18th Power Systems Computation Conference Wroclaw, Poland – August 18-22, 2014

Wavelet-Demodulation-Method Based

Out Of Step Detection And Damping Estimation In Japan Campus Wams

Khairudin, Yaser S Qudaih, Yasunori Mitani, Masayuki Watanabe, Thongchart Kerdphol Department of Electrical Engineering and Electronics

Kyushu Institute of Technology Fukuoaka, Japan

M589505b@tobata.isc.kyutech.ac.jp

Abstract—some previous research based on Fast Fourier Transform (FFT) estimated the damping ratio and frequency oscillation from Eigen value of the matrix associated to a Single Machine Infinite Bus (SMIB) model. Damping constant can be calculated for every 20 minutes cycles. However, it failed to explain how to calculate the damping ratio without associating the system to a SMIB Model. Furthermore, there was no way to verify the validity of the analysis since no network parameters could be included in the calculation.

This paper promotes a novel approach in analyzing Phasor Measurement Unit (PMU) data to identify out of step phenomena and the calculation of damping ratio by applying a Continuous Wavelet Transform (CWT) algorithm. A linear regression method is performed to extract the damping ratio from the wave skeleton. The validity of the method is verified by comparing the calculated and real data from mathematically generated signals with known parameters.

Keywords—PMU; Campus WAMS; CWT; FFT filter; demodulation; Damping Coefficient; out of step detection

I. INTRODUCTION The deployment of Phasor Measurement Unit (PMU) in

Japan power system has been started from 2002. Since then some work has been carried out to analyze the state of overall Japan Power system through an Inter Campus Wide Area Measurement (WAMS). Based on the application practices of Campus WAMS, it would be possible to discover the state of the system, in this case the characteristics of low-frequency oscillation mode which usually hidden in the bus voltage phase angle or tie line power variations due to random and constant load variations without considering any generator and line parameters [1].

On the previous researches [1, 2] which was based on Fast Fourier Transform (FFT) analysis, the damping ratio and frequency oscillation were estimated from Eigen value of the matrix associated to a Single Machine Infinite Bus (SMIB) model. An output-only-based simplified oscillation model is developed to estimate the characteristic of inter-area power oscillation based on extracted oscillation data. However, this previous method was unsuccessful to explain how to calculate

damping ratio without considering any simplification model, especially when the system considered cannot be modeled as a SMIB. Furthermore, there was no way to verify the validity of the analysis since no network parameters could be included in the calculations.

Hilbert Huang Transform (HHT) analysis also has been attempted to deal with PMU data. However, the ability of this approach to estimate damping ratio and modal parameters cannot satisfactorily distinguish two separate modes unless there is a large difference in either frequency or damping ratio [11].

This paper promotes a novel approach in analyzing PMU data to identify low-frequency oscillation parameters, i.e. out of step phenomena and the calculation of damping ratio based on Continuous Wavelet Transform (CWT) algorithm and demodulating the slicing signal at a particular frequency. The modulation signal is the signals envelop which measures the dissipation of oscillation energy caused by damping. To identify the damping, the signal envelop is extracted using a certain demodulation methods. The logarithmic Modulus and phase decaying of the Complex Morlet CWT (CM-CWT) are estimated using linear regression method to extract the damping ratio and frequency mode from the signal. A procedure for selecting the center frequency and bandwidth parameters, the scaling factor and the translation factor are given in the paper.

In this paper, the PMU signal is transformed to Time-Frequency-Modulus and plotted in three dimension curve so that it is easy to investigate any oscillation mode in the system both by vision and by numeric calculations. The parameters calculations are purely based on information from the signal regardless to any model assumption.

The contributions of this paper to other previous researches are the ability to detect modal frequency oscillation which was unseen on the previous methods and calculating the damping ratio based on the information extracted from the PMU signal without assuming any simplified network model. The validity of this method is verified by analyzing a synthesized signal contains of three ring-down mode which represents a real signal from PMU. The results are compared to the known

18th Power Systems Computation Conference Wroclaw, Poland – August 18-22, 2014

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parameters and it is clearly shown that this method gives the result within an acceptable range of error.

The rest of this paper is organized as follows. Section-1 describes the back ground of the research, previous work and the significance discovery from this current approach. Section-2 gives a brief description of Japan Campus WAMS. Section-3 talks about basic wavelet theory and the application of this method to analyze the signal waveform. Step by step problem solving on dealing with a signal and verifying the validity of the method are presented. Section-4 analyzes original PMU data when there was a disturbance and discusses the system damping trend on a holiday and working day. Section-5 concludes what has been done in this work, limitation and recommendations for future work.

II. THE CAMPUS WAMS Fig. 1 shows PMU locations in Western Japan 60-Hz power

system. This Campus WAMS, consisting of eight commercial PMUs which are installed at eight universities covers typical power supply area of all six electric power companies of Western Japan 60-Hz power system. Because of each power company is independent operating entity; there is no way to collect synchronized phasor measurements of transmission high voltage level from all power companies at present. But with the Campus WAMS it becomes possible to observe and analysis system wide dynamics for overall Western Japan 60-Hz power system [1].

For the analysis, three groups are defined for eight PMUs. The lower-end group includes University of Miyazaki, Kumamoto University and Kyushu Institute of Technology. The upper-end group includes University of Fukui and Nagoya Institute of Technology. The center group includes Hiroshima University, University of Tokushima and Osaka University.

All PMUs measure the single phase voltage phasor of 100V outlet on the wall of laboratory with GPS-synchronized time tag. The voltage phasor is calculated by using 96 sample data per voltage sine-wave cycle. The calculated voltage phasor data are saved in PMU at interval of 1/30s from H:50 min to H:10 min, H:10 min to H:30 and from H:30 min to H:50 min, in every hour. All phasor measurements of all locations are automatically collected into a data server through internet. The background application program running in other computers reads data from server and performs analysis.

For the Campus WAMS, two following points need to be addressed. First point is that the single phase voltage of end user voltage level is recorded by PMUs. Due to the constant sampling interval at off-nominal frequencies, the single phase phasor measurement will produce some slight errors. Second point is that low voltage switching events are also measured and may interfuses with oscillation mode. Based on these two points, the previous work results have verified the validity of phasor data of the Campus WAMS. The strong correlation between two sets of data confirms the validity of the phase difference data of PMUs measured from household voltage level. Moreover, as in second point, the influence caused by relative high frequency low voltage switching events could be eliminated by FFT filter [1].

The experiences and research practices show that the Campus WAMS has following features: simple installation, easy maintenance and good expandability; each PMU representing one typical power supply area. The system wide area dynamics can be observed and analyzed by measured multiple single phase voltage phasor data of household voltage level [2].

III. WAVELET TRANSFORM

A. Selecting Mother Wavelet Function The wavelet transform is more alike to the well-known

Windowed Fourier Transform (WFT). However, they are in a completely different advantage and purpose. The disparity is that Fourier transform decomposes the signal into sines and cosines, which means that the function is localized in a Fourier space. On the other hand, the wavelet transform uses functions that are localized in both the real and Fourier space [3].

The wavelet transform decomposes signals over dilated and translated wavelets. A wavelet is a function of f(t)∈L2(R) with a zero average. It has been proved that the CWT is very dexterous to identify the damping ratio and shown to be highly resistant to noise, i.e. of up to 0 dB signal-to-noise ratio [4].

Suppose that all function x(t) satisfy the condition:

| ( )|2 < ∞,+∞−∞

Then, the CWT of a signal can be defined as:

( , ) = ( )ψ ,∗ ( ) ,+∞−∞

Where u and s are the translation and scale parameters respectively. ψ*u,s(t) is the translated and scaled complex conjugate of the mother wavelet function ψ*(t)∈L2(R). The wavelet function is a normalized function i.e. the norm is equal to 1 with an average of zero [3].

The scaled-and-translated wavelet function is expressed as:

University of Fukui

Nogoya Institute of Technology

Hiroshima University

Kyushu Institute of Technology

Kumamoto University

University of Miyazaki

Osaka University

University of Tokushima

University of Fukui

Nogoya Institute of Technology

Hiroshima University

Kyushu Institute of Technology

Kumamoto University

University of Miyazaki

Osaka University

University of Tokushima

Fig. 1. PMU location in Western Japan 60-Hz system

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ψ( , )( ) = 1√ ψ−

It can be noted that the CWT is the sum over all time of the signal f(t) multiplied by scaled, shifted versions of the mother wavelet (which are also called son wavelets). Thus, the CWT possesses localization properties in both time and frequency domains and consequently provides valuable information about f(t) at different levels of resolution and measures the similarity between and each son wavelet [5].

The admissibility condition implies ψ(0) = 0, which means that a wavelet must integrate to zero. In some literature, it is mentioned that there are several different types of mother wavelet functions satisfying the admissibility condition such as the Mexican hat, Gabor and Morlet, which can be selected according to the nature of the signal to be analyzed. According to those literatures the complex Morlet wavelet would be appropriate for the analysis of ringdown signals due to its capabilities in time-frequency localization for analytical signals. According to [5], the CWT is capable of analyzing data in a multi-resolution domain which means it can automatically filter out the noise from f(t) and thus no additional filters are needed.

In this research, CM-CWT is selected and formulated as:

ψ( ) = 2 − 2

Let’s have a look at a function:

( ) = − ( + )

Also can be written as:

( ) = ( ) ( + )− ( + )2

Where A(t) = ae-αt , a is the mode relative amplitude and θ is the mode phase shift. t is lying in a certain interval of time.

The exponential decay constant α and the angular frequency ω correspond to the real and the imaginary components, respectively. The Eigen values of the ith mode expressed as λi =αi + jωi. fc is the wavelet central frequency parameter and fb is a bandwidth parameter that controls the shape of the wavelet [5].

Let us represent A(t) by its Taylor Series in the neighborhood of the reference point t = b.

( ) = ( ) + ( − )∞=1

( )( )!

By substituting (7) into (6), the Morlet wavelet transform of x(t) is expressed as:

ℎ ( , ) = 1√ ( ) ( + ) + − ( + )2 ℎ∗ − ,+∞−∞

In the form of time varying amplitude and phase angel [5], the equation can be written as:

ℎ ( , ) = −2 ( + )

The logarithm of the modulus Whx(ak,t) can be written as:

| ℎ ( , )| = − + 2

ℎ ( , ) = − +

= − ∑ | ℎ ( , )| − ∑ ∑ | ℎ ( , )|=1=1=1 ∑ 2=1 − (∑ =1 )2

= − ∑ | ℎ ( , )| − ∑ ∑ | ℎ ( , )|=1=1=1 ∑ 2=1 − (∑ =1 )2

ℎ =1 ( , ) = ℎ ( , )=1

The exponential decay constant α and the angular frequency ω are estimated using linear regression analysis of the wave skeleton at the sliced signals at ridge of frequency oscillation. The damping ratio can be then calculated using:

ζ = −√ 2 + 2

B. Determining CWT parameters The performance of CWT-Demodulation method is based

on the selection of parameters. The center of frequency fc can be approximated near the typical modal frequency in the case of small signal stability analysis. Typically, these oscillatory modes have frequencies in the range of 0.1 to 1.0 Hz, which is lower compared to the local modes with frequencies ranging from 1 to 2 Hz. The center of frequency also can be calculated using Auto spectrum method, contour plot of CWT, Wavelet Scalograms or Wavelet Coefficients Charts [4].

When selecting the range of scales, these two issues have to be taken into consideration. First, the lower scales correspond to the most compressed wavelets which allow detecting rapidly changing signal features related to high-frequency components. Second, the higher scales correspond to the most stretched wavelets which allow detecting slowly changing signal features related to low-frequency components. In fact, selecting an

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appropriate range of scales will determined the accuracy of the calculation as practiced in this research. Also, a suitable selection of scales range is very important since in practice the CWT is computed within a predefined range of scale and it must be able to identify the individual oscillatory modes. When the complex Morlet mother-wavelet function is dilated by a scaling factor s, then the center frequency becomes fc=fb.Δt.s.

To dealing with PMU Data, first the signals are read from database center in *.csv format. Auto-spectrum method is then employed to this data to determine the center of low frequency oscillation. The next is using CW-CWT method to transform the data to three dimensional form; i.e. Time-Frequency-Modulus. Using a special function written in Matlab the ridge and peak of the 3D wave is decided. The damping ratio begin to be calculated starting from the peak of the wave using demodulation method and finally linear regression is applied to estimate decay constant and angular velocity of the signals. Fig. 2 presents this process in a flow chart.

C. Validation process To validate the method some known parameters signals are

employed. Cases 1 to 3, individual signal with a random noise are used for representing the signal from PMU. Case 4 is a synthesized of three ringdown signal to verify the ability of the method to identify any mode change which is hidden in a set of signal input. The parameters of individual modes are given in Table I.

Case 1,

( ) = ( ) + −0.2639 cos(2 (0.35) + 00)

The contour plot is given in Fig. 3. This figure shows the center of frequency as well as the ridge of the signal in the frequency axis.

In Fig. 4, it is clearly shown ridge of the signal as well as how it decays along the time. Fig. 5 and Fig. 6 demonstrate the logarithmic decay of the wave and phase plot of the corresponding signal at the center of frequency oscillation respectively. This calculation results damping ratio estimation (ζcalculation) = 0.1191. Comparing to the real parameter value of damping (ζreal) = 0.12, the error of calculation is about 0.7%.

A 3D visualization in Fig. 4 reflects a ringdown signal behavior simultaneously in the time domain as well as in frequency domain. This is actually the advantage of this method i.e. Wavelet analysis is able to reveal signal information that other analysis techniques miss them, such as trends, breakdown points, and discontinuities. As it has been mentioned in section-3.A, using wavelet analysis makes it possible to perform a multi-resolution analysis

Similar to the above case, the proses is employed to the others following signals.

Case 2,

( ) = ( ) + −0.1571 cos(2 (0.5) + 300)

Case 3,

( ) = ( ) + −0.1131 cos(2 (0.9) + 0)

Figure 5 and 6 are logarithmic plot of demodulating signal at center of frequency oscillation and its phase plot respectively. The next step is applying linear regression method to determine decaying constant (α) and its angular

Retrieving PMU Database

Estimate Center of Oscillation

Complex Morlet CWT Transform

Peak and Ridge Detection

Slicing Wave at Particular Frequency

Signal Demodulation and Considering its edge effect

Damping Calculation

START

End

Fig. 2. CWT-Demodulation flowchart

TABLE I. SIGNAL PARAMETERS OF EACH MODE

Mode f a ζ θ

1 0.35 1.0 0.12 00

2 0.5 0.5 0.05 300

3 0.9 0.9 0.02 1650

time(s)

freq

uenc

y (H

z)

TIME-FREQUENCY Wavelet Transform

0 10 20 30 40 50 600.1

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0.7

0.8

0.9

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0.9

1

1.1

Fig. 3. Contour plot of the signal

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velocity (ω) to calculate damping ratio (ζ). The result of calculation and the comparison between real and calculated value for each case are presented in Table II.

To observe the ability of this approach to identify different mode of signals hidden in a set of waveform, a synthesized signals contains of three modes are presented below. The parameters are given in Table III.

Case 4, using synthesized (three modes) signals

( ) = ( ) + Mie−αit cos(2π(fi)t + θi)3i=1

In this case all the signals are blended together and a random noise is applied to represent a real condition of PMU signal. The synthesized signal of these three modes is shown in Fig. 7.

Fig.8 and 9 show the modes contained in signals and center of frequency of each mode as well as the ridge of the wave.

The comparison between real value and calculated value in Table IV are convincing the worth of this method. The precision of this method is more than 99 % according to this experiment.

TABLE II. REAL AND CALCULATED VALUE OF DAMPING RATIO

Case f (Hz) ζreal ζcalculated Error (%)

1 0.35 0.12 0.1191 0.70

2 0.50 0.05 0.05 0

3 0.9 0.02 0.02 0

TABLE III. SIGNAL PARAMETERS OF EACH MODE

Mode

i

Signals Parameters

Mi fi αi ζi

1 1.0 0.35 0.2639 0.12

2 0.5 0.50 0.1571 0.05

3 0.9 0.90 0.1131 0.02

Fig. 4. 3D Plot of the signal

TABLE IV. COMPARISON OF REAL AND CALCULATED VALUE

Mode f(Hz) fd = ωd/2π ζreal ζcalculated Error (%)

1 0.35 0.3472 0.12 0.1192 0.67

2 0.50 0.50 0.05 0.0501 0.2

3 0.90 0.901 0.02 0.0200 0

0 10 20 30 40 50 60-2

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0.5

1Synthesized Signal

time

ampl

itude

Fig. 7. Synthesized signal of three modes

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Time(s)

ln|W

(t,w

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Signal Slice at 0.58 Hz

Fig. 5. Logarithmic decay of the wave at the center of frequency oscillation

0 10 20 30 40 50 60-120

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20

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arg|

W(t

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phase plot at 0.58 Hz

Fig. 6. Phase plot of the wave at center of frequency oscillation

18th Power Systems Computation Conference Wroclaw, Poland – August 18-22, 2014

D. Evaluation on Real PMU Data Fig.10 shows waveforms of phase difference measured

between University of Miyazaki and Nagoya Institute of Technology (NIT) from 13:30 to 13:50 in 14th of October, 2011. During that time the Genkai nuclear power unit 4 which belongs to Kyushu Electric Power Company stop automatically. The fluctuation pattern of the oscillation is presented in the figure.

Contour plot of the corresponding signal shows the center of oscillation. It is match the theory that small signal stability appears in the range of 0.4 to 1 Hz [10].

Fig. 11 displays the center of frequency oscillation while Fig. 12 shows the ridge of the signal. The damping ratio can be calculated from demodulating the slice signal at the center of frequency oscillation. Fig. 13 and 14 show logarithmic decay and phase plot of the signal from the ridge of the oscillation until the oscillation disappear at 624 second. Using linear regression analysis the value of αd and ωd can be estimated and based on the equation (15) the damping ratio is determined as 0.7 at damped frequency fd = 0.4572 Hz.

.

time(s)

freq

uenc

y (H

z)TIME-FREQUENCY Wavelet Transform

0 10 20 30 40 50 60

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1

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Fig. 8. Contour plot of the synthesized signal

Fig. 9. 3D plot Morlet-CWT of the synthesized signal

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ln|W

(t,w

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Signal Slice at 0.45 Hz

Fig. 13. Logaritmic decay of the signal at 0.45 Hz

0 200 400 600 800 1000 1200130

135

140

145

150Data in Time Domain

Time [sec]

Pha

se D

iffre

nce

[deg

]

Fig. 10. PMU signal on 14th Oct, 2011 from Miyazaki to NIT

time(s)

freq

uenc

y (H

z)

TIME-FREQUENCY Wavelet Transform

200 400 600 800 10000.1

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Fig. 11. Contour plot of PMU signal

Fig. 12. 3D plot of PMU signal

18th Power Systems Computation Conference Wroclaw, Poland – August 18-22, 2014

E. Damping ratio trend and out of step detection November 3th, 2013 was a national holiday in Japan and it

was in a long holiday from Saturday to Monday. Typically at this time a very small activity during the day. November 5th, 2013 was an ordinary working day. The damping calculation during the holiday and working day are compared in Fig. 15 and Fig 16. Since the damping ratio is calculated three times in one hour, so the red line makes the 3 steps of moving average of the damping. It can be observed, around 07.00 am the damping ratio reached the lowest value on the working day. It can be understand that at that some activity are started whether in domestic or in some commercial load. The rest of the trend remains about the same on both days.

Any out of step phenomenon would be possible to identify by evaluating the oscillation mode from the contour and 3D plot of each signal. For the reason of conciseness they cannot be attached in this paper. From the analysis, it can be observed

that there was no out of step phenomenon detected since all the dominant oscillations are fluctuated around 0.45 Hz.

IV. CONCLUSION The CWT-Demodulation approach is capable to detect

modal frequency oscillation as well as calculating the damping ratio based on the information extracted from the PMU data without associating the parameters to a SMIB model.

The validity of this method is verified by analyzing a ringdown signal contains of three modes representing a real signal from PMU. It has been demonstrated, by using some known parameters signals, CWT-Demodulation approach showed the capability to estimate the damping ratio and investigate the center of oscillation frequency of each signal mode as well as early detection of out of step phenomena. The results are compared to the real parameters and it is clearly shown that this method gives the result within an acceptable range of error. When applied to the real signal it also shows a sensible result in calculating damping ratio and describing the oscillation mode.

For the future work, this method will be applied to the PMU signals which are installed in the substation and also verifying using a standard network test.

REFERENCES

[1] Changsong Li, K. Higuma, M. Watanabe and Y. Mitani, “Monitoring and Estimation of Inter area Power Oscillation Mode Based on Application of Campus WAMS”, 16th PSCC, Glasgow, Scotland, July 14-18, 2008

[2] Dikpride Despa, Y. Mitani, Changsong Li, and M. Watanabe, “Inter-Area Oscillation Mode for Singapore-Malaysia Interconnected Power System Based on Phasor Measurement with Auto Spectrum Analysis”, 17th PSCC, Stockholm, Sweden, August 22-26, 2011

[3] S. Mallat, “A Wavelet Tour of Signal Processing”, 2nd edition, Academic Press, New York, 1999

[4] J. L. Rueda, C. A. Juarez and I. Erlich, “Wavelet-Based Analysis of Power System Low-Frequency Electromechanical Oscillations”, IEEE Transaction on Power Systems, Volume: 26 , Issue: 3, 2011, Page(s): 1733 – 1743

[5] J. L. Rueda and I. Erlich, “Enhanced wavelet-based method for modalidentification from power system ringdowns”, PowerTech, IEEE Trondheim , 2011, Page(s): 1 - 8

[6] W. J. Staszewski, “Identification of damping in MDOF systems using time-scale decomposition”, Journal of Sound and Vibration 203 (1997), page: 283-305

[7] J. Slavič, I. Simonovski and M. Boltežar, “Damping identification using a continuous wavelet transform: application to real data”, Journal on Sound and Vibration, 2003, vol. 262, 2, page: 291-307

[8] J. Slavič, and M. Boltežar, “Enhancements to the continuous wavelet transform for damping identifications on short signals”, Mechanical Systems and Signal Processing 18 (2004), page 1065–1076

[9] M. Klein, G. J. Rogers and P. Kundur, “A Fundamental Study of Inter-Area Oscillations in Power Systems”, IEEE Trans. Power Systems, vol. 6, no. 4, pp. 914-92,1st August 1991.

[10] P. Kundur, Power System Stability and Control., New York: McGraw-Hill, 1994.

[11] Liu Qing, Y. Mitani, “ Application of HHT for oscillation mode analysis in power system based on PMU”, 2nd International Conference on Electric Power and Energy Conversion Systems (EPECS), 2011, Page(s): 1 – 4.

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Fig. 14. Phase plot of PMU signal at 0.45 Hz

Fig. 15. Damping Ration Trend during Holiday

Fig. 16. Damping Ratio Trend during working day