Saturation Scheme for Single-Phase Photovoltaic
Inverters in Multifunctional Operation
Lucas S. Xavier1, João H. de Oliveira3, Allan F. Cupertino1,2,3, Victor F. Mendes3 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
lsantx@gmail.com, heverton.pereira@ufv.br
3
Graduate Program in Electrical Engineering
Federal University of Minas Gerais
Av. Antônio Carlos 6627, 31270-901
Belo Horizonte, MG, Brazil
victormendes@cpdee.ufmg.br
Abstract—Single and three-phase photovoltaic inverters are
responsible to extract the photovoltaic array power and inject it
into the grid. Due to variations in solar irradiance, inverters have
a current margin, which is not explored during the day. Thereby,
many works have proposed multifunctional operation. This
concept consists in aggregate to the inverter control strategy other
functions, such as harmonics and reactive power compensation.
However, most important fact and less related in literature is the
necessity of techniques to compensate partially reactive power and
harmonics of the load, ensuring the inverter work below the rated
current. Hence, the present work proposes a current dynamic
saturation scheme in order to compensate partially reactive
power and harmonics of the load during the multifunctional
operation. Simulations show that the dynamic saturation
prevents the inverter of inject low-order harmonics while
ensuring the operation below the system rated current. By
applying the multifunctional operation, the grid current THD is
reduced from 104.64% to 1.54% and reactive power is fully
compensated, resulting in a considerable grid improvement.
Keywords—Multifunctional inverter, dynamic saturation,
reactive power and harmonic compensation.
I.
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
INTRODUCTION
In conventional operation, single-phase photovoltaic
inverters are responsible to extract the maximum power from
the photovoltaic array and inject it into the grid with unitary
power factor [1]. Due to variations in solar irradiance,
photovoltaic system works below the rated power during most
of the time. Therefore, inverters has a current margin, which is
not explored during the day.
In this context, some works proposes multifunctional
operation [2, 3]. This concept consists in aggregate to the
inverter control strategy other functions, such as harmonic and
reactive power compensation. This possibility can be
This work is supported by the Brazilian agencies CAPES, FAPEMIG
and CNPQ.
interesting in terms of power factor improvement and the
distortion index improvement of the grid current, caused by
large number of non-linear loads connected into the grid [4].
Moreover, the solar irradiance is minimal in the night,
therefore, the photovoltaic inverter can be used as active
harmonic filter [5].
For multifunctional operation, the inverter control should
detect the load current harmonic content. In literature, several
methods for harmonic and reactive current detection are
proposed, such as: instantaneous power theory based method
[6], Fourier transform based method [7], second-order
generalized integrator (SOGI) based method [8], cancellation
of delayed signals based method [9] and conservative power
theory based method [10, 11].
Among the controllers used, there are: proportional-integral
(PI) [12, 13], proportional-resonant (PR) [12, 5, 14] and
nonlinear controllers [12, 13]. PR controller can compensate
only one frequency and it is necessary to implement one PR
controller for each harmonic frequency. This fact increases the
algorithm complexity. Furthermore, when load harmonic
content is not defined, PI controllers are an interesting solution.
However, most important fact and less related in literature
is the inverter current saturation strategy. Inverter switches have
a current limit that cannot be exceeded [15]. In multifunctional
operation, generally, current reference is composed by active
(due to the photovoltaic system), reactive (due to the reactive
power compensation) and harmonic components. If the
resultant waveform has a maximum value higher than the
inverter current limit, this reference needs to be saturated. In
this situation, injected current will contain low order harmonics
[16]. Thereby, techniques to compensate partially load reactive
power and harmonics are necessary.
In conventional operation, single-phase inverter control is
responsible for tasks as: maximum power point tracking
(MPPT), grid current control, voltage amplification and dc-bus
control. This excess tasks can occasion instability in the inverter
control strategy. Therefore, this work uses a boost converter to
connect the inverter to solar array [17]. Thereby, the inverter is
isolated from the MPPT algorithm.
(a)
In this context, the present work proposes the development
of a current dynamic saturation scheme in single-phase
multifunctional inverter, connected to a photovoltaic system, in
order to compensate partially loads reactive power and
harmonics. The conservative power theory (CPT) is used in
harmonic and reactive current detection method. The control
system is based on linear proportional-integral controllers. The
solar panel electrical model is based on the mathematical model
proposed in [18].
(b)
Figure 2. Complete control strategy. (a) Boost control loop. (b) Inverter control
loop.
Converter synchronization with the grid uses PLL based on
second order generalized integrator SOGI, proposed by [20]. A
band pass and low pass filter SOGI is used for emulating an
orthogonal system to the phase detection SRF-PLL [20, 21].
SOGI- PLL complete structure is shown in Fig. 3.
Figure 1.
inverter.
Grid-connected photovoltaic system based on multifunctional
II.
MODELING OF THE SYSTEM
In this section, a detailed discussion about the proposed
control strategy is presented.
A. Control strategy
Complete control strategy is presented in Fig. 2. The MPPT,
used in the boost control loop, maintains the solar array
delivering maximum power to the system at various levels of
solar irradiance and temperature. The operating principle of this
algorithm is based on perturbation and observation strategy
[19]. The boost control strategy has a voltage control loop
cascading with current control loop as shown in Fig. 2a.
Inverter control strategy is shown in Fig. 2b. The PI
compensator calculates the active current amplitude i∗ that
needs to be injected into the power system. This signal is
synchronized with PCC voltage, resulting in a sinusoidal wave
i∗ (t). This current reference is added to load harmonic and
reactive current component, generating the inverter current
reference i∗ (t). This current is saturated and compared with the
inverter current i (t). The next PI compensator calculates the
converter modulation index ∗ to set the converter switches
pulses through the PWM algorithm.
Generally, loads in the installation are connected in
different points and the direct measurement of their current can
be difficult. This work estimates the load current in terms of the
injected current by inverter and grid. Therefore, multifunctional
inverter can compensates harmonics and reactive power of all
loads.
Figure 3. SOGI-PLL Complete structure [21].
B. CPT based harmonic detection method
The conservative power theory based method is used for
detect the load harmonic and reactive current component. This
method decomposes a current signal in three orthogonal
components: the active component, reactive component and the
residual component. Description details about the CPT is
shown in [22, 23].
According to the CPT, the active current i ( ) , reactive
current i (t) and the harmonic current i (t) of the load is:
P
v(t)
V
W
i (t) =
v( )
V
i (t) = i(t) − i (t) − i ( )
i (t) =

(1)
(2)

(3)
 Where P is the active power in the system, v(t) is the voltage
instantaneous value at PCC, W is the new term established by
CPT called reactive energy and V is the vector of unbiased
voltage integrals [22].
C. Dynamic Saturation
In order to ensure the inverter current does not exceed the
rated current, harmonic and reactive current dynamic saturation
are proposed. Furthermore, this strategy provides partial
compensation of load reactive power and harmonic current.
The priority in this work is the active power injection
followed by the load reactive power compensation and, lastly,
load harmonic current compensation. Therefore, the dynamic
saturation consists in two parts, in the following order:
harmonic current saturation and reactive current saturation.
A peak detection algorithm is used to detect the waveform
resultant maximum value. This algorithm compares samples of
one fundamental period and determines the maximum value.
An anti-windup proportional integral controller generates
the dynamic factor ( ) (limited between 0 and 1) and it
determines if the compensation will be total or partial. This
action ensures the inverter working below the rated current.
Control loop (Fig. 2) has a saturator to ensure that the current
reference do not exceed the rated current while the factor
does not reach the steady-state.
Therefore, if the inverter is compensating all reactive power
and exists current margin, the control strategy will compensate
harmonic current. However, if reactive power compensation is
partial, the inverter will not compensate harmonic current.
C.1) Reactive Saturation
Reactive current saturation is performed as shown in Fig.
4a, where the inverter rated current is i
and the reactive
energy is W. Note that, the saturation is done directly on the
reactive current RMS value i . As component of active and
reactive current has a unique frequency, the first saturation limit
can be found by phasor calculation. Thereby, resultant current
amplitude is composed by two orthogonal components: ı∗⃗ and
ı⃗.
Figure 5. Harmonic current saturation loop during the detection method
application.
III.
RESULTS
Study case presents a solar array consists in 5 parallel
strings with 13 panels of 48 W in series. The inverter rated
power is 3.2 kVA, corresponding to 2.5% of overcurrent. The
boost and inverter switching frequency is 9 kHz. Voltage at
point of common couple is 220 V. All simulations were
implemented in Matlab/Simulink environment.
(a)
(b)
Figure 4. (a) Reactive current saturation loop during the detection method
application. (b) Circle of radius
to determine the saturation limit.
As shown in Fig. 4b, resultant current of ı∗⃗ and ı⃗ should be
contained in the circumference of radius i , otherwise,
reactive compensation will be partial for ensure operation
below the rated current. Equation that describes this fact is:
+
∗
<

(4)
C.2) Harmonic Saturation
When there are multiple frequencies in the current signal,
analytical expression of the saturation point is complex. This
work proposes a method to ponder the harmonic compensation
according with the inverter current peak value, ensuring it
works below the nominal value.
Harmonic current saturation scheme is presented in Fig. 5.
Basically, the inverter instantaneous current is found adding
harmonic component to active and reactive components. The
waveform resultant maximum value is detect and compared
with the inverter current limit.
In the first test, a comparison between multifunctional
operation with and without dynamic saturation is made, with
solar irradiance of 1000 W/m2. In this case the inverter does not
have margin for compensation of all harmonic content. Two
scenarios are evaluated:


Scenario 1: Multifunctional
dynamic saturation (Sat = 0).
operation
without
Scenario 2: Multifunctional operation with dynamic
saturation (Sat = 1).
Fig. 6 shows that, without dynamic saturation factor does
not exist to ponder the harmonic compensation. Thereby, the
inverter current reference saturator (Fig. 2b) prevents that
current exceeds the rated value. However, the action of this
saturator causes the appearance of low-order odd harmonics
with in the inverter current reference, as shown in Fig. 6b.
Consequently, these harmonics are reflected in the grid
current, as shown in Fig. 6a.
With dynamic saturation, factor ponders the harmonic
compensation, eliminating saturator action on the inverter
current reference, as shown in Fig. 6b. In this case, inverter has
margin to compensate approximately 40% of the load
harmonic content.
Action of the dynamic saturation under the inverter current
reference is shown in Fig. 7, in the same cycle that the previous
study case. Fig. 7a shows there is no factor
to ponder harmonic compensation. In Fig. 7b, the factor ponders the harmonic compensation approximately 40% and, consequently,
the saturation disappears.
I G [A]
15
2
0
0 1
20
4
10
2
0
2
4
6
8
10
12
Harmonic Order
(a)
14
16
18
20
Sat = 0
Sat = 1
0
0 1
2
4
6
8
10
12
Harmonic Order
(b)
14
16
18
20
6
40
I L [A]
Sat = 0
Sat = 1
5
0
I S [A]
4
10
Sat = 0
Sat = 1
4
20
2
0
0
0 1
2
4
6
8
10
12
Harmonic Order
(c)
14
16
18
20
Figure 6. Current spectrum with and without dynamic saturation during
inverter multifunctional operation. (a) Grid current spectrum. (b) Inverter
current spectrum. (c) Load current spectrum.
60
50
I*S
40
20.05
Imax
19.8
In the last study case, harmonic current and reactive power
compensation are performed. The solar irradiance profile starts
in 1000 / , as shown in Fig. 8a. At 0.6 seconds, the
reactive power compensation is started. At 1.5 seconds, the
solar irradiance reduces to 700 /
and at 2.5 seconds
reduces to 400 / .
Solar array voltage is shown in Fig. 8b, this voltage is used
in the boost control loop. This voltage follows the maximum
power point voltage due to boost converter control strategy.
Fig. 8c shows the inverter dc-bus voltage response. The
inverter control strategy maintains the voltage at 390 V and
few oscillations are observed during solar irradiance
variations.
Active power ( ) and reactive power ( ) injected into the
grid are shown in Fig 9. At 0.6 seconds, the inverter has margin
to compensate partly the load reactive power.
At 1 second, the harmonic compensation is enabled,
however, the factor K continues in zero, to ensure the inverter
works below the rated current, as shown in Fig. 10. Total
harmonic distortion (THD) of the grid current ( ), inverter
current ( ) and load current ( ) are shown in TABLE I.
At 1.5 seconds, due to decreased irradiance to 700 / ,
the inverter presents margin to compensate all load reactive
power, as shown in Fig. 9. Furthermore, the inverter presents
margin to compensate, approximately, 33% of the load
harmonic current, as shown in Fig. 10. Grid current THD
decreases from 104.4 % to 54.94%. The grid current
improvement is detailed in Fig. 11. It is important to reiterate
that the grid current reaches the steady-state when factor k
stabilizes.
30
19.55
2.0025
I*S[A]
20
At 2.5 seconds, due to the decrease of irradiance to 400
/ , the inverter presents margin to compensate 100% of
the load harmonic current, as shown in Fig. 10. Grid current
THD decreases from 54.94 % to 1.54 %. The grid current
improvement in this instant is detailed in Fig. 12.
2.0033
10
0
-10
TABLE I.
-20
-30
2
2.01
2.02
2.03
2.04
2.05 2.06
Time [s]
(a)
2.07
2.08
2.09
2.1
70
I* S [A]
60
I*S
40
Imax
IV.
19.8
19.55
2.0028
10
0
-10
-20
2
2.02
THD (%)
0.72
0.72
13.04
50.12
THD (%)
27.51
27.51
27.51
27.51
2.04
2.06
Time [s]
(b)
2.08
CONCLUSIONS
This work presented a grid connected photovoltaic system
based on multifunctional inverter. Dynamic saturation strategy
is included in the control strategy prioritizing reactive power
compensation.
2.0036
20
-30
THD (%)
104.64
104.64
54.94
1.54
20.05
50
30
Interval
0.6 ≤ ≤ 1
1 < ≤ 1.5
1.5 < ≤ 2.5
2.5 < ≤ 4
TOTAL CURRENT HARMONIC DISTORTION
2.1
Figure 7. Inverter current reference details. (a) Without dynamic saturation. (b)
With dynamic saturation.
The harmonic compensation is adjusted in accordance with
the current margin remaining after active power and load
reactive power compensation. This is the main advantage of the
dynamic saturation strategy proposed.
Simulations show that the dynamic saturation prevents the
inverter of inject low-order harmonics while ensuring the
operation below the system rated current. By applying the
1
0.8
0.6
K
2
Irradiance [W/m]
multifunctional operation, the grid current THD is reduced
from 104.64% to 1.54% and reactive power is fully
compensated, which is considerable improvement in terms of
power quality.
1000
0.4
500
0.2
0
0
0.5
1
1.5
2
Time [s]
(a)
2.5
3
3.5
4
0
-0.2
0.5
1
1.5
1.5
2
2.5
Time [s]
(b)
3
3.5
3.5
4
20
0
-20
1.4
380
370
0.5
1
1.5
2
Time [s]
(c)
2.5
3
1.45
1.5
1.55
1.6
1.65
1.7
1.6
1.65
1.7
Time [s]
(a)
Inverter
3.5
20
Figure 8. (a) The solar irradiance profile. (b) Array solar voltage, detected by
the MPPT. (c) Response of the inverter dc-bus voltage.
Electrical Grid
6
1.4
Q
P
4
0
-20
1.45
1.5
1.55
Time [s]
(b)
2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Figure 11. Current details before and after irradiance decrease to 700
1.5 seconds. (a) Electrical grid current. (b) Inverter current.
Time [s]
(a)
Inverter
/
at
Electrical Grid
6
20
I G [A]
Q
P
4
2
0
-20
0
0
0.5
1
1.5
2
2.5
3
3.5
2.4
4
2.45
2.5
8
6
4
2
0
Q
P
2.55
2.6
2.65
2.7
2.6
2.65
2.7
Time [s]
(a)
Inverter
Time [s]
(b)
Load
20
I S [A]
P[kW] / Q[kVar]
3
Electrical Grid
4
I G [A]
1
390
P[kW] / Q[kVar]
2.5
Figure 10. Dynamic factor ( ).
400
P[kW] / Q[kVar]
2
Time [s]
230
220
0.5
Vd c[V]
0
240
I S [A]
Vp v [V]
250
0
-20
0
0.5
1
1.5
2
2.5
3
3.5
4
Time [s]
(c)
Figure 9. Active and reactive power dynamics during the reactive power and
harmonic compensation. (a) Reactive and active power of the grid. (b) Reactive
and active power of the inverter. (c) Reactive and active power of the load.
2.4
2.45
2.5
2.55
Time [s]
(b)
Figure 12. Current details before and after irradiance decrease to 400
2.5 seconds. (a) Electrical grid current. (b) Inverter current.
/
at
REFERENCES
[1] E. Romero-Cadaval, G. Spagnuolo, L. Garcia Franquelo, C. RamosPaja, T. Suntio and W. Xiao, "Grid-Connected Photovoltaic Generation
Plants: Components and Operation," Industrial Electronics Magazine,
IEEE, vol. 7, no. 3, pp. 6-20, Sept. 2013.
[2] S. Rahmani, A. Hamadi, K. Al-Haddad and H. Kanaan, "A
multifunctional power flow controller for photovoltaic generation
systems with compliance to power quality standards," IECON 2012 38th Annual Conference on IEEE Industrial Electronics Society, pp.
894-903, 25-28 Oct. 2012.
[3] D. Geibel, "Multifunctional Photovoltaic Inverter Systems - energy
management and improvement of Power Quality and Reliability in
industrial environments," Energy Conversion Congress and Exposition,
2009. ECCE 2009. IEEE, pp. 3881-3888, 20-24 Sept. 2009.
[4] I. Quesada, A. Lazaro, A. Barrado, R. Vazquez, I. Gonzalez and N.
Herreros, "Extension of the Harmonic Elimination Technique in the
Presence of Non Linear Loads," Power Electronics Specialists
Conference, 2007. PESC 2007. IEEE, pp. 43-46, 17-21 June 2007.
[5] J. He, Y. W. Li, F. Blaabjerg and X. Wang, "Active Harmonic Filtering
Using Current-Controlled, Grid-Connected DG Units With ClosedLoop Power Control," Power Electronics, IEEE Transactions on, vol.
29, no. 2, pp. 642-653, Feb. 2014.
[6] H. Akagi, Y. Kanazawa and A. Nabae, "Instantaneous Reactive Power
Compensators Comprising Switching Devices without Energy Storage
Components," Industry Applications, IEEE Transactions on, vol. IA20,
no. 3, pp. 625-630, May 1984.
[7] B. McGrath, D. Holmes and J. Galloway, "Power converter line
synchronization using a discrete Fourier transform (DFT) based on a
variable sample rate," Power Electronics, IEEE Transactions on, vol.
20, no. 4, pp. 877-884, July 2005.
[8] P. Rodríguez, A. Luna, I. Candela, R. Mujal, R. Teodorescu and F.
Blaabjerg, "Multiresonant Frequency-Locked Loop for Grid
Synchronization of Power Converters Under Distorted Grid
Conditions," Industrial Electronics, IEEE Transactions on, vol. 58, no.
1, pp. 127-138, Jan. 2011.
[9] Y. F. Wang and Y. W. Li, "Three-Phase Cascaded Delayed Signal
Cancellation PLL for Fast Selective Harmonic Detection," Industrial
Electronics, IEEE Transactions on, vol. 60, no. 4, pp. 1452-1463, April
2013.
[10] H. Paredes, D. Brandao, T. Terrazas and F. Marafao, "Shunt active
compensation based on the Conservative Power Theory current's
decomposition," Power Electronics Conference (COBEP), 2011
Brazilian, pp. 788-794, 11-15 Sept. 2011.
[11] D. Brandao, F. Marafao, H. Paredes and A. Costabeber, "Inverter
control strategy for DG systems based on the Conservative power
theory," Energy Conversion Congress and Exposition (ECCE), 2013
IEEE, pp. 3283-3290, 15-19 Sept. 2013.
[12] A. Cupertino, L. Carlette, F. Perez, J. Resende, S. Seleme and H.
Pereira, "Use of control based on passivity to mitigate the harmonic
distortion level of inverters," Innovative Smart Grid Technologies Latin
America (ISGT LA), 2013 IEEE PES Conference On, pp. 1-7, 15-17
April 2013.
[13] F. Wang, J. Duarte, M. Hendrix and P. Ribeiro, "Modeling and Analysis
of Grid Harmonic Distortion Impact of Aggregated DG Inverters,"
Power Electronics, IEEE Transactions on, vol. 26, no. 3, pp. 786-797,
March 2011.
[14] I. Abdel-Qawee, N. Abdel-Rahim, H. Mansour and T. Dakrory,
"Closed-loop control of single phase selective harmonic elimination
PWM inverter using proportional-resonant controller," Modelling,
Identification & Control (ICMIC), 2013 Proceedings of International
Conference on, pp. 169-174, Aug. 31 2013-Sept. 2 2013.
[15] J. Bonaldo, H. Morales Paredes and J. Antenor Pomilio, "Flexible
operation of grid-tied single-phase power converter," Power Electronics
Conference (COBEP), 2013 Brazilian, pp. 987-992, 27-31 Oct. 2013.
[16] T. Qian, B. Lehman, G. Escobar, H. Ginn and M. Molen, "Adaptive
saturation scheme to limit the capacity of a shunt active power filter,"
Control Applications, 2005. CCA 2005. Proceedings of 2005 IEEE
Conference on, pp. 1674-1679, 28-31 Aug. 2005.
[17] S. Kjaer, J. Pedersen and F. Blaabjerg, "A review of single-phase gridconnected inverters for photovoltaic modules," Industry Applications,
IEEE Transactions on, vol. 41, no. 5, pp. 1292-1306, Sept.-Oct. 2005.
[18] M. Villalva, J. Gazoli and E. Filho, "Comprehensive Approach to
Modeling and Simulation of Photovoltaic Arrays," Power Electronics,
IEEE Transactions on, vol. 24, no. 5, pp. 1198-1208, May 2009.
[19] J. H. d. Oliveira, A. L. Malta, A. F. Cupertino and H. A. Pereira,
"Comparison of Four MPPT Algorithms Applied in Batteries Charging
with Photovoltaic Panels," V Simpósio Brasileiro de Sistemas Elétricos
- SBSE, Apr. 2014.
[20] R. Teodorescu, M. Liserre and P. Rodriguez, Grid Converters for
Photovoltaic and Wind Power Systems, Chichester, U.K.: John WileyIEEE, 2011.
[21] M. Ciobotaru, R. Teodorescu and F. Blaabjerg, "A New Single-Phase
PLL Structure Based on Second Order Generalized Integrator," Power
Electronics Specialists Conference, 2006. PESC '06. 37th IEEE, pp. 16, 18-22 June 2006.
[22] P. Tenti, H. Paredes and P. Mattavelli, "Conservative Power Theory, a
Framework to Approach Control and Accountability Issues in Smart
Microgrids," Power Electronics, IEEE Transactions on, vol. 26, no. 3,
pp. 664-673, March 2011.
[23] H. Paredes, F. Marafao, T. Terrazas and P. Serni, "Harmonic, reactive
and unbalance compensation by means of CPT framework," Power
Electronics Conference, 2009. COBEP '09. Brazilian, pp. 741-748,
Sept. 27 2009-Oct. 1 2009.