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Towards a Real-time Measurement Platform for Microgrids in Isolated Communities

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Abstract and Figures

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.
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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 dierent, 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 eorts 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 aordable, 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-eects 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.
(c) Normalized voltage, von , measured at the grid-
connected microgrid (see setup in fig. 4(a)).
(d) Normalized current, ion , measured at the grid-
connected microgrid (see setup in fig. 4(a)).
(e) Normalized voltage, vo, measured at the standalone
microgrid (see setup in fig. 4(b)).
(f) Normalized current, io, 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 dierent 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 eect 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 eorts 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.
cvo3cio6
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 vo(t) measured at the stand alone microgrid was decomposed like von(t), into IMFs. Three
IMFs, cvo1to cvo3, were necessary to describe vo(t). Unlike von(t), none of vo(t)’s IMFs were discarded. The Hilbert
spectrum of vo(t) is shown in fig. 10(a). The blue line at the bottom represent the grid frequency, cvo3. The yellow
graph above it represent cvo2and the brown graph at the top is cvo1.cvo1s frequency has periodic properties with
cycles of 10 ms, and an amplitude up to -34 dB. As shown in fig. 9(a), cvo3does also have frequency fluctuations
with periods of 10 ms, but its frequency cycles are phase shifted, compared to that of cvo1s instantanious frequency.
The magnitude of the frequency fluctuations on cvo3is 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 cvo3(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 cio6(t).
Fig. 9: Grid frequency of vo(t) and io(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 vo(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 io(t).
Fig. 10: Hilbert spectra of electrical waveforms measured at the stand-alone microgrid.
The corresponding current waveform, io(t), was decomposed to six IMFs, cion1to cion 6. The Hilbert spectrum of
io(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 cvo3s
frequency cycles. cio2has similar frequency cycles. The last IMF, cio6, 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 dierence 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
eorts will be put in distinguishing this dierence 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.
References
[1] IEEE Standard 519, IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems, New York, IEEE Power
Energy Society, 2014
[2] Norden E. Huang, Zheng Shen, Steven R. Long, Manli C. Wu, Hsing H. Shih, Quanan Zheng, Nai-Chyuan Yen, Chi Chao Tung and Henry H.
Liu, The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis, London, United
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.
Ltd., 2014
[4] Hirofumi Akagi, Edson Hirokazu Watanabe, Mauricio Aredes, Instantaneous Power Theory and Applications to Power Conditioning, IEEE
Computer Society Press, New York, Wiley, 2007
[5] Mohan, Undeland, Robbins, Power electronics - Converters, Applications, and Design, 3rd ed. New York, Wiley, 2003
... An extensive study of IEC Standard 6100-4-7 measuring methods states that these methods do not produce accurate results in environments with timevarying angular frequency [4]. Keeping the aforementioned problems of nonlinearities and time-varying quantities in mind, measurements and estimation in isolated microgrids should rather be based on instantaneous amplitude and frequency rather than the usage of average values [1,5]. With improved data acquisition-and measurement tools, the supervisory control systems in isolated microgrids may perform better actions, and earlier hidden distortions may be revealed. ...
Thesis
Full-text available
Modern electrical systems have introduced distributed generations and power converters. This brings out different issues such as low inertia of the grids and an increasing number of harmonics and non linear distortions injected. However, the fluctuations of instantaneous frequency are arguably the most characteristic feature of microgrids. Frequency drift during step load change as well all quasi-periodic fluctuation has an impact on various conditions as generators’ prime movers and governor’s characteristic. Quasi periodic frequency fluctuations can have besides detrimental effect on electrical receivers’ work, especially electric motors will be affected. The thesis aims at providing a deep insight into the phenomena of non-constant instantaneous frequency. Origin of instantaneous frequency fluctuations are analyzed, tools for the phenomenon identification are proposed. These considerations are based on careful analysis of data from the Norwegian power system and behavior of three real marine systems onboard of a ro-ro ship with shaft generator, research-training ship during work of auxiliary generating sets as well as integrated power system of ship with electrical propulsion. For each ship, the cases of rough and calm sea are compared. To analyze data, the empirical mode decomposition algorithm and the Hilbert transform implemented in Matlab will be used.
... Within the fastest time scale of powerelectronics devices, such as that of the AC current controller, the assumption for stationary network may not be satisfactory since they are more sensitive and fragile to rapid fluctuations. As one example, in [7], an empirical mode decomposition analysis of the electrical voltage and current waveforms recorded from microgrids in the Royal University of Bhutan's College shows that the frequency of the microgrid network admittance model considering network dynamics is established in the frequency domain. In [10], a small signal impedance model of the dynamic network is established in the polar coordinates based on the transfer function matrix, and the generalized impedance concept of the network is defined. ...
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In the traditional power systems, power flow studies focus on the stationary relationship of the active and reactive powers versus bus voltage under the quasi-steady state approximation. With increasing penetration of power electronics devices including renewable generations interfaced through converters , the system dynamical behaviour changes substantially. Due to the fast dynamics of converters, such as the AC current controller, the quasi-stationary state approximation may not be applicable. In order to catch the network characteristics accurately, we derive the explicit small-signal relation between instantaneous power and voltage vectors. Further, we study a simple power system model, which includes a network equation considering dynamics relationship and a swing equation. The numerical and analytical results demonstrate a novel negative resistance effect induced by generators on network dynamics. This effect may be weak for the traditional power systems, however, it may become significant for the new-generation power-electronic-based power systems.
... Steady and stable frequency has been one essential attribute of a stable electric power system and a pre-condition of stable operation. In this short communication, we discuss the notion of instantaneous frequency in electrical systems as first presented in [2] and use Hilbert Huang Transform [1] to detect its existence in a single-phase microgrid. This new notion might significantly change our understanding of the stability of electric power systems. ...
... Steady and stable frequency has been one essential attribute of a stable electric power system and a pre-condition of stable operation. In this poster, we discuss the notion of instantaneous frequency in electrical systems as first presented in [2] and use Hilbert Huang Transform [1] to detect its existence in a single-phase microgrid. This new notion might significantly change our understanding of the stability of electric power systems. ...
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This short communication shows a case in which instantaneous frequencies are detected on synthetic signals by both Wavelet (WT) and Hilbert Huang Transform while Fourier Transnsform (FT) is not effective in identifying them. The selected synthetic signal is an example of how using FT in electric power systems with time varying frequencies, can mislead the interpretation of the results. The problem of leakeage is showcased in the example. This is confirmed by the results obtained from the analysis of a single-phase microgrid voltage in which Fourier based WT did not detect the presence of a time varying frequency on the microgrid, as this frequency fluctuates faster than the fundamental frequency.
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This paper aims to develop a combination method for the evaluation of power quality disturbances. First, we apply the Fast Fourier Transform, Wavelet Transform and Hilbert Huang Transform on a synthetic signal that represents typical behavior in a power system with high penetration of Renewable Energies. Then, we combine the methods to extract the best of each of these and achieve a better signal decomposition. The paper seeks to generate decision criteria on the method of analysis of signals to be used according to the application.
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This paper describes the development and implementation of a methodology for the signal analysis in non-conventional energy systems. The proposed methodology involves the Hilbert-Huang transform supported by Empirical Mode Decomposition (EMD) to decompose one signal in its intrinsic mode function (IMF). A computational tool designed in MATLAB is used to detect oscillations and different frequencies of a non-linear and non-stationary system
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The paper addresses the impact that time varying angular frequencies observed in electrical signals can have on the calculation and separation of components from the instantaneous electric power signal. Instantaneous power theories provide various methods for calculating the instantaneous power components in an electrical network. These methods are based on the basic assumption of constant fundamental frequency and harmonics that are multiple of the fundamental frequency. Recent field measurements in isolated electrical systems have however reported the existence of time varying angular frequencies or instantaneous frequencies. This new observation will affect the very foundation of the established methods for instantaneous power calculation and components separation. This paper analyses the separation of instantaneous average and oscillatory components of powers by using linear and non-linear filtering approaches in systems that exhibit time varying angular frequencies. The results of this comparison reveals the limitations of the assumption of fundamental and harmonic frequency when using linear filtering techniques in the presence of time varying angular frequencies. Non-linear filtering may offer a more robust and accurate estimation of the instantaneous values of powers and a power quality assessment that better reflects the actual system conditions.
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A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the `empirical mode decomposition' method with which any complicated data set can be decomposed into a finite and often small number of 'intrinsic mode functions' that admit well-behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and non-stationary processes. With the Hilbert transform, the 'instrinic mode functions' yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert spectrum. In this method, the main conceptual innovations are the introduction of `intrinsic mode functions' based on local properties of the signal, which make the instantaneous frequency meaningful; and th
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The prelims comprise: Half Title Title Copyright Dedication Contents Preface
Chapter
Power Definitions Under Sinusoidal Conditions Voltage and Current Phasors and the Complex Impedance Complex Power and Power Factor Concepts of Power Under Non-Sinusoidal Conditions—Conventional Approaches Electric Power in Three-Phase Systems Summary References
IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems
IEEE Standard 519, IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems, New York, IEEE Power Energy Society, 2014