Correction of Saturated Current Transformers ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 21, NO. 1, JANUARY 2006

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Correction of Saturated Current Transformers Secondary Current Using ANNs H. Khorashadi-Zadeh and M. Sanaye-Pasand

Abstract—Current transformers (CTs) provide instrument-level current signals to meters and protective relays. Protective relays’ accuracy and performance are directly related to steady-state and transient performance of CTs. CT saturation could lead to protective relay maloperation or even prevent tripping. This paper proposes the use of an artificial neural networks scheme to correct CT secondary waveform distortions. The proposed module uses samples of current signals to achieve the inverse transfer function of CT. Simulation studies are preformed and the influence of changing different parameters is studied. Performance studies results show that the proposed algorithm is accurate and reliable. The proposed algorithm has also been implemented and tested on a digital signal processor board. Details of the implementation and experimental studies are provided in this paper. Index Terms—Artificial neural networks (ANNs), current transformers (CTs), CT saturation.

I. INTRODUCTION

P

Several methods for compensating distortions of the CT secondary current have been presented in the literature [5]–[11]. In [5] and [6], a compensation algorithm is proposed which estimates the CT magnetizing current. The magnetizing current is added to the measured secondary current to estimate the correct secondary current. This algorithm performs well for various power system and fault conditions. However, it assumes that the remnant flux is zero before occurrence of the fault. Algorithms presented in [7] and [8] were used to improve the accuracy of a measurement CT. The initial core flux was estimated and used in conjunction with the hysteresis curve to calculate the exciting current. The technique is valid for slight saturation and relies on the assumption that there is no remnant flux in the core. An alternative approach is to use an artificial neural network to approximate a function that corrects the distorted CT secondary currents caused by CT saturation. A nonlinear multilayer recursive artificial neural network (ANN) for correcting the distorted secondary current was reported in [9]. In this approach, structure of the neural network should change for different CT burdens. In another ANN-based method, a feedforward ANN attempts to learn the nonlinear characteristics of CT magnetization and restructures the waveform based on the learned characteristics [10], [11]. This method has not investigated all of the factors which could affect CT saturation (i.e., the dc component, the primary time constant, and the remnant flux in the core). This paper presents a novel ANN-based technique for the compensation of saturated CT secondary current. This method accurately estimates the secondary current corresponding to the CT ratio, in particular, when the CT is saturated both with and without the presence of remnant flux. Obtained simulation results clearly demonstrate the ability of the proposed method to provide good estimate of the secondary current in the presence of CT saturation. The proposed method has also been implemented and tested on a digital-signal-processor (DSP) board. Details of the implementation and experimental studies are given in the paper as well.

OWER SYSTEMS have grown both in complexity and size, presenting increased levels of fault currents. Power system protective relays are playing an increasingly important role in the new power systems. They should clear system faults with a high degree of reliability and as fast as possible. To be able to perform properly, they require reasonably accurate reproduction of the primary current and voltage signals during system faults. In this respect, current transformers (CTs) are employed to provide a reduced version of the primary current. Most CTs use iron core to maximize the flux linkage between primary and secondary windings. Iron-cored CTs, however, are not ideal because of the nonlinearity of their excitation characteristics and their ability to retain large flux levels in their cores known as remnant flux. As a result, they are prone to saturation. Many studies on the analysis of steady-state and transient behavior of iron-cored CTs have been reported in the literature [1]–[4]. It is well known that the exciting current drawn by the core increases far more rapidly for the points above the CT magnetization curve knee-point. If the CT flux increases beyond the knee-point, then the CT saturates. In this case, CT secondary current does not represent its primary current and the CT ratio error increases considerably. This could lead to the malfunction of the system protective relays.

A. CT Modeling

Manuscript received October 4, 2004; revised January 3, 2005. Paper no. TPWRD-00466-2004. H. Khorashadi-Zadeh is with the Department of Power Engineering, University of Birjand, Birjand 97175-36, Iran (e-mail: [email protected]). M. Sanaye-Pasand is with the Center of Excellence in Control and Intelligent Processing, School of Electrical and Computer Engineering, University of Tehran, Tehran 14395-515, Iran (e-mail: [email protected]). Digital Object Identifier 10.1109/TPWRD.2005.858799

The training data set of an ANN should contain the necessary information to generalize the problem. A 230-kV power system is simulated using an EMTDC electromagnetic transient program [12] and various types of faults with different conditions and parameters are modeled. A CT has also been considered in the simulated system model for the study of a CT saturation problem.

II. TRAINING PATTERNS GENERATION

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Fig. 1.


CT circuit diagram.

TABLE I SIMULTED CT PARAMETERS

The modeled CT circuit diagram is shown in Fig. 1 and its parameters are given in Table I. This component models a CT based on the Jiles–Atherton theory of ferromagnetic hysteresis. The effects of saturation, hysteresis, remnance, and minor loop formation are modeled based on the physics of the magnetic material [12]. The accuracy of the CT model based on the Jiles–Atherton theory of ferromagnetic hysteresis has been checked by means of many tests in [13]. The test results confirm a high degree of accuracy for this CT model. B. Influence of Different Parameters For a CT, the magnitude of the magnetizing current and time to saturation are dependent upon different parameters. The time to saturation is defined by the time from the moment of occurrence of short circuit to the moment that the flux reaches its maximum value [1]. Various parameters, which influence CT saturation, include short-circuit current magnitude, short-circuit time constant, CT turn ratio, magnetizing characteristic of the core, inductance and resistance of the secondary and burden, flux remnant in the CT core, and fault inception time. Some of these parameters are considered in the modeling of the CT. Some other parameters, which are the most important factors and have a major role in CT saturation problem, are considered and studied in the following subsections. Influence of Remnant Flux: The residual flux of CT would either improve or worsen the transient response of the CT. The worst effect of remnance is to force the CT into the state of saturation sooner than anticipated and it will shorten the time to saturation. Fig. 2 shows the CT primary and secondary waveforms for remnant fluxes of 0%, 50%, and 75%, respectively. In these figures, the maximum dc offset for the short-circuit current is assumed. As shown, the output deteriorates earlier in time for a higher amount of remnance. Influence of Occurrence Moment of Short Circuit: The fault incidence angle determines the characteristic of the fault current decaying dc component. Faults which involve significant dc offset can saturate CTs at much smaller currents than symmetrical currents without dc offset. Here, two fault inception

r = 0%, (b) r =

Fig. 2. Primary and secondary current waveforms for (a) 50%, and (c) 75%.

r=

cases with 0 and 45 were studied and their results are shown in Figs. 3 and 4, respectively. As shown in Fig. 3, for zero-fault inception angle, the dc component is very large and the CT is saturated severely. As expected, the degree of saturation is less severe for the case shown in Fig. 4 as the dc component is reduced in this case. Influence of Time Constant: In extremely-high-voltage (EHV) systems, the time constant is very large, which could cause severe CT saturation. The time constant ranges from several tens of milliseconds up to the maximum of about 200 ms. Two fault cases with time constants of 50 and 200 ms were surveyed and their results are shown in Figs. 5 and 6, respectively. Case 2 is more severely distorted in comparison with case 1.

KHORASHADI-ZADEH AND SANAYE-PASAND: CORRECTION OF SATURATED CTs SECONDARY CURRENT USING ANN

Fig. 5. Primary and secondary current waveforms for fault with

75

= 50 ms.

Fig. 3. Primary and secondary currents and flux waveforms for fault inception angle 0 . Fig. 6.

Primary and secondary current waveforms for fault with

= 200 ms.

TABLE II TRAINING PATTERNS DATA GENERATION

C. Training Patterns Training patterns were generated by simulating different types of faults on the power system. Fault current magnitude, flux remnant, burden, time constant, and fault inception angle were changed to obtain training patterns covering a wide range of different power system conditions. A combination of different fault conditions considered for training pattern data generation is shown in Table II. III. NEURAL-NETWORK-BASED SCHEME

Fig. 4. Primary and secondary currents and flux waveforms for fault inception angle 45 .

CT saturation and distortion of its secondary current usually arise for large short-circuit currents. CT saturation leads to inaccurate current measurement and, therefore, may cause a malfunction of protective relays and control devices that use currents as their input signal. For example, a distorted current

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Fig. 7. Current selection switching algorithm for reconstruction of the secondary current.

waveform may result in delayed operation of inverse-time overcurrent relays due to an underestimation of the root mean-square (rms) value of current waveforms. Distance relays may experience both over-reach and under-reach problems in fault impedance calculations due to inaccurate current phasor measurement [14]. A. Proposed Algorithm This section describes the design of an ANN-based scheme to compensate CT saturation caused by faults in power systems. ANNs are trainable systems, which could estimate input–output functions. They are essentially model-free estimations that learn from experience. In this application, an ANN was trained to provide the inverse function of the CT under study. The proposed ANN was trained for different power system conditions for which CT saturation occurs. The network is then used for processing CT output to provide a reliable estimate of the primary current. The provided estimated current can be used by existing protection algorithms as their input. A switching algorithm has been used to bypass the network for unsaturated faults [15]. This switching algorithm is shown in Fig. 7. Output current is selected by using (1) to verify whether the CT is saturated. Then, the switching algorithm determines the appropriate input current of the protection algorithm. If the current signal is determined to be saturated, the saturation is compensated by the ANN. Otherwise, the ANN is bypassed and the current signal is used directly as the input of the protection algorithm

Other

way (1)

B. Network Structure and Training Multilayer feedforward networks were chosen to process the prepared training input data. A few different networks were selected initially. For designing an appropriate neural network, different networks with 30 inputs and 1 output were considered. The network inputs included the sampled current and its previous samples. The sampling rate was chosen to be 20 samples per 50-Hz cycle. The networks’ architectures were decided empirically, which involved training and testing a different number of networks. Numbers of the neurons for the hidden layers were chosen to be 12 and 8 neurons, respectively. For all of the networks, a tan-sigmoid function was used as the activation func-

Fig. 8. Variation of error during the training process.

tion of the hidden layer neurons. A linear function was used for the output layer [16]. Various networks with different number of neurons in their hidden layer were trained with both conventional backpropagation (BP) and Marquardt–Levenberg (ML) algorithms [16], [17]. While BP is a steepest descent algorithm, the ML algorithm is an approximation to Newton’s method. The ML algorithm is a nonlinear least square algorithm applied to the learning of the multilayer perceptrons. The ML update rule is (2) where is the Jacobian matrix of derivatives of each error to each weight, is a scalar, and is an error vector. If the scalar is very large, the above expression approximates gradient descent, while if it is small, then it becomes the Gauss–Newton method. The comparison between the learning rate of BP and ML algorithms for the selected network is presented in Fig. 8. As shown in this figure, the ML algorithm training is faster. It is also found that the networks trained with the ML algorithm provide better results compared with the results of the networks trained with the BP algorithm. Therefore, the decision was made to use the ML training algorithm for this application. IV. SIMULATION TEST RESULTS A validation data set consisting of about 80 different fault types was generated using the simulated power system model. The validation set patterns were different than patterns used to train the network. For different conditions of the validation set, fault current magnitude, flux remnant, burden, time constant, and fault inception angle were changed to investigate the effects of these factors on performance of the proposed algorithm. The proposed ANN output for a few different conditions is shown in Figs. 9–12. For these cases, the relay output is shown for the first 250 ms after the fault inception, which is of utmost interest. The ANN output for a fault without any flux remnant is shown in Fig. 9. For this case, the fault inception angle fault was 0 , with a burden resistance of 0.5 and time constant of 50 ms.


Fig. 12.

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CT primary and secondary currents and ANN output for a fault with = 200 ms.

Fig. 9. CT primary and secondary currents and ANN output for a fault with 0; 0; Rb = 0.5, and = 50 ms.

r = 75%; = 135; Zb = 0:5 + j0:2 , and

Fig. 10. CT primary and secondary currents and ANN output for a fault with r = 0; = 180; Rb = 0.5, and = 50 ms.

The next example tests the ANN’s performance for another condition. Fig. 10 shows the output of the ANN for another fault with similar conditions as the previous case except that the fault inception angle is chosen to be 180 . The ANN performs correctly and appropriately, as shown in this figure. The ANN output for a fault with a flux remnant of 45% is depicted in Fig. 11. In this case, the fault inception angle was 45 , and time constant of with a burden impedance of 100 ms. Fig. 12 shows the CT primary and secondary currents and ANN output for a fault with an inception angle of 135 , a time constant of 200 ms, CT flux remnant of 75%, and a burden . It shows that the ANN output estiimpedance of mates primary current appropriately for these cases as well. A validation data set consisting of about 80 different fault types was considered and performance of the proposed algorithm was studied. From the obtained results, including the four cases shown, it could be concluded that this approach successfully estimates the true primary current from a distorted secondary current caused by the CT saturation. The designed module’s performance could also be checked using test patterns obtained from a different CT. It was found that similar results were obtained using the proposed module to estimate the true secondary current for a new CT, provided that the new CT has almost similar characteristics as the CT used in the paper. In other words, the ANN does not require additional training for a new CT if the new CT’s characteristic is not very different from the modeled CT. If the training set of a neural network is selected appropriately covering a wide range of conditions, the trained network would be able, without any further training, to perform appropriately with little error for the systems which have almost similar characteristics. This fact is also shown in some other research studies using neural-network-based protective relays [18], [19].

=

=

Fig. 11. CT primary and secondary currents and ANN output for a fault with r = 45%; = 45; Zb = 0:5 + j0:2 , and =100 ms.

As shown in this figure, the proposed ANN is able to estimate the primary current correctly.

V. HARDWARE IMPLEMENTATION After computer simulation studies, the proposed algorithm has been implemented using a TMS320C DSP board and its performance is investigated. It verifies whether the proposed algorithm could be applied in real time and determines the required

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TABLE III HARDWARE IMPLEMENTATION TEST RESULTS

Fig. 13.

Hardware implementation block diagram.

Fig. 14.

Test setup block diagram.

computer processing power to implement the module to compensate the saturated CT output quickly. The hardware implementation block diagram of the proposed scheme is shown in Fig. 13. The designed hardware is comprised of one data-acquisition system (DAS) card and a minimum system card. Active low-pass filters, sample holders, an analog multiplexer, and an analog-to-digital (A/D) converter are furnished for sampling and analog-to-digital conversion of the instantaneous current signal. The prepared digitized data are then introduced to the minimum system card. A sampling rate of 20 samples per cycle is assumed in the data-acquisition module. The minimum system card includes a TMS320C DSP from Texas Instruments. This card controls the DAQ process. It also processes the acquired signals and implements the proposed technique. The complete algorithm for three-phase secondary currents is executed in real time on the digital processor in about 501 s (167 s per phase); this corresponds to 50% of the duty cycle of the processor based on the sampling period of 1000 s. The algorithm requires less than 2.4 K memory. When the compensation module is executed, its output could be used by the existing protection algorithms. The ANN-based technique can promptly compensate the secondary saturated currents in about 0.5 ms. As a result, the compensation can be achieved quickly enough to have a negligible impact on protective relaying performance. The performance of the proposed ANN-based compensation module has been verified in real time using the data obtained through simulating various faults. The test data are obtained for different power system operating conditions and various CT characteristics. An overview of the test setup is shown in Fig. 14. Computer simulations are performed using EMTDC software and the obtained data are sent to the compensation module designed hardware through the computer parallel port and an interface circuit including a digital-to-analog converter. Prepared data received by the designed hardware are processed and corrected samples are generated by the module. The compensation module performance for different faults with different conditions was studied in real time and some of the test results are presented in Table III. The rms estimation

error, which is the difference between the estimated rms value and true rms value of the fault current signal, is presented in the last column of the table. The rms value of a fault current signal is calculated as

(3) where , and is the current signal value at the th sample. The percentage error is computed as follows: (4) and I refer to the measured rms value where I by the correction module and true rms value of the fault current signal, respectively. As shown in Table III, the proposed module performs quite accurately and reliably for a wide range of variations in fault conditions and CT parameters. For most of the cases, the rms estimation error is less than 2.5%. Therefore, the proposed module is able to accurately estimate the CT primary current from the CT saturated secondary current. It could be incorporated into the hardware of a digital protection relay. VI. CONCLUSION This paper proposes a novel algorithm for the correction of saturated CT secondary currents using an ANN-based scheme. Simulation and real-time studies are performed and the proposed ANN’s performance for different system parameters and conditions is investigated. Performance studies results indicate that the proposed algorithm has the following features. • The proposed scheme can successfully and accurately estimate true primary current from a saturated secondary output with and without the presence of remnant flux under realistic fault conditions. • A detailed model of the CT is not required, and characteristics of the CT are learned by the network during the training stage.


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H. Khorashadi-Zadeh received the B.Sc. degree in electrical engineering from Mashhad Ferdowsi University, Mashhad, Iran, in 1998, and the M.Sc. degree from the University of Tehran, Tehran, Iran, in 2000. Currently, he is a Lecturer/Instructor in the Department of Power Engineering, University of Birjand, Birjand, Iran. His areas of interest include high-voltage substation design, power system protection, digital relays, and applications of AI.

M. Sanaye-Pasand received the M.Sc. and Ph.D. degrees from the University of Calgary, Calgary, AB, Canada, in 1994 and 1998, respectively. Currently, he is an Associate Professor and Associate Head with the School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran. His areas of interest include power system analysis and control, digital protective relays, and applications of AI.