Comparison of control strategies for grid-connected
photovoltaic systems during unbalanced voltage dips
Edmar F. Cota1,3, Lucas S. Xavier1, Allan F. Cupertino1,2,3 and Heverton A. Pereira1,3
1
Gerência de Especialistas em Sistemas Elétricos de Potência
Universidade Federal de Viçosa
Av. P. H. Rolfs s/nº, 36570-000
Viçosa, MG, Brazil
edmar.elt@gmail.com, lsantx@gmail.com
3
2
Departamento de Engenharia de Materiais
Centro Federal de Educação Tecnológica de Minas Gerais
Av. Amazonas 5253, 30421-169
Belo Horizonte, MG, Brazil
allan.cupertino@yahoo.com.br
Graduate Program in Electrical Engineering
Federal University of Minas Gerais
Av. Antônio Carlos 6627, 31270-901
Belo Horizonte, MG, Brazil
hevertonaugusto@yahoo.com.br
Abstract— Unbalanced voltage dips are common disturbances in power
systems. Therefore, grid-connected photovoltaic systems need to be able
to work during these disturbances. Conventional control strategies do not
consider the negative sequence current control, which is an important
limitation. In this context, this paper compares through simulations four
strategies of negative sequence current control: Notch filter based
strategy, measured signals decoupling based strategy, reference and error
signals decoupling based strategy and resonant controllers based
strategy. All simulations are performed in Matlab/Simulink environment.
Representation of point of common coupling voltage (PCC) uses
experimental data of an unbalanced voltage sag. Comparisons during
unbalanced voltage sags and the impact of voltage harmonics on
techniques are analyzed. Obtained results shows resonant controllers
based strategy has a superior behavior, in terms of robustness and
simplicity.
I. INTRODUCTION
Dispersed generations (DGs) have put significant
challenges to voltage regulation in distribution systems.
Among these renewable sources, photovoltaic (PV) technology
is one of the main candidates to play an important role in the
future of electricity generation [1].
A system with significant PV penetration can be seriously
affected with the variation of generation caused by cloud
movement that may result in voltage variation condition [2].
Serious voltage drops may occur due to the intermittent loss of
PV generation during cloudy days.
Interconnection of large scale PV into the power system
demands the continuous revision of grid codes and power
quality standards in order to fulfill restrictive constraints.
Furthermore, most host utilities also require that PV must
tolerate system disturbances.
The increasing installation of single-phase solar systems
contribute to the system unbalance [3]. Ideally, a network
voltage is balanced in normal conditions. But, the most usual
The Brazilian agencies CAPES, CNPq and FAPEMIG support this work.
grid faults are two and single-phase faults, that although less
severe than a three-phase fault, cause voltage unbalance, which
leads to voltage oscillation due to appearance of negative
sequence voltages and currents [4], [5], [6], [7].
Under these conditions, the dc-link voltage harmonics and
odd ac input currents harmonics will appear [5], [8]. The
appearance of a negative sequence current component
deteriorates the control performance [8].
Even for well-balanced three-phase source voltages,
different parameters of the power lines or unbalanced load
conditions will also cause unbalanced voltages to the gridconnected converters. Under unbalanced input voltages,
desirable features, such as unity power factor, constant dc bus
voltage, and sinusoidal input currents cannot be guaranteed
using those methods developed under balanced voltage
conditions [6].
In such a case, voltage ripples in the dc bus arise, which
may affect negatively the inverters connected through the grid.
The dc link voltage oscillation provokes low-order harmonics
in the current injected by the inverter into the grid and should
be minimized [4]. Other consequences of unbalances are
increase of electric losses, rise of temperature in electrical
machines and transformers, appearance of torque pulsations,
noise and ripple in rectifiers, and in cases of zero sequence
currents can affect the protection system [7], [1], [9].
Nowadays, there are grid operators that allow providing
unbalanced currents so that the power at the PCC remains
constant. This is very useful in weak grids because it allows
connecting all loads to a balanced PCC voltage, which is
especially important for sensitive loads that could disconnect
if the AC voltage does not meet restrictive voltage standards
[8].
Thus, PV systems operating as a high-reliability current
source must contributed to balance the grid voltage [1]. In this
work, some technics to improve the current injected by three
phases PV system are analyzed and the main contributions of
each one are discussed during unbalanced voltage sag.
II. MODELING OF THE SYSTEM
Figure 1 presents the studied system. Photovoltaic panels
are connected to the grid through a three phase inverter
modulated by the space-vector pulse-width modulation
(SVPWM) technique. In order to reduce the harmonics
generated by converter switching, LCL filter topology is used.
The design of LCL filter follows the methodology proposed by
[10].
The PV panel electrical model is showed in Figure 2. The
series resistance ( ) and parallel resistance ( ) represent the
voltage drop when charge migrates from the electrical contacts
and the reverse leakage current of diode, respectively.
According to [11], the value of these resistances can be
obtained through the parameters informed by manufactures.
More details about this model can be found in references [11]
and [12].
⎧
=
⎨
⎩
=−
−
+
−
=−
−
+
−
=
−
−
,
+
−
,
,
,
(2)
In equations (1) and (2), the symbols + and – represents
the positive and negative sequence components. The indexes
and represent the terms of direct and quadrature axis. is grid
current, is inverter voltage and
is PCC voltage.
=
+
,
=
+
and
is the grid fundamental
frequency.
The DC bus dynamic is given by:
=
(3)
−
Where C is capacitance of DC bus,
is the solar panel
current and
is the current that flows to the inverter.
The term
is a disturbance and is disregarded.
Furthermore, considering a balanced grid voltage and
negleging the converter losses, equation (2) is obtained:
∗
=
3
2
,
(4)
A maximum power point tracker (MPPT) algorithm
calculates the reference of the DC bus voltage in order to
extract the maximum power of the solar panel. There are many
structures of MPPT in literature. This work implement the
incremental conductance algorithm proposed in [14].
Next section presents the control strategies in details.
Figure 2 – Photovoltaic panel electrical model.
In this work, all control strategies are implemented in
synchronous reference frame. Therefore, a PLL (Phase-Locked
Loop) structure is necessary. Due to its robustness during
unbalanced voltages and harmonics, the Dual Second Order
Generalized Integrator based PLL (DSOGI-PLL) is used.
Details about this structure are found in [13].
The following points are considered in order to obtain the
inverter dynamic model:
•
Only the fundamental
considered;
•
The capacitor of LCL filter is considered an open
circuit at fundamental frequency;
•
The point of common couple (PCC) voltage is
unbalanced. However, the dynamic of the zero
component is neglected.
dynamic
+
(1)
Figure 1 – Topology of a grid-connected photovoltaic system.
frequency
−
is
In this situation, removing the coupling of symmetric
components, it is possible to obtain the following system of
equations in synchronous reference frame [14]:
III.
CONTROL STRATEGIES
A. Conventional control strategy (CONV)
Firstly, conventional control strategy is presented. This
structure neglects the negative sequence components of the
PCC voltage and is based on a cascade control with aninner
loop, faster, controlling the currents of the inverter and an outer
loop, slower, controlling the dc bus voltage.
The crossed couplings of dynamic equations presented in
(1) are removed through feed-forward actions. Figure 3
presents the block diagram of conventional control strategy.
All compensators are proportional-integral actions
designed through pole assignment method. The gains of
current compensators are [15]:
,
=2
(5)
,
=2
(6)
Where is the crossover frequency of current loop. This value
is limited up to 10 times smaller than the switching frequency
[15].
The block diagram model of the DC bus voltage control is
presented in Figure 4. Considering DC bus voltage loop 10
times slower than current loop and faster than MPPT
algorithm, it is possible to obtain the following gains of the DC
bus compensator [15]:
current control loops. The block diagram of this structure is
presented in Figure 6.
Influence of the filter in current dynamic response and
increase in complexity of the control algorithm are drawbacks
of this structure.
Figure 3 – Control block diagram for conventional control strategy.
Figure 4 – DC bus voltage control model.
=
2
=
Where
=
∗
4
(
+
)
Figure 5 – Control block diagram for NOTCH, MSD and RESD strategies.
(7)
(8)
.
This control structure does not compensate the negative
sequence components during unbalanced voltage dips. Next
control strategies will compensate the negative sequence
components in order to improve the performance of this
technique. However, the controller gains are maintained for all
strategies.
B. Notch filter based strategy (NOTCH)
The largest limitation of the conventional control strategy
is the current controller, which cannot compensate the
oscillations of 120 Hz generated by interactions between
positive and negative sequence. In this situation, during
unbalanced voltage dips the inverter will inject unbalanced
currents into the grid.
One possible solution is controlling separately the positive
and negative current as shown in Figure 5. The negative
sequence structure is similar to the positive sequence. In this
situation, the same gain controllers are used in this structure.
However, a structures able to detect the variables , ,
and
separately are necessary in order to implement the
control algorithm shown in Figure 5.
In order to remove the oscillations in the variables
and
and detect the positive and negative currents, reference
[16] proposes use of notch filters. These filters remove the 120
Hz components and detects the current signals that will used in
Figure 6 – Positive and negative sequence detector based on notch filters
(NOTCH).
C. Measured signals decoupling based method (MSD)
This strategy is based on the block diagram of Figure 5 and
detects the positive and negative sequence based on a
decoupling of the measured signals.
The 120 Hz oscillations in positive sequence current are
generated by the value of negative sequence component
referred to the positive synchronous reference frame.
Therefore, the negative component detected pass through
a first order filter that collects its mean value. Then, this signal
is referred to the positive synchronous reference frame through
the
transformation and subtracted of positive sequence as
feed-forward action. A similar methodology is used in negative
sequence detection. Complete detection structure is presented
in Figure 7.
Influence of the filter in current dynamic response and
increase in complexity of the control algorithm are also
drawbacks of this structure. Furthermore, when current
compensator has error in steady state, this technique cannot
remove all oscillations [17].
( )=
D. Reference and error signals decoupling based method
(RESD)
Other option is use reference and error signals instead of
measured signals to implement the decoupling network, as
shown in Figure 8 [17].
This strategy results in a complete decoupling, even
current compensator has error in steady state. As drawbacks,
this strategy also increases the complexity of control algorithm.
+
+
2
+
Where
is resonant gain and
this case, 120 Hz).
(9)
is resonance frequency (in
Figure 9 – Control block diagram for RES strategy.
IV.
Figure 7 – Positive and negative sequence detector based on measured signals
decoupling (MSD).
METHODOLOGY
Photovoltaic array considered presents 5 strings of 13
panels. Model KD250 manufactured by Kyocera is used. Table
I present the studied system parameters. All simulations was
performed in Matlab/Simulink environment. The control
techniques described are implemented with sampling
frequency of 12 kHz (2 times the switching frequency of the
converter). Digital filters and integrators are discretized
through trapezoidal method.
All simulations considered constant irradiance at 1000 /
on the panels. In order to compare the techniques,
experimental data of unbalanced voltage dip are used. These
data are presented in Figure 10. The harmonic spectrum of this
signal around 1.8 seconds are presented in Figure 11.
Therefore, results analyze the techniques performance during
unbalanced voltage dip and influence of harmonics in each
control strategy.
TABLE I. PARAMETERS OF THE SIMULATED SYSTEM: POWER
INVERTER.
First inductance of LCL filter
2,9
Second inductance of LCL filter
95
Capacitance of LCL filter
45
Damping resistor of LCL filter
2,9 Ω
DC bus Capacitance
3
Figure 8 – Positive and negative sequence detector based on reference and error
signals decoupling (RESD).
Switching frequency
6
Rated Power
17
E. Resonant Controller based method (RES)
Other solution to compensate the oscillations generated by
the negative sequence is using resonant controllers. In fact, a
proportional integral resonant controller (PI-RES) is
implemented in current loops, as shown in Figure 9.
In this situation, resonant part of the controller
compensates the negative sequence without detects separately
positive and negative current components.
The transfer function of the PIR controller is given by:
Grid Voltage
220
500
200
400
VdcCONV
0
300
480
VdcMSD
460
VdcRESD
440
VdcRES
VdcNOTCH
-200
2
2.1
Vdc [V]
VCONV
200
2.05
100
420
400
407.5
380
406.5
0
360
405.5
340
-100
320
0
-200
0.27
0.271
1
1
2
3
4
5
5
0
0
4
5
3
4
5
450
400
5
10
15
Harmonic order
20
25
MPPT Signal
DC Voltage
350
300
0
0
3
500
Vdc CONV [V]
VPhase A [%]
VPhase B [%]
VPhase C [%]
Figure 10 – Experimental PCC voltage profile used in simulations: Complete
waveform and detail of voltage dip at 2.05 seconds.
5
2
(a)
Time [s]
0
0
0.273
Time [s]
0
5
0.272
0
1
2
Time [s]
(b)
5
10
15
Harmonic order
5
10
15
Harmonic order
20
20
25
25
Figure 11 – Spectrum of PCC voltage.
V.
RESULTS
Dynamic behavior of dc bus voltage are presented in Figure
12 (a). All Techniques have similar transient response and a
small difference in steady state ripple. During the unbalanced
voltage dip, the dc bus ripple increases.
During voltage dip, dc bus voltage increases because the
inverter cannot injects rated power in this situation, due to
overcurrent limitation. Injected power decreases and MPPT
algorithm try to reduce voltage reference. In this situation will
appear error in steady state on dc bus voltage control loop.
When the voltage dip finishes, the dc bus voltage follow the
reference, which will return the system to the maximum power
point. This behavior is presented in Figure 12 (b).
Figure 12 – DC bus voltage dynamic behavior during voltage dip: (a)
Comparison of 5 techniques; (b) DC bus voltage and reference calculated by
MPPT algorithm for CONV strategy.
Dynamic behavior of
current components for CONV
control strategy is presented in Figure 13. Negative
components, which are not compensated, appears as
oscillations in
variables. On the other hand, the RES
control technique remove the oscillations due to the resonant
controller, as shown in Figure 14.
Figure 15, Figure 16 and Figure 17 shows the positive and
negative sequence components for MSD, RESD and NOTCH
strategies. In these three techniques, negative grid current
components are controlled to zero. RESD technique has a
higher oscillation. Furthermore, MSD and NOTCH techniques
presented similar dynamics.
Behavior of active and reactive power injected to the grid
are presented in Figure 18. During the voltage dip, the CONV
control strategy has the smaller value of active power.
Furthermore, MSD and NOTCH control strategies have a
slower response if compared with CONV strategy.
In terms of reactive power, the NOTCH control strategy has
the worst behavior in transient response with a higher
overshoot. The RESD control strategy has the best behavior
with small overshoot and fast response.
Finally, Figure 19 shows the current harmonic spectrum for
each control technique at time 1.8 seconds. RES control
strategy has the smaller current distortion followed by NOTCH
and MSD control strategies. RESD control strategy has the
worst behavior due to a large component of 17th harmonic.
100
100
80
80
60
60
40
Id-,q- MSD [A]
Id,q CONV [A]
40
20
0
20
0
-20
-20
-40
-40
-60
-60
-80
-100
0
1
2
3
Id CONV
-80
Iq CONV
-100
4
5
Time [s]
Figure 13 – Direct and Quadrature current dynamic behavior for CONV
technique.
Id- MSD
Iq- MSD
0
1
2
3
4
5
Time [s]
(b)
Figure 15 – Direct and Quadrature current dynamic behavior for MSD
technique: (a) Positive sequence; (b) Negative sequence.
100
100
80
80
60
60
40
Id+,q+ RESD [A]
Id,q RES [A]
40
20
0
-20
20
0
-20
-40
-40
-60
-60
Id RES
-80
Iq RES
-100
0
1
2
3
4
Id+ RESD
-80
Iq+ RESD
-100
0
1
2
5
3
4
5
Time [s]
Time [s]
(a)
Figure 14 – Direct and Quadrature current dynamic behavior for RES
technique.
100
Id- RESD
80
60
80
40
Id-,q- RESD [A]
100
60
Id+,q+ MSD [A]
40
20
20
0
-20
-40
0
-60
-20
-80
-40
-100
-60
Id+ MSD
-80
-100
Iq- RESD
1
2
3
Time [s]
(a)
4
1
2
3
4
5
Time [s]
Iq+ MSD
0
0
(b)
5
Figure 16 – Direct and Quadrature current dynamic behavior for RESD
technique: (a) Positive sequence; (b) Negative sequence.
100
2
80
1
60
0
20
Q [KVAr]
Id+,q+ NOTCH [A]
40
0
-20
QCONV
-60
Id+ NOTCH
-80
-3
Iq+ NOTCH
0
1
2
3
4
-4
5
Time [s]
0
QMSD
QRESD
QNOTCH
2.24
1
2
3
4
5
(b)
Figure 18 – Active and reactive power dynamic behavior: (a) Active power;
(b) Reactive power.
100
Id- NOTCH
80
Iq- NOTCH
4
IPhase A [%]
60
40
20
2
0
0
CONV
MSD
RESD
(a)
NOTCH
RES
CONV
MSD
RESD
(b)
NOTCH
RES
CONV
MSD
RESD
(c)
NOTCH
RES
-20
4
IPhase B [%]
-40
-60
-80
-100
QRES
2.28
Time [s]
(a)
Id-,q- NOTCH [A]
0
-0.08
-0.16
-0.24
-0.32
-0.4
2.2
-2
-40
-100
-1
2
0
0
1
2
3
4
5
Time [s]
Figure 17 – Direct and Quadrature current dynamic behavior for NOTCH
technique: (a) Positive sequence; (b) Negative sequence.
IPhase C [%]
4
(b)
2
0
20
Figure 19 – Current harmonic spectrum for each control technique at time 1.8
seconds.
15
VI.
P [KW]
10
PCONV
5
PMSD
13.2
PRESD
0
PNOTCH
12.8
PRES
-5
12.4
2.25
-10
0
1
2.3
2.35
2
3
Time [s]
(a)
4
5
CONCLUSIONS
This paper presented a comparison of 4 techniques of
control negative sequence in a PV inverter and the
conventional strategy. Comparisons during unbalanced voltage
dips and harmonics are performed.
During unbalanced voltage dips, RES and RESD control
techniques presents a better performance in terms of reactive
power dynamic response. However, all techniques controlled
the negative sequence component, which appeared as a large
fluctuation in CONV control strategy.
Harmonic spectrum of injected current indicates RESD
technique is more influenced by voltage harmonics than other
techniques.
In this situation, the RES control strategy obtains the best
behavior in terms of unbalanced voltage dips and harmonic
distortion in PCC voltage. Furthermore, this technique is
simpler than others, because it do not control separately the
positive and negative sequence.
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BIOGRAPHIES
Edmar Ferreira Cota received the B.S. degree in
electrical engineering from the Federal University
of Viçosa (UFV), Viçosa, Brazil, in 2014.
Currently he is Master student from Federal
University of Minas Gerais (UFMG), Belo
Horizonte, Brazil., where developed works about
power electronics applied in renewable energy
systems.
Lucas Santana Xavier was born in Viçosa -MG,
Brazil. He is student of Electrical Engineering at
Federal University of Viçosa (UFV), Viçosa,
Brazil. He is integrant of GESEP, where
developed works about power electronics applied
on renewable energy systems. The interests of his
research include photovoltaic systems and
multifunctional power inverters.
Allan Fagner Cupertino received the B.S. degree
in electrical engineering from the Federal
University of Viçosa (UFV), Viçosa, Brazil, in
2013. He is integrant of GESEP, where developed
works about power electronics applied in
renewable energy systems. Currently he is Master
student from Federal University of Minas Gerais
(UFMG), Belo Horizonte, Brazil. He has been
with the Department of Materials Engineering of
CEFET-MG, Brazil. His research interests include solar photovoltaic, wind
energy, control applied in power electronics.
Heverton Augusto Pereira received the B.S.
degree in electrical engineering from the
Universidade Federal de Viçosa (UFV), Brazil, in
2007 and M.Sc. degree in electrical engineering
from the Universidade Estadual de Campinas
(UNICAMP), Brazil, in 2009. Currently is Ph.D.
student from the Universidade Federal de Minas
Gerais (UFMG), Brazil. He has been assistant
professor at the Electric Engineering Department
in the UFV, Brazil, since 2009.