- Email: [email protected]
Detection and classification of single and combined power quality disturbances using fuzzy systems oriented by particle swarm optimization algorithm
Electric Power Systems Research 80 (2010) 1552–1561
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Detection and classification of single and combined power quality disturbances using fuzzy systems oriented by particle swarm optimization algorithm R. Hooshmand ∗ , A. Enshaee Department of Electrical Engineering, University of Isfahan, Hezar-Jerib St., Isfahan 8174673441, Iran
a r t i c l e
i n f o
Article history: Received 23 December 2009 Received in revised form 30 June 2010 Accepted 1 July 2010 Available online 31 July 2010 Keywords: Power quality Disturbances classification Fourier transform Wavelet analysis Fuzzy logic Particle swarm optimization (PSO) algorithm
a b s t r a c t In this paper, a new approach for the detection and classification of single and combined power quality (PQ) disturbances is proposed using fuzzy logic and a particle swarm optimization (PSO) algorithm. In the proposed method, suitable features of the waveform of the PQ disturbance are first extracted. These features are extracted from parameters derived from the Fourier and wavelet transforms of the signal. Then, the proposed fuzzy system classifies the type of PQ disturbances based on these features. The PSO algorithm is used to accurately determine the membership function parameters for the fuzzy systems. To test the proposed approach, the waveforms of the PQ disturbances were assumed to be in the sampled form. The impulse, interruption, swell, sag, notch, transient, harmonic, and flicker are considered as single disturbances for the voltage signal. In addition, eight possible combinations of single disturbances are considered as the PQ combined types. The capability of the proposed approach to identify these PQ disturbances is also investigated, when white Gaussian noise, with various signal to noise ratio (SNR) values, is added to the waveforms. The simulation results show that the average rate of correct identification is about 96% for different single and combined PQ disturbances under noisy conditions. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The increasing growth in the use of sensitive loads by customers and the demand for high quality electricity have drawn special attention to the causes, effects, and solutions of PQ problems. By providing and installing various types of power quality monitoring equipment in the distribution systems, electric power utilities try to ensure a high quality of service. In most cases, analysis to identify the type of PQ disturbances requires large quantities of data to be collected by this equipment. This requires fast and efficient methods that can be implemented in hardware or software implementation to detect and classify the PQ disturbances [1]. Most single type PQ disturbances can be described as a voltage impulse, interruption, swell, sag, notch, transient, harmonic, or flicker in the distribution systems [2]. The major factors that contribute to the occurrence of these disturbances include the starting of large electric motors, switching capacitor banks, non-linear loads, arc furnace operation, the use of equipment with solid state switching devices, distribution system faults, and so forth [2]. The PQ disturbances include a wide range of events. The discrete Fourier transform is often used for the signal processing of low frequency PQ disturbances such as flicker, but it is more appropri-
∗ Corresponding author. Tel.: +98 311 7934073; fax: +98 311 7933071. E-mail addresses: Hooshmand [email protected] (R. Hooshmand), [email protected] (A. Enshaee). 0378-7796/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2010.07.001
ate to employ wavelet transform for the signal processing of high frequency PQ disturbances such as transients [3–8]. Some prior researchers have used these two techniques to extract suitable features of the PQ disturbance waveforms, simplifying the identification and classification of these disturbances [3–7]. In most papers, fuzzy rules are used to make decisions regarding the occurrence and classification of the type of the disturbance [3–6]. In these methods, the large number of inputs to the fuzzy system increases the correct identification rate of the disturbances, but also increases the method complexity and decreases its speed [3,4]. In references [5–7], the fuzzy system complexity for the classification of disturbances is reduced to some extent, and the correct identification rate is not significantly changed compared with references [3,4]. However, no attention has been paid to the detection of combined PQ disturbances. Furthermore, it seems that determining the parameters of the membership functions for the fuzzy systems is only performed based on human reasoning, and the correct identification rate is increased through trial-and-error modification of these parameters. Therefore, there has been no guarantee of optimality for these parameters in the prior research. Of course, other different methods have also been presented for the detection and classification of PQ disturbances [8–15]. Some of these methods have good performance under noisy conditions [14,15]. However, these methods either do not consider [8,11–13] or only consider a few numbers [9,10,14,15] of combined disturbances. In this paper, a new method is proposed for the detection and classification of single and combined PQ disturbances using two
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
fuzzy systems oriented with a PSO algorithm. The first fuzzy system is employed for detection and the other system is used to classify PQ disturbances. The PSO algorithm is used to provide optimized values for the parameters of the membership functions of these systems. The features extracted from the windowed discrete Fourier transform (WDFT) and wavelet transform of the waveforms of the disturbances form the inputs of these systems. The number and type of the inputs are selected to prevent the complexity of this input set. In addition, the rule base of these systems is established to achieve high accuracy in the detection and classification of single and combined PQ disturbances. It should be noted that all single types of PQ disturbances mentioned in second paragraph of this section can be detected in the proposed approach. Harmonic with swell, swell with harmonic, swell with transient, flicker with swell, harmonic with sag, sag with harmonic, sag with transient and flicker with sag are also considered as the combined disturbances of the voltage signal. Furthermore, to show the effectiveness of the proposed method, its sensitivity to noise is tested under different noisy conditions. The paper is organized as follow: first, the method of extraction of suitable features from the waveform of disturbances is presented. Then, the process of designing the fuzzy systems is described in Section 3. In Section 4, the application of the PSO algorithm in the proposed fuzzy systems is explained. In Section 5, simulation results are presented to demonstrate the capability of the proposed algorithm to correctly identify PQ disturbances. Finally, conclusions are discussed in Section 6. 2. Feature extraction from the waveform of disturbances In this section, in order to detect and classify the PQ disturbances, eight features extracted from the waveform of these disturbances, are introduced [3–7]. 2.1. Fundamental component (Vn ) This feature calculates the fundamental component of the signal in each cycle, which is given by [3–7,9] √ (1) Vn = 2abs(V n [1])/N where Vn [k] is a complex value denoting the discrete frequency content for the samples contained in the nth data window of the sampled signal and is written as [3–7,9]: n
V [k] =
N−1
v[i + (n − 1)N]e
−j(2ki/N)
(2)
In this equation, v[i] covers 10 cycles of the sampled signal with a sampling rate of 256 points per cycle. Therefore, the length of the v[i] shall be equal to 2560; k = 0, 1,. . .,N − 1; and the parameter N is the number of the samples in one data window. Because the data window length is equal to one cycle, N shall be equal to 256. Also, the parameter j is the imaginary unit and n = 1, 2,. . .,10 is the index of the data window. Because the aim of Eq. (1) is the calculation of the fundamental component of the nth data window of the sampled signal, k is taken to be equal to 1 in Eq. (2). 2.2. Phase angle shift (PSn ) This feature calculates the angle difference between discrete Fourier transform for the nth cycle and the first cycle of the sampled signal for its fundamental component. Therefore
where angle(.) returns the phase angle of the input argument.
2.3. Total harmonic distortion (THDn ) This quantity is defined as the ratio of the square root of the total squared magnitude of each harmonic component of the distorted waveform to the fundamental component of that waveform. So,
int(N/2) 2 {abs(V n [k])} k=2
THDn =
abs(V 1 [1])
(4)
In this equation, abs(.) gives the absolute value of the argument. Also, int(N/2) equals N/2 if N is even and equals (N − 1)/2 if N is odd. 2.4. Number of maximums of the absolute value of wavelet coefficients (Nn ) This feature is defined as follows: Nn = max(abs(WCn ))
(5)
WCn
where the matrix includes the third scale wavelet detail coefficients resulting from the analysis of the nth cycle of the sampled signal. Also, the max(.) function returns the number of maximums of the argument, and if the maximum value is less than 0.1, it can be neglected. After reviewing simulation results, it was found that the fourthorder Daubechies wavelet (Db4) yields the best performance for detection and classification of PQ disturbances using the proposed approach. Thus, the fourth-order Daubechies wavelet was chosen as the mother wavelet for this analysis. In general, Daubechies wavelet filters are widely used in terms of shorter filter lengths, and thus fast computation times, for real-time applications such as PQ issues [3–5,14,15]. 2.5. Energy of the wavelet coefficients (EWn ) This feature considers the total absolute value of the WCn matrix components. This is called the energy of the wavelet coefficients. It is computed by EWn =
le
abs(WCn [k])
(6)
k=1
where le is the length of WCn .
i=0
PSn = angle(V n [1]) − angle(V 1 [1])
1553
(3)
2.6. Number of zero-crossings of the missing voltage (OSn ) This feature is determined by counting the number of zerocrossings of the missing voltage waveform. This waveform is obtained by computing the difference between the disturbance and a pure sinusoidal waveform. This feature denotes the rate at which the disturbance voltage waveform separates from ideal sinusoidal voltage waveform. Therefore, OSn = root(vsmiss )
(7)
In this equation, the root(.) function calculates the number of zero-crossing points of the argument. Also, vsmiss is defined as an array consisting of vmiss [i], i = 0, 1,. . .,N − 1. The terms of vmiss [i] are calculated by
vmiss [i]=v[i] − 2/N × abs(V 1 [1]) × cos{angle(V 1 [1]) + 2(i − 1)/N} (8)
1554
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
2.7. Lower harmonic distortion (TSn ) This feature is similar to the total harmonic distortion (THDn ) feature, but in this calculation, only components up to 10th order are used. So,
10 {abs(V n [k])}2
TSn =
Fig. 1. The schematic representation of the fuzzy system for the detection of PQ disturbances.
k=2
(9)
abs(V 1 [1])
3. The proposed fuzzy systems
2.8. Number of peaks of rms value (RN) This feature is defined as s ) RN = peak(Vrms
(10)
In this equation, the peak(.) function returns the number of significant variations (increasing or decreasing) of the argument s n is defined as an array consisting of Vrms where n = 1, and Vrms n is also the rms value of nth cycle of the 2,. . .,10. The term Vrms sampled signal obtained from the following equation: n Vrms
N−1 1 = v2 [i + (n − 1)N] N
(11)
i=0
It should be noted that for most PQ disturbances, the rms value of the starting and ending cycles of the disturbance will be significantly different from the rms value of cycles that are before and after them, respectively. Observations show that the number of these variations depends on the type of the disturbance. So, the RN feature can help to classify these disturbances by counting the number of variations. This issue will be discussed in detail in Section 3.3. Employing the windowed discrete Fourier transform to compute Vn , PSn , THDn , OSn and TSn possibly decreases the correct identification rate of PQ disturbances under noisy conditions. Instead, selecting the fourth-order Daubechies wavelet, and third level decomposition for the computation of Nn and EWn , enables the proposed approach to classify noisy PQ disturbances with high accuracy using the above features. Of course, proper establishment of the rule base, presented in Section 3.2, also helps the proposed system to perform acceptably.
The two following fuzzy systems are designed for detection and classification of the PQ disturbances. The overall structures of these two systems are depicted in Figs. 1 and 2. As illustrated in these figures, the components of the two fuzzy systems are described in the next subsections. Then, the interaction process between the two systems for the detection and classification of single and combined PQ disturbances is presented. 3.1. Inputs, outputs, and their membership functions 3.1.1. Fuzzy system for disturbance detection The inputs of this system are the following features: THDn , PSn and Vn . The output is the “Disturb” variable, which shows the occurrence or non-occurrence of a disturbance by taking the values one or zero, respectively. The membership functions (MFs) of each input to this system, along with the selected parameters, are indicated in Table 1. 3.1.2. Fuzzy system for disturbance classification The inputs of this system are the following features: Vn , THDn , THDn+1 , PSn , EWn , Nn , Nn−1 , Nn+1 , OSn , TSn and TSn+1 . The outputs of the system are the following variables: “Impulse”, “Interruption”, “Swell”, “Sag”, “Notch”, “Transient”, and “Harmonic”. When each output takes a non-zero value, this indicates a detection of that disturbance, as will be explained in Section 3.3. Also, the membership functions of each input of this system along with the selected parameters are given in Table 2. It should be noted that determination of membership function parameters of these systems using the PSO algorithm will be presented in Section 4.2.
Fig. 2. The schematic representation of the fuzzy system for the classification of PQ disturbances.
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
1555
Table 1 The membership function of fuzzy system inputs for the disturbance detection. Labels
Range
Membership function labels
Membership function types
Membership function parameters
THDn PSn Vn
[0,1] [0,180] [−0.01, 2.5]
A1 B1 C1 C2
Trapezoidal Trapezoidal Trapezoidal
[0.038 0.04 1.1 1.2] [0.8 1 180 190] [−0.18 −0.02 0.98 1] [1 1.02 2.6 2.7]
Table 2 The membership function of fuzzy system inputs for the disturbance classification. Labels
Range
Membership function labels
Membership function types
Membership Function Parameters
Vn
[0,2]
Trapezoidal
THDn , THDn+1
[0,1]
PSn
[−3,180]
EWn Nn−1 , Nn , Nn+1
[0,4] [−1,30]
OSn TSn , TSn+1
[0,100] [0,1]
A1 A2 A3 A4 A5 B1 B2 C1 C2 D1 F1 F2 F3 G1 H1 H2 H3
[−0.18 −0.02 0.097 0.1] [0.103 0.11 0.89 0.9] [0.94 0.96 1.01 1.03] [0.997 1 1.09 1.11] [1.1 1.12 2.1 2.2] [−0.2 −0.1 0.048 0.05] [0.048 0.05 1.1 1.2] [−3.8 −3 4.8 5.5] [4.8 5.5 181 182] [0.58 0.829 3 3.2] [−1.8 −1 3 3.3] [3.7 4 6 6.3] [672930] [7.8 8.2 104 105] [−0.18 −0.02 0.018 0.021] [−0.18 −0.02 0.038 0.041] [0.038 0.041 1.1 1.2]
Trapezoidal Trapezoidal Trapezoidal Trapezoidal
Trapezoidal Trapezoidal
3.2. Rule base in the systems
3.3. Operational mechanism in the fuzzy systems
The establishment of a more accurate rule base for these two fuzzy systems increases the detection capability for more various cases of PQ disturbances. These rules have the advantage of expert knowledge.
To make a decision regarding the occurrence of disturbance, the features of THDn , PSn and Vn for each of the cycles of the desired waveform are calculated and considered as fuzzy system inputs for PQ disturbance detection. Based on these inputs, this fuzzy system specifies whether there has been any disturbance during the associated cycle. If the response is “Negative”, the above process is repeated for the next cycle; otherwise, a disturbance has been detected and its type should be identified. At this stage, the RN feature of the desired waveform is calculated. If the value of this parameter is more than four, the disturbance is defined as a flicker. In the event of a single PQ disturbance such as impulse, interruption, swell, sag or transient, we will have two significant variations in the rms values of the disturbance waveforms: one at the start and the other at the end of the disturbance. Therefore, the value of the RN feature will be equal to two for these disturbances. In a similar way, it can be found that the maximum value of the RN feature will be equal to four for combined PQ disturbances. Simulation results show that the value of the RN feature will be more than four, only if a flicker disturbance occurs. Let the starting cycle of the disturbance be denoted by index “n”, and the cycles that are before and after this cycle be denoted by “n − 1” and “n + 1” indices, respectively. Thus, the features of Vn , THDn , THDn+1 , PSn , EWn , Nn , Nn−1 , Nn+1 , OSn , TSn and TSn+1 can be extracted from the desired waveform. By implementing these features in the fuzzy system for PQ disturbance classification, the outputs of this system take zero or non-zero values, where the one with the largest non-zero value indicates the type of disturbance. If several outputs have the same largest non-zero value, all of them are considered to describe the type of disturbance detected. Fig. 3 shows the interaction mechanism between the two fuzzy systems for decision making on the occurrence and identification of the disturbance type.
3.2.1. Fuzzy system for disturbance detection Table 3 presents the rule base of this system; e.g., the first rule extracted from this table is as follows: Rule 1: if (THDn is A1 or PSn is B1 or Vn is C2 ) then Disturb = 1where setting the “Disturb” variable to one indicates the occurrence of a disturbance and setting it to zero indicates the non-occurrence of a disturbance. 3.2.2. Fuzzy system for disturbance classification Table 4 presents the rule base of this system; e.g., the first rule extracted from this table is as follows: Rule 1: if (Vn is A4 and PSn is C1 and EWn is D1 and Nn−1 is F1 and Nn is F2 and Nn+1 is F1 ) then Impulse = 1where setting “Impulse” to one indicates the occurrence of an impulse disturbance, and setting it to zero indicates non-occurrence of an Impulse disturbance. It should be noted that the fuzzy inference engine in these two fuzzy systems are of the Sugeno type, because this type of engine is very suitable for modelling expert reasoning [16]. Due to its simplicity, the “Max” and “Min” functions are employed for fuzzy operators of union (OR) and common (AND), respectively [17]. The weighted sum (wtsum) method, which is the best defuzzification method, is selected for the defuzzification process [16].
Table 3 The rule base in the fuzzy system for the disturbance detection.
Rule 1 Rule 2
Inputs THDn
PSn
Vn
Outputs Disturb
4. Proposed fuzzy systems oriented by PSO algorithm
A1 –
B1 –
C2 C1
1 1
One of the main problems in designing the fuzzy systems presented in the previous section was to determine the membership
1556
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
Table 4 The rule base in the fuzzy system for the disturbance classification.
Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 Rule 6 Rule 7 Rule 8 Rule 9 Rule 10 Rule 11 Rule 12
Inputs THDn Vn
THDn+1
PSn
EWn
Nn−1
Nn
Nn+1
OSn
TSn
TSn+1
Outputs Impulse
Interruption
Swell
Sag
Notch
Transient
Harmonic
A4 A1 A5 A5 A5 A2 A2 A2 A3 – – –
– – – – – – – – B2 B1 B1 B2
C1 – – C2 – – C2 – C1 – – –
D1 – – – D1 – – D1 – – – –
F1 – – – – – – – – F1 F1 –
F2 – – – – – – – F3 F3 F3 –
F1 – – – – – – – F3 F1 F1 –
– – – – – – – – G1 – – –
– H1 – – H1 – – H1 H2 – – H3
– – – – – – – – H2 H1 H1 H3
1 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0
0 0 0 0 0 1 1 1 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 0 1
– B1 – – – – – – B2 B1 B2 B2
functions parameters of the input variables. Accurate determination of the value of these parameters has an important role in the correct operation of the proposed algorithm for the identifying the type of disturbance. The PSO algorithm has been employed to accurately determine the membership function parameters mentioned in Tables 1 and 2. In this section, first a brief review of the PSO algorithm is presented. Then, the application of this algorithm to the proposed fuzzy systems for PQ disturbance detection and classification is described. 4.1. A review of PSO algorithm The PSO algorithm was introduced in 1995 by Eberhart and Kennedy [18], and is a type of group-based evolutionary algorithm. Like other group-based evolutionary algorithms, it starts with an initial group consisting of “n” particles (potential solutions to the optimization problem) in a multi-dimensional search space. It is evident that some of the particles have better positions than the others. The particles change their positions in this space until they encounter one of the stop-criteria of the algorithm. These criteria can include reaching an optimal state or ending the number of specific repetitions in the algorithm. For each iteration, the position of each particle is changed based on knowledge of the particle’s previous movements and knowledge of the neighbouring particles. In fact, each particle is aware of its best previous position and the best position among all particles. For each iteration, the velocity vector of the ith particle is updated according to Eq. (12):
vi (t + 1) = wvi (t) + c1 r1 (Pbesti (t) − xi (t)) + c2 r2 (Gbest(t) − xi (t)) (12)
In this equation, w is the inertia weight factor, vi (t) is the previous velocity of the particle, vi (t + 1) is the present velocity of the particle, c1 and c2 are weighting acceleration constants, Pbesti is the best position that a particle of the group has achieved up to now, and Gbest is the best position that a whole group has achieved up to now. r1 and r2 are random numbers with uniform distribution in the range [0–1], with values produced for each particle in each iteration. It should be noted that w > 0 is a factor that controls the effect of vi (t) in vi (t + 1). Also, c1 > 0 and c2 > 0 make the particle move toward Pbesti and Gbest, respectively. The values of c1 and c2 are usually equal and selected in a way that c1 + c2 ≤ 4. After the velocity of the ith particle is updated, the particle moves toward its new position (xi (t + 1)) from its present position (xi (t)) by Eq. (13): Fig. 3. The proposed algorithm for detection and classification of PQ disturbances.
xi (t + 1) = xi (t) + vi (t + 1)
(13)
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
1557
Fig. 4. The flowchart of the implementation of the PSO algorithm to determine the membership function parameters.
Then, the objective function (f) is evaluated at the new position of the ith particle. If the minimization of the objective function is the aim of optimization, then Pbesti and Gbest are updated by Eqs. (14) and (15), respectively.
Pbesti (t + 1) =
Pbesti (t)
if f (Pbesti (t)) ≤ f (xi (t + 1))
xi (t + 1)
if f (Pbesti (t)) > f (xi (t + 1))
Gbest(t + 1) ∈ {Pbest1 (t + 1), . . . , Pbestn (t + 1)}| f (Gbest(t + 1)) = min{f (Pbest1 (t + 1)), . . . , f (Pbestn (t + 1))}
(14)
(15)
The term vi in Eq. (12) lies in the range of (−vmax , vmax ) to reduce the probability that the particle exits from the search space. In many experiences with PSO, vmax is set at a typical value of 10–20% of (xmax − xmin ). It should be noted that if too high a value is chosen for vmax , particles may fly past good positions and if vmax is set at too small values, particles may not explore sufficiently beyond local positions [19]. On the other hand, suitable selection of w allows the algorithm to converge to the optimal point in less iteration. In the conventional PSO algorithm, the w factor is reduced from the value of 0.9 to 0.4 during the iteration of the algorithm based on the following equation: w = wmax −
wmax − wmin ×k kmax
Fig. 5. The flowchart of the calculation of the mistaken identification rate for each disturbance using the Fuzzy–PSO algorithm.
known collection of waveforms of each single disturbance type (impulse, interruption, swell, sag, notch, transient or harmonic). It is expected that an acceptable rate for correct identification will be achieved for any other unknown collection of disturbance waveforms. The flowchart of the calculation of the mistaken identification rate for 200 cases of each disturbance is depicted in Fig. 5. This figure is a combination of the flowcharts presented in Figs. 3 and 4. 5. Simulation results
(16)
where kmax is the maximum number of iterations and k is the present iteration number. 4.2. The application of the PSO algorithm to the proposed fuzzy systems To accurately determine the parameters of the membership functions for the inputs to the proposed fuzzy systems, the PSO algorithm is employed. To specify the variation intervals of these parameters, we first need to obtain the variation range for each feature describing the waveform of each type of disturbance. Then, the variation range of the membership function parameters for each rule is specified by analyzing the variation range of these features. Fig. 4 shows the flowchart of the implementation of the PSO algorithm to determine the parameters of the membership functions used to identify each disturbance. As illustrated, the PSO algorithm varies the membership function parameters until the mistaken identification rate is minimized for a
5.1. Initial data In order to investigate the fuzzy systems for detection and classification of PQ disturbances, 200 cases of each desired disturbance are produced. These disturbances are generated using ‘MATLAB’ software, and each waveform is based on the models presented in Tables 5 and 6, where the controlling parameters in these models are determined randomly. These models represent mathematical relations adapted to different types of disturbances present in the distribution systems. In this set of disturbances, the impulse disturbance is generated using the model presented in reference [20] for a 100/1000 s voltage impulse waveform. The voltage notch disturbance was generated based on the normal operation of a three-phase, full-bridge thyristor-based rectifier [21]. For the harmonic disturbance, the presence of at least three frequency components is required; one is the fundamental component and the two others are harmonic components. The rms values of the harmonic components and the total harmonic distortion of this waveform are also selected according to reference [22].
1558
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
Table 5 Mathematical models and waveforms of single PQ disturbances [10,11,20–22]. Disturbance type Pure sinusoidal
Equations √ v(t) = 2 sin(2 × 50t + ϕ)
Controlling parameters − ≤ ϕ ≤
0.2 ≤ vp ≤ 1 2 (t−T ) s
v(t) = 1.11vp (e−7.5×10
2 (t−T ) s )(u(t
− e−3.44×10
− Ts ) − u(t − Te ))
T ≤ Ts ≤ 7T Te = Ts + 1 ms
0 ≤ vn ≤ 0.1 √
v(t) = 2vn sin(2 × 50t + ϕ)[u(t − Ts ) − u(t − Te )]
−/4 ≤ ϕ ≤ /4 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
1.1 ≤ vn ≤ 1.8 √
v(t) = 2vn sin(2 × 50t + ϕ)[u(t − Ts ) − u(t − Te )]
−/4 ≤ ϕ ≤ /4 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
0.1 ≤ vn ≤ 0.9 √
v(t) = 2vn sin(2 × 50t + ϕ)[u(t − Ts ) − u(t − Te )]
−/4 ≤ ϕ ≤ /4 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
v(t) =
⎧√ ⎪ 2[sin(ωt + ) + 0.5 ⎪ 6 ⎪ ⎪ √ ⎨ 2[sin(ωt + ) − 0.5
sin(ωt +
5 )] 6
cos(ωt)] 6 √ ⎪ 2[sin(ωt + ) − sin(ωt + )] ⎪ 6 6 ⎪ ⎪ ⎩ √2 sin(ωt + ) 6
k = 1, 7 k = 3, 9 k = 5, 11 otherwise
ω = 2 × 50, = 0.5 0 ≤ ˛ ≤ /2, < ˛ 36500 × 2/20, 000 √ 2 × 460 sin(˛) k k ωt ∈ [˛ + ,˛ + + ] 6 6
=
0.3 ≤ vn ≤ 1 √
√
v(t) = 2 sin(2 × 50t)[1 + 2vn e−˛(t−Ts ) sin(2fn (t − Ts ) + ϕ)]
150 ≤ ˛ ≤ 1000 Ts = T, 2T, . . . , 7T 300 ≤ fn ≤ 900 0 ≤ ϕ ≤ 2 − ≤ ϕ ≤ , THD ≥ 5% 0.015 ≤ ˛2k ≤ 0.03
√
v(t) = 2[sin(2 × 50t + ϕ) + . . . + ˛2k sin(2(2k) × 50t + ϕ2k ) + ˛2k+1 sin(2(2k + 1) × 50t + ϕ2k+1 ) + . . .]
0.03 ≤ ˛2k+1 ≤ 0.06 − ≤ ϕ2k ≤ − ≤ ϕ2k+1 ≤ k = 1, 2, . . . , 10
√
0 ≤ ϕ ≤ 2
v(t) = 2 sin(2 × 50t + ϕ)[1 + vn sin(2fn t)]
0.05 ≤ vn ≤ 0.1 8 ≤ fn ≤ 25
In real electric power systems, the PQ disturbances also contain noise; therefore, the proposed approach must be analyzed under noisy conditions. Gaussian white noise is commonly considered in studies of PQ issues [14,15]. In this paper, in order to test the per-
formance of the proposed approach under noisy conditions, noisy signals are generated for all 16 classes by adding different levels of noise with signal to noise ratio values of 30, 40 and 50 dB.
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
1559
Table 6 Mathematical models and waveforms of combined PQ disturbances. Disturbance type
Equations
Controlling parameters 0.1 ≤ vn ≤ 0.8 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
√
v(t) = 2[sin(2 × 50t + ϕ) + . . . + ˛2k sin(2(2k) × 50t + ϕ2k ) + ˛2k+1 sin(2(2k + 1) × 50t + ϕ2k+1 ) + . . .][1 + vn (u(t − Ts ) − u(t − Te ))]
− ≤ ϕ ≤ , THD ≥ 5% 0.015 ≤ ˛2k ≤ 0.03 0.03 ≤ ˛2k+1 ≤ 0.06 − ≤ ϕ2k ≤ , − ≤ ϕ2k+1 ≤ k = 1, 2, . . . , 10 1.1 ≤ vn ≤ 1.8 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
√ v(t) = 2vn [sin(2 × 50t + ϕ) + . . . + ˛2k sin(2(2k) × 50t + ϕ2k ) + ˛2k+1 sin(2(2k + 1) × 50t + ϕ2k+1 ) + . . .][u(t − Ts ) − u(t − Te )]
− ≤ ϕ ≤ , THD ≥ 5% 0.015 ≤ ˛2k ≤ 0.03 0.03 ≤ ˛2k+1 ≤ 0.06 − ≤ ϕ2k ≤ , − ≤ ϕ2k+1 ≤ k = 1, 2, . . . , 10 0.3 ≤ vnt ≤ 1, 1.1 ≤ vns ≤ 1.8 0 ≤ ϕt ≤ 2, −/4 ≤ ϕs ≤ /4
√ √ v(t) = 2 sin(2 × 50t)[ 2vnt e−˛(t−Tst ) sin(2fn (t − Tst ) + ϕt ) + √ 2vns sin(2 × 50t + ϕs )[u(t − Tss ) − u(t − Tes )]
150 ≤ ˛ ≤ 1000 Tss = T, 2T, . . . , 8T Tes − Tss = T, 2T, . . . , 9T Tst = T, 2T, . . . , (Tes − Tss ) − T 300 ≤ fn ≤ 900 0.05 ≤ vnf ≤ 0.1 8 ≤ fn ≤ 25
√
√
v(t) = 2 sin(2 × 50t)[vnf sin(2fn t)] + 2vns sin(2 × 50t +
ϕ)[u(t − Ts ) − u(t − Te )]
1.1 ≤ vns ≤ 1.8 −/4 ≤ ϕ ≤ /4 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T 0.1 ≤ vn ≤ 0.9 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
√ v(t) = 2[sin(2 × 50t + ϕ) + . . . + ˛2k sin(2(2k) × 50t + ϕ2k ) + ˛2k+1 sin(2(2k + 1) × 50t + ϕ2k+1 ) + . . .][1 − vn (u(t − Ts ) − u(t − Te ))]
− ≤ ϕ ≤ , THD ≥ 5% 0.015 ≤ ˛2k ≤ 0.03 0.03 ≤ ˛2k+1 ≤ 0.06 − ≤ ϕ2k ≤ , − ≤ ϕ2k+1 ≤ k = 1, 2, . . . , 10 0.1 ≤ vn ≤ 0.9 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
√
v(t) = 2vn [sin(2 × 50t + ϕ) + . . . + ˛2k sin(2(2k) × 50t + ϕ2k ) +
˛2k+1 sin(2(2k + 1) × 50t + ϕ2k+1 ) + . . .][u(t − Ts ) − u(t − Te )]
− ≤ ϕ ≤ , THD ≥ 5% 0.015 ≤ ˛2k ≤ 0.03 0.03 ≤ ˛2k+1 ≤ 0.06 − ≤ ϕ2k ≤ , − ≤ ϕ2k+1 ≤ k = 1, 2, . . . , 10 0.3 ≤ vnt ≤ 1, 0.1 ≤ vns ≤ 0.9 0 ≤ ϕt ≤ 2, −/4 ≤ ϕs ≤ /4
√ √ v(t) = 2 sin(2 × 50t)[ 2vnt e−˛(t−Tst ) sin(2fn (t − Tst ) + ϕt ) + √ 2vns sin(2 × 50t + ϕs )[u(t − Tss ) − u(t − Tes )]
150 ≤ ˛ ≤ 1000 Tss = T, 2T, . . . , 8T Tes − Tss = T, 2T, . . . , 9T Tst = T, 2T, . . . , (Tes − Tss ) − T 300 ≤ fn ≤ 900 0.05 ≤ vnf ≤ 0.1 8 ≤ fn ≤ 25
√ √ v(t) = 2 sin(2 × 50t)[vnf sin(2fn t)] + 2vns sin(2 × 50t + ϕ)[u(t − Ts ) − u(t − Te )]
0.1 ≤ vns ≤ 0.9 −/4 ≤ ϕ ≤ /4 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
1560
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
Table 7 Classification results for the single PQ disturbances using the proposed approach. Correct identification rate (%)
Correct identification rate (%) under different levels of noises
Type of PQ disturbances
No noise is added to the PQ disturbances waveforms
SNR = 50 dB
SNR = 40 dB
SNR = 30 dB
Impulse Interruption Swell Sag Notch Transient Harmonic Flicker Average
95 100 100 100 100 98.5 97.5 97 98.5
93.5 100 100 100 99.5 97 97 97 98
91 100 99.5 100 99 95 94.5 96 96.875
80.5 100 89.5 99.5 99.5 94 96 90 93.625
Table 8 Classification results for the combined PQ disturbances using the proposed approach.
Type of PQ disturbances
Correct identification rate (%) No noise is added to the PQ disturbances waveforms
Correct identification rate (%) under different levels of noises SNR = 50 dB SNR = 40 dB SNR = 30 dB
Harmonic with Swell Swell with Harmonic Swell with Transient Flicker with Swell Harmonic with Sag Sag with Harmonic Sag with Transient Flicker with Sag Average
90.5 95.5 100 100 98 90 100 100 96.75
89.5 95.5 99 99.5 97.5 90 100 100 96.375
5.2. Detection and classification results for single disturbances The proposed approach presented in Section 4.2 was implemented and the percentage of correct identification cases was determined for each type of single disturbance. Table 7 shows the results. When no noise is added to these signals, the proposed algorithm can identify all desired single disturbances with 0% error, except the impulse, transient, harmonic and flicker disturbances. The detection errors of impulse, transient, harmonic and flicker disturbances are 5%, 1.5%, 2.5% and 3%, respectively, as explained below. The fuzzy system for disturbance classification may sometimes classify harmonic disturbance waveforms as a voltage notch disturbance. This classification error is due to the similar features between these types of disturbances. Also, the fuzzy system sometimes mistakenly identifies some cycles of flicker disturbances as sag or swell disturbances, too. This is because the characteristic of the fundamental component of such cycles is placed in the variation range of this feature for voltage sag or swell disturbance waveform, respectively. In some cases, the value of Vn for the waveform containing an impulse disturbance may fall within the variation range of this feature for swell disturbance; therefore the fuzzy system classifies this case as a swell disturbance rather than an impulse disturbance. The value of Nn for the waveform containing an impulse disturbance can sometimes fall within the variation range of this feature for transient disturbances in some other cases, so the fuzzy system considers such case as a transient disturbance instead of an impulse disturbance. The disturbance classification system can identify a transient disturbance only if the detection system first identifies an occurrence of a disturbance. However, in some cases, the fuzzy detection system may not detect a transient disturbance and considers it as a pure sinusoidal signal. Therefore, the correct identification rate of this type of disturbance is not equal to 100%. Additionally, Table 7 shows that the proposed approach can classify noisy single PQ disturbances with a high correct identifi-
90 96 95 100 98 90.5 98.5 100 96
87 93 66 90 96 88.5 94 99 89.1875
cation rate. It should be noted that the correct identification rate of the proposed method increases as the SNR gets bigger. 5.3. Classification and detection results of the combined disturbances In order to determine the percentage of correct identification cases for each type of combined disturbance, the method proposed in Section 4.2 is also implemented. Table 8 depicts the results. In this table, the mistaken identification cases for the combined disturbances of harmonic with swell and harmonic with sag resulted from mistaken identification of harmonic single disturbance by the fuzzy classification system. For the combined swell with harmonic and sag with harmonic disturbances in Table 8, mistaken identification occurs in some cases because the system cannot identify harmonic disturbances for this type of waveform. Because the correct identification rates for swell or sag single disturbances are 100% in Table 7, the fuzzy system for PQ disturbance detection can detect combined swell with transient and sag with transient disturbances. Therefore, classification of these disturbances by the fuzzy classification system is not prone to error. In addition, Table 8 shows that the proposed approach can effectively classify the noisy combined PQ disturbances. 6. Conclusion In this paper, a new approach to detect and classify single and combined PQ disturbances has been presented. The method uses a fuzzy system to detect disturbances, and a second fuzzy system to classify the disturbances. The inputs to these fuzzy systems are features extracted from Fourier and wavelet transforms of the voltage waveforms. The proposed approach can identify a wide range of combined and single PQ disturbances. The accuracy of the method is improved by using a PSO algorithm to specify the optimal parameters for the membership functions in these fuzzy systems. The simulation results demonstrate that the method has great capability and accuracy in correct detection and classification
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
of different types of PQ disturbances even under noisy conditions. The low computational burden and high accuracy of this method make it feasible in practical applications for the classification of PQ disturbances. References [1] H. Andami, A. Jalilian, Voltage notch detection using fuzzy expert system, IEEE Can. Conf. Electr. Comput. Eng. 1 (2003) 479–482. [2] IEEE recommended practice for monitoring electric power quality, IEEE Std. 1159–2009, 2009. [3] M. Kezunovic, Y. Liao, A novel software implementation concept for power quality study, IEEE Trans. Power Deliv. 17 (2) (2002) 544–549. [4] Y. Liao, J.B. Lee, A fuzzy-expert system for classifying power quality disturbances, Int. J. Electr. Power Energy Syst. 26 (3) (2004) 199–205. [5] A. Thapar, T.K. Saha, Z.Y. Dong, Investigation of power quality categorization and simulating it’s impact on sensitive electronic equipment, Power Eng. Soc. Gen. Meeting 1 (2004) 528–533. [6] B. Bizjak, P. Planinsic, Classification of power disturbances using fuzzy logic, Int. Conf. Power Electr. Motion Control (2006) 1356–1360. [7] G.S. Hu, J. Xie, F.F. Zhu, Classification of power quality disturbances using wavelet and fuzzy support vector machines, Int. Conf. Machine Learn. Cybern. 7 (2005) 3981–3984. [8] S. Kaewarsa, K. Attakitmongcol, T. Kulworawanichpong, Recognition of power quality events by using multiwavelet-based neural networks, Int. J. Electr. Power Energy Syst. 30 (4) (2008) 254–260. [9] T. Nguyen, Y. Liao, Power quality disturbance classification utilizing Stransform and binary feature matrix method, Int. J. Electr. Power Syst. Res. 79 (4) (2009) 569–575.
1561
[10] T.K.A. Galil, M. Kamel, A.M. Youssef, E.F.El. Saadany, M.M.A. Salama, Power quality disturbance classification using the inductive inference approach, IEEE Trans. Power Deliv. 19 (4) (2004) 1812–1818. [11] T.K.A. Galil, A.M. Youssef, E.F.El. Saadany, M.M.A. Salama, Disturbance classification using hidden Markov models and vector quantization, IEEE Trans. Power Deliv. 20 (3) (2005) 2129–2135. [12] H.Y. Zhu, S. Chen, A wavelet transform method for characterization of voltage variations, Int Conf. Power Syst. Technol. (2006) 1–7. [13] A.M. Gargoom, N. Ertugrul, W.L. Soong, Automatic classification and characterization of power quality events, IEEE Trans. Power Deliv. 23 (4) (2008) 2417–2425. [14] M. Uyar, S. Yildirim, M.T. Gencoglu, An effective wavelet-based feature extraction method for classification of power quality disturbance signals, Int. J. Electr. Power Syst. Res. 78 (10) (2008) 1747–1755. [15] B.K. Panigrahi, V.R. Pandi, Optimal feature selection for classification of power quality disturbances using wavelet packet-based fuzzy k-nearest neighbour algorithm, IET Gen. Trans. Distrib. 3 (3) (2009) 296–306. [16] S.N. Sivanandam, S. Sumathi, S.N. Deepa, Introduction to Fuzzy Logic Using Matlab, Springer, 2006. [17] MathWorks Inc., Matlab Help Files, version7.6.0.324, MathWorks, Inc., February 2008. [18] J. Kennedy, R.C. Eberhart, Particle swarm optimization, IEEE Int. Conf. Neural Netw. 4 (1995) 1942–1948. [19] R.C. Eberhart, Y. Shi, Comparison between genetic algorithms and particle swarm optimization, IEEE Int. Conf. Evol. Comput. (1998) 611–616. [20] M.S. Naidu, V. Kamaraju, High Voltage Engineering, Mc Graw Hill, 1999. [21] R. Ghandehari, A. Shoulaie, D. Habibinia, The Problems of Voltage Notch Phenomena in Power AC/DC Converters, Universities Power Engineering Conf. (UPEC’07), 2007, pp. 992–996. [22] IEC 61000-2, Electromagnetic Compatibility (EMC), sections 2 and 4, 2002.
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Detection and classification of single and combined power quality disturbances using fuzzy systems oriented by particle swarm optimization algorithm R. Hooshmand ∗ , A. Enshaee Department of Electrical Engineering, University of Isfahan, Hezar-Jerib St., Isfahan 8174673441, Iran
a r t i c l e
i n f o
Article history: Received 23 December 2009 Received in revised form 30 June 2010 Accepted 1 July 2010 Available online 31 July 2010 Keywords: Power quality Disturbances classification Fourier transform Wavelet analysis Fuzzy logic Particle swarm optimization (PSO) algorithm
a b s t r a c t In this paper, a new approach for the detection and classification of single and combined power quality (PQ) disturbances is proposed using fuzzy logic and a particle swarm optimization (PSO) algorithm. In the proposed method, suitable features of the waveform of the PQ disturbance are first extracted. These features are extracted from parameters derived from the Fourier and wavelet transforms of the signal. Then, the proposed fuzzy system classifies the type of PQ disturbances based on these features. The PSO algorithm is used to accurately determine the membership function parameters for the fuzzy systems. To test the proposed approach, the waveforms of the PQ disturbances were assumed to be in the sampled form. The impulse, interruption, swell, sag, notch, transient, harmonic, and flicker are considered as single disturbances for the voltage signal. In addition, eight possible combinations of single disturbances are considered as the PQ combined types. The capability of the proposed approach to identify these PQ disturbances is also investigated, when white Gaussian noise, with various signal to noise ratio (SNR) values, is added to the waveforms. The simulation results show that the average rate of correct identification is about 96% for different single and combined PQ disturbances under noisy conditions. © 2010 Elsevier B.V. All rights reserved.
1. Introduction The increasing growth in the use of sensitive loads by customers and the demand for high quality electricity have drawn special attention to the causes, effects, and solutions of PQ problems. By providing and installing various types of power quality monitoring equipment in the distribution systems, electric power utilities try to ensure a high quality of service. In most cases, analysis to identify the type of PQ disturbances requires large quantities of data to be collected by this equipment. This requires fast and efficient methods that can be implemented in hardware or software implementation to detect and classify the PQ disturbances [1]. Most single type PQ disturbances can be described as a voltage impulse, interruption, swell, sag, notch, transient, harmonic, or flicker in the distribution systems [2]. The major factors that contribute to the occurrence of these disturbances include the starting of large electric motors, switching capacitor banks, non-linear loads, arc furnace operation, the use of equipment with solid state switching devices, distribution system faults, and so forth [2]. The PQ disturbances include a wide range of events. The discrete Fourier transform is often used for the signal processing of low frequency PQ disturbances such as flicker, but it is more appropri-
∗ Corresponding author. Tel.: +98 311 7934073; fax: +98 311 7933071. E-mail addresses: Hooshmand [email protected] (R. Hooshmand), [email protected] (A. Enshaee). 0378-7796/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2010.07.001
ate to employ wavelet transform for the signal processing of high frequency PQ disturbances such as transients [3–8]. Some prior researchers have used these two techniques to extract suitable features of the PQ disturbance waveforms, simplifying the identification and classification of these disturbances [3–7]. In most papers, fuzzy rules are used to make decisions regarding the occurrence and classification of the type of the disturbance [3–6]. In these methods, the large number of inputs to the fuzzy system increases the correct identification rate of the disturbances, but also increases the method complexity and decreases its speed [3,4]. In references [5–7], the fuzzy system complexity for the classification of disturbances is reduced to some extent, and the correct identification rate is not significantly changed compared with references [3,4]. However, no attention has been paid to the detection of combined PQ disturbances. Furthermore, it seems that determining the parameters of the membership functions for the fuzzy systems is only performed based on human reasoning, and the correct identification rate is increased through trial-and-error modification of these parameters. Therefore, there has been no guarantee of optimality for these parameters in the prior research. Of course, other different methods have also been presented for the detection and classification of PQ disturbances [8–15]. Some of these methods have good performance under noisy conditions [14,15]. However, these methods either do not consider [8,11–13] or only consider a few numbers [9,10,14,15] of combined disturbances. In this paper, a new method is proposed for the detection and classification of single and combined PQ disturbances using two
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
fuzzy systems oriented with a PSO algorithm. The first fuzzy system is employed for detection and the other system is used to classify PQ disturbances. The PSO algorithm is used to provide optimized values for the parameters of the membership functions of these systems. The features extracted from the windowed discrete Fourier transform (WDFT) and wavelet transform of the waveforms of the disturbances form the inputs of these systems. The number and type of the inputs are selected to prevent the complexity of this input set. In addition, the rule base of these systems is established to achieve high accuracy in the detection and classification of single and combined PQ disturbances. It should be noted that all single types of PQ disturbances mentioned in second paragraph of this section can be detected in the proposed approach. Harmonic with swell, swell with harmonic, swell with transient, flicker with swell, harmonic with sag, sag with harmonic, sag with transient and flicker with sag are also considered as the combined disturbances of the voltage signal. Furthermore, to show the effectiveness of the proposed method, its sensitivity to noise is tested under different noisy conditions. The paper is organized as follow: first, the method of extraction of suitable features from the waveform of disturbances is presented. Then, the process of designing the fuzzy systems is described in Section 3. In Section 4, the application of the PSO algorithm in the proposed fuzzy systems is explained. In Section 5, simulation results are presented to demonstrate the capability of the proposed algorithm to correctly identify PQ disturbances. Finally, conclusions are discussed in Section 6. 2. Feature extraction from the waveform of disturbances In this section, in order to detect and classify the PQ disturbances, eight features extracted from the waveform of these disturbances, are introduced [3–7]. 2.1. Fundamental component (Vn ) This feature calculates the fundamental component of the signal in each cycle, which is given by [3–7,9] √ (1) Vn = 2abs(V n [1])/N where Vn [k] is a complex value denoting the discrete frequency content for the samples contained in the nth data window of the sampled signal and is written as [3–7,9]: n
V [k] =
N−1
v[i + (n − 1)N]e
−j(2ki/N)
(2)
In this equation, v[i] covers 10 cycles of the sampled signal with a sampling rate of 256 points per cycle. Therefore, the length of the v[i] shall be equal to 2560; k = 0, 1,. . .,N − 1; and the parameter N is the number of the samples in one data window. Because the data window length is equal to one cycle, N shall be equal to 256. Also, the parameter j is the imaginary unit and n = 1, 2,. . .,10 is the index of the data window. Because the aim of Eq. (1) is the calculation of the fundamental component of the nth data window of the sampled signal, k is taken to be equal to 1 in Eq. (2). 2.2. Phase angle shift (PSn ) This feature calculates the angle difference between discrete Fourier transform for the nth cycle and the first cycle of the sampled signal for its fundamental component. Therefore
where angle(.) returns the phase angle of the input argument.
2.3. Total harmonic distortion (THDn ) This quantity is defined as the ratio of the square root of the total squared magnitude of each harmonic component of the distorted waveform to the fundamental component of that waveform. So,
int(N/2) 2 {abs(V n [k])} k=2
THDn =
abs(V 1 [1])
(4)
In this equation, abs(.) gives the absolute value of the argument. Also, int(N/2) equals N/2 if N is even and equals (N − 1)/2 if N is odd. 2.4. Number of maximums of the absolute value of wavelet coefficients (Nn ) This feature is defined as follows: Nn = max(abs(WCn ))
(5)
WCn
where the matrix includes the third scale wavelet detail coefficients resulting from the analysis of the nth cycle of the sampled signal. Also, the max(.) function returns the number of maximums of the argument, and if the maximum value is less than 0.1, it can be neglected. After reviewing simulation results, it was found that the fourthorder Daubechies wavelet (Db4) yields the best performance for detection and classification of PQ disturbances using the proposed approach. Thus, the fourth-order Daubechies wavelet was chosen as the mother wavelet for this analysis. In general, Daubechies wavelet filters are widely used in terms of shorter filter lengths, and thus fast computation times, for real-time applications such as PQ issues [3–5,14,15]. 2.5. Energy of the wavelet coefficients (EWn ) This feature considers the total absolute value of the WCn matrix components. This is called the energy of the wavelet coefficients. It is computed by EWn =
le
abs(WCn [k])
(6)
k=1
where le is the length of WCn .
i=0
PSn = angle(V n [1]) − angle(V 1 [1])
1553
(3)
2.6. Number of zero-crossings of the missing voltage (OSn ) This feature is determined by counting the number of zerocrossings of the missing voltage waveform. This waveform is obtained by computing the difference between the disturbance and a pure sinusoidal waveform. This feature denotes the rate at which the disturbance voltage waveform separates from ideal sinusoidal voltage waveform. Therefore, OSn = root(vsmiss )
(7)
In this equation, the root(.) function calculates the number of zero-crossing points of the argument. Also, vsmiss is defined as an array consisting of vmiss [i], i = 0, 1,. . .,N − 1. The terms of vmiss [i] are calculated by
vmiss [i]=v[i] − 2/N × abs(V 1 [1]) × cos{angle(V 1 [1]) + 2(i − 1)/N} (8)
1554
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
2.7. Lower harmonic distortion (TSn ) This feature is similar to the total harmonic distortion (THDn ) feature, but in this calculation, only components up to 10th order are used. So,
10 {abs(V n [k])}2
TSn =
Fig. 1. The schematic representation of the fuzzy system for the detection of PQ disturbances.
k=2
(9)
abs(V 1 [1])
3. The proposed fuzzy systems
2.8. Number of peaks of rms value (RN) This feature is defined as s ) RN = peak(Vrms
(10)
In this equation, the peak(.) function returns the number of significant variations (increasing or decreasing) of the argument s n is defined as an array consisting of Vrms where n = 1, and Vrms n is also the rms value of nth cycle of the 2,. . .,10. The term Vrms sampled signal obtained from the following equation: n Vrms
N−1 1 = v2 [i + (n − 1)N] N
(11)
i=0
It should be noted that for most PQ disturbances, the rms value of the starting and ending cycles of the disturbance will be significantly different from the rms value of cycles that are before and after them, respectively. Observations show that the number of these variations depends on the type of the disturbance. So, the RN feature can help to classify these disturbances by counting the number of variations. This issue will be discussed in detail in Section 3.3. Employing the windowed discrete Fourier transform to compute Vn , PSn , THDn , OSn and TSn possibly decreases the correct identification rate of PQ disturbances under noisy conditions. Instead, selecting the fourth-order Daubechies wavelet, and third level decomposition for the computation of Nn and EWn , enables the proposed approach to classify noisy PQ disturbances with high accuracy using the above features. Of course, proper establishment of the rule base, presented in Section 3.2, also helps the proposed system to perform acceptably.
The two following fuzzy systems are designed for detection and classification of the PQ disturbances. The overall structures of these two systems are depicted in Figs. 1 and 2. As illustrated in these figures, the components of the two fuzzy systems are described in the next subsections. Then, the interaction process between the two systems for the detection and classification of single and combined PQ disturbances is presented. 3.1. Inputs, outputs, and their membership functions 3.1.1. Fuzzy system for disturbance detection The inputs of this system are the following features: THDn , PSn and Vn . The output is the “Disturb” variable, which shows the occurrence or non-occurrence of a disturbance by taking the values one or zero, respectively. The membership functions (MFs) of each input to this system, along with the selected parameters, are indicated in Table 1. 3.1.2. Fuzzy system for disturbance classification The inputs of this system are the following features: Vn , THDn , THDn+1 , PSn , EWn , Nn , Nn−1 , Nn+1 , OSn , TSn and TSn+1 . The outputs of the system are the following variables: “Impulse”, “Interruption”, “Swell”, “Sag”, “Notch”, “Transient”, and “Harmonic”. When each output takes a non-zero value, this indicates a detection of that disturbance, as will be explained in Section 3.3. Also, the membership functions of each input of this system along with the selected parameters are given in Table 2. It should be noted that determination of membership function parameters of these systems using the PSO algorithm will be presented in Section 4.2.
Fig. 2. The schematic representation of the fuzzy system for the classification of PQ disturbances.
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
1555
Table 1 The membership function of fuzzy system inputs for the disturbance detection. Labels
Range
Membership function labels
Membership function types
Membership function parameters
THDn PSn Vn
[0,1] [0,180] [−0.01, 2.5]
A1 B1 C1 C2
Trapezoidal Trapezoidal Trapezoidal
[0.038 0.04 1.1 1.2] [0.8 1 180 190] [−0.18 −0.02 0.98 1] [1 1.02 2.6 2.7]
Table 2 The membership function of fuzzy system inputs for the disturbance classification. Labels
Range
Membership function labels
Membership function types
Membership Function Parameters
Vn
[0,2]
Trapezoidal
THDn , THDn+1
[0,1]
PSn
[−3,180]
EWn Nn−1 , Nn , Nn+1
[0,4] [−1,30]
OSn TSn , TSn+1
[0,100] [0,1]
A1 A2 A3 A4 A5 B1 B2 C1 C2 D1 F1 F2 F3 G1 H1 H2 H3
[−0.18 −0.02 0.097 0.1] [0.103 0.11 0.89 0.9] [0.94 0.96 1.01 1.03] [0.997 1 1.09 1.11] [1.1 1.12 2.1 2.2] [−0.2 −0.1 0.048 0.05] [0.048 0.05 1.1 1.2] [−3.8 −3 4.8 5.5] [4.8 5.5 181 182] [0.58 0.829 3 3.2] [−1.8 −1 3 3.3] [3.7 4 6 6.3] [672930] [7.8 8.2 104 105] [−0.18 −0.02 0.018 0.021] [−0.18 −0.02 0.038 0.041] [0.038 0.041 1.1 1.2]
Trapezoidal Trapezoidal Trapezoidal Trapezoidal
Trapezoidal Trapezoidal
3.2. Rule base in the systems
3.3. Operational mechanism in the fuzzy systems
The establishment of a more accurate rule base for these two fuzzy systems increases the detection capability for more various cases of PQ disturbances. These rules have the advantage of expert knowledge.
To make a decision regarding the occurrence of disturbance, the features of THDn , PSn and Vn for each of the cycles of the desired waveform are calculated and considered as fuzzy system inputs for PQ disturbance detection. Based on these inputs, this fuzzy system specifies whether there has been any disturbance during the associated cycle. If the response is “Negative”, the above process is repeated for the next cycle; otherwise, a disturbance has been detected and its type should be identified. At this stage, the RN feature of the desired waveform is calculated. If the value of this parameter is more than four, the disturbance is defined as a flicker. In the event of a single PQ disturbance such as impulse, interruption, swell, sag or transient, we will have two significant variations in the rms values of the disturbance waveforms: one at the start and the other at the end of the disturbance. Therefore, the value of the RN feature will be equal to two for these disturbances. In a similar way, it can be found that the maximum value of the RN feature will be equal to four for combined PQ disturbances. Simulation results show that the value of the RN feature will be more than four, only if a flicker disturbance occurs. Let the starting cycle of the disturbance be denoted by index “n”, and the cycles that are before and after this cycle be denoted by “n − 1” and “n + 1” indices, respectively. Thus, the features of Vn , THDn , THDn+1 , PSn , EWn , Nn , Nn−1 , Nn+1 , OSn , TSn and TSn+1 can be extracted from the desired waveform. By implementing these features in the fuzzy system for PQ disturbance classification, the outputs of this system take zero or non-zero values, where the one with the largest non-zero value indicates the type of disturbance. If several outputs have the same largest non-zero value, all of them are considered to describe the type of disturbance detected. Fig. 3 shows the interaction mechanism between the two fuzzy systems for decision making on the occurrence and identification of the disturbance type.
3.2.1. Fuzzy system for disturbance detection Table 3 presents the rule base of this system; e.g., the first rule extracted from this table is as follows: Rule 1: if (THDn is A1 or PSn is B1 or Vn is C2 ) then Disturb = 1where setting the “Disturb” variable to one indicates the occurrence of a disturbance and setting it to zero indicates the non-occurrence of a disturbance. 3.2.2. Fuzzy system for disturbance classification Table 4 presents the rule base of this system; e.g., the first rule extracted from this table is as follows: Rule 1: if (Vn is A4 and PSn is C1 and EWn is D1 and Nn−1 is F1 and Nn is F2 and Nn+1 is F1 ) then Impulse = 1where setting “Impulse” to one indicates the occurrence of an impulse disturbance, and setting it to zero indicates non-occurrence of an Impulse disturbance. It should be noted that the fuzzy inference engine in these two fuzzy systems are of the Sugeno type, because this type of engine is very suitable for modelling expert reasoning [16]. Due to its simplicity, the “Max” and “Min” functions are employed for fuzzy operators of union (OR) and common (AND), respectively [17]. The weighted sum (wtsum) method, which is the best defuzzification method, is selected for the defuzzification process [16].
Table 3 The rule base in the fuzzy system for the disturbance detection.
Rule 1 Rule 2
Inputs THDn
PSn
Vn
Outputs Disturb
4. Proposed fuzzy systems oriented by PSO algorithm
A1 –
B1 –
C2 C1
1 1
One of the main problems in designing the fuzzy systems presented in the previous section was to determine the membership
1556
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
Table 4 The rule base in the fuzzy system for the disturbance classification.
Rule 1 Rule 2 Rule 3 Rule 4 Rule 5 Rule 6 Rule 7 Rule 8 Rule 9 Rule 10 Rule 11 Rule 12
Inputs THDn Vn
THDn+1
PSn
EWn
Nn−1
Nn
Nn+1
OSn
TSn
TSn+1
Outputs Impulse
Interruption
Swell
Sag
Notch
Transient
Harmonic
A4 A1 A5 A5 A5 A2 A2 A2 A3 – – –
– – – – – – – – B2 B1 B1 B2
C1 – – C2 – – C2 – C1 – – –
D1 – – – D1 – – D1 – – – –
F1 – – – – – – – – F1 F1 –
F2 – – – – – – – F3 F3 F3 –
F1 – – – – – – – F3 F1 F1 –
– – – – – – – – G1 – – –
– H1 – – H1 – – H1 H2 – – H3
– – – – – – – – H2 H1 H1 H3
1 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0
0 0 0 0 0 1 1 1 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 1 1 0
0 0 0 0 0 0 0 0 0 0 0 1
– B1 – – – – – – B2 B1 B2 B2
functions parameters of the input variables. Accurate determination of the value of these parameters has an important role in the correct operation of the proposed algorithm for the identifying the type of disturbance. The PSO algorithm has been employed to accurately determine the membership function parameters mentioned in Tables 1 and 2. In this section, first a brief review of the PSO algorithm is presented. Then, the application of this algorithm to the proposed fuzzy systems for PQ disturbance detection and classification is described. 4.1. A review of PSO algorithm The PSO algorithm was introduced in 1995 by Eberhart and Kennedy [18], and is a type of group-based evolutionary algorithm. Like other group-based evolutionary algorithms, it starts with an initial group consisting of “n” particles (potential solutions to the optimization problem) in a multi-dimensional search space. It is evident that some of the particles have better positions than the others. The particles change their positions in this space until they encounter one of the stop-criteria of the algorithm. These criteria can include reaching an optimal state or ending the number of specific repetitions in the algorithm. For each iteration, the position of each particle is changed based on knowledge of the particle’s previous movements and knowledge of the neighbouring particles. In fact, each particle is aware of its best previous position and the best position among all particles. For each iteration, the velocity vector of the ith particle is updated according to Eq. (12):
vi (t + 1) = wvi (t) + c1 r1 (Pbesti (t) − xi (t)) + c2 r2 (Gbest(t) − xi (t)) (12)
In this equation, w is the inertia weight factor, vi (t) is the previous velocity of the particle, vi (t + 1) is the present velocity of the particle, c1 and c2 are weighting acceleration constants, Pbesti is the best position that a particle of the group has achieved up to now, and Gbest is the best position that a whole group has achieved up to now. r1 and r2 are random numbers with uniform distribution in the range [0–1], with values produced for each particle in each iteration. It should be noted that w > 0 is a factor that controls the effect of vi (t) in vi (t + 1). Also, c1 > 0 and c2 > 0 make the particle move toward Pbesti and Gbest, respectively. The values of c1 and c2 are usually equal and selected in a way that c1 + c2 ≤ 4. After the velocity of the ith particle is updated, the particle moves toward its new position (xi (t + 1)) from its present position (xi (t)) by Eq. (13): Fig. 3. The proposed algorithm for detection and classification of PQ disturbances.
xi (t + 1) = xi (t) + vi (t + 1)
(13)
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
1557
Fig. 4. The flowchart of the implementation of the PSO algorithm to determine the membership function parameters.
Then, the objective function (f) is evaluated at the new position of the ith particle. If the minimization of the objective function is the aim of optimization, then Pbesti and Gbest are updated by Eqs. (14) and (15), respectively.
Pbesti (t + 1) =
Pbesti (t)
if f (Pbesti (t)) ≤ f (xi (t + 1))
xi (t + 1)
if f (Pbesti (t)) > f (xi (t + 1))
Gbest(t + 1) ∈ {Pbest1 (t + 1), . . . , Pbestn (t + 1)}| f (Gbest(t + 1)) = min{f (Pbest1 (t + 1)), . . . , f (Pbestn (t + 1))}
(14)
(15)
The term vi in Eq. (12) lies in the range of (−vmax , vmax ) to reduce the probability that the particle exits from the search space. In many experiences with PSO, vmax is set at a typical value of 10–20% of (xmax − xmin ). It should be noted that if too high a value is chosen for vmax , particles may fly past good positions and if vmax is set at too small values, particles may not explore sufficiently beyond local positions [19]. On the other hand, suitable selection of w allows the algorithm to converge to the optimal point in less iteration. In the conventional PSO algorithm, the w factor is reduced from the value of 0.9 to 0.4 during the iteration of the algorithm based on the following equation: w = wmax −
wmax − wmin ×k kmax
Fig. 5. The flowchart of the calculation of the mistaken identification rate for each disturbance using the Fuzzy–PSO algorithm.
known collection of waveforms of each single disturbance type (impulse, interruption, swell, sag, notch, transient or harmonic). It is expected that an acceptable rate for correct identification will be achieved for any other unknown collection of disturbance waveforms. The flowchart of the calculation of the mistaken identification rate for 200 cases of each disturbance is depicted in Fig. 5. This figure is a combination of the flowcharts presented in Figs. 3 and 4. 5. Simulation results
(16)
where kmax is the maximum number of iterations and k is the present iteration number. 4.2. The application of the PSO algorithm to the proposed fuzzy systems To accurately determine the parameters of the membership functions for the inputs to the proposed fuzzy systems, the PSO algorithm is employed. To specify the variation intervals of these parameters, we first need to obtain the variation range for each feature describing the waveform of each type of disturbance. Then, the variation range of the membership function parameters for each rule is specified by analyzing the variation range of these features. Fig. 4 shows the flowchart of the implementation of the PSO algorithm to determine the parameters of the membership functions used to identify each disturbance. As illustrated, the PSO algorithm varies the membership function parameters until the mistaken identification rate is minimized for a
5.1. Initial data In order to investigate the fuzzy systems for detection and classification of PQ disturbances, 200 cases of each desired disturbance are produced. These disturbances are generated using ‘MATLAB’ software, and each waveform is based on the models presented in Tables 5 and 6, where the controlling parameters in these models are determined randomly. These models represent mathematical relations adapted to different types of disturbances present in the distribution systems. In this set of disturbances, the impulse disturbance is generated using the model presented in reference [20] for a 100/1000 s voltage impulse waveform. The voltage notch disturbance was generated based on the normal operation of a three-phase, full-bridge thyristor-based rectifier [21]. For the harmonic disturbance, the presence of at least three frequency components is required; one is the fundamental component and the two others are harmonic components. The rms values of the harmonic components and the total harmonic distortion of this waveform are also selected according to reference [22].
1558
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
Table 5 Mathematical models and waveforms of single PQ disturbances [10,11,20–22]. Disturbance type Pure sinusoidal
Equations √ v(t) = 2 sin(2 × 50t + ϕ)
Controlling parameters − ≤ ϕ ≤
0.2 ≤ vp ≤ 1 2 (t−T ) s
v(t) = 1.11vp (e−7.5×10
2 (t−T ) s )(u(t
− e−3.44×10
− Ts ) − u(t − Te ))
T ≤ Ts ≤ 7T Te = Ts + 1 ms
0 ≤ vn ≤ 0.1 √
v(t) = 2vn sin(2 × 50t + ϕ)[u(t − Ts ) − u(t − Te )]
−/4 ≤ ϕ ≤ /4 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
1.1 ≤ vn ≤ 1.8 √
v(t) = 2vn sin(2 × 50t + ϕ)[u(t − Ts ) − u(t − Te )]
−/4 ≤ ϕ ≤ /4 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
0.1 ≤ vn ≤ 0.9 √
v(t) = 2vn sin(2 × 50t + ϕ)[u(t − Ts ) − u(t − Te )]
−/4 ≤ ϕ ≤ /4 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
v(t) =
⎧√ ⎪ 2[sin(ωt + ) + 0.5 ⎪ 6 ⎪ ⎪ √ ⎨ 2[sin(ωt + ) − 0.5
sin(ωt +
5 )] 6
cos(ωt)] 6 √ ⎪ 2[sin(ωt + ) − sin(ωt + )] ⎪ 6 6 ⎪ ⎪ ⎩ √2 sin(ωt + ) 6
k = 1, 7 k = 3, 9 k = 5, 11 otherwise
ω = 2 × 50, = 0.5 0 ≤ ˛ ≤ /2, < ˛ 36500 × 2/20, 000 √ 2 × 460 sin(˛) k k ωt ∈ [˛ + ,˛ + + ] 6 6
=
0.3 ≤ vn ≤ 1 √
√
v(t) = 2 sin(2 × 50t)[1 + 2vn e−˛(t−Ts ) sin(2fn (t − Ts ) + ϕ)]
150 ≤ ˛ ≤ 1000 Ts = T, 2T, . . . , 7T 300 ≤ fn ≤ 900 0 ≤ ϕ ≤ 2 − ≤ ϕ ≤ , THD ≥ 5% 0.015 ≤ ˛2k ≤ 0.03
√
v(t) = 2[sin(2 × 50t + ϕ) + . . . + ˛2k sin(2(2k) × 50t + ϕ2k ) + ˛2k+1 sin(2(2k + 1) × 50t + ϕ2k+1 ) + . . .]
0.03 ≤ ˛2k+1 ≤ 0.06 − ≤ ϕ2k ≤ − ≤ ϕ2k+1 ≤ k = 1, 2, . . . , 10
√
0 ≤ ϕ ≤ 2
v(t) = 2 sin(2 × 50t + ϕ)[1 + vn sin(2fn t)]
0.05 ≤ vn ≤ 0.1 8 ≤ fn ≤ 25
In real electric power systems, the PQ disturbances also contain noise; therefore, the proposed approach must be analyzed under noisy conditions. Gaussian white noise is commonly considered in studies of PQ issues [14,15]. In this paper, in order to test the per-
formance of the proposed approach under noisy conditions, noisy signals are generated for all 16 classes by adding different levels of noise with signal to noise ratio values of 30, 40 and 50 dB.
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
1559
Table 6 Mathematical models and waveforms of combined PQ disturbances. Disturbance type
Equations
Controlling parameters 0.1 ≤ vn ≤ 0.8 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
√
v(t) = 2[sin(2 × 50t + ϕ) + . . . + ˛2k sin(2(2k) × 50t + ϕ2k ) + ˛2k+1 sin(2(2k + 1) × 50t + ϕ2k+1 ) + . . .][1 + vn (u(t − Ts ) − u(t − Te ))]
− ≤ ϕ ≤ , THD ≥ 5% 0.015 ≤ ˛2k ≤ 0.03 0.03 ≤ ˛2k+1 ≤ 0.06 − ≤ ϕ2k ≤ , − ≤ ϕ2k+1 ≤ k = 1, 2, . . . , 10 1.1 ≤ vn ≤ 1.8 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
√ v(t) = 2vn [sin(2 × 50t + ϕ) + . . . + ˛2k sin(2(2k) × 50t + ϕ2k ) + ˛2k+1 sin(2(2k + 1) × 50t + ϕ2k+1 ) + . . .][u(t − Ts ) − u(t − Te )]
− ≤ ϕ ≤ , THD ≥ 5% 0.015 ≤ ˛2k ≤ 0.03 0.03 ≤ ˛2k+1 ≤ 0.06 − ≤ ϕ2k ≤ , − ≤ ϕ2k+1 ≤ k = 1, 2, . . . , 10 0.3 ≤ vnt ≤ 1, 1.1 ≤ vns ≤ 1.8 0 ≤ ϕt ≤ 2, −/4 ≤ ϕs ≤ /4
√ √ v(t) = 2 sin(2 × 50t)[ 2vnt e−˛(t−Tst ) sin(2fn (t − Tst ) + ϕt ) + √ 2vns sin(2 × 50t + ϕs )[u(t − Tss ) − u(t − Tes )]
150 ≤ ˛ ≤ 1000 Tss = T, 2T, . . . , 8T Tes − Tss = T, 2T, . . . , 9T Tst = T, 2T, . . . , (Tes − Tss ) − T 300 ≤ fn ≤ 900 0.05 ≤ vnf ≤ 0.1 8 ≤ fn ≤ 25
√
√
v(t) = 2 sin(2 × 50t)[vnf sin(2fn t)] + 2vns sin(2 × 50t +
ϕ)[u(t − Ts ) − u(t − Te )]
1.1 ≤ vns ≤ 1.8 −/4 ≤ ϕ ≤ /4 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T 0.1 ≤ vn ≤ 0.9 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
√ v(t) = 2[sin(2 × 50t + ϕ) + . . . + ˛2k sin(2(2k) × 50t + ϕ2k ) + ˛2k+1 sin(2(2k + 1) × 50t + ϕ2k+1 ) + . . .][1 − vn (u(t − Ts ) − u(t − Te ))]
− ≤ ϕ ≤ , THD ≥ 5% 0.015 ≤ ˛2k ≤ 0.03 0.03 ≤ ˛2k+1 ≤ 0.06 − ≤ ϕ2k ≤ , − ≤ ϕ2k+1 ≤ k = 1, 2, . . . , 10 0.1 ≤ vn ≤ 0.9 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
√
v(t) = 2vn [sin(2 × 50t + ϕ) + . . . + ˛2k sin(2(2k) × 50t + ϕ2k ) +
˛2k+1 sin(2(2k + 1) × 50t + ϕ2k+1 ) + . . .][u(t − Ts ) − u(t − Te )]
− ≤ ϕ ≤ , THD ≥ 5% 0.015 ≤ ˛2k ≤ 0.03 0.03 ≤ ˛2k+1 ≤ 0.06 − ≤ ϕ2k ≤ , − ≤ ϕ2k+1 ≤ k = 1, 2, . . . , 10 0.3 ≤ vnt ≤ 1, 0.1 ≤ vns ≤ 0.9 0 ≤ ϕt ≤ 2, −/4 ≤ ϕs ≤ /4
√ √ v(t) = 2 sin(2 × 50t)[ 2vnt e−˛(t−Tst ) sin(2fn (t − Tst ) + ϕt ) + √ 2vns sin(2 × 50t + ϕs )[u(t − Tss ) − u(t − Tes )]
150 ≤ ˛ ≤ 1000 Tss = T, 2T, . . . , 8T Tes − Tss = T, 2T, . . . , 9T Tst = T, 2T, . . . , (Tes − Tss ) − T 300 ≤ fn ≤ 900 0.05 ≤ vnf ≤ 0.1 8 ≤ fn ≤ 25
√ √ v(t) = 2 sin(2 × 50t)[vnf sin(2fn t)] + 2vns sin(2 × 50t + ϕ)[u(t − Ts ) − u(t − Te )]
0.1 ≤ vns ≤ 0.9 −/4 ≤ ϕ ≤ /4 Ts = T, 2T, . . . , 8T Te − Ts = T, 2T, . . . , 9T
1560
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
Table 7 Classification results for the single PQ disturbances using the proposed approach. Correct identification rate (%)
Correct identification rate (%) under different levels of noises
Type of PQ disturbances
No noise is added to the PQ disturbances waveforms
SNR = 50 dB
SNR = 40 dB
SNR = 30 dB
Impulse Interruption Swell Sag Notch Transient Harmonic Flicker Average
95 100 100 100 100 98.5 97.5 97 98.5
93.5 100 100 100 99.5 97 97 97 98
91 100 99.5 100 99 95 94.5 96 96.875
80.5 100 89.5 99.5 99.5 94 96 90 93.625
Table 8 Classification results for the combined PQ disturbances using the proposed approach.
Type of PQ disturbances
Correct identification rate (%) No noise is added to the PQ disturbances waveforms
Correct identification rate (%) under different levels of noises SNR = 50 dB SNR = 40 dB SNR = 30 dB
Harmonic with Swell Swell with Harmonic Swell with Transient Flicker with Swell Harmonic with Sag Sag with Harmonic Sag with Transient Flicker with Sag Average
90.5 95.5 100 100 98 90 100 100 96.75
89.5 95.5 99 99.5 97.5 90 100 100 96.375
5.2. Detection and classification results for single disturbances The proposed approach presented in Section 4.2 was implemented and the percentage of correct identification cases was determined for each type of single disturbance. Table 7 shows the results. When no noise is added to these signals, the proposed algorithm can identify all desired single disturbances with 0% error, except the impulse, transient, harmonic and flicker disturbances. The detection errors of impulse, transient, harmonic and flicker disturbances are 5%, 1.5%, 2.5% and 3%, respectively, as explained below. The fuzzy system for disturbance classification may sometimes classify harmonic disturbance waveforms as a voltage notch disturbance. This classification error is due to the similar features between these types of disturbances. Also, the fuzzy system sometimes mistakenly identifies some cycles of flicker disturbances as sag or swell disturbances, too. This is because the characteristic of the fundamental component of such cycles is placed in the variation range of this feature for voltage sag or swell disturbance waveform, respectively. In some cases, the value of Vn for the waveform containing an impulse disturbance may fall within the variation range of this feature for swell disturbance; therefore the fuzzy system classifies this case as a swell disturbance rather than an impulse disturbance. The value of Nn for the waveform containing an impulse disturbance can sometimes fall within the variation range of this feature for transient disturbances in some other cases, so the fuzzy system considers such case as a transient disturbance instead of an impulse disturbance. The disturbance classification system can identify a transient disturbance only if the detection system first identifies an occurrence of a disturbance. However, in some cases, the fuzzy detection system may not detect a transient disturbance and considers it as a pure sinusoidal signal. Therefore, the correct identification rate of this type of disturbance is not equal to 100%. Additionally, Table 7 shows that the proposed approach can classify noisy single PQ disturbances with a high correct identifi-
90 96 95 100 98 90.5 98.5 100 96
87 93 66 90 96 88.5 94 99 89.1875
cation rate. It should be noted that the correct identification rate of the proposed method increases as the SNR gets bigger. 5.3. Classification and detection results of the combined disturbances In order to determine the percentage of correct identification cases for each type of combined disturbance, the method proposed in Section 4.2 is also implemented. Table 8 depicts the results. In this table, the mistaken identification cases for the combined disturbances of harmonic with swell and harmonic with sag resulted from mistaken identification of harmonic single disturbance by the fuzzy classification system. For the combined swell with harmonic and sag with harmonic disturbances in Table 8, mistaken identification occurs in some cases because the system cannot identify harmonic disturbances for this type of waveform. Because the correct identification rates for swell or sag single disturbances are 100% in Table 7, the fuzzy system for PQ disturbance detection can detect combined swell with transient and sag with transient disturbances. Therefore, classification of these disturbances by the fuzzy classification system is not prone to error. In addition, Table 8 shows that the proposed approach can effectively classify the noisy combined PQ disturbances. 6. Conclusion In this paper, a new approach to detect and classify single and combined PQ disturbances has been presented. The method uses a fuzzy system to detect disturbances, and a second fuzzy system to classify the disturbances. The inputs to these fuzzy systems are features extracted from Fourier and wavelet transforms of the voltage waveforms. The proposed approach can identify a wide range of combined and single PQ disturbances. The accuracy of the method is improved by using a PSO algorithm to specify the optimal parameters for the membership functions in these fuzzy systems. The simulation results demonstrate that the method has great capability and accuracy in correct detection and classification
R. Hooshmand, A. Enshaee / Electric Power Systems Research 80 (2010) 1552–1561
of different types of PQ disturbances even under noisy conditions. The low computational burden and high accuracy of this method make it feasible in practical applications for the classification of PQ disturbances. References [1] H. Andami, A. Jalilian, Voltage notch detection using fuzzy expert system, IEEE Can. Conf. Electr. Comput. Eng. 1 (2003) 479–482. [2] IEEE recommended practice for monitoring electric power quality, IEEE Std. 1159–2009, 2009. [3] M. Kezunovic, Y. Liao, A novel software implementation concept for power quality study, IEEE Trans. Power Deliv. 17 (2) (2002) 544–549. [4] Y. Liao, J.B. Lee, A fuzzy-expert system for classifying power quality disturbances, Int. J. Electr. Power Energy Syst. 26 (3) (2004) 199–205. [5] A. Thapar, T.K. Saha, Z.Y. Dong, Investigation of power quality categorization and simulating it’s impact on sensitive electronic equipment, Power Eng. Soc. Gen. Meeting 1 (2004) 528–533. [6] B. Bizjak, P. Planinsic, Classification of power disturbances using fuzzy logic, Int. Conf. Power Electr. Motion Control (2006) 1356–1360. [7] G.S. Hu, J. Xie, F.F. Zhu, Classification of power quality disturbances using wavelet and fuzzy support vector machines, Int. Conf. Machine Learn. Cybern. 7 (2005) 3981–3984. [8] S. Kaewarsa, K. Attakitmongcol, T. Kulworawanichpong, Recognition of power quality events by using multiwavelet-based neural networks, Int. J. Electr. Power Energy Syst. 30 (4) (2008) 254–260. [9] T. Nguyen, Y. Liao, Power quality disturbance classification utilizing Stransform and binary feature matrix method, Int. J. Electr. Power Syst. Res. 79 (4) (2009) 569–575.
1561
[10] T.K.A. Galil, M. Kamel, A.M. Youssef, E.F.El. Saadany, M.M.A. Salama, Power quality disturbance classification using the inductive inference approach, IEEE Trans. Power Deliv. 19 (4) (2004) 1812–1818. [11] T.K.A. Galil, A.M. Youssef, E.F.El. Saadany, M.M.A. Salama, Disturbance classification using hidden Markov models and vector quantization, IEEE Trans. Power Deliv. 20 (3) (2005) 2129–2135. [12] H.Y. Zhu, S. Chen, A wavelet transform method for characterization of voltage variations, Int Conf. Power Syst. Technol. (2006) 1–7. [13] A.M. Gargoom, N. Ertugrul, W.L. Soong, Automatic classification and characterization of power quality events, IEEE Trans. Power Deliv. 23 (4) (2008) 2417–2425. [14] M. Uyar, S. Yildirim, M.T. Gencoglu, An effective wavelet-based feature extraction method for classification of power quality disturbance signals, Int. J. Electr. Power Syst. Res. 78 (10) (2008) 1747–1755. [15] B.K. Panigrahi, V.R. Pandi, Optimal feature selection for classification of power quality disturbances using wavelet packet-based fuzzy k-nearest neighbour algorithm, IET Gen. Trans. Distrib. 3 (3) (2009) 296–306. [16] S.N. Sivanandam, S. Sumathi, S.N. Deepa, Introduction to Fuzzy Logic Using Matlab, Springer, 2006. [17] MathWorks Inc., Matlab Help Files, version7.6.0.324, MathWorks, Inc., February 2008. [18] J. Kennedy, R.C. Eberhart, Particle swarm optimization, IEEE Int. Conf. Neural Netw. 4 (1995) 1942–1948. [19] R.C. Eberhart, Y. Shi, Comparison between genetic algorithms and particle swarm optimization, IEEE Int. Conf. Evol. Comput. (1998) 611–616. [20] M.S. Naidu, V. Kamaraju, High Voltage Engineering, Mc Graw Hill, 1999. [21] R. Ghandehari, A. Shoulaie, D. Habibinia, The Problems of Voltage Notch Phenomena in Power AC/DC Converters, Universities Power Engineering Conf. (UPEC’07), 2007, pp. 992–996. [22] IEC 61000-2, Electromagnetic Compatibility (EMC), sections 2 and 4, 2002.