A multiple power quality (MPQ) disturbance has two or more power quality (PQ) disturbances superimposed on a voltage signal. A compact and robust technique is required to identify and classify the MPQ disturbances. This manuscript investigated a hybrid algorithm which is designed using parallel processing of voltage with multiple power quality (MPQ) disturbance using stockwell transform (ST) and hilbert transform (HT). This will reduce the computational time to identify the MPQ disturbances, which makes the algorithm fast. A MPQ identification index (IPI) is computed using statistical features extracted from the voltage signal using the ST and HT. IPI has different patterns for various types of MPQ disturbances which effectively identify the MPQ disturbances. A MPQ time location index (IPL) is computed using the features extracted from the voltage signal using ST and HT. IPL effectively identifies the initiation and end of PQ disturbances and thereby locates the MPQ events with respect to time. Classification of MPQ disturbances is performed using decision rules in both the noise-free and noisy environments with a 20 dB noise to signal ratio (SNR). The performance of the proposed hybrid algorithm using ST and HT with rule-based decision tree (RBDT) is better compared to the ST and RBDT techniques in terms of accuracy of classification of MPQ disturbances. MATLAB software is used to perform the study.

Equipment used in industrial processes is sensitive to the quality of power. Hence, bad or poor power quality (PQ) affects the efficiency of industrial production and the quality of the finished products [

This section details the research work reported in the literature related to the detection and classification of PQ disturbances, with emphasis on multiple PQ disturbances. In [

This is inferred from detailed analysis of PQ identification and classification techniques discussed in the above paragraph, that existing methods effectively identify the PQ disturbances of a single nature with high accuracy, greater than 98%, whereas the efficiency reduces for multiple-nature PQ disturbances. Further, the efficiency of these methods decreases in the presence of high noise levels. Additionally, it is also established that the existing methods require a large number of features (7 to 10 or more) for classification of multiple PQ disturbances. These research gaps can be mitigated using the hybrid combination of the various signal processing methods. This will help in the identification and classification of MPQ disturbances with an accuracy higher than 98% even in the presence of noise at higher levels using only four features. Hence, this paper has considered carrying out further research using a hybrid combination of ST, HT, and decision rules to design a hybrid algorithm to identify and categorize MPQ disturbances. The main contributions of this manuscript are summarized below:

A hybrid algorithm using the parallel approach supported by ST and HT with decision rules is investigated to identify and classify the MPQ disturbances.

An MPQ identification index is proposed which has different patterns for various types of MPQ disturbances. Hence, it effectively identifies all the MPQ disturbances.

The MPQ time location index is computed using the features extracted from the voltage signal with an associated MPQ disturbance, applying the ST and HT for time location of MPQ disturbances. It effectively identifies the initiation and end of the MPQ disturbances and thereby locates the MPQ events.

The MPQ algorithm is effective in classifying the MPQ events using decision rules with the help of four features in both the noise-free and noisy environments.

Performance of the technique using ST and HT with RBDT is better compared to ST and RBDT technique in terms of accuracy of classification of MPQ disturbances.

The paper is organized into seven sections. The first section, describes the review of literature, research gaps, and contribution of this manuscript. The formulation of MPQ disturbances is described in the second section. All the steps of the proposed algorithm are detailed in the third section. The results used to identify the MPQ disturbances and their discussions are included in

Multiple PQ disturbances have been formulated as per standards defined in the IEEE-1159 standard using mathematical formulations reported in [

S. No. | Event | Symbol of multiple |
Simulated parameters |
---|---|---|---|

1 | Voltage signal with no PQ disturbance | MPD0 | |

2 | Voltage sag + Harmonics | MPD1 | |

3 | Voltage MI + OT | MPD2 | |

4 | Voltage flicker + OT | MPD3 | |

5 | Voltage sag + IT | MPD4 | |

6 | Voltage harmonics + IT | MPD5 | |

7 | Voltage sag + notch | MPD6 | |

8 | Voltage sag + harmonics + OT | MPD7 | |

9 | Voltage flicker + harmonics + IT | MPD8 |

1. Voltage signal having sinusoidal nature [

2. Voltage with sag and harmonics multiple PQ disturbance [

3. Voltage with momentary interruption (MI) and oscillatory transient (OT) multiple PQ disturbance [

4. Voltage with flicker and OT multiple PQ disturbance [

5. Voltage sag and impulsive transient (IT) multiple PQ disturbance [

6. Voltage signal with harmonics and IT multiple PQ disturbance [

7. Voltage signal with sag and notch multiple PQ disturbance [

8. Voltage with sag, harmonics and OT multiple PQ disturbance [

9. Voltage signal with flicker, harmonics and IT multiple PQ disturbance [

Hybrid algorithm used to identify and classify the MPQ disturbances is described in

Different features are computed by processing the voltage having an associated MPQ disturbance using ST as described below:

Process voltage signal with a MPQ disturbance (

The MATLAB command

where

Hence, the output matrix (which is complex in nature) of the ST based decomposition of voltage signal with MPQ disturbances (STM) can be given by the following relation [

The STOM matrix is a complex valued matrix. Absolute values matrix is computed by taking the absolute values of every element.

Matrix ASTOM is used to extract the information of frequency and amplitude of the voltage signal with MPQ disturbance and used for computation of various features utilized for identification of MPQ disturbances.

Compute median of ASTOM matrix (SM) using the below detailed relation.

Here, MATLAB command ‘

Compute variance of ASTOM matrix (SV) using the below detailed relation.

Here, MATLAB command ‘

Compute standard deviation of ASTOM matrix (SSTD) using the below detailed relation.

Here, MATLAB command ‘

Different features are computed by processing the voltage with an associated MPQ disturbance applying HT as described below:

Process voltage with a MPQ disturbance (

The function

Here, PV: Cauchy’s principle value integral,

Compute variance of ASTOM matrix using the below detailed relation.

An index is computed using the features extracted from the voltage signal with an associated MPQ disturbance applying the ST and HT for identification of MPQ disturbances which is given the name IPI. Computation of IPI is detailed below:

Here, AHTOM is a row matrix which is directly used for computation of IPI and WFI is the weight factor used for identification of MPQ disturbances. WFI equal to 10^{4} is considered for this study. The relation of IPI index is fixed after testing on 80 data set of each disturbance which is obtained by variation of parameters such as amplitude, time interval of disturbance, frequency, combination of various PQ disturbances, etc. Further, various features have also been considered using the statistical formulations and it is established that combination of SV, SSTD and AHTOM gives the best results in terms of maximum efficiency.

An index is computed using the features extracted from the voltage signal with an associated MPQ disturbances applying the ST and HT for time location of MPQ disturbances which is given the name IPL. Computation of IPL is detailed below:

Here, WFL is the weight factor used for time location of MPQ disturbances. WFL equal to 10^{4} is considered for this study. The relation of IPL index is fixed after testing on 80 data set of disturbances, which has the magnitude and transient components. This data set is obtained by variation of parameters such as amplitude, time interval of disturbance, frequency, combination of various PQ disturbances, etc. Further, various features have also been considered using the statistical formulations and it is established that combination of HV, and SM gives the best results in terms of effective time location of disturbances.

The MPQ disturbances have been classified using the decision rules which are derived from the features (MPF1 to MPF4) computed from the IPI and IPL as detailed below:

MPF1: Covariance of IPI

MPF2: Summation of all elements of IPI

MPF3: Covariance of IPL

MPF4: Summation of all elements of IPL

The MATLAB commands ‘

The results to identify and classify the multiple PQ disturbances and their discussion are elaborated in this section. MPQ disturbances with multiplicity two and three are described in this section.

A voltage signal without any MPQ disturbance is simulated by modelling the expressions described in

S. No. | Event | Symbol of multiple PQ disturbance | Time of PQ identification (s) |
---|---|---|---|

1 | Voltage signal with no PQ disturbance | MPD0 | 0.084507 |

2 | Voltage sag + Harmonics | MPD1 | 0.252790 |

3 | Voltage MI + OT | MPD2 | 0.161229 |

4 | Voltage flicker + OT | MPD3 | 0.061164 |

5 | Voltage sag + IT | MPD4 | 0.074325 |

6 | Voltage harmonics + IT | MPD5 | 0.163903 |

7 | Voltage sag + notch | MPD6 | 0.080542 |

8 | Voltage sag + harmonics + OT | MPD7 | 0.070415 |

9 | Voltage flicker + harmonics + IT | MPD8 | 0.084994 |

A voltage signal with an associated MPQ disturbance of degree two multiplicities, including sag and harmonics, is simulated using a mathematical formulation, as shown in

In order to investigate the impact of noise on the efficacy of the algorithm, a voltage signal with an associated MPQ disturbance of two multiplicities comprising of sag and harmonics is simulated using a mathematical formulation. A noise of level 20 dB SNR is superimposed on this voltage signal, which is elaborated in

Voltage with MPQ disturbance and noise is decomposed by applying ST and HT to compute the MPQ identification index (IPI) and MPQ time location index (IPL). The IPI and IPL for MPQ disturbance of sag and harmonics in a noisy environment are elaborated in

The mathematical formulation is used to simulate a voltage with an associated MPQ disturbance of degree two multiplicity consisting of MI and OT, as shown in

In

A voltage signal with an associated MPQ disturbance of degree two multiplicities, consisting of sag and IT, is simulated using a mathematical formulation, as shown in

A voltage with an associated MPQ disturbance of degree two multiplicities, consisting of harmonics and IT, is simulated using a mathematical formulation, as shown in

A voltage with an associated MPQ disturbance of degree two multiplicities, consisting of sag and notch, is simulated and elaborated in

In

A voltage signal with a three-degree multiplicity MPQ disturbance consisting of flicker, harmonics, and IT is simulated using a mathematical formulation and illustrated in

The MPF1, MPF2, MPF3, and MPF4 features are computed using the mathematical relations described in

The classification of MPQ disturbances started using the feature MPF1 and was grouped into two groups. If MPF1 > 100, then disturbances are included in Group-GA else grouped in Group-GB. Disturbances of Group-GA are categorized in two groups using the feature MPF3. If MPF3 > 500, then disturbances are included in Group-GA1, which are MPD2, MPD3, and MPD7. If MPF3 > 500, then disturbances are included in Group-GA2, which are MPD4, MPD5, and MPD8. The disturbances MPD0, MPD1 and MPD6 are grouped in Group-GB. Disturbances of Group-GB, Group-GA1 and Group-GA2 are categorized one by one using the decision rules described in

S. No. | Event | Symbol of multiple PQ disturbance | Features | |||
---|---|---|---|---|---|---|

MPF1 | MPF2 | MPF3 | MPF4 | |||

1 | Voltage signal with no PQ disturbance | MPD0 | 1.0593 × 10^{−7} |
0.0306 | 4.4375 × 10^{−4} |
680.0156 |

2 | Voltage sag + Harmonics | MPD1 | 0.5912 | 125.4954 | 0.1834 | 539.9058 |

3 | Voltage MI + OT | MPD2 | 885.5890 | 4.6550 × 10^{3} |
1.2616 × 10^{3} |
5.9830 × 10^{3} |

4 | Voltage flicker + OT | MPD3 | 148.2177 | 4.9268 × 10^{3} |
1.1746 × 10^{3} |
6.1244 × 10^{3} |

5 | Voltage sag + IT | MPD4 | 290.7279 | 1.7157 × 10^{3} |
1.3626 | 727.8720 |

6 | Voltage harmonics + IT | MPD5 | 203.9100 | 1.5627 × 10^{3} |
0.9966 | 1.009 × 10^{3} |

7 | Voltage sag + notch | MPD6 | 12.5194 | 1.9025 × 10^{3} |
0.0910 | 394.9824 |

8 | Voltage sag + harmonics + OT | MPD7 | 187.5045 | 2.2808 × 10^{3} |
1.2838 × 10^{3} |
6.3930 × 10^{3} |

9 | Voltage flicker + harmonics + IT | MPD8 | 159.8895 | 9.8232 × 10^{3} |
0.9327 | 940.6127 |

The performance of the hybrid parallel algorithm and decision rules-based approach is evaluated for identification and classification of the 80 disturbances for every MPQ event. This set of data is computed by varying parameters such as amplitude, frequency, noise levels, etc. The performance is measured in both noise-free and noisy environments. A list of accurately and inaccurately identified and classified MPQ disturbances is included in

S. No. | MPQ disturbance | Correctly classified MPQ disturbances | Incorrectly classified MPQ disturbances | Efficiency of recognition (%) | |||
---|---|---|---|---|---|---|---|

Without |
20 dB |
Without |
20 dB |
Without |
20 dB |
||

1 | MPD0 | 80 | 80 | 0 | 0 | 100 | 100 |

2 | MPD1 | 80 | 79 | 0 | 1 | 100 | 98.75 |

3 | MPD2 | 80 | 80 | 0 | 0 | 100 | 100 |

4 | MPD3 | 79 | 78 | 1 | 2 | 98.75 | 97.50 |

5 | MPD4 | 80 | 80 | 0 | 0 | 100 | 100 |

6 | MPD5 | 80 | 79 | 0 | 1 | 100 | 98.75 |

7 | MPD6 | 80 | 79 | 0 | 1 | 100 | 98.75 |

8 | MPD7 | 78 | 77 | 2 | 3 | 97.50 | 96.25 |

9 | MPD8 | 78 | 76 | 2 | 4 | 97.50 | 95.00 |

Total | 715 | 708 | 5 | 12 | 99.30 | 98.33 |

The performance of the RBDT based classifier driven by the features computed from the IPI and IPL indices is also evaluated using the indices such as root mean square error (RMSE), mean absolute error (MAE), precision, and recall. RMSE is a principal metric which effectively measures the difference between the values predicted by the classifier and their true value, as defined by the below relation [

where

Precision indicates the capability of the classifier for determining the positive labels using one

where

where

The performance of the RBDT based classifier driven by the features computed using ST and HT is evaluated in terms of RMSE, MAE, precision and recall. This is achieved using the 80 data sets of every MPQ disturbance used by the user.

S. No. | Index | Value of index in noise free scenario | Value of index in noisy scenario |
---|---|---|---|

1 | RMSE | 0.032 | 0.069 |

2 | MAE | 0.011 | 0.023 |

3 | Precision | 0.991 | 0.982 |

4 | Recall | 0.993 | 0.983 |

The efficacy of the results of the study introduced in this manuscript is compared with the technique using the ST and RBDT and reported in [

S. No. | MPQ disturbance | Efficiency of recognition (%) | |
---|---|---|---|

Proposed technique (%) | Reference [ |
||

1 | Voltage sag + Harmonics | 100 | 93.33 |

2 | Harmonics + IT | 100 | 93.33 |

3 | Voltage sag + IT | 100 | 96.67 |

Overall efficiency of techniques | 99.30 | 96.67 |

The proposed ST and HT with RBDT based algorithm for recognition of MPQ disturbances has been tested to identify the MPQ disturbances associated with the line-to-ground (LG) fault event incident on the practical power system network of Rajasthan State of India. Details of the real-time transmission network, such as generations, number of grid sub-stations (GSS), circuit length of the transmission lines of all voltages, and loads used for the study are available in [^{th} cycle and the 9^{th} cycle due to the incidence of the LG fault. Further, a high magnitude peak at the time of the 9^{th} cycle indicates the presence of an IT disturbance. Ripples from the 4^{th} cycle indicate the presence of transients during the fault period and post-fault period. ^{th} cycle and 9^{th} cycle locate the MI disturbance in the time range, while continuous ripples from the 4^{th} cycle indicate the presence of transient components available during the fault period and post-fault period.

This paper designed a robust technique to identify and classify MPQ disturbances. This is achieved using the ST, HT and decision rules. The IPI and IPL indices are used to identify and locate the MPQ disturbances. These MPQ disturbances have been classified in different categories using the decision rules. It is concluded that IPI has different patterns for various types of MPQ disturbances which effectively identify all the MPQ disturbances. Further, the proposed IPL effectively identifies the initiation and end of the MPQ disturbances and thereby effectively locates the MPQ events. All the investigated MPQ events have been effectively classified using the decision rules in both the noise-free and noisy environments with a 20 dB SNR with accuracy higher than 98%. This is achieved in a time period less than 0.3 s. Further, the effectiveness of the proposed RBDT classifier is also established using indices such as RMSE, MAE, precision, and recall. The performance of the technique is found to be superior compared to the ST and RBDT techniques in terms of classification accuracy of MPQ disturbances and reduced computational time. The proposed algorithm effectively identified MPQ disturbance incidents on the real-time power system network.