Signal Analysis in Power Systems with High
Penetration of Non-Conventional Energy Sources
J. M. Sanabria-Villamizar1, M. Bueno-L´opez1, E. Bernal-Alzate2
1Department of Electrical Engineering,
Universidad de la Salle, Bogot´a, Colombia,
2Department of Automation, Engineering,
Universidad de la Salle, Bogot´a, Colombia,
Abstract. This paper describes the development and implementation
of a methodology for the signal analysis in non-conventional energy sys-
tems. 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 de-
signed in MATLAB is used to detect oscillations and diﬀerent frequencies
of a non-linear and non-stationary system.
Keywords: Smart Grid, Hilbert-Huang Transform, Hilbert Spectrum,
Power Quality, Harmonics, Energy, Non-conventional, Instant frequency,
The new technologies, such as non-conventional sources of renewable energies
(NCSRE), Non-linear loads and electronic devices, are producing critical varia-
tions in the behavior of the transmitted wave form, therefore it is necessary to
develop new methodologies for the analysis of signals which have a wide range
of characteristics . The results with the traditional methods are not the best
because the time-frequency resolution has some problems in the detection of low
frequencies and small variations in the oscillations. The quality in power systems
is focus in ensure a voltage supply with an excellent waveform and reliability for
the correct operation of the electronic equipment, which are handling critical
processes of great importance for the customers.
In modern power systems it is necessary to analyze harmonic signals whose
behaviour is non-linear and non-stationary, as these are used to the control of
multiple variables. As for example System Average Interruption Frequency In-
dex and System Average Interruption Duration Index (SAIFI and SAIDI, respec-
tively) are Used to detect failures in the network, also, indicate the contributions
of the distributed generators on the dynamic behavior of the power system, and
in a general way in the optimization of the distributed power systems .
2 J. M. Sanabria-Villamizar et al.
The process of data analysis and monitoring becomes complex in systems
with high penetration of non-linear loads, mostly in renewable energy systems,
which hinders the estimation of power required by the users. One of the most
common strategies for signal analysis in power systems has been the Fast Fourier
transform (FFT). However, a limitation of FFT is the resolution in the time
domain. Therefore, new methods are needed to ensure good resolution in both
time and frequency domain, involving the concept of instantaneous frequency
for accurate and rapid detection of disturbances. The Hilbert-Huang transform
has emerged as an aid to solve this problem ,  and .
HHT is an adaptive method for analysis in both domains, that allows to
be used to work on signals with the behavior previously described , based
on the principle of instantaneous frequency, seeking an accurate and immediate
detection of disturbances. When comparing the HHT with the FFT, it is possible
to say that the ﬁrst can detect behavior patterns more easily in signals with
strong oscillations, in less computational time .
In the present research an analysis methodology is developed capable of ex-
tract the behavior characteristics of a signal transmitted in the time-frequency
domain. Based on the HHT, the proposed methodology not only can display the
estimation of the instantaneous frequency-amplitude, but also the fundamental
frequency of operation of the system. Furthermore, with the advantage of re-
quiring less computational time with greater eﬃciency compared to the other
conventional methods of analysis for this type of signals.
2 Non-Linear and Non-Stationary Signal Analysis
2.1 Hilbert-Huang Transform (HHT)
The Hilbert-Huang transform of a function x(t) is a concept presented by Norden
E. Huang in . The HHT consists of two important parts: empirical modal
decomposition (EMD) and Hilbert spectrum (HS). EMD consists of decomposing
the original signal in several signals, which allow to detect diﬀerent oscillations,
called IMFs (intrinsic mode function), This decomposition should be developed
to ﬁnd a monotonic function that indicates the inability to extract more IMFs.
The IMF, which according to Huang , should be a function that fulﬁls two
conditions: 1) The number of ends and the number of crosses by zero should be
diﬀerent from just one, and 2) Its local medial is zero. Once the decomposition is
ﬁnished, the HT is applied to each of the IMFs that compose the original signal
and with this process the HS is obtained.
For a signal x(t), the analysis signal z(t) is deﬁned as:
z(t) = x(t) + iy (t) = a(t)eiθ(t)(1)
where y(t) is the Hilbert transform of x(t), so that:
y(t) = 1
Signal Analysis in Non-Conventional Energy Systems 3
Where P is the ”Cauchy principal value”. Of (1) amplitude and phase are:
a(t) = px2+y2(3)
θ(t) = arctan y(t)
From the phase the instantaneous frequency is extracted, as a function of the
time, is deﬁned by:
f(t) = 1
Masking Signal In 2005, Deering and Kaiser  Deﬁne an improvement method
for EMD, based on the use of mask signals. The algorithm is deﬁned as follows:
–A mask signal is constructed, s(t), from the original signal information, x(t).
–The EM D is made to the following two signals, obtained from the original
and the Mask:
x+(t) = x(t) + s(t) (6)
x−(t) = x(t)−s(t) (7)
–Subsequently, IM F +and I M F −are obtained.
–Where the resulting IMF is deﬁned as:
IMF (t) = IM F +(t) + I MF −(t)
–So on, applying each iteration to the resulting residue.
Table 1. Comparison of time-frequency analysis methodologies
FFT WVD WT HHT
Base Priority Priority Priority Adaptive
Non-linear x XxX
Non-stationary x x X X
x x x X
Table 1 shows the advantages and disadvantages of the methodologies of the
analysis in time frequency. The FFT has the problem of aliasing which consists in
4 J. M. Sanabria-Villamizar et al.
the inability to break down a wave in a monotonic signal, being a low-eﬃciency
strategy for non-linear and non-stationary wave signals. The WT and WVD
are like the FFT, decomposing a signal in a series of basic functions, but with
diﬀerent problems. One of the most critical aspects in the WT is the selection
of the type of wavelet (window) that best matches the signal to be analyzed, to
conform to the components of low and high frequencies of the signal. The WVD
has a better resolution in diﬀerent applications, but like the FFT does not have
the capacity to break down a signal in monotonic signals, therefore, it generates
a distortion of the frequency spectrum.
However, HHT is not free of problems, its weakness is in the heuristic way
of selecting EMD type, like the WT it depends on a mother function; although
the time frequency results have a higher resolution and decomposition capacity
for any type of signal, If the appropriate base function is not selected, the result
of the IMFs will not be indicated.
3 Case Study
3.1 Synthetic Signal
To clarify the concepts presented above, we present the analysis based on the
EMD and the EMD masking, on a synthetic signal. The signals present a phe-
nomenon called mixture of modes, to solve this applies the methodology of the
signal mask in .
The synthetic signal is described in equation (9) and (10), also shown in Fig.
1, with its corresponding frequency modes.
x(t) = sen (2π·6t) + sen (2π·12t) + S3(9)
3.2 Power System
The analysis based on HHT and EMD, as shown formerly, is also applied to
signals from electrical systems. In this case, the study will be carried out to a
photo-voltaic system of a residential house , with the capacity to supply power
to the distribution network, as shown in Fig. 2.
The data correspond to the voltage of the electrical system, taken at a sam-
pling frequency of 16.7kHz for 186 days. For the purposes of the study, 2 seconds
of the data are analyzed, as shown in Fig. 3.
Unlike the synthetic case, no characteristic of the wave is known (Fig. 3).
The voltage signal presents a switch that shows the changes of supply to the
network in the ﬁrst instance the system consumes the generated power, on the
other hand, about 1 second the system commutates to deliver power to the grid.
Signal Analysis in Non-Conventional Energy Systems 5
Fig. 1. Synthetic signal with their respective frequencies.
P1,Q1 P2,Q2 P3,Q3
SM Smart Meter
Smart PV Inverter
Fig. 2. Low voltage distribution sys-
Fig. 3. Voltage wave obtained from the test sys-
tem in the point M2
4 Case Study Results
4.1 Synthetic Signal Results
The empirical modal decomposition is shown in Fig. 4, where the ﬁrst IMF shows
a mixture of modes between the frequencies of 12 and 18 Hz, the following IMF
also presents a mixture of modes between 6 and 12 Hz and ﬁnally the third is
the 4 Hz frequency component. Similarly, in Fig. 5 the instantaneous frequencies
corresponding to each IMF are shown.
It should be noted that, when knowing the signal to be analyzed, it is ex-
pected that in the decomposition of the signal the separation of the frequency
modes that make up the signal will be visible. For this reason, the mask signal is
applied with the form s(t) = A0sen(2πf t), where a0and fis obtained accord-
ing to Deering, As shown in . In this case the mask signal that was used was
s(t) = 2sen(2π28T).
6 J. M. Sanabria-Villamizar et al.
Fig. 4. Decomposition using EMD standard.
Fig. 5. Instantaneous frequency obtained with EMD standard.
The results of this process can be seen in ﬁgures 6 and 7, which show the
IMFs obtained by performing the empirical decomposition and the respective
instantaneous frequencies. In Figure 6, it may be noted that the frequency com-
ponents are extracted as expected, the frequencies of 18, 12 and 6 appear in the
IMFs 1, 2 and 3 respectively.
4.2 Power System Results
The empirical decomposition in modes is shown in Fig. 8, where in the ﬁrst IMF
there is a noise in the wave, in the same way a mixture of modes in the IMF 1,
2 and 3, ﬁnally the IMF 4 is with the frequency component of 1 Hz. Similarly,
in Fig. 9 the instantaneous frequencies corresponding to each IMF are shown.
Signal Analysis in Non-Conventional Energy Systems 7
Fig. 6. Decomposition using EMD with Masking signal.
Fig. 7. Instantaneous frequency obtained with EMD - Masking signal
By not knowing the characteristics of the signal, The mask signal is applied
with the form s(t) = A0sen(2πf t) in the same way as the previous case. In this
case the mask signal that was used was s(t)=2sen(2π70T).
The results of this process can be seen in ﬁgures 10 and 11, which show the
IMFs obtained by performing the empirical decomposition and the respective
instantaneous frequencies. Note that the frequency components and signal noise
are extracted from Figure 10. IMFs 1 and 2 shown in Fig. 10, correspond to the
noise of the signal, the following IMF describes the behavior of the wave, accord-
ing to Fig. 11; ﬁnally, in the fourth IMF is characterized by being responsible
for varying the amplitude of the wave.
Moreover, a problem is detected since the implementation of the standard
EMD. In Fig. 4 the 3 IMFs obtained from the synthetic study signal are ob-
served. In the ﬁrst and second IMFs, a mixture of modes is observed in t= 1s
and t= 2s. This phenomenon is visible in Fig. 5 where the corresponding in-
8 J. M. Sanabria-Villamizar et al.
Fig. 8. Voltage wave decomposition using EMD standard.
Fig. 9. Instantaneous frequency of the voltage wave obtained using EMD standard.
Fig. 10. Voltage wave decomposition using EMD with Masking signal
Signal Analysis in Non-Conventional Energy Systems 9
Fig. 11. Instantaneous frequency of the voltage wave obtained by EMD with Masking
stantaneous frequencies are observed. To give solution to this problem has been
created a masking signal according to the methodology proposed in . Fig. 6
shows without diﬃculty how each of the IMFs obtained observes and identiﬁes a
single type of oscillation and this is conﬁrmed in Fig. 7 where the instantaneous
frequency can be deduced with greater precision than Fig. 5.
In this paper we have discussed the importance when using diﬀerent methods
for signal analysis in power systems with high penetration of non-conventional
energy sources. It has been possible to decompose the original signal into a
set of components that allow analyzing the behavior of a physical phenomenon
related to each IMF, for the speciﬁc case of the electrical system one of the main
applications that will be investigated is the detection of faults in real time. The
procedure is eﬀective when you know in advance the frequency components that
appear, if on the contrary these are not known you would not have the necessary
information to develop the methodology. Therefore, the analysis of the case study
was based on a small part of the strategy described in  and on the average of
the frequencies found from the standard EMD method shown in Fig 9. On the
other hand, this strategy emerges as an alternative for those signals where there
is a set of data, knowing its amplitude value, but not its frequency, the results
obtained, which are presented in this article, give beginning to a new strategy
for the choice of the mask signal. However, the Hilber-Huang transform presents
diﬃculties in mixing modes and edge eﬀect.
The implementation of the standard EMD and EMD with the mask signal
showed excellent results. Figures 10 and 11 showed how the number of IMFs is
reduced by applying the method with the mask signal, therefore, it is indicated
that the frequency components of the signal are grouped with greater precision.
Besides, it is possible to observe the oscillations with greater clarity from the
10 J. M. Sanabria-Villamizar et al.
third IMF obtained, describing better the behavior of the system, the ﬁrst two
IMFs show the characteristic noise of the signal of a photo-voltaic system.
This paper is part of the project number 111077657914 and contract number
031-2018, funded by the Colombian Administrative Department of Science, Tech-
nology and Innovation (COLCIENCIAS) and developed by the ICE3 Research
Group at Universidad Tecnologica de Pereira (UTP) and CALPOSALLE Group
at Universidad de La Salle.
1. G. Kulia, M. Molinas, L. Lundheim, and B. B. Larsen, “Towards a real-time mea-
surement platform for microgrids in isolated communities,” Procedia engineering,
vol. 159, pp. 94–103, 2016.
2. V. Puliaﬁto, S. Vergura, and M. Carpentieri, “Fourier, wavelet, and hilbert-huang
transforms for studying electrical users in the time and frequency domain,” Energies,
vol. 10, no. 2, p. 188, 2017.
3. N. E. Huang, “Introduction to the hilbert–huang transform and its related mathe-
matical problems,” in Hilbert–Huang transform and its applications, pp. 1–26, World
4. J. A. Antonino-Daviu, M. Riera-Guasp, M. Pineda-Sanchez, and R. B. Perez, “A
critical comparison between dwt and hilbert–huang-based methods for the diag-
nosis of rotor bar failures in induction machines,” IEEE Transactions on Industry
Applications, vol. 45, no. 5, pp. 1794–1803, 2009.
5. J. M. O’Toole, M. Mesbah, and B. Boashash, “A new discrete analytic signal for
reducing aliasing in the discrete wigner-ville distribution,” IEEE Transactions on
Signal Processing, vol. 56, no. 11, pp. 5427–5434, 2008.
6. L. Peng, G. Jing, X. Duo, W. Chang, and Y. Xavier, “Hilbert-huang transform
with adaptive waveform matching extension and its application in power quality
disturbance detection for microgrid,” Journal of Modern Power Systems and Clean
Energy, vol. 4, no. 1, pp. 19–27, 2016.
7. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C.
Tung, and H. H. Liu, “The empirical mode decomposition and the hilbert spectrum
for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Soci-
ety of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 454,
no. 1971, pp. 903–995, 1998.
8. R. Deering and J. F. Kaiser, “The use of a masking signal to improve empirical
mode decomposition,” in Proceedings.(ICASSP’05). IEEE International Conference
on Acoustics, Speech, and Signal Processing, 2005., vol. 4, pp. iv–485, IEEE, 2005.
9. E. B. Alzate, Q. Li, and J. Xie, “A novel central voltage-control strategy for smart lv
distribution networks,” in International Workshop on Data Analytics for Renewable
Energy Integration, pp. 16–30, Springer, 2015.