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swell detection algorithm
Electrical Power and Energy Systems 71 (2015) 131–139
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
A novel wavelet transform based voltage sag/swell detection algorithm Mohammad Barghi Latran ⇑, Ahmet Teke Department of Electrical and Electronics Engineering, Çukurova University, Adana, Turkey
a r t i c l e
i n f o
Article history: Received 2 September 2014 Received in revised form 27 January 2015 Accepted 20 February 2015
Keywords: Wavelet transform Power quality disturbances Voltage sag/swell detection
a b s t r a c t This paper proposes a novel sag/swell detection algorithm based on wavelet transform (WT) operating even in the presence of flicker and harmonics in source voltage. The developed algorithm is the hybrid of Daubechies wavelets of order 2 (db2) and order 8 (db8) to detect voltage sag/swell with and without positive/negative phase jumps. The hybrid detection algorithm can detect the start and end times of voltage sag/swell with and without phase jumps within 0.5 ms and 1.15 ms, respectively. The performance of the proposed voltage sag/swell detection method is compared with the results of dq-transformation, Fast Fourier Transform (FFT) and Enhanced Phase Locked Loop (EPLL) based voltage sag/swell detection methods. The good robustness and faster processing time to detect balanced and unbalanced voltage sag/swell are provided using proposed method. With the proposed hybrid detection algorithm consisting of db2 and db8 wavelet functions, a robust sag/swell detection is achieved which can give precise and quick response. The performance of proposed hybrid algorithm is validated and confirmed through simulation studies using the PSCAD/EMTDC analysis program. Ó 2015 Elsevier Ltd. All rights reserved.
Introduction Nowadays, the end users are affected and exposed to the unexpected malfunction and outage due the widespread application of power electronic loads that are more sensitive to voltage/current disturbances and high frequency transients [1]. Power quality (PQ) problems can be described as any variation in the electrical power supply such as voltage sags/swell, interruption, flicker, harmonic and notch. Also, The International Electrotechnical Commission (IEC) defines the PQ in IEC 61000-4-30 [2] as: ‘‘Characteristics of the electricity at a given point on an electrical system, evaluated against a set of reference technical parameters’’. This definition is related to the possibility of measuring and quantifying the performance of the power system. Another standardized PQ definition is given by IEEE standard 1100 [3] as: ‘‘The concept of powering and grounding sensitive equipment in a matter that suitable to the operation of that equipment’’ [4]. The voltage sag/swells are short duration variations of the root mean square (RMS) value of the voltage from the nominal value. The voltage sag/swells are characterized by their magnitude and duration. Depending on their duration they can be instantaneous, momentary or temporary. The different definitions and limits for magnitude and duration of voltage sag/swell are mentioned in ⇑ Corresponding author. E-mail addresses: [email protected] (M.B. Latran), [email protected] (A. Teke). http://dx.doi.org/10.1016/j.ijepes.2015.02.040 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.
European Standard EN50160 [5] and in IEEE Std. 1159-2009 [6]. The voltage sag/swells are usually associated with system faults or with switching or heavy loads. They constitute one of the most important PQ disturbances because of their detrimental effect on equipment. Their fast detection and analysis are one of the most important problems in modern power systems [7]. There is no standard method defined to detect and analyze the voltage sag/swell. There are several methods used in the literature that can be applied to this end, although none of them is dominant. Standard IEC 61000-4-7 and Refs. [1,8] report some of the most commonly used methods. They can be divided into two categories: time-domain and frequency-domain methods. The time-domain methods are the comparative, the envelope, the sliding window, the dv/dt and the RMS methods. The time-domain methods are easy to implement than the frequency-domain methods but they can present worse detection performance than the frequencydomain methods. The most common frequency-domain methods are FFT, Kalman filter, wavelets and S-transform. The use of wavelets allows the decomposition of a signal into components as a function of time and frequency, providing a more precise time location of a transient than other frequency-domain methods [9]. The voltage sags/swell can be exactly detected using discrete wavelet transform (DWT), which is a powerful and useful tool to analyze non-stationary signals. The well-known application of the DWT is to detect, characterize and locate power system transients [10]. Much research efforts have focused on wavelet-based techniques applied on analyzing power system transients [9],
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detecting and classifying PQ disturbances [11–17] and faults [18–20]. The start and end times of voltage sags and faults were also detected by means of the wavelet transform analysis [21–23]. In addition, the wavelet transform can be used for harmonic indices assessment [24], the detection of harmonic sources [25], fault location detection [26,27], computation of power quantities [28] and islanding detection in PV systems [29]. In the previous studies, to classify the PQ disturbances and to detect the voltage sags/swell, the effect of disturbances was analyzed individually and the effectiveness of system under different combinations of PQ disturbances was not analyzed. But in real power systems the voltage waveform is non-stationery and distorted with flicker and harmonics. In this research paper, a novel algorithm to detect the voltage sag/swell in harmonics and flicker distorted non-stationary voltage signals is proposed. The hybrid discrete wavelet transform (DWT) is developed to detect fast changes in the voltage signals, which allows time localization of differences frequency components of a signal with different frequency wavelets. The organization of this paper is as follows. Section ‘Theoretical background of discrete wavelet transform’ introduces the basics of wavelet transforms. In Sections ‘Proposed voltage sag/swell detection method’ and ‘Conventional sag/swell detection methods’, the proposed and conventional voltage sag/swell detection algorithms are presented. In Section ‘Analysis and discussions’, the validity and effectiveness of the proposed algorithm is validated for several test cases and compared with conventional sag/swell detection methods. Finally, main points and significant results of the paper are summarized in conclusions.
The control parameters m and n contain the set of positive and negative integers. WT of a continuous signal x(t) gives the decomposition wavelets by using the discrete form of Eq. (2). In other words, the scale-location of the signal in the time–frequency-domain is determined by the Eq. (3).
Z 1 ts dt xðtÞw wðs; sÞ ¼ pffiffiffiffiffi s jsj Z 1 xðtÞam=2 wðam=2 t nb0 Þdt T m;n ¼ 0 0
ð2Þ ð3Þ
1
where the values of T are the scale-location grid of the signal in the time–frequency-domain according to indexes m and n. The values of Tm,n are known as wavelet coefficients or detail coefficients. Common choices for DWT parameters, a0 and b0 are selected as two and one, respectively. The term ‘‘power of two’’ is emerged for the practical application. This power of two is known as the dyadic grid arrangement for dilation and translation steps. The dyadic grid is perhaps the simplest and most efficient discretization for practical purposes and lends itself to the construction of an orthonormal wavelet basis [32,33].
wm;n ðtÞ ¼ 2m=2 wð2m t nÞ
ð4Þ
By choosing an orthonormal wavelet basis wm,n(t), the original signal can be reconstructed by utilizing the wavelet coefficients Tm,n and inverse discrete wavelet transform (IDWT) as presented by the Eq. (5).
xðtÞ ¼
1 1 X X
T m;n wm;n ðtÞ
ð5Þ
m¼1n¼1
Theoretical background of discrete wavelet transform In electrical engineering, the application of wavelet transform was popular for some time under the various names of multirate-sampling, quadrature mirror filters [29]. The term ‘‘wavelet’’ means a small wave and the wave refers to the condition that this function is an oscillatory. Wavelet functions are generated by using a prototype wavelet named as mother wavelet. In other words, the functions used in the transformation process are derived from a main function or the mother wavelet. WT has also another term ‘‘Translation (s)’’. This term is used in the same sense as it was used in FFT. It is related with the location of the window, as the window is shifted through the signal as visualized in Fig. 1 [29–31]. Discrete wavelet transform (DWT) is the form of WT that uses the discrete values of the signal in the time-domain. The mathematical expression of DWT is presented by the Eq. (1).
1 t nb0 am 0 wm;n ðtÞ ¼ pffiffiffiffiffiffi am am 0 0
ð1Þ
where the integers m and n control the wavelet dilation and translation respectively, a0 is a specified fixed dilation step parameter which should be greater than one and b0 is the location parameter which should be greater than zero [28].
Signal
(a)
..
..
..
..
Wavelet
(b)
There are many wavelet functions defined by the mathematician. Haar wavelet proposed firstly, Meyer wavelet, Morlet wavelet and Daubechies wavelet are the most common wavelets adapted to the applications of WT in the power system applications. Each wavelet includes the high pass filter (HPF) and low pass filter (LPF) in the decomposition process. The decomposition can be realized using filtering and down-sampling and can be iterated with successive approximations subsequently decomposed. Finally, one signal is broken down into lower resolution components. The approximations are the low frequency signal components that are obtained from the LPF for each decomposition stage. The details are the high frequency components that are obtained from the HPF. Finally, the LPF is related to the scaling function and the HPF is related to the mother wavelet. After the approximations, the low frequency content represents the identity of the signal [21]. This decomposition halves the time resolution since only half the number of samples characterizes the whole signal. However, this operation doubles the frequency resolution, since the frequency band of the signal spans only half the previous frequency band, highly decreasing the uncertainty in the frequency by half. This procedure can be repeated for further decomposition. In each level, the filtering and subsampling will result in half the number of samples (and hence half the time resolution) and half the frequency band spanned (and hence double the frequency resolution). Fig. 2 shows this procedure, where F(n) is the original signal to be decomposed, and cA1 and cD1 are high HPF and LPF, respectively. In each resolution level, the input signal in the upper resolution n-level is divided into the approximation by an LPF and the detail by the HPF in the lower resolution level. The detail signals and output approximation are then decimated by two [34].
Signal
Proposed voltage sag/swell detection method
Wavelet
Fig. 1. Translated versions of wavelet function.
The proposed voltage sag/swell detection process of the improved WT algorithm is realized in two steps. The decomposition
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0.30
F(n)
Phase voltage-Va
Voltage Sag
0.20
cD1
cA1
0.10
(a)
0.00 -0.10
cA2
-0.20 -0.30 0.00
cD2
0.02
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
Haar
0.01
(b)
cAn-1
0.00 -0.01
cA n
cD n
-0.02 0.00
Fig. 2. The filtering process of wavelet transforms.
0.03
db2
0.02
(c) Magnitude (V)
process is applied to the input voltage (VA) without using any discretization process. In other words, the sampling process of the input signal is eliminated in this algorithm. The filter types of the decomposition process are very important since they can slow down the response of the voltage sag/swell detection unit. The types of filters that the number of the coefficients is less are preferred to use in the voltage sag/swell detection algorithm. The HPF output (high) of the first decomposition gives the impulses during any disturbances are occurred. This situation can be utilized in the improved voltage sag/swell detection algorithm of various WT as illustrated in Fig. 3. The output of the first decomposition process (high) consists of both the positive and negative pulses. Then, an algorithm is written using the FORTRAN code to compare the impulse values with the threshold value. The right selection of an adequate wavelet filter is very important to identify the features of the fault voltage signals. However, if the filters are not ideal half band, then perfect reconstruction cannot be achieved. Although it is not always possible to realize ideal filters, under certain conditions it is possible to use filters that provide perfect reconstruction. The most famous one is known as Daubechies wavelets that are the family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support [34]. With each wavelet type of this class, there is a scaling function that generates an orthogonal multiresolution analysis. The Daubechies wavelets are chosen to obtain the highest number A of vanishing moments for given support width N = 2A. The index number refers to the number N of coefficients. There are two schemes in use, DN using the length or number of taps and dbA referring to the number of vanishing moments. Among the 2A1 possible solutions of the algebraic equations for the moment and orthogonality conditions, the one is chosen whose scaling filter has extremal phase [35]. To minimize the time delay of the voltage sag/swell detection response, db2 wavelet can be used. As shown in Fig. 4, the db2 shows different behaviors during voltage sag with positive/negative and without phase jump. Note that due to successive subsampling by 2, the signal length should be a power of 2 or at least a multiple of power of 2. The length of the signal determines the number of levels that the signal can be decomposed to [34]. As seen from Fig. 4, the voltage sag with positive and negative phase jump can be exactly detected by db2. However, the db2 does not give any peak at the start and end of the voltage sag without phase jump. So, the voltage sag without phase jump cannot be detected by db2. The voltage sag with and without phase jump can be detected by db8 as shown in Fig. 5. However, the performance of db8 to detect the voltage sag/swell with phase jump is worse than that of db2. The various drawbacks with db2 and db8
(d)
(e)
(f)
0.01 0.00 -0.01 -0.02 -0.03 0.00 0.04 0.03 0.02 0.01 0.00 -0.01 -0.02 -0.03 -0.04 0.00 0.04 0.03 0.02 0.01 0.00 -0.01 -0.02 -0.03 -0.04 0.00 0.04 0.03 0.02 0.01 0.00 -0.01 -0.02 -0.03 -0.04 0.00
db4
db8
Dmey
Time (s) Fig. 3. WT decomposition process: (a) phase voltage signal with sag, (b)–(f) detail coefficients of Haar, db2, db4, db8 and Dmey wavelet transform, respectively.
performance are analyzed and therefore a combination of db2 and db8 has been proposed. Thus this paper brings out the concept referred as hybrid sag/swell detection algorithm consisting of db2 and db8 which offers new features to overcome the individual weakness of both the approaches. By combining both algorithms of db2 and db8 together, a robust sag/swell detection is achieved which can give precise and quick response. Due to this reasons, a hybrid algorithm is developed by combining the superior properties of db2 which quickly detects the voltage sag/swell with positive and negative phase jump and db8 to detect the voltage sag/swell without phase jump. The db2 and db8 wavelets include 2 vanishing moments with 4 coefficients and 8 vanishing moments with 16 coefficients, respectively. The voltage swells with and without phase jump have same characteristics with voltage sag and can be detected using this type of method. Fig. 6 illustrates the software structure of the hybrid
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M.B. Latran, A. Teke / Electrical Power and Energy Systems 71 (2015) 131–139 db2
0.02 0.01 0.00
(a)
(b)
Magnitude (V)
-0.01 -0.02 0.00
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
db2
0.02 0.01 0.00 -0.01 -0.02 0.00
db2
0.02 0.01
bands detects the end point of sag/swell, however this can be a starting point of sag/swell for another hysteresis band. For this reason, if one of this hysteresis bands detect the voltage sag/swell, the input of two others hysteresis bands becomes zero. Also due the db2 detects the voltage sag/swell with less time delay than db8, if ether of H(1) or H(2) detects the voltage sag/swell, H(3) and H(4) becomes zero and the H(3) and H(4) cannot detect the voltage sag/swell with phase jump. Thus it is provided that the hysteresis bands cannot detect the voltage sag/swell at the same time. The desired value of DWT should be defined to detect the voltage sag/swell. This desired value is the DWT response to voltage sag/swell between ±10% Vnominal and predetermined level. With the use of this approach, the effectiveness of impulse and oscillatory transients can be eliminated from voltage sag/swell detection process. Conventional sag/swell detection methods
0.00
(c)
-0.01 -0.02 0.00
0.10
0.20
0.30
0.40
0.50
Time (s) Fig. 4. WT decomposition with db2 wavelet for voltage sag with (a) negative phase jump, (b) positive phase jump and (c) without phase jump.
The developed voltage sag/swell detection algorithm is compared with dq-transformation, EPLL and FFT methods to illustrate the superiority of the developed detection algorithm. In the dqtransformation based sag/swell detection method, the phase voltages VA, VB and VC are transformed to the dq plane as given by the Eq. (6). With the use of Eq. (7), the sag/swell depth is obtained [36].
detection method consisting of db2 using 128 sampling numbers and db8 using 512 sampling numbers. The algorithm consists of three hysteresis bands. The first hysteresis band is used to detect the voltage sag/swell with negative phase jump. The second hysteresis band detects the voltage sag/swell with positive phase jump. The third hysteresis band is used to detect the voltage sag/swell without phase jump. In Fig. 6, H(1), H(2), H(3) and H(4) denote the input of hysteresis bands 1, 2, 3 and 4, respectively. The input of H(1) and H(2) is the output of db2 and the input of H(3) and H(4) is the output of db8. The hysteresis bands, especially H(1) and H(2), have the inverse characteristic to detect the voltage sag/swell. So, at the end of voltage sag/swell, one of the hysteresis
db8
0.01 0.00
(a)
Magnitude (V)
-0.01
(b)
0.00
db8
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
0.01 0.00 -0.01 0.00 0.8m
db8
0.5m 0.3m (c)
0.00 -0.3m -0.5m -0.8m 0.00
Time (s) Fig. 5. WT decomposition with db8 wavelet for voltage sag with (a) negative phase jump, (b) positive phase jump and (c) without phase jump.
Vd Vq
¼
" # 2 cos h cos h 23p cos h þ 23p 3 sin h sinðh 23pÞ sin h þ 23p
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Sdq ¼ 1 V 2d þ V 2q
ð6Þ
ð7Þ
The dq-transformation based voltage sag/swell detection algorithm is illustrated in Fig. 7(a). After the three phase voltages are transformed into d and q components, the square root of the sum of squares of these components is obtained. The calculated value is subtracted from set value and then the absolute value of the resulting variable is filtered out with a LPF to extract the positive sequence component of voltage. If a negative sequence component is generated by voltage sag and/or unbalance, it appears as an oscillating error in the dq-transformation based voltage sag/swell detection method. To extract the positive sequence component separately from the negative sequence component, the dq-transformation based method uses a narrow-band LPF. But this kind of filter can cause phase or time delay and hence the response time of the detection method tends to be lengthened [36,37].The filtered output is subjected to a hysteresis comparator and the output of this comparator generates the voltage sag/swell detection signal. The signal is high if voltage sag/swell occurs and otherwise the output is low. This method detects the three phase balanced voltage sag/swell with acceptable performance. However, the important drawback of this method is that it uses three phase voltage measurements for the detection [37]. The method cannot detect the voltage sag lower than a definite depth. For example, due the method uses the average value of the three phase voltage magnitudes and calculates the single phase voltage sag as an average value of 6%, a single phase to ground fault resulting in 18% of voltage sag cannot be sensed by this method if the voltage sag detection limit is set as 10% of nominal [36]. To suppress the drawbacks of the dq-transformation sag/swell detection method, EPLL based sag/swell detection method can be used to detect balanced and unbalanced voltage sag/swell. The EPLL is applied to each supply phase separately and is adjusted to respond to phase jumps as shown in Fig. 7(b). The system receives the input signal A(t) (supply voltage or load current) and provides an on-line estimate of the following signals.
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H(1)=DWT1 H(2)=DWT1 H(3)=DWT2 H(4)=DWT2 Flag-detector1=0 Flag-detector2=0 Flag-detector3=0 Flag-detector4=0
Input Phase Voltage
Detection of voltage sag with negative phase jump and voltage swell with positive phase jump
db2
db8
Sampling Number=128
Sampling Number=512 Detection of voltage sag with positive phase jump and voltage swell with negative phase jump
Calculate DWT1
H(1)
NO
Flag-detector1=0 H(2)Input=DWT1 H(3)Input=DWT2 H(4)Input=DWT2
NO
D
NO
Flag-detector3=1 H(1)Input=0 H(2)Input=0 H(4)Input=0
NO
YES Flag-detector3=0 H(1)Input=DWT1 H(2)Input=DWT1 H(4)Input=DWT2
D
NO
YES
Flag-detector2=0 H(1)Input=DWT1 H(3)Input=DWT2 H(4)Input=DWT2
Flag-detector2=1 H(1)Input=0 H(3)Input=0 H(4)Input=0
NO
YES Flag-detector2=0 H(1)Input=DWT1 H(3)Input=DWT2 H(4)Input=DWT2
D>Desired Negative Value YES
Flag-detector1=0 H(2)Input=DWT1 H(3)Input=DWT2 H(4)Input=DWT2
H(4)
D>Desired Positive Value
YES
D
Flag-detector1=1 H(2)Input=0 H(3)Input=0 H(4)Input=0
NO
D
YES NO
H(3)
H(2)
D>Desired Positive Value
Detection of voltage sag/swell without phase jump
Calculate DWT2
D>Desired Positive Value
Flag-detector4=0 H(1)Input=DWT1 H(2)Input=DWT1 H(3)Input=DWT2
YES
Flag-detector3=0 H(1)Input=DWT1 H(2)Input=DWT1 H(4)Input=DWT2
Flag-detector4=1 H(1)Input=0 H(2)Input=0 H(3)Input=0
Flag-detector4=0 H(1)Input=DWT1 H(2)Input=DWT1 H(3)Input=DWT2
Sag/Swell flag-detector=(Flag-detector1)+(Flag-detector2)+(Flag-detector3)+(Flag-detector4) End
Fig. 6. The flowchart of proposed sag/swell detection algorithm.
Vd (a)
-
+
x2 abc-dq transform
+
1 Reference
x2 cosθ
Vq
A(t) +
K
*
B(t)
+
*
(b)
Phase Voltage
π Cos
1 sT
Hysteresis Comparator
Low Pass Filter
θ(t)
1 sT
+
-
Sag/swell Detection Signal
+
sinθ PLL
Sdq
C(t) -
SEPLL
+
E(t) Sin
1
C(t)
Sag/swell Detection Signal Hysteresis Comparator
*
Reference
D(t) EPLL
(c)
Phase Voltage
FFT
VRMS
SFFT
-
Sag/swell Detection Signal
+ 1
Hysteresis Comparator
Reference Fig. 7. Block diagram of (a) dq-transformation, (b) EPLL and (c) FFT based voltage sag/swell detection methods.
B(t) is the difference of input and the synchronized fundamental component, C(t) is the amplitude of D(t), D(t) is the synchronized fundamental component, E(t) is the PLL signal and h(t) is the phase angle of D(t) [37,38].
BðtÞ ¼ AðtÞ k2 t A k2 hðtÞ ¼ cos hðtÞ cos xt t x 2 A k2 EðtÞ ¼ sin cos hðtÞ cos xt t 2 þ pt x 2 k3 A k2 k3 2 cos xt t CðtÞ ¼ x 2 CðtÞ DðtÞ ¼ CðtÞ sin þ pt k3
ð8Þ ð9Þ ð10Þ ð11Þ ð12Þ
There exists a compromise between speed and accuracy. For large K1, K2 and K3, the convergence of the estimated values to actual values is faster and the steady state misadjustment is higher. This is an inherent characteristic of an adaptive algorithm. Parameters K1, K2 and K3 should be selected appropriately according to the field of application. If only the total ‘‘flicker content’’ of a signal is to be extracted, then the filter can be set to operate in an alternative mode. In this mode, the filter is set to operate at a low speed to track only the fundamental signal and not the flicker. The result is that the smooth ‘‘averaged’’ fundamental is extracted on the output and the total distortion signal at the error terminal [38]. In EPLL the C(t) gives the amplitude of the tracked signal A(t). By subtracting the C(t) from ideal voltage magnitude, the voltage sag/ swell depth (SEPLL) can be detected.
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Table 1 The performance comparison of proposed and conventional sag/swell detection methods.
ð13Þ
The application of Fourier Transform (FT) to each supply phase is another method that can provide information regarding the state of a system supply. This method can accurately reveal magnitude and phase of each frequency component of the supply in the presence of harmonics in the system. To eliminate errors occurring with the information returned regarding the fundamental component, the previous methods effectively filter out harmonics other than the fundamental. This process can cause transient delays in detecting changes in the phase of the fundamental component [39,40]. In FFT based algorithm, the RMS variation of input voltage is measured to judge the voltage sag/swell. A discrete Fourier transform (DFT) algorithm is used to calculate the RMS value of the fundamental component [41]. The source voltage V(t) can be expressed using the Fourier series as presented by the Eq. (14). 1 1 X X a v ðtÞ ¼ 0 þ an cos nx0 t þ bn sin nx0 t 2 n¼0 n¼0
ð14Þ
a1 ¼ b1 ¼
Magnitude (V)
(a)
v ðtÞ cos x0 t dt
ð15Þ
v ðtÞ sin x0 t dt
ð16Þ
0
Z
T
0
pffiffiffi N T i 2X v t i cos 2p N N N i¼0 pffiffiffi N T i 2X b1 ¼ v t i sin 2p N N N i¼0
V RMS ¼
ð18Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 a21 þ b1
Va
400 300 200 100 000 -100 -200 -300 -400
Vb
ð19Þ
Voltage Swell
Vc
0.15
0.10
0.20
0.25
0.30
0.35
0.40
dq-transform based method 0.15
0.20
0.25
0.30
0.35
0.40
1.00
(b)
dq-transform based method
0.202
1.00
0.203
0.00 0.10
(b) 0.202
ð17Þ
Using the value of a1 and b1, the RMS value of the fundamental component can be calculated as the following:
Voltage Sag
Vc
T
a1 ¼
(a) Vb
2 T
Z
Eqs. (17) and (18) are obtained by applying the DFT to Eqs. (15) and (16).
The fundamental component for n = 1 is calculated by the Eq. (15) and Eq. (16), separating the imaginary and real parts Va 400 300 200 100 000 -100 -200 -300 -400 0.10
2 T
Magnitude (V)
SEPLL ¼ j1 CðtÞj
0.15
0.205
0.15
0.302 0.303 0.304 0.305
0.20
0.25
0.30
0.35
0.40
0.302 0.303 0.304 0.305
0.203 0.204 0.205
0.00 0.10
0.204
0.20
0.25
0.30
0.35
0.40
EPLL based method
1.00 EPLL based method
(c)
1.00
(c) 0.203 0.204 0.205
0.00
0.10
0.206
0.15
0.301 0.302 0.303
0.20
0.250
0.30
0.00 0.10
0.304
0.35
0.203 0.204
0.205 0.206
0.15
0.301 0.302 0.303 0.304
0.20
0.250
0.30
0.35
0.40
0.40
FFT based method
1.00
FFT based method
1.00
(d)
(d)
0.212 0.214
0.00 0.10
0.215
0.216
0.217
0.15
0.00 0.10
0.304 0.305 0.306 0.307
0.20
0.25
0.30
0.35
0.214
0.303 0.304 0.305 0.306
0.215
0.15
0.20
0.250
0.30
0.35
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By subtracting the VRMS signal from RMS value of the ideal voltage, the voltage sag/swell depth (SFFT) can be detected as shown in Fig. 7(c).
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 SFFT ¼ 1 a21 þ b1
Case 3: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for single phase 13% voltage sag with 10° phase jump. As seen from Fig. 10 and Table 1, the proposed algorithm has superior performance to detect the voltage sag with minimum time delay. In this case, the dq-transformation based method has the worst detection performance. Also, due to the presence of phase jump the EPLL based method has low accuracy to detect voltage sag. FFT based method also has large time delay to detect the voltage sag. Case 4: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for single phase 13% voltage sag with 20° phase jump. The proposed algorithm has superior performance to detect the voltage sag with minimum delay as seen from Fig. 11 and Table 1. The dq-transformation based method has the worst detection performance. Comparing with the previous case (a voltage sag with 10° phase jump), FFT and EPLL based methods have the poor detection performance because these methods can be affected by phase jump degree. Case 5: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for single phase 13% voltage sag with 20° phase jump condition for distorted phase voltage with harmonic. The distorted phase voltage contains 5%, ground fault with 20° phase jump when the source voltage includes harmonic orders. 5%, 4%, 2% and 1.5% p.u. in 5th, 7th, 11th and 13th harmonic orders, respectively. As seen from Fig. 12 and Table 1, the proposed algorithm performs superior performance
ð20Þ
Analysis and discussions The performance of the proposed algorithm is compared with different case studies. The results of test cases are summarized in Table 1. The sag event occurs between 0.2 and 0.3 s.
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Case 1: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for three phase balance (without phase jump) 13% voltage sag. As seen from Fig. 8 and Table 1, the proposed algorithm has superior performance to detect the start and end times of voltage sag. FFT based method has the worst performance to detect the start and end time of voltage sag due to its large computation time. Case 2: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for three phase balance (without phase jump) 13% voltage swell. The proposed algorithm has superior performance to detect the start and end times of voltage swell as seen from Fig. 9 and Table 1. FFT based method again performs the worst performance to detect the start and end times due to its large computation time.
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M.B. Latran, A. Teke / Electrical Power and Energy Systems 71 (2015) 131–139 Phase voltage-Va 400 300 200 100 0 -100 -200 -300 -400 0.10 0.15
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to detect the voltage sag with minimum time delay. In this case, due the EPLL and FFT based detection methods extract the harmonics from fundamental components, they are not affected by harmonics. The harmonics in the system can cause an increase on the RMS value of reference signal. In this condition, the dq-transformation based method can detect the voltage sag wrongly because this method cannot extract the harmonic component. This situation can lead to wrong detection of sag or swell when the magnitude of voltage is within the standard limits. Case 6: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for single phase 13% voltage sag with 20° phase jump condition for distorted phase voltage with harmonic and flicker. The distorted phase voltage contains 10% p.u. at 8 Hz flicker with 5%, 4%, 2% and 1.5% p.u. in 5th, 7th, 11th and 13th harmonic orders, respectively. The proposed algorithm achieves superior performance to detect the voltage sag with less time delay as seen from Fig. 13 and Table 1. In this case, due the dq-transformation based detection method cannot extract the flicker and harmonic orders from signals, so in normal operation condition it also detects voltage sag or swell. In EPLL based detection method, the EPLL parameters should be adjusted to extract the flicker and harmonic orders from phase voltage waveform in steady state. So this can cause a large time delay for detection process. The accuracy of EPLL based detection method is related with its parameters, voltage sag/swell level and phase jump degree. FFT based detection method cannot completely extracts the flicker and harmonics from fundamental components. This method can operate incorrectly especially within the standard limits.
Fig. 13. The performance of sag detection methods for single phase to ground fault with 20° phase jump when the source voltage includes flicker and harmonic orders.
Conclusions In the present paper, a new wavelet transform based voltage sag/swell detection algorithm which can be even applied in the presence of flicker and harmonic polluted source voltage has been introduced. The proposed detection algorithm has the advantage of being a hybrid structure consisting of a db2 and a db8 to detect sag/swell with or without phase jump. The proposed algorithm can detect the start and end times of voltage sag/swell with and without phase jump within 0.5 ms and 1.15 ms, respectively. The feasibility of proposed algorithm is validated through test cases using the PSCAD/EMTDC 4.2.0. The performance of developed voltage sag/swell detection algorithm is compared with dq-transformation, FFT and EPLL based voltage sag/swell detection methods. Compared with conventional detection methods, the case results reveal good robustness, accuracy and faster processing time to detect balanced and unbalanced voltage sag/swell. The solution step of the simulation model is adjusted at 10 ms which can be easily adapted to future hardware implementations. The developed sag/swell detection algorithm can be effectively utilized in Custom Power Devices for fast compensation of voltage sag/swell in the sensitive loads. References [1] Bollen MHJ, Gu YH. Signal processing of power quality, disturbances. Wiley Interscience & IEEE Press; 2006. [2] IEC Electromagnetic compatibility (EMC), Part 4, Section 30: testing and measurement techniques – power quality measurement methods. Standard IEC 61000-4-30; 2003. [3] IEEE recommended practice for powering and grounding sensitive electronic equipment. IEEE standard 1100; 1992.
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
A novel wavelet transform based voltage sag/swell detection algorithm Mohammad Barghi Latran ⇑, Ahmet Teke Department of Electrical and Electronics Engineering, Çukurova University, Adana, Turkey
a r t i c l e
i n f o
Article history: Received 2 September 2014 Received in revised form 27 January 2015 Accepted 20 February 2015
Keywords: Wavelet transform Power quality disturbances Voltage sag/swell detection
a b s t r a c t This paper proposes a novel sag/swell detection algorithm based on wavelet transform (WT) operating even in the presence of flicker and harmonics in source voltage. The developed algorithm is the hybrid of Daubechies wavelets of order 2 (db2) and order 8 (db8) to detect voltage sag/swell with and without positive/negative phase jumps. The hybrid detection algorithm can detect the start and end times of voltage sag/swell with and without phase jumps within 0.5 ms and 1.15 ms, respectively. The performance of the proposed voltage sag/swell detection method is compared with the results of dq-transformation, Fast Fourier Transform (FFT) and Enhanced Phase Locked Loop (EPLL) based voltage sag/swell detection methods. The good robustness and faster processing time to detect balanced and unbalanced voltage sag/swell are provided using proposed method. With the proposed hybrid detection algorithm consisting of db2 and db8 wavelet functions, a robust sag/swell detection is achieved which can give precise and quick response. The performance of proposed hybrid algorithm is validated and confirmed through simulation studies using the PSCAD/EMTDC analysis program. Ó 2015 Elsevier Ltd. All rights reserved.
Introduction Nowadays, the end users are affected and exposed to the unexpected malfunction and outage due the widespread application of power electronic loads that are more sensitive to voltage/current disturbances and high frequency transients [1]. Power quality (PQ) problems can be described as any variation in the electrical power supply such as voltage sags/swell, interruption, flicker, harmonic and notch. Also, The International Electrotechnical Commission (IEC) defines the PQ in IEC 61000-4-30 [2] as: ‘‘Characteristics of the electricity at a given point on an electrical system, evaluated against a set of reference technical parameters’’. This definition is related to the possibility of measuring and quantifying the performance of the power system. Another standardized PQ definition is given by IEEE standard 1100 [3] as: ‘‘The concept of powering and grounding sensitive equipment in a matter that suitable to the operation of that equipment’’ [4]. The voltage sag/swells are short duration variations of the root mean square (RMS) value of the voltage from the nominal value. The voltage sag/swells are characterized by their magnitude and duration. Depending on their duration they can be instantaneous, momentary or temporary. The different definitions and limits for magnitude and duration of voltage sag/swell are mentioned in ⇑ Corresponding author. E-mail addresses: [email protected] (M.B. Latran), [email protected] (A. Teke). http://dx.doi.org/10.1016/j.ijepes.2015.02.040 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.
European Standard EN50160 [5] and in IEEE Std. 1159-2009 [6]. The voltage sag/swells are usually associated with system faults or with switching or heavy loads. They constitute one of the most important PQ disturbances because of their detrimental effect on equipment. Their fast detection and analysis are one of the most important problems in modern power systems [7]. There is no standard method defined to detect and analyze the voltage sag/swell. There are several methods used in the literature that can be applied to this end, although none of them is dominant. Standard IEC 61000-4-7 and Refs. [1,8] report some of the most commonly used methods. They can be divided into two categories: time-domain and frequency-domain methods. The time-domain methods are the comparative, the envelope, the sliding window, the dv/dt and the RMS methods. The time-domain methods are easy to implement than the frequency-domain methods but they can present worse detection performance than the frequencydomain methods. The most common frequency-domain methods are FFT, Kalman filter, wavelets and S-transform. The use of wavelets allows the decomposition of a signal into components as a function of time and frequency, providing a more precise time location of a transient than other frequency-domain methods [9]. The voltage sags/swell can be exactly detected using discrete wavelet transform (DWT), which is a powerful and useful tool to analyze non-stationary signals. The well-known application of the DWT is to detect, characterize and locate power system transients [10]. Much research efforts have focused on wavelet-based techniques applied on analyzing power system transients [9],
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detecting and classifying PQ disturbances [11–17] and faults [18–20]. The start and end times of voltage sags and faults were also detected by means of the wavelet transform analysis [21–23]. In addition, the wavelet transform can be used for harmonic indices assessment [24], the detection of harmonic sources [25], fault location detection [26,27], computation of power quantities [28] and islanding detection in PV systems [29]. In the previous studies, to classify the PQ disturbances and to detect the voltage sags/swell, the effect of disturbances was analyzed individually and the effectiveness of system under different combinations of PQ disturbances was not analyzed. But in real power systems the voltage waveform is non-stationery and distorted with flicker and harmonics. In this research paper, a novel algorithm to detect the voltage sag/swell in harmonics and flicker distorted non-stationary voltage signals is proposed. The hybrid discrete wavelet transform (DWT) is developed to detect fast changes in the voltage signals, which allows time localization of differences frequency components of a signal with different frequency wavelets. The organization of this paper is as follows. Section ‘Theoretical background of discrete wavelet transform’ introduces the basics of wavelet transforms. In Sections ‘Proposed voltage sag/swell detection method’ and ‘Conventional sag/swell detection methods’, the proposed and conventional voltage sag/swell detection algorithms are presented. In Section ‘Analysis and discussions’, the validity and effectiveness of the proposed algorithm is validated for several test cases and compared with conventional sag/swell detection methods. Finally, main points and significant results of the paper are summarized in conclusions.
The control parameters m and n contain the set of positive and negative integers. WT of a continuous signal x(t) gives the decomposition wavelets by using the discrete form of Eq. (2). In other words, the scale-location of the signal in the time–frequency-domain is determined by the Eq. (3).
Z 1 ts dt xðtÞw wðs; sÞ ¼ pffiffiffiffiffi s jsj Z 1 xðtÞam=2 wðam=2 t nb0 Þdt T m;n ¼ 0 0
ð2Þ ð3Þ
1
where the values of T are the scale-location grid of the signal in the time–frequency-domain according to indexes m and n. The values of Tm,n are known as wavelet coefficients or detail coefficients. Common choices for DWT parameters, a0 and b0 are selected as two and one, respectively. The term ‘‘power of two’’ is emerged for the practical application. This power of two is known as the dyadic grid arrangement for dilation and translation steps. The dyadic grid is perhaps the simplest and most efficient discretization for practical purposes and lends itself to the construction of an orthonormal wavelet basis [32,33].
wm;n ðtÞ ¼ 2m=2 wð2m t nÞ
ð4Þ
By choosing an orthonormal wavelet basis wm,n(t), the original signal can be reconstructed by utilizing the wavelet coefficients Tm,n and inverse discrete wavelet transform (IDWT) as presented by the Eq. (5).
xðtÞ ¼
1 1 X X
T m;n wm;n ðtÞ
ð5Þ
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Theoretical background of discrete wavelet transform In electrical engineering, the application of wavelet transform was popular for some time under the various names of multirate-sampling, quadrature mirror filters [29]. The term ‘‘wavelet’’ means a small wave and the wave refers to the condition that this function is an oscillatory. Wavelet functions are generated by using a prototype wavelet named as mother wavelet. In other words, the functions used in the transformation process are derived from a main function or the mother wavelet. WT has also another term ‘‘Translation (s)’’. This term is used in the same sense as it was used in FFT. It is related with the location of the window, as the window is shifted through the signal as visualized in Fig. 1 [29–31]. Discrete wavelet transform (DWT) is the form of WT that uses the discrete values of the signal in the time-domain. The mathematical expression of DWT is presented by the Eq. (1).
1 t nb0 am 0 wm;n ðtÞ ¼ pffiffiffiffiffiffi am am 0 0
ð1Þ
where the integers m and n control the wavelet dilation and translation respectively, a0 is a specified fixed dilation step parameter which should be greater than one and b0 is the location parameter which should be greater than zero [28].
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There are many wavelet functions defined by the mathematician. Haar wavelet proposed firstly, Meyer wavelet, Morlet wavelet and Daubechies wavelet are the most common wavelets adapted to the applications of WT in the power system applications. Each wavelet includes the high pass filter (HPF) and low pass filter (LPF) in the decomposition process. The decomposition can be realized using filtering and down-sampling and can be iterated with successive approximations subsequently decomposed. Finally, one signal is broken down into lower resolution components. The approximations are the low frequency signal components that are obtained from the LPF for each decomposition stage. The details are the high frequency components that are obtained from the HPF. Finally, the LPF is related to the scaling function and the HPF is related to the mother wavelet. After the approximations, the low frequency content represents the identity of the signal [21]. This decomposition halves the time resolution since only half the number of samples characterizes the whole signal. However, this operation doubles the frequency resolution, since the frequency band of the signal spans only half the previous frequency band, highly decreasing the uncertainty in the frequency by half. This procedure can be repeated for further decomposition. In each level, the filtering and subsampling will result in half the number of samples (and hence half the time resolution) and half the frequency band spanned (and hence double the frequency resolution). Fig. 2 shows this procedure, where F(n) is the original signal to be decomposed, and cA1 and cD1 are high HPF and LPF, respectively. In each resolution level, the input signal in the upper resolution n-level is divided into the approximation by an LPF and the detail by the HPF in the lower resolution level. The detail signals and output approximation are then decimated by two [34].
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Fig. 1. Translated versions of wavelet function.
The proposed voltage sag/swell detection process of the improved WT algorithm is realized in two steps. The decomposition
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(c) Magnitude (V)
process is applied to the input voltage (VA) without using any discretization process. In other words, the sampling process of the input signal is eliminated in this algorithm. The filter types of the decomposition process are very important since they can slow down the response of the voltage sag/swell detection unit. The types of filters that the number of the coefficients is less are preferred to use in the voltage sag/swell detection algorithm. The HPF output (high) of the first decomposition gives the impulses during any disturbances are occurred. This situation can be utilized in the improved voltage sag/swell detection algorithm of various WT as illustrated in Fig. 3. The output of the first decomposition process (high) consists of both the positive and negative pulses. Then, an algorithm is written using the FORTRAN code to compare the impulse values with the threshold value. The right selection of an adequate wavelet filter is very important to identify the features of the fault voltage signals. However, if the filters are not ideal half band, then perfect reconstruction cannot be achieved. Although it is not always possible to realize ideal filters, under certain conditions it is possible to use filters that provide perfect reconstruction. The most famous one is known as Daubechies wavelets that are the family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support [34]. With each wavelet type of this class, there is a scaling function that generates an orthogonal multiresolution analysis. The Daubechies wavelets are chosen to obtain the highest number A of vanishing moments for given support width N = 2A. The index number refers to the number N of coefficients. There are two schemes in use, DN using the length or number of taps and dbA referring to the number of vanishing moments. Among the 2A1 possible solutions of the algebraic equations for the moment and orthogonality conditions, the one is chosen whose scaling filter has extremal phase [35]. To minimize the time delay of the voltage sag/swell detection response, db2 wavelet can be used. As shown in Fig. 4, the db2 shows different behaviors during voltage sag with positive/negative and without phase jump. Note that due to successive subsampling by 2, the signal length should be a power of 2 or at least a multiple of power of 2. The length of the signal determines the number of levels that the signal can be decomposed to [34]. As seen from Fig. 4, the voltage sag with positive and negative phase jump can be exactly detected by db2. However, the db2 does not give any peak at the start and end of the voltage sag without phase jump. So, the voltage sag without phase jump cannot be detected by db2. The voltage sag with and without phase jump can be detected by db8 as shown in Fig. 5. However, the performance of db8 to detect the voltage sag/swell with phase jump is worse than that of db2. The various drawbacks with db2 and db8
(d)
(e)
(f)
0.01 0.00 -0.01 -0.02 -0.03 0.00 0.04 0.03 0.02 0.01 0.00 -0.01 -0.02 -0.03 -0.04 0.00 0.04 0.03 0.02 0.01 0.00 -0.01 -0.02 -0.03 -0.04 0.00 0.04 0.03 0.02 0.01 0.00 -0.01 -0.02 -0.03 -0.04 0.00
db4
db8
Dmey
Time (s) Fig. 3. WT decomposition process: (a) phase voltage signal with sag, (b)–(f) detail coefficients of Haar, db2, db4, db8 and Dmey wavelet transform, respectively.
performance are analyzed and therefore a combination of db2 and db8 has been proposed. Thus this paper brings out the concept referred as hybrid sag/swell detection algorithm consisting of db2 and db8 which offers new features to overcome the individual weakness of both the approaches. By combining both algorithms of db2 and db8 together, a robust sag/swell detection is achieved which can give precise and quick response. Due to this reasons, a hybrid algorithm is developed by combining the superior properties of db2 which quickly detects the voltage sag/swell with positive and negative phase jump and db8 to detect the voltage sag/swell without phase jump. The db2 and db8 wavelets include 2 vanishing moments with 4 coefficients and 8 vanishing moments with 16 coefficients, respectively. The voltage swells with and without phase jump have same characteristics with voltage sag and can be detected using this type of method. Fig. 6 illustrates the software structure of the hybrid
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0.02 0.01 0.00
(a)
(b)
Magnitude (V)
-0.01 -0.02 0.00
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
db2
0.02 0.01 0.00 -0.01 -0.02 0.00
db2
0.02 0.01
bands detects the end point of sag/swell, however this can be a starting point of sag/swell for another hysteresis band. For this reason, if one of this hysteresis bands detect the voltage sag/swell, the input of two others hysteresis bands becomes zero. Also due the db2 detects the voltage sag/swell with less time delay than db8, if ether of H(1) or H(2) detects the voltage sag/swell, H(3) and H(4) becomes zero and the H(3) and H(4) cannot detect the voltage sag/swell with phase jump. Thus it is provided that the hysteresis bands cannot detect the voltage sag/swell at the same time. The desired value of DWT should be defined to detect the voltage sag/swell. This desired value is the DWT response to voltage sag/swell between ±10% Vnominal and predetermined level. With the use of this approach, the effectiveness of impulse and oscillatory transients can be eliminated from voltage sag/swell detection process. Conventional sag/swell detection methods
0.00
(c)
-0.01 -0.02 0.00
0.10
0.20
0.30
0.40
0.50
Time (s) Fig. 4. WT decomposition with db2 wavelet for voltage sag with (a) negative phase jump, (b) positive phase jump and (c) without phase jump.
The developed voltage sag/swell detection algorithm is compared with dq-transformation, EPLL and FFT methods to illustrate the superiority of the developed detection algorithm. In the dqtransformation based sag/swell detection method, the phase voltages VA, VB and VC are transformed to the dq plane as given by the Eq. (6). With the use of Eq. (7), the sag/swell depth is obtained [36].
detection method consisting of db2 using 128 sampling numbers and db8 using 512 sampling numbers. The algorithm consists of three hysteresis bands. The first hysteresis band is used to detect the voltage sag/swell with negative phase jump. The second hysteresis band detects the voltage sag/swell with positive phase jump. The third hysteresis band is used to detect the voltage sag/swell without phase jump. In Fig. 6, H(1), H(2), H(3) and H(4) denote the input of hysteresis bands 1, 2, 3 and 4, respectively. The input of H(1) and H(2) is the output of db2 and the input of H(3) and H(4) is the output of db8. The hysteresis bands, especially H(1) and H(2), have the inverse characteristic to detect the voltage sag/swell. So, at the end of voltage sag/swell, one of the hysteresis
db8
0.01 0.00
(a)
Magnitude (V)
-0.01
(b)
0.00
db8
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
0.10
0.20
0.30
0.40
0.50
0.01 0.00 -0.01 0.00 0.8m
db8
0.5m 0.3m (c)
0.00 -0.3m -0.5m -0.8m 0.00
Time (s) Fig. 5. WT decomposition with db8 wavelet for voltage sag with (a) negative phase jump, (b) positive phase jump and (c) without phase jump.
Vd Vq
¼
" # 2 cos h cos h 23p cos h þ 23p 3 sin h sinðh 23pÞ sin h þ 23p
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Sdq ¼ 1 V 2d þ V 2q
ð6Þ
ð7Þ
The dq-transformation based voltage sag/swell detection algorithm is illustrated in Fig. 7(a). After the three phase voltages are transformed into d and q components, the square root of the sum of squares of these components is obtained. The calculated value is subtracted from set value and then the absolute value of the resulting variable is filtered out with a LPF to extract the positive sequence component of voltage. If a negative sequence component is generated by voltage sag and/or unbalance, it appears as an oscillating error in the dq-transformation based voltage sag/swell detection method. To extract the positive sequence component separately from the negative sequence component, the dq-transformation based method uses a narrow-band LPF. But this kind of filter can cause phase or time delay and hence the response time of the detection method tends to be lengthened [36,37].The filtered output is subjected to a hysteresis comparator and the output of this comparator generates the voltage sag/swell detection signal. The signal is high if voltage sag/swell occurs and otherwise the output is low. This method detects the three phase balanced voltage sag/swell with acceptable performance. However, the important drawback of this method is that it uses three phase voltage measurements for the detection [37]. The method cannot detect the voltage sag lower than a definite depth. For example, due the method uses the average value of the three phase voltage magnitudes and calculates the single phase voltage sag as an average value of 6%, a single phase to ground fault resulting in 18% of voltage sag cannot be sensed by this method if the voltage sag detection limit is set as 10% of nominal [36]. To suppress the drawbacks of the dq-transformation sag/swell detection method, EPLL based sag/swell detection method can be used to detect balanced and unbalanced voltage sag/swell. The EPLL is applied to each supply phase separately and is adjusted to respond to phase jumps as shown in Fig. 7(b). The system receives the input signal A(t) (supply voltage or load current) and provides an on-line estimate of the following signals.
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H(1)=DWT1 H(2)=DWT1 H(3)=DWT2 H(4)=DWT2 Flag-detector1=0 Flag-detector2=0 Flag-detector3=0 Flag-detector4=0
Input Phase Voltage
Detection of voltage sag with negative phase jump and voltage swell with positive phase jump
db2
db8
Sampling Number=128
Sampling Number=512 Detection of voltage sag with positive phase jump and voltage swell with negative phase jump
Calculate DWT1
H(1)
NO
Flag-detector1=0 H(2)Input=DWT1 H(3)Input=DWT2 H(4)Input=DWT2
NO
D
NO
Flag-detector3=1 H(1)Input=0 H(2)Input=0 H(4)Input=0
NO
YES Flag-detector3=0 H(1)Input=DWT1 H(2)Input=DWT1 H(4)Input=DWT2
D
NO
YES
Flag-detector2=0 H(1)Input=DWT1 H(3)Input=DWT2 H(4)Input=DWT2
Flag-detector2=1 H(1)Input=0 H(3)Input=0 H(4)Input=0
NO
YES Flag-detector2=0 H(1)Input=DWT1 H(3)Input=DWT2 H(4)Input=DWT2
D>Desired Negative Value YES
Flag-detector1=0 H(2)Input=DWT1 H(3)Input=DWT2 H(4)Input=DWT2
H(4)
D>Desired Positive Value
YES
D
Flag-detector1=1 H(2)Input=0 H(3)Input=0 H(4)Input=0
NO
D
YES NO
H(3)
H(2)
D>Desired Positive Value
Detection of voltage sag/swell without phase jump
Calculate DWT2
D>Desired Positive Value
Flag-detector4=0 H(1)Input=DWT1 H(2)Input=DWT1 H(3)Input=DWT2
YES
Flag-detector3=0 H(1)Input=DWT1 H(2)Input=DWT1 H(4)Input=DWT2
Flag-detector4=1 H(1)Input=0 H(2)Input=0 H(3)Input=0
Flag-detector4=0 H(1)Input=DWT1 H(2)Input=DWT1 H(3)Input=DWT2
Sag/Swell flag-detector=(Flag-detector1)+(Flag-detector2)+(Flag-detector3)+(Flag-detector4) End
Fig. 6. The flowchart of proposed sag/swell detection algorithm.
Vd (a)
-
+
x2 abc-dq transform
+
1 Reference
x2 cosθ
Vq
A(t) +
K
*
B(t)
+
*
(b)
Phase Voltage
π Cos
1 sT
Hysteresis Comparator
Low Pass Filter
θ(t)
1 sT
+
-
Sag/swell Detection Signal
+
sinθ PLL
Sdq
C(t) -
SEPLL
+
E(t) Sin
1
C(t)
Sag/swell Detection Signal Hysteresis Comparator
*
Reference
D(t) EPLL
(c)
Phase Voltage
FFT
VRMS
SFFT
-
Sag/swell Detection Signal
+ 1
Hysteresis Comparator
Reference Fig. 7. Block diagram of (a) dq-transformation, (b) EPLL and (c) FFT based voltage sag/swell detection methods.
B(t) is the difference of input and the synchronized fundamental component, C(t) is the amplitude of D(t), D(t) is the synchronized fundamental component, E(t) is the PLL signal and h(t) is the phase angle of D(t) [37,38].
BðtÞ ¼ AðtÞ k2 t A k2 hðtÞ ¼ cos hðtÞ cos xt t x 2 A k2 EðtÞ ¼ sin cos hðtÞ cos xt t 2 þ pt x 2 k3 A k2 k3 2 cos xt t CðtÞ ¼ x 2 CðtÞ DðtÞ ¼ CðtÞ sin þ pt k3
ð8Þ ð9Þ ð10Þ ð11Þ ð12Þ
There exists a compromise between speed and accuracy. For large K1, K2 and K3, the convergence of the estimated values to actual values is faster and the steady state misadjustment is higher. This is an inherent characteristic of an adaptive algorithm. Parameters K1, K2 and K3 should be selected appropriately according to the field of application. If only the total ‘‘flicker content’’ of a signal is to be extracted, then the filter can be set to operate in an alternative mode. In this mode, the filter is set to operate at a low speed to track only the fundamental signal and not the flicker. The result is that the smooth ‘‘averaged’’ fundamental is extracted on the output and the total distortion signal at the error terminal [38]. In EPLL the C(t) gives the amplitude of the tracked signal A(t). By subtracting the C(t) from ideal voltage magnitude, the voltage sag/ swell depth (SEPLL) can be detected.
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Table 1 The performance comparison of proposed and conventional sag/swell detection methods.
ð13Þ
The application of Fourier Transform (FT) to each supply phase is another method that can provide information regarding the state of a system supply. This method can accurately reveal magnitude and phase of each frequency component of the supply in the presence of harmonics in the system. To eliminate errors occurring with the information returned regarding the fundamental component, the previous methods effectively filter out harmonics other than the fundamental. This process can cause transient delays in detecting changes in the phase of the fundamental component [39,40]. In FFT based algorithm, the RMS variation of input voltage is measured to judge the voltage sag/swell. A discrete Fourier transform (DFT) algorithm is used to calculate the RMS value of the fundamental component [41]. The source voltage V(t) can be expressed using the Fourier series as presented by the Eq. (14). 1 1 X X a v ðtÞ ¼ 0 þ an cos nx0 t þ bn sin nx0 t 2 n¼0 n¼0
ð14Þ
a1 ¼ b1 ¼
Magnitude (V)
(a)
v ðtÞ cos x0 t dt
ð15Þ
v ðtÞ sin x0 t dt
ð16Þ
0
Z
T
0
pffiffiffi N T i 2X v t i cos 2p N N N i¼0 pffiffiffi N T i 2X b1 ¼ v t i sin 2p N N N i¼0
V RMS ¼
ð18Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 a21 þ b1
Va
400 300 200 100 000 -100 -200 -300 -400
Vb
ð19Þ
Voltage Swell
Vc
0.15
0.10
0.20
0.25
0.30
0.35
0.40
dq-transform based method 0.15
0.20
0.25
0.30
0.35
0.40
1.00
(b)
dq-transform based method
0.202
1.00
0.203
0.00 0.10
(b) 0.202
ð17Þ
Using the value of a1 and b1, the RMS value of the fundamental component can be calculated as the following:
Voltage Sag
Vc
T
a1 ¼
(a) Vb
2 T
Z
Eqs. (17) and (18) are obtained by applying the DFT to Eqs. (15) and (16).
The fundamental component for n = 1 is calculated by the Eq. (15) and Eq. (16), separating the imaginary and real parts Va 400 300 200 100 000 -100 -200 -300 -400 0.10
2 T
Magnitude (V)
SEPLL ¼ j1 CðtÞj
0.15
0.205
0.15
0.302 0.303 0.304 0.305
0.20
0.25
0.30
0.35
0.40
0.302 0.303 0.304 0.305
0.203 0.204 0.205
0.00 0.10
0.204
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0.35
0.40
EPLL based method
1.00 EPLL based method
(c)
1.00
(c) 0.203 0.204 0.205
0.00
0.10
0.206
0.15
0.301 0.302 0.303
0.20
0.250
0.30
0.00 0.10
0.304
0.35
0.203 0.204
0.205 0.206
0.15
0.301 0.302 0.303 0.304
0.20
0.250
0.30
0.35
0.40
0.40
FFT based method
1.00
FFT based method
1.00
(d)
(d)
0.212 0.214
0.00 0.10
0.215
0.216
0.217
0.15
0.00 0.10
0.304 0.305 0.306 0.307
0.20
0.25
0.30
0.35
0.214
0.303 0.304 0.305 0.306
0.215
0.15
0.20
0.250
0.30
0.35
0.40
0.40 Proposed method
Proposed method
1.00
1.00
(e)
(e) 0.199 0.200 0.201 0.202
0.00 0.10
0.213
0.15
0.199 0.200 0.201 0.202
0.299 0.300 0.301 0.302
0.299 0.300 0.301 0.302
0.20
0.25
0.30
0.35
0.40
Time (s) Fig. 8. The performance of sag detection methods for three phase to ground fault without phase jump.
0.00 0.10
0.15
0.20
0.25
0.30
0.35
0.40
Time (s) Fig. 9. The performance of detection methods for three phase swell without phase jump.
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By subtracting the VRMS signal from RMS value of the ideal voltage, the voltage sag/swell depth (SFFT) can be detected as shown in Fig. 7(c).
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 SFFT ¼ 1 a21 þ b1
Case 3: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for single phase 13% voltage sag with 10° phase jump. As seen from Fig. 10 and Table 1, the proposed algorithm has superior performance to detect the voltage sag with minimum time delay. In this case, the dq-transformation based method has the worst detection performance. Also, due to the presence of phase jump the EPLL based method has low accuracy to detect voltage sag. FFT based method also has large time delay to detect the voltage sag. Case 4: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for single phase 13% voltage sag with 20° phase jump. The proposed algorithm has superior performance to detect the voltage sag with minimum delay as seen from Fig. 11 and Table 1. The dq-transformation based method has the worst detection performance. Comparing with the previous case (a voltage sag with 10° phase jump), FFT and EPLL based methods have the poor detection performance because these methods can be affected by phase jump degree. Case 5: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for single phase 13% voltage sag with 20° phase jump condition for distorted phase voltage with harmonic. The distorted phase voltage contains 5%, ground fault with 20° phase jump when the source voltage includes harmonic orders. 5%, 4%, 2% and 1.5% p.u. in 5th, 7th, 11th and 13th harmonic orders, respectively. As seen from Fig. 12 and Table 1, the proposed algorithm performs superior performance
ð20Þ
Analysis and discussions The performance of the proposed algorithm is compared with different case studies. The results of test cases are summarized in Table 1. The sag event occurs between 0.2 and 0.3 s.
400 300 200 100 0 -100 -200 -300 -400 0.10
Phase voltgae-Va Voltage Sag
(a)
0.15
0.20
0.25
0.30
0.35
0.40
Magnitude (V)
(a)
Magnitude (V)
Case 1: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for three phase balance (without phase jump) 13% voltage sag. As seen from Fig. 8 and Table 1, the proposed algorithm has superior performance to detect the start and end times of voltage sag. FFT based method has the worst performance to detect the start and end time of voltage sag due to its large computation time. Case 2: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for three phase balance (without phase jump) 13% voltage swell. The proposed algorithm has superior performance to detect the start and end times of voltage swell as seen from Fig. 9 and Table 1. FFT based method again performs the worst performance to detect the start and end times due to its large computation time.
400 300 200 100 0 -100 -200 -300 -400 0.10
dq-transform based method
Phase voltage-Va
0.15
Voltage Sag
0.20
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dq-transform based method
1.00
1.00
(b)
(b) 0.00 0.10
0.15
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0.35
0.00 0.10
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EPLL based method
0.15
EPLL based method
1.00
1.00
(c)
(c) 0.00 0.10
0.15
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0.00 0.10
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FFT based method
0.15
FFT based method
1.00
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(d)
(d) 0.00 0.10
0.15
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0.00 0.100
0.40
Proposed method
0.150
Proposed method
1.00
1.00
(e)
(e) 0.00 0.10
0.15
0.20
0.25
0.30
0.35
0.40
Time (s) Fig. 10. The performance of sag detection methods for single phase to ground fault with 10° phase jump.
0.00 0.10
0.15
Time (s) Fig. 11. The performance of sag detection methods for single phase to ground fault with 20° phase jump.
M.B. Latran, A. Teke / Electrical Power and Energy Systems 71 (2015) 131–139 Phase voltage-Va 400 300 200 100 0 -100 -200 -300 -400 0.10 0.15
Voltage Sag
(a)
0.20
0.25
0.30
0.35
0.40
Magnitude (V)
(a)
Magnitude (V)
138
400 300 200 100 0 -100 -200 -300 -400 0.10
dq-transform based method
Phase voltage-Va
0.15
Voltage Sag
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dq-transform based method
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(b)
(b) 0.00 0.10
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0.00 0.10
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EPLL based method
0.15 EPLL based method
1.00
1.00
(c) (c) 0.00 0.10
0.15
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0.00 0.10
FFT based method
(d)
0.15 FFT based method
1.00
1.00 (d)
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0.00 0.100
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Proposed method
0.150
Proposed method
1.00
1.00
(e) (e) 0.00 0.10
0.15
0.20
0.25
0.30
0.35
0.40
Time (s)
0.00 0.10
0.15
Time (s) Fig. 12. The performance of sag detection methods for single phase to ground fault with 20° phase jump when the source voltage includes harmonic orders.
to detect the voltage sag with minimum time delay. In this case, due the EPLL and FFT based detection methods extract the harmonics from fundamental components, they are not affected by harmonics. The harmonics in the system can cause an increase on the RMS value of reference signal. In this condition, the dq-transformation based method can detect the voltage sag wrongly because this method cannot extract the harmonic component. This situation can lead to wrong detection of sag or swell when the magnitude of voltage is within the standard limits. Case 6: In this case, the performance of developed sag/swell detection algorithm is compared with conventional sag/swell detection methods for single phase 13% voltage sag with 20° phase jump condition for distorted phase voltage with harmonic and flicker. The distorted phase voltage contains 10% p.u. at 8 Hz flicker with 5%, 4%, 2% and 1.5% p.u. in 5th, 7th, 11th and 13th harmonic orders, respectively. The proposed algorithm achieves superior performance to detect the voltage sag with less time delay as seen from Fig. 13 and Table 1. In this case, due the dq-transformation based detection method cannot extract the flicker and harmonic orders from signals, so in normal operation condition it also detects voltage sag or swell. In EPLL based detection method, the EPLL parameters should be adjusted to extract the flicker and harmonic orders from phase voltage waveform in steady state. So this can cause a large time delay for detection process. The accuracy of EPLL based detection method is related with its parameters, voltage sag/swell level and phase jump degree. FFT based detection method cannot completely extracts the flicker and harmonics from fundamental components. This method can operate incorrectly especially within the standard limits.
Fig. 13. The performance of sag detection methods for single phase to ground fault with 20° phase jump when the source voltage includes flicker and harmonic orders.
Conclusions In the present paper, a new wavelet transform based voltage sag/swell detection algorithm which can be even applied in the presence of flicker and harmonic polluted source voltage has been introduced. The proposed detection algorithm has the advantage of being a hybrid structure consisting of a db2 and a db8 to detect sag/swell with or without phase jump. The proposed algorithm can detect the start and end times of voltage sag/swell with and without phase jump within 0.5 ms and 1.15 ms, respectively. The feasibility of proposed algorithm is validated through test cases using the PSCAD/EMTDC 4.2.0. The performance of developed voltage sag/swell detection algorithm is compared with dq-transformation, FFT and EPLL based voltage sag/swell detection methods. Compared with conventional detection methods, the case results reveal good robustness, accuracy and faster processing time to detect balanced and unbalanced voltage sag/swell. The solution step of the simulation model is adjusted at 10 ms which can be easily adapted to future hardware implementations. The developed sag/swell detection algorithm can be effectively utilized in Custom Power Devices for fast compensation of voltage sag/swell in the sensitive loads. References [1] Bollen MHJ, Gu YH. Signal processing of power quality, disturbances. Wiley Interscience & IEEE Press; 2006. [2] IEC Electromagnetic compatibility (EMC), Part 4, Section 30: testing and measurement techniques – power quality measurement methods. Standard IEC 61000-4-30; 2003. [3] IEEE recommended practice for powering and grounding sensitive electronic equipment. IEEE standard 1100; 1992.
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