2nd Canadian Solar Buildings Conference
Calgary, June 10 - 14, 2007 1
Cascaded Multilevel Converters and Their
Applications in Photovoltaic Systems
S. Ali Khajehoddin∗, Praveen Jain§, and Alireza Bakhshai‡
∗ email@example.com, § firstname.lastname@example.org, ‡ email@example.com
ECE Department, Queen’s University, Kingston, Canada
Tel: (613)-533-6000 Ext.:75388, (613)-533-6984, Fax: (613)-533-3216
Type of Paper: Refereed
Abstract— Unique features of multi-level converters have re-
cently nominated them as signiﬁcant alternatives for solid-state
power converting units, even in the low and medium power range.
The fact that Multilevel converters need several DC sources in the
DC side, makes them attractive for Photovoltaic(PV) applications.
This paper presents a new control strategy to control Cascaded
Multilevel converters in a multi-string conﬁguration for single
phase grid connected systems. Eventually, simulation results are
provided to validate the control system under various insolation
I. I NTRODUCTION
Nowadays, the main energy supplier of the worldwide
economy is fossil fuel. This, however has led to many prob-
lems such as global warming and air pollution. Therefore,
with regard to the worldwide trend of green energy, solar
power technology has become one of the most promising
energy resources. The number of PV installations has had an
exponential growth , mainly due to the governments and
utility companies who support the idea of the green energy.
One of the most important types of PV installation is the
grid connected inverter conﬁgurations. These grid connected
PV systems can be categorized from two viewpoints: PV
cell and inverter conﬁgurations, see Fig. 1. The PV cell ar-
rangements fall into four broad groups: centralized technology,
string technology, multi-string technology and AC-module and
Fig. 1. PV systems categorized by different PV cell conﬁgurations and
AC-cell technologies . inverter types.
All approaches have advantages and disadvantages , ;
and will compromise various attributes such as harmonic
generation, complexity, efﬁciency, ﬂexibility, reliability, safety,
modularity and cost. However, for residential PV installations, topologies which are able to generate better output quality,
the most suitable conﬁguration seems to be the string or multi- while operating at lower switching frequency. This implies
string technologies where one or more strings of PV cells are lower switching dissipation and higher efﬁciency. Moreover,
connected to a single inverter. Using this type of conﬁguration, this topology utilizes switches with lower breakdown voltage;
there will be no losses associated with the string diodes therefore, it can be used in higher power applications at
compared to centralized technology. Moreover, independent lower cost. It is worth mentioning that although the number
Maximum Power Point Tracking (MPPT) is possible for of switches in this approach is higher than other two level
all strings which might be installed in different sizes and topologies, for a sufﬁcient high number of levels, the output
orientations. This also increases the overall efﬁciency under ﬁlter can be avoided which means less weight, cost and space.
special circumstances like partial shadowing. On the other hand, even with the same size of ﬁlter at the
There are different approaches to implement string and output, the switching frequency can be decreased which means
multi-string topologies. Usually, these modules consist of a higher efﬁciency. In general, a greater number of switches in
solar array and a DC to DC converter controlled by a MPPT multilevel converters can be justiﬁed since the semiconductor
algorithm. Afterwards, the output of the DC/DC converters cost decreases at a much greater rate than the ﬁlter components
build up a DC voltage which is then converted to AC by means cost. This projects the total cost of multilevel converters to be
of an inverter . The other possibility is to use multilevel comparable or even lower than that of two-level converters.
Among various multilevel topologies, the most important
ones are : Diode-Clamped Multilevel Converter(DCMC)
 and Flying Capacitors Multilevel converters (FCMC) and
Cascaded Multilevel Converters (CMC). The ﬁrst, simplest
and the most modular topology is CMC. However, the main
problem associated with the CMC topology is the need for
isolated DC sources which are not usually available without
the use of transformers. In some speciﬁc applications such
as photovoltaic systems, separate dc sources exist and can be
used in the CMC topology , . A diversity of multilevel
converter topologies have been used in photovoltaic applica-
tions , ,  and a comparison of some topologies is
presented in .
This paper presents a new control strategy to control Cas-
caded Multilevel converters in a multi-string conﬁguration for (a)
single phase grid connected systems. This topology generates
high quality output current under any circumstances specif-
ically in partial shading, while tracking the MPP of each
string independently. The topology does not consist of any
extra DC-DC converter stage which causes some limitation
in the performance but deﬁnitely reduces the overall cost
and efﬁciency. Simulation results are provided to validate the
proposed control system.
II. C ASCADED M ULTILEVEL C ONVERTERS
A. Basic Principle of Operation
The Cascaded Multilevel Converters (CMC) are simply a
number of conventional two-level bridges, whose AC terminals
are simply connected in series to synthesize the output wave-
forms. Fig. 2(a) shows the power circuit for a ﬁve-level inverter
with two cascaded cells. The CMC needs several independent
DC sources which may be obtained from batteries, fuel cells
or solar cells.
Through different combinations of the four switches of
each cell, each converter level can generate three different
voltage outputs, +Vdc , 0, −Vdc. The AC output is the sum
of the individual converter outputs. The number of output-
phase voltage levels is deﬁned by n = 2N+1, where N is the (b)
number of DC sources. For instance the output range of the
Fig. 2(a) swings from −2Vdc to +2Vdc with ﬁve levels. If the Fig. 2. (a) Cascaded multilevel converter with separate dc sources, (b) Phase
straightforward fundamental frequency modulation technique shifted modulation strategy and the associated outputs.
is chosen it can be shown that, the charge and discharge of
the cells in different levels will not be equal which results
in capacitor voltage unbalance or unequal loading of input • The modularity of this topology is an important feature,
sources. It is possible to utilize CMCs without input sources and because of that some redundancy is possible by using
as a reactive power compensator. But, if the output load in more cells per phase than is actually required.
a CMC is resistive, these capacitors should be connected to • Because of its modular structure, control is more easily
”isolated DC sources” to supply the real power. applied.
• Compared to other multilevel topologies, CMC requires
B. Features least number of components, because there is no need for
clamping diodes and ﬂying capacitors.
In summary, the advantages and disadvantages of the CMC
are as follows: 2) Cons:
1) Pros: • Each cell needs an isolated DC supply and normally this
• Device voltage sharing is automatic and there is no requires some sort of complicated transformer arrange-
restriction on switching patterns. ment.
• CMC has smaller dvo /dt compared to series connected The aforementioned disadvantage is not an issue in Photo-
2-level. voltaic applications, because discrete strings of PV modules
Fig. 4. Vector diagram of the output power circuit shown in Fig. 2(a).
Fig. 3. Equivalent circuit for a PV cell.
Using this PV array model it is possible to simulate the
provide isolated input voltage sources. As shown in Fig. 1, dynamic performance of the power and control systems and
in photovoltaic applications the inverter stage can be imple- MPPT strategy in response to the radiation and temperature
mented with or without a DC-DC converter. However, in this step changes.
paper the topology without a DC-DC stage is examined. There
are different options for modulation of multilevel converters IV. P OWER C ONTROL A LGORITHM
. One of the simplest strategies is the phase shifted carrier A. Basic Principle of Operation
modulation technique where the n carriers of the full bridge
The basic structure of the grid connected multilevel multi-
cascaded converters are phase shifted by 180/n degrees, as
string PV system is shown in Fig. 2(a). Since the output
shown in Fig. 2(b). This modulation technique is utilized in
voltage and current of the PV arrays change with the irradiance
this paper due to its simplicity. However, it can be shown
and the temperature of the cells the operating point of the PV
that under partial shading the harmonic cancellation is not as
arrays has to be controlled to be held on the Maximum Power
perfect as the ideal case but still much better than a two level
Point. This objective can be satisﬁed simply by setting the DC
voltage of the capacitors to a reference voltage provided by a
MPPT algorithm. Examination of different MPPT algorithms
III. S IMULATION M ODEL FOR PV C ELL seems to be out of place in this paper and thus it is assumed
The building block of the PV array is the solar cell, which is that a reference DC voltage is provided for each string.
basically a p − n semiconductor junction that directly converts Since the power delivered by each full bridge converter can
light energy into electricity. The equivalent circuit is shown in be controlled by switches, the power provided by the DC
Fig. 3. capacitors is controllable. On the other hand, at any speciﬁc
To simulate a PV array, a PV simulation model which was time the power supplied to the DC capacitors is known because
obtained using PSIM(Power SIMulator) software, was used the voltage of the PV arrays is ﬁxed by the DC voltage of the
based on the following equation: capacitors. Therefore, whenever the capacitor voltage needs to
be increased/decreased, it is possible to decrease/increase the
power delivered to the power circuit and the difference of the
q VP V
IP V = np Iph − np Irs exp −1 (1) active power controls the voltages of the DC capacitors.
kT A ns
Fig. 4 shows the vector diagram of the voltages and the
where IP V is the PV array output current (A); VP V is current of the output power circuit. It is desired to have the
the PV array output voltage (V); ns is the number of cells output current in phase with the grid voltage in order to
connected in series; np is the number of strings connected have zero reactive power delivered to the grid. By simply
in parallel; q is the charge of an electron; k is Boltzmanns controlling the angle of this current and the grid voltage,
constant; A is the pn junction ideality factor; T is the cell reactive power compensation is feasible which is not examined
temperature (K); and Irs is the cell reverse saturation current. here. It can be shown that the power delivered to the grid is:
The factor A in Eq. (1) determines the cell deviation from Vo .Vgrid
the ideal p − n junction characteristics. The ideal value ranges Ptot = sin ϕ (3)
between 1 and 5 and in our case, A equals 2.15. The cell
reverse saturation current Irs varies with temperature and the Therefore, by means of changing the output voltage of the
photocurrent Iph depends on the solar radiation and the cell multilevel inverter the power delivered to the grid can be
temperature as shown in the following equation: controlled. If the power supplied by each string is Pi , the
total power sent to the grid is Ptot = ΣPi . The power
s supplied by each string is Pi = Voi .IL cos ϕ and the angle
Iph = [Iscr + ki (T − Tr )] (2)
100 is cos ϕ = Vgrid /ΣVoi . Therefore, Pi = Voi .Ptot /ΣVoi which
where Iscr is the cell short-circuit current at reference means that if the input power provided by a string is changed
temperature and radiation, ki is the short-circuit current tem- the output voltage of that cell has to be adjusted accordingly.
perature coefﬁcient, and s is the solar radiation in mW/cm2. However, as shown by the dotted line in Fig. 4, if the output
cD v o l t a g e r e g u l a t o r
PB zH0 21
-- ot hct iwS
120 Vc1 − Vc120
. ts noc V c1
Vdc1 e v ita ge n f i Vc1 × Vdc1
.tsnoC -- )t(1feri MWP oT
1niP f e ri V
rota ludo m
∏ ∏ ∏ + IP ∏ rewop dna
-- t iucr ic
dirgV/2 )t(dirgV LLP
2n i P Pin1 + Pin 2
C o n t r i b u t i o n f a c t o r
Fig. 5. Control system block diagram of cell #1 of the circuit shown in Fig. 2(a)
voltage of one cell is reduced, the output voltage of other cells of the PV voltage leads to a reduction in power generation,
have to be increased to keep the output current in phase with which may even descend to zero value. When the input
the grid voltage. It can be shown that for a given input power, power becomes zero the contribution factor also becomes
grid voltage and inductance, the output voltage of the cells zero. This is multiplied by the feedback signal and then,
will be set to: causes the current reference signal to become negative, which
4 2 leads to instability. Once this occurs, the stabilizer switches
Pi Vgrid + XL Ptot2
the reference signal to be a constant positive number, which
Voi = . (4)
Ptot Vgrid discharges the DC capacitors and causes the control system to
exit from the unstable state.
B. Control Strategy If the fundamental components of the grid voltage and
As shown in Fig. 5, the control system consists of different current are in phase, the instantaneous power injected into the
sections. The main objective is to generate output voltages grid equals to:
according to Eqn. (4) so that each string contributes its maxi-
Ptot = P tot (1 − cos(2ωgrid t)) (5)
mum available power to the grid. This task is accomplished by
the main control loop. Based on the calculated input power, This power has to be drawn from the input sources, which
the reference output current is found which will be multiplied leads to an oscillation in the voltage and power of the PV
by a sinusoidal waveform in phase with the grid voltage. The arrays. By increasing the size of the capacitors, this oscillation
difference of this reference current and the measured output can be limited to a desired value. To reduce the output current
current is used for the feedback loop which in turn can be harmonics, a compensation factor is multiplied by the output
used as a reference for the output voltage. Since there is more reference voltage. In the end this compensation factor is
than one cell that builds the output voltage each cell generates divided by the average capacitor voltage to limit the control
an output voltage equal to Voi = ΣVoi .Pi /Ptot . Therefore, the signal to [−1, 1]. Nevertheless, this oscillation is not desired
measured feedback current is scaled down by a contribution because it causes the PV arrays to operate slightly off of the
factor as shown in the block diagram in Fig. 5. MPP.
By increasing the reference current signal, the output power
will be increased. Therefore, to regulate the DC voltage of
V. S IMULATION R ESULTS
the capacitors it is sufﬁcient to feedback the error of the
capacitor voltage to the current loop as demonstrated in the In order to demonstrate the impact of the shading and
block diagram. Because of the contribution factor which is irradiance level on the performance of the proposed system, a
a feed-forward compensation, and because of the existence simulation is setup as shown in Table I.
of two control loops for each cell, the control system can It is worth mentioning that the output voltage of the PV
become unstable. Speciﬁcally this happens in the transient string arrays should be chosen based on the grid nominal
state when the dc capacitor voltage overshoots. Escalation voltage and the minimum desired operating power of each
Fig. 7. Simulation results when the grid voltage is smaller than the voltage
Fig. 6. Simulation results for a step change in the input power when the grid of the individual PV strings.
voltage (180V) is larger than the voltage of the individual PV strings(120V).
current are not increased in case of partial shading. Without
cell. If the power generated by all strings are equal, the output the stabilizer section in the controller, the system becomes
voltage of all cells will be equal. In this case, by referring to unstable after the irradiance decrease at t=0.7s.
Eq. (3) it can be observed that the inverter output voltage has
to be slightly larger than the grid voltage as shown in Fig. 6
VI. C ONCLUSION
and the DC voltage of an individual string is at least Vgrid /N ,
where N is the number of strings. However, as discussed After a brief introduction of different possible choices for
before, in case of partial shading the output voltage of the inverters in Photovoltaic applications, it is shown that the
shaded string will decrease accordingly, and the output voltage Cascaded Multilevel Converter is a suitable choice for PV
of the other cells have to increase. But this is not possible systems. Then after describing the basic principle of operation,
because the DC voltage of each string is not designed to cover the paper presents a new control strategy for cascaded multi-
the whole output voltage. As shown in Fig. 6 this will increase level converters. To choose the best size for the PV strings, a
the harmonic components of the output current. In order to guideline is introduced so as to gain the best performance of
avoid this problem, the minimum power of PV strings should the system under all environmental conditions. The simulation
be selected and then the DC output voltage of the PV strings results show that for partial shading and different input powers,
can be calculated. the system is able to inject the maximum available power to
Fig. 7 demonstrates the dynamic performance of the PV the grid.
system for a step changes in irradiance. At the time t=0.5s
the insolation of the second PV string is decreased by 50
percent, and then at t=0.5s the normal irradiance is applied. At
t=0.75s the whole insolation is decreased by 70 percent and it The authors would like to thank the contribution of the Solar
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