A real-time power quality events recognition using variational mode decomposition and online-sequential extreme learning machine

Journal Pre-proofs A Real-Time Power Quality Events Recognition Using Variational Mode Decomposition and Online-Sequential Extreme Learning Machine Mrutyunjaya Sahani, P.K. Dash, Debashisa Samal PII: DOI: Reference:

S0263-2241(20)30134-2 https://doi.org/10.1016/j.measurement.2020.107597 MEASUR 107597

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Measurement

Received Date: Revised Date: Accepted Date:

3 May 2017 7 January 2020 6 February 2020

Please cite this article as: M. Sahani, P.K. Dash, D. Samal, A Real-Time Power Quality Events Recognition Using Variational Mode Decomposition and Online-Sequential Extreme Learning Machine, Measurement (2020), doi: https://doi.org/10.1016/j.measurement.2020.107597

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A Real-Time Power Quality Events Recognition Using Variational Mode Decomposition and Online-Sequential Extreme Learning Machine Mrutyunjaya Sahani, P.K. Dash*, Debashisa Samal Siksha O Anusandhan Deemed to be University, Bhubaneswar, India. * Corresponding author. E-mail address:[email protected] (P.K. Dash) Abstract—In this paper, variational mode decomposition (VMD) and online-sequential extreme learning machine (OSELM) are integrated to detect and classify power quality events (PQEs) in real-time. Empirical Wavelet transform (EWT), empirical mode decomposition (EMD) and variational mode decomposition (VMD) are used to decompose the non-stationary power quality (PQ) signals into intrinsic mode functions (IMFs) or band-limited mode of oscillations. Four felicitous features are extracted by applying the Hilbert transform (HT) on the decomposed PQE signals. The synthetic, as well as practical PQE signals, are considered to test and examine the overall performance of the proposed method. OSELM is an efficient and advanced classifier which is implemented to recognize the single as well as multiple PQEs. The robust anti-noise performance, faster learning speed, lesser computational complexity, superior classification accuracy and short event detection time prove that the proposed VMDOSELM method can be implemented in the electrical power system. Finally, a PC interface based hardware prototype is developed to verify the cogency of the proposed method in realtime. The feasibility of the proposed method is tested and validated by both the simulation and laboratory experiments. Index Terms—Empirical Wavelet transform, empirical mode decomposition, online-sequential extreme learning machine, power quality events, real-time analysis, variational mode decomposition.

Nomenclature

A fε

β

Approximation coefficients. Random bias. Output weight matrix.

βˆ

Estimated output weight matrix.

D εf

ξ

Detail coefficients. Dirac distribution. Mean of root mean square error.

H H† k K

Hidden node output matrix. Moore-Penrose generalized inverse. Number of band-limited modes. Activation or kernel function.

b

δ

L λ m ωk

Number of hidden nodes. Lagrangian multiplier. Number of classes. Center frequency of subcomponent uk .

ˆ nk 1 ω

Update value of  k .

T ψˆ n

Predefined target vector. Empirical Wavelet function.

θ

uk

Phase angle. Decomposed subcomponent.

u nk 1

Update value of uk .

w

Random weight.

1.

Introduction

Power quality is persuaded with different issues due to nonlinear and unbalanced load, fast switching power electronic load, large data processing unit, industrial plant inverters, and rectifiers etc. and causes malfunctions, impairments, system ambiguity, reduced life expectancy of the sophisticated electrical and electronic equipment. To overcome the undesired situations due to different power quality events (PQEs) [1], it is necessary to develop an intelligent hardware system for the purpose of detection and categorization of the PQEs from the enormous real-time data in an efficient way. The real-time PQEs detection and recognition method mainly associated with the suitable signal processing algorithm for efficacious feature extraction, the robust artificial intelligence technique for the accurate classification of single as well as multiple PQEs and the high speed embedded processor is implemented to validate the proposed method. In recent years, many signal processing algorithms such as short-time Fourier transform, Wavelet transform (WT), Stock-well transform (ST), Kalman filter, Hilbert-Huang transform (HHT), mathematical morphology in addition with artificial intelligence technique includes fuzzy logic, artificial neural network (ANN), probabilistic neural network (PNN), genetic algorithm, support vector machine (SVM), extreme learning machine (ELM) are proposed to evaluate the detection and recognition ability of PQEs in realtime using high speed embedded processors like digital signal processor (DSP), field-programmable gate array (FPGA), National Instruments compact data acquisition chassis (NIcDAQ), dSPACE, ARM-cortex core processor. The single-sideband modulation with the Wavelet packet transform (WPT) and Hilbert transform (HT) are used [2] to estimate the instantaneous power quality indices (PQIs) and fluck i200s monitored the PQEs in real-time by interfacing the isolation amplifier ISO124PND through signal conditioning

circuit. The discrete Wavelet transform (DWT) [3] based root mean square value and global disturbance ratio index are computed from the six-level decomposed Wavelet coefficients to recognize the PQEs using a multi-layer support vector machine classifier. A low cost NIUSB-6259 DAQ high-speed module is used to monitor a few PQEs in real-time on the graphical user interface. An FPGA based intelligent PQEs recognition structure is developed [4] using Wavelet transform with decision tree and least-square support vector machine (LSSVM) classifiers for real-time diagnosis of a few PQEs. An internet-based power quality monitoring system (IPQMS) is proposed [5] based on FPGA for monitoring, reporting and permanently sorting the PQEs using real-time automation software and web applications that run on the server computer. The overall performance of WT is satisfying in ideal condition but it degrades significantly in the noisy environments. The hybrid method based on dynamics [6] is used to reduce the run time of ST by considering few efficacious features and a DSP-FPGA based system is developed to test the performance in real-time. Fast dyadic ST (FDST) with a fuzzy decision tree (FDT) is proposed by Milan et al. [7] to evaluate the single as well as multiple PQEs recognition in DSP based hardware platform. ST based ANN classifier and the decision tree is proposed [8] to detect and classify the PQEs in real-time by using NI-cDAQ module. In [9], the hardware test platform is developed based on DSP TMS320VC6745 and processor management unit ARM cortex-M4 to categorize the PQEs in real-time by using double-resolution ST (DRST) and directed acyclic graph support vector machines (DAG-SVM). The extensive computational complex O(N3) ST needs more runtime to extract the efficacious features. The ST in addition to the multi-layer architecture of advanced classifiers is not suitable to implement in any high-speed embedded processor for online monitoring the PQEs. Zhang Y. et al. [10] proposed the open-closing and closeopening undecimated Wavelet (GMOCOW) mathematical morphology technique to identify the PQEs in real-time by using PC based hardware platform with a recordable oscilloscope. A PC interfaced low-cost online PQEs monitoring system is developed based on down-sampling empirical mode decomposition [11]. Symmetrical component based modified method with a decision tree (DT) is proposed [12] to recognize the PQEs in real-time by using a DSP-dSPACE 1104. In most of the aforementioned PQEs recognition methods, the signal processing algorithms are not able to detect the PQEs effectively in noisy environments. A few methods such as virtual impulse response, higher order spectrum, and virtual frequency response function with eigensystem realization algorithm are proposed to identify the precise mode of oscillations and accurate frequency band identification in civil engineering [13-15]. Moreover, computationally complex multilayer artificial intelligence technique architectures consume more processing time which leads to difficulty for the implementation in real-time. To contribute accurate detection capability with better recognition architecture of single as well as multiple PQEs in real-time, this paper demonstrates the newly developed variational mode decomposition (VMD) [16] with the online sequential extreme learning machine (OSELM). The real-time PQEs are associated with the system noise and the advanced

VMD algorithm is the most suitable to distant out the bandlimited intrinsic mode functions (BLIMFs) of the complex PQEs as it is embedded with the Wiener filter. The Hilbert transform in addition to VMD enhances the PQEs detection capability in the time-frequency plane. Proper selection of the suitable features leads to the categorization of the fourteen single as well as combined PQ signals automatically with lesser time and higher accuracy using the single-layer feed-forward neural network (SLFNN) OSELM classifier. The performance of VMD is compared with the empirical Wavelet transform (EWT) [17] and HHT [18], the recently developed signal processing algorithms. The OSELM [19] is introduced to improve the learning speed and accuracy with less computational time over other advanced classifiers such as support vector machine (SVM) [20], least-square support vector machine (LSSVM) [21] and regularized extreme learning machine (RELM) [22]. The robust recognition architecture of VMD-OSELM is tested and compared with EWT-OSELM and HHT-OSELM to detect single as well as multiple PQEs in both noise-free and noisy environments. Finally, PC with NI-cDAQ based hardware test platform is developed to validate the feasibility and practicability of VMDOSELM method in real-time. The structure of the paper is organized as follows. Section 2 describes briefly the theoretical background of the advanced signal processing algorithms. The suitable feature extraction process is presented in Section 3. Section 4 explains the methodology for pattern recognition. The experimental verification of the proposed VMD-OSELM method is described in Section 5 followed by the conclusion and future works in Section 6. 2.

Signal processing algorithm

2.1. Empirical Wavelet Transform EWT is a full adaptive sub-band decomposition technique based on the maxima of the given signal f ( t ). Based on the Shannon criteria, it considers the range of frequency   [0, ] and the spectrum of the test signal is symmetrical with respect to   0. The segment is existing between 0  0 and n  , and each segment is represented as n  [n 1 , n ]. The bandpass filter on each  n is known as empirical Wavelets. The detail coefficients [D f (n , t )] are given by the inner products with empirical Wavelets 

    D f (n , t )  f ,  n   f ()   n (  t ) d  f ()  () (1)   ˆ n () is the empirical Wavelet function and given as where 

Step-3: Extract the residue r1 (t)  x(t)  I1 (t). If r1 ( t ) is satisfied with the predefined standard deviation (SD) as stopping value () of 0.01 between two consecutive sifting results.

1 if n   n    n 1   n 1    1   (   n 1   n 1 )  Cos      2  2 n 1  if n 1   n 1    n 1   n 1 ˆ n ()        1  (   n   n )  Sin      2  2 n  if n   n    n   n   otherwise 0

T

(2)

t 0

T

 I2k 1 (t )

2



(6)

t 0

where k represents the k difference of x(t) and eM (t). Else repeat step-2 to obtain the next IMF and new residue. Fig. 1(b) shows the IMFs of the signal having multiple disturbances. The signal is reconstructed by using the following equation. th

The approximation coefficient [A f (0, t )] is the inner product of scaling function and defined as     A f (0, t )  f ,  n   f ()   n (  t ) d  f ()   n ()   ˆ where  () is the empirical scaling function such as

SD(k ) 

 Ik 1 (t )  Ik (t )



n

(3)

x ( t )   Ii ( t )  rn ( t )

(7)

i 1

where n is the number of orthogonal IMFs.

n

1 if   n   n    1     ˆ ()  Cos  2  2 (   n   n )  n    n  if n   n    n   n  0 otherwise 

(4)

0 if x  0   ( x)   and  (x)   (1 - x)  1  x [0,1] 1 if x  1 

(5)

2.3. Variational Mode Decomposition

The (x) is an arbitrary C k [0,1] function is defined as

The complete detail of EWT is described in [17] and the decomposed coefficient of multiple PQEs per unit (p.u.) synthetic signal is shown in Fig. 1(a). 2.2. Empirical Mode Decomposition EMD decomposes the signal into a discrete number of monocomponent signals, called intrinsic mode functions (IMFs). An IMF can be both amplitude and frequency modulated, or even have finite bandwidth. The time-varying frequencies of IMFs explain the local characteristics of the highly non-stationary PQE signals. Each IMF is associated with an equal number of extrema and zero-crossing, and symmetrical around the local mean. The steps involve the iterative sifting process of EMD [18] as follows Step-1: Determine the maxima and minima of the signal x ( t ) and find the upper envelop eU (t) and lower envelop eL (t) by using the cubic spline interpolation technique. Calculate the envelop mean eM (t)  eU (t)  eL (t) 2. Step-2: Compute I1 (t)  x(t)  eM (t). If the mean value of

I1 (t ) is zero and the number of maxima is equal or more than one from the zero-crossing, then I1 (t ) is an IMF otherwise repeat step-1 on I1 (t ) until the newly obtain I1 (t ) satisfy it.

VMD algorithm is used to decompose non-recursively the real-valued signal f (t) into the number of BLIMFs u k with certain sparsity properties and each mode k is strictly bound around the center frequencies k . The constrained variational problem of VMD [16] is illustrated in the following equation. 2     jk t  j  min   t   (t )    u k (t ) e  {uk } {k } k t     2  Subjected to  u k  f (8) k

where  is the Dirac distribution and  denotes convolution. Each unilateral frequency spectrum bandwidth is estimated from the positive frequency component on Hilbert transformed analytic signal using the squared H1 norm of its baseband. The combination of Lagrangian multiplier  and the quadratic penalty is addressed in equation (9). The augmented Lagrangian L with the data fidelity balancing factor  is illustrated as follows

L{u k },{ k },      k

  j  t   (t )    u k (t ) e  jk t t   

2

2

2

 f ( t )   u k ( t )  ( t ), f ( t )   u k ( t ) k

(9)

k

2

To solve the variational problem of (9) alternative direction method of multipliers (ADMM) algorithm is employed during every sifting operation. Each BLIMF in spectral-domain is defined as fˆ ()  i  k uˆ i ()  ˆ () 2 uˆ k ()  (10) 1  2(  k ) 2 The BLIMFs of the multiple PQEs signal based on VMD [16] is shown in Fig. 1(c) and the factors associated with VMD are described in the following steps.





Step-2: Center frequency update.  is updated from the corresponding BLIMFs power spectrum as the center of gravity, shown in (12). 



n 1 k

2

  uˆ k () d  0 2 n 1 0 uˆ k () d n 1

(12)

Step-3: Dual ascent update. The Lagrangian multiplier ˆ n 1 is the dual ascent for all   0 and updated until the convergence

k

uˆ nk 1  uˆ nk

2 2

uˆ nk

2 2

  as follows

D1 Magnitude in p.u.

  (13) ˆ n 1  ˆ n   fˆ   uˆ nk 1  k   The complete VMD algorithm [16] is embedded in the Wiener filter to prove the robustness in a noisy environment. The data fidelity factor ( ) plays an important role to extract the monocomponent mode of oscillation accurately. If the  value is large the band-limit is narrow and causes the elimination of extremely useful frequency components. For a small value of  , the band-limit is wide and causes the sharing of frequency components with the neighbor BLIMFs. To avoid the mode mixing problem and elimination of most important information, a large value of 10000 is considered for the low-frequency content flicker signal and a small value of 250 is considered for all other PQEs empirically with the initial center frequency () greater than zero. Original signal 1 0 -1 1 0 -1

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Fig. 1. Decomposition of multiple PQEs synthetic signal using (a) EWT (b) EMD (c) VMD algorithms

2.4. Hilbert Transform

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IMF 2

n 1 k

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(11)

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

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

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Residue

Fourier spectrum with the updated center frequency nk . fˆ ()  i  k uˆ in 1 ()  i  k uˆ in ()  ˆ () 2 uˆ kn 1 ()  1  2(  kn ) 2

BLIMF 5 BLIMF 4 BLIMF 3 BLIMF 2 BLIMF 1 Magnitude in p.u.

Step-1: Mode update. The Wiener filter is embedded to produce the non-recursively decomposed modes uˆ kn 1 () from the

Time in second

(a)

The imaginary part of a real-valued signal is calculated by applying HT and is required to extract the instantaneous parameters. The HT is used in this work to capture the magnitude, phase, and frequency of the decomposed signals. The Hilbert transform [18] of a continuous signal X (t ) is computed as shown in (14) ˆ (t)  Y(t)  X



X(τ) dτ  t  τ



(14)

The Hilbert transform shifts each frequency component of

X (t ) by 90  . The discrete Hilbert transform (DHT) is computed as shown in (15) - J 0  ω  π  H(ω)   0 ω  0 and ω  π J  π  ω  0 

N

(15)

The DHT is related to Fourier transform [23] and the complete procedure for applying HT is given below. step 1) Apply DFT to the signal S(k ) , k  1,2....N, so,

S F  DFT[S (k )]

; θ (t)  arctan

Y(t) S(t)

and

the

Feature Extraction

To elicit the efficacious features suitable for the specific signal processing algorithm is a ponderous errand to detect and recognize the multiple concurrent PQEs. The felicitous feature vector for a particular signal decomposition tool can recognize the PQEs accurately with an efficient classifier but may not be promising for others. Real-time PQEs recognition system is required a few puissant features to reduce the computational burden on the processing unit, consume less processing time and support the less memory-based hardware platform. In this work, several meaningful features are extracted from the Hilbert transformed array H (n) of the decomposed signal and four specific features are selected as given below. 3.1. The Standard deviation of the magnitude The standard deviation (SD) of the magnitude of the ith Hilbert array Hi (n) of length N can be computed as follows

1 N  H i (n)  mean( H i ) N  1 n 1

2

(17)

3.2. Energy The energy (E ) of the Hi (n) can be analyzed as follows

Ei 

 H i ( n)

2

n 1

3.3. Shannon entropy

(18)

CFi 

 n  m i FH i2 (n)  H i2 (n) m  N 1  n  m i H i2 (n)

(20)

where m=1,2,  ,length Hi (n)  Ni  1 and the ith fundamental frequency decomposed signal component is computed as FHi (n)  H if (n) / 50 ; H if (n)  H i (n)  frequency=50 Hz. The aforementioned feature vector is constructed from the decomposed results of EWT, EMD, and VMD to ensconce as an input to the classifier. The fourteen different types of synthetic, synthetic with noise and real single as well as multiple PQEs are considered and given in Table 1. To localize the detection of multiple PQEs, a 50 Hz fundamental frequency synthetic signal with higher frequency transient, voltage sag, and the spike is generated is shown in Fig. 2. The timefrequency representation of magnitude response, phase response, and frequency response show better visualization on the occurrence of multiple PQEs is shown in Fig. 2. The aforestated four features are extracted from the signal at the different levels of decomposition and fed as an input to the classifier to classify the PQEs patterns. Table 1 Types of PQ Events. Types Sag with Transient Voltage Sag Swell with Harmonics Voltage Swell Sag with Harmonics Harmonics Harmonics with Notch Magnitude in p.u.

2

(16)

1 d (t ) . 2 dt In this way, the instantaneous amplitude, frequency, and phase of the signal S (t ) can be calculated by using HT.

N

This feature is important to measure the content disturbances in terms of squared normalized frequencies weighted by its energy [24]. The value is one for pure signal and is defined as

Magnitude in p.u.



1

instantaneous frequency [ (t )] 

SDi 

3.4. Crest factor

Phase in Radian

Z (t )  S (t )  iY (t )  a (t )e j (t )

3.

(19)

n 1

Inst-Frequency in Hz

The HT can convert S (t ) into an analytic function Z (t ) by adding Y (t ) as the imaginary part i.e.



SEi    H i (n) 2 log[ H i (n) 2 ]

m  N 1

where the dimension of S F vector is same as that of S (k ) . step 2) S F is multiplied by the mask M 1 which is defined as M1  {0, j, j,,0, j, j,, j}if n is even. M1  {0, j, j,, j, j, j,, j}if n is odd. step 3) Apply inverse DFT to compute Y (t )  IDFT [ S F  M 1 ]

2 2 where a(t)  S(t)  Y(t)

The uncertainty measures and degree of disorders are accurately quantified using Shannon entropy (SE ). This can be computed as follows

Class Labels CL 1 CL 2 CL 3 CL 4 CL 5 CL 6 CL 7

Types Voltage Notch Spike/Impulsive Transient Swell with Transient Transient Flicker Harmonics with Flicker Spike with Transient

Class Labels CL 8 CL 9 CL 10 CL 11 CL 12 CL 13 CL 14

Input Signal

2 0 -2

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.14

0.16

0.18

0.2

0.14

0.16

0.18

0.2

0.14

0.16

0.18

0.2

Magnitude spectrum

2 1 0

0

0.02

0.04

0.06

0.08

0.1

0.12

Phase response

0.5 0 -0.5

1000 500 0 -500

0

0.02

0.04

0.06

0.08

0.1

0.12

Frequency spectrum

0

0.02

0.04

0.06

0.08

0.1

0.12

Fig. 2. Visualization the occurrence of multiple PQEs

4.

Methodology For Pattern Recognition

To construct a robust decisive structure the suitable features are extracted and an advanced artificial intelligence technique is used to recognize the fourteen different PQEs patterns. The simple and efficient classification decision tree (CDT) and the generalized single layer feed-forward neural network method, ELM are used to realize and validate the proposed method in real-time. The CDT, SVM, LSSVM, ELM and OSELM classifiers are trained with the efficacious feature vectors of the single and multiple PQEs to utterly recognize at the testing stage. Lesser training and testing time, lesser computational complexity, superior classification accuracy and independent of user intervention are the prime advantages of the recently developed classifier, OSELM as compared to other pattern classifiers. 4.1. Classification decision tree Classification decision trees have been widely used as a powerful prediction method and an extremely popular approach for inductive inference over supervised data. CDT follows a procedure to classify categorical and continuous data with specified attributes. The simplicity and self-explanatory nature of CDT is appropriate for exploratory knowledge discovery. It is a decisive structure that includes a root node, internal node, branches, and leaf node. Internal nodes are used to compute the node impurity based on the optimum set of features for the best split and the branches provide the decisive results. Many optimality criteria are available to minimize the node impurity, ambiguity error and misclassification error such as a minimum number of expected node and path, minimum error rate and maximum average information gain in multiclass classification. To frame a robust decisive structure at each node the following three optimality criteria are considered. 4.1.1. Gini's diversity index This approach is used to make the internal node impurity to the minimum by measuring the probability of misclassification. The Gini's diversity index is expressed as m   (21)  Gnl (1 Gnl ) n 1



where m is the output patterns of different PQEs and G nl is the fraction of class n observations in node l. 4.1.2. Entropy index This is used for the measurement of diversification of node impurity. The entropy index is evaluated as m   (22)  Gnl log Gnl n 1

4.1.3. Twoing rule This method is suitable to eliminate the complexity of multiclass problems as it concentrates on splitting the nodes categorically. In twoing rule, the philosophy is to search for two classes that will make up togetherness more than 50% of the data. Twoing rule reveals the belongingness between the classes in multi-class classification.

The decision tree induction system produces an overly grown tree to obtain maximum classification accuracy with minimum node impurity. An overly large tree undergoes the drawbacks of data overfitting. Several techniques are used to prune back the overly large tree to an optimal size by using cross-validation with the least classification error. The leaf node finally categorizes the decision to fall under the predefined classes. 4.2. Regularized Extreme Learning Machine ELM is an efficient united single layer feed-forward neural network classifier proposed by Huang et al. [22]. It can be employed to categorize the multiclass PQEs in real-time as shown in Fig. 3. The inherent higher learning speed, less computational time and superior classification accuracy prove its performance in many applications over the competent support vector machine classifier [22].

Fig. 3. The internal architecture of the extreme learning machine classifier th

Consider N input samples of the i feature vector for PQEs signal is [I i1 , I i 2 ,  , I iN ]T  R n . The SLFN has L hidden nodes associated with a random weight w i between inputs and hidden nodes

is

[ w i1 , w i 2 , , w iL ]T ,

and

the

bias

bi

is

[b i1 , b i 2 ,  , b iL ] . The m PQEs classes have a predefined target T

Ti  [Ti1 , Ti 2 , , Tim ]T  R m

and the output weight vector

 i  [ i1 ,  i 2 , ,  im ] is computed from the i th hidden neuron and output nodes. The mathematical model of standard SLFN [22] by considering the non-regular, infinitely differentiable K (I ) with the network output kernel function T

Oi  [Oi1 , Oi 2 ,, Oim ]T is L

L

i 1

i 1

  i K i ( I j )    i K i ( wi  I j  bi )  O j , j  0,1,, N. (23)

The SLFN can approximate by taking into account the value of w i , bi and i to accomplish zero mean error [22] i.e. L

 O j  T j 0 such that j 1

L

  i K i (wi  I j  bi )  T j , i 1

j  0,1,  , N.

(24)

The aforementioned N equations can be represented in terms of hidden layer output matrix H of the SLFN [25, 26] as

H  T

(25)

 K ( w 1  I1  b 1 )  K ( w L  I1  b L )   ; where H       K ( w 1  I N  b1 )  K ( w L  I N  b L ) N L

0

 1T  T1T          and T      T  T T   m  Lm  N  N m

The output weight matrix is computed as ˆ  H †  T

0

weight

(26)

†



 H T HH 

ˆ  







if HH T  0

T

1

(27)

T T T   H H H T if H H  0 If h ( I ) is the hidden layer feature mapping vector for the new



h( I )  H T HH T 1T if N  L  F (I )   (28) 1 T T  h ( I )  H H H T if N  L  A various kind of kernel function K(w,b,I) can be implemented which is not restricted to Table 2 to provide better performance for the “generalized” SLFNs.





1

Consider the new chunk of feature vector N1 with N 0 , the new T

 H 0  T0  output weight matrix  (1)  W11      H1  T1  T



(29)



H 0  H 0  H 0  where W1       H 0T H 1T    W0  H 1T H 1 (30)  H1   H1   H1  T

 H 0  T0  and      H 0T T0  H 1T T1  W0  (0)  H 1T T1  H 1  T1 





 W1  H 1T H 1  (0)  H 1T T1

input sample I, the output of ELM classifier is



( 0)  H T0 H 0  H T0 T  W01H T0 T. Where

matrix

W0  H T0 H 0 .

where H is the Moore-Penrose generalized inverse of the hidden layer output matrix H [27, 28]. To avoid singularities by applying the original projection method [22], the ˆ is defined as T 1

time without user intervention the OSELM [19] is an excellent choice over other batch learning-based ELM. Let us extract the chunk of input feature vector from the PQEs signal and set as initial training sample N N 0  (I i , t i )i1  R n  R m and N 0  L. Compute the hidden layer output matrix [ H 0 ] N  L using equation (25) and the output

 W1

( 0)

 H 1T H 1 (0) (1) ( 0)

Combining (30) and (31) 

 H 1T T1



(31)

 W11 H 1T T1  H 1  (0)





For (n  1) chunk of input feature sample along with all the th

 Nj observation of previous chunks N n 1  (Ii , t i ) j0 n  . i    N j  1  j0  n 1

The hidden layer output matrix is

Table 2 Expressions of the different kernel function. Kernel function Expression 1 if w. I  b ≥ 0 K(w, b, I)   Hard limit 0 otherwise Sinusoid

K(w, b, I)  exp( ( w .I  b ) 2 ) K(w, b, I)  sin( w .I  b )

Sigmoid

K(w, b, I) =

Radial basis

1 1 + exp(-w.I + b)

Tan hyperbolic

K(w, b, I)  tan( w .I  b )

Triangular basis

1 - abs(w.I  b) if - 1  w. I  b  1 K(w, b, I)   otherwise 0

4.3. Online-Sequential Extreme Learning Machine (OSELM) To recognize the single as well as multiple PQEs in real-time, it is de rigueur to extract the feature vector data chunk by chunk continuously from the numerous power supply data. An advanced classifier is necessary to test the feature vector extracted from the chunk of real-time data successively through an embedded system to classify the PQEs automatically. Many variants of ELM such as error minimize ELM [29], incremental constrictive ELM [30], convex incremental ELM [31], enhanced incremental ELM [32], optimally pruned ELM [33] and bidirectional ELM [34] have been proposed based on batch learning. Liang et al. proposed OSELM [19] to learn the training sample one by one as well as chunk by chunk to enhance the learning speed and classification accuracy with the specified number of hidden nodes. To classify the PQEs in real-

K(w  I n b )  K(wL  I n N 1 bL) j0 j  1 j0 N j 1 1      Hn1      K(w1  In1 N j  b1)  K(wL  In1 N j  bL)  j0 j0  Nn1L



and Wn11  Wn  H nT1H n 1





1

 Wn1  Wn1H nT1 I  H n 1Wn1H nT1

Let

1 n 1

Z n 1  W

(32)

, then



1 n 1

W

1

H n 1Wn1

can

Z n 1  Z n  Z n H nT1 I  H n 1Z n H nT1 Z H HT Z  Z n  n n 1 n 1 T n I  H n 1Z n H n 1  ( n 1)   ( n )  Wn11 H nT1 (Tn 1





1

rewrite

(33)

as

H n 1Z n (34)

 H n 1 ( n ) )

(35)

Original signal

E re tu a e F

OSELM Algorithm Training Phase Initialization Stage: (n  0) Input: Consider the initial input training chunk I i , ti iN01  R n  R m ; N 0  L with randomly engender

Input: Receive the new (n  1)th chunk as an input sample with randomly chosen weight and bias. Output: a) Find the hidden node output H n1 using equation (32). b) Find the output weight matrix 

( n 1)

using equation (35).

c) Repeat the online sequential learning stage until n  n max. Where nmax is the maximum number of predefined training chunk. Testing Phase Input: Consider the initial testing data

I j , Tj kj1  R n  R m ;

I1  I11 , I12 ,, I1N T and T1  T11 , T12 ,, T1m T . Where N is the samples in the feature vector, m is the number of PQEs classes and k is the numbers of PQEs signals are being tested. m Receive the output weight matrix ( j ) j1 from the online

sequential training stage. Output: a) Compute the testing hidden node matrix H T using equation (32) by choosing randomly the weight and bias. b) Compute the network output function F(o)  HT with reference to m number of classes. c) Compute min F(o) j  Tj 5.

m j1

to classify the test input sample.

Hardware Implementation Verification

and

Experimental

BL IMF3

Online-SequentialExtreme Learning Machine

C la s s if ic a ti o n

S ta g e

Feature Extraction

CL1 CL 2 CL3 CL 4 CL5 CL 6 CL 7 CL8 CL9 CL10 CL11 CL12 CL13 CL14

n io is c e e Dc a Sp

Output: a) Find the hidden node output matrix H 0 using equation (25). b) Compute the output weight matrix  (0) . Online Sequential Learning Stage: (n  n  1)

BLIMF1 BLIMF2

e g ta S

wi , bi iL1.

Variational Mode Decomposition n o ti c a tr x

hidden node parameters

t u e p c a In p S

Thus the summary of OSELM [19] intelligent learning algorithm is as follows

Fig. 4. The architecture of VMD-OSELM PQEs monitoring system

In this section, the hardware module is designed and assembled to generate different real-world PQEs by switching the linear and nonlinear loads. Laboratory testing is presented to show the performance of the proposed VMD-OSELM algorithm shown in Fig. 4. 5.1. Practical PQEs generation and analysis It is required to generate real-time PQEs to detect and classify it. Fig. 5(a) shows the schematic diagram of the developed hardware prototype to generate and capture the different PQEs in real-time and Fig. 5(b) shows the laboratory hardware setup. A voltage transducer (AD202JY) is interfaced with the power driver circuit to sense the different voltage disturbances such as sag, swell, harmonics etc. by varying the linear/nonlinear loads in three-phase supply followed by an induction motor, capacitor switching, etc. The power signal conditioning circuit is designed to protect the voltage sensor and to acquire the proper scale down PQEs data through the high-speed 12bit analog to digital converter (ADC) of buspower multifunction national instrument (NI) DAQ USB-6008 device. NI USB-6008 is a USB microcontroller-based data acquisition device embedding multiple analog input-output (AIO) and digital input-output (DIO) channels with a full speed analog input (AI) sampling rate up to 10 kS/s. The interconnections of the microcontroller with the different peripherals through the port pins are shown in Fig 5(c). The firmware NI-DAQmx in MATLAB interface can capture the real-time PQEs signals. The data exchange is performed using serial peripheral interface (SPI) and USB bus between the NI USB-6008 and Host PC. The selective features of the captured PQEs are trained in Host PC using ELM in MATLAB environment. Once the PC interface based hardware system is trained completely, the recognition of real-time input PQEs signal is monitored through the digital output (DO) pins of NI USB-6008 by interfacing an LED for each fault class or online in MATLAB window on the Host PC at the testing stage.

detection are presented in Table 3.

(a)

(a)

(b)

(b) Fig. 6. Generation and categorization of real-time (a) voltage transient (b) voltage harmonic signal

(c) Fig. 5. (a) Schematic diagram of developed hardware to generate real-time PQEs (b) the hardware laboratory setup and (c) block diagram representation of the interconnection of different IO ports with microcontroller through buses Table 3 Typical real-time estimated values of the different PQEs PQEs type Duration Magnitude Spectral content Voltage Sag >0.5 cycle 0.1 to 0.9 p.u. --Voltage Swell >0.5 cycle 1.1 to 1.8 p.u. --Momentary >0.5 cycle < 0.15 p.u. --Interruption Voltage Flicker >0.5 cycle 0.85 to 1.15 p.u <25 Hz Voltage Harmonic Steady state 0 to 0.25 p.u. 0 to 5 kHz Voltage Transient ns to ms 0 to 8 p.u. 5 kHz to 5 MHz

The voltage harmonics, oscillatory transients, and notches are generated by connecting the rectifier and switching the capacitor in a three-phase supply system. By switching a high rated linear load the voltage sag 0.85 per unit (p.u.) and voltage swell 1.15 p.u. are recorded. Figs. 6(a)-(b) show the different PQEs generated by our hardware setup in MATLAB interface and also real-time PQEs are classified in MATLAB at a sampling frequency of 3.2 kHz of 50 Hz distributed network. Furthermore, the estimated range of magnitude in p.u. and spectral content in Hz of the different PQEs for real-time

5.2. Result and Discussion The suitable features are extracted from the five cycles windowed PQEs signal and represented by the feature extraction stage in Fig. 4. Based on the normalized feature vectors, the CDT is constructed by Gini-diversity index, entropy-based index, and twoing rule. The decisive rules are extracted from the CDT to test the PQEs patterns. The best classification accuracy is obtained from the tested PQEs patterns using Gini-diversity index and is summarized in Table 4. Nine distinct decisive rules are constructed and the best decision tree of VMD-CDT with five-level decompositions is shown in Fig. 7. The conventional SVM [20] and its variant LSSVM [21] are used to test the performance of PQEs patterns. Both the algorithms are simulated in MATLAB environment by using different kernel functions but the best result based on the popular Gaussian kernel is given in Table 5. For each of the PQEs 150 cases are taken and 50 PQEs are used for training and 100 PQEs for testing the OSELM with four different kernel functions. The overall classification accuracy is taken as the ratio of the number of PQEs recognized meticulously to the total PQEs tested. The classification accuracy of the EMDOSELM, EWT-OSELM, and VMD-OSELM in both noise-free and noisy conditions is given in Table 6. It can be noted that VMD-OSELM has a robust anti-noise performance and high classification accuracy in a noisy condition. Table 4 Performance comparison on the percentage (%) of classification accuracy using EMD-CDT, EWT-CDT, and VMD-CDT in noise-free and noisy conditions. Signal to noise ratio (SNR) value Noise-free Algorithms case 20dB 30dB 40dB EMD-CDT 91.6 89 89.9 90.8 EWT-CDT 94.8 91.8 92.5 93.6

VMD-CDT

97.7

96.2

96.8

VMD- SVM VMD-LSSVM

97.1

x3 < 0.118779

x17 < 0.000237514

x1 < 0.444469

x1 >= 0.444469

CL12

CL11

x1 < 0.495286

CL13

x8 < 0.0364691

x1 >= 0.345177

CL1

CL8

91.8 93.2

93.8 95.9

x1 >= 0.481516

x3 >= 0.118779

x17 >= 0.000237514x1 < 0.345177

90.1 91.5

From the simulation results, it is observed that the VMDOSELM having better PQEs recognition than EMD-OSELM and EWT-OSELM methods. The performance comparison in terms of training time, testing time, training root mean square error (RMSE), testing RMSE and accuracy of VMD-OSELM in noise-free and 25 dB noisy condition with two different decomposition levels, training chunk size 23, 80 hidden nodes

Table 5 Performance comparison on the percentage (%) of classification accuracy of EMD, EWT and VMD using SVM and LSSVM in noisefree and noisy conditions. SNR value Noise-free Algorithms case 20dB 30dB 40dB EMD-SVM 88.5 81.8 84.3 86.1 EMD-LSSVM 89.2 83.9 85.8 87.4 EWT- SVM 92.1 87.2 88.7 90.0 EWT-LSSVM 93.6 88.9 90.2 91.8 x1 < 0.481516

95.5 96.8

x7 < 0.24065

x7 >= 0.24065

CL4

CL7

x1 >= 0.495286

x3 < 0.254524

x8 >= 0.0364691

x12 < 0.861773

x12 >= 0.861773

x8 < 0.1149

x8 >= 0.1149

CL14

CL5

x4 < 0.0020832

CL3

CL9

x3 >= 0.254524

x4 >= 0.0020832x3 < 0.599729

CL10

CL2

x3 >= 0.599729

CL6

Fig. 7. CDT of VMD with Gini-diversity index optimal criteria Table 6 Performance comparison on the percentage (%) of classification accuracy using EMD-OSELM, EWT-OSELM and VMD-OSELM in noise-free and noisy conditions [number of decomposition (D)=5, training chunk size=23 and number of hidden node=80]. EMD-OSELM EWT-OSELM VMD-OSELM SNR value SNR value SNR value NoiseNoiseNoiseHidden free case free case free case 20dB 30dB 40dB 20dB 30dB 40dB 20dB 30dB 40dB Node Type Sigmoid Radial basis Tan hyperbolic Sine

Accuracy

Accuracy

Accuracy

Accuracy

Accuracy

Accuracy

Accuracy

Accuracy

Accuracy

Accuracy

Accuracy

Accuracy

90.14 88.71

87 82.3

88.3 86.4

89.6 87.6

94.41 91.62

90.2 84.1

92.1 89.2

92.4 90.3

99.7 98.6

99.3 97.8

99.7 98.2

99.7 98.3

88.14

81.4

85.9

86.5

90.81

83.5

86.9

88.7

98.1

97.5

98.0

98.0

87.90

80.9

83.6

84.9

89.60

82.7

84.5

86.8

97.4

96.5

96.8

96.9

Table 7 Performance comparison of VMD-OSELM at different decomposition levels [sigmoid kernel function, training chunk size=23 and number of hidden node=80]. Classes CL 1 CL 2 CL 3 CL 4 CL 5 CL 6 CL 7 CL 8 CL 9 CL 10 CL 11 CL 12 CL 13 CL 14 Mean Value

VMD-OSELM (Number of Decomposition (D)=3) Accuracy (%) Training Testing Training Testing Noise-free Time (s) Time (s) RMSE RMSE 25 dB case 0.0178 0.0129 0.0038 0.0121 94 90 0.0157 0.0104 0.0060 0.0226 93 92 0.0162 0.0144 0.0037 0.0428 100 100 0.0159 0.0129 0.0040 0.1324 100 100 0.0163 0.0107 0.0117 0.1811 96 96 0.0176 0.0119 0.0071 0.1386 100 100 0.0168 0.0132 0.0104 0.1842 100 100 0.0165 0.0116 0.0161 0.3051 100 100 0.0163 0.0138 0.0184 0.3014 100 100 0.0182 0.0144 0.0130 0.0634 100 100 0.0178 0.0119 0.0038 0.0117 100 100 0.0184 0.0144 0.0078 0.1675 100 100 0.0165 0.0122 0.0042 0.0609 100 100 0.0163 0.016 0.0052 0.1459 100 100 0.0168 0.0129 0.0082 0.1264 98.78 98.42

Training Time (s) 0.0295 0.0274 0.0279 0.0276 0.0280 0.0293 0.0285 0.0282 0.0280 0.0299 0.0295 0.0301 0.0282 0.0280 0.0285

VMD-OSELM (Number of Decomposition (D)=5) Accuracy (%) Testing Training Testing Noise-free Time (s) RMSE RMSE 25dB case 0.0196 0.0008 0.0056 100 97 0.0171 0.0030 0.0160 96 94 0.0211 0.0007 0.0360 100 100 0.0196 0.0010 0.1150 100 100 0.0174 0.0087 0.1706 100 100 0.0186 0.0041 0.1259 100 100 0.0199 0.0074 0.1735 100 100 0.0183 0.0131 0.2868 100 100 0.0205 0.0154 0.2886 100 100 0.0211 0.0100 0.0590 100 100 0.0186 0.0008 0.0055 100 100 0.0211 0.0048 0.1624 100 100 0.0189 0.0012 0.0440 100 100 0.0227 0.0022 0.1370 100 100 0.0196 0.0052 0.1161 99.71 99.35

and activation function has been used as sigmoid is presented in Table 7. In Table 7, we calculate the mean of RMSE ( ) for training and testing using the following equation.



 1 N  L w j  f j (I i )  Ti      N i1  j1 

2

(36)

where N is the number of trained or tested sample and L is the number of hidden neurons. Table 8 presents the performance comparison of VMD-OSELM in noise-free and noisy environments with the same 80 hidden nodes, sigmoid activation function, three decomposition levels and training chunk size 23. Table 8 Performance comparison on the percentage (%) of classification accuracy using VMD-OSELM in noise-free and noisy conditions at decomposition level (D) =3. SNR value Noise-free condition Hidden Node Type 20dB 30dB 40dB Accuracy Accuracy Accuracy Accuracy 98.78 Sigmoid 98.4 98.6 98.6 98.28 Radial basis 97.8 98.0 98.1 98.00 Tan hyperbolic 97.6 97.8 97.8 97.14 Sine 96.2 96.6 96.8

The overall performance of the real-time PQEs monitoring system can be measured by using the following expressions. Number of PQEs signals recognized % Accuracy   100 (37) Total number of PQEs signals tested % Sensitivity 

% Specificity 

Number of negative signals recognized  100 (39) Total number of negative signals tested

The work considers the pure sinusoidal voltage signal as the true positive signal and the total number of PQEs as a true negative signal. The sensitivity and specificity of the hardware system represent the faultless and faulty nature of supply power respectively. The real-time PQEs monitoring system is necessary to avoid the undesired situation in a power system. The developed VMD-OSELM based real-time PQEs recognition hardware system performance on fourteen different real-time PQEs with five decomposed levels, 23 training chunk size, 50 hidden nodes, and sigmoid activation function is shown in Table 9. The proposed VMD-OSELM method performs unsatisfactorily for only CL2 of synthetic data making classification accuracy 99.71%. However, a few of the real PQEs misclassified are of CL1, CL2, CL5, and CL10 make the classification accuracy 98.86% and specificity is 98.78%. Interestingly, from our testing result, it is concluded that the OSELM has a better PQEs recognition structure with a lesser number of hidden nodes over SVM, LSSVM, RELM classifiers, and the proposed VMD-OSELM method has better performance over EMD-OSELM and EWT-OSELM method. Table 10 contains the performance accuracy of the novel VMDOSELM method in comparison with other existing methods.

Number of positive signals recognized  100 (38) Total number of positive signals tested

Table 9 Classification results of VMD-OSELM with the practical test PQES signal [number of decomposition (D)=5, training chunk size=23 and number of hidden node=50]. CLASES CL1 CL2 CL3 CL4 CL5 CL6 CL7 CL8 CL9 CL10 CL11 CL12 CL13 CL14 Voltage Sine CL1 94 2 0 0 0 0 0 0 0 0 2 0 0 0 2 CL2 1 95 0 0 1 0 0 0 0 0 0 0 0 0 3 CL3 0 0 100 0 0 0 0 0 0 0 0 0 0 0 0 CL4 0 0 0 100 0 0 0 0 0 0 0 0 0 0 0 CL5 0 0 2 0 96 2 0 0 0 0 0 0 0 0 0 CL6 0 0 0 0 0 100 0 0 0 0 0 0 0 0 0 CL7 0 0 0 0 0 0 100 0 0 0 0 0 0 0 0 CL8 0 0 0 0 0 0 0 100 0 0 0 0 0 0 0 CL9 0 0 0 0 0 0 0 0 100 0 0 0 0 0 0 CL10 0 0 0 1 0 0 0 0 0 98 1 0 0 0 0 CL11 0 0 0 0 0 0 0 0 0 0 100 0 0 0 0 CL12 0 0 0 0 0 0 0 0 0 0 0 100 0 0 0 CL13 0 0 0 0 0 0 0 0 0 0 0 0 100 0 0 CL14 0 0 0 0 0 0 0 0 0 0 0 0 0 100 0 Voltage Sine 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 Accuracy=98.86%, sensitivity=100%, and specificity=98.78%.

Table 10 Comparison of the VMD-OSELM method with the prevalent methods. Signal processing technique WT ST WT IMF-H DRST FDST

Types of classifier

Number of PQEs

Types of PQEs

NN PNN Neural Fuzzy PNN DAG-SVMs CFDT

6 11 13 9 9 13

Synthetic Synthetic Synthetic Synthetic synthetic Real

% of Classification Accuracy 94.37 [35] 95.55 [36] 96.50 [37] 97.22 [38] 99.38 [9] 92.69 [7]

FFT GMOCUW

ANN Thresholding

4 13

Real Real

VMD

OSELM

14

Real

VMD

OSELM

14

Synthetic

99.30 [39] 95.79 [10] 98.86 (proposed) 99.71 (proposed)

There are many prevalent methods used to recognize the PQEs but the proposed method VMD-OSELM is more efficient in detection and classification of the single as well as multiple PQEs meticulously in real-time (0.019 seconds) for both noise-

free and noisy environments. The immediate detection capability, enhanced classification accuracy, robust anti-noise performance, and the real-time ability prove the robustness of the proposed methodology effectively. 6.

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[7]

Conclusion and Future Works

The EMD, EWT, and VMD provide significantly superior time-frequency representation to analyze the single and multiple non-stationary PQEs. The mode mixing problem of EMD is not able to produce the highly correlated IMFs and EWT suffers to perform in a noisy environment. But VMD produces the highly correlated BLIMFs without mode mixing, based on the center frequency in both the noise-free and noisy environments. The magnitude response, phase response, and frequency response contribute to the effective visual understanding of the detection of PQEs. The distinct efficacious features are extracted from the highly correlated BLIMFs and applied to the OSELM classifier. The OSELM classifier trains its network by taking chunk by chunk data based on the minimum training error to produce the superior classification accuracy in the multiclass classification. The suitable feature extraction, robust anti-noise performances, faster learning speed, lesser computational time and superior classification accuracy are the major advantages that prove the proposed VMD-OSELM over EWT-OSELM and HHT-OSELM is a promising as well as competent method to categorize the single and multiple PQEs in real-time. A PC interfaced hardware system is designed using USB based NI-cDAQ to test the proposed method. The experimental performances validate the real-time ability with better recognition capability. The comparisons of classification accuracy conclude that the VMDOSELM has a powerful structure to recognize the PQEs. In future works, (1) an optimization-based VMD can be developed to compute k and  automatically from the complex PQE signals for the extraction of the mono-component mode of oscillations without mode mixing. (2) An online data compression technique needs to be introduced for avoiding the manual computation of features which leads to degradation of the overall performance of the PQE recognition method. (3) The recently developed deep learning method can be implemented to avoid the manual extraction and selection of features. Also, it can be applied to recognize the complex PQE in a fast learning neural network platform without using an extra classifier.

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Magnitude in volt

Magnitude in volt

Graphical abstract Input Signal

2 0 -2

0

0.02

0.04

0.06

Phase in radian

0.1

0.12

0.14

0.16

0.18

0.2

0.14

0.16

0.18

0.2

0.14

0.16

0.18

0.2

0.14

0.16

0.18

0.2

Time in second Magnitude response

2 1 0

0

0.02

0.04

0.06

0.08

0.1

0.12

Time in second Phase response

0.5 0

-0.5

Inst-Frequency in Hz

0.08

0

0.02

0.04

0.06

0.08

0.1

0.12

Time in second Frequency response

1000 0

-1000

0

0.02

0.04

0.06

0.08

0.1

0.12

Time in second

Visualization the occurrence of multiple PQEs

HIGHLIGHTS > Variational Mode decomposition is used to decompose the power quality signals > On-line sequential ELM is used for power quality pattern recognition using VMD >Comparison with EWT and EMD based decompositions prove the efficiency of VMD > A real-time hardware validation has been also presented in the paper>

Author Contribution P.K. Dash: Conceptualization of problem of power quality M. Sahani: Data analysis and development of the computer codes and their implementation P.K. Dash and M. Sahani: Edited the full paper in its present form