
BOOST VOLTAGE/CURRENT SOURCE INVERTER BASED ON SOLAR POWER
HEV
1
T. NAGA SUJITHA MR. M. PURUSHOTHAM.2
1
2
PG Scholar, Shree Institute Of Technical Education JNTU Anantapur University
Associate Professor, Shree Institute Of Technical Education JNTU Anantapur University
Abstract: This paper proposes a new
INTRODUCTION
Hybrid Electric Vehicle (HEV) which works with
In recent years, photovoltaic (PV) systems
Solar power and battery based on Buck-Boost
have received unprecedented attention due to the
Voltage/Current Source Inverter using Space
concerns about adverse effects of extensive use of
Vector
Modulation
fossil fuels on the environment and energy security.
(SVPWAM) technique. It mainly focuses on control
Also, these have got more attention in Electric
technique for an VSI/CSI. The switching losses are
vehicles.
reduced by 87% for VSI, 60% for CSI with
topologies are used for electric vehicles (EVs), they
SVPWAM technique compared to conventional
are the conventional three-phase inverter with a
Sinusoidal PWM technique. In both cases power
high voltage battery and a three-phase pulse width
density is increased by 2 to 3 times. It is also
modulation (PWM) inverter with a dc/dc boost
verified that the output harmonic distortions of
front end. The conventional PWM inverter imposes
SVPWAM is lower than SPWM, by using only one-
high stress on switching devices and motor thus
third of switching frequency of latter one. A
limits the motor’s constant power speed range
Maximum
(MPPT)
(CPSR), which can be overcame through the dc–dc
technique is used to track maximum power from
boosted PWM inverter. A typical configuration of
solar panel and store the energy in battery. It is
the Solar Hybrid electric vehicle (SHEV) is shown
obtained that it is feasible to use SVPWAM to make
in Fig. 1. The inverter is required to inject low
the buck–boost inverter suitable for applications
harmonic current to the motor, in order to reduce
that require high efficiency, high power density,
the winding loss and core loss. For this purpose, the
high temperature, and low cost the simulation
switching frequency of the inverter is designed
results are carried out for which the result shows
within a high range from 15 to 20 kHz, resulting in
its reliability and performance.
the switching loss increase in switching device and
Pulse
Width
Power
Amplitude
Point
Tracking
Currently,
two
existing
inverter
Index Terms: Solar panels, Buck-
also the core loss increase in the motor stator. To
Boost converter, SVPWAM, Total Harmonic
solve this problem, various soft-switching methods
Distortion.
have been proposed [1]–[3]. Active switching
rectifier or a diode rectifier with small DC link
capacitor has been proposed in [4], [5], [8]–[12].
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Volume V /Issue 5 /SEP 2015
can be achieved in VSI and CSI, respectively. If a
unity power factor is assumed, an 87% switching
loss reduction can be implemented in VSI, and a
74% reduction can be implemented in CSI.
Therefore, a high-efficiency, high-power density,
high-temperature, and low-cost inverter is achieved
by using an SVPWAM method.
CHARACTERISTICS OF PV ARRAY
AND CORRESPONDING MPPT
Fig 1 Typical configuration of a Solar HEV.
ALGORITHM
Various types of modulation methods such as
optimized pulse-width-modulation [13], improved
Space-Vector-PWM
control
for
different
The PV array – characteristic is described by the
optimization targets and applications [14]–[16],
following
and discontinuous PWM (DPWM) [17]have been
[9]:
proposed previously. Different switching sequence
arrangement can also affect the harmonics, power
=
−
−1
loss and voltage/current ripples [18]. DPWM has
(1)
been widely used to reduce the switching
frequency, by selecting only one zero vector in one
Equation (1) is the unit charge, the Boltzmann’s
sector. It results in 50% switching frequency
constant, the p-n junction ideality factor, and Tc the
reduction. However, if an equal output THD is
cell temperature. Current irsis the cell reverse
required, DPWM cannot reduce switching loss than
saturation current, which varies with temperature
SPWM. Moreover, it will worsen the device heat
according to
transfer because of the temperature variation. A
double 120 flattop modulation method has been
=
−
(2)
cell
reference
proposed in [6] and [7] to reduce the period of
PWM switching to only 1/3 of the whole
In
(2),
Tref
is
the
fundamental period. However, these papers didn’t
temperature, the reverse saturation current at Tref.
compare the spectrum of this method with others,
and EG the band-gap energy of the cell. The PV
which is not fair. In addition, the method is only
current iph depends on the insolation level and the
specified to a fixed topology, which cannot be
cell temperature according to
applied widely. This paper proposes a novel
generalized space vector pulse width amplitude
modulation (SVPWAM) method for the buck/boost
= 0.01
+
−
(3)
voltage source inverter (VSI) and current source
inverter (CSI). By eliminating the conventional
In (3), iscr is the cell short-circuit current at
zero vector in the space vector modulation, two-
the reference temperature and radiation, Kv a
third and one-third switching frequency reduction
temperature coefficient, and the insulation level in
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kW/m . The power delivered by the PV array is
calculated by multiplying both sides of (2) by vpv.
In this algorithm, PV-output voltage (Vk) and PV
output current (Ik) are sensed. Then power is
calculated (Pk) and compared with the power vale
=
calculated in the previous sample (Pk1) in order to
−
−
get Pk . If the results of Pk is zero the system is
working in MPP. Otherwise and according to the
1 (4)
sign of Pk and to the sign of Vk the command
voltage to control the duty cycle  of the converter
Substituting iph from (3) in (4), Ppv becomes
= 0.01
+
−
(let’s say the perturbation), will be decreased or
0
increased in order to force the working point of the
PV module towards the MPP. The algorithm is
−
−1
(6)
illustrated in the flowchart shown in Fig. 2.
VSI EMPLOYING SVPWAM
Based on (6), it is evident that the power delivered
by the PV array is a function of insulation level at
any given temperature. Since the inverter employed
in the PV system of this paper is of current-source
type, the power-versus-current characteristic of the
PV array has to be examined.
A. SVPWAM Control Principle in VSI
The principle of an SVPWAM control is to
eliminate the zero vectors in each sector. The
modulation principle of SVPWAM is shown in Fig.
3.
MPPT Control algorithm
There are many MPPT methods available in the
literature; the most widely-used technique is
described in the following section.
Perturbation and Observation (P&O)
Perturb and Observe (P&O) technique has been
selected to implement a MPPT control algorithm
due to its simplicity and the possibility to introduce
improvements.
Fig3. SVPWAM for VSI.
In each sector, only one phase leg is doing PWM
switching; thus, the switching frequency is reduced
by two-third. This imposes zero switching for one
phase leg in the adjacent two sectors. For example,
in sector VI and I, phase leg A has no switching at
all. The dc-link voltage thus is directly generated
from the output line-to-line voltage.
Fig. 2: Flowchart of P&O method
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Fig 4 DC-link voltage of SVPWAM in VSI .
Volume V /Issue 5 /SEP 2015
Fig 6 Theoretic waveforms of dc-link voltage,
In sector I, no zero vectors are selected. Therefore,
S1andS2keep constant ON, andS3and S6are doing
PWM switching. As a result, if the output voltage
is kept at the normal three-phase sinusoidal
voltage, the dc-link voltage should be equal to line-
output line-to-line voltage and switching signals.
Where θ∈[0,π/3]is relative angle from the output
voltage vector to the first adjacent basic voltage
vector like in Fig. 3. If the time period for each
vector maintains the same, the switching frequency
to-line voltage Vac at this time. Consequently, the
will vary with angle, which results in a variable
dc-link voltage should present a6ωvaried feature to
inductor current ripple and multi frequency output
maintain
a
desired
output
voltage.
The
corresponding waveform is shown in solid line in
Fig. 4.
harmonics. Therefore, in order to keep the
switching period constant but still keep the same
pulse width as the original one, the new time
A dc–dc conversion is needed in the front stage
periods can be calculated as
to generate this 6ωvoltage. The topologies to
implement this method will be discussed later. The
original equations for time periodT1andT2are
=
√
−
=
;
√
′
/
=
/(
+
)
(8)
The vector placement within one switching cycle
( )
(7)
in each sector is shown in Fig. 5. Fig. 6 shows the
output line-to-line voltage and the switching
signals ofS1.
B. SWITCHING LOSS REDUCTION FOR VSI
For unity power factor case, the inverter
switching loss is reduced by 86% because the
voltage phase for PWM switching is within [−60◦
,60◦], at which the current is in the zero-crossing
region.
In VSI, the device voltage stress is equal to dclink voltage VDC, and the current stress is equal to
Fig 5 Vector placement in each sector for VSI.
output current ia. Thus the switching loss for each
switch is
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As indicated, the worst case happens when
=
|
1
2
|
+
√
=
sin(
sin(
power factor is equal to zero, where the switching
)|.
.
loss reduction still reaches 50%. In conclusion,
SVPWAM can bring the switching loss down by
)|.
.
50–87%.
CSI EMPLOYING SVPWAM
.
.
.
(9)
A. Principle of SVPWAM in CSI
Where ESR,Vref, Iref are the references
The principle of SVPWAM in CSI is also to
eliminate the zero vectors. As shown in Fig. 8, for
each sector, only two switches are doing PWM
switching, since only one switch in upper phase
legs and one switch in lower phase legs are
conducting together at any moment. Thus, for each
switch, it only needs to do PWM switching in two
sectors, which is one-third of the switching period.
Compared to SVPWM with single zero vectors
selected in each sector, this method brings down
the switching frequency by one-third. Similarly, the
dc-link current in this case is a6ωvaried current. It
is the maximum envelope of six output currents
Fig 7 Conventional CSI and its corresponding
SVPWAM diagram.
:Ia,Ib,Ic,−Ia,−Ib,−Ic,. For example, in sector I,S1
always keeps ON, so the dc-link current is equal to
Ia. The difference between dc-link current in CSI
Since the SVPWAM only has PWM switching in
and dc-link voltage in VSI is dc-link current in CSI
two 60◦sections, the integration over 2πcan be
is overlapped with the phase current, but dc-link
narrowed down into integration within two 60◦
voltage in VSI is overlapped with the line voltage,
not the phase voltage. The time intervals for two
_
=
√
.
.
.
(10)
adjacent vectors can be calculated in the same way
as (7) and (8). According to diagram in Fig. 8, the
The switching loss for a conventional SPWM
method is
_ ′
= .
vector placement in each switching cycle for six
switches can be plotted in Fig. 10.The SVPWAM
.
.
is implemented on conventional CSI through
(11)
In result, the switching loss of SVPWAM over
SPWM is f=13.4%. However, when the power
factor decreases, the switching loss reduction
amount decreases because the switching current
simulation. Fig.8 shows the ideal waveforms of the
dc current Idc, the output phase ac current and the
switching signals of S1. The switching signal has
two sections of PWM in positive cycle, but no
PWM in negative cycle at all.
increases as Fig. 7 show.
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B. Switching Loss Reduction for CSI
Volume V /Issue 5 /SEP 2015
proposed SVPWAM, a spectrum analysis is
In CSI, the current stress on the switch is equal to
conducted to be compared with other methods on
the dc link current, and the voltage stress is equal to
the basis of an equal average switching frequency,
output line-to-line voltage, as shown the shadow
which has not been considered in paper [16].
area in Fig. 9 Thus, the switching loss for a single
A.
switch is determined by
SVPWAM, SPWM, and SVPWM
Spectrum
Comparison
between
The object of spectrum analysis is the output
=
_
√
.
_
.
.
(12)
voltage or current before the filter. The reason is
that certain orders of harmonics can be eliminated
by sum of switching functions in VSI or
subtraction of switching functions in CSI. The
comparison is between SVPWAM, DPWM, and
continuous SVPWM in VSI/CSI. The switching
frequency selected for each method is different,
because the comparison is built on an equalized
average
switching
frequency over
a
whole
fundamental cycle, in order to make the harmonics
Fig 8 Theoretic waveforms of dc-link current,
output line current and switching signals.
comparable at both low modulation and high
modulation range. Assume that the base frequency
When compared to discontinuous SVPWM, if
is f0 =10.8 kHz. Thus, 3f0 should be selected for
the half switching frequency is utilized, then the
SVPWAM, andf0should be selected for continuous
switching loss of it becomes half of the result in
SVPWM in VSI. In CSI, 3f0,2f0, andf0should be
(12). The corresponding switching loss ratio
selected for SVPWAM, discontinuous SVPWM,
between SVPWAM and discontinuous SVPWM is
and
shown in Fig. 11.
modulation index selected here is the maximum
continuous
SVPWM,
respectively.
The
modulation index 1.15, since the SVPWAM always
SPECTRUM ANALYSIS OF
SVPWAM
only
has
the
maximum
modulation
index.
Theoretically, the THD varies with modulation
index. The dc-link voltage is designed to be a
A fair comparison in switching loss should be
based on an equal output harmonics level. Thus,
the switching loss may not be reduced if the
switching frequency needs to be increased in order
to compensate the harmonics. For example,
discontinuous SVPWM has to have double
switching frequency to achieve the same THD as
constant for SVPWM and an ideal6ωenvelope of
the output six line-to-line voltages for SVPWAM.
Thus, the harmonic of the SVPWAM here does not
contain the harmonics from the dc–dc converter
output. It is direct comparison between two
modulation methods from mathematics point of
view.
continuous PWM. So the switching loss reduction
is much smaller than 50%. Therefore, for the newly
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B Analytical Double Fourier Expression for
Volume V /Issue 5 /SEP 2015
TOPOLOGIES FOR SVPWAM
SVPWAM
Basically,
The expression of double Fourier coefficient is
the
topologies
that
can
utilize
SVPWAM have two stages: dc–dc conversion
+
which converts a dc voltage or current into
()
=
()
1
a6ωvaried dc-link voltage or current; VSI or CSI
(
2
()
)
for which SVPWAM is applied. One typical
()
(13)
example of this structure is the boost converter
inverter discussed previously. However, the same
the
function can also be implemented in a single stage,
one
such as Z/quasi-Z/trans-Z source inverter [37]–
switching cycle. The double Fourier expression
[40]. The front stage can also be integrated with
coefficients can be derived as long as the rising
inverter to form a single stage. Take current-fed
edge of each PWM waveform is known. The output
quasi-Z-source inverter as an example. Instead of
line-to-line voltage Vab is used as an illustrative
controlling the dc-link current Ipn to have a constant
example. It is a function of switching function
average value, the open zero state duty cycle Dop
Where
fundamental
y∈[0,2π]
cycle;
represents
x∈[0,2π]
represents
will be regulated instantaneously to control Ipm to
( )=
( ( )−
( ))
(14)
TABLE I
INTEGRATIONLIMIT FORLINE-TO-LINE
VOLTAGE Vab(t)
have a 6ω fluctuate average value, resulting in a
pulse type 6ωwaveform at the real dc-link current
Ipn, sinceI1is related to the input dc current Iin by a
transfer function
=
(15)
CASE STUDY:1-KW BOOSTCONVERTER FOR EV MOTOR
DRIVE APPLICATION
A. Basic Control Principle
The circuit schematic and control system for a 1kW boost converter inverter motor drive system is
So its double Fourier equation is equal to the
shown in Fig. 15. A 6ωdc-link voltage is generated
subtraction of two double Fourier equations for
from a solar PV array by a boost converter, using
switching functions. The integration limits for
open-loop
control.
Inverter
Vab (t)is shown in Tables I. The coefficients finally
modulated
by
SVPWAM
could be simplified into a closed-form expression
specifications for the system are input voltage is
in terms of Bessel functions, which will not be
100–200 V; the average dc-link voltage is 300 V;
discussed here.
output line-to-line voltage rms is 230 V; and
a
then
could
method.
be
The
frequency is from 60 Hz to 1 kHz.
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Fig 10 Operation region of boost-converter-inverter
EV traction drive .
In SVPWAM control of boost mode, dc-link
voltage varies with the output voltage, in which the
modulation index is always kept maximum. So,
when dc-link voltage is above the battery voltage,
dc-link voltage level varies with the output voltage.
The voltage utilization increased and the total
power stress on the devices has been reduced.
Fig 9 SVPWAM-based MPPT boost-converter
motor drive system.
B. Voltage Constraint and Operation
Region
It is worth noting that the SVPWAM technique
Fig.11(a)
after filter
can only be applied when the batteries voltage falls
into the region
≤
√
√
due to the step-up
nature of boost converter. The constraint is
determined by the minimum point of the6ω dc-link
voltage. Beyond this region, conventional SPWM
can be implemented. However, the dc-link voltage
in this case still varies with6ωbecause of the small
(b)
before filter
film capacitor we selected. Thus, a modified
SPWM with varying dc-link voltage will be
adopted during the motor start up as shown in Fig.
16. Hence, the system will achieve optimum
efficiency when the motor is operating a little
below or around nominal voltage. When the motor
demands a low voltage during start up, efficiency is
Fig.12 (a)
after filter
the same as the conventional SPWM-controlled
inverter.
(b)
before filter
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1.
C. Variable DC-Link SPWM Control at
The switching power loss is reduced by
90% compared with the conventional
High Frequency
SPWM inverter system.
When the output needs to operate at a relative
2.
high frequency, like between 120 Hz and 1 kHz, it
of 2 because of reduced dc capacitor (from
is challenging to obtain a6ω dc-link voltage
40 to 6 μF) and small heat sink is needed.
without increasing the switching frequency of a
3.
boost converter because the controller does not
switching loss. The reason is because it switches at
a complete current region. Also a normal SPWM
cannot be used in this range because the capacitor
is designed to be small that it cannot hold a
passives,
heat
sink,
and
semiconductor stress.
boost converter switching frequency would cause a
because it takes up more than 75% of the total
The cost is reduced by 30% because of
reduced
have enough bandwidth. Furthermore, increasing
substantial increase of the total switching loss,
The power density is increased by a factor
A high-efficiency, high-power density, hightemperature, and low-cost 1-kW inverter engine
drive system has been developed on matlab
software. The effectiveness of the proposed method
in reduction of power losses has been validated by
the simlation results.
constant dc link voltage. Therefore, the optimum
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T. NAGA SUJITHA currently pursuing M.Tech in
Power Electronics at Shree Institute of Technical
Education Affiliated to JNTU Anantapur
University.
Email:sujitha.tummalapalli@gmail.com
Mr. M. PURUSHOTHAM Associate Professor
and Head Of Department at Shree Institute Of
Technical Education Affiliated to JNTU Anantapur
University. E-mail: purush239@gmail.com
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