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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,

jsanabria16, maxbueno@unisalle.edu.co

2Department of Automation, Engineering,

Universidad de la Salle, Bogot´a, Colombia,

ebernalal@unisalle.edu.co

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,

Event detection

1 Introduction

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 [1]. 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].

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 [3], [4] and [5].

HHT is an adaptive method for analysis in both domains, that allows to

be used to work on signals with the behavior previously described [3], 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 [6].

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 [7]. 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 [7], 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

πPZ∞

−∞

x(τ)

t−τdτ (2)

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)

x(t)(4)

From the phase the instantaneous frequency is extracted, as a function of the

time, is deﬁned by:

f(t) = 1

2π

dθ (t)

dt (5)

Masking Signal In 2005, Deering and Kaiser [8] 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)

2(8)

–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

Feature

extraction

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 [8].

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)

S3=

sen(2π·18t)si 1<t<2

0other wise

(10)

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 [9], 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.

SM

SM

SM

SM

SM

P1,Q1 P2,Q2 P3,Q3

P4,Q4

P5,Q5

Substation

M1

M2

M3

SM Smart Meter

Smart PV Inverter

123

4

5

DC

AC

Fig. 2. Low voltage distribution sys-

tem

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 [8]. 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

signal

stantaneous frequencies are observed. To give solution to this problem has been

created a masking signal according to the methodology proposed in [9]. 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.

5 Conclusions

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 [8] 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.

Acknowledgment

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.

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