Digital protection schemesName: Deepak SoniREg. no. 11103365

Roll no. a13ABSTRACTFor a modern power system, selective high speed clearance of faults on high voltage transmission lines is critical and this term paper indicates the efficient and promising implementations for fault detection, classification and fault location in power transmission line protection. The work done in this area favor computerized relays, digital communication technologies and other technical developments, to avoid cascading failures and facilitate safer, secure and reliable power systems.[1]Efforts have been made to include almost all the techniques and philosophies of power system protection. The focus of this article is on the most recent techniques, like artificial neural network, fuzzy logic, fuzzy-neuro, fuzzy logic wavelet based and phasor measurement unit-based concepts as well as other conventional methods used in power system protection.[3]

INTRODUCTIONProtective relaying technology has evolved from single function electromechanical units to static units and now into the digital arena. The development of low cost microprocessor technology has made possible the digital relay where many relaying functions can be combined into a single unit.

In the past, the engineer applied many relays with proper planning; the digital relays can provide the level of redundancy that was available in the past and provide a better overall protective system. When applying single function electromechanical relay, the cost of each protective function needs to be justified versus the added protection the relay provides.

In many cases, typically on less critical generators, only minimal protection was applied in order to reduce costs. Today, with digital relays, these compromises do not need to be made. The multifunction relays provide a high level of protection at a very attractive cost. This allows the protection engineer to design a complete protection system with less concern about costs.[4],[6]

DIGITAL RELAYS

History of Protective RelayAround 1980s the digital relay entered the market. Compared to the Solid State Relay, the digital relay takes the advantages of the development of microprocessors and microcontrollers. Instead of using analog signals, the digital relay converts all measured analog quantities into digital signals.Digital protection relays is a revolution step in changing Relay technology.In Digital Relay Microprocessors and micro controllers are used in replacement of analogue circuits used in static relays to implement relay functions. Digital protection relays introduced in 1980.However, such technology will be completely superseded within the next five years by numerical relays.By the mid-1990s the solid state and electromechanical relay had been mostly replaced by digital relay in new construction. In distribution applications, the replacement by the digital relay proceeded a bit more slowly.While the great majority of feeder relays in new applications today are digital, the solid state relay still sees some use where simplicity of the application allows for simpler relays, and which allows one to avoid the complexity of digital relays.[3], [6]

Measuring principlesCompared to static relays, digital relays introduce Analogue to Digital Convertor (A/D conversion) of all measured analogue quantities and use a microprocessor to implement the protection algorithm. The microprocessor may use some kind of counting technique, or use the Discrete Fourier Transform (DFT) to implement the algorithm.The Microprocessors used in Digital Relay have limited processing capacity and memory compared to that provided in numerical relays. [3], [6]

Function of RelayThe functionality tends therefore to be limited and restricted largely to the protection function itself.Additional functionality compared to that provided by an electromechanical or static relay is usually available, typically taking the form of a wider range

of settings, and greater accuracy. A communications link to a remote computer may also be provided.The limited power of the microprocessors used in digital relays restricts the number of samples of the waveform that can be measured per cycle. This, in turn, limits the speed of operation of the relay in certain applications. Therefore, a digital relay for a particular protection function may have a longer operation time than the static relay equivalent.However, the extra time is not significant in terms of overall tripping time and possible effects of power system stability.[4],[2]

Operation of RelayDigital relay consists of:1. Analogue input subsystem,2. Digital input subsystem,3. Digital output subsystem,4. A processor along with RAM (data scratch pad),5. main memory (historical data file) and6. Power supply

Digital relaying involves digital processing of one or more analog signals in three steps:1. Conversion of analogue signal to digital form2. Processing of digital form3. Boolean decision to trip or not to trip.

Advantages of Digital Relay

1. Economical: The major reason for the acceptance of digital relays is that they present many features at reasonable price.2. Fast operation: There are two reasons for fast operation of digital relays. One, digital relays barely use any mechanical parts. Two, the use of high speed processors have made these relays very fast.3. Self monitoring: Digital relays monitor themselves continuously. On the other hand, electromechanical relays must be tested by personnel at regular intervals. Self monitoring feature saves time as well as money.4. Multiple functions: Relays, meters, control switches, indicators, and communication devices can be integrated into a single microprocessor-based

protective relay. Substation/system schematics and wiring diagrams are easy to generate due to the reduced number of devices and related wiring.5. Reduced commissioning time: Commissioning is a process of verifying the performance of an equipment before it is put into operation. Microprocessor based relays have metering features and remote capabilities, which makes commissioning, simple and less time consuming.6. Less outage time: Fast operation and fault location capability of microprocessor based relays for transmission line protection reduce the power outage time considerably. When relays, without a fault location capability, detect a fault, crew spends a lot of time in finding the location of the fault by patrolling the line.7. Flexibility: Digital relays can be designed and built using general purpose hardware. A relay can be used to protect different power system components by loading different software programs.8. Small size: Digital relays are lighter in weight and need less space than the electromechanical and solid-state relays. For this reason, digital relays are easy to transport.9. Easy replacement: Due to economical advantage, digital relays, if fail, can be replaced in full. This saves time and labor needed for repairs.[4],[2]

MICROPROCESSOR BASED RELAY DESIGNS

The function of the analog–digital converter is to convert the sampled values into digital form, usually an 8 or 16 bit word. The digital data are then passed along to the microprocessor in which algorithms act upon it to mathematically produce phasor representations of the measured quantities. Various algorithms then manipulate the phasor quantities to produce results required for making relaying decisions.Protection engineers need to identify the input quantities required by the specific type and model of numerical relay applied. Additional input quantities that might be needed include signals that indicate breaker position, that reset targets, that enable pilot logic, that indicate the status of pilot receivers, along with various other types of similar signals.Some microprocessor relays are designed as discreet replacements for electromechanical relays. Such designs often allow the relay to be directly inserted into the case that housed the electromechanical relay that is replaced.The number of protection and control functions available in numerical relays can vary from a few to

meet simple or specialized needs to a number suitable for providing complete protection for a line terminal or a generator. A simple design may include several over current elements. A design that is little more complex may add automatic reclosing functions along with the over current elements. As noted earlier, a more complex relay may include all functions required for protecting a specific power system facility along with logic to provide control for the facility.[7] [8] [9]

Programable logic controllerPLCs have been developed to replace electromechanical relays as logic elements. PLCs use a digital computer with a stored program, which emulates the interconnection of many relays to perform certain logical tasks. The programing for PLCs is keyed in as input and displayed as ‘‘ladder’’ diagrams.Such diagrams represent logic as it occurs in sequence in an elementary diagram form. The term ladder is used for these diagrams because they resemble a ladder and logic flows from rung to rung since each line in the ladder is scanned sequentially by the computer. A PLC has numerous input terminals through which are inputted logical states from a variety of elements such as sensors and switches. Logical states can have only two positions, which can be called ‘‘high’’ and ‘‘low,’’ ‘‘on’’ and ‘‘off,’’ or ‘‘1’’ and ‘‘0.’’ PLCs also have numerous output terminals that can be used to initiate other events such as to operate trip coils, energize solinoids, or light lamps. The PLC program dictates which output gets energized under which input conditions.While the program by itself appears as a ladder logic diagram, the related contacts and relay coils are imaginary and imbedded into the control software. PLC programs are entered and viewed by using a computer connected to the PLC’s programing port.PLCs have the ability to communicate with numerical relays and other digital devices..[7] [8] [9]

Applications of microprocessor-based relaysProtection personnel tend to be highly conservative with regard to the application of new technology. It is safer to adhere to what has been used in the past as the benefits derived from trying something new are slow to be recognized but problems encountered with new applications pose significant risks. Developing basic setting specifications for numerical relays is a tedious process that requires significant input data but, for the most part, is relatively straightforward. A basic understanding of Boolean expressions and methodologies is helpful in developing the required programing to obtain the

desired logic and for effectively using the full power that is designed into numerical relays. The capabilities and power that are built into microprocessor relay designs are continually expanding. In addition to providing an array of protective functions, capability to fulfill most of the control and data acquisition requirements at substations is provided. Many modern numerical relays possess the power to replace other digital devices that are required within substation control and data acquisition systems such as PLCs, RTUs, meters, and control switches. An obstacle to the practical use of the expanded power that is made available in microprocessor-based protective devices is the complexity of the programing that is required to use this power. [8] [9]

Attributes of microprocessor-based relaysThe vast majority of relays currently manufactured and purchased are microprocessor based. Some of the major beneficial characteristics of numerical relays that have propelled this movement include the following:1. More protection for less cost.2. Wiring simplification.3. Greater flexibility.4. Less maintenance requirements.5. Reduction in panel space—less devices required.6. Event recording capability.7. Ability to calculate and display distance to fault.8. Data acquisition for metering.9. Built-in logic for control and automation.10. Self-checking capability.11. Communication capability—ability to design enhanced protection schemes.12. Capability for remote interrogation and setting application.13. Ability to change settings automatically based on system conditions.Some disadvantages of using microprocessor-based relays that have been cited include the following:1. Single failure may disable many protective functions.2. Instruction manuals are complicated and difficult to understand.3. Excessive input data required for settings and logic.4. Frequent firmware upgrades—create tracking and documentation problems.5. Difficulty in matching input software with relays, especially when relays have been field modified.[10],[11]

DIGITAL DIFFERENTIAL PROTECTION OF POWER TRANSFORMER Differential protection difficultiesGenerally, three main difficulties handicap the conventional differential protection. They induce the differential relay to release a false trip signal without the existing of any fault.These complications must be overcome in order to make the differential relay working properly [2], [3]:1. Magnetizing inrush current during initial

energization,2. CTs Mismatch and saturation,3. Transformation ratio changes due to Tap changer.

Magnetizing inrush currentThis phenomenon, the transient magnetizing inrush or the exciting current, occurs in the primary side of the transformer whenever the transformer is switched on (energized) and the instantaneous value of the voltage is not at 90o. At this time, the first peak of the flux wave is higher than the peak of the flux at the steady state condition. This current appears as an internal fault, and it is sensed as a differential current by the differential relay. The value of the first peak of the magnetizing current may be as high as several times the peak of the full load current. The magnitude and duration of the magnetizing inrush current is influenced by many factors, some of these factors are [2], [6], [7];1)The instantaneous value of the voltage waveform at

the moment of closing CB.2)The value of the residual (remnant) magnetizing

flux.3)The sign of the residual magnetizing flux.4)The type of the iron laminations used in the

transformer core.5)The saturation flux density of the transformer core.6)The total impedance of the supply circuit.7)The physical size of the transformer.8)The maximum flux-carrying capability of the iron

core laminations.9)The input supply voltage level.

The effect of the inrush current on the differential relay is false tripping the transformer without of any existing type of faults. From the principle of operation of the differential relay, the relay compares the currents coming from both sides of the power transformer as explained above. However, the inrush current is flowing only in the primary side of the power transformer. So that, the differential current will have a significant value due to the existence of current in only one side. Therefore, the relay has to be designed to recognize that this current is a normal phenomenon and to not trip due to this current.

False trip due to C.T characteristicsThe performance of the differential relays depends on the accuracy of the CTs in reproducing their primary currents in their secondary side. In many cases, the primary ratings of the CTs, located in the high voltage and low voltage sides of the power transformer, does not exactly match the power transformer rated currents. Due to this discrepancy, a CTs mismatch takes place, which in turn creates a small false differential current, depending on the amount of this mismatch. Sometimes, this amount of the differential current is enough to operate the differential relay. Therefore, CTs ratio correction has to be done to overcome this CTs mismatch by using interposing CTs of multi taps [8].Another problem that may face the perfect operation of the CTs is the saturation problem. When saturation happens to one or all CTs at different levels, false differential current appears in the differential relay. This differential current could cause mal-operation of the differential relay. The dc component of the primary side current could produce the worst case of CT saturation. In which, the secondary current contains dc offset and extra harmonics [9], [10].

False trip due to tap changerOn-Load Tap-Changer (OLTC) is installed on the power transformer to control automatically the transformer output voltage. This device is required wherever there are heavy fluctuations in the power system voltage. The transformation ratio of the CTs can be matched with only one point of the tap-changing range. Therefore, if the OLTC is changed, unbalance current flows in the differential relay operating coil. This action causes CTs mismatches. This current will be considered as a fault current which makes the relay to release a trip signal [11], [12].

Digital differential protectionMany digital algorithms have been used so far after the invention of the computer. These algorithms do the same job with different accuracy and speed. The acceptable speed according to IEEE standard for transformer protection is 100 msec. All modern algorithms are faster than this IEEE standard. Nowadays, there are some algorithms performs their function in less than 10 msec. In this chapter, a fast algorithm is introduced. Its speed is in the range of 1 to 15 msec. This algorithm is based on the Fast Fourier algorithm (FFT). This algorithm is not new, however, significant changes has been introduced to make it much faster.The proposed digital differential relay is designed using a simulation technique in Matlab Simulink environment. The design is implemented to protect

the power transformer against internal faults and prevent interruption due to inrush currents.This algorithm is built on the principle of harmonic current restraint, where the magnetizing-inrush current is characterized by large harmonic components content that are not noticeably present in fault currents. Due to the saturated condition of the transformer iron, the waveform of the inrush current is highly distorted. The amplitude of the harmonics, compared with the fundamental is somewhere between 30% to 60% and the third harmonic 10% to 30%. The other harmonics are progressively less [3][6], [13]. Fast Fourier Transform (FFT) is used to implement this approach.In general, any periodic signal f(t) can be decomposed to its sine and cosine components as follows:

Where: a0 is the DC component of the f (t), and Ck, Sk

are the cosine and sine coefficients of the frequencies present in f(t), respectively. The discrete forms of the coefficients Ck, Sk are expressed in the following equations:

The Fourier harmonic coefficients can be expressed as [13]:

Where: Fkis the Kth harmonic coefficient for k = 1, 2,...,N and x(n) is the signal f(t) in its discrete form. The FFT produces exactly the same results as the DFT; however, the FFT is much faster than DFT, where the speed of calculation is the main factor in this process [13-16].Fig 1 illustrates the flow chart of the designed digital Fourier Transform based logic technique algorithm. In this algorithm the output currents of the CTs undergo over two analysis processes, amplitude comparison process and harmonic content calculation process. The amplitude comparison between the RMS values of the CTs output current ( |Id1 – Id2| ) is in the left hand side of the flowchart, and the harmonic calculation is in the right hand side of the flowchart.The software is implemented according to the following steps [13-16]:Step 1. Reading data from the CTs.Step 2. Data calculation, which is given as follows;For the amplitude calculation, if the absolute difference ( |Id1 – Id2| ) between the CTs output currents is greater than zero the logic (1) takes place, which indicates the case of an inrush current or an internal fault. Otherwise, the logic (0) takes place, which indicates a detection of an external fault.

Fig. 1 Flow chart of the proposed Digital Differential Relay Scheme

In the meantime, the harmonic calculation is performed. If the percentage value of the second harmonic amplitude is in the range of (0.3 to 0.6) of the fundamental component amplitude, then the logic (0) occurs, that means recognition of inrush current. Otherwise, the logic (1) takes place, which indicates a detection of an internal or external fault.

Step 3. Taking the final decision: If the logic cases received from both cases (a & b) in step two are both (1), that indicates a detection of an internal fault. Then a trip signal is released to stop the simulation.For the other logic options of (0,1) means an external fault, (1,0) means an inrush current, or (0,0) indicate an occurrence of an inrush current or an external fault, and the simulation goes back to step two to start the calculation again for the next sample.

PROTECTION SCHEME FOR TRANSMISSION LINE BASED ON CORRELATION COEFFICIENTSThe fault selection algorithm is based on the auto-correlation technique of two half successive cycles with the same polarity. For transmission lines protection, this method needs only three line-current measurements available at the relay location (ia, ib, ic).

A. Correlation Coefficients CalculationThe auto-correlation coefficient is estimated as follows for any two dependant variables, y1(x) and y2(x) [15]. The auto-correlation coefficient (r) calculated as follows:

Where, Ns = the number of samples per cycle used in the simulationr: empirical correlation coefficient of y1 (x), and y2(x).y1 (x): is the initial instantaneous value of the current at time t0.y2 (x): is the instantaneous value of the current at next cycle.Y1,Y2: arithmetic means of y1 (x) and y2 (x), respectively.

The strength of linear association between two variables is quantified by the correlation coefficient (r), its value lies between - 1 and +1 [15].

B. Fault Detection and Faulty Phase SelectionTo implement our technique, three tasks are starting in parallel: fault detection, fault confirmation, and faulty phase selection as follows:(1) Fault Detection (Initiation)A transition is detected if: ∆I > 20% In, where In is the line nominal current.(2) Faulty Phase SelectionFault confirmation and faulty phase selection are done according to the following sequences.

Three-phase current correlation coefficients values are calculated. If fault is detected, phase current correlation values are sorted in ascending order and compared.- If fault is detected, phase current correlation values are sorted into ascending order and compared. The possible fault cases are:(a) If the three-phase correlation coefficients are nearly equal and their values are less than 0.7, then the fault is three-phase fault- If ra = rb = rc < 0.7, the fault is three-phase (a-b-c fault)

(b) If the two-phase correlation coefficients are equal and their values are nearly 1, while the third phase correlation coefficient is less than 0.7, the fault is single-phase to groundfault.- If ra < 0.7, rb = 1, rc = 1, the fault is single phaseto-ground fault (a-g fault)- If rb < 0.7, ra = 1, rc = 1, the fault is single phaseto-ground fault (b-g fault)- If rc < 0.7, ra = 1, rb = 1, the fault is single phaseto-ground fault (c-g fault)(c) If the two-phase correlation coefficients are equal and their values are less than 0.7, while the third phase correlation coefficient is nearly 1, the fault is double phase-to-ground fault.- If ra = rb < 0.7, rc = 1 the fault is double phase-to-ground fault (a-b-g fault)- If rb = rc < 0.7, ra = 1 the fault is double phase-to-ground fault (b-c-g fault)- If ra = rc < 0.7, rb = 1 the fault is double phase-to-ground fault (a-c-g fault)(d) If the three-phase correlation coefficients are not equal and their values: one phase is less than 0.3, second phase is less than 0.7, while the third phase alienation coefficient is nearly 1, the fault is phase-to-phase fault.- If ra < 0.7, rb < 0.7, rc = 1 the fault is phase-to- phase fault (a-b fault)- If rb < 0.7, rc < 0.7, ra = 1 the fault is phase-to-phase fault (b-c fault)- If ra < 0.7, rc < 0.7, rb = 1 the fault is phase-to-phase fault (a-c fault)- To make sure of distinguishing between double phase and double phase-to-ground faults, the cross correlation between the two phase currents of the faulted phases is calculated.If the value of cross-correlation is nearly -1, the fault is double phase fault.- If rab = -1 the fault is phase-to-phase (a-b fault) otherwise the fault is double phase-toground (a-b-g fault).

- If rbc = -1 the fault is phase-to-phase (b-c fault) otherwise the fault is double phase-toground (b-c-g fault).- If rac = -1 the fault is phase-to-phase (a-c fault) otherwise the fault is double phase-toground (a-c-g fault).

DEVELOPMENT IN FUTURE AND OTHER APPROACHES

WAVELET BASED DIGITAL SCHEMES FORPOWER SYSTEM PROTECTIONAny intentional or unintentional change in an electrical network is accompanied by transients, which is a natural process by which the power system moves from one steady state condition to another. The duration of these transients can vary from a few microseconds to milliseconds and can be broadly classified into those having an impulsive or an oscillatory nature. Faults in power system typically cause low frequency oscillatory type of transients, the spectral content of which is less than 5 kHz, before settling into the post fault steady state condition. Since the transient information is not obvious in the time domain representation of signals obtained from the Current Transformers (CT) and Potential Transformers (PT), some mathematical transformation has to be applied to extract the required information. The required information is the frequency spectrum of the signal during transients and its time localization.The voltage and current signals obtained from the power system are analog signals. In order to do further processing of these signals by digital techniques, they have to be converted into digital signals. Hence, a signal processing unit is the first stage of any digital/numerical relay. The proposed scheme depends on extracting embedded information from the transients generated during faults and disturbances. For 50 and 60 Hz systems, the frequency band of 0 to 1000 Hz is found to be more informative. The transducers here are the CT and PT, with their burdens, which also provide the necessary isolation.A second order Butterworth low pass filter with a cut-off frequency of 800 Hz is used for anti-aliasing. The frequency band of interest for this work is 500 to 1000 Hz. Hence, the sample and hold unit has a sampling frequency of 2 kHz, which is twice the highest frequency of interest. The multiplexer is an array of analog switches controlled by digital logic.

Analog to Digital Converter (ADC) of 16 bit output is assumed.[12],[13,[16]

Busbar ProtectionThe disturbances are detected if the disturbance signal is high for any one voltage signal. A directional signal based on high frequency power details is found for each phase of every connected branch. A trip signal is issued for a phase, if the directional signals for all the branches of that phase are same. The overall block diagram of the proposed algorithm for a busbar with N branches is given in Fig.2 [12],[13,[16]

Fig 2. Block diagram of proposed scheme for busbar protection

Transformer ProtectionAs in the case of busbar protection, here also, the disturbance detection for each phase is achieved. A detect signal is issued if a disturbance is indicated in any of the six voltage signals (3_ HV and LV). Six power signals corresponding to three phases of two windings are derived as per. In order to make the protection scheme independent of the transformer configuration, the directional signal is derived from the total 3_ instantaneous power on HV and LV side. The direction signals for HV and LV sides is the cumulative sum of these total power signals. If the directions of two signals are same, an internal fault is indicated and trip is issued. Fig. 3 shows the functional block diagram of the proposed scheme.[12],[13,[16]

Fig 3 .Block diagram of proposed scheme for transformer protection

ARTIFICIAL NEURAL NETWORK APPROACH

Enabling the introduction of new relaying concepts capable to design smarter, faster, and more reliable digital relays.

Examples of new concepts: integrated protection schemes, adaptive protection & predictive protection.[14],[15,[16]

FUZZY LOGIC APPROACH

In fuzzy logic based protection system, accuracy cannot be guaranteed for wide variations in system conditions. So consequently a more dependable and secure relaying algorithm during real time implementation is needed for classifying the faults under a variety of time-varying network configurations. The fuzzy-neuro approaches are sensitive to system frequency changes and require large training sets and a large number of neurons

affecting their accuracy and speed in protecting large power networks. [12],[13,[16]

CONCLUSIONThis termpaper has described the development concepts behind new series of digital relays and some example applications.This new series of digital relays is the realization of a number of development concepts, including a compact design contributing to reduction of wiring, more precise analog data processing,

higher reliability, better operational characteristics, and a configuration that uses replaceable units.High demands are imposed on power transformer protective relays. Requirements include dependability (no missing operations), security (no false tripping), and speed of operation (short fault clearing time). The operating conditions of power transformers do not make the relaying task easy. Protection of large power transformers is one of the most challenging problems in the power system relaying area. Advanced digital signal processing techniques and artificial intelligence (Al) approaches to power system protection provide the means to enhance the classical protection principles and facilitate faster, more secure, and dependable protection for power transformers. Also, it is anticipated that, in the near future, more measurements will be available to transformer relays, owing to both substation integration and novel sensors installed on power transformers. All of this will change the practice for power transformer protection. This article briefly reviews the state of the art, but is primarily devoted to discussion of new approaches and future directions in digital relaying for power transformers.

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[7]. A.Guzman, S. Zocholl, and H. Alturve “performance analysis of traditional and improved transformer differential protectiverelays”, SEL Paper, 2000.[8]. Walter A. Elmore. “Protective Relaying Theory and Applications”, Marcel Diker, second edition 2003.[9]. Rahman, M.A. and B. Jeyasurya, 1988, A State-of-the-art Review of Transformer Protection Algorithms. IEEE Transactionson Power Delivery, 3(2): 534-544.[10]. A. G. Phadke and J. S. Thorp, “Computer relaying for power system”, Researches studies Press, England, 1988.[11]. T.J. Ross, a book on “Fuzzy logic with Engineering applications”, University of New Mexico, USA, 1995.[12]. K. Yabe, “Power differential method for discrimination between fault and magnetizing inrush current in transformers”, IEEETransactions on Power Delivery. 12 (3), 1109– 1118, 1997.[13] M. A. Rahman, Y.V.V.S. Murthy and Ivi Hermanto, "Digital Protective Relay for PowerTransformers", U.S. Patent No. 5,172,329, December 1992.[14] P.K. Dash and M.A. Rahman, "A New Algorithm for Digital Protection of PowerTransformer", Canadian Electrical Association Transactions, Vol. 26, Part 4, 1987, pp. 1-8, (87-SP-169), 1987.[15] A. Gangopadhay, M.A. Rahman, B. Jeyasurya, "Simulation of Magnetizing InrushCurrents in Single Phase Transformers", International Journal of Energy Systems, Vol. 7,No. 1, 1987, pp. 34-38.[16] M.A. Rahman and A. Gangopadhay, "Digital Simulation of Magnetizing InrushesCurrents in Three-Phase Transformers", IEEE Transactions on Power Delivery, Vol.PWRD-1, No. 4, October 1986, pp. 235-242. (Over 100 citations)