This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
1
Multi-String Five-Level Inverter with Novel
PWM Control Scheme for PV Application
Nasrudin A. Rahim, Senior Member, IEEE and Jeyraj Selvaraj
Abstract— This paper presents a single-phase multi-string
DC
DC
PV String 1
DC
DC
Index Terms— PWM inverter, photovoltaic (PV), PI current
control, multilevel inverter, grid-connected, multi-string.
I.
A
Manuscript received February 23, 2009. Accepted for publication August
26, 2009.
Copyright © 2009 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to pubs-permissions@ieee.org
N. A. Rahim and J. Selvaraj are with the Center of Research for Power
Electronics, Drives, Automation and Control (UMPEDAC), Department of
Electrical Engineering, University Malaya, 50603 Kuala Lumpur, Malaysia
(phone: +603-79675305; fax: +603-79674478; e-mail: jeyraj95@um.edu.my)
DC
Grid
AC
PV String 2
DC
INTRODUCTION
s the world is concerned with fossil fuel exhaustion and
environmental problems caused by the conventional
power generation, renewable energy sources particularly solar
energy and wind energy have become very popular and
demanding. PV sources are used today in many applications
as they have the advantages of being maintenance and
pollution free [1]. Solar-electric-energy demand has grown
consistently by 20%-25% per annum over the past 20 years,
which is mainly due to the decreasing costs and prices. This
decline has been driven by 1) an increasing efficiency of solar
cells; 2) manufacturing-technology improvements; 3)
economies of scale; [2]. PV inverter which is an important
element in the PV system is used to convert DC power from
the solar modules into AC power to be fed into the grid.
A general overview of different types of PV inverters is
given in [3]-[4]. This paper presents a multi-string five-level
inverter for PV application. The multi-string inverter shown in
Fig. 1 is a further development of the string inverter, where
several strings are interfaced with their own dc-dc converter to
a common dc-ac inverter [5]. This is beneficial, compared
with the centralized system, since every string can be
DC BUS
five-level PV inverter topology for grid-connected photovoltaic
(PV) systems with a novel PWM control scheme. Three PV
strings are cascaded together in parallel configuration and
connected to a five-level inverter to produce output voltage in
five levels: zero, +1/2Vdc, Vdc, -1/2Vdc and -Vdc. Two reference
signals identical to each other with an offset equivalent to the
amplitude of the triangular carrier signal were used to generate
PWM signals for the switches. DSP TMS320F2812 is used to
implement this PWM switching scheme together with a digital PI
current control algorithm. The inverter offers much less THD
and can operate at near unity power factor. The validity of the
proposed inverter is verified through simulation and
implemented in a prototype. The experimental results are
compared with conventional single-phase multi-string three-level
grid-connected PWM inverter.
controlled individually. Thus, the operator may start his/her
own PV power plant with a few modules. Further
enlargements are easily achieved since a new string with a dcdc converter can be plugged into the existing platform. A
flexible design with high efficiency is hereby achieved [3]. In
this work, a five-level inverter is used instead of a
conventional three-level PWM inverter because it offers great
advantages such as mproved output waveforms, smaller filter
size, lower EMI, lower THD, and others [6]-[12].
DC
PV String 3
Fig. 1. Configuration of multi-string inverters
This paper proposes a single-phase multi-string five-level
inverter topology. It consists of three strings of PV arrays
connected to their own dc-dc boost converter. An auxiliary
circuit comprising of four diodes and a switch is configured
together with a conventional full-bridge inverter to form this
topology. A novel PWM control scheme is introduced to
generate switching signals for the switches and to produce
five output voltage levels: zero, +1/2Vdc, Vdc, -1/2Vdc and -Vdc
(assuming Vdc is the supply voltage). This inverter topology
uses two reference signals instead of one to generate PWM
signals for the switches. Both the reference signals Vref1 and
Vref2 are identical to each other except for an offset value
equivalent to the amplitude of the carrier signal Vcarrier as
shown in Fig. 2.
Vcarrier
-Vcarrier
V ref1
Vref2
Fig. 2. Carrier and reference signals
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
2
than 2 of the grid voltage Vg to ensure power flow from the
PV arrays into the grid [13]-[14]. As a step-up transformer
with a ratio of 1:2 is used, Vinv should be:
Vinv >
Vinv >
2V g
2
Vg
DC-DC Boost
Converter
D1
DC Bus
Auxiliary Circuit
Full-Bridge Inverter
L1
PV String 1
The proposed single-phase multi-string five-level inverter
topology is shown in Fig. 3. It consists of three dc-dc boost
converters connected to a common dc bus, an auxiliary circuit
and a full-bridge inverter configuration. Input sources, PV
string 1, PV string 2 and PV string 3 are connected to the
inverter via the dc-dc boost converters. Since the proposed
inverter is used in a grid-connected PV system, the utility grid
is used instead of a load. The dc-dc boost converters are used
to track the maximum power point (MPP) independently as
well as to step-up the inverter output voltage Vinv to be more
injected into the grid. The injected current must be sinusoidal
with low harmonics distortion. In order to generate sinusoidal
current, sinusoidal PWM is used since it is one of the most
effective methods. Sinusoidal PWM is obtained by comparing
a high-frequency carrier signal with a low-frequency sinusoid
signal, which is the modulating signal or reference signal. The
carrier has a constant period; therefore the switches have
constant switching frequency. The switching instant is
determined from the crossing of the carrier and the modulating
signal.
S1
L2
PV String 2
II. MULTI-STRING FIVE-LEVEL INVERTER TOPOLOGY
A filtering inductance L f is used to filter the current
Vpv/2
C1
S5
Lf
S4
D3
S7
D6
D4
D2
S2
L3
PV String 3
Since the inverter is used in a PV system, a PI current
control scheme is employed to keep the output current
sinusoidal and to have high dynamic performance under
rapidly changing atmospheric conditions and to maintain the
power factor at near unity. Simulation and experimental
results are presented to validate the proposed inverter
configuration.
Vpv/2
C2
Ig
1:2
D7
D5
Vg
Vinv
S6
S8
S3
Fig. 3. Single-phase multi-string five-level inverter topology.
or
(1)
(2)
2
Therefore, the dc bus voltage is assumed to be approximately
200V.
In this work, multi-string approach is adopted since each
dc-dc-converter can independently perform maximum power
point tracking (MPPT) for its PV strings. This will
compensate for mismatches in panels of like manufacture,
which can be up to 2.5% [15]. It offers the further advantage
of allowing panels to be given different orientations and so
open up new possibilities in architectural applications.
Furthermore, a greater tolerance to localized shading of panels
can be achieved. Another advantage of multi-string
configuration is the mixing of different sources becomes
possible i.e. existing PV panel strings could be extended by
adding new higher output panels without compromising
overall string reliability or performance. Besides that, greater
safety during installation and maintenance adds to the
advantages of multi-string configuration. Depending on the
design, each converter module may be able to isolate its
connected power source, so that the wiring of series or parallel
connection of these strings can be performed safely. The
power-source-converter connection is a safe low-voltage
connection [16].
The dc-dc boost converters are connected in parallel to
avoid high dc bus voltage which eventually will increase the
size of the capacitors and the inverter’s cost. Therefore, only
two capacitors with equal capacitance rating are used as the dc
bus and the other dc-dc boost converters is connected to this
dc bus as shown in Fig. 3.
III. PWM MODULATION
Modulation index Ma for five-level PWM inverter is given
as [17]
A
(3)
Ma = m
2Ac
where Ac is the peak-to-peak value of carrier and Am is the
peak value of voltage reference Vref. Since in this work two
reference signals identical to each other are used, equation (3)
can be expressed in terms of amplitude of carrier signal Vc by
replacing Ac with Vc. and Am = V ref1 = V ref2 = V ref .
M =
V ref
(4)
2Vc
If M>1, higher harmonics in the phase waveform is
obtained. Therefore, M is maintained between 0 and 1. If the
amplitude of the reference signal is increased higher than the
amplitude of the carrier signal, i.e. M>1, this will lead to
overmodulation. Large values of M in sinusoidal PWM
techniques lead to full overmodulation [18]. Fig. 4 shows the
carrier and reference signals for different values of M.
Vcarrier
−Vcarrier
Vref1
Vref2
(a)
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
3
Vref1
Vcarrier
An =
4V dc
nπ
∑ [(− 1)
P
m
]
sin(nα m )
(8)
m =1
Vref2
−Vcarrier
IV. OPERATIONAL PRINCIPLES OF MULTI-STRING FIVELEVEL INVERTER
Combinations of PV strings are used as the input voltage
sources. The voltage across the strings are known as Vpv1, Vvp2
and Vpv3. Referring to equations (1) and (2), Vpv1, Vvp2 and Vvp3
are boosted by the dc-dc boost converters to exceed the grid
voltage Vg and the voltage across the dc bus is known as Vpv.
The operational principle of the proposed inverter is to
generate five-level output voltage i.e. 0, +Vpv/2, +Vpv, -Vpv/2, Vpv as in Fig. 5. As illustrated in Fig 3, an auxiliary circuit
which consists of four diodes and a switch S4 is used between
the dc bus capacitors and the full-bridge inverter. Proper
switching control of the auxiliary circuit can generate halflevel of PV supply voltage i.e. +Vpv/2 and -Vpv/2. [7].
Two reference signals Vref1 and Vref2 will take turns to be
compared with the carrier signal at a time. If Vref1 exceeds the
peak amplitude of the carrier signal Vcarrier, Vref2 will be
compared with the carrier signal until it reaches 0. At this
point onwards, Vref1 takes over the comparison process until it
exceeds Vcarrier. This will lead to a switching pattern as shown
in Fig. 5. Switches S4-S6 will be switching at the rate of the
carrier signal frequency while S7 and S8 will operate at a
frequency equivalent to the fundamental frequency. Table 1
illustrates the level of Vinv during S4-S8 switch on and off.
(b)
Vcarrier
Vref1
Vref2
−Vcarrier
(c)
Vref1
Vcarrier
Vref2
−Vcarrier
Vref1
(d)
Fig. 4. Carrier and reference signals for different values of modulation index,
M (a) M=0.3. (b) M=0.5. (c) M=0.7. (d) M=1.2.
From the PWM modulation, the analysis of harmonic
components in the proposed inverter can be preformed. The
output voltage produced by comparison of the two reference
signals and the carrier signal can be expressed as [7]
Vo (θ) = A0 +
∞
∑ (A
n
cos nθ + B n sin nθ )
(5)
n =1
If there are P pulses per quarter period, and it is an odd
number, the coefficients Bn and Ao would be a zero where n is
an even number. Therefore, the equation (5) can be rewritten
as
Vo (θ) =
∞
∑ A cos nθ
(6)
n
n =1,3....
2V
An = − dc
nπ
∑∑ [(− 1)
P
4
int (i/2 )
]
sin(nα m + i )
Vinv
Vpv
Vref2
Vpv/2
0
-Vpv/2
-Vpv
S4
S5
S6
S7
S8
α1
α2
π
α3
α4
2π
Fig. 5. Inverter output voltage, Vinv and switching pattern for single-phase
five-level inverter
(7)
m =0 i =1
where m is a pulse number and α is the phase displacement
angle. The Fourier series coefficients of the conventional
single-phase full-bridge inverter by sinusoidal PWM is given
as
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
4
TABLE 1
INVERTER OUTPUT VOLTAGE DURING S4-S8 SWITCH ON AND OFF
S4
ON
OFF
OFF
ON
OFF
S5
OFF
ON
ON
or
OFF
OFF
OFF
S6
OFF
OFF
OFF
or
ON
OFF
ON
S7
OFF
OFF
ON
or
OFF
ON
ON
S8
ON
ON
OFF
or
ON
OFF
OFF
Vinv
+Vpv/2
+Vpv
0
-Vpv/2
-Vpv
If one of the PV strings is disconnected from the dc bus, the
operation of the other dc-dc boost converters will not be
affected as they are connected in parallel. As the dc-dc boost
converters is used to track the maximum power point tracking
(MPPT) point, it can be concluded that the MPPT tracking of
the PV strings is done independently. Later expansion of the
PV strings is also possible by adding a dc-dc boost converter
as shown in Fig. 6.
PV String 1
L1
C1
PV String 2
D2
S2
L3
PV String 3
+
S1
L2
0
Variables m1, m2 and m3 are obtained from the MPPT
algorithm as illustrated in the flowchart in Fig. 8. Variables
m1, m2 and m3 correspond to MPPT algorithm for string 1,
string 2 and string 3 respectively. The values of m1, m2 and m3
change with respect to irradiance level. If irradiance level is
high, the corresponding values of m1, m2 and m3 are also high.
Thus, by referring to equation (10), it will lead to high value
of m. Since Iref is proportional to m, high value of Iref is
obtained. As a result, the inverter’s output current Ig will be
high as it follows Iref to minimize the instantaneous error
between Ig and Iref.
The instantaneous current error is fed to a PI controller.
The integral term in the PI controller improves the tracking by
reducing the instantaneous error between the reference and the
actual current. The resulting error signal u which forms Vref1
and Vref2 is compared with a triangular carrier signal and
intersections are sought to produce PWM signals for the
inverter switches. This is to ensure Ig to be in phase with grid
voltage Vg and always at near unity power factor.
A. Mathematical Formulation
The PI algorithm can be expressed in the continuous time
domain as:
D3
C2
S3
Ln
PV String n
D1
the current injected into the grid also known as grid current Ig
is sensed and fed back to a comparator which compares it with
the reference current Iref. Iref is obtained by sensing the utility
grid voltage Vg. The sensed Vg signal is converted into the
reference signal before it is multiplied with variable m.
Therefore
Iref = Vg x m
(9)
Variable m is the sum of m1, m2 and m3 i.e,
m = m1 + m2 + m3
(10)
t
Dn
-
Sn
PV String Extention
Fig. 6. PV string extension for existing configuration.
V. CONTROL SYSTEM ALGORITHM AND IMPLEMENTATION
One of the problems in the PV generation systems is the
amount of the electric power generated by the solar arrays is
always changing with weather conditions, i.e., the intensity of
the solar radiation. A MPPT method or algorithm, which has
quick response characteristics and is able to make good use of
the electric power generated in any weather, is needed to solve
the above problem [19]. Various MPPT control methods have
been discussed in detail in [20]-[22].
In this paper, Perturb and Observe (P&O) algorithm is used
to extract maximum power from the PV arrays and deliver it
to the inverter. The feedback controller used for the inverter is
the proportional –integral (PI) algorithm. As shown in Fig. 7,
u(t) = K p e(t) + K i
∫ e( τ )dτ
(11)
τ =0
where:
u (t ) is the control signal
e(t ) is the error signal
t
is the continuous-time domain time variable
τ is the calculus variable of integration
K p is the proportional mode control gain
K i is the integral mode control gain
Implementing this algorithm by using a DSP requires one to
transform it into the discrete time domain. Trapezoidal sum
approximation is used to transform the integral term into the
discrete time domain since it is the most straightforward
technique. The proportional term is directly used without
approximation.
(12)
P term: K p e(t) = K p e(k)
t
k
h
(
)
K
e
τ
dτ
≅
K
[e(i) + e(i − 1)] (13)
I term: i ∫
i∑
2
=
i
0
τ =0
Time relationship : t = k * h
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
5
where :
h is the sampling period
k is the discrete-time index: k = 0,1,2,......
For simplification, it is convenient to define the new controller
gains as:
h
K i' = K i
(14)
2
From which one can construct the discrete-time PI control law
as:
u(k) = K p e(t) + K i'
k
∑ [e(i) + e(i − 1)]
To eliminate the need to calculate the full summation at each
time step (which would require an ever increasing amount of
computation as time goes on), the summation is expressed as a
running sum:
sum(k) = sum(k − 1 ) + [e(k) + e(k − 1 )]
(16)
u( k ) = K p e( k ) + K i' sum( k )
(17)
These two equations, which represent the discrete-time PI
control law, are implemented in the DSP TMS320F2812 to
control
the
overall
operation
of
the
inverter.
(15)
i =0
L1
PV String 1
IPV1
S1
VPV1
C1
IPV2
L2
S5
D2
D4
S7
D6
PV String 2
Lf
VPV2
S2
S4
Ig
D5
D3
L3
IPV3
PV String 3
D1
Vg
1:2
D7
C2
VPV3
Vinv
S6
S8
S3
S4-S8
Gate
Drivers
IPV1
X
PPV1
MPPT1
m1
u
VPV1
IPV2
X
PPV2
MPPT2
m2 +
X
VPV3
m
X
Iref +
error
-
Ig
+
VPV2
IPV3
+
PI Controller
PPV3
MPPT3
m3
Vg
DSP TMS320F2812
Fig. 7. Multi-string five-level inverter with control algorithm implemented in DSP TMS320F2812.
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
6
START
KP
Ig -
Sense V(k) & I(k)
+
error
+
u’
+
Anti-windup
Ki
Yes
P(k)-P(k-1)=0
u
Anti-windup
No
No
Fig. 9. PI control algorithm implemented in DSP TMS320F2812
Yes
P(k)-P(k-1)>0
V(k)-V(k-1)>0
Yes
No
Increase mx
VI. SIMULATION AND EXPERIMENTAL RESULTS
V(k)-V(k-1)>0
No
Decrease mx
Yes
Increase mx
Decrease mx
RETURN
x=1,2,3,……….
Fig. 8. MPPT flowchart
B. Algorithm Implementation
Control signal saturation and integral mode anti-windup
limiting are easily implemented in software. In this work, the
control signal itself takes the form of pulse-width modulated
(PWM) outputs from the DSP. Therefore, the control signal is
saturated at the value that corresponds to 100% duty cycle for
the PWM. An undesirable side-effect of saturating the
controller output is the integral mode windup. When the
control output saturates, the integral mode control term (i.e.,
the summation) will continue to increase, but will not produce
a corresponding increase in the controller output (and hence
will not produce any additional increase in the plant response).
The integral can become quite large, and it can take a long time
before the controller is able to reduce it once the error signal
changes sign. The effect of windup on the closed-loop output
is larger transient overshoot and undershoot, and longer
settling times.
One approach for overcoming the integral-mode windup is to
simply limit in the software the maximum absolute value
allowed for the integral, independent of the controller output
saturation [23], as shown in Fig. 9.
A. Simulation Results
Simulations were performed by using MATLAB
SIMULINK to verify that the proposed inverter can be
practically implemented in a PV system. It helps to confirm the
PWM switching strategy for the multi-string five-level
inverter. Then, this strategy is implemented in a real-time
environment i.e. the DSP to produce PWM switching signals
for the switches. Fig. 10(a) shows the way the PWM switching
signals are generated by using two reference signals and a
triangular carrier signal. The resulting PWM signals for
switches S4 to S8 are shown in Fig. 10(b)-(f).
Note that one leg of the inverter is operating at a high
switching rate equivalent to the frequency of the carrier signal
while the other leg is operating at the rate of fundamental
frequency (i.e. 50Hz) . The switch at the auxiliary circuit S4
also operates at the rate of the carrier signal. As mentioned
earlier, the modulation index M will determine the shape of the
inverter output voltage Vinv and the grid current Ig. Fig. 11
shows simulation results of Vinv and Ig for different values of
M.
Referring to equations (1) and (2), the dc bus voltage is set
to 200V ( > V g / 2 , in this case Vg is 240V) to inject current
into the grid. Fig. 11(a) shows Vinv is less than V g / 2 due to
M being less than 0.5. The inverter should not operate at this
condition because the current will be injected from the grid
PWM Signal Generation
40
PWM Switching Signal for Switch S4
2
Vref1
30
1.5
20
S4
Amplitude
1
10
0.5
0
0
Vcarrier
-10
-20
0
0.002
0.004
0.006
Vref2
0.008
0.01
Time (s)
0.012
0.014
0.016
-0.5
0.018
0.02
-1
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
Time (s)
(a)
(b)
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
7
PWM Switching Signal for S5
1.5
1.5
1
1
0.5
0.5
0
0
-0.5
-0.5
-1
0
0.002
0.004
0.006
0.008
0.01
0.012
PWM Switching Signal for S6
2
S6
S5
2
0.014
0.016
0.018
-1
0.02
0
0.002
0.004
0.006
0.008
0.01
Time (s)
(c)
0.018
0.02
1.5
1
S8
1
S7
0.016
PWM Switching Signal for S8
2
1.5
0.5
0.5
0
0
-0.5
-0.5
-1
0.014
(d)
PWM Switching Signal for S7
2
0.012
Time (s)
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
-1
0.02
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
Time (s)
Time (s)
(e)
(f)
Fig. 10. PWM switching strategy and PWM signal for S4-S8
Inverter Output Voltage (Vinv)
100
2
50
1
0
0
-50
-1
-100
-2
-150
0
0.005
0.01
0.015
0.02
0.025
Grid Current (Ig)
3
Current (A)
Voltage (V)
150
0.03
0.035
-3
0.04
0
0.005
0.01
0.015
0.02
(a)
0.03
0.035
0.04
(b)
Inverter Output Voltage (Vinv)
250
0.025
Time (s)
Time (s)
Grid Current (Ig)
15
200
10
150
5
Current (A)
Voltage (V)
100
50
0
-50
0
-5
-100
-150
-10
-200
-250
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
-15
0
0.005
0.01
0.015
Time (s)
(c)
8
150
6
100
4
Current (A)
Voltage (V)
0.03
0.035
0.04
Grid Current (Ig)
10
200
50
0
-50
2
0
-2
-100
-4
-150
-6
-200
-250
0.025
(d)
Inverter Output Voltage (V)
250
0.02
Time (s)
-8
0
0.005
0.01
0.015
0.02
Time (s)
0.025
0.03
0.035
0.04
-10
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Time (s)
(e)
(f)
Fig. 11. Inverter output voltage (Vinv) and grid current (Ig) for different values of M (a) Vinv for M < 0.5. (b) Ig for M < 0.5. (c) Vinv for M > 1.0. (d) Ig for M > 1.0.
(e) Vinv for 0.5 ≤ M ≤ 1.0. (f) Ig for 0.5 ≤ M ≤ 1.0.
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
8
into the inverter as shown in Fig. 11(b). Over modulation
condition, which happens when M > 1.0, is shown in Fig.
11(c). It has a flat top at the peak of the positive and the
negative cycles because both the reference signals exceed the
maximum amplitude of the carrier signal. This will cause Ig to
have a flat portion at the peak of the sine waveform as shown
in Fig 11(d). To optimize the power transferred from the PV
arrays to the grid, it is recommended to operate at 0.5 ≤ M ≤
1.0. Vinv and Ig for optimal operating condition are shown in
Fig. 11 (e) and (f). As Ig is almost a pure sinewave, the total
harmonic distortion (THD) can be reduced compared with that
under other values of M.
B. Experimental Results
The simulation results are verified experimentally by using a
DSP TMS320F2812. Three PV strings with different types of
solar modules and locations are connected to the five-level
inverter via a common dc bus. Table 2 illustrates the PV
modules’ characteristics and their location while Table 3
shows the multi-string five-level inverter’s specifications and
its controller parameters. The prototype inverter is shown in
Fig. 12. PWM switching signals for the switches is generated
by comparing a triangular carrier signal with two reference
signals as shown in Fig. 13.
TABLE 3
PV MULTI-STRING FIVE-LEVEL INVERTER SPECIFICATIONS
AND CONTROLLER PARAMETERS
: IGBT IRG4PC40UDPBF VCE =600, IC=20A
S1-S8
: RHRP30120 VRR=1200V, I=30A
D1-D7
L1-L3
: 2.2mH
Lf
: 3mH
: 2200uF VDC=500V Aluminium Electrolytic
C1-C2
: 10
Kp
: 0.1
Ki
Switching Frequency : 20kHz
Sampling Frequency : 78kHz
TABLE 2
CHARACTERISTICS OF PV MODULES
PV STRING 1
Model : SIEMENS SP75
No. of Panels
: 6 in series
Max Power
: 75W
: 4.8A
Short circuit current, ISC
: 4.4 A
MPPT current, IMPPT
Open Circuit voltage, VOC : 21.7V
:17.0V
MPPT voltage, VMPPT
Location
: Roof Top
Fig. 12. Prototype of the multi-string five-level PWM inverter.
PV STRING 2
Model : SIEMENS SP85
No. of Panels
: 4 in series
Max Power
: 85W
: 5.45A
Short circuit current, ISC
: 4.95 A
MPPT current, IMPPT
Open Circuit voltage, VOC : 22.2V
:17.2V
MPPT voltage, VMPPT
Location
: Gnd Floor
(a)
PV STRING 3
Model : MITSUBISHI PV-AE125MF5N
No. of Panels
: 4 in series
Max Power
: 125W
: 7.90 A
Short circuit current, ISC
: 7.23 A
MPPT current, IMPPT
Open Circuit voltage, VOC : 21.8V
:17.3 V
MPPT voltage, VMPPT
Location
: Roof Top
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
9
(b)
(c)
Fig. 13. PWM switching signals for S4 - S8, (a) S4. (b) S5 and S6 (c) S7 and S8.
Code Composer Studio (CCS), the programming platform
for DSP TMS320F2812, programs the control algorithm for
the proposed multi-string five-level inverter. CCS offers the
advantage of graph displaying, which can be used to
investigate the results as in Figs. 14 to 18. As the input voltage
of each string is converted into floating point values for DSP
manipulation, the values corresponding to Figs. 14 to 18 do not
represent the actual values of the input voltage but are good
enough for investigation and analysis. Fig. 14 shows the input
of PV strings 1, 2 and 3. Here, PV string 1 is on while PV
string 3 is off. When PV string 2 is turned from off to on, m
increases to increase the amplitude of Iref because more power
is generated at the input, subsequently increasing the current
injected into the grid. As PV string 2 shuts down, its voltage
goes to zero while PV string 1 maintain its MPP as illustrated
in Fig. 15. m decreases to decrease the amplitude of Iref as the
current injected into the grid is less because PV string 2 stops
producing power.
The same phenomena happen when PV string 1 is on, PV
string 2 is off and PV string 3 is turned from off to on as
shown in Fig. 16. When PV string 3 is turned off, m decreases
as in Fig. 17 to decrease Iref. As a result, less current is injected
into the grid compared with the previous condition when PV
string 3 was on. Fig. 18 is captured when all three strings are
on initially. Then PV string 3 is turned off followed by string
2. m decreases when PV string 3 is turned off and it decreases
further when PV string 2 is turned off. This shows that the
strings are working independently and later expansion of the
strings is possible.
Fig. 19 shows experiment results for the grid voltage Vg and
the inverter’s output voltage, Vinv. As the grid voltage had been
stepped down to half the actual voltage by using a 1:2 ratio
transformer, the magnitude of Vg is now 120V. To inject
current into the grid, Vinv > 2 Vg; Vinv is thus set at 200V.
Fig. 20-22 illustrates the experiment results for Vinv and Ig
for 8A, 5A, and 3A, respectively. It can be seen that Vinv
consists of five levels of output voltage, and Ig has been
filtered to resemble a pure sinewave. The magnitude of Vinv did
not change, but maintained at 200V as the current injected into
the grid decreased when irradiance level decreased. The
modulation index M is 0.8. For M less than 0.5, Vinv is less than
Vg / 2 . Therefore, current will be injected from the grid into
the inverter as shown in Fig. 23. This condition should be
avoided to protect the PV system from damage.
In the case of M being more than 1.0, the results are not
shown since the PV system is designed to operate at conditions
of M being less than 1. This is done by calculating the input
current and input voltage corresponding to the output voltage
and output current. Then, M is varied accordingly, for the
inverter to operate at minimum and maximum power
conditions. Below the minimum power condition (for example,
during heavy clouds or night time) or above the maximum
power condition (for example, over rating of PV arrays which
exceeds the rating of the inverter) the inverter should not
operate to ensure the safety of the PV system and the
environment.
To prove that the proposed multi-string five-level inverter
has advantages over the conventional multi-sting three-level
inverter in terms of THD and power factor, the corresponding
measurements were made on both inverters. FLUKE 43B
Power Quality Analyzer was used for this purpose. The
conventional multi-string three-level inverter for gridconnected PV application is shown in Fig. 24. The same
current control techniques were used to control the overall
performance of the inverter. The only difference between both
inverters is the elimination of the auxiliary circuit, and
therefore only one dc bus capacitor is used. Fig. 25 shows the
THD measurement for the multi-string five-level inverter while
Fig. 26 shows the THD measurement for the multi-string threelevel inverter. The %THD for five-level inverter is recorded as
5.7% while the %THD for three-level inverter is 9.5%. From
both illustrations the THD measurement for multi-string fivelevel inverter is much lower than that of the multi-string threelevel inverter. The power factor measurement is shown in Fig.
27. It is notable that both the grid voltage Vg and the current
injected into the grid Ig are in phase with a power factor of
0.99.
Fig. 28 illustrates the relationship between Ig and the THD
measurement. It shows that as Ig increases, the THD decreases.
Since Ig is increased by increasing the modulation index M to
force more current injected into the grid, it can be concluded
that M is proportional to Ig.
Efficiency measurements were carried out to compare the
efficiency of the multi-string three-level PWM inverter with
the multi-string five-level PWM inverter for PV application.
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
10
Table 4 illustrates the measured efficiency of both inverters
operating at different output powers. At 960W and 600W
operating conditions, the measured efficiency of the multistring three-level PWM inverter was approximately 90% while
the measured efficiency for the multi-string five-level PWM
inverter was 86%. For 360W operating condition, the
efficiency decreased to 89%, and to 84%, for the three-level
PWM inverter, and the five-level PWM inverter, respectively.
As expected, the efficiency of the multi-string five-level
PWM inverter is lower compared to the conventional multistring three-level PWM inverter. The main reason is the
addition of the auxiliary circuit between the dc-dc boost
TABLE 4
MEASURED EFFICIENCY OF THREE-LEVEL AND FIVE-LEVEL
PWM INVERTER AT DIFFERENT OUTPUT POWER
Efficiency,
Three-level
PWM inverter
(%)
90
90
89
Power (W)
960 @ Ig=8A
600 @ Ig=5A
360 @ Ig=3A
Efficiency,
Five-level
PWM inverter
(%)
86
86
84
P V s tr in g 1
On
P V s tr in g 3
O ff
P V s tr in g 2
On
V MPPT
P V s tr in g 2
On
Fig. 14. Conditions during PV string 1’s being switched on and PV string 2’s being switched from off to on.
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
11
P V s trin g 1
On
P V s trin g 3
O ff
P V s trin g 2
O ff
P V s trin g 2
O ff
Fig. 15. Conditions during PV string 1’s being switched on and PV string 2’s being switched off .
V MPPT
P V s trin g 2
O ff
P V s trin g 3
On
P V s trin g 1
On
P V s trin g 3
On
Fig. 16. Conditions during PV string 1’s being switched on and PV string 3’s being switched from off to on.
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
12
P V s tr in g 3
O ff
P V s tr in g 2
O ff
P V s tr in g 3
O ff
P V s tr in g 1
On
Fig. 17. Conditions during PV string 1’s being switched on and PV string 3’s being switched off .
P V s t r in g 1
On
P V s tr in g 3
O ff
P V s tr in g 3
O ff
P V s tr in g 2
O ff
P V s t r in g 2
O ff
Fig. 18. Conditions during PV string 1’s being switched on, and PV strings 2’s and 3’s being switched off.
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
13
converters and the full-bridge inverter configuration.
Switching losses of switch S4 in the auxiliary circuit caused the
efficiency of the multi-string five-level PWM inverter to be
approximately 4% less than the multi-string three-level PWM
inverter. However, simulation and experimental results show
that the THD of the proposed inverter is lower as compared
with the conventional three-level PWM inverter which is an
important element for grid-connected PV systems.
Fig. 22. Experimental result of Vinv and Ig at Ig=3A for M=0.8.
Fig. 19 Experimental result of Vg and Vinv for M=0.8.
Fig. 23. Experimental result of Vinv and Ig for M =0.2.
PV String 1
IPV1
Fig. 20. Experimental result of Vinv and Ig at Ig=8A for M=0.8.
L1
D1
S1
VPV1
S4
PV String 2
IPV2
L2
VPV2
IPV3
S6
D2
Lf
C1
S2
Ig
1:2
PV String 3
S5
VPV3
Vg
Vinv
D3
L3
S7
S3
S4-S7
Gate
Drivers
IPV1
X
PPV1
MPPT1
m1
u
VPV1
IPV2
X
PPV2
MPPT2
m2 +
X
m
X
PPV3
MPPT3
m3
error
-
Ig
Vg
VPV3
Fig. 21. Experimental result of Vinv and Ig at Ig=5A for M=0.8.
PI Controller
Iref +
+
VPV2
IPV3
+
DSP TMS320F2812
Fig. 24. Conventional multi-string three-level PWM inverter for PV application
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
14
THD vs Ig
30
27
%THD
25
20
20.1
15.2
15
11.8
10
8.5
6.3
5
5.9
5.7
0
1
1.5
2
2.5
3
3.5
4
4.5
Ig (A)
Fig. 28. Relationship between Ig and THD measurement
VII. CONCLUSION
Fig. 25. THD result of multi-string five-level PV inverter
This paper presented a single-phase multi-string five-level
inverter for PV application. A novel PWM control scheme
with two reference signals and a carrier signal were used to
generate the PWM switching signals. The circuit topology,
control algorithm, and operational principle of the proposed
inverter were analyzed in detail. The configuration is suitable
for PV application as the PV strings operate independently and
later expansion is possible. Furthermore, experimental results
indicate that the THD of the multi-string five-level inverter is
much less than that of the conventional multi-string three-level
inverter. In addition, both the grid voltage and the grid current
are in-phase at near-unity power factor.
REFERENCES
[1]
Fig. 26. THD result of multi-string three-level PV inverter
Fig. 27. Grid Voltage Vg and Grid Current Ig at near -unity power factor
N. A. Rahim, Saad Mekhilef, “Implementation of Three- Phase grid
Connected Inverter for Photovoltaic Solar Power Generation System”
Proceedings IEEE. PowerCon 2002. Vol 1, pp. 570 – 573., Oct 2002.
[2] J. M. Carrasco, L. G. Franquelo, J. T. Bialasiewicz, E. Galvan, R. C.
PortilloGuisado, M. A. M. Prats, J. I. Leon, N. Moreno-Alfonso, "PowerElectronic Systems for the Grid Integration of Renewable Energy
Sources: A Survey," IEEE Trans. on Industrial Electronics, vol. 53, no.
4, pp. 1002- 1016, Aug 2006.
[3] S. B. Kjaer, J. K. Pedersen, F. Blaabjerg, “A Review of Single-Phase
Grid Connected Inverters for Photovoltaic Modules,” IEEE Trans. Ind.
Appl., vol. 41, no. 5, pp. 1292–1306, Sept/Oct. 2005.
[4] S. Daher, J. Schmid, F. L. M. Antunes, “Multilevel Inverter Topologies
for Stand-Alone PV Systems,” IEEE Trans. on Industrial Electronic, vol.
55, no. 7, pp. 2703-2712, July. 2008.
[5] M. Meinhardt, G. Cramer, “Past, Present and Future of Grid-Connected
Photovoltaic and Hybrid-Power-Systems,” in Proc. IEEE-PES Summer
Meeting, vol. 2, pp. 1283-1288, July 2000.
[6] S. Kouro, J. Rebolledo, J. Rodriguez, "Reduced Switching-FrequencyModulation Algorithm for High-Power Multilevel Inverters," IEEE
Trans. on Industrial Electronics, vol. 54, no. 5, pp. 2894-2901, Oct.
2007.
[7] S. J. Park, F. S. Kang, M. H. Lee, C. U. Kim, “A New Single-Phase FiveLevel PWM Inverter Employing a Deadbeat Control Scheme,” IEEE
Trans. Power Electronics., vol. 18, no. 18, pp. 831-843, May. 2003.
[8] L. M. Tolbert, T. G. Habetler, “Novel Multilevel Inverter Carrier-Based
PWM Method,” IEEE Trans. Industry Application., vol. 35, no.5, pp..
1098-1107, Sept/Oct 1999.
[9] Y. Liu, H. Hong, A. Q. Huang, “Real-Time Calculation of Switching
Angles Minimizing THD for Multilevel Inverters with Step Modulation,”
IEEE Trans. on Industrial Electronic, vol. 56, no. 2, pp. 285-293, Feb.
2009.
[10] N. S. Choi, J. G. Cho, G. H. Cho, “A General Circuit Topology of
Multilevel Inverter,” Power Electronics Specialists Conference, 1991.
SC’ 91. 1991 IEEE 22th Annual Volume, 24-27 June 1991 pp. 96 – 103.
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
15
[11] G. Carrara, S. Gardella, M. Marchesoni, R. Salutari, G. Sciutto, “A New
Multilevel PWM method: A Theoretical Analysis,” IEEE Trans. Power
Electronics., vol. 7, no. 3, pp. 497 - 505, July. 1992.
[12] R. Gonzalez, E. Gubia, J. Lopez, L. Marroyo, “ Transformerless SiinglePhase Multilevel-Based Photovoltaic Inverter,” IEEE Trans. on
Industrial Electronic, vol. 55, no. 7, pp. 2694-2702, July. 2008.
[13] M. Calais “A Cascaded Inverter for Transformerlss Single Phase GridConnnected” Power Electronics Specialists Conference, 2000. PESC 00.
2000 IEEE 31th Annual Volume 3, 18-23 June 2001 pp: 1173 - 1178
Vol.3.
[14] J. Selvaraj, N. A. Rahim, “Multilevel Inverter for Grid-Connected PV
System Employing Digital PI Controller,” IEEE Trans. on Industrial
Electronics, vol. 56, no. 1, pp. 149- 158, Jan 2009.
[15] T. Noguchi, S. Togashi, R. Nakamoto, “Short-Circuit Pulse-Based
Maximum-Power-Point Tracking Method for Multiple Photovoltaic-andConverter System,” IEEE Trans. on Industrial Electronics, vol. 49, pp.
217- 223, Feb 2002.
[16] G. R. Walker, P. C. Sernia, “Cascaded DC-DC Converter Connection of
Photovoltaic Modules,” IEEE Trans. Power Electronics., vol. 19, no. 4,
pp. 1130-1139, July. 2004.
[17] V. G. Agelidis, D. M. Baker, W. B. Lawrance, C. V. Nayar, “A
Multilevel PWM Inverter Topology for Photovoltaic Application,” in
Proc. IEEE ISIE’97, Guimaraes, Portugal, 1997, pp. 589-594.
[18] Muhammad H. Rashid, Power electronics: Circuits, Devices, and
Applications, 3rd ed. Pearson Prentice Hall, 2004, pp.267.
[19] Nobuyoshi Mutoh, Takayoshi Inoue, “A Control Method to Charge
Series-Connected Ultraelectric Double-Layer Capacitors Suitable for
Photovoltaic Generation Systems Combining MPPT Control Method,”
IEEE Trans. on Industrial Electronics, vol. 54, no. 1, pp. 374-383, Feb.
2007.
[20] Esram T, Chapman P.L, “Comparison of Photovoltaic Array Maximum
Power Point Tracking Techniques,” IEEE Trans. Energy Conversion, vol.
22, no. 2, pp. 439-449, June 2007.
[21] Femia N., Petrone G., Spagnuolo G., Vitelli M.: “Optimizing duty-cycle
perturbation of P&O MPPT technique” Power Electronics Specialists
Conference, 2004. PESC 04. 2004 IEEE 35th Annual Volume 3,20-25
June 2004 pp. 1939 - 1944 Vol.3.
[22] Liu X., Lopes L.A.C.: “An improved perturbation and observation
maximum power point tracking algorithm for PV arrays” Power
Electronics Specialists Conference, 2004. PESC 04. 2004 IEEE 35th
Annual Volume 3, 20-25 June 2004 pp. 2005 - 2010 Vol.3.
[23] David M.Aletr, “Thermoelectric cooler control using TMS320F2812 DSP
and a DRV592 power amplifier” Texas Instruments Application Report.
Nasrudin A. Rahim (M’89-SM’08) was
born in Johor, Malaysia, in 1960. He received
the B.Sc. (Hons.) and M.Sc. degrees from the
University of Strathclyde, Glasgow, U.K.,
and the Ph.D. degree in 1995 from HeriotWatt University, Edinburgh, U.K. He is
currently a Professor in the Department of
Electrical Engineering, University of Malaya,
Kuala Lumpur, Malaysia and Director of
Center of Research for Power Electronics,
Drives,
Automation
and
Control
(UMPEDAC)..
Prof. Rahim is the Chairman of the
Working Group WG-8 Covering Reluctance Motor of the IEEE Motor Subcommittee under IEEE-PES Electric Machinery Committee His research
interests includes power electronics, real-time control systems, and electrical
drives.
Jeyraj Selvaraj was born in Kedah,
Malaysia in 1980. He received the
B.Eng(Hons) from Multimedia University,
Malaysia and M.Sc in Power Electronics and
Drives from University of Birmingham and
University of Nottingham, U.K in 2002 and
2004 respectively. He also obtained his PhD
degree from University Malaya, Malaysia in
2009.
He is currently pursuing his carrier at the
Center of Research for Power Electronics,
Drives,
Automation
and
Control
(UMPEDAC), Department of Electrical Engineering, University Malaya,
Malaysia. His research interests are single-phase and three-phase multi-level
inverters, digital PI current control techniques, photovoltaic inverters and dc-dc
converters.
Copyright (c) 2009 IEEE. Personal use is permitted. For any other purposes, Permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
Authorized licensed use limited to: University of Malaya. Downloaded on November 4, 2009 at 04:53 from IEEE Xplore. Restrictions apply.