Influence analysis of local heat source on internal temperature distribution of power transformer

BAO Yanyan,FENG Tingna,ZHANG Guangdong,LIU Kang,MA Jianqiao,ZHOU Xiaodong

(1. State Grid Gansu Electric Power Research Institute，Lanzhou 730070，China； 2. School of Automation and Electrical Engineering,Lanzhou Jiaotong University，Lanzhou 730070，China； 3. China Railway Second Bureau Electric Co.,Ltd.，Chengdu 610031，China)

Abstract：Oil immersed power transformer is the main electrical equipment in power system.Its operation reliability has an important impact on the safe operation of power system.In the process of production,installation and operation,its insulation structure may be damaged,resulting in partial discharge and even breakdown inside the transformer.In this paper,S9-M-100/10 oil immersed distribution transformer is taken as the research object,and the distribution laws of electromagnetic field and temperature field in transformer under normal operation,inter turn short circuit and inter layer short circuit are simulated and analyzed.The simulation results show that under normal conditions,the temperatures at the oil gap between the transformer core and the high and low voltage windings and the middle position of the high-voltage winding are high.When there are inter turn and inter layer short circuit faults,the electromagnetic loss of the fault part of the transformer increases,and the temperature rises suddenly.The influence of the two faults on the internal temperature field of the transformer is different,and the influence of the inter turn short circuit fault on the temperature nearby is obvious.The analysis results can provide reference for the thermal fault interpretation and fault classification of transformer．

Key words：oil immersed power transformer;finite element method;electromagnetic field;short circuit fault;temperature field

0 Introduction

Oil immersed power transformer is one of the key electrical equipments for energy conversion and transmission in power system,and its operation reliability has a great impact on the stable operation of power system[1-4].In the process of safe and stable operation of power transformer,the temperature distribution inside the transformer and around the winding is uneven.If local overheating occurs in the transformer,it will not only affect the operation state of the transformer,but also affect the service life of the transformer[5-8].Therefore,it is of great practical engineering significance to study the influence of local heat source on the internal temperature distribution of oil immersed power transformer.The internal heat of transformer mainly comes from eddy current loss and resistance loss in the core and winding,so the electromagnetic heat in the transformer is a multi physical field coupling simulation calculation problem of electromagnetic field and temperature field.The internal temperature change of transformer is calculated by coupling magnetic field and temperature field.

At present,scholars at home and abroad have obtained a lot of research achievements by using multi physical field coupling method to simulate the internal temperature of oil immersed power transformer.Domestic researchers calculated the winding temperature distribution of oil immersed power transformer by using the multi physical field coupling finite element method,and the temperature distribution showed a trend of increasing first and decreasing subsequently.Refs.[9-10] compared and analyzed the advantages and disadvantages of the finite difference method and the finite volume method,established a three-dimensional (3D)simulation model according to the actual structural parameters of the transformer,carried out the simulation calculation by using the multi physical field coupling method of electromagnetic field,temperature field and fluid field,and obtained the electromagnetic loss and internal temperature field distribution of the transformer.Refs.[11-12] established the two-dimensional (2D)and 3D simulation models of transformer by using the multi physical field coupling analysis method of electromagnetic field,fluid field and temperature field,took the electromagnetic loss calculated by electromagnetic field as the load condition to solve the fluid and temperature field,and obtained the temperature distribution inside the transformer.Refs.[13-14] established the transformer simulation model with different structure iron cores,conducted electromagnetic field simulation calculation by using the finite element method,obtained the total loss of the transformer,and then simulated and calculated the hottest spot temperature of the transformer.They have established the simulation model of 160 kVA oil immersed transformer,simulated and calculated its temperature field by using the finite element analysis software ANSYS,and obtained the temperature change of transformer winding and insulating oil.For large-scale oil-immersed power transformers,domestic scholars have carried out simulation calculations and verifications on the internal temperature field,and carried out simulation calculations in combination with the flow field[15-18].To sum up,researchers have done a lot of research on the simulation of transformer temperature field,but little research has been done on the distribution and change of temperature field in the fault state of inter turn short circuit and inter layer short circuit.Therefore,in this paper,the multi physical field coupling method of electromagnetic field and temperature field is used to simulate the heat generated by the internal loss of transformer and the temperature change law of short circuit position after short circuit fault occurs.

In this paper,a 2D simulation model of transformer is established through the finite element analysis software COMSOL,and the temperature field distribution and temperature variation law of transformer in normal state and short circuit fault state are simulated and analyzed.The research results can offer reference to the interpretation of thermal fault and fault classification of transformer.

1 Theoretical analysis and modeling

1.1 Heat load calculation

Oil immersed power transformer in operation will produce losses in iron core,winding and other structural parts.The core eddy current loss and winding resistance loss are the main heat sources of the transformer.The resistance loss and eddy current loss in the winding account for more than 80% of the total loss.Therefore,this paper mainly studies the resistance loss in the winding and the thermal energy generated by eddy current loss in the core of oil immersed power transformer.The calculation formulas of resistance loss,eddy current loss and total loss are[19]

pR=I2R0[1+β(TC-T0)],

(1)

(2)

(3)

whereTCis the winding temperature;T0is the oil temperature;βis the temperature coefficient of resistance,β=1/235;fis the percentage of eddy current loss of coil in its resistance loss.The heat production rate per unit volume is calculated by

(4)

wherePis the loss value of the heat generator;Vis the volume of the heat generator.

The heat transfer process of oil immersed transformer is:firstly,the heat is transferred from the inside of the heat generator to the external surface cooled by the transformer oil,and then the heat is transferred from the surface of winding and iron core to other parts of the transformer box through heat conduction,finally,all the heat on the external surface of the box will be dissipated by air convection and radiation.Therefore,the time-varying temperature distribution problem can be solved by

(5)

whereQis the internal heating rate;Tis the temperature;ρis the material density;Kis the thermal conductivity;cis the specific heat capacity;tis the time.

If the temperature distribution inside the object is not uniform or the temperatures between two objects in contact are different,the parts of the general object will not change or move.The micro particles inside the material will move after being heated to realize the heat transfer.This way is mainly the energy exchange inside the object,and the heat is diffused from the area with higher heat and temperature to the area with lower heat and temperature.The heat conduction calculation formula is[20]

(6)

whereqγis the heat flow rate;γis the heat conduction coefficient;nis the normal vector flowing out from the boundary.

The thermal convection of air on the outer surface of the oil tank is different from that of oil inside the oil tank.The heat dissipated into the air by convection is determined by the external wall of the tank,the height of the tank,the shape of the tank wall,the air temperature,the atmospheric pressure and other factors.Therefore,the calculation formula of unit convective heat dissipation rate is

(7)

whereqKis the heat dissipated into the air per unit area when the temperature difference between the tank wall and the air is 1 ℃;Tyis the temperature difference between the surface temperature of the tank wall and the air temperature;Kis the heat dissipation coefficient;Kφis the shape coefficient.

The calculation formula of total heat dissipation of convection on the surface of oil tank is

QK=qKTyAK,

(8)

whereAKis the sum of the convective surface area of the tank.

The heat radiation does not depend on the propagation of the intermediate medium,while the heat conduction requires the direct contact between objects,and the thermal convection depends on the fluid.The calculated relationship between the heat radiated into the air and the radiation temperature and the temperature of the surrounding objects is

(9)

whereqλis the heat radiated from the unit surface of the radiator when the temperature difference is 1 ℃;T1andT2are the absolute temperatures of the radiator and the air.

The calculation formula of radiant heat on all surfaces of oil tank is

Qλ=qλTyAλ,

(10)

whereAλis the total radiation surface area of the oil tank.

1.2 Geometric model

1.2.1 Normal model of transformer winding

The basic structural parameters of power transformer (S9-M-100/10)are shown in Table 1.

Table 1 Basic structural parameters of transformer

The 2D model of transformer is established according to the structural parameters of transformer in Table 1.

Because the actual structure of transformer is complex,it is difficult to model according to the actual structural parameters of transformer.Therefore,the actual model of transformer is reasonably simplified,and the low-voltage coil is simplified as a single conductor equivalent to two copper cores.Corrugated paper and support strip are replaced by insulation paper with the same thickness.Considering the symmetry of transformer structure,this paper only draws the transformer intermediate phase winding for simulation calculation to improve the calculation speed.The simplified geometric model of transformer is shown in Figs.1 and 2.

Fig.1 2D structure of transformer

Fig.2 Partial schematic diagram of 2D structure of transformer

1.2.2 Short circuit model of transformer winding

The transformer model under normal condition is segmented by using the division domain command,which destroys half of the insulation layers between two adjacent windings,and sets the material between the two windings as copper conductor to achieve the effect of inter turn short circuit.The equivalent inter turn short circuits model of transformer is shown in Fig.3.

Fig.3 Inter turn short circuit model

The inter layer short circuit is a short circuit caused by insulation damage between two adjacent coil layers.Therefore,the inter layer short circuit model is set at the end of the transformer high-voltage winding and near the oil gap,and the material of the middle short circuit part is set with copper conductor.The equivalent inter layer short circuit model of the transformer is shown in Fig.4.

Fig.4 Inter layer short circuit model

1.3 Simulation model

In this paper,multi physical field coupling method is used to calculate the field circuit coupling of electromagnetic field and temperature field in COMSOL,and the total loss of electromagnetic field is used as the heat source of temperature field for simulation calculation.In the process of electromagnetic field calculation,the materials and properties of transformer components are set as shown in Table 2.The grid type is physical field control grid.The excitation source of high and low voltage winding is voltage,and the voltage of high voltage winding is 8 165 V (phase voltage assignment).According to the transformation ratio of 1:25 concerning S9-M-100/10 power transformer and the connection mode of Yyn type,the voltage of 326.6 V (phase voltage assignment)is applied to the low voltage winding.After the calculation,the unit volume loss density calculated from the derived value is added to the temperature field,and the loss is set as the excitation source of the temperature field,the temperature of the transformer shell is set as the ambient temperature of 20℃,the electromagnetic heat is set in the multi physical field,the secondary solver is steady state,and the internal loss and temperature field distribution of the transformer are simulated and calculated.

Table 2 Material properties of each component

2 Simulation results and analysis

2.1 Temperature field distribution of winding in normal state

According to the 2D structure and simulation model of power transformer in normal state,the distributions of internal magnetic field and temperature field in power transformer are calculated,as shown in Figs.5 and 6.

Fig.5 Electromagnetic field distribution nephogram

Fig.6 Temperature distribution nephogram

It can be seen from Fig.5 that the magnetic fields at the oil gap and both ends between the high and low voltage windings of the transformer are larger,and the farther away from the winding,the weaker the magnetic field.From Fig.6,it can be seen that the temperatures of the transformer core,the high and low voltage windings and the middle position of the high voltage winding are higher.The reason is that the distance between the iron core and the high and low voltage windings is relatively close,and the temperature difference at the same axial height is relatively small,which is not conducive to heat transfer.

And the oil gap between the transformer core,the high and low voltage windings and the middle of the high voltage winding is smaller than that between the high voltage winding and the transformer tank wall of the transformer,and the flow speed of insulating oil is relatively gentle,which is not conducive to convective heat transfer and radiation heat dissipation.

2.2 Temperature field distribution of inter turn short circuit fault

The electromagnetic field distribution nephogram of transformer winding after inter turn short circuit is obtained by simulation,as shown in Fig.7.At the same time,a straight line connecting the two ends of the high voltage winding is drawn by using the command of 2D line cutting,that is,the dotted line in Fig.8.The temperature data on the 2D cut-off line is extracted for comparative analysis.The comparison results are shown in Fig.9.Because the highest temperature of transformer winding is in the middle of high-voltage winding,the middle part of high-voltage winding is selected to establish inter turn and inter layer short circuit model,and the influence of short circuit in the middle of high voltage winding on its temperature is simulated and analyzed.

Fig.7 Electromagnetic field distribution nephogram of inter turn short circuit

Fig.8 2D line cut

Fig.9 Comparison curve of inter turn short circuit

Combined with Figs.8 and 9,it can be seen that the electromagnetic loss at the position where the inter turn short circuit occurs increases,and the temperature also increases.From the normal state curve in Fig.9,it can be seen that the overall temperature of the winding increases first and then decreases,and shows a regular wavy decline.The curve is symmetrical,and the maximum temperature reaches 82.66 ℃.From the curve of inter turn short circuit,the maximum temperature reaches 84.98 ℃ and increases by 2.32 ℃.Since the short circuit only occurs between two turns,the temperature rise is relatively small.When the inter turn short circuit of transformer winding occurs,firstly,the current in the winding at this position increases sharply,which makes the active power loss of the short circuit coil inside the transformer increase obviously,that is the calorific value of the resistance increases.Secondly,the magnetic circuit changes correspondingly,and the leakage magnetic field also changes,resulting in the increase of the additional loss of the transformer[21].Since the loss of transformer is the main heat source of transformer,the total loss increases and the heat generated increases.

2.3 Temperature field distribution of inter layer short circuit fault

Fig.10 shows the electromagnetic field distribution nephogram of inter layer short circuit obtained by simulation,and Fig.11 shows the temperature data comparison curve of oil immersed power transformer after inter layer short circuit occures at the middle position of high-voltage winding.

Fig.10 Electromagnetic field distribution nephogram of inter layer short circuit

Fig.11 Comparison curve of inter layer short circuit

It can be seen from Figs.10 and 11 that the electromagnetic loss at the place where the inter layer short circuit occurs increases,and the temperature increases accordingly.The overall temperature of the winding shows a trend of first increasing and then decreasing,and it decreases regularly in a wavy shape,and the curve is symmetrically distributed.When there is a short circuit between two adjacent layers of the transformer winding,the temperature at the short circuit position increases,and the maximum temperature reaches 84.36 ℃,which is 1.7 ℃ higher than the maximum temperature of winding under normal state.With the increase of the number of short circuit layers,the maximum temperature at the short circuit position increases.When the number of short circuit layers is four,the maximum temperature reaches 86.02 ℃,which is 3.36 ℃ higher than the normal temperature.Therefore,when the number of short circuit layers increases,the maximum temperature will also increase.

Fig.12 shows the temperature contrast curve of different short circuit fault types.

Fig.12 Comparison curve of different short circuit types

It can be seen from Fig.12 that no matter the inter turn short circuit or inter layer short circuit occurs,the temperature increases first and then decreases from the upper end to the lower end of the high voltage winding,and the influence of the inter layer short circuit fault on the temperature is greater than that of the inter turn short circuit fault.The reason is that with the increase of the number of short circuits,the electromagnetic loss and additional loss of the winding increase,and the temperature caused by the loss increases.The short circuit location of the inter turn short circuit model is closer to the oil gap than that of the inter layer short circuit model,and the loss is more.Therefore,the inter turn short circuit fault at the same position has a greater impact on the temperature nearby than that of the inter layer short circuit fault.

3 Conclusions

In this paper,the influences of normal state,inter turn short circuit and inter layer short circuit on the internal temperature field of 10 kV oil immersed power transformer are simulated and analyzed.The conclusions are as follows.

1)As for the oil immersed power transformer under the normal operation condition,the temperatures at the oil gap between the iron core,the high and low voltage windings and the middle position of the high voltage winding are higher,and the temperature between the high and low voltage windings is the highest.

2)With the increase of the number of short circuit turns and short circuit layers,the greater the temperature change,the higher the maximum temperature.

3)The influence of inter turn short circuit fault on the internal temperature of oil immersed transformer is greater than that of inter layer short circuit fault.