A novel adaptive single-phase reclosure scheme based on improved variational mode decomposition and energy entropy

Electrical Power and Energy Systems 118 (2020) 105771

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A novel adaptive single-phase reclosure scheme based on improved variational mode decomposition and energy entropy

T

⁎

Qiuqin Suna, , Fei Linb, Rong Jianga, Feng Wanga, She Chena, Lipeng Zhonga a b

College of Electrical & Information Engineering, Hunan University, Changsha 410082, China Yongzhou Electric Power Company, State Grid, Yongzhou 425000, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Secondary arc Extended grading capacitor Single phase adaptive reclosure Variational mode decomposition Energy Entropy

The extended grading capacitor (GC) for multi-break circuit breaker is a cost-effective method to suppress secondary arc. Since the integration of GC alter the topology of the system, the existing adaptive auto-reclosure scheme should be changed. Considering the characteristics of line voltage waveforms under various faulty conditions, a novel adaptive single-phase reclosing scheme is proposed based on an improved variational mode decomposition (VMD) and energy entropy (EE). The voltage signal extracted from capacitive voltage transformer is decomposed into a series of finite bandwidth intrinsic mode functions (IMF), and then the energy entropy (EE) of each IMF component is computed. To avoid modal mixing, the concept of quality factor is raised. In the case of permanent fault, the natural component of the voltage attenuates fast due to the continuous discharge through the fault point. As time goes, such component approaches zero, and the total voltage becomes more smooth and regular. The EE value also decreases gradually. The EE value is considerably large for the transient fault due to the repetitive re-strike of electric arc, and the EE value has an oscillating trend. The fault type can be distinguished by setting a reasonable threshold. The performance of the proposed method is almost not affected by the installation mode of shunt reactor bank, the fault location, the shunt compensation degree, fault resistance, etc. Both the theoretical analysis and simulation results demonstrate that the proposed method can quickly and accurately identify the fault type.

1. Introduction Single-phase reclosure is an effective method to improve the transient stability and synchronism of power system. It could also reduce the torsional impact on generator shafts and minimize the switching overvoltage. The single-phase reclosure has been widely applied to ultra high voltage transmission line [1]. The reclosing commander would be sent to the associated phase after a time delay following the trip. In order to prevent re-closing into faults and avoid unnecessary resynchronization, the identification method, which distinguishes between a permanent fault and a transient fault, is vitally important for power system [2,3]. Several criteria have been raised so far to address this subject ever since the concept of single phase adaptive reclosure (SPAR) scheme is put forward. Based on mode current, a dual-window transient energy ratio is proposed in Refs. [4,5]. It is implemented with the high frequency transient current. In [6], the discrete wavelet transform is adopted to analyze the waveforms; the wavelet result is used as the feature vectors of the neural network to identify fault type and to

⁎

determine the arc extinction moment. The zero-sequence instantaneous power is monitored to detect the instant of secondary arc quenching [7]. Moreover, considering shunt reactors, the ratio of even harmonic to odd harmonic changes drastically during the evolution of fault. It is sometimes used as an indicator to determine secondary arc extinction moment [8]. However, the existing methods have many drawbacks. For instance, in order to keep the transient stability of power system, the reclosure should be generally completed within 2 s, and mostly around 1 s, including the circuit breaker opening and closing time, the dielectric recovery time for secondary arc column, etc. It has a high realtime requirement for SPAR scheme and poses a challenge to the computational burden of the algorithm. Besides the effectiveness, many factors should also be considered in practice, especially the amount of the processed data and the procedure of the algorithm itself; some travelling wave-based methods utilizing high frequency data requires a great sampling frequency to discriminate the detailed waveform information; the maximum sampling frequency for existing industrial product has reached 36 MHz, which drastically increase the computational burden [9,10]. The methods based on beat frequency spectrum

Corresponding author. E-mail address: [email protected] (Q. Sun).

https://doi.org/10.1016/j.ijepes.2019.105771 Received 29 May 2019; Received in revised form 18 October 2019; Accepted 9 December 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

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3.1. Forced component

are only applicable to recovery voltage stage. Because of complexity of approach, the design of a reclosing relay based on some methods is sophisticated. The use of artificial neural network needs considerable sample data, and the training of such data would take a relatively long duration. The methods based on beat frequency spectrum are only applicable to recovery voltage stage. Because of complexity of approach, the design of a reclosing relay based on some methods is sophisticated. The VMD algorithm, which is a non-recursive adaptive decomposition method, is proposed by Dreagomiretskiy and Zosso [11]. An alternate direction method of multipliers is used to iteratively search the optimal solution of variational model, so as to achieve the minimum estimated bandwidth of each mode. The VMD has been recently applied to many industrial areas [12,13]. In Ref. [14], the raw signal during the milling process is processed to obtain the chatter indicator, and an automatic selection method based on Kurtosis is proposed. A seismic signal is decomposed into several band-limited quasi-orthogonal intrinsic mode functions to interpret the geological information in Ref. [15]. By exploring the frequency properties of the infrared small target, a nonnegativity-constrained VMD model is constructed, and the potential target signal is obtained by solving the model [16]. Based on the VMD and Hilbert transform, the features of partial discharge signals are extracted to assess the power transformer condition. However, the performances of these methods are highly dependent on given case, and have certain limitations, e.g., sensitive to noise and may fail at some conditions. More importantly, the decomposition mode number is often determined empirically, which has a great impact on the results [11]. The algorithm may be either under-decomposed or over-decomposed. In this work, the electromagnetic transients of system under different fault conditions are analyzed. A novel SPAR scheme is proposed based on VMD combined with Energy Entropy. The concept of decomposition quality factor is proposed to determine the mode number and hence the fault type. Finally, the proposed method is validated.

Suppose phase A fails, the circuit breaker is switched off. After the secondary arc is extinguished, the fault point disappears. Due to the coupling effect between the faulty phase and sound phase, there is still a recovery voltage on phase A. The equivalent circuit model for the forced component is illustrated in Fig. 2. According to the Node's theorem,

⎛ 1 + 1 + 1 ⎞ Ur = EA + −0.5EA Z1 Z2 ⎠ Z0 Z1 ⎝ Z0 ⎜

⎟

(1)

Here, C −C

CG = 1 3 0 ⎧ ⎪ 1 Z0 = jωC ⎪ G ⎪ 3jωLp − p ⎨ Z1 = 6 − 2ω2Lp − p (C1 − C0 ) ⎪ jωR ⎪Z = ⎪ 2 jωLp − g + R (1 − ω2Lp − g C0 ) ⎩

(2)

Substituting (9) into (8),

Uf =

(2Z1 Z2 − Z0 Z2) EA 2(Z0 Z1 + Z1 Z2 + Z2 Z0)

(3)

In practice, Z1 ≪ Z2 , Eq. (9) can be further reduced to,

Uf =

(2Z1 − Z0) EA ≈ 0 2(Z0 + Z1)

(4)

The terminal voltage may be slightly different from that of the fault point, depending on fault location and line impedance. The forced component of the terminal voltage can be ideally reduced to zero by means of GC. 3.2. Natural component

2. Principle of extended grading capacitor for suppressing secondary arc

After the extinction of secondary arc, the energy trapped in reactors and capacitors would discharges. Taking the transient fault as an example, the circuit for the natural component is obtained using the Laplace Transform, as illustrated in Fig. 3. The characteristic equation for the circuit is,

The double-break structure is commonly used for high voltage circuit breakers. A capacitor is connected in parallel with each unit to ensure uniform recovery voltage distribution, as illustrated in Fig. 1 [17]. The GC can be further extended to suppress secondary arc by increasing the capacitance only [18]. The equivalent circuit for the system with GC is illustrated in Fig. 1(b). Under normal condition, the CBs are kept closed and the GCs have little influence on the system. In the event of fault, the interrupter would be immediately opened. Then, the GCs would be automatically inserted into the line. On one hand, the sound phases B and C can contribute a current through electrostatic coupling between the phases, as denoted by ic in (b). Meanwhile, the fault phase A would also inject a small current component, represented by ig, into the fault point due to the presence of GC. The secondary arc current is the sum of these two components. The presence of GC would completely neutralize the effect of capacitive coupling between faulted and un-faulted phases. After the extinction of secondary arc, the CBs are reclosed, and the GCs would be shorted again. The common neutral reactor can be cancelled. Moreover, despite its great performance in reducing arcing time, the use of GC is also free of the installation of shunt reactor. Compared with the FLSR, the shunt reactor can be equipped either on the bus or on the line [18], as shown in Fig. 1(c).

a6 s 6 + a5 s5 + a4 s 4 + a3 s 3 + a2 s 2 + a1 s + a0 = 0

(5)

Substituting the line parameters into (14), the normalized coefficients of the characteristic equation are obtained. 2

a6 = 4LCLp2 C ⎧ G ⎪ 2 ⎪ a5 = 4RCLp2 C G ⎪ ⎪ a4 =4Lp CG (4Lp CG +4CLp + 4LC ) a3 =4RCLp CG ⎨ ⎪ = a Lp CG +2CLp + LC 16 2 ⎪ ⎪ a1 = RC ⎪ a0 = 4 ⎩

(6)

The general solution of the natural component can be expressed as,

u n (t ) = b0 + b1 es1t + b2 es2t + b3 es3t + +b4 es4 t

(7)

and,

si = δi + jωi

(8)

where b1, b2, b3 and b4 are constants determined by the initial condition when the secondary arc is extinguished; ωi is the oscillating frequency and δi is the damping factor. The terminal voltage is a superposition of multiple components, and it requires a duration to reach the steady state until the coefficient drops near zero. The damping is closely associated with the line resistance. Normally, the smallest damping factor

3. Terminal voltage analysis The full response of terminal voltage is comprised of the natural component and the forced component [19]. 2

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C B A

Fig. 1. Topology of double-break circuit breaker with GC. (a) Profile of circuit breaker. (b) Equivalent circuit of GC and transmission line. (c) Single line diagram of substation with GC, unit 1-shunt reactor is installed at the line, and unit 2-shunt reactor is installed on the bus.

component of permanent fault would die out more rapidly due to continuous discharge through the fault resistance. From the perspective of electric circuit, the extended GC provides a path for the release of the energy input into the fault. Its presence would smooth the slope and the rate of rise of recovery voltage.

would play a decisive role in the attenuation of the total natural component. As far as the permanent case, the characteristic equation is still a fifth-order function but the variation of the coefficients due to the branch R. The initial condition for the circuit is also different and hence the components. Compared with the transient fault, the natural 3

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following equation, 2

j ⎧ min ⎧∑K ∂t ⎡ δ (t ) + πt ∗ uk (t ) ⎤ e−jωk t ⎫ ⎪ k=1 ⎣ ⎦ {uk },{ωk } ⎨ 2⎬ ⎭ ⎩ ⎨ K ⎪ s. t . ∑k = 1 uk (t ) = f (t ) ⎩

(

)

(10)

where uk is the kth mode, ωk is the center frequency around which uk is mostly compact, and δ(t) is the Dirac delta function. In order to obtain the solution, a quadratic penalty factor α and a Lagrangian multiplier λ are applied for quick convergence and enforcement of the constraint. The objective function to be minimized becomes an unconstraint one.

L ({uk }, {ωk }, λ ) K

j ⎞ ∗ uk (t ) ⎤ e−jωk t = α ∑ ∂t ⎡ ⎛δ (t ) + ⎢ ⎥ πt ⎝ ⎠ ⎣ ⎦ k=1

2

K

+ f (t ) − 2

2

∑ uk (t ) k=1

+ 2

K

λ (t ), f (t ) −

∑ uk (t )

(11)

k=1

The solution to the original minimization problem (17) is now found as the saddle point of the augmented Lagrangian in a sequence of iterative sub-optimizations called alternate direction method of multipliers. Eq. (18) is converted into the frequency domain by using Fourier equidistant transform. The updated expressions for variables uk̂ (ω) , ωk and λ (ω) are as follows:

Fig. 2. Equivalent circuit for the forced component of terminal voltage. (a) transient fault. (b) permanent fault.

ukn̂ + 1 (ω) =

 f (ω) − ∑i ≠ k uin̂ (ω) +

λ ̂(ω) 2

1 + 2α (ω − ωk )2

(12)

∞

ωkn + 1 =

λ̂

n+1

∫0 ω |uk̂ (ω)|2 dω ∞ ∫0 |uk̂ (ω)|2 dω

n ⎛ (ω) = λ ̂ (ω) + τ ⎜^f (ω) − ⎝

(13) K

∑ unk̂ +1 (ω) ⎞⎟ k=1

⎠

(14)

How to choose K value to avoid modal mixing is a crucial step [12]. To address this, two quantities are introduced here. Suppose the information entropies of K intrinsic mode function components are S1, S2, S3, …, and SK, respectively, the variance of information entropies are:

C = (S1 − S)̂ 2 + (S2 − S)̂ 2 + ···+(Sk − S)̂ 2

(15)

where S ̂ is the mean of information entropies. The larger the variance, the greater the dispersion for each component. The other quantity is the error between the original signal and the reconstructed one.

Δ = |f (t) − IMF1 − IMF1 − ···−IMFK| Fig. 3. Equivalent circuit for natural component. (a) transient fault. (b) permanent fault.

The decomposition quality factor is intended to find a balance between the variance and the error. It is defined as,

4. Variational mode decomposition and energy entropy

Q=

4.1. Principle of VMD

C Δ

(17)

A higher quality factor suggests that not only the reconstructed signal is more close to the original one but also the discrimination of each intrinsic mode function components is obvious and hence a better decomposition result. The decomposition number K can be determined by the quality factor. The pseudocode of improved VMD algorithm is listed in Table 1.

The VMD is an adaptive, quasi-orthogonal, and completely non-recursive signal processing algorithm [11]. A signal can be decomposed into several natural modes with limited bandwidth, and most of them are around the central frequencies. Given an input signal f, it is decomposed into K finite bandwidth intrinsic mode functions,

uk (t) = Ak (t)cos(ϕk (t))

(16)

4.2. Energy entropy

(9)

where Ak(t) is the amplitude and Ak(t) ≥ 0, ϕk (t ) denotes the phase, a non-decreasing function; ϕk' (t ) = ωk (t ) , the instantaneous frequency of each function. The VMD is a constrained variation problem represented by the

The entropy is a quantity to describe the uncertainty of information, which suggests the probability of occurrence of each component in the information. After obtaining K intrinsic mode functions, the energy of each component is computed. The energy of each IMF is [20–21], 4

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Table 1 Pseudocode of improved VMD algorithm. Algorithm: VMD Signal, α = 2000, τ = 0.3, K = 2, DC = 0, init = 1, ε = 10−7, N = 500 u is the collection of decomposed modes; u_hat is the spectra of the modes; omega is estimated mode center-frequencies. function [u, u_hat, omega] = VMD (signal, alpha, tau, K, DC, init, tol);

Input: Output: 1 2

1

Initialize{ωk1} , {uk1}, {λ ̂ } and n to 0;

3 4

Define n = n + 1 to execute the loop; Define k = 0, k = k + 1; when k < K, Update uk and ωk according to Eqs.(12) and (13); Update λ according to Eq. (14); Determine whether the iteration stop condition is satisfied; if ε < 10−7do end loop, output u; otherwise repeat steps 4–7. end

5 6 7 8 9

+∞

∫−∞

Ei =

|ui (t )|2 dt

(18)

The energy of signal is the sum of all components, K

∑ Ei

E=

(19)

i=1

The EE of VMD can be expressed as [21]: K

HEE = − ∑ pi ln (pi )

(20)

i=1 th

where pi = Ei/E represents the percentage of i IMF component. The flowchart of the proposed SPAR scheme is depicted in Fig. 4. 5. Results & discussion 5.1. Simulation The model of UHV transmission line is established in the environment of EMTP. Based on the A. T. Johns' equation, the dynamic conductance of electric arc g a can be approximately expressed as,

dga dt

=

1 (Ga − ga) τa

(21)

where Ga is the stationary arc conductance, τa is the time constant of the arc channel. The subscript a indicate p and s, which denote primary and secondary, respectively. Here,

Ga =

|ia (t )| va (t ) ∙la (t )

(22)

where ia (t) is the instantaneous arc current; la (t) is the arc length; va (t) is the voltage gradient. For primary arc, the voltage gradient is nearly constant whereas the value for secondary arc is controlled by the peak of the current Is ,

⎧ vp = 15V cm ⎨ vs = 75Is−0.4 ⎩

(23)

The time constant is another crucial parameter, and the following expressions are considered, −5

⎧ τp = 2.85 × 10 Ip ⎪ lp ⎨ 2.51 × 10−3Is1.4 ⎪ τs = ls ⎩

Fig. 4. Flowchart of proposed adaptive reclosing scheme.

(24)

Since the faulted phase is often cleared within 0.1 s, the duration of primary arc is very short, and the length lp is often considered to be invariant, which is 10% longer than the length of insulator string. In our work. The secondary arc is drastically elongated due to the resultant of 5

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Fig.5. Simulation model (a) Single line diagram of UHV power system. (b) Schematic diagram of electric arc model. R0 = 0.1542 Ω/km, L0 = 2.6452mH/km, C0 = 0.0093μF/km, R1 = 0.0076 Ω/km, L1 = 0.8391mH/km, C1 = 0.0139μF/km.

Lorenz force and wind force. Its length is quite random, and two expressions are also considered.

1fortr ≤ 0.1s ls =⎧ 10 ⎨ lp ⎩ tr fortr > 0.1s

(25)

where tr is the time from the initiation of secondary current, and ξ is equal to 3.25. The secondary arc is normally extinguished when its current crosses zero. The dielectric theory is employed in our work, and the strength can be roughly expressed by

1620Te ⎤ vr = ⎡5 + (tr − Te ) h (tr − Te) l s ⎢ 2.15 + Is ⎥ ⎦ ⎣

(26)

wherevr is the arc reigniting voltage, Te is the time from the initiation to a current zero, h (tr − Te) is a delayed unit-step function. Following the polarity reversal, the secondary arc current would be held zero if the recovery voltage is below the dielectric strength, and vice versa. The block diagram of electric arc is depicted in Fig. 5. The Laplace Transfer Function is employed to solving the differential equations for the arc [2,17].

Fig.6. Terminal voltage waveform. (a) transient fault. (b) permanent fault.

6

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Fig. 7. Quality factor.

Fig. 9. Spectrums of the VMD output for the original signal. (a) Spectrums of the transient fault output. (b) Spectrums of the permanent fault output.

•

• Fig. 8. Improved VMD decomposition results. (a) transient fault; (b) permanent fault.

5.2. Results Assuming that a single phase-to-ground fault occurs on the midpoint of the line at t = 0.04 s, the phase is then cleared after 100 ms. The terminal voltage waveform is shown in Fig. 6. For the purpose of comparison study and further signal processing, the entire voltage waveforms are illustrated. The results in Figs. 7–10 are all obtained based on Fig. 6.

recovery voltage contains a large proportion of high frequency components which oscillates quite rapidly. Once the high frequency components died out, the recovery voltage is in steady state. Due to the quench-reignition behavior of electric arc, the secondary arc resistance has a high degree of non-linearity. Hence, the recovery voltage has a beat behavior for the transient fault, as shown in Fig. 6(a). Regarding the permanent fault, however, the fault point is always present and the line-to-ground capacitor is continuously discharged. The fault phase voltage, as shown in Fig. 6(b), contains only the power frequency component and an attenuated DC component only. The terminal voltage is processed using the proposed method. Due to the electromagnetic interference, the measured signal is likely to be contaminated by noise. It is firstly filtered and then sampled at a frequency of 10 kHz, and each fault is intercepted by a group of 200 points. The sampling time window is 20 ms, the moving step is 20 ms. The voltage signals is decomposed with the modal number K = 2 ~ 8, and the bandwidth constraint α takes 2000, the fidelity τ = 0.3. The tolerance ε is set as 1E-7. The decomposition quality factor is show in Fig. 7, and the associated frequency centers are listed in Table 2. When K = 2, the quality factor reaches the highest up to 0.542. The difference between the IMF components is large, and the decomposition performance is great. When K exceeds 3, some central frequencies are close to each other, and the so-called over-decomposition behavior occurs. In this paper, K = 2 is selected, and the IMF components are plotted in Fig. 8.

To get the frequency information, the IMFs are processed by Fast Fourier Transform, and the spectrum is plotted in Fig. 9. It can be seen that the frequencies mainly locate in the ranges of [48 Hz, 52 Hz] and [380 Hz 390 Hz]. The power frequency component is mainly reflected in IMF1 whereas the high frequency component is mainly reflected in IMF2. The mode is separated without modal mixing. The IMF components are reconstructed and compared with the original signal, as shown in Fig. 10. Clearly, the discrepancy between the reconstructed signal and the original one is quite small. Due to the

• Clearly, the secondary arc is rapidly extinguished while using GC

and the arcing time is less than 0.1 s. The transient process can be generally divided into three stages, as depicted in Fig. 6. The 7

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Fig. 10. Comparison of the reconstructed signal with the original signal. (a) Transient fault. (b) Permanent fault. Table 2 Frequency center of different K values. K Frequency center (Hz) 2 3 4 5 6

49 49 49 49 48

385 274 227 218 59

• 459 360 341 233

494 453 347

605 456

609

high nonlinearity of electric arc as well as the complexity of voltage signal, the value at this stage is relatively large but still far below the associated standards. For the purpose of comparison, the voltage signal obtained from capacitive voltage transformer (CVT) is also decomposed by means of empirical mode decomposition (EMD), and the result is plotted in Fig. 11. Compared with VMD, the decomposition mode number of EMD is fixed and cannot be prescribed. Here, IMF1–IMF6 of EMD represent the frequency band from high to low. There is a mode aliasing near the low frequency area. The central frequency of the mode cannot be effectively separated. The mode mixing can be found in IMF1, and it presents difficulties in recognizing the individual contributions of each component. The following IMFs would all be distorted and affected by IMF1. It may give rise to misjudgment for the fault type. The decomposition result of our method is better than that of traditional EMD. Fig. 12

•

• •

5.3. Discussion

• The energy entropy values of each IMF components are computed,

and the results are given in Fig. 13. It suggests that the energy entropy mainly focuses on IMF2. It is the domain frequency bands and can be considered as the key feature for a fault. Compared with

8

IMF2, the waveform of IMF1, as well as the energy contained, is more close to the original signal. According to the definition of EE, the value is less than that of IMF2. The total EE of transient fault and permanent fault are 0.0749 and 0.0148, respectively. In practice, the amplitude of transient fault is much larger than that of permanent fault. Meanwhile, the secondary arc resistance exhibits a highly nonlinear and re-ignition behavior [22–24], resulting in extremely complex signal frequency components for the transient fault. Generally, the wider the information range, the higher the entropy, and the EE value of former is much larger than that of the latter. It provides a solution to identify fault types. Due to the continuous discharge, the natural component attenuates fast through the fault point. As time goes, such components finally approach zero for the permanent fault. The voltage waveform becomes more smooth and regular, and only the single power frequency dominates. The EE value would drop until the secondary arc is eventually extinguished. The sensitivity analysis is also performed in this section [25]. The impacts of fault location, the shunt compensation degree, the installation mode of shunt reactor banks on the energy entropy value are discussed, and the results are listed in Tables 3 and 4. Clearly, the EE value for transient faults is quite large, generally above 0.07. In the case of the permanent faults, it drops drastically below 0.01. To prevent misjudgment, a reasonable threshold HT is set as 0.05. If the energy entropy is greater than the threshold, it can be regarded as transient and vice versa. The selection of a reasonable threshold HT is a key to this method. It is oriented to maximize the separability of the resultant fault type classification. The EE value is essentially the reflection of the voltage waveform complexity. Given the line parameters, the signal waveform is determined to some extent, and hence Hset is also located in a certain range. The threshold selection problem involved in many other

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Fig. 11. EMD results. (a) Transient fault. (b) Permanent fault.

Fig. 13. Energy entropy of IMFs. Table 3 Energy entropy values of different compensation of shunt reactor. Compensation of shunt reactor

Fig. 12. Spectra of the EMD output for the original signal. (a) Spectra of the transient fault output. (b) Spectra of the permanent fault output.

•

60% 70% 80% 90%

industry areas [26], especially in pattern recognition. The automatic and adaptive thresholding techniques provides useful references and needs to be further studied for our case [27,28]. The EE value of faulty phase under different fault condition is constantly changing. Meanwhile, the variations for the permanent 9

Transient fault Permanent fault IMF1

IMF2

HEE

IMF1

IMF2

HEE

0.0143 0.0142 0.0142 0.0142

0.0609 0.0609 0.0608 0.0607

0.0752 0.0751 0.0750 0.0749

0.0020 0.0020 0.0020 0.0021

0.0124 0.0125 0.0126 0.0127

0.0144 0.0146 0.0147 0.0148

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Table 4 Energy entropy values of faulty phase. The mode of shunt reactor

Fault location

Transient fault

Permanent fault Rf = 100 Ω Rf = 300 Ω

Line side

Busbar side

Without shunt reactor

20% 40% 60% 80% 20% 40% 60% 80% 20% 40% 60% 80%

IMF1

IMF2

HEE

IMF1

IMF2

HEE

IMF1

IMF2

HEE

0.0097 0.0142 0.0204 0.0116 0.0101 0.0145 0.0204 0.0124 0.0103 0.0145 0.0203 0.0122

0.0452 0.0607 0.0799 0.0518 0.0465 0.0617 0.0800 0.0546 0.0472 0.0619 0.0798 0.0542

0.0549 0.0749 0.1002 0.0633 0.0565 0.0762 0.1004 0.0669 0.0575 0.0764 0.1001 0.0664

0.0009 0.0021 0.0033 0.0027 0.0003 0.0018 0.0029 0.0049 0.0010 0.0019 0.0030 0.0049

0.0067 0.0127 0.0190 0.0159 0.0029 0.0116 0.0167 0.0260 0.0068 0.0119 0.0172 0.0260

0.0076 0.0148 0.0224 0.0186 0.0032 0.0135 0.0196 0.0309 0.0078 0.0137 0.0202 0.0309

0.0007 0.0018 0.0011 0.0087 0.0004 0.0004 0.0005 0.0014 0.0003 0.0004 0.0005 0.0043

0.0048 0.0115 0.0075 0.0177 0.0020 0.0032 0.0036 0.0310 0.0018 0.0032 0.0036 0.0159

0.0055 0.0134 0.0086 0.0264 0.0024 0.0036 0.0041 0.0324 0.0021 0.0036 0.0041 0.0202

Table 5 Statistics of energy entropy values of faulty phase. Quantity

Mean value Standard value Variance value

Transient fault

Permanent fault

0.0745 0.0172 2.9448 × 10−4

R = 100 Ω

R = 300 Ω

0.0169 0.0087 7.5137 × 10−5

0.0105 0.0103 1.0698 × 10−4

•

Table 6 Energy entropy value using EMD method. The mode of shunt reactor

Line side

Busbar side

Without shunt reactor

Fault location

20% 40% 80% 20% 40% 80% 20% 40% 80%

Transient fault

Permanent fault R = 100 Ω

R = 300 Ω

HEE

HEE

HEE

1.6925 1.7330 1.0729 1.8037 1.6139 1.0668 1.5695 1.6926 1.5954

1.4978 0.5902 1.1851 1.6260 1.2333 0.8999 1.2446 1.2485 1.1765

1.1727 0.8617 1.5610 1.3656 1.4347 0.9694 1.2623 1.3610 1.3321

Table 5. The results suggest that the influences the installation mode of shunt reactor bank, the shunt compensation degree, the fault location, etc., on the fault type identification are very small. The criterion and the threshold value are still applicable and can judge the fault type even with the variation of aforementioned factors. It is should be noted that the computational burden for the proposed scheme in this work is relatively moderate. The running time is about tens of milliseconds only on a 2.40 GHz Intel Core i5-4258U CPU-based personal computer. For the purpose of comparison, the EE value is also computed using EMD method, as listed in Table 6. However, the discrimination is comparatively small and not distinct. The value for transient fault is sometimes even smaller than that of the other. For instance, when the fault location is 80% and the shunt reactor is installed on the line side, the EE value for the former drops drastically to 1.0729 whereas the EE value for the latter are 1.1851 and 1.5610 when R = 100 Ω and R = 300 Ω, respectively. There is no obvious distinct boundary, and some areas are intersected. Principally, the EMD is effective in mono-component decomposition; however, it is susceptible to mode mixing under singularities, instable under fitting due to cubic spline interpolation Table 7.

6. Conclusion The conclusions are drawn as follows:

• The concept of quality factor, along with the energy entropy, is in-

Table 7 Statistics of energy entropy values using EMD method. Quantity

Mean value Standard value Variance value

Transient fault

1.5408 0.2755 0.0759

Permanent fault R = 100 Ω

R = 300 Ω

1.1891 0.3036 0.0922

1.2578 0.2231 0.0498

•

fault and transient fault versus the fault condition are different. However, it should be noted at most case, the EE value for the transient fault is located in the range from 0.0548 to 0.1004 whereas the value for the permanent fault is located in the range from 0.0086 to 0.0324. The maximum value for the former is 0.1004 whereas the minimum value for the latter is only 0.0021. Clearly, there is a great discrimination between the two fault types. From the perspective of statistics, the mean value for the former reaches 0.0745 whereas the latter is only 0.0105 in the case that R = 300 Ω. The statistics of the EE value for both the transient and permanent value is presented in

•

troduced into variational mode decomposition process. Compared with the EMD algorithm, the proposed algorithm can effectively avoid the modal mixing and enhance the accuracy of signal feature extraction. Since the secondary arc resistance exhibits a highly nonlinear and re-ignition behavior, resulting in extremely complex signal frequency components for the transient fault, and hence a wider information range. The EE of transient fault is much larger than the other. It provides a solution to identify fault types. The performance of the proposed method is almost not affected by the installation mode of shunt reactor bank, the fault location, the shunt compensation degree, fault resistance, etc. It can be also applied to determine the extinction time, and provides an alternative to SPAR scheme.

Declaration of Competing Interest The authors declared that there is no conflict of interest. 10

Electrical Power and Energy Systems 118 (2020) 105771

Q. Sun, et al.

Acknowledgements [14]

This work is supported by the National Natural Science Foundation of China under Grant 51507058.

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