Electric Power Systems Research 83 (2012) 41–50

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Characterization of power quality disturbances using hybrid technique of linear Kalman filter and fuzzy-expert system Abdelazeem A. Abdelsalam a,∗ , Azza A. Eldesouky b , Abdelhay A. Sallam b a b

Department of Electrical Engineering, Suez Canal University, Ismailia 41522, Egypt Department of Electrical Engineering, Port-Said University, Port-Said 42523, Egypt

a r t i c l e

i n f o

Article history: Received 13 January 2011 Received in revised form 5 August 2011 Accepted 22 September 2011 Available online 15 October 2011 Keywords: Power quality disturbance DWT Kalman filter Fuzzy expert system

a b s t r a c t This paper presents a hybrid technique for characterizing power quality (PQ) disturbances. The hybrid technique is based on Kalman filter for extracting three parameters (amplitude, slope of amplitude, harmonic indication) from the captured distorted waveform. Discrete wavelet transform (DWT) is used to help Kalman filter to give a good performance; the captured distorted waveform is passed through the DWT to determine the noise inside it and the covariance of this noise is fed together with the captured voltage waveform to the Kalman filter. The three parameters are the inputs to fuzzy-expert system that uses some rules on these inputs to characterize the PQ events in the captured waveform. This hybrid technique can classify two simultaneous PQ events such as sag and harmonic or swell and harmonic. Several simulation and experimental data are used to validate the proposed technique. The results depict that the proposed technique has the ability to accurately identify and characterize PQ disturbances. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Power quality (PQ) disturbances such as voltage sags, swells, interruptions, flicker and harmonic distortion may lead to maloperation or failure of any sensitive electric facilities such as computer based processor or automatic system. The critical aspect of PQ studies is the ability to perform PQ data analysis and classification. The important step in understanding and hence improving the quality of electric power is to extract sufficient information about the events that cause the PQ issues. A number of papers based on different techniques for detection and classification of power quality phenomena have been published over the past years. Some survey studies can be found in [1–3]. Traditionally, Fourier transform permits mapping signals from time domain to frequency domain by decomposing the signals into several frequency components [4]. This technique is critical where the time information of transients is totally lost. In order to overcome this limitation, the short-time Fourier transform (STFT) technique is adopted in [5]. But STFT is well suited for stationary signal where frequency does not vary with time. For non-stationary

∗ Corresponding author. E-mail addresses: [email protected] (A.A. Abdelsalam), [email protected] (A.A. Eldesouky), [email protected] (A.A. Sallam). 0378-7796/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2011.09.018

signal STFT does not recognize the signal dynamics property due to the limitation of fixed window width. To overcome the drawback of STFT, the wavelet transform (WT) provides the time-scale analysis of the non-stationary signal. It decomposes the signal into time scale representation rather than time-frequency representation. The wavelet transform has been explored extensively in various studies as an alternative to the STFT [6–14]. The S-transform [15–20] is an extension to the idea of wavelet transform and is based on a moving and scalable localization Gaussian window and has characteristics superior to either of the transform. The S-transform is fully convertible from time domain to two dimension frequency translation domain and then familiar Fourier frequency domain. Using the change in magnitude of the fundamental component of supply voltage, Kalman filter can be employed to detect and to analyze voltage event [21–24]. The results of Kalman filter depend on the model of the system used and the suitable selection of the filter parameters. If the selection of the Kalman filter parameters is not suitable, the rate of convergence of the results will be slow or the results will diverge. Hybrid technique for detecting and characterizing various types of power quality disturbances, including harmonics distortion is proposed in this paper. First, the captured voltage waveform is passed through discrete wavelet transform (DWT) to identify its noise. The covariance of this noise together with the captured voltage waveform is fed to the Kalman filter to enhance and speed

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A.A. Abdelsalam et al. / Electric Power Systems Research 83 (2012) 41–50

up its rate of convergence. After that the outputs of Kalman filter, amplitude of fundamental frequency component and amplitudes of harmonic components of the captured voltage waveform, are used to prepare the inputs of fuzzy-expert system. Second, the amplitude of fundamental component and its rate of change with time (slope) are passed through a fuzzy expert system that identifies the class to which the disturbance waveform belongs. Although the power system disturbances fall into five categories like outage, sag, normal, swell and surge, the harmonic distortion can be present in each of them. The characterization of distorted waveform can be made by defining a third input to fuzzy system. This input is used to indicate the harmonics present in the distorted waveform or not. Several digital simulation results using MATLAB and experimental results are presented to satisfy and ensure the capability of the proposed technique for characterizing the disturbances successfully. 2. The proposed technique The proposed technique is shown in Fig. 1. The two stages are performed with each new voltage sample: (i) evaluating a new value of the amplitude and slope using Kalman filter with the help of DWT and (ii) characterizing the disturbance using fuzzy-expert system according to the evaluated values.

different harmonic components and is expressed by the following equation: Zk =

n 

Zk+1 =

1 Xa,b = √ |a| a,b (t)

t − b

∞

x(t) −∞

1 = √ |a|

a

t − b a

dt

(1)

(2)

(t) is the mother wavelet, a and b are the time shift and where scale, respectively. The DWT calculations are made for a chosen subset of scales and time shift. This scheme is conducted by using filters and computing the so-called approximations and details. The approximations (A) are the high-scale, low frequency components of the signal. The details (D) are the low-scale, high-frequency components. The DWT coefficients are computed using the equation: Xa,b = Xj,k =



n 

x[n]gj,k [n]

(3)

n∈Z

where a = 2j, b = k × 2j, j ∈ N, k ∈ N. The wavelet filter g plays the role of .

Ai sin(iω(k + 1) T + i )

(6)

i=1

Each frequency component requires two state variables. Thus, the total number of state variables is 2n. These state variables are defined, at any time instant k, as follows: For 1st harmonic : For 2nd harmonic : ··· For nth harmonic :

x1 = A1 cos(1 ) x3 = A2 cos(2 ) ··· x2n−1 = An cos(n )

x2 = A1 sin(1 x4 = A2 sin(2 ) ··· x2n = An sin(n )

The following relationship can be obtained:

⎛ ⎜ ⎜

The continuous wavelet transform (WT) of a signal x (t) is defined as [25]:

(5)

where n is the number of harmonics, A is the amplitude and T is the sampling interval. For the next time step k + 1:

2.1. Wavelet transform



Ai sin(iωk T + i )

i=1

xk+1 = ⎜ ⎜

⎝x

x1 x2 .. .

2n−1

⎞

⎡

⎟ ⎟ ⎟ ⎟ ⎠

x2n

k+1

1 ⎢0 ⎢. =⎢ ⎢ .. ⎣0 0

0 ··· 1 ··· .. . . . . 0 ··· 0 ···

⎤⎛

0 0 .. . 1 0

(7)

⎞

0 x1 0 ⎥ ⎜ x2 ⎟ ⎜ ⎟ .. ⎥ ⎥⎜ . ⎟ . ⎥ ⎜ .. ⎟ + wk 0 ⎦ ⎝ x2n−1 ⎠ 1 x2n k

(8)

Consequently, the measurement equation can be then expressed as:

⎛

⎞T ⎛

sin(ωk T ) ⎜ cos(ωk T ) ⎟ ⎜ ⎟ .. ⎟ zk = Hk xk + vk = ⎜ . ⎜ ⎟ ⎝ sin(nωk T ) ⎠ cos(nωk T )

⎜ ⎜ ⎜ ⎜ ⎝x

x1 x2 .. .

2n−1

x2n

⎞

⎟ ⎟ ⎟ + vk ⎟ ⎠

(9)

k

where H is the matrix giving the ideal connection between the measurement and the state vector at time tk and vk is the measurement error, vk is the details of the first level of DWT of the measurement signal. The estimation of the process covariance, P− , in the next time step k + 1 can be obtained by the following equation: − Pk+1 = k Pk kT + Qk

(10)

2.2. Linear Kalman filter

Qk is the covariance matrix of wk and is assumed to be equal to the identity matrix in this model [27]. The Kalman gain, K, can be computed as:

Kalman algorithm is applied in order to compute the amplitude of the waveform. The Kalman filtering performs the following operations [26].

Kk = Pk− HkT (Hk Pk− HkT + Rk )

1) Vector modeling of the random processes under consideration. 2) Recursive processing of the noisy measured (input) data. The random process to be estimated can be modeled in the following form: xk+1 = K xk + wk

(4)

where xk , xk+1 are the state vector at time instant k and k + 1, respectively. Фk is the usual state transition matrix, wk is assumed to be a white noise with known covariance structure. It is assumed that the system signal under study (voltage signal) corresponds to a sinusoidal signal of fundamental frequency ω and

−1

(11)

Rk is the covariance matrix of vk . The value of Rk is not assumed but it is considered the covariance of the details coefficients of the first level of DWT of the measurement signal. E



vk vTi





=

Rk , 0,

i=k i= / k



(12)

With this information the state estimation can be updated knowing the measured xˆ k = xˆ k− + Kk (zk − Hk xˆ k− )

(13)

and the process covariance can be updated according to: Pk = (I − Kk Hk )Pk−

(14)

A.A. Abdelsalam et al. / Electric Power Systems Research 83 (2012) 41–50

43

Fig. 1. Block diagram of the proposed system.

The amplitude of the fundamental frequency, the first input to fuzzy system, is directly computed at any time instant k from the estimated state variables as follows:



A1,k =

2 + x2 x1,k 2,k

(15)

The amplitudes of the different harmonic components are computed using the following relationship: Ai,k =



2 2 , x2i−1,k + x2,ki

i = 1, 2, . . . , n

(16)

and the slope, the second input to fuzzy system, is obtained from the following relationship: slopek =

(A1,k − A1,k−1 ) T

(17)

where A1,k , A1,k−1 are the fundamental component amplitudes, equation (15), at the time instants k and k − 1, respectively. After calculating the amplitudes of fundamental frequency and different harmonic components, the third input to fuzzy system is determined using the following equation: Mi = mean (Ai ),

i = 1, 2, . . . , n

⎛

M2 /M1

⎜ M3 /M1 ⎜ .. STD Mean = STD ⎜ . ⎜ ⎝ M /M n−1

(18)

⎞

1

⎟ ⎟ ⎟ ⎟ ⎠

(19)

Mn /M1 where STD is the standard deviation.

2.3. Fuzzy-expert systems Fuzzy logic refers to a logic system which represents knowledge and reasons in an imprecise or fuzzy manner for reasoning under uncertainty. Unlike the classical logic systems, it aims at modeling the imprecise modes of reasoning that play an essential role in the human ability to infer an approximate answer to a question based on a store of knowledge that is inexact, incomplete, or not totally reliable. It is usually appropriate to use fuzzy logic when a mathematical model of a process does not exist or does exist but is too difficult to encode and too complex to be evaluated fast enough for real time operation. The accuracy of the fuzzy logic systems is based on the knowledge of human experts; hence, it is only as good as the validity of the rules. The fuzzy system designed and implemented to perform the classification process is a Mamdani-type fuzzy inference system with three inputs, two outputs, and 13 rules. The system uses Max–Min composition, and the centroid of area method for defuzzification. The first input to the system is the value of the amplitude of the distorted waveform. This input was partitioned into five trapezoidal membership function sets, as shown in Fig. 2. These sets are designated as VSA (very small amplitude), SA (small amplitude), NA (normal amplitude), LA (large amplitude), and VLA (very large amplitude). The second input is the value of the slope of the amplitude. This input was broken into three trapezoidal membership function sets, as shown in Fig. 3. These sets are designated as PS (positive slope), NS (negative slope) and ZS (zero slope). The third input is the value of STD Mean. This input is two trapezoidal membership function sets as shown in Fig. 4.

1.2 VSA

1

SA

NA

LA

Degree of membership

Degree of membership

1.2 VLA

0.8 0.6 0.4 0.2

1

NS

PS

ZS

0.8 0.6 0.4 0.2

0 0

0.5

1

1.5

2

2.5

3

3.5

4

amplitude (pu) Fig. 2. Input 1, the amplitude, membership function.

4.5

5

0 -1.5

-1

-0.5

0

0.5

Slope Fig. 3. Input 2, the slope, membership function.

1

1.5

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The brief rule sets of fuzzy expert system are below:

Degree of membership

1.2 Large

Small 1 0.8 0.6 0.4 0.2 0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

STD Mean Fig. 4. Input 3, STD Mean, membership function.

Degree of membership

1.2 Interruption

1

Sag

Normal

Swell

Surge

In the previous rules, the classification of some PQ events such as a voltage sag and swell can be only based on the amplitude input but the second input (slope), in the rules 3&4 for a sag event and in the rules 8&9 for a swell event, is used to identify the beginning and the end of these events, consequently these rules are useful for both classifying and characterizing the PQ disturbances.

0.8 0.6 0.4 0.2 0 0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Fuzzy output Fig. 5. Output 1 membership function.

The first output of the fuzzy system comprises five trapezoidal membership function sets. The labels of these sets are normal, interruption, sag, swell and surge as shown in Fig. 5. The crisp output of the Mamdani fuzzy system can assume values between 0.5 and 5.5 for output 1, where Interruption = 1 Surge = 5

Sag = 2

Normal = 3

Swell = 4

The second output of the fuzzy system is partitioned into two trapezoidal membership function sets. The labels of these sets are Pure and Harmonics as shown in Fig. 6, where Harmonics = 1

Pure = 0

The parameters of amplitude membership function are determined according to the definition of each PQ event as explained in Section 3. The slope and fuzzy output membership functions are determined by training method.

1.2

Degree of membership

Pure

Harmonics

1 0.8 0.6 0.4 0.2 0 -0.5

1) If (amplitude is VSA) and (slope is NS) then (output 1 is INTERRUPTION). 2) If (amplitude is VSA) and (slope is ZS) then (output 1 is INTERRUPTION). 3) If (amplitude is SA) and (slope is NS) then (output 1 is SAG). 4) If (amplitude is SA) and (slope is ZS) then (output 1 is SAG). 5) If (amplitude is NA) and (slope is NS) then (output 1 is NORMAL). 6) If (amplitude is NA) and (slope is ZS) then (output 1 is NORMAL). 7) If (amplitude is NA) and (slope is PS) then (output 1 is NORMAL). 8) If (amplitude is LA) and (slope is PS) then (output 1 is SWELL). 9) If (amplitude is LA) and (slope is ZS) then (output 1 is SWELL). 10) If (amplitude is VLA) and (slope is PS) then (output 1 is SURGE). 11) If (amplitude is VLA) and (slope is ZS) then (output 1 is SURGE). 12) If (STD Mean is small) then (output 2 is PURE). 13) If (STD Mean is large) then (output 2 is HARMONICS).

0

0.5

Output 2 Fig. 6. Output 2 membership function.

1

1.5

3. Simulation results The tested signals of power quality disturbances are seven signals including voltage sag, swell, interruption, surge, harmonic distortion, sag with harmonic and swell with harmonics. These signals are simulated using Matlab according to the power system model shown in Figs. 7 and 8. The power system model consists of a generator supplying a power network that comprises a short transmission line section and three loads (normal, heavy, and nonlinear loads) at the point of common coupling (PCC). The heavy and nonlinear loads are connected to the system through a circuit breaker. Each generated waveform consists of 25 cycles of a voltage waveform sampled at a rate of 6.4 kHz with 50 Hz frequency, which is equal to 128 samples per cycle. The following case studies are presented to illustrate the aptness of the proposed system: • Voltage interruption An interruption may be seen as a loss of voltage on a power system. Such disturbance describes a drop of 90–100% of the rated system voltage for duration of 0.5 cycles to 1 min. A waveform of the exponential decaying voltage interruption generated by a 10 cycle three phase short circuit fault at PCC is shown in Fig. 9(a). The amplitude and the slope outputs of the Kalman filter are shown in Fig. 9(b) and (c). The output 1 of the fuzzy expert system is shown in Fig. 9(d) and fuzzy expert system output 2 equals zero, this means that there is no harmonic distortion in this waveform. It is observed that the proposed system can accurately detect the interruption in the distorted waveform. The tracking error of Kalman filter is found to be less than 0.8%. The tracking error describes the amplitude estimated using Kalman filter. If the amplitude is estimated with high accuracy-low tracking error, the slope is accurately evaluated. Consequently, the fuzzy inputs (amplitude and slope) are accurate. This means that the fuzzy classifier will give exact results. • Voltage sag The voltage sag is a decrease of 10–90% of the rated system voltage for duration of 0.5 cycles to 1 min. The sag disturbance is

A.A. Abdelsalam et al. / Electric Power Systems Research 83 (2012) 41–50

45

Fig. 7. System configuration of the model used for testing.

Fig. 8. MATLAB simulation block diagram of the simulated system.

b 1

Amplitude (pu)

Signal Waveform

a 0.5 0 -0.5 -1 0

0.1

0.2

0.3

0.4

1.5 1 0.5 0

0.5

0

0.1

Time (sec)

d

1

Fuzzy output 1

c Slope

0.5 0 -0.5 -1

0

0.1

0.2

0.3

Time (sec)

0.2

0.3

0.4

0.5

0.4

0.5

Time (sec)

0.4

0.5

5 4 3 2 1 0

0

0.1

0.2

0.3

Time (sec)

Fig. 9. The voltage interruption: (a) waveform, (b) amplitude, (c) slope and (d) fuzzy output 1.

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A.A. Abdelsalam et al. / Electric Power Systems Research 83 (2012) 41–50

b 1

Amplitude (pu)

Voltage Waveform

a 0.5 0 -0.5 -1 0

0.1

0.2

0.3

0.4

1.5 1 0.5 0

0.5

0

0.1

Time (sec)

d

1

Slope

0.5 0 -0.5 -1

0

0.1

0.2

0.3

0.3

0.4

0.5

0.4

0.5

Time (sec) Fuzzy output 1

c

0.2

0.4

5 4 3 2 1 0

0.5

0

0.1

Time (sec)

0.2

0.3

Time (sec)

Fig. 10. The voltage sag: (a) waveform, (b) amplitude, (c) slope and (d) fuzzy output 1.

generated by the occurrence of a single line to ground fault for 10 cycles at the end of the short transmission line. The exponential decaying sag waveform is shown in Fig. 10(a). The amplitude and the slope outputs of the Kalman filter are shown in Fig. 10(b) and (c). The output 1 of the fuzzy expert system is shown in Fig. 10(d) and fuzzy expert system output 2 equals zero. The tracking error of results is less than 0.2%. • Voltage swell In the case of voltage swell, there is a rise of 10–90% in the voltage magnitude for 0.5 cycles to 1 min. The swell is generated by disconnecting the heavy load for 10 cycles. From the results depicted in Fig. 11, the proposed system clearly detects and characterizes the swell disturbance and fuzzy expert system output 2 equals zero, this means that there is no harmonic distortion in this waveform. The tracking error is less than 0.4%. • Voltage surge The surge occurs on disconnecting the heavy load for onequarter cycle as shown in Fig. 12(a) and (b), where the amplitude is suddenly increased from 1 to 3 pu. Such a distorted waveform

c

Amplitude (pu)

b 1 0 -1 0

0.1

0.2 0.3 Time (sec)

0.4

d

1 0.5

Slope

0 -0.5 -1 -1.5

0

0.1

0.2 0.3 Time (sec)

0.4

0.5

2 1.5 1 0.5

0.5

Fuzzy output 1

Voltage Waveform

a

is tested by the proposed system and the results are shown in Fig. 12(d). The tracking error of the magnitude is less than 0.5%. • Voltage distortion The distortion of voltage waveform is generated by connecting the nonlinear load for 10 cycles where the harmonic is generated. The original distorted waveform and the corresponding Kalman filter and fuzzy expert system outputs are shown in Fig. 13. The output 2 of fuzzy expert system equals to 1, this means that the voltage waveform contains harmonic distortion. The values of harmonics amplitudes are estimated using Kalman filter. The tracking error of the magnitude is less than 0.8%. • Sag with harmonics This complicated disturbance type is occurred by connecting the nonlinear load during the simulation period and occurrence of a single line to ground fault for 5 cycles at the end of the short transmission line. The results are shown in Fig. 14. Fig. 14(d) shows that the waveform contains sag event and the output 2 of fuzzy expert system equals 1, this means that the distorted waveform contains a harmonic distortion with sag. The tracking error of the magnitude is less than 1%.

0

0.1

0.2 0.3 Time (sec)

0.4

0.5

0

0.1

0.2 0.3 Time (sec)

0.4

0.5

5 4 3 2 1 0

Fig. 11. The voltage swell: (a) waveform, (b) amplitude, (c) slope and (d) fuzzy output 1.

A.A. Abdelsalam et al. / Electric Power Systems Research 83 (2012) 41–50

b 3

3 Amplitude (pu)

Voltage Waveform

a 2 1 0 -1 0

0.1

0.2

0.3

0.4

2 1 0

0.5

0

0.1

1

Slope

0.5 0 -0.5 -1

0

0.1

0.2

0.3

0.2

0.3

0.4

0.5

0.4

0.5

Time (sec)

0.4

d

5

Fuzzy output 1

Time (sec)

c

47

4 3 2 1 0

0.5

0

0.1

Time (sec)

0.2

0.3

Time (sec)

Fig. 12. The voltage surge: (a) waveform, (b) amplitude, (c) slope and (d) fuzzy output 1.

amplitude (pu)

0.5 0 -0.5 -1

c

b

1

0

0.1

0.2 0.3 Time (sec)

0.4

d

1

Slope

0.5 0 -0.5 -1

0

0.1

0.2 0.3 Time (sec)

0.4

1 1

1

1

0.5

Fuzzy output 1

Voltage Waveform

a

0.1

0.2 0.3 Time (sec)

0.4

0.5

0

0.1

0.2 0.3 Time (sec)

0.4

0.5

5 4 3 2 1 0

0.5

0

Fig. 13. The voltage distortion: (a) waveform, (b) amplitude, (c) slope and (d) fuzzy output 1.

a

b amplitude (pu)

Voltage Waveform

1 0.5 0 -0.5 -1

0

0.1

0.2

0.3

0.4

1.5

1

0.5

0

0.5

0

0.1

Time (sec)

d

1

Slope

0

-1

-2

0

0.1

0.2

0.3

Time (sec)

0.3

0.4

0.5

0.4

0.5

Time (sec)

Fuzzy output 1

c

0.2

0.4

0.5

3.5 3 2.5 2 1.5

0

0.1

0.2

0.3

Time (sec)

Fig. 14. The sag with harmonic distortion: (a) waveform, (b) amplitude, (c) slope and (d) fuzzy output 1.

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A.A. Abdelsalam et al. / Electric Power Systems Research 83 (2012) 41–50

b 1 0 -1 0

c

0.1

0.2 0.3 Time (sec)

0.4

1.2 1 0.8

d

0 -0.5

0

0.1

0.2 0.3 Time (sec)

0.4

0

0.1

0.2 0.3 Time (sec)

0.4

0.5

0

0.1

0.2 0.3 Time (sec)

0.4

0.5

4.5

Fuzzy output 1

0.5 Slope

1.4

0.5

1

-1

1.6

amplitude (pu)

Voltage Waveform

a

4 3.5 3 2.5

0.5

Fig. 15. The swell with harmonic distortion: (a) waveform, (b) amplitude, (c) slope and (d) fuzzy output 1.

b

1 0.5 0 -0.5 -1

0.8

Amplitude (pu)

Voltage Waveform

a

0

0.02

0.04

0.06

0.08

0.6 0.4 0.2 0

0.1

0

0.02

Time (sec)

d

1

Slope

0.5 0 -0.5 -1

0

0.02

0.04

0.06

0.06

0.08

0.1

0.08

0.1

0.08

0.1

0.08

0.1

Time (sec) 3

Fuzzy output 1

c

0.04

0.08

2.5 2 1.5 1

0.1

0

0.02

Time (sec)

0.04

0.06

Time (sec)

Fig. 16. Case study 1: (a) waveform, (b) amplitude, (c) slope and (d) fuzzy output 1.

b

1.5

Amplitude (pu)

Voltage Wave form

a

1 0.5 0 -0.5 -1

1 0.8 0.6 0.4 0.2

0

0.02

0.04

0.06

0.08

0

0.1

0

0.02

Time (sec)

d

1

Slope

0.5 0 -0.5 -1 -1.5

0

0.02

0.04

0.06

Time (sec)

0.06

Time (sec)

Fuzzy output 1

c

0.04

0.08

0.1

3.5 3 2.5 2 1.5

0

t1 0.02

t2 0.04

0.06

Time (sec)

Fig. 17. Case study 2: (a) waveform, (b) amplitude, (c) slope and (d) fuzzy output 1.

A.A. Abdelsalam et al. / Electric Power Systems Research 83 (2012) 41–50

49

Table 1 The classification results of disturbances. Waveform type

SNR 20 db

Interruption Sag Swell Surge Harmonic Sag with harmonic Swell with harmonic Mean accuracy (%)

SNR 30 db Correct samples

Tested samples

Correct samples

Tested samples

100 100 100 100 100 100 100

92 93 94 92 90 93 92

100 100 100 100 100 100 100

98 99 99 96 94 97 96

100 100 100 100 100 100 100

92.3

The classification results are presented in Table 1. Simulation results show that the average classification accuracies are 98.71%, 97%, and 92.3% with SNR 40 dB, 30 dB, and 20 dB, respectively. These studies show that the proposed method for feature extraction and decision making are efficient for the classification. 4. Experimental results This section presents some of results obtained by applying the new approach on practical data. The practical data are obtained from the IEEE Project Group 1159.2 [28]. The sample frequency used

• Case study 1 The voltage waveform of this case study is shown in Fig. 16(a). This waveform contains the sag power quality event. The amplitude of the voltage waveform and its slope are shown in Fig. 16(b) and (c), respectively. As can be seen in Fig. 16(d) the fuzzy output clearly points out the sag PQ event in the waveform; the magnitude is 60%. The output 2 of fuzzy expert system equals zero, this means that this waveform does not contain any harmonic distortion. • Case study 2 In this case study, the sag in voltage waveform is detected using Kalman filter and is characterized using the results of fuzzy expert system. Fig. 17 shows the voltage waveform with voltage sag. Fig. 17(d) shows how the fuzzy system identifies the beginning and the end of the voltage sag event (instants t1 and t2 , respectively). The magnitude of the voltage sag (defined as the remaining voltage during the sag), computed from Fig. 17(b), is 20% and its duration (time difference t2 − t1 ), computed from Fig. 17(d), is 50 ms. The output 2 of fuzzy expert system equals 1, this means that this waveform contains a harmonic distortion. • Case study 3

b 1.5

0.8 Amplitude (pu)

1 0.5 0 -0.5 -1 -1.5

0

0.02

0.04 0.06 Time (sec)

0.08

d

1

0 -0.5 -1

0

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0.08

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0.6 0.4 0.2 0

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0.5 Slope

is fs = 15,360 Hz, or 256 samples per 60 Hz cycle. Three different case studies are reported to show the overall performance of the proposed technique.

Fuzzy output 1

Voltage Waveform

a

Correct samples 100 100 100 98 97 98 98 98.71

97

• Swell with harmonics This disturbance type is occurred by permanent connection of the nonlinear load during the simulation period and disconnecting the heavy load for 5 cycles. The results are shown in Fig. 15. Fig. 15(d) shows that the waveform contains swell event and the output 2 of fuzzy expert system equals 1, this means that the distorted waveform contains a harmonic distortion with swell. The tracking error of the magnitude is less than 1%. For each kind of power system disturbances, another 100 case studies were prepared by changing the values of all loads (normal, heavy, and nonlinear) and changing the beginning and the end time instant of each disturbance. The generated signals are mixed with random white noise of zero mean and different values of the signal to noise ratio SNR (40 db, 30 db and 20 db).

c

SNR 40 db

Tested samples

0

0.02

0

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0.04 0.06 Time (sec)

0.08

0.1

0.08

t3 0.1

3 2.5 2 1.5 1 0.5

t1

t2 0.04

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Fig. 18. Case study 3: (a) waveform, (b) amplitude, (c) slope and (d) fuzzy output 1.

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In this case study, the test waveform contains three power quality events; voltage interruption, sag and harmonic distortion, as shown in Fig. 18(a). The amplitude of the voltage waveform and its slope are shown in Fig. 18 (b) and (c), respectively. The beginning and the end of interruption and sag are detected using fuzzy output. The duration of voltage interruption, t1 , evaluated from Fig. 18(d), is 36 ms. The sag event starts after an overshot occurrence in the voltage that returns the voltage magnitude to its nominal value, 1 pu, for a small time duration, t2 − t1 . The sag magnitude is 73% with a time duration equals t3 − t2 as shown in Fig. 18(d). The above simulation and experimental results reveal the proposed hybrid technique is computationally simple and Kalman filter has accurate results as the value of the measurement error covariance is not assumed and instead it is accurately extracted with the help of DWT. 5. Conclusions A hybrid technique based on linear Kalman filter and fuzzyexpert system has been proposed in this paper for characterizing power quality disturbances. The main advantage of the proposed technique comes from its ability to classify complicated power quality disturbances such as sag with harmonics and swell with harmonics. Besides the ability of the proposed technique to classify PQ disturbances, it can identify the characteristics of the PQ disturbance; amplitude, time duration and harmonic contents with high accuracy. Several simulation and experimental tests have been conducted to validate the performance of the proposed technique. The results show that the proposed system performs very well in the detection and characterization of various power system disturbances. References [1] I.Y. Gu, E. Styvaktakis, Bridge the gap: signal processing for power quality applications, Electric Power Syst. Res. 66 (1) (2003) 83–96. [2] W.R.A. Ibrahim, M.M. Morcos, Artificial intelligence and advanced mathematical tools for power quality applications: a survey, IEEE Trans. Power Deliv. 17 (2) (2002) 668–673. [3] R.A. Flores, State of the art in the classification of power quality events an overview, in: Proc. 10th Int. Conf. Harmonics Quality of Power, vol. 1, 2002, pp. 17–20. [4] G.T. Heydt, P.S. Fjeld, C.C. Liu, D. Pierce, L. Tu, G. Hensley, Applications of the windowed FFT to electric power quality assessment, IEEE Trans. Power Deliv. 14 (4) (1999) 1411–1416. [5] P.S. Wright, Short-time Fourier transforms and Wigner–Ville distributions applied to the calibration of power frequency harmonic analyzers, IEEE Trans. Instrum. Meas. 48 (2) (1999) 475–478.

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