Multilevel Power Converter for the Integration of a
PV System with Supercapacitor Energy Storage
V. Fernão Pires
ESTSetúbal / Instituto Politécnico Setúbal
INECS-ID, Lisboa
vitor.pires@estsetubal.ips.pt
J. F. Martins, J. Murta-Pina,
V. Delgado-Gomes, Pedro Pereira
FCT / UNL, Lisboa
CTS / UNINOVA
jf.martins@fct.unl.pt
Abstract-The paper presents a multilevel power converter that allows a direct integration of a grid connected photovoltaic system
with a supercapacitor energy storage. This system can be used in island operation or grid connected operation. The supercapacitor
bank can be used to storage the energy generated by the photovoltaic system or from the grid. This integration with the
supercapacitor energy storage also allows for fault ride through and the minimization of the power fluctuation. This solution allows
to operate with different DC voltages for the photovoltaic system and supercapacitor energy storage.
I.
INTRODUCTION
Renewable energies play now an important role due to increasing energy demand and depleting fossil fuels. Among several
forms of renewable energy, photovoltaic (PV) systems has become an important choice, especially due to decrease in
investment cost cost/kW and increase in efficiency. These systems can be used with or without storage solutions. In fact, a
photovoltaic system that integrates storage solutions can be used for two mode types, feed the power generated from the PV
panel into the electrical system of the installation and into the battery system for self-consumption improvement or into the
utility grid. Among the storage solutions, the use of supercapacitors in this system is now a reality due to advantages such as, a
very high power density long cycle life, environment pollution free and maintenance-free. Thus, the use of this storage element
has been implemented and studied [1-3]. The integration of supercapacitors can also be used to improve the low voltage ridetrough capability of the system according to the grid connection requirement [4,5].
Photovoltaic systems require power converters to obtain their maximum power and convert a DC voltage to an AC voltage
to interconnect to the grid or in the case of alternate loads. Many power converter topologies have been proposed for gridconnected PV systems. The most used topology is the single or three-phase voltage source inverter. However, multilevel
topologies have also been used due to advantages such as, low THD and device stress [6-9]. Several topologies have been
proposed. However, one of the multilevel topologies that were proposed is the dual inverter [10]. This topology presents the
advantage of use only two classical three-phase voltage source inverter. However, this topology is used to interconnect two
separate PV systems to the grid.
Under this context, this paper presents a new power converter structure for a photovoltaic system that integrates a storage
system. The proposed structure is based on the multilevel dual inverter topology, but adapted for a unique PV system with a
supercapacitor energy storage. The characteristics and advantages of this structure will be presented. A fast and robust control
system for this power converter is also proposed. Several simulation results are presented in order to confirm the presented
characteristics.
II.
PROPOSED STRUCTURE
There are two major structures that supercapacitors could be connected to a photovoltaic system. In the first structure the
supercapacitors are connected directly to the intermediate dc link, as can be seen by Fig. 1 a) [4,11]. This is the simplest
structure. However the maximum use of the supercapacitors is limited due to the dc link voltage limitations imposed by the ac
grid. To overcome this limitation, a dc/dc converter between the dc link and the supercapacitors should be used (second
structure). This solution has also some drawbacks since will increase the system cost and power losses. In order to overcome
these limitations, a structure where the supercapacitors are directly connected to the grid by a three-phase inverter is proposed.
Thus structure also presents the advantage of generate a multilevel AC voltage. Fig. 1 b) shows the proposed structure. The
photovoltaic system is connected to the grid by a dc/dc converter and a three-phase dc/ac converter. The dc/dc converter will
be associated to a maximum power point algorithm (MPPT). The supercapaciotors are connected to the grid also by a threephase dc/ac converter. The dc/ac converters are connected to a three-phase transformer with the primary in open windings.
a) Classical structure
b) Proposed structure
Fig. 1. Classical and proposed structure for a photovoltaic system with the integration of supercapacitor energy storage.
The proposed multilevel DC/AC converter can be described by the following voltage and current equations (considering the
switches as ideal):
⎡ v s1 ⎤ ⎡ v1 ⎤
⎡ i1 ⎤
⎡ i1 ⎤
⎢v ⎥ − ⎢v ⎥ = L d ⎢i ⎥ + R ⎢i ⎥
2
⎢ s 2 ⎥ ⎢ 2 ⎥
⎢ 2 ⎥
dt ⎢ ⎥
⎢⎣v s 3 ⎥⎦ ⎢⎣v 3 ⎥⎦
⎢⎣i3 ⎥⎦
⎢⎣i3 ⎥⎦
(1)
Using the dp transformation [9] with the equations described by (2), the following new set of equations are obtained:
d
dt
⎡ R
⎡i d ⎤ ⎢− L
⎢i ⎥ = ⎢
⎣ q ⎦ ⎢ ω
⎣
⎤
ω ⎥ ⎡i ⎤
d
⎡v sd − v d ⎤
+ ⎢
⎢
⎥
⎥
R i
v − v q ⎥⎦
− ⎥ ⎣ q ⎦ ⎣ sq
L ⎦
(2)
!
!
Where v sd and vsq are the d and q axis components of the v s , and id and iq are the d and q axis components of the is .
!
In the same way, vd and vq are the d and q components of the v .
III.
CONTROL SYSTEM
The DC/DC converter will be controlled in order to obtain the maximum power from the PV panel. Thus a maximum power
tracking algorithm associated to the DC/DC converter was used. In this work it was adopted a method based on a dP/dV
feedback. This method is based on the calculation of the slope (dp/dV) to find the MPP operation [12,13]. The implementation
scheme of this method is presented in Fig. 2. In this case, the PI controller adjusts the duty cycle of the switch of the DC/DC
converter in order to obtain the maximum power of the PV panel.
Fig. 2. Scheme of the of the method based on the dP/dV feedback.
The control system for the multilevel DC/AC converter will be achieved through the dc voltage links. A PI controller that
gives the reference value for the grid current d component will be used to control the dc-link of the power converter connected
to the photovoltaic panel. The ac currents of the multilevel dc/ac converter will be implemented by a current sliding mode
controller associated to an alfa-beta vectorial modulator. The reference of dc voltage of the power converter associated to the
supercapacitors will be defined as a percentage of the dc voltage reference of the other three-phase converter. Thus, this
voltage will be regulated by the amplitude of the ac currents and alfa-beta modulator. In discharge mode the reference of this
voltage will be set to a minimal value that will allow to maintain the ac currents sinusoidal. The sliding surfaces will be
obtained from the state space equations of the system represented by (2). Thus, the d and q axis components of the ac currents
will be controlled in order to be sinusoidal and in phase with the voltages grid. According to the sliding mode theory [14], the
following set of sliding surfaces is obtained:
⎧S1 (ei , t ) = k (iα* − iα ) = 0
⎪
α
⎨
*
S
(
e
⎪⎩ 2 iβ , t ) = k (iβ − iβ ) = 0
(3)
The sliding mode stability condition is achieved by the product between the sliding surfaces and the correspondent derivate.
This product must be less than zero. To assure this and the condition (3) at a limited switching frequency, hysteretic
comparators will be used at the output of the sliding surfaces. On other hand, in order to achieve the control condition
presented by (3), the right switching combination of the transistors should be chosen. Thus, analyzing all the possible
combinations of the multilevel ac power converter, it is possible to verify that 64 voltage space vectors are obtained in the αβ
plane. However, only 19 different output voltage vectors can be obtained, as can be seen by Fig. 2. According to this, at the
output of the sliding surfaces it will be used a seven-level and a five-level hysteretic comparators (with hysteresis ε in order to
limit the maximum switching frequency).
Vb
7
9
6
8
10
11
3
14
4
1
0
12
13
5
17
15
2
Va
18
16
Fig. 3. Output voltage vectors.
The block diagram of the full control system of the multilevel inverter is presented in Fig. 4. The PI controller will give the
reference for the id component of the ac currents. At the output of the sliding surfaces there are the hysteretic comparators. The
output of the hysteretic comparators will be the input of the alfa-beta vectorial modulator that will choose the switches that
must be on. However, in order to maintain the voltage of the supercapacitors and dc capacitor connected to the photovolgaic
system, the vectors must also be chosen according to these voltages and the redundant vectors. Thus, the vectorial modulator
will be ensure that the sliding surfaces will be zero, and at the same time balance the DC voltages of the supercapacitors and
the inverter connected to the photovoltaic system. As referred the redundant vector will allow to balance the dc voltages. In
fact, for example, for vector 3 there are 5 possible combinations for the multilevel inverter switches as can be seen through
table 1. Thus, for that vector the combination of the switches must be made in order to increase the voltage in the dc capacitor
connected to the photovoltaic system and decrease the voltage in the supercapacitors, the vice-versa and even to maintain the
voltage in one of them.
Fig. 4. Block diagram of the control system.
TABLE I
VOLTAGE VECTORS ACCORDING THE SWITCHING STATES
S11
0
0
1
1
1
S12
0
1
0
1
1
S13
0
0
0
0
1
S21
0
0
1
1
0
S22
0
1
0
1
0
IV.
S23
1
1
1
1
1
V
0.41 VDC
0.41 VDC
0.41 VDC
0.41 VDC
0.41 VDC
α
V
0.71 VDC
0.71 VDC
0.71 VDC
0.71 VDC
0.71 VDC
β
RESULTS
Some simulations tests were performed using the Matlab/Simulink program. Fig. 5 shows the time behavior of the output
voltage of the power converter (at the terminals of the transformer primary) and ac currents. From this figure it is possible to
verify the multilevel operation of the power converter since the ac voltage of the power converter presents 9 voltage levels. In
this test, the power is transferred from the converter to the grid. From Fig. 5 b) it is possible to confirm that the ac currents of
the converter currents are almost sinusoidal.
a) Voltage of the transformer primary
b) Grid currents
Fig. 5. Results at the grid side of the proposed power converter structure.
Fig. 6 shows the time behavior of the of the output voltage of the power converter and ac currents for a change in the solar
irradiation. From this figure it is possible to verify that the amplitude of the currents will rapidly increase following the
increase of the irradiation. The voltage still maintains their multilevel operation and the currents maintain the low THD even
after the change of the amplitude.
a) Voltage of the transformer primary
b) Grid currents
Fig. 5. Results at the grid side of the proposed power converter structure.
V.
CONCLUSIONS
In this work a new structure for a photovoltaic system with the integration of a supercapacitor energy storage was proposed.
This system allows to directly integrate the storage system to the grid by a classical three-phase voltage source inverter.
Besides the advantage of this direct integration, this structure also allows to obtain a multilevel output voltage operation. The
multilevel operation of obtained from the connection of two two-level voltage source inverters connected to a three-phase
transformer with open windings in the primary. A system controller for this power converter structure was also proposed. This
controller is based on a sliding mode approach. Results show the multilevel operation of the converter and that the ac currents
present a very low THD.
ACKNOWLEDGMENTS
This work was supported by national funds through FCT – Fundação para a Ciência e a Tecnologia, under projects PestOE/EEI/LA0021/2013 and PEst-OE/EEI/UI0066/2014. Authors also like to thank Faculdade de Ciêmcias e Tecnologia for
financial support.
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