SUGGESTIONS FOR THE POSSIBILITY OF DETERMINING

THE


Introduction
Problem Statement.The attacks on the state's critical (energy) infrastructure during the large-scale armed aggression of the Russian Federation against Ukraine have shown that the provision of electricity to all spheres of life and work is a very important component of the proper and comprehensive functioning of the state as a whole.First of all, this relates to the power supply systems (PSS) of military units and divisions within the Armed Forces of Ukraine, where a lack of power supply can lead to the failure of a combat mission.
The experiences gained from the armed aggression of the Russian Federation have highlighted that the utilization of various weapons and military equipment, and particularly aviation of the Armed Forces of Ukraine, to ensure the conduct of combat operations is an indispensable component of the successful execution of combat missions.
Considering that the main component of the military airfields' PSS is transformer substations, and many of them are outdated (having operated for more than (30-40) years)), their failure can be unforeseen, and during armed aggression, it can be heightened.
Therefore, the challenge of enhancing the methods and techniques that ensure the functionality of power transformers within the PSS, both at military airfields and other units of the Armed Forces of Ukraine, is a highly relevant task.
Analysis of Recent Research and Publications.In order to ensure the long-term and reliable functioning of power transformers, prevent accidents in power systems, and ensure the successful fulfilment of combat missions, it is imperative to conduct timely diagnostics of potential defects arising both during regular operation and as a consequence of enemy weapons or sabotage and reconnaissance activities.
The determination of the technical condition of transformers is given attention in the studies [1-7; 11; 17; 18].The main ones are considered to be [1; 5-7; 17; 18], but the application of the methods considered there does not provide a comprehensive evaluation of the actual technical condition of transformers that have reached the end of their warranty resource and it fails to provide insights for predicting potential accidents and defects.
One of the effective approaches to extend the service life of power transformers that have fully utilized their warranty resource is to establish opportunities for continuous monitoring of changes in the main parameters of the transformer during its operation and to implement protective measures in response to unfavourable measurement results.Clearly, for transformers in active use, deploying a monitoring system is based on the fact that in the context of armed aggression it is extremely necessary to enhance the service life of power transformers in operation.
Considering the overall state of power transformers, it is necessary to extend their service life to the economically viable level.It is also imperative to urgently reduce operating costs associated with scheduled repairs of existing transformers.A substantial cost reduction can be achieved by transitioning from the normatively established repair periods for power transformers to a system based on their actual condition.The primary mechanism for implementing such a paradigm shift is a monitoring system that facilitates tracking the condition of the transformer by comparing the previous values of the measured indicators with the subsequent ones during the period of scheduled maintenance.
If the transformer is regularly monitored, its aging can be managed (controlled), and thereby its service life can be extended.The prolonged service life, coupled with the associated improvement in reliability, contributes to a reduction in operating costs.
The purpose of the article is to provide suggestions for the possibility of determining the actual technical condition of power transformers by comparing the results of the transformer's control indicators with the nameplate data and the results of control measurements.

The Main Body
To achieve the stated purpose, namely, the ability to determine the actual technical condition of power transformers, it is suggested using the following algorithm: analysis of operating modes, accident rate, nature of defects, and the underlying reasons that trigger the accumulation of parameter deviations over an extended period of operation; mathematical description of emergency processes that occur during the operation of a power transformer within a power supply system [1; 2]; minimization of the impact of deviations accumulating in the core structure and windings, particularly when exceeding the stipulated terms of the warranted resource; inspection of the transformer and collection of technical information (year of manufacture, previous maintenance data, operating characteristics, and repair history).
Upon identifying a transformer that requires additional research, it is first of all suggested performing: calculations of control indicators; control measurements on an operating transformer in both load and no-load (NL) modes, including its infrared imaging inspection; control measurements on a transformer that is turned off; analysis of the degree of deviation between parameters obtained from the nameplate data and those obtained experimentally; development of two virtual models of the transformer based on the nameplate data and the data obtained experimentally; selection of the available mode of operation of the real transformer and simulation of the same on the virtual model.Based on the analysis of the differences between the real and virtual parameters, to make a prediction about the actual state of the transformer; sampling of oil from the tank and subsequent physical and chemical analysis; preparation of a technical report, which outlines the results of the inspection, analysis of the findings, conclusions regarding the condition of the transformer and recommendations for its operation, and, if necessary, details on the scope and methodology of (scheduled) repair work.
The transition to a system for monitoring the technical condition of power transformers will be successful if it is possible to ensure that previous information is stored for future comparisons.This will make it possible to draw predictable conclusions about the development of specific deviations related to the service life and take preventive measures to eliminate emergencies associated with equipment aging.
Thus, according to the suggested work algorithm, first, we learn about transformer malfunctions by the deviation of the parameters under study, such as: short circuit (SC) losses (indicator  U )indicative of the disorder of the magnetic circuit and coils relative positioning, along with magnetic circuit malfunctions; inductive NL mode resistance ( NL X )indicative of the disruption of the mutual positioning of the magnetic circuit and coils, as well as inter-turn short circuit; equivalent active NL mode resistance ( NL R )associated with the deterioration of core steel quality, "core burnout", and insulation failure of the charge plates.
In accordance with the proposed algorithm, the subsequent step involves minimizing the impact of the deviations accumulation in the core structure and windings in cases of exceeding the terms of the warranted service life.Let us analyze this issue in greater detail.
During the operation of a power transformer, its insulation undergoes wear and tear.The service life of transformer insulation is primarily dictated by the heating temperature of its windings, which depends on the load and cooling conditions.As the windings' heating temperature fluctuates from the limit value to a lower one, the windings' insulation wear diminishes, and the transformer's service life increases accordingly.Under rated cooling temperature conditions and load, the service life of a transformer is about 20-25 years.However, power transformers in operation often surpass their designated service life significantly.
While power transformers incur damage less frequently than power lines, a failure in a transformer results in severe consequences, demanding an extended duration to restore its performance.
In certain instances, an emergency situation arises not due to a malfunction of a specific system element, but by a coincidental alignment of time, location, and the combination of certain variable quantity values.
For example, the moment when a power transformer is turned off concerning the voltage sinusoid is completely random, but the amount of residual magnetization of the core depends on it.Subsequently, the situation can develop in different ways, based on when the transformer is switched on, as well as in what combination with the load it occurs.Under specific circumstances, transformer protection is triggered by the SC current, leading to abnormally long transients [6; 9].This sets off further deviations, etc.As a result, we get a situation where individual elements are in good condition, yet there is a total emergency outage.
The frequency of such outages during the period of operation depends on many random factors, including the consequences of attacks by the Russian Federation, and cannot be predicted.However, each such tripping pushes the transformer core into supersaturation, leaving a lasting "trace" in the domain structure of the material.
Similar phenomena occur during short circuits [10].The magnitude of the SC shock current depends both on the nature of the transformer load and on the moment of occurrence of the short circuit in relation to the voltage sinusoid.In this case, irreversible changes occur in the transformer windings.
The problem is that the design of the windings and cores, was chosen based on a specific warranted service life, namely, 25 years.Anything occurring beyond that period was excluded from the research.Notably, instances exist where the same transformer modification within the same military unit has been in service for (40-60) years, while a transformer serving residential and administrative areas rarely exceeds 30 years.In such cases, normal emergencies are discussed, but they manifest as integral accumulations that impact the quality of transformer components.Emergencies may share similarities, but they are never repetitive.
In particular, parameters such as: the magnitude of the SC current; the magnitude of the SC shock current present before the incident; load before the accident (whether large or small); the nature of the load (active, active-inductive) observed when an unloaded transformer is switched on; the moment of switching on the transformer concerning the input voltage sinusoid, as well as its previous outage history.
Secondly, the transformer undergoes inspection and technical information collection, including: determining the year of manufacture and the manufacturer of the transformer; analysing information about the maintenance and repairs, the amount of oil, the date of its replacement, samples for analysis and their results; determining the operability of the voltage regulating elements; infrared spectrum inspection of the transformer (using a thermal imager) at different times of the day (preferably at different loads), to identify the presence or absence of local overheating centres and establish the nature of the oil heat exchange in the transformer.
Also, based on the data of the operational switching log, for a certain period, it is found out: the dominant level of the supply voltage (an overestimated level leads to over-excitation of the transformer, overloading of the magnetic system with all the accompanying consequences: heating of the magnetic circuitworsens the structure of the magnetic circuit material and systematically increases magnetization losses, increased vibration of the platesmechanically damages the insulation, loosening of the yoke tie, local damage to the insulation between the plates and the magnetic circuit mounting hardware); the presence of emergency shutdowns, what factors provoked them, and the course of events related to them; the number of times the automatic resetting system has been activated, the value of SC currents, the nature and duration of the SC and the resulting consequences; transformer loading rate (the number of hours of maximum load usage per year); the nature of the dominant loadlinear (motors, lighting, heating elements), nonlinear (rectifiers, converters, digital and computer equipment), active, inductive, active-inductive, capacitive (typical for air-fields), which makes it possible to create an objective model of transformer operation; dynamic characteristics of the power supply system in which the transformer is operatedthe nature of load changes (seasonal, monthly, daily), voltage deviation range, voltage fluctuation range, and the presence of higher harmonics.
Based on the analysis of the operating conditions and the results of previous maintenance and repairs, a prognosis is made about the anticipated state of the transformer.Measures are taken to provide the necessary electrical measuring devices and to have the transformer oil analyzed.The causes and consequences of the recorded emergency outages and the nature of the planned outages are investigated.
The first step after identifying a transformer that requires additional research is to calculate its control parameters using nameplate data.Creating a virtual model of a transformer allows us to solve the following tasks, namely, based on the nameplate data, we create a model of a specific transformer and investigate how it should operate in different modes and experimentally determine real static indicators on the same transformer.
We input them into the model and get the necessary dynamic indicators.As a result, we have two models, one of how the transformer operated when it left the factory and the other of how it actually functions.Based on the differences, decisions are made regarding extending the service life or imposing specific restrictions.
To perform calculations of the control parameters of a power transformer, the nameplate data is utilized, namely the following static indicators (these are indicators that do not depend on time, within a small time scale of up to several seconds): Using these indicators, it is possible to determine various aspects that correspond to a technically correct transformer and also to find them empirically.By making a comparison at this stage, it is possible to make a certain prognosis about the expected discrepancies in the condition of the transformer elements.
The next step is to create a virtual model of the transformer, based on the nameplate data, which corresponds to a technically correct transformer.To create a virtual model, it is necessary to select its replacement scheme.In most cases, the L-shaped transformer replacement scheme is commonly used, but it may not be adequately for modeling various processes of its operation.In particular, it does not take into account the coupling factor between the primary and secondary wind-ings in the NL and SC modes, and it does not account for additional losses in the primary winding copper and steel in the SC mode [1].
As a result, when modeling not just one mode, but the entire linkturning on the transformer with or without load, changing the load, changing the load nature, an emergency situations accumulate, the result loses its reliability.Therefore, the SimPower System employs a T-shaped substitution system [1].
The construction of the model is demonstrated using the example of a typical serial transformer TM-25/10, with its nameplate data provided in Table 1.

Table 1
Nameplate data of the power transformer The basic expressions used for the calculation are outlined below.
Since it is widely accepted that in a three-phase transformer, the power of the phases is equal, and their parameters are identical, calculations are performed for one of the phases.For this purpose, we refer to the nameplate data for the phase.
Rated power output: Rated voltage of the primary winding: Rated voltage of the secondary winding: Rated current of the primary winding: SC voltage: Full resistance of the SC mode: 1 Active resistance of the SC mode: Reactive resistance of the SC mode: Active resistance of the primary winding: The inductive dissipation resistance of the primary winding for a T-shaped substitution scheme: The SimPowerSystem utilizes inductance data, and consequently, the primary winding's dissipation inductance is represented as where Current in the NL mode in the primary winding: Total NL resistance: Active NL resistance: Inductive NL resistance: Active losses in the core without taking into account NL mode losses on the primary winding copper: Inductive resistance of the magnetization circuit without taking into account the inductive dissipation resistance of the primary winding: To implement the T-shaped substitution scheme, it is necessary to find the equivalent parameters of the parallel magnetization circuit instead of the parameters of the series magnetization circuit.According to [1; 2], the following expressions are used: Inductance of the magnetizing circuit Inductance of the primary winding Resistance reflecting equivalent losses in transformer steel Thus, the parameters for modeling a power transformer in the SimPowerSystem environment have been obtained.In our case, for the TM-25/10 transformer, the parameters obtained for modeling are presented in Table 2.The obtained static parameters allow to develop a model of the transformer with the properties it had when it was initially released from the factory.In general, the model enables determining the dynamic parameters that the transformer had at the beginning of operation and which are not provided in the nameplate data.These dynamic parameters include the duration of the transient period during the transformer's no-load switching, at different points in time, the maximum current inrush, and the switching angle corresponding to it.When operating with a load, these include shock currents in the event of a short circuit, the duration of transients during load fluctuations.For three-phase transformers, additional considerations include transient current in the neutral conductor during load switching, shock currents in various types of short circuits, etc.
To obtain objective indicators that characterize the actual state of the transformer, it is necessary to carry out control measurements on the power transformer, encompassing procedures such as: thermal imaging control; determination of the transformation factor; determination of transformer NL mode parameters; determination of transformer winding parameters; conducting a transformer test SC mode; determination of transformer insulation parameters; determination of the transformer dielectric loss angle; inspection of transformer switchgear; checking the transformer tightness; determining the possibility of parallel operation of transformers.
Here is a refined description of these procedures.The first step involves using thermal imaging to identify areas with impaired oil circulation, "stagnant" zones, and checking for air cushions in the upper part of the tank due to incorrect installation of the transformer (no inclination of 4 %).Abnormally heated by circulating currents, the tank connectors and bolted connections of the current lines are identified.The oil level and the performance of the oil dipstick are determined.
This procedure makes it possible to detect abnormally heated elements, which indicates certain deviations from the norm.Areas of excessive temperature on the lead-in pins indicate a malfunction of the connection contacts, uneven heating of the tank indicates areas of heating of the magnetic circuit due to Foucault currents, or excessive magnetization losses indicate a malfunction of the magnetic circuit properties (aging).An irregular temperature distribution across the tank may indicate an insufficient amount of oil.
Next, the transformation factor is monitored, and the measurement results are compared with the datasheet and the model.According to [12], the permissible deviations are up to 2 %.This accuracy may not be sufficient to detect the number of turns; according to the international standard [15], a deviation of ±0.5 % is allowed for a serviceable transformer.
To determine the transformation factor, the two voltmeter method, the compensation method, and the reference transformer (differential) methods are used [5].
The next step involves measuring the values of the transformer's NL mode current and determine the losses in iron.A deviation of these parameters of more than 5 % in one of the phases indicates the need to loosen the upper yoke of the magnetic circuit.At the same time, a uniform increase in losses in each phase indicates a decrease in iron quality due to aging and can be assessed as a fault-free transformer.In terms of NL mode current, a transformer is deemed defective if the differences in currents across phases exceed 10 %.An effective diagnostic characteristic of the transformer windings is the losses from magnetic core dissipation currents.They increase significantly due to deformation of windings or element damage.
Consequently, power losses in a transformer are primarily determined by hysteresis and eddy current losses: During operation, power losses due to thermal shock can increase due to SC of the magnetic circuit steel sheets and insulation failure of the tie rods.A reduction in pressing density of steel sheets, increased gaps in the rods, etc. can also lead to an increase in the magnetic circuit current.
The measurement results are considered satisfactory if they differ from the nameplate data: no more than +15 % for the NL mode power loss; no more than +30 % for the NL mode current.The next procedure involves measuring the resistance of the transformer windings for DC and AC, obtaining the parameters ph Z and ph R , comparing the obtained values with the calculated ones and entering them into the virtual model.If there are facts indicating an unsatisfactory condition of the magnetic circuit, it is necessary to proceed to more accurate measurements, namely, to measure the DC power losses of the primary and secondary windings and the AC power losses.The difference in DC and AC power losses provides more accurate data on the condition of the magnetic circuit.
This procedure detects contact deterioration at lead-to-terminal connections and live control contacts.It also reveals open or shorted parallel conductors and the presence of intermittent contacts.Such occurrences result in a resistance increase by several percent.Overheating or erosion of the contacts causes an increase in the transient resistance by several times.To restore normal operation, it is necessary to replace the contacts.
Measurement results are considered satisfactory if the phase resistance values of the same winding differ from each other by no more than 2 %.The next step is to investigate the SC, which is the limit mode of operation of the transformer, which allows determining the parameters of the transformer at any load.During the SC test, the secondary winding of the transformer is short-circuited, and the primary winding is supplied with a reduced voltage SC U , at which the rated currents flow in the windings.This voltage is called the SC voltage and is measured as a percentage of the rated voltage: In our case (military power supply systems), we typically have 6, 10 or 35 kV on the primary winding.Therefore, we apply the voltage on the low side and use current clamps to monitor the currents.According to [13], the SC voltage is (%) (5,5 10,5) Next, to detect the deterioration of individual insulation elements in a timely manner, a series of measurements is conducted, and the results of which are used to make their final assessment.
The measurements are performed using a 2500 V megohmmeter with an upper measurement limit of at least 10 GΩ [16 ; 18].The readings are recorded 15 s and 60 s after the voltage is applied to the tested insulation.
If the insulation resistance falls below the norms or its value has decreased by more than 30 % compared to the factory data, indicating suspicion of moisture in the transformer insulation, the absorption coefficient is determined abs R : where 15 Rinsulation resistance value obtained in 15 seconds after the voltage is applied, 60 Rinsulation resistance value obtained in 60 seconds.The values of the absorption coefficient for a transformers at a temperature of (10-30) C should be at least 1,3.
For transformers with moisture or insulation defects, this factor is closer to 1.0.In this case, it is necessary to conduct an additional test by capacitive methods and measure dielectric losses ( tg ).
The measurement of tg is performed in the same sequence and according to the same schemes as when measuring insulation resistance [16; 17].
The voltage of transformers is primarily regulated during operation by changing the number of winding turns.For this purpose, the windings have branches connected to special switching devices designed to alter the transformation factor.
Depending on the type and purpose of power transformers, they can be equipped with a branch switching device with disconnection of the transformer from the mains (no-excitation switch (NES)) or a winding branch switching device on-load tap-changer (OLTC).
NES transformers typically have five branches to obtain four voltage levels relative to the nominal +5; +2.5; -2.5 and -5.OLTC transformers with on-load tapchangers have more branches and a wider range of regulation.
The results of checking the sequence of switching on the contacts in combination with the measured DC resistances and transformation ratios allow us to draw a final conclusion about the suitability of the transformer for further operation.
To verify the leaktight integrity of the transformer, a pipe with a funnel is installed in the plug of the expander or cover.The pipe in the cover opening is sealed and filled with oil.The height of the oil level in the funnel above the cover for transformers with a tubular radiator and smooth tanks should be 1.5 m, and with wavy and radiator tanks -0.9 m.The height above the top point of the expander is 0.6 m and 0.3 m, respectively.Beforehand, the internal pipe of the air dryer is sealed with a plug.The set oil level must remain unchanged for 3 hours.If during this time there are no oil seeps or outflows, the tank is considered to have passed the test, otherwise the tank must undergo repair.
Next, the possibility of parallel operation of transformers is considered.
The main challenge that arises when transformers are operated in parallel is ensuring that the load is distributed evenly between them.When transformers of the same power and design are switched on in parallel, the load is distributed evenly between them automatically due to the symmetry of all parallel circuits.However, in practice, it appears that it is often necessary to connect transformers of different power and design in parallel.In this case, achieving an even distribution of loads between the transformers operating in parallel is often impossible.When transformers are switched on in parallel, their secondary windings form a closed circuit in which no unbalanced voltages should occur, i.e. the sum of the electromotive forces of the secondary windings should be zero.
For normal operation of parallel transformers, the following conditions must be fulfilled [8; 19]: the connection groups are the same, and the ratio between capacities is no more than 1:3; transformation ratios are equal or differ by no more than ±0.5 %; -SC voltages differ by no more than ±10 % of the arithmetic mean of the SC voltage of the transformers to be connected for parallel operation.Before switching on transformers, their phasing is performed.
Based on the results obtained from the nameplate data and the results of control measurements with the use of the MATLAB application program, we create two virtual models that will allow us to analyze the differences in parameters of real and virtual models by simulating the operation of the power transformer, thereby drawing a conclusion about the actual technical condition of the power transformer that has used its warranty resource.
The virtual model includes a power source, a transformer, a consumer, and auxiliary elements.The transformer's nameplate parameters and current load values are recorded.At a selected time, the readings of the substation's instruments are recorded and subsequently compared with the values obtained from the model.The magnitude of the discrepancy between them is used to judge the condition of the transformer.
Therefore, the transformer for the study is determined, its nameplate data is taken and, in accordance with the calculation of the control indicators, the parameters are found from the nameplate data (Table 2), which are then entered into the block of Fig. 1.The power source is a power supply unit (Fig. 2).The line voltage, number of phases, and internal resistance of the source are entered in the corresponding windows.
Fig. 3 shows a blocka three-phase key that simulates a 10 kV oil circuit breaker and allows introducing delays in the operation of phases to simulate their nonsimultaneous operation.
A load block is used to study the operation of the transformer in different modes (Fig. 4).It allows changing both the size of the load and its nature (active, ac-tive-inductive, active-inductive-capacitive).The transients caused by the switching on the oil circuit breaker are shown in Fig. 5.
In general, the model is shown in Fig. 6 and works as follows.From a 10 kW source, a signal is transmitted through high-voltage current and voltage meters to convert the instantaneous linear values of current and voltage into effective values, it then goes through a product multiplier by the signalms unit, resulting in 4 values of the full power entering the 3010 3 VA transformer on the display 3.   The values of the control parameters which are displayed correspond to the scenario when the load is 20 kW of active power and 7.4 kVAR of reactive power.In fact, to fully simulate the processes which take place in the power supply system, it is necessary to record the real values of load, input and output voltage, active and reactive power, and current from the devices at the substation and compare them with the corresponding value on the model.
The alignment of the control indicators on the model with the values taken at the substation implies that the transformer is in a satisfactory condition, its actual data deviates little from the previous nameplate data, and therefore it is safe to continue its operation.To increase the reliability of the results, it is recommendable to choose a different time so that the load changes slightly and compare the indicators again.If the readings are the same again, it is safe to say that the transformer is in good condition.If discrepancies are evident, for example, in the NL mode current, it is advisable to adjust the parameters of the magnetization circuit link of the substitution circuit in such a way as to bring the model readings and the data of the substation instruments closer to each other to match.After that, based on the magnitude of the discrepancy between the nameplate data and the actual data, a conclusion can be drawn about the further use of the transformer.
For further study of the transformer, a transformer SC study is carried out on a real transformer and a vir-tual model of the said study is made in accordance with the model shown in Fig. 7.The parameters obtained from the model and the real transformer are compared.If the previous stage was focused on the magnetic system of the transformer, this stage assesses the quality of the transformer windings.
If discrepancies are identified, the parameters of the transformer replacement circuit are adjusted to fully correspond to the actual values.Based on the magnitude of the discrepancies and the previously obtained benchmarks, a conclusion is made about the condition of the windings.The parameters obtained from the model and those from the actual transformer are compared.If the previous stage focused more on the magnetic system of the transformer, then at this stage the qualitative condition of the transformer windings is assessed.
If any discrepancies arise, the parameters of the transformer replacement circuit are adjusted to fully correspond to the actual values.Based on the magnitude of the discrepancies and the benchmarks previously obtained, a conclusion is drawn regarding the condition of the windings.

Conclusions
The article suggests that, in order to determine the actual technical condition of power transformers, the existing transformers should be "digitized" and, based on the obtained parameters, groups of transformers should be classified as dangerous, while others should be deemed suitable for operation.
To achieve this objective, we suggest an algorithm for determining the actual technical condition of power transformers that have exceeded their warranty resource.The presented step-by-step procedure outlined allows obtaining comprehensive data regarding the technical condition of a real transformer, namely: basic expressions are presented that allow obtaining the transformer's control indicators from its nameplate data; the list and procedure of control measurements on a real transformer are suggested; the creation of virtual models from the nameplate data and data obtained by empirical means and with subsequent modeling of transformer operating modes is suggested.The result of which is obtaining discrepancies between the parameters of real and virtual ones.
A model of a three-phase power transformer is suggested, which allows obtaining control parameters of an existing transformer.
The presented procedures allow drawing final conclusions about the state of the magnetic system of the transformer, the condition of its windings and to providing suggestions for the possibility of further operation of the transformer or repair of its specific components.

rS
rated power of the transformer; 12 , UUprimary and secondary voltages; NL (%) I current in the NL mode; efficiency factor; cos transformer power factor; SC ΔP , NL ΔP and SC (%) U .

Fig. 1 .
Fig. 1.Block with the incorporated parameters of transformer TM-25/10, Y/Y0 Source: developed by the authors using the MATLAB application program.

Fig. 2 .
Fig. 2. Power supply for a 10 kV transformer Source: developed by the authors using the MATLAB application program.

Fig. 3 .
Fig. 3. Blockthree-phase key Source: developed by the authors using the MATLAB application program.

Fig. 4 .
Fig. 4. Load block Source: developed by the authors using the MATLAB application program.

Fig. 5 .
Fig. 5.The transient current process when the load is turned on Source: developed by the authors using the MATLAB application program.

Fig. 6 .
Fig. 6.The virtual model for the transformer research Source: developed by the using the MATLAB application program.

Fig. 7 .
Fig. 7. Model of transformer short circuit study Source: developed by the authors using the MATLAB application program.