Single-phase multifunctional inverter with dynamic saturation scheme for
partial compensation of reactive power and harmonics
1
Heverton A. Pereira1,3, Lucas S. Xavier1 and Allan F. Cupertino 2,3, Victor F. Mendes3,
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
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
victormendes@cpdee.ufmg.br
Keywords
Dynamic saturation, harmonic compensation, multifunctional photovoltaic inverter and reactive
power compensation.
Abstract
Single and three-phase photovoltaic inverters are essential components of the photovoltaic (PV)
systems to extracting the PV power and injecting it into the grid. Thus, in order to extract the
maximum power of the solar array for various solar irradiation tracks, it is used a maximum power
point tracker (MPPT) algorithm. Due to variations in solar irradiance, inverters have a current margin,
which is not explored during the day. Thereby, many works have proposed the 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 that the inverter works 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 to inject low-order harmonics, while ensuring the operation below the system rated
current. Furthermore, control performance is evaluated for five grid-connected PV system in parallel
association, in order to show the effectiveness of proposed control strategy for various dispersed PV
systems in the grid. To ensure that the proposed method is applied with the maximum efficiency of the
PV system, this work compares, during inverter multifunctional operation, the instantaneous and
dynamic efficiency between three MPPT algorithms proposed in literature: perturb and observe; dP –
perturb and observe; modified perturb and observe.
Introduction
The number of grid-connected PV systems has increased along with requirements for converters
with advanced technologies to include, in addition to injection of maximum power from the PV array
into the grid, other services such as: reactive power injection during voltage sags [1, 2] and harmonic
current and reactive power compensation of the loads connected to the point of common coupling
(PCC) [3 6].
With increasing of nonlinear loads connected to the distribution system, power quality issues,
especially harmonics, are becoming a concern in power systems [3]. If a photovoltaic system is
already installed, a modification in the control strategy for harmonic compensation methods can be an
interesting solution if compared with active and passive filters [7, 8]. Therefore, the wide dispersion of
PV systems can give support to the distribution system through multifunctional operation mode,
improving the power quality index of an installation [9].
An important issue for multifunctional operation is the harmonic and reactive current detection
method. In literature, several methods are proposed, such as: instantaneous power theory based
method [10] , Fourier transform based method [11], second-order generalized integrator (SOGI) based
method [12], cancellation of delayed signals based method [13] and conservative power theory based
method (CPT) [6, 14, 15].
With regard to the controllers, in single-phase applications, many works use PR controllers because
references of current loop are sinusoidal [16]. However, PR controller can compensate only one
frequency and is necessary to implement one PR controller for each harmonic frequency. For example,
reference [7] implements resonant controllers of fundamental until 15th harmonic. This fact increases
the algorithm complexity. Furthermore, when load harmonic content is not well defined, the PI
controllers can be an interesting solution.
However, most important fact and less related in literature is the limitation strategy of the inverter
current. Inverter switches have a current limit that cannot be exceeded, to preserve its lifetime and
safety [17, 18]. 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 (due to harmonic current compensation). If resultant waveform has a maximum value
higher than the limit of the inverter, this reference needs to be saturated. In this situation, injected
current will contain low order harmonics [18]. Therefore, techniques to compensate partially reactive
power and harmonics of the PCC are necessary.
In this context, the main contribution of this paper is the development of a current dynamic
saturation scheme in multifunctional inverter, connected to a photovoltaic system, in order to
compensate partially reactive power and harmonics of the load. The current detection method is based
on the CPT. The control system is based on linear proportional-integral (PI) controllers. The proposed
method is applied in a single-phase system as shown in Fig. 1. Electrical model of the solar panel is
based on the mathematical model proposed in [19].
The solar panels presents characteristic curves (I-V & P-V) for each level of solar irradiance, with
three remarkable points: short circuit, maximum of power point (MPP) and open circuit, as detailed in
[19]. Therefore, it is necessary to extract as much power as possible from a solar panel. For this
reason, in PV systems there is a maximum power point tracker (MPPT) algorithm. The MPPT acts in
order to force the operating point of PV modules on their peak power. Several MPPT algorithms have
been proposed in the literature. This work studies three strategies: perturbation and observation (P&O)
[20], dP-P&O [21] and Modified P&O (MP&O) [22]. For a better performance of the system, it is
important to use the most efficient MPPT method [23]. Simulations were performed to evaluate the
instantaneous and dynamic efficiency of the three MPPT algorithms, applied in the inverter
multifunctional operation, during changes in solar irradiance.
Finally, to complete this work, control performance is evaluated for five grid-connected PV system
in parallel association. Power quality indexes of the grid are analysed in order to show the
effectiveness of the proposed control strategy when several PV systems are connected to the grid.
Fig. 1: Grid-connected photovoltaic system based on multifunctional inverter.
Control Strategy
Complete control strategy is presented in Fig. 2. Generally, the dc/dc stage is responsible for the
MPPT algorithm [24], which maintains the solar array delivering maximum power to the system at
various levels of solar irradiance and temperature. The boost control strategy has a voltage control
loop associated with a 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 reference wave i . This current reference is added to the load
harmonic and reactive current component, generating the inverter current reference iS . This current is
saturated and compared with the inverter current iS t . The next PI compensator calculates the
converter modulation index v 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 inverter and grid
current. Therefore, the inverter can compensates harmonic current and reactive power of all loads.
Converter synchronization with the grid is made by the phase-locked loop (PLL) based on second
order generalized integrator (SOGI-PLL, Fig. 3) proposed in [25]. SRF-PLL is responsible for phase
0 of the rotating reference frame [25, 26, 27]. Generally, the PCC voltage has
detection making i
some distortions that can affect the current reference. For this reason, a band pass filter based on SOGI
is used. The parameters of the SOGI-PLL are defined in [27].
Fig. 2: Complete control strategy.
Fig. 3: Complete structure SOGI-PLL.
Maximum Power Point (MPPT)
Due to low algorithm complexity and low computational power requirement, the most traditional
MPPT method is the Perturb and Observe (P&O). This algorithm periodically increments or
decrements the solar array voltage and compares the output power with the previous value. If the
delivered power increased, the solar array voltage perturbation will continue in the same direction.
When the supplied power starts to decrease, the system has reached the maximum power point (MPP)
and the P&O algorithm will oscillate around it [20, 28].
However, in rapidly changing in the solar irradiation, the P&O algorithm can get confused and
track wrong direction. This can happen when the power variation, due to irradiance variation, is higher
than the caused by own algorithm action. Thereby, the algorithm interprets the power variation only as
an effect of its own action [21, 29]. Hence, variations of the P&O method are proposed in literature, in
order to solve problems caused by the rapidly changing in irradiance, such as: Modified P&O method
(MP&O) [22] and the dP-P&O method [21, 29].
In order to solve the P&O problem with rapidly changing in the solar irradiation, the MP&O
divides the algorithm in two modes [22]. Mode 1 is responsible for measuring the power variation due
to the previous voltage change and atmosphere change, maintaining constant the solar array voltage
for the next period. Mode 2 is responsible for measuring the power variation and determines the next
solar array voltage based on present and previous power variation [22].
The dP-P&O method, proposed in [21, 29], determines the correct tracking by means of additional
measurement of power in the middle of the MPPT sampling period without any perturbation. Thereby,
during rapidly changing in the solar irradiance, the action of this MPPT is able to interpret correctly if
the change of power is caused as an effect of its own action or due solar irradiance change [21].
Instantaneous and Dynamic MPP-Tracking Efficiency
At locations where there are often variable cloudy conditions, the dynamic MPPT behavior has to
be considered. Therefore, the measuring of the MPPT efficiency is important to determine which
algorithm is more stable during solar irradiance variations [30]. Inverters with a fast MPP-tracker have
a somewhat higher energy yield under quickly changing irradiance than devices with a slow MPPT.
Thus, two methods are used to measure the efficiency of an MPPT algorithm, they are: dynamic
MPPT efficiency, given by (1) and instantaneous MPPT efficiency, given by (2) [30].
η
η
%
%
100
100
TM
P
TM
P
PPV_
PPV_
PV
(1)
PV_
2
is the output power measured in the panel and PPV_
where PPV
the panel available.
is the maximum power of
Current Detection Method Based on CPT
The conservative power theory based method is used to detect the harmonic and reactive current
components of the load. This method decomposes a current signal in three orthogonal components: the
active component, reactive component and the residual component. Description details about the CPT
are shown in [14, 15, 31, 32].
According to the CPT, the active current i , reactive current i t and the void current (residual
term) i t are:
P
v t
V
W
i t
v
V
i t
i t
i
i t
3
4
i
5
where P is the active power on the system, v t is the instantaneous voltage value at PCCC. V is the
RMS voltage of v t . W is the new term established by CPT, called reactive energy [14, 15, 31, 32]
and V is the RMS voltage of unbiased time integral of v t .
According to the CPT, when the grid voltage is free from distortions, the current distortion caused
by non-linear loads i t is equal to residual term i t [32].
Dynamic Saturation
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.
In order to ensure that 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.
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
Reactive Saturation
is the inverter rated
Reactive current saturation is performed as shown in Fig. 4a, where i
current, i is the amplitude of the active current injected by PV system. Note that, the saturation is
done directly on the reactive current RMS value i , . As the current components have a unique
frequency, the first saturation limit can be found by phasor calculation. Thereby, the resultant current
amplitude is composed by two orthogonal components: ı and ı .
As shown in Fig. 4b, resultant current of ı and ı should be contained in the circumference of
radius i
, otherwise, reactive compensation will be partial, ensuring the operation below the rated
current.
Fig. 4: (a) Reactive current saturation loop during the detection method application. (b) Phasor
calculation scheme to determine the saturation limit.
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.
Harmonic current saturation scheme is presented in Fig. 5a. The instantaneous current of the
inverter is found adding harmonic component to active and reactive components. The maximum value
of the waveform resultant is detect and compared with the inverter current limit.
A peak detector algorithm is used to detect the maximum value of the waveform resultant. This
algorithm compares samples of one fundamental period and determines the maximum value. As
detailed in Fig. 5b, the action of this algorithm has a delay of half cycle. However, the peak detector
does not induce delays in the reactive current injection.
An anti-windup PI controller generates the dynamic factor (K) and it determines if the
compensation will be total or partial. The inverter control loop has a saturator to ensure that the current
reference does not exceed the rated current while the K factor does not reach the steady-state.
Simulations and Results
MPPT Efficiency
The performances of the MPPT algorithms are compared during multifunctional operation of the
PV system. For this purpose, characteristics of the solar irradiance variations, such as inclination and
duration of the ramps, are based in tests conducted in [30]. The first irradiance profile presents a ramp
with variation between 30 and 100%. The second irradiance profile is a ramp between 20 and 50%.
i*p
30
i peak
Current [ A ]
20
10
0
-10
-20
3.9
(a)
3.95
4
4.05
Time [ s ]
4.1
4.15
(b)
Fig. 5: (a) Harmonic current saturation loop during the detection method application. (b) Peak detector
algorithm operation.
The instantaneous MPPT efficiency for the first irradiance profile is represented in Fig. 6a. When
irradiance increases to 100%, both methods had ripple, but the P&O method presents a faster response.
When irradiance decrease to 30%, P&O presented a higher ripple, however it showed a rapid
stabilization. The dynamic efficiencies for the three methods are shown in Table I, for the first
irradiance profile. Note that, the three methods have similar performance.
For the second irradiance profile, the P&O and MP&O presents difficulty in tracking the value of
the maximum power, as illustrated in Fig. 6b. The dP-P&O method is more stable during irradiance
transients. Inspection of Table I (dynamic efficiency) indicates that dP-P&O and MP-P&O methods
have an advantage over P&O algorithm for the second irradiance profile.
Thereby, the dP-P&O method is more efficient than the other methods for rapid variations in solar
irradiance, especially involving transitions between low irradiance. Therefore, dP-P&O is used as the
MPPT algorithm for the next analysis, ensuring greater efficiency and stability of the PV system.
40
600
99
98
400
97
96
20
0
2.1
2.2
2.3
Time [s]
(a)
100
60
40
20
0
0
2.5
98
200
96
94
2.6
2.4
P&O
MP&O
400
dP-P&O
Irradiance
300
80
200
2.2
2.4
Time [s]
500
Efficiency [%]
Efficiency [%]
Efficiency[%]
100
60
800
Efficiency[%]
P&O
MP&O
dP-P&O
Irradiance
80
100
2.1
2.2
100
2.2
2.4
Time [s]
2.3
Time [s]
(b)
2.4
0
2.5
Fig. 6: Instantaneous efficiency for the three studied algorithms. (a) First profile. (b) Second profile.
Table I: Dynamic efficiencies for both irradiance profiles.
P&O
MP&O
dP-P&O
Efficiency for Profile 1 (%)
99.64
99.35
99.60
Efficiency for Profile 2 (%)
98.62
99.30
99.63
Multifunctional Operation with Dynamic Saturation Scheme
Study case presents a solar array consisting in 5 parallel strings with 13 panels of 48 W in series.
The inverter rated power is 3.2 kVA. The switching frequency of the boost and inverter is 6 kHz.
Voltage at point of common couple is 220 V. All simulations were implemented in Matlab/Simulink
environment.
The total load connected to the PCC is composed by a resistive-inductive load of 3,35 kVA with
power factor of 0.9 and nonlinear loads, represented by current sources injecting 3th and 5th harmonic
of 7A and 5A, respectively.
The solar irradiance dynamic is shown in Fig. 7a. The solar array voltage is illustrated in Fig. 7b,
this voltage is used in the boost control loop. This voltage follows the maximum power point due to
control strategy of the boost converter. The inverter dc-bus voltage response is detailed in Fig. 7c. The
inverter control strategy maintains the voltage at 390 V and some oscillations are observed during
solar irradiance variations.
1200
250
410
240
2
Vp v [ V ]
800
600
Vd c [ V ]
Irradiance [ W / m ]
420
1000
230
400
390
380
220
200
0
400
370
0
2
4
Time [ s ]
(a)
6
210
1
2
3
4
Time [ s ]
(b)
5
6
360
1
2
3
4
Time [ s ]
(c)
5
6
Fig. 7: (a) Solar irradiance profile. (b) Array solar voltage, detected by the MPPT. (c) Dc-bus voltage.
Irradiance [W/m2]
1000
Irradiance [W/m2]
100
Active power P and reactive power Q injected into the grid are shown in Fig. 8. The reactive
power compensation is enabled at 0.8 seconds. Note that, the inverter presents current margin to
compensate partly the load reactive power between 0.8 and 2 seconds and after 5 seconds. However,
the inverter supplies all load reactive power between 2 and 5 seconds.
The harmonic current compensation is enabled at 1.2 seconds. Nevertheless, in this instant the K
factor is zero, ensuring that the inverter works below the rated current, as shown in Fig. 9. Waveforms
detail of the grid and inverter current, at this precise moment, are shown in Fig. 10a. THD of the grid
current (iG , inverter current (iS and load current (iL are shown in Table II.
Initially, the inverter is supplying all active power to the load, while the grid current only has the
harmonic distortions caused by the load. For this reason, the grid current THD is 303.50 %.
At 2 seconds, the inverter presents current margin to supply all reactive power of the load, due to
decreasing of irradiance to 600 / , as detailed in Fig. 8. Furthermore, the inverter presents current
margin to compensate, approximately, 72% of the load harmonic current, as can be observed in Fig. 9.
Grid current THD decreases from 303.50 % to 24.44%. The grid current improvement is detailed in
Fig. 10b. It is important to reiterate that the grid current reaches the steady-state when K factor
stabilizes.
at 3 seconds, the inverter presents margin to
Due to decreasing of irradiance to 200 /
compensate 100% of the load harmonic current, as can be observed in Fig. 9. At this instant, grid
current THD decreases from 24.44 % to 1.53 %. This grid current improvement is detailed in Fig. 10c.
at 4 seconds and K factor ponders the harmonic
The solar irradiance increases to 700 /
compensation, as can be seen in Fig. 9. The action of the K factor prevents the saturator performance,
in the inverter control loop as illustrated in Fig. 2b, and detailed in Fig. 11a.
In the same cycles detailed in Fig. 11, the spectra of the system currents during multifunctional
operation with and without dynamic saturation are depicted in Fig. 12. Note that, without dynamic
saturation, the inverter compensates the majority of the 3th e 5th harmonic of the grid. However, the
saturator acts under the inverter current reference (Fig. 11b), contributing to the appearance of odd
harmonics in the inverter current, such as: 7th, 9th, 11th and 15th harmonic. This odd harmonics are
reflected into the grid current, potentially causing damage and losses in the power system.
With dynamic saturation, the compensation of 3th and 5th harmonic of the load current is pondered
as shown in Fig. 9, Preventing the action of the saturator and avoiding the injection of unwanted
harmonic orders into the grid.
Electrical Grid
3
2
1
0
1
2
3
4
Time [ s ]
(a)
5
4
Q
P
→ Starts the reactive
power compensation
3
2
1
0
-1
6
5
1
2
3
4
Time [ s ]
(b)
5
6
P[ kW ] / Q[ kVar ]
Q
P
P[ kW ] / Q[ kVar ]
P[ kW ] / Q[ kVar ]
5
4
-1
Load
Inverter
5
Q
P
4
3
2
1
0
-1
1
2
3
4
Time [ s ]
(c)
5
6
Fig. 8: Active and reactive power dynamics during the reactive power and harmonic compensation. (a)
Grid. (b) Inverter. (c) Load.
Table II: Total current harmonic distortion.
→ Starts the harmonic
current compensation
1
Interval
0.8
1
1.2
2
3
4
K
0.6
0.4
0.2
0
-0.2
0
1.2
2
3
4
5
6
Time [s]
Fig. 9: Dynamic factor ( ).
1.2
2
3
4
5
5
THD iG
(%)
307.50
303.50
24.44
1.53
59.01
303.72
THD iS
(%)
0.73
0.72
44.51
86.53
29.83
0.71
THD iL
(%)
39.84
39.84
39.84
39.84
39.84
39.84
→ harmonic compensation is enabled
20
0
-20
1.15
1.2
1.25
iS
Inverter
1.3
1.35
iS[A ]
iG[ A ]
Electrical Grid
1.4
i max
20
0
-20
1.15
1.2
1.25
1.3
1.35
1.4
2
→ irradiance = 600 W/m
20
0
-20
1.95
2
2.05
2.1
iS[A ]
i G[ A ]
(a)
2.15
2.2
2.25
20
0
-20
1.95
2
2.05
2.1
2.15
3
3.05
2.2
2.25
(b)
2.95
3
3.05
3.1
iS[A ]
iG[ A ]
2
→ irradiance = 200 W/m
20
0
-20
3.15
20
0
-20
3.2
2.95
3.1
3.15
3.2
20
0
-20
3.95
2
→ irradiance = 700 W/m
4
iS[A ]
i G[ A ]
(c)
4.05
4.1
Time [ s ]
4.15
4.2
20
0
-20
3.95
4
4.05
4.1
Time [ s ]
(d)
4.15
4.2
Fig. 10: Waveforms detail of the grid and inverter current, when: (a) harmonic current compensation is
enabled. (b) Irradiance decreases to 600 / . (c) Irradiance decreases to 200 / . (d) Irradiance
goes to 700 / .
100
25
80
60
100
20
i* S
15
i m ax
25
80
10
60
20
0
0
-20
-40
-40
4.45
4.5
Time [ s ]
(a)
4.55
4.554 4.556
20
-20
-60
4.4
-60
4.4
4.6
4.45
/
Fig. 11: Details of the inverter current reference to irradiance 700
saturation. (b) Without dynamic saturation.
8
5
0
2
0
1
5
0
1
10
15
Harmonic Order
(a)
2
20
4
10
2
0
0
1
4.6
Sat = 0
Sat = 1
6
40
20
5
IL [ A ]
4
4.55
8
Sat = 0
Sat = 1
6
10
IS [ A ]
IG [ A ]
6
4.5
Time [ s ]
(b)
. (a) With dynamic
8
Sat = 0
Sat = 1
i max
5
40
i* S [A]
i* S [ A ]
4.554 4.556
i* S
15
10
5
40
20
0
1
10
15
Harmonic Order
(b)
4
20
0
2
2
20
0
1
5
0
1
10
15
Harmonic Order
(c)
2
20
Fig. 12: Currents spectra without dynamic saturation (Sat = 0) and with dynamic saturation (Sat =1)
during inverter multifunctional operation. (a) Grid current spectrum. (b) Inverter current spectrum. (c)
Load current spectrum.
Impact of Several Multifunctional Inverters on the PCC Voltage Quality
The last study case presents five grid-connected PV system in parallel association. Two scenarios
are evaluated:
• Scenario 1: The inverters do not have the multifunctional operation (m = 0)
• Scenario 2: The inverters have the multifunctional operation (m = 5)
The multifunctional operation is enabled at 2.5 seconds. The solar irradiance of 400 /
is
simulated. Thus, the five inverters have current margin to compensate all harmonics of the loads. The
grid current for both scenarios is detailed in Fig. 13a. Note that, the grid current reaches the steadystate when all inverters K factor keep constant.
This operation mode provides a considerable quality improvement at local grid, mainly in the
reduction of low-frequency harmonics. This improvement is more evident in Fig. 13b. With
multifunctional operation of the PV systems, grid current THD decreases from 116.37% to 2.20%.
Conclusion
This work presented a grid-connected photovoltaic system based on multifunctional inverter
operation. This concept consists in aggregate to the inverter control strategy other functions such as
harmonics and reactive power compensation. Thus, for a better performance of the system, it is
important to use the most efficient MPPT method. This work presents a comparison between three
MPPT algorithms (P&O, MP&O and dP-P&O) applied in the inverter multifunctional operation,
during changes in solar irradiance. The dP-P&O method is more efficient than the other methods for
rapid variations in solar irradiance, especially involving transitions between low irradiance, because it
tracks correctly the MPP direction under these circumstances.
A current dynamic saturation scheme is proposed in order to compensate partially reactive power
and harmonics of the load during the multifunctional operation. The harmonic compensation is
adjusted in accordance with the current margin remaining after active power and load reactive power
compensation, ensuring that the inverter works below the rated current and preserving its lifetime.
Simulations show that the dynamic saturation prevents the inverter of inject low-order harmonics.
With multifunctional operation, the grid current THD is reduced and the reactive power is fully
compensated, which is considerable improvement in the grid quality index.
In the end, the proposed method is evaluated for five grid-connected PV system in parallel
association with multifunctional operation. In this situation, results showed a considerable
improvement in terms of power quality.
Electrical Grid
100
80
35
m = 0 ←→ m = 5
m=0
m=5
30
60
40
60
25
I G [A]
i G[ A ]
20
0
-20
40
20
20
15
0
-40
10
0
1
2
-60
5
-80
-100
2.45
2.5
2.55
2.6
Time [ s ]
(a)
2.65
2.7
0
2
4
6
8
10
12
Harmonic Order
(b)
14
16
18
20
Fig. 13: (a) Grid current detail during scenarios 1 and 2. (b) Improvement detail in power quality of
the local grid.
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