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This paper describes a new approach for power transformer differential protection which is based on the wave-shape recognition technique. An algorithm based on neural network principal component analysis (NNPCA) with back-propagation learning is proposed for digital differential protection of power transformer. The principal component analysis is used to preprocess the data from power system in order to eliminate redundant information and enhance hidden pattern of differential current to discriminate between internal faults from inrush and overexcitation conditions. This algorithm has been developed by considering optimal number of neurons in hidden layer and optimal number of neurons at output layer. The proposed algorithm makes use of ratio of voltage to frequency and amplitude of differential current for transformer operating condition detection. This paper presents a comparative study of power transformer differential protection algorithms based on harmonic restraint method, NNPCA, feed forward back propagation neural network (FFBPNN), space vector analysis of the differential signal, and their time characteristic shapes in Park’s plane. The algorithms are compared as to their speed of response, computational burden, and the capability to distinguish between a magnetizing inrush and power transformer internal fault. The mathematical basis for each algorithm is briefly described. All the algorithms are evaluated using simulation performed with PSCAD/EMTDC and MATLAB.

Power transformer is one of the most important components in power system, for which various types of protective and monitoring schemes have been developed for many years. Differential protection is one of the most widely used methods for protecting power transformer against internal faults. The technique is based on the measurement and comparison of currents at both side of transformer: primary and secondary lines. The differential relay trips whenever the difference of the currents in both sides exceeds a predetermined threshold. This technique is accurate in most of the cases of transformer internal faults however mal-operation of differential relay is possible due to inrush currents, which result from transients in transformer magnetic flux. The transients in transformer magnetic flux may occur due to energization of transformer, voltage recovery after fault clearance or connection of parallel transformers.

The existence of such current disturbances has made the protection of power transformers a challenging problem for protection engineers. Therefore, accurate classification of currents in a power transformer is need of this challenging problem, in preventing maloperation of the differential relay under different nonfault conditions including magnetizing inrush, over-excitation, external fault, and saturation of current transformers [

Since last 1960s, researchers have considerable interest in the area of digital protection of power apparatus [

Early methods were based on desensitizing or delaying the relay to overcome the transients [

In this paper, a simple decision-making method based on the NNPCA is proposed for discriminating internal faults from inrush currents. The algorithm has been developed by considering different behaviors of the differential currents under internal fault and inrush condition. The NNPCA method extracts the relevant features from the differential current and reduces a training dataset to a lower dimension. The algorithm uses a data window of 12 samples per cycle. The algorithm also considers CT saturation and distinct scenarios such as changes in transformer load, source impedance, and remanent flux. All the mentioned conditions are simulated in PSCAD/EMTDC.

The accuracy in classification, speed of response, and computational burden of the harmonic restraint method, NNPCA, feed-forward back-propagation neural network (FFBPNN), and symmetrical component based method are compared in the presented work.

Neural network principal component analysis (NNPCA) is basically an adaptive nonparametric method of extracting relevant information from confusing datasets [

A typical architecture of NNPCA is shown in Figure

Typical neural network principal component analysis architecture.

For a

Connecting weight,

The weight adapting (

Power transformer operating conditions may be classified as

normal condition,

magnetizing inrush/sympathetic inrush condition,

over-excitation condition,

internal fault condition,

external fault condition.

In the normal condition, rated or less current flows through the transformer. In this condition normalized differential current is almost zero (only no load component of current). Whenever there is large and sudden change in the input terminal voltage of transformer, either due to switching-in or due to recovery from external fault getting, a large current is drawn by the transformer from the supply. As a result, the core of transformer gets saturated. This phenomenon is known as magnetizing inrush, or in other words, inrush can be described by a condition of large differential current occurring when either the transformer is just switched on or the system recovers from an external fault. Similar condition occurs when transformer is energized in parallel with another transformer that is already in service; it is known as “

heavy faults,

medium level fault and,

low level fault.

In all the cases, the abnormality nature is almost same but the magnitudes of currents resulting due to that are quite different. If the level of fault can be detected and accordingly protective action is taken, then the major damage to the protected element can be prevented.

A simulation software PSCAD/EMTDC is used to generate the training and testing signals under different operating conditions of transformer that are normal, overexcitation, magnetizing inrush, sympathetic inrush, and fault (phase-to-phase, phase-to-ground, and external fault) conditions. While simulating different operating conditions of transformer, energization angle, remanent flux in the core and load condition are considered as the magnitude and the wave-shape of differential current depends on these factors. Energization angle is varied from 0 to 360 degrees in interval of 30 degrees and remanent flux varying from 0% to 80% of the peak flux linkages generated at rated voltage with no-load and full-load conditions to generate training signals while, in case of testing signals energization angle is varied in interval of 15 degrees. The desired remanence can be set in unenergized transformer with controlled DC current sources in PSCAD/EMTDC model [

Three-phase transformers of 315 MVA at 400/220 kV, 200 MVA at 220/110 kV and 160 MVA at 132/220 kV, are modeled by using PSCAD/EMTDC. For the simulation of these transformers through PSCAD/EMTDC, the realistic data obtained from the M P State Electricity Board, Jabalpur India, is used. Typical connection of a 3-phase transformer of 315 MVA, 400/220 kV, 50 Hz, delta-star grounded connection is shown in Figure

Typical three-phase power system.

(a) Typical PSCAD/EMTDC transformer model to simulate internal fault (b) Typical PSCAD/EMTDC transformer model to simulate internal faults at different locations.

In [

Consider

The test signals (typical magnetizing inrush and internal fault conditions) obtained by simulation of transformer are shown in Figures

Typical magnetizing inrush current waveform.

Typical phase-to-ground fault current waveform.

The differential current is typically represented in discrete form as a set of 12 uniformly distributed samples obtained over a data window of one cycle of fundamental frequency signal, that is, the sampling rate is 12 samples per cycle. These 12 samples are called a “

Each row of the input training matrix represents one pattern while corresponding row of target matrix represents desired output. Suppose that the inrush condition signal is characterized by the following sequence:

The first row of inrush matrix takes 12 samples of

Two types of principal component analysis (PCA) data processors had been used for the purpose. The first one is called the preprocessor PCA, which is responsible for preprocessing input training data, to eliminate correlation in training patterns. The second is called postprocessor PCA, used to transform the validation and test datasets according to their principal components. The implementation was carried out with aid of built-in function supported by MATLAB Neural Network Toolbox.

In proposed NNPCA architecture three-layered structure is used. The input layer has 12 neurons. The hidden layer consists of 11 neurons, as the number of neurons in hidden layer increases, the error decreases but after certain number of neurons it increases again, and in this case the minimum error is obtained for 11 neurons in the hidden layer. Therefore, the number of neurons in the hidden layer is optimal for this application. As only single output (trip or not) is required, the output layer consists of just one neuron. After much experimentation on various neural network architectures, the presented model is proposed which has lesser neurons in all three layers.

To differentiate between the fault and inrush conditions, the inrush condition is indicated by “0” and “1” indicates the fault condition. Out of 925 sets of data (patterns), 777 pattern sets are used to train the proposed NNPCA model. Out of these 777 pattern sets, 444 pattern sets are for the inrush (including sympathetic inrush patterns) and 333 are for the internal fault. The remaining 148 sets (which are not made part of training sets) are used to test the network’s generalization ability. These 148 test exemplar pattern sets contain internal fault and inrush condition only as these two conditions are very difficult to discriminate as compared to other operating conditions such as external fault, overexcitation, and normal condition. Out of 148 test patterns, 74 test sets were inrush patterns and remaining 74 test sets were internal fault patterns. The inrush test patterns consist of sympathetic inrush patterns and magnetizing inrush patterns at different switching-in angles, while internal fault test patterns are made up of phase-to-ground fault and phase-to-phase fault at different locations.

After the NNPCA model had been trained, their generalization performances were calculated based on the mean absolute error (MAE) given by

Flow chart of the proposed algorithm (Figure

Flow chart of presented algorithm.

For different conditions of the test set, fault current magnitude, load condition, remanent flux, and switching angle are changed to investigate the effects of these factors on the performance of the proposed algorithm. Since the wave-shape of inrush current changes with variation of switching-in instant of transformer, hence it is varied between 0 to 360 degrees. Similarly, due to the presence of the remanence flux, magnitude of inrush current may be as high as 2 to 6 times of inrush current without that, although the wave-shape remains same. It is found that the NNPCA classifier-based relay is stable even with such high magnitude of inrush current caused by remanence flux whereas, the conventional harmonic-based relay may maloperate due to such high magnitude of inrush current [

Performance of NNPCA and FFBPNN having topology of 12-11-1

Neural network topology | Training error | Max. epoch | Inrush | Fault | ||
---|---|---|---|---|---|---|

P | A | P | A | |||

NNPCA | 0.0001 | 1000 | −1.0 | 0.0 | 0.96 | 1.0 |

FFBPNN | 0.0001 | 1000 | −1.0 | 0.0 | 0.96 | 1.0 |

P: predicted, A: actual.

Accuracy in classification (%)

Trained transformer ratings | Tested transformer ratings | |||||
---|---|---|---|---|---|---|

315 MVA | 200 MVA | 160 MVA | ||||

FFBPNN | NNPCA | FFBPNN | NNPCA | FFBPNN | NNPCA | |

315 MVA | 99.32 | 100 | 94.59 | 100 | 98.64 | 100 |

200 MVA | 94.59 | 100 | 99.32 | 100 | 98.64 | 100 |

160 MVA | 94.59 | 100 | 96.32 | 100 | 100 | 100 |

We halve the following:

Number of postdisturbance samples required for decision by NNPCA-based relay.

Cases | Number of samples required |
Maximum samples required |
---|---|---|

Magnetizing inrush ( |
8 | 12 |

Internal fault (5% to 98%) | 6 | 12 |

Internal fault (light phase-to-ground fault at 2%) | 9 | 12 |

The same power transformers are tested with symmetrical component method and harmonic restraint (HR) method based on discrete fourier transform (DFT) (see the section Appendix).

Park’s vector

Plot for an inrush ((a), primary winding currents, (b) centre secondary winding currents, (c) differential current).

Plot for internal fault condition ((a), primary winding currents, (b) centre secondary winding currents, (c) differential current).

Discrete fourier-transform- (DFT-) based harmonic restraint method is implemented, to compare performance of the proposed optimal NNPCA-based algorithm in power transformer differential protection. Figure

Ratio of second harmonic to fundamental of the differential current under typical inrush and internal fault condition.

However, the harmonic restraint method and symmetrical component method are capable to discriminate between these two conditions but do not seem to be intelligent to take decision in case of fluctuating ratio of second harmonic to fundamental of the differential current due to different loading conditions, severity of internal faults, switching-in angles, and so forth, and hence maloperation of relay will occur. In case of symmetrical component method, Park’s space plot is to be analyzed for its symmetry than only relay can take decision. Moreover, these methods take more time to take decision as compared to NNPCA-based transformer differential method and depend on the harmonic contain present in the relaying signal.

This paper presents a novel intelligent approach based on neural network principal component analysis (NNPCA) model to solve the problem of distinguishing between transformer internal fault and magnetizing inrush condition. The performance of NNPCA-based method is compared with feed-forward back-propagation neural network (FFBPNN), harmonic restraint method, and Park’s plot method.

The proposed NNPCA algorithm is based on waveform identification technique which is more accurate than traditional harmonic-restraint-based technique, especially in case of modern power transformers which use high-permeability low-coercion core materials. The conventional harmonic restraint technique may fail because high second harmonic components may be generated during internal faults and low second harmonic components during magnetizing inrush with such core materials.

However, the harmonic restraint method and symmetrical component method are capable to discriminate between these two conditions but do not seem to be intelligent to take decision in case of fluctuating ratio of second harmonic to fundamental of the differential current. Moreover, these methods take more time to take decision as compared to NNPCA-based transformer differential method.

The proposed optimised NNPCA technique is simple in architecture, fast in operation, and robust. The present neural network model issues tripping signal in the event of internal fault within 6–15 ms of fault occurrence. The method is also immune from the DC offset in relaying signals due to saturation of CT core in the event of internal or external fault. Moreover, the NNPCA-based algorithm has 100% accuracy in classification which is not possible to achieve by using FFBPNN in the application of power transformer differential application.

Any continuous waveform

Hence, for 12 samples per data window, 12 Fourier coefficients will have an array size of

For power transformers protection,

A function of instantaneous line currents

Park’s vector

Park’s vectors are obtained from the instantaneous line currents by means of the [

The plot in Park’s plane of the

In Park’s space,