Power System Disturbance Modeling Under Deregulated Environment

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Journal of the Franklin Institute 344 (2007) 507–519 www.elsevier.com/locate/jfranklin

Power system disturbance modeling under deregulated environment A.M. Gaouda Electrical Engineering Department, UAE University, United Arab Emirates Received 7 February 2006; accepted 7 February 2006

Abstract The paper proposes a new tool that utilizes windowed-wavelet multi-resolution analysis to model and monitor different disturbances that may take place in a multi-ownership system. PSCAD/ EMTDC simulator is used to model part of Al Ain distribution system and the proposed technique is implemented to model different power system disturbances. The local maxima of wavelet expansion coefficients show the ability to model all expected disturbances utilizing a small set of expansion coefficients. Furthermore, the maximum multi-resolution expansion level restricted for each wavelet function can be extended to monitor simultaneously stationary and non-stationary disturbances as well as high and low-frequency components. r 2006 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. Keywords: Local maxima; Kaiser’s Window; Multi-resolution analysis; Wavelet transform.

1. Introduction One of the most significant tasks of today’s deregulated power industry is to maintain high reliability in addition to improving the quality of service to customers. Different condition monitoring as well as wide-area monitoring techniques are proposed as tools to monitor and control the quality of service in an electrical power system [1–8]. While running a distribution system, there are some daily based operations generate disturbances that may cause distortion currents to propagate through the system. Fast surges, transformer inrush currents, a multi-stage capacitor bank switching, beside faults may cause a distortion event to propagate and results a false tripping of protection relays E-mail address: [email protected]. 0016-0032/$30.00 r 2006 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jfranklin.2006.02.008

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[2]. The magnitude of the generated transient event depends on the system configuration and its operating conditions. It is not always easy to define the source of such disturbances. In the near future, utilities responsible for such disturbances may be penalized for causing interruptions in the power supply that result in customer downtime. As a result, the ability to locate disturbance sources will become increasingly important [1]. This problem becomes more difficult if the system is owned by different utilities. Furthermore, the participation of independent power producers (IPPs) increasingly makes distribution systems more complex. Distributed generators are considered as an alternative source that releases feeder’s capacity. However, distributed generation is located close to customer loads and usually considered as a source of harmonic and modeled as a converter–inverter unit. The accepted distortion levels at certain locations in a utility may propagate in the system and appears at higher unacceptable levels in another locations that controlled by other utility. There are different techniques can be implemented to model different disturbances by extracting the time–frequency features. Fast fourier transform (FFT) is a very efficient computational tool for spectrum analysis of periodic signals. However, there are large numbers of disturbances with transient behavior, consequently event magnitude and time information, which can help monitoring the time features of the transient event, are lost. Windowed Fourier transform or short-time Fourier transform (STFT) are used to overcome the deficiency in FFT. The quality of the results in STFT depends on the window side of the data under process. Since disturbances at distribution level could be localized at frequency band varies between some hertz up to hundreds of kilohertz, the concept of selecting a suitable window is unachievable. This indicates that the signal’s feature (frequency component) and location’s feature (position at which that frequency component is found) cannot both be measured to an arbitrary degree of precision simultaneously. This paper presents a windowed-wavelet multi-resolution analysis technique to model power system disturbances in terms of a small set of coefficients. The coefficient model of the disturbances is utilized to measure the compatibility between the quality of service and customers’ sensitive equipment during faults in a system. The proposed technique is used to study the quality of services in a wide-area of multi-owner distribution system. Part of Al Ain city distribution system is simulated using PSCAD/EMTDC and disturbance model in the windowed-wavelet domain is used to measure the severity of a faulted feeder on the other healthy feeders. Computer business equipment manufacturer association curves are used as a reference to measure compatibility between the supply voltage and customer equipment. The paper is organized as follows. Disturbance modeling is presented in Section 2. The application of the proposed technique and results are presented in Section 3. The simulated part of Al Ain distribution system (AADS) is presented in the same section. Finally, the conclusion and references are presented in Sections 4 and 5, respectively.

2. Disturbance modeling Disturbance modeling under deregulated environment require sharp tools to detect different disturbances that may be localized in a wide time–frequency range. Applying multi-resolution analysis, the distorted signal, f ðtÞ 2 L2 ðRÞ, can be presented as a series

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expansion by using a combination of these scaling functions and wavelets functions as: f ðtÞ ¼

X

c0 ðkÞfðt  kÞ þ

J 1 XX

k

k

dj ðkÞ2j=2 cð2j t  kÞ

(1)

j¼0

where, L2(R) is the Hilbert space. cj(k) is the set of approximate coefficients and dj(k) is the set of j-level detail coefficients and mathematically presented as X cj ðkÞ ¼ hf ðtÞ; jj;k ðtÞi ¼ hðm  2kÞcjþ1 ðmÞ, (2) m

d j ðkÞ ¼ hf ðtÞ; cj;k ðtÞi ¼

X

h1 ðm  2kÞcjþ1 ðmÞ

(3)

m

and h(n) are the scaling function coefficients and h1(n) are the wavelet function coefficients. The distortion event can be modeled in terms of the expansion coefficients as C Signal ¼ ½c0 jd 0 jd 1 j . . . d J1 j

(4)

and the feature vector (M) that represents the distortion event at certain resolution level can be extracted from the norm of the expansion coefficients (jjd j jj2 ) at that resolution. M ¼ ½jjd 1 jj2 jjd 2 jj2 . . . jjd J jj2 0 .

(5)

The w avelet expansion coefficients measure the similarity between the signal and the scaled and translated versions of the selected wavelet function. As long as there is a strong similarity between the scaled wavelet function and the signal under process, the energy of the expansion coefficients at certain resolution level (dj)Energy will represent accurately the energy component of the distorted signal at that resolution. Utilizing multi-resolution analysis, the selected wavelet function is dilated or compressed to extract the expansion coefficients at other frequency bands. For a pure (50 Hz) signal, utilizing Db1 or Db40 wavelet functions model the pure signal with sets of coefficients localized at the sixth, seventh, ninth and tenth, eleventh, twelveth and thirteenth. This results in a set of expansion coefficients that does not represent the original signal and hence incorrect model as shown in Fig. 1. 120 100

|| dj (k) ||2

Db40

Db1

80 60 40 20 0 0

2

3

4

5

6

7

8

9

10

11

12

Resolution Level Fig. 1. Pure signal feature vector using rectangular window with Db1 or Db40.

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Wavelet multi-resolution analysis (WMRA) can be achieved by convolution and decimation. Convolving the wavelet function by the approximate coefficients results a set of coefficients at the starting and ending process of the convolution that does not represent the signal at that scale. These unwanted coefficients are resulted from utilizing the FFT as an impeded tool to allow fast computation of the convolution process. These coefficients will generate other coefficients at other resolution levels and hence scatter the pure signal’s energy on other resolutions. Furthermore, for a wideband monitoring, the number of resolution levels must be extended to cover all the expected disturbances, therefore the size of data becomes enormous. Windowed-wavelet transform is proposed as the first stage in modeling power system disturbances. This can be achieved by multiplying the original distorted signal f[n] by another function W[n], a selected window function, that decaying smoothly and has zero magnitude outside the interval. Kaiser’s window of length L is selected in the windowing process. Multiplying the original signal f[n] by Kaiser’s Window W[n] will generate a windowing version of the original signal where the set of expansion coefficients is X Wd j ðkÞ ¼ hWf ðtÞ; cj;k ðtÞi ¼ h1 ðm  2kÞWcjþ1 ðmÞ. (6) m

Utilizing the windowing process, the new model for the distortion can be detected and localized using the expansion coefficient: WC Signal ¼ ½Wc0 jWd 0 jWd 1 j . . . Wd J1 j

(7)

and the modified feature vector that represents the distortion event is extracted from the norm of the expansion coefficients (jjWd d jj2 ) at that resolution. The signal generated from the windowing process is similar to the wavelet function and has the following features:







First, the similarity between the original signal and the selected wavelet function is strengthened. Multiplying the original signal by a window function results an oscillatory signal that has its amplitude quickly decaying to zero (similar features of the wavelet function). Secondly, wavelet-decomposition process depends on convolution and decimation. Windowed wavelet transform generates expansion coefficients Wdj with a dramatic reduction in their magnitudes. The magnitude of the expansion coefficients Wdj generated at the starting and ending intervals of the convolution process are wiped out. This overcomes the drawback in generating a set of expansion coefficients dj that does not represent the original signal. Moreover, the maximum wavelet decomposition level (MaxRes) assigned for each wavelet function can be extended. Therefore, more accurate time–frequency features of any signal can be extracted simultaneously at both low and high frequency bands.

The windowing stage shows enhancement in correctly modeling the signal and expanding the maximum number of the resolution level that certain wavelet function can achieve. Fig. 2 shows the expansion coefficients (dj(k) and Wdj(k)) at the ninth resolutions before (Fig. 2a) and after windowing stage (Fig. 2b). The magnitude of these coefficients show large reduction, therefore, the leakage energy to other resolutions is eliminated and hence a sharp and a clear reference is formed that will be used for

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8

511

x 10 -3

6 0.5

4

Wd9 (k)

d9 (k)

2 0 -2

0

-0.5

-4 -6

(a)

-8

0

20

40

60

80

100

(b)

-1

0

20

40

60

80

100

Fig. 2. Expansion coefficients at the ninth resolutions, (a) dj(k) and (b) Wdj(k).

automating the monitoring process in deregulated environment. However, the size of the detail coefficients’ set Wdj(k) for each resolution used in the monitoring process is huge. To reduce Wdj(k) to a small size, only important coefficients that have most of the signal’s energy are considered. This can be achieved by: 1. Ignore all the coefficients that have small values: ( 0 jWdjoy; ½Wd j ðkÞy ¼ jWd j ðkÞj jWdjXy:

(8)

A threshold value (y) is used to ignore small values. The standard deviation of the of expansion coefficients of windowed version of the signal under process is selected, y ¼ stdðWC Signal Þ ¼ stdf½Wc0 jWd 0 jWd 1 j . . . Wd J1 jg.

(9)

2. Consider local-maxima coefficients at each resolution level. The absolute value of the detail coefficients (Wdj(k)) are used to localize either positive or negative expansion coefficients with most of the signal’s energy. ½Wd j ðN j Þloc ¼ local maxima ½Wd j ðkÞy .

(10)

A new set of expansion coefficients Wdj(Nj), such that Wd j ðN j Þ5Wd j ðkÞ, is resulted. This set has localized coefficients and represent most of the signal’s energy. The index Nj localizes the coefficients in time-frequency and hence detects the distortion event sequence. The new modified feature vector becomes: M ¼ ½jjWd 1 ðN 1 Þjj2 jjWd 2 ðN 2 Þjj2 . . . jjWd J ðN J Þjj2 0 .

(11)

The proposed technique is implemented to extract the feature vector for 50 Hz pure signal. The variations in the norms of Wdj and dj are studied and compared as shown in Fig. 3. Direct application of WMRA with rectangular window and implementing the proposed modeling technique using Kaiser’s window are used to construct the feature vector. Utilizing the proposed technique (Fig. 2) shows that the norm of the coefficients

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120 100

|| dj (k) ||2 || dj ||2

80

|| Wdj (Nj) ||2 60 40 20 0 1

2

3

4

5

6

7

8

9

10

11

12

Resolution Level Fig. 3. Pure signal feature vector using Wdj(Nj) and dj(k).

jjWd j jj2 is reduced in magnitude due to windowing process; however, all the energy of the expansion coefficients (Wd j ðN j Þ) for the 50 Hz pure signal is concentrated at the 8th resolution (35–70 Hz). This generates a sharp and clear model that will be used for automating the disturbance monitoring. 3. Application and results The proposed technique is implemented to study different cases on AADS. The goal of these applications is to emphasize on the efficiency of the proposed technique in modeling different disturbances during the following cases: 1. Compatibility measures of utility service and customer sensitive equipment during faults in a multi-owner system. 2. Multi-Stage Capacitor bank switching in distorted environment. AADS is a radial system utilizing underground cables and overhead lines for supplying different customers. The distribution system is connected to the 220 kV transmission system through transco grid stations (TGS). Fig. 4 shows part of AADS 33 kV primary system and some of the 11/0.4 kV distribution LV substations that considered in this paper. Only feeders shown as solid lines are considered in this paper. The majority of loads at AADS are inductive (air-condition). The city is located in a geographical area with temperature reaches to more than 30 1C for long period of the year. Only the solid feeders shown in the system are modeled using PSCAD and studied in this paper. 3.1. Case 1: compatibility of utility supply voltage and customer equipment The proposed tool will be utilized to predict sag characteristics a sensitive load will find at 33/11/0.4 kV system while this system operating by different utilities. It is impossible to predict exactly where each fault will occur, but it is reasonable to assume that many faults

ARTICLE IN PRESS A.M. Gaouda / Journal of the Franklin Institute 344 (2007) 507–519 220 kV

220 kV

Y Y

Y

Y 1 2

220 kV

220/33kV Y SS

220/33/11kV Y Δ SS

513 220 kV

220/33kV SS

Y Y

3 4 5

SS2 SS5

SS3

SS9

11 kV SS1

SS7

C SS6

SS8

SS4

Fig. 4. Part of Al Ain City 33/11 kV distribution system.

Table 1 Monitored signals at 0.4 kV substations Substation

SS1

SS2

SS3

SS4

SS5

Signal nos. Distance from fault

1, 2, 3 4.15 km/33 kV 0.8 km/11 kV

4, 5, 6 7.25 km/33 kV 0.5 km/11 kV

7, 8, 9 6.5 km/33 kV 0.5 km/11 kV

10, 11, 12 7.2 km/33 kV 1.0 km/11 kV

13, 14, 15 7.2 km/33 kV 1.2 km/11 kV

will occur. The most accurate predictions require sag automated monitoring tool that can detect, classify and quantify different sag phenomenon generated at AADS during faults. The problem is to determine which components in a deregulated network causes a ‘‘significant’’ voltage sag when faulted. Furthermore, the tool should be able to monitor the variation in other health locations in the system due to faulted element. Lines, feeders, as well as branch circuits present special problems because the voltage sag magnitude depends upon the fault location and type. Sags farther away are generally less severe. A complete picture requires studying for every possible fault and every possible fault impedance. It is often convenient to identify which parts at AADS may cause ‘‘significant’’ sags when those portions experience a fault. Repeating this study for all components where faults will cause ‘‘significant’’ voltage sags gives utility and customers a clear idea of what might be called the area of vulnerability[1–4]. Table 1 represents 15 signals of phase voltages at five 11/0.4 kV LV distribution substations. These LV substations are supplied from 33/11 kV primary substations as specified in Table 1.

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The following working conditions are considered in this paper: (1) Normal operation condition (NOC) (2) Fault condition, single-line to ground (SLG), at 33 kV main out going feeders and their effect on 0.4 kV customer voltages in the system connected from 33 kV healthy feeders. (3) Fault condition, double-line to ground (DLG), at 11 kV Substation 3 and their effect on 0.4 kV customer voltages connected to healthy substations in the system.

3.1.1. Normal Operation Condition (NOC) The proposed technique is used for modeling and monitoring the voltage variation in the system. The index (Nj) of Wdj is used to detect the duration of any sag disturbance. The first and the last indices are used to measure the sag duration. The norm of the coefficients at eigth resolution, jjWd 8 ðN 8 Þjj2 , that covers the frequency band 35–70 Hz, where the sag phenomenon resides, is used to detect and classify the sag event. The coefficients Wd 8 ðN 8 Þ are used to quantify the sag event in pu. Fig. 5 shows NOC of the system modeled in terms of the coefficients Wd 8 ðN 8 Þ for 0.4 kV LV substations connected to feeders from SS1 to SS5. The figure shows that all the voltages are close to the nominal value. There is a small voltage drop at SS3 (signals 7, 8 and 9) and SS5 (signals 13, 14 and 15) resulted from the radial connection of the two substations and heavy load connected to them. Substation’s voltage drop is compensated by connecting a capacitor banks. The NOC case represents the reference case that will be used to detect any sag phenomenon at any 0.4 kV point of common coupling (PCC). 3.1.2. SLG Faults at 33 kV level and its effect on other healthy feeders: Different faults are simulated at the 33 kV outgoing feeder from main 33 kV SS to SS4 (signals 10, 11 and 12). The fault impedance is ignored and the fault clearing time is adjusted to 0.2 s. The norm of the coefficients at eigth resolution, jjWd 8 ðN 8 Þjj2 , is used to

1

pu.

0.8 0.6 0.4 0.2 0 1 A

2 B SS1

3 C

4 A

5 B SS2

6 C

7 A

8 B SS3

9 C

10 11 A B

12 C

13 A

SS4

14 B SS5

Signal number (substation phase voltage) Fig. 5. Customer 0.4 kV monitoring under normal operation conditions.

15 C

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monitor and model the effect of this fault on different bus voltages of customer side (0.4 kV). The variations in voltages are modeled as shown in Fig. 6. This fault shows that all the three phases are affected and produce a sag event. The SLG fault generates large sag at one of the phases and small sag at other two phases. CBEMA curve is used to quantify the fault effect on the IT and other sensitive equipment. This fault modeled by jjWd 8 ðN 8 Þjj2 generates a sag event that may interrupt 30% of IT equipment connected into the system. Fig. 7 indicates that equipment connected to phase ‘‘B’’ (signals 2, 5, 8, 11 and 14) will be affected by this fault.

1 0.8

pu.

0.6 0.4 0.2 0 1 A

2 B SS1

3 C

4 A

5 B

6 C

SS2

7 A

8 B

9 C

SS3

10 A

11 B

12 C

SS4

13 A

14 B

15 C

SS5

Signal number (substation phase voltage ) Fig. 6. Sag monitoring at 0.4 kV side due to SLG fault at 33 kV system.

Nominal Voltage %

100

Sag Magnitude at Customer Side during SLG Fault at 33kV SS

* * * * * *

80

60 Under Voltage Condition

40

* * * 20

0 10-1

100 20 ms

101

102 0.5 s

Cycle Fig. 7. CBEMA curve during SLG fault.

103 10 s

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3.1.3. DLG Faults at 11 kV substation and its effect on other buses in the system DLG fault is simulated at SS3 with fault clearing time adjusted to 0.2 s. The jjWd 8 ðN 8 Þjj2 is used to monitor different sag phenomenon generated at customer side (0.4 kV). The variations in voltages in the system are monitored as shown in Fig. 8. This fault shows that all the three phases of both 33/11 kV SS2 and SS3 are seriously affected. The CBEMA curve, shown in Fig. 9, indicates that all sensitive equipment connected into SS2 and SS3 will be interrupted. The per unit values of peak-magnitude of the phase

1 0.8

pu.

0.6 0.4 0.2 0 1 A

2 B SS1

3 C

4 A

5 B

6 C

SS2

7 A

8 B

9 C

SS3

10 A

11 B

12 C

13 14 A B

SS4

15 C

SS5

Signal number (substation phase voltage ) Fig. 8. Sag monitoring at 0.4 kV side due to DLG fault at 11 kV system.

100

Nominal Voltage %

80

Sag Magnitude at Customer Side during DLG Fault at 11kV SS

* * *

60

* *

40

* * Under Voltage Condition

20

0 10-1

*

100 20 ms

101

102 0.5 s

Cycle Fig. 9. CBEMA curve during DLG fault.

103 10 s

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Table 2 Peak phase voltage at 0.4 kV LV side during faults at 11 kV side SS #

SS2

SS3

SS4

Phase mon.

4A 5B 6C 7A 8B 9C 10 A 11 B 12 C

Peak phase Voltage in pu. SLG Fault

LLG Fault

0.65 0.63 0.88 0.47 0.47 0.89 0.93 0.93 0.96

0.45 0.62 0.65 0.19 0.40 0.40 0.91 0.93 0.93

voltages at SS2, SS3 and SS4 during the sag event are measured using normalized value of jjWd 8 jj during fault event with respect to that during NOC and results are as tabulated in Table 2.

3.2. Case 2: monitoring capacitor bank voltage interaction with harmonic distortion AADS utilizes capacitor banks for voltage support and power factor correction. The capacitor bank is rated at 5 MVAR, 11 kV automatically switched suitable for outdoor use. The capacitor connected as double-star, ungrounded and working in four stages each of 1.25 MVAR. The capacitor banks are provided with series reactors for detuning purposes. The detuning reactors are designed to protect each of the capacitor bank stages against impermissible loading due to harmonics and reducing the capacitor energizing transient. The reactor is rated in such a way that the resonance frequency of the reactor and capacitor bank is sufficiently below the dominant fifth harmonic (250 Hz). Each stage of the capacitor bank is switched ON/OFF as the bus voltage varies between 95% and 105%. The customer voltage at 0.4 kV side of feeders connecting SS3 is monitored. Non-linear loads are connected to 11 kV side of SS5. The harmonic distortion in SS5 is simulated by injecting the fifth harmonic component which is dominant at distribution systems. Similarly, the proposed technique is implemented to monitor the effect of energizing each stage of the capacitor bank on customer voltage quality. The coefficients Wd6(N6) at sixth resolution level (140–280 Hz) of the phase-a voltage, at customer feeders supplied from SS3, are used to model the voltage. The norm jjWd 6 ðN 6 Þjj2 is used to extract features for monitoring voltage interaction with capacitor bank switching in a harmonic distorted environment. The harmonic voltage variation, as proceeding in capacitor energizing stages, with and without detuning reactors is shown in Fig. 10. The first time interval represents the steady-state condition before energizing the capacitor bank. The time intervals 2, 4, 6 and 8 represent customer’s transient voltage during the four capacitor bank switching instants. Intervals 3, 5, 7 and 9 represent the steady-state voltage after switching each stage. Comparing the two cases show that without using a detuning reactor the distortion level increases to up to three times its original value. Detuning reactor reduces the voltage

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6th resolution Without Reactor

2

6th resolution Without Reactor

|| Wd6 ||2

1.5 1 0.5 0 1

2

3

4

5

6

7

8

Stage 1 OFF

During Stage 1 ON

After Stage 1

During Stage 2 ON

After Stage 2

During Stage 3 ON

After Stage 3

During Stage 4 ON

9 After S tage 4

Time intervals Fig. 10. Harmonic distortion variation in phase a voltage during four capacitor bank energizing stages.

distortion level of the system up to 1/3 its original value before switching stage 1 of the capacitor bank. 4. Conclusion Utilizing windowed-wavelet transform and the local maxima of the expansion coefficients one can overcome the draw back in the existing wavelet-based tools. The technique shows that we can get a sharp and clear model for the NOC. This model can detect any disturbance at low or high-frequency bands. The distortion model can be presented in terms of a small set of coefficients. The maximum level of decomposition is extended accurately to monitor simultaneously the expansion coefficients at both high and low-resolution levels. The index of the local-maxima coefficients can be used to define the fault-time and fault propagation sequence in a multi-owner system. The proposed technique shows promising results in wide-area monitoring under deregulated environment. Acknowledgements This work was financially supported by the Research Affairs at the UAE University under a contract no. 04-04-7-11/03. The authors wish to thank the Electrical Distribution Department at Al Ain city in the UAE for their help and support. References [1] A.C. Parsons, W.M. Grady, E.J. Powers, J.C. Soward, A direction finder for power quality disturbances based upon disturbance power and energy, IEEE Trans. Power Delivery 15 (3) (2000). [2] O.A.S. Youssef, A wavelet-based technique for discrimination between faults and magnetizing inrush currents in transformers, IEEE Trans. Power Delivery 18 (1) (2003). [3] Y. Han, Y.H. Song, Condition monitoring techniques for electrical equipment—a literature survey, IEEE Trans. Power Delivery 18 (1) (2003).

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[4] H. Ukai, K. Nakamura, N. Matsui, DSP- and GPS-Based Synchronized Measurement System of Harmonics in Wide-Area Distribution System, IEEE Trans. Ind. Electron. 50 (6) (2003). [5] A.K. Pradhan, A. Routray, Applying distance relay for voltage sag source detection, IEEE Trans. Power Delivery 20 (1) (2005). [6] P.L. Mao, R.K. Aggarwal, Classification of the transient phenomena in power transformers using combined wavelet transform and neural network, IEEE Trans. Power Delivery 16 (4) (2001). [7] M.A.S. Masoum, A. Jafarian, M. Ladjevardi, E.F. Fuchs, W.M. Grady, Fuzzy approach for optimal placement and sizing of capacitor banks in the presence of harmonics, IEEE Trans. Power Delivery 19 (2) (2004). [8] J. Arrillaga, M. H. J. Bollen, Power quality following deregulation, Proceedings of the IEEE, vol. 88 No. 2, February 2000.

Further reading [1] A.M. Gaouda, Windowing Wavelet Transform for Power System Disturbance Monitoring, Complex Systems, Intelligence and Modern Technology Applications, France, September 2004. [2] A.M. Gaouda, S.H. Kanoun, M.M.A. Salama Chikhani, Pattern recognition applications for power system disturbance classification, IEEE Transaction on Power Delivery 17 (3) (2002) 677–683. [3] M.V. Chilukuri, P.K. Dash, Multiresolution S-transform-based fuzzy recognition system for power quality events, IEEE Trans. Power Delivery 9 (1) (2004) 323–330. [4] S. Santoso, W.M. Grady, E.J. Powers, J. Lamoree, S.C. Bhatt, Characterization of distribution power quality events with Fourier and wavelet transforms, IEEE Trans. Power Delivery 15 (1) (2000) 247–254. [5] C. Parameswariah, M. Cox, Frequency Characteristics of Wavelets, IEEE Trans. Power Delivery 17 (3) (2002) 800–804. [6] F. Jurado, J. R. Saenz, Comparison between discrete STFT and wavelets for the analysis of power quality events, Int. J. Electric Power System Res. (2002) 183–190. [7] Perrier, Philipovitch, Basdevant, Wavelet spectra compared to Fourier spectra, J. Math. Phys. 36 (3) (1995) 1506–1519. [8] T. Tarasiuk, Hybrid wavelet-fourier spectrum analysis, IEEE Trans. Power Delivery 9 (3) (2004) 957–964.