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Procedia Engineering 00 (2016) 000–000
www.elsevier.com/locate/procedia
Humanitarian Technology: Science, Systems and Global Impact 2016, HumTech2016
Towards a Real-time Measurement Platform for Microgrids in
Isolated Communities.
Geir Kuliaa,∗, Marta Molinasb, Lars Lundheima, Bjørn B. Larsena
aDepartment of Electronics and Telecommunications, NTNU, 7491 Trondheim
bDepartment of Engineering Cybernetics, NTNU, 7491 Trondheim
Abstract
This paper describes a platform for obtaining and analyzing real-time measurements in Microgrids. A key building block
in this platform is the Empirical Mode Decomposition (EMD) used to analyze the electrical voltage and current waveforms to
identify the instantaneous frequency and amplitude of the monocomponents of the original signal. The method was used to analyse
the frequency fluctuation and obtain information about the linearity of electrical current and voltage waveforms measured in the
field. Comparison between grid-connected and stand-alone microgrid voltage and currents’ monocomponents were conducted.
Fluctuations in the grid frequency occurred in both the grid-connected and stand-alone microgrid, but the degree of the observed
fluctuations were different, revealing more apparent nonlinear distortions in the latter. The observed instantaneous frequency from
the collected data indicates potential nonstationary electrical signals when compared to synthetic data containing periodic signals
coming from nonlinear loads. This observation leads us to expect the next generation of real-time measuring devices for the micro
power grids to be designed on the principle of instantaneous frequency detection. Further efforts will be directed to a more rigorous
characterization of the nonstationary nature of the signals by analyzing more and longer set of data.
©2016 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the Organizing Committee of HumTech2016.
Keywords: Instantaneous frequency, Hilbert-Huang Transform, Empirical mode decomposition, Microgrid, Frequency stability, Power systems
1. Introduction
Access to modern energy services is a necessity for economic development and particularly challenging in isolated
communities. The fall in prices of photovoltaic (PV) cells opens the possibility for affordable, clean and sustainable
energy to rural areas where, in most cases, extending the power grid is too expensive to be a realistic alternative. The
nature of the location for such systems require near to maintenance free supervisory control systems. Good access
to reliable data is essential to the supervisory control system to make correct actions. The nonlinearities of modern
power electronic equipment and the stochastic nature of the photovoltaic sources of energy advocate the need for
∗Corresponding author. Tel.: +47 992 99 867
E-mail address: geir@kulia.no
1877-7058 ©2016 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the Organizing Committee of HumTech2016.
2G. Kulia, M. Molinas, L. Lundheim, B. B. Larsen /Procedia Engineering 00 (2016) 000–000
data acquisition systems based on real-time measurements and estimation of essential values, such as instantaneous
amplitude and frequency. Existing measurement devices for microgrids do not fulfill this requirement, as they are
generally based on average value calculations [1].
This paper explores methods for decomposing the electrical waveforms to extract their instantaneous frequency
components. The frequency components are used to investigate the frequency stability of the waveforms. The resulting
analysis will lay the foundation for future development of a real-time software platform for detection, analysis and
correction capabilities for electrical waveform distortions in microgrid power systems, based on the principle of
instantaneous frequency.
As physical data is the first step for a meaningful analysis, this project has, through a collaboration between
Norwegian University of Science and Technology (NTNU) and the Royal University of Bhutan (RUB)’s College
of Science and Technology, collected current and voltage measurements from two nearly identical systems: one
was a grid-connected PV microgrid, and the other was the same PV microgrid in stand-alone mode. Voltage and
current waveforms measured at Hundhammerfjellet windmill park in Norway were used as a reference for a qualitative
comparison. The data obtained were analysed using the Hilbert-Huang Transform (HHT).
2. Analysis Method
The concept of instantaneous frequency and amplitude for a general signal is not well-defined. For near-sinusoidal
signal shapes, such as those coming from a stable rotary generator, the instantaneous frequency can be associated with
the rotational speed, and other variations could be ascribed to an instantaneous amplitude. In other situations with
more complicated waveform, it is less clear how such parameters should be defined.
The voltage and current shapes studied in our context could be characterized as near periodic. In that case, using
several (more or less) near-sinusoidal components, each with its own instantaneous frequency and amplitude is a
possible approach. One method along these lines is the one suggested by Huang [2]. This approach, called the
Hilbert-Huang Transform (HHT)1, has been chosen for application on microgrid power systems in this paper, and is
outlined in the following.
2.1. Instantaneous frequency
Any real signal X(t) can be represented as an analytic signal Z(t) in the form given by (1)
Z(t)=X(t)+jY(t)=a(t)·ejθ(t)(1)
where Y(t) is the Hilbert transform of X(t), a(t) is the amplitude and θ(t) are the phase of Z(t). From this, it is possible
to define the instantaneous frequency of X(t) as in (2) [2, pp. 911-915].
ω(t)=dθ(t)
dt (2)
2.2. Hilbert-Huang Transform
Central to the HHT is the notion of Intrinsic Mode Functions (IMFs). An IMF is a function whose extrema are
alternatingly positive and negative, i.e. there is always a zero crossing between each extremum. For such functions
the instantaneous frequency will always be positive. By using a method called the Empirical Mode Decomposition
(EMD) as described in [2, pp. 917-923] it is possible to decompose a genaral signal s(t) into a set of IMFs, c1(t),
c2(t),...,cN(t) such that
s(t)=r(t)+
N
X
i=1
ci(t) (3)
1The version of the method used in this paper was the Normalized Hilbert-Huang Transform [3, p. 15].
G. Kulia, M. Molinas, L. Lundheim, B. B. Larsen /Procedia Engineering 00 (2016) 000–000 3
s
-1
0
1
cs1
-1
0
1
cs2
-1
0
1
cs3
-1
0
1
time [s]
0 0.02 0.04 0.06 0.08
rs
-1
0
1
Fig. 1: Intrinsic mode functions and residue of s(t) normalized between -1 and 1.
where r(t) is a residual part of the signal that cannot be modeled as an IMF.
As an example of the EMD we will consider a normalized test signal s(t). It’s defined by (4) and corresponds to a
three-term Fourier series.
s(t)=cos(2π50 ·t)+1
3
·sin(2π150 ·t)+1
5
·cos(2π500 ·t) (4)
By applying the EMD on the simulated waveform s(t) the IMFs were obtained. The IMFs of the signal s(t) is
depicted in fig. 1. The first row is the original signal. The intrinsic mode functions follow this. The first IMF, c1(t),
has the highest frequency, the second, c2(t), has the second highest frequency and so on until the lowest frequency
component. In this example, there are only three frequency components, i.e. cs1(t), cs2(t), and cs3(t). The sum of
all the IMFs should ideally be equal to the raw data. For electrical systems, the last IMF (cs3(t) for s(t)) is the grid
frequency, i.e. the 50 Hz sine component of the signal. The previous IMFs contain all distortions, such as noise and
harmonics.
2.3. Hilbert Spectrum
The Hilbert Spectrum is a way to represent the instantaneous frequency and amplitude as a function of time for all
IMFs. By applying the EMD the intrinsic mode function of the signal are obtained. Each IMF, ci(t), can be represented
as an analytic signal, Zi(t) as shown in (1), with the amplitude ai(t), and frequency ωi(t) as defined in (2). Equation
(5) shows the definition of the Hilbert spectrum, Hi(ω, t), for a given IMF, ci.
Hi(ω, t)=
ai(t) for ω=ωi(t)
0 otherwise (5)
Fig. 2(a) displays the Hilbert spectrum of s(t)’s third intrinsic mode function, c3(t). It is possible to obtain the
Hilbert spectrum of any signal by summing all the intrinsic mode functions as shown in (6).
H(ω, t)=
N
X
i=1
Hi(ω, t) (6)
The Hilbert spectrum, Hs, of s(t), is depicted in fig. 2(b). For all Hilbert spectra in this paper, the amplitudes are
normalized between -1 and 1, such that 0 dB =1.
4G. Kulia, M. Molinas, L. Lundheim, B. B. Larsen /Procedia Engineering 00 (2016) 000–000
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
30
35
40
45
50
55
60
65
70
a(t) [dB]
-50
-40
-30
-20
-10
0
(a) Hilbert spectrum of s(t)’s third intrinsic mode func-
tion, cs3(t).
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
0
100
200
300
400
500
600
700
a(t) [dB]
-50
-40
-30
-20
-10
0
(b) Hilbert spectrum of s(t).
Fig. 2: Hilbert spectra of s(t)
Table 1: Summary of frequency fluctuations on the generated test signal s(t).
cs3cs2cs1
Mean frequency 49.96 Hz 150.10 Hz 499.99 Hz
Max frequency 51.12 Hz 153.16 Hz 501.35 Hz
Min frequency 49.12 Hz 147.79 Hz 498.49 Hz
Deviation from mean frequency 2.32 % 2.04 % 0.30 %
The generated test signal s(t) should be represented as perfect, horisontal lines in the frequency spectrum. Fig. 2
shows ripples on s(t) up to 2.32 % (see table 1). This is an error introduced by the implementation of the method.
20 ms of samples on the start and end of the signals were discarded from the summary in the tables to remedy for
end-effects when calculating the instantanious frequency.
3. Measurements
Electrical current and voltage measurements were performed at RUB College of Science and Technology’s two
PV microgrids. The grids are similar, with the exception that one is connected to the public power grid while the
other is not. Fig. 4(a) and 4(b) shows the grid-connected and stand-alone microgrid respectively. The load is the load
impedance of the parts of the college that the microgrid provide with electricity.
The point of measurements is marked on both figures. The resulting measurements of the electrical voltage and
current waveforms are displayed in fig. 3.
Measurements of the Norwegian grid, shown in fig. 3(a) and 3(b), was used as a reference. The measurements
were conducted by Sintef Energi AS at Hundhammerfjellet windmill park.
The voltage waveforms should ideally be pure 50 Hz sine waves. Harmonics on the power system is caused by
nonlinear loads and is undesirable. By visual inspection, it is apparent that the waveforms measured in Bhutan are far
more distorted compared to the waveforms measured in Norway. It is also evident that the stand-alone microgrid has
more distortions compared to the grid-connected one.
All the measurements are normalized between -1 and 1.
G. Kulia, M. Molinas, L. Lundheim, B. B. Larsen /Procedia Engineering 00 (2016) 000–000 5
time [s]
0 0.02 0.04 0.06 0.08
vs(t)
-1
-0.5
0
0.5
1
(a) Normalized voltage measured, vs, at Hundhammerf-
jellet windmill park, Norway.
time [s]
0 0.02 0.04 0.06 0.08
is(t)
-1
-0.5
0
0.5
1
(b) Normalized current measured, is, at Hundhammerfjel-
let windmill park, Norway.
time [s]
0 0.02 0.04 0.06 0.08
von(t)
-1
-0.5
0
0.5
1
(c) Normalized voltage, von , measured at the grid-
connected microgrid (see setup in fig. 4(a)).
time [s]
0 0.02 0.04 0.06 0.08
ion(t)
-1
-0.5
0
0.5
1
(d) Normalized current, ion , measured at the grid-
connected microgrid (see setup in fig. 4(a)).
time [s]
0 0.02 0.04 0.06 0.08
voff (t)
-1
-0.5
0
0.5
1
(e) Normalized voltage, voff, measured at the standalone
microgrid (see setup in fig. 4(b)).
time [s]
0 0.02 0.04 0.06 0.08
ioff (t)
-1
-0.5
0
0.5
1
(f) Normalized current, ioff, measured at the standalone
microgrid (see setup in fig. 4(b)).
Fig. 3: Electrical waveforms measured.
6G. Kulia, M. Molinas, L. Lundheim, B. B. Larsen /Procedia Engineering 00 (2016) 000–000
=
˜
PV Elements DC/AC Inverter Load
Point of measurement
ion
von
Grid
(a) Voltage and current measurement setup for a grid-
connected PV-microgrid.
=
˜
PV Elements DC/AC Inverter Load
Point of measurement
ioff
voff
(b) Voltage and current measurement setup for a stand
alone PV-microgrid.
Fig. 4: The two different voltage and current measurement setups.
Table 2: Summary of frequency fluctuations measured at Hundhammerfjellet windmill park.
cvs1cis2
Mean frequency 47.75 Hz 47.80 Hz
Max frequency 48.89 Hz 51.72 Hz
Min frequency 46.53 Hz 44.76 Hz
Deviation from mean frequency 2.57 % 8.2074 %
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
30
35
40
45
50
55
60
65
70
a(t) [dB]
-50
-40
-30
-20
-10
0
(a) Hilbert spectrum of vs(t).
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
0
500
1000
1500
2000
a(t) [dB]
-50
-40
-30
-20
-10
0
(b) Hilbert spectrum of is(t).
Fig. 5: Hilbert spectra of electrical waveform data collected at Hundhammerfjellet windmill park, vs(t) and is(t).
4. Results
4.1. Analysis of electrical waveform data collected at Hundhammerfjellet windmill park, Norway
The voltage and current waveforms collected at Hundhammerfjellet windmill park in Norway, vs(t) and is(t), were
analyzed using the Hilbert-Huang transform. Their Hilbert spectra are shown in fig. 5. vs(t) is a monocomponent
signal and have therefore only one IMF, cvs1(t)=vs(t). The fluctuation of the instantaneous frequency was measured
and a summary is shown in table 2. The frequency fluctuations observed on vs(t) are relatively modest, and slightly
higher than the frequency fluctuation artifacts introduced on s(t). It’s important to note that the mean frequency
measured using HHT is 47.75 Hz, while it was 50 Hz using zero crossing frequency. While our current implementation
of HHT can analyze frequency patterns, it often struggles to determin the exact frequency values for short samples.
In contrast, is(t) consists of two IMF, cis1(t) and cis2(t). The first intrinsic mode function, cis1(t), contains all
harmonics and other distortions of is(t). It’s showed by the yellow graph on the Hilbert Spectrum in fig. 5(b). cis1(t)’s
amplitude is low and always below -35 dB. It has two spikes with increased frequency, that most probably is caused
by nonlinear loads, i.e. loads that draw a nonsinusoidal current from a sinusoidal voltage source [4].
G. Kulia, M. Molinas, L. Lundheim, B. B. Larsen /Procedia Engineering 00 (2016) 000–000 7
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
30
35
40
45
50
55
60
65
70
a(t) [dB]
-50
-40
-30
-20
-10
0
Fig. 6: Hilbert spectrum of cis2(t).
Table 3: Summary of frequency fluctuations measured at the grid-connected microgrid.
cvon6cion 6
Mean frequency 49.65 Hz 49.26 Hz
Max frequency 54.31 Hz 64.63 Hz
Min frequency 45.65 Hz 37.86 Hz
Deviation from mean frequency 9.38 % 31.18 %
is(t)’s second intrinsic mode function, cis2(t) is the blue graph located around 50 Hz. Table 2 shows that it has
considerable more variations in it’s frequency than cvs1(t). It is expected that the current is more distorted compared to
its corresponding voltage source. Both the frequency fluctuations on cis2(t) and cvs1(t) have a high periodic behavior.
4.2. Analysis of electrical waveform data collected at the grid-connected microgrid
The voltage waveform, von(t), measured at the grid-connected microgrid was decomposed into six IMFs, cvon 1
to cvon6, where cvon 6corresponds to the grid frequency. The three first IMFs, cvon 1to cvon3, were discarded as their
frequency fluctuations are higher than the band limit described in [2, p. 929]. The summary of the fluctuations in the
grid frequency is shown in table 3. The frequency variations on von(t) are 3.65 times higher than that on vs(t), with
fluctuations up to 9.37 % from the mean. From fig. 7(a) it is notable to see that the frequency has a periodic behavior,
with a new cycle every 10 ms.
The Hilbert spectrum of von(t) is shown in fig. 8(a) and shows considerable distortions. In this figure, the blue line
at the bottom is cvon6, the graph shifting between blue-green and yellow is cvon 5, and the yellow graph at the top is cvon3.
The corresponding current waveform, ion(t), was divided into seven IMFs, cion1to cion7, where the first two IMFs
were discarded due to reasons described above. ion (t)’s Hilbert spectrum is depicted in fig. 8(b). The light blue, green
and orange graphs above it corresponds to higher frequency distortions and is represented by the first six IMFs, cion1
to cion6. These have amplitudes up to -21 dB, so frequency fluctuations on ion(t) has a higher magnitude than is(t)’s.
The blue line at the bottom of the Hilbert spectrum corresponds to the 50 Hz of the current ion(t), i.e. cion 7. As
observed, cion7’s instantaneous frequency also has a periodic behavior, with frequency cycles of 10 ms, just like cvon6
(see fig. 7(b)). This is probably a cause for much of the distortions on von (t).
The observed 100 Hz instantaneous frequency is a property of the instantaneous power in single phase alternating
current systems. This effect being observed in the voltage and current might indicate a propagation of the power
oscillations on the ac side through the inverter dc bus voltage and the control feedback of the inverter. To elucidate
the nature of this instantaneous frequency transfer from the power to the voltage and current, further efforts will be
directed towards matching this measured 100 Hz instantaneous frequency with an analytical model of the votlage and
current of the inverter.
8G. Kulia, M. Molinas, L. Lundheim, B. B. Larsen /Procedia Engineering 00 (2016) 000–000
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
30
35
40
45
50
55
60
65
70
a(t) [dB]
-50
-40
-30
-20
-10
0
(a) Hilbert spectrum of cvon6(t).
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
30
35
40
45
50
55
60
65
70
a(t) [dB]
-50
-40
-30
-20
-10
0
(b) Hilbert spectrum of cion6(t).
Fig. 7: Grid frequency of von (t) and ion(t).
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
0
200
400
600
800
1000
1200
1400
1600
a(t) [dB]
-50
-40
-30
-20
-10
0
(a) Hilbert spectrum of von(t).
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
0
200
400
600
800
1000
1200
1400
1600
a(t) [dB]
-50
-40
-30
-20
-10
0
(b) Hilbert spectrum of ion(t).
Fig. 8: Hilbert spectra of electrical waveforms measured at grid-connected microgrid.
Table 4: Summary of frequency fluctuations measured at the stand alone micromicrogrid.
cvoff3cioff6
Mean frequency 50.04 Hz 49.48 Hz
Max frequency 58.10 Hz 64.09 Hz
Min frequency 41.25 Hz 33.98 Hz
Deviation from mean frequency 17.56 % 31.33 %
4.3. Analysis of electrical waveform data collected at the stand-alone microgrid
The voltage waveform voff(t) measured at the stand alone microgrid was decomposed like von(t), into IMFs. Three
IMFs, cvoff1to cvoff3, were necessary to describe voff(t). Unlike von(t), none of voff(t)’s IMFs were discarded. The Hilbert
spectrum of voff(t) is shown in fig. 10(a). The blue line at the bottom represent the grid frequency, cvoff3. The yellow
graph above it represent cvoff2and the brown graph at the top is cvoff1.cvoff1’s frequency has periodic properties with
cycles of 10 ms, and an amplitude up to -34 dB. As shown in fig. 9(a), cvoff3does also have frequency fluctuations
with periods of 10 ms, but its frequency cycles are phase shifted, compared to that of cvoff1’s instantanious frequency.
The magnitude of the frequency fluctuations on cvoff3is 1.87 and 6.83 times higher than that observed on cvon6and cvs1
respectively.
G. Kulia, M. Molinas, L. Lundheim, B. B. Larsen /Procedia Engineering 00 (2016) 000–000 9
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
30
35
40
45
50
55
60
65
70
a(t) [dB]
-50
-40
-30
-20
-10
0
(a) Hilbert spectrum of cvoff3(t).
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
30
35
40
45
50
55
60
65
70
a(t) [dB]
-50
-40
-30
-20
-10
0
(b) Hilbert spectrum of cioff6(t).
Fig. 9: Grid frequency of voff(t) and ioff(t).
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
0
200
400
600
800
1000
1200
1400
1600
a(t) [dB]
-50
-40
-30
-20
-10
0
(a) Hilbert spectrum of voff(t).
time [s]
0 0.02 0.04 0.06 0.08
ω/2π[Hz]
0
200
400
600
800
1000
1200
1400
1600
a(t) [dB]
-50
-40
-30
-20
-10
0
(b) Hilbert spectrum of ioff(t).
Fig. 10: Hilbert spectra of electrical waveforms measured at the stand-alone microgrid.
The corresponding current waveform, ioff(t), was decomposed to six IMFs, cion1to cion 6. The Hilbert spectrum of
ioff(t) is shown in fig. 10(b). The first IMF cion 1is the light blue graph at the top of the Hilbert spectrum. Its amplitude
peaks at -15 dB, and the frequency has varying cycles with a period around 10 ms, that are phase shifted to cvoff3’s
frequency cycles. cioff2has similar frequency cycles. The last IMF, cioff6, corresponds to the 50 Hz component of the
signal. Its frequency also varies with cycles of 10 ms (see fig. 9(b)).
It is remarkable how much more distorted the stand-alone grid is compared to the grid-connected one. It is also
noteworthy that also in this case there is a systematic 10 ms fluctuation on the stand alone microgrid as the one
observed in the grid connected microgrid. As explained above, this originates from the typical 100 Hz oscillations
observed in the power of single phase systems [4].
5. Discussion
Foundations for a software platform for real-time data acquisition and analysis of distorted electrical measurements
for isolated microgrids have been outlined in this paper. The HHT-EMD lies at the core of this platform by enabling
the identification of instantaneous frequencies in the monocomponents of the original data. The Empirical Mode
Decomposition divides the electrical voltage and current waveforms into useful and easy-to-analyze modes, where
each component carries information about particular aspects of the signal and the system behind the signal. Showing
that the instantaneous grid frequency is not stable with considerable fluctuations on both grids connected and stand
10 G. Kulia, M. Molinas, L. Lundheim, B. B. Larsen /Procedia Engineering 00 (2016) 000–000
alone microgrids displays the strength of the method, which has enabled us to identify a transfer of frequency (10 ms
Cycle) from the power to the voltage and currents of the microgrid. A similar identification was not possible to achieve
with an FFT analysis of the data. An apparent difference that emerges from our comparison is the characteristics of
the frequency fluctuation of the synthetically generated data and the field data. The synthetic data shows periodic
characteristics with constant frequency while the field data appears to have high-frequency fluctuations. Further
efforts will be put in distinguishing this difference more categorically by analyzing data more extensively.
From these results, we expect that measurement equipment able to acquire, analyze and detect electrical grid prob-
lems in the types of grid studied in this paper, will require information about the instantaneous values of frequencies
of the monocomponents of the signal. Our results also indicate that tools such as the EMD will provide a better under-
standing of the electrical waveforms, enabling in the future, better and more accessible microgrid control possibilities.
Acknowledgments
This research was partially supported by Ren-Peace, IUG NTNU, and Department of Electronics and Telecommu-
nications at NTNU.
We thank Norden Huang who provided insight and expertise in his methods by spending tens of hours teaching
and discussing them with us. His open-mindedness and generosity have been a tremendous source of inspiration.
The data analysis would not have been verified without the measurements preformed at RUB. It is therefore in place
to thank Tshewang Lhendupand, Cheku Dorji and my travel partner and coworker Håkon Duus for their assistance in
collecting data from the microgrids.
We would also like to acknowledge the contribution of Helge Seljeseth at Sintef AS for providing data from
Hundhammerfjellet windmill park.
The icons in fig. 4 were designed by Freepik.
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Kingdom, Royal Society, 1996
[3] Norden E. Huang, Samuel S. P. Shen Hilbert-Huang Transform and Its Applications, 2nd ed. Singapore, World Scientific publisher Co. Pte.
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[4] Hirofumi Akagi, Edson Hirokazu Watanabe, Mauricio Aredes, Instantaneous Power Theory and Applications to Power Conditioning, IEEE
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