Prediction of transformer fault in cooling system using combining advanced thermal model and thermography

Thermal models are widely used for diagnosing thermal faults, predicting the thermal behaviour, estimating hot spots, and evaluating the loading capacity. This paper uses a new advanced thermal model, thermography method, and computational ﬂuid dynamic separately to obtain the top-oil and radiator temperatures. The model consists of four thermal points: the ambient, top-oil, winding, and radiator. The heat transfer phenomena between these points are modelled by nonlinear thermal resistors. Adding the radiator thermal point to the model improves the accuracy. This is shown by comparing the proposed model with the standard and physical thermal models. The proposed thermal model is validated using the experimental results of three distribution transformers. The thermography camera and image processing technique are also employed to take thermal images and analyse them, respectively. By analysing the thermal images with the image processing method, the top-oil temperature and radiator temperature are obtained. Fur-thermore, the computational ﬂuid dynamic model is used to analyse and obtain more accurate prediction of the thermal behaviour of the transformer. Finally, it is proposed to detect faults inside the transformer cooling system by comparing the top-oil and

equations. The accuracy of physical modelling depends on the two following essential points: • Considering the factors affecting the thermal behaviour in the model, such as the oil viscosity, tap changer position, radiation capability, winding resistance, unbalanced and harmonic loads, sun radiation, wind, and the characteristics of the measurement data. It is noted that some of the factors mentioned above can be neglected depending on the type, position of the transformer, and the temperature points needed to be estimated. • Types of thermal resistances in the model. These resistors model the heat transfer between different thermal points inside and outside of the transformer. The thermal resistances can be of linear or nonlinear types. Linear resistors are constant and independent of the loading conditions. However, nonlinear resistors depend on the loading conditions and change with the thermal condition of the transformer.
The physical thermal models are divided into three groups [12]: • Thermal models loading guide. The thermal resistance of these models is linear and, thus, the accuracy of these models is limited. In the loading guides, the linear thermal resistance is assumed as an exponential differential equation to obtain TOT and hot spots [13][14][15]. • The developed thermal models. These models are based on the loading guide, but various thermal resistances are assumed for each transformer segment. In some cases, the Susa and Swift modelling is included to gain better accuracies. • The advanced thermal models. These models are provided to compensate for the weakness of two previous models. In this modelling, precise nonlinear thermal resistances are used.
An excellent thermal model must have the following characteristics [16]. First, it should maintain its simplicity despite structural complexity. Second, it should be accurate enough, that is, influencing factors should be included to improve the accuracy of the model. Thirdly, it should use a few design-dependent variables and be independent of transformer conditions. Some recent contributions focus on considering different factors in the thermal model to improve its accuracy. Oil viscosity variations with temperature are considered in [17] for the physical model of transformers with different cooling modes. The oil viscosity change causes different time constants in various cooling modes, while other oil parameters, such as density, heat capacity, thermal conductivity, and specific conductivity, are constant. The effect of coil temperature rise on the oil circulation, and its viscosity is discussed in [18]. Moreover, the difference between mineral oil and natural ester fluid and its effect on viscosity is investigated in [19].
The tap-changer position has a direct effect on the losses in the transformer and, thus, its temperature rise. Tapchanger positions at different loads are considered in a threedimensional thermal model in [20]. In this model, losses are obtained from the finite element computation, and the oil temperature rises at each step from a hydraulic network thermal model. An advanced thermal model introduced in [21] considers the tap-changer position and heat transfer modes, including natural and forced convection of the oil and the air and radiation, to calculate TOT accurately.
The error sources due to measurement data and the influence of the samples on the accuracy of the thermal model are addressed in [22][23][24], while different methods are presented for dealing with them. The effect of different tank colours on the temperature rise is also investigated in [25].
The losses and their calculations are other vital factors in thermal modelling. Increasing the coil temperature results in more copper losses and higher eddy current losses. The unbalanced and harmonic loads also cause higher losses, which generate higher temperatures in the winding and reduce the loading capacity. A method is introduced in [8] for calculating losses in the case of harmonic currents. The intensity and angle of solar radiation and wind blowing, which affects the losses and transformer cooling, can be considered in a thermal model depending on the type and location of the transformer [26][27][28]. For instance, [29] shows that solar radiation increases the temperature of the transformer by 3.7 • C.
In indoor and underground transformers, ventilation, shape, and dimensions of the room, thermal transfer phenomena in different parts of the transformer and the station have a strong influence on the accuracy of the thermal model. A thermal, mathematical model based on distributed parameters can be used for the underground distribution transformer to include the effects of the ground and room conditions in the cooling [30,31]. Using this thermal model, the temperature of the different parts of the transformer and their time constants are determined. For an underground distribution transformer located in a rectangular chamber, the effect of horizontal convection above and below the tank and vertical convection along the tank should be taken into account [32]. In indoor transformers, ventilation holes affect the temperature rise of the transformer. In addition to the heat transfer phenomena inside and outside the transformer, the ventilation holes in these models are considered to improve the accuracy of predicting TOT, the tank temperature, and transformer loading capacity [12,33].
Some contributions propose a fault prediction method based on the temperature difference between the measured and calculated TOT. Moreover, large variations in the estimated parameters of the thermal model are considered as another indicator of faults within the thermal system of the transformer [8,34,35]. In [36], the expanded Kalman filter algorithm is employed to predict and estimate the transformer life span, TOT, and winding hot spots.
Alongside the standard temperature measurement sensors, thermography cameras are used as a powerful tool for measuring the temperature distribution of equipment in the industry [37]. They take thermal images from each part of the transformer, including tank, radiator, tap-changer, and bushings. Each transformer thermal image can be divided into three areas: Bottom, middle and top sections. If the temperature of the lower and middle part is higher than that of the upper part, then there exists a thermal fault in the transformer [38]. An alert system based on comparing thermal images with basic images is used in [39] to report electrical equipment faults. Thermal image analysis methods based on image processing and neural networks are also implemented to increase the speed and accuracy of fault detection and classification process in electrical equipment [40,41]. In this paper, two different methods are utilized to obtain the radiator temperature and TOT. The first method uses a new proposed advanced thermal model. The main advantage of this model is considering the radiator as an extra thermal point, which improves the accuracy of the thermal model. The second method uses thermography and image processing to control the transformer temperature distribution and obtain the top-oil and radiator temperatures. By comparing the obtained TOT or radiator temperature from these two methods, it is possible to detect the thermal faults inside the transformer and its cooling system. Thermography, which is a standard tool for transformer diagnosis, does not have a methodological evaluation procedure. A model with different thermal points, similar to the one proposed in this paper, can serve as a baseline for the evaluation of thermography results. In summary, the contributions can be listed as follows: • Improving the thermal model accuracy by adding the radiator thermal point to the model. • Improving the transformer thermal monitoring by adding the radiator point to the monitored parameters. • Providing a baseline for the evaluation of the thermography images. The temperature gradient between the top-oil and the radiator, which is not available in previous thermal models, can be used to assess the temperature gradients derived from the thermography imaging.

EXPERIMENTAL SETUP AND DATA MEASUREMENT
Experimental results are obtained for three distribution transformers: 50, 400, and 630 kVA with natural air and natural oil (ONAN) cooling. Table 1 summarizes the specifications of these three distribution transformers. To control the tempera- The 50 kVA transformer and the installed temperature sensors. Sensors 1, 2, and 3 measure the top-oil, radiator, and ambient temperatures, respectively ture distribution in the transformer, three sensors are installed on the outer surfaces of the transformer, as shown in Figure 1. The sensors 1, 2, and 3 measure TOT, the radiator temperature, and the ambient temperature, respectively. One wattmeter records the transformer power consumption. The accuracy of the measured data depends on the time intervals and the number of measured data [14]. The following assumptions are made for modelling the transformers: • The temperature changes only with the height of the transformer. In other words, the temperature is uniform along the transformer width and length. • The temperature difference between the top-oil and the point on the top cover is neglected. The same is true for the radiator temperature, where the temperature drop on the metallic radiator crust is assumed to be infinitesimal. As a result, sensors can be put on the metallic surface and read the temperature of the top-oil and radiator.
The measured data of the 50 kVA transformer are sampled over approximately 8 h every 1 min (450 samples). Figure 2 shows the measured data (load factor, ambient temperature, TOT, and radiator temperature) versus time. The transformer load factor equals 0.9, 1, and 0, respectively. By applying the full-load to the transformer, the top-oil and radiator temperatures gradually load rise. At the no-condition, the top-oil and radiator temperature decreases. Besides, the ambient temperature varies due to changes in the laboratory temperature.
The data of the 400 and 630 kVA distribution transformers are sampled over approximately 3 h every 5 min. The load factor is equal to 1 during the experiments. It is noteworthy that these two experiments are the temperature rise tests of transformers. In the first phase of the test, a thermal insulator made  of glass wool is utilized to cover the radiators and to shorten the transformer warming time. In the second phase, the thermal insulation is removed to let the transformer reach the final temperature point. Table 2 reports the temperature changes during these two phases. Figure 3 also shows the measured data for the two transformers versus time in the second phase. It must The equivalent circuit of the advanced thermal model [11] be noted that in the first phase of the test, there is no natural convection of air in the radiator, and the cooling is less than the normal situation. Therefore, only the data of the second phase are employed for modelling, where transformers are in the normal cooling state.

2.1
Advanced thermal model for prediction of thermal behaviour

Model circuit and the resistances in mode
In this section, a new advanced thermal model is developed based on physical and thermal modelling. This model includes nonlinear thermal resistors, current sources, voltage sources, and capacitors, as shown in Figure 4. This thermal model contains four thermal points: the ambient, bottom of the radiator, top-oil, and the winding. To increase the accuracy of this thermal model, all heat transfer phenomena and influential factors are considered. A series of nonlinear thermal resistances are considered between various points, which represent temperature changes between thermal points with entirely different conditions. Current sources, voltage sources, and capacitors indicate losses (no-load loss and short circuit loss), the ambient temperature, and the transformer heat capacity, respectively. Figure 5 shows the equivalent thermal circuit obtained by simplifying the circuit of Figure 4. The thermal resistance of Figure 5 is obtained from series resistors and parallel resistors in Figure 4 as follows: where: The resistors in Equation 1 are based on convection and radiation heat transfer. The relationships between these resistances are described in the following sections.
1. Nonlinear resistance of natural air convection: In this model, there is natural air convection in the top-oil and radiator points. These thermal resistances indicate the temperature difference of the top-oil and radiator from the ambient. This nonlinear resistance is calculated as follows [42]: T n is replaced by T r in Equation (6) when calculating the resistance between T r and T a . Similarly, T n is replaced by T to for calculating the thermal resistance between T to and T a .
3. Nonlinear resistance between top-oil and radiator: This resistance models all the heat transfer phenomena and factors between the top-oil and the radiator. This resistance indicates the temperature changes between these two thermal points. This resistance is calculated as follows: , 4. Nonlinear resistance of natural oil convection: The natural movement of oil in the transformer due to convection results in heat transfer. Temperature changes between the winding and the top-oil are modeled by the oil natural convection nonlinear resistance as follows [42]: Gr oil (T ) = s 3 oil .

Differential equations for solving the model
If the difference between the measured and computed temperature of the radiator increases, it indicates a fault in the transformer. Therefore, prediction and calculation of the radiator temperature are essential for fault detection.
The differential equation, which is employed for calculating the radiator temperature, is as follows: where: A similar differential equation can be utilized to define TOT for the oil-immersed transformer [24]: In Equations (24) and (26), the heat capacity is obtained as follows [24]: Estimation of empirical factor and design-dependent parameters In the advanced analytical thermal model, the empirical factors (EF) and the design-dependent parameters (DDP) are used. Table 3 summarizes the inputs, EF and DDP of the transformer, constants, and outputs. The EF and DDP are different for various parts of the transformer, including the top-oil and the radiator. Usually, the EF and DDP are not provided by manufacturers [8], and they must be estimated based on the measurement data obtained during the regular operation of the transformer. EF and DDP are considered as constant variables, which do not change during transformer operation. Nonlinear regression theory can be used to estimate EF and DDP. The equation of the nonlinear regression is as follows [44]: In the regression theory, it is tried to minimize the squared error between the estimated parameters and the measured ones. The sum of the squared error is calculated as follows: Which can be simplified as follows: To obtain the minimum points for each EF and DDP, a partial derivative is taken from Equation (30). The equation is changed to a linear least-squares problem by applying the partial derivative to the EF and transformer DDP and by forming the equation matrix of minimum points. This matrix consists of n rows and 1 column. The partial derivative of each EF and transformer DDP is determined as follows: By implementing the Gauss-Newton repeating algorithm and the Taylor series, the real values of EF and transformer DDP are estimated. Finally, can be obtained:

CFD simulation for thermal behaviour prediction
To compare the calculation and experimental results, a CFD simulation is carried out using a finite volume method based  . The geometry is assumed to be periodical-symmetry, so just a cross-sectional area of the cylindrical shape and radiator fin is considered, planes parallel to the xy plane are used as the plane of periodicalsymmetry. An established model, which reflects the half of a real surface shape of the radiator fin, is considered as an element with an internal oil flow and a constant temperature of ambient air on the outer surfaces. The domains of the model of a radiator fin, the inner oil, the yoke, and windings are discretized into a finite set of control volumes. For a precise prediction, there need to be extremely fine numerical grids because the grids have significant impacts on the level of resolution of the flow filed. Thus, a grid-independent solution is worth finding before comparisons with experimental results. In the present study, all small enough quadrant grid size of 4 million is chosen to ensure that the results are independent of the grid. All flows are specified as laminar and as transient. The boundary conditions are listed in Table 4. The constant heat flux of 808.2 (W/m 2 ) comes from the total transformer losses of 1283.9 W obtained from Table 1 per the total area of windings and cores (709.5 cm 2 ). The outer wall of transformer has natural convection with ambient air, and for shortening the computation time, it is assumed as a constant temperature wall. The difference between the maximum of TOT with lowest ambient temperature is less than 30 • C in the experimental data, and also the thickness of the transformer tank and radiator fins are large enough (more than 2mm) to assure that the assumptions are reasonable. The segregated 3D solver is then set to solve the model, and residuals are set under 10 -6 for the determination of convergence. Figure 6 shows a schematic view of the 3D model and the cross-sectional area. The rectangular elements present the slice of cylindrical discs of the LV and HV windings as well as the yoke. Insulating oil heats in a transformer winding and runs to the radiators via thermal driving force. Although radiators have radiating loss and it is relatively small due to the symmetrical shapes of the design. Radiating loss is thus not considered in this calculation.
The incompressible Navier-Stokes system of equations with the Boussinesq formulation of buoyancy is employed to obtain the temperature and flow field. The Boussinesq model allows a faster convergence than setting up the problem with the fluid density as a function of temperature. The model treats density as a constant value in whole solved equations, except for the buoyancy term in the momentum equation of the portion of fluid displaced by the following density variation: It is obtained based on the Boussinesq approximation which implies that the changes in density must be small. The governing equations are as follow: Continuity Since the flow velocities are relatively low and the oil viscosity is high, the flow is laminar, and no turbulence model is required. Pressure velocity coupling is PISO in the case of transient simulations. For the spatial discretization, the Green-Gauss node based is used for the gradients and the PRESTO is used for the pressure. The 2nd order upwind spatial discretization is utilized for both momentum and energy. The 1st order integration in time is preferred because of its increased stability in the time integration, also given that the flow analysed shows prolonged variations in time. A time step of 0.1 s is used and the quality of the solution obtained with this time step is confirmed by the comparison of the results obtained with a solution on the same mesh using a time step of 0.1 s. The maximum number of iterations per time step is set to 30. The other required properties are listed in Table 5.
The maximum temperature and minimum temperature in the oil zone and fin wall are monitored to assess whether the simulation is stabilized on the physical solution or not. After 336 min, which corresponds to 201,600 time-steps of 0.1 s with maximum 30 iterations each, a physical solution is reached. On a laptop of eight cores, this corresponds to a simulation time of around 7 days. Figure 7 shows the 3D views for the temperature contour of the solution of the transient simulation for various  In the final region of the transformer, there is the development of recirculation regions, that determines a nonsteady behaviour of the system and consequently, a transient simulation is required. The presence of 3D vortex structures is mainly due to the uneven distribution of the oil flow at the bottom of the radiator fin. The presence of the semi-recirculation regions at the top of oil tank is due to the many sharp corners of windings and core cross section that the oil encounters in its path. Figure 8 shows the TOT, radiator, and maximum oil temperature in the simulation of the 50 kVA transformer. As seen in Figure 7, the oil near the windings and core has the highest temperature. In this case, clear oscillations in time appear, highlighting the development of an non-steady flow field of the oil.
To assess the accuracy of the developed simulation model, a comparison with the experimental data is performed. Figure 8 shows the comparison between the simulated and the measured temperature in the radiator and top-oil of the 50 kVA transformer. As far as the temperature distribution in the space is concerned, there is a quite good match between the results from the simulation and the experimental; in particular, the correct location of the hotspot is identified. The maximum record value of TOT in the experimental results is 324.75 K (51.6 • C), while in the simulation is 324.0 K (50.85 • C). The maximum relative error between the experimental results and the values from the simulation is 1.9% and the average error is 1.2%. Since the precise location of the temperature sensors in the experimental set up was not clearly specified, this simulation approach can be considered quite accurate. However, there are some differences between the simulation and measured temperatures ( Figure 8). These differences are probably due to some inaccuracies in the evaluation of the heat losses in the windings and slight differences between the geometrical parameters in the test transformer and the one analysed in the simulation.

Validation of thermal mode
The advanced thermal model is validated using the measured data obtained from the three distribution transformers during their regular operation. Part of the measured data are used to estimate EF and DDP, and the rest of the data are utilized for comparing the thermal model. Figure 8 shows the validation of the proposed thermal model for the three distribution transformers.
As seen in Figure 8, the measured and calculated/predict data of the radiator and top-oil temperature are consistent, which validates the thermal model. To show the accuracy of the proposed thermal model, the root-mean-square error (RMSE), and maximum error (ME) of this thermal model are calculated and compared with the CFD model, the standard thermal model, and with the base thermal model (a physical thermal model without the radiator point). The results of these three models are also demonstrated in Figure 8. RMSE and ME are calculated as follows: RMSE and ME of the four thermal models are reported in Table 6. As can be seen, the proposed model is more accurate than the standard and the base model since the RMSE and ME are lower than that. However, the CFD model is more accurate than the proposed thermal model, because this model considers more details of the geometry of the transformer, but it has a very low-performance speed in comparison with other thermal models. In the other words, the CFD model cannot be utilized for online purposes. RMSE of the proposed thermal model for the top-oil and radiator temperature is 0.90 and 1.14, respectively. Besides, the ME for these two points is 2.00 and 2.51, respectively. In summary, the proposed thermal model is more accurate than the standard model and the base model because RMSE and ME are lower than that. Moreover, this indicates the high accuracy of the predicted temperatures of different points based on the advanced thermal model. In summary, the model has RMSE ⋍ 2 and ME ⋍ 3.

THERMOGRAPHY AND IMAGE PROCESSING METHODS
A thermography camera is utilized to photograph the 50 kVA distribution transformer at different loadings. Four thermal images are taken every 15 min for 8 h. Figure 9 shows one of the thermal images. This part uses the image processing method to analyse the thermal images. Each colour image is a matrix consisting of a large number of pixels. The thermal images show the temperature distribution in different parts of the transformer in different colours. By using the image processing method, the position and characteristics of the pixel with the highest temperature are extracted, which indicates the hot spots on the radiator and top cover. As mentioned before, the temperature of the top cover can be taken as TOT. In summary, the use of the thermal image and image processing can provide the position and temperature of the hot spots of the radiator and the top-oil every 15 min. At this point, the top-oil and radiator temperatures are available from two sources, measurement and simulation. By comparing these values, it is possible to detect a thermal fault within the transformer. Figure 10 shows the flowchart of transformer fault detection by combining the thermal models and thermography imaging.
The likelihood of damage to the transformer can be prevented by timely error calculation between the two values obtained for thermal points. The maximums of RMSE between two methods for the top-oil and radiator temperature are 0.47 and 0.41, respectively. Moreover, the maximum ME for the top-oil and radiator temperature are 3.34 and 3.57, respectively. These values correspond to a healthy transformer. A threshold with a sufficient margin from these numbers can be set to detect faults. Moreover, a lower margin can be defined to raise the alarm. Accordingly, ME = 4 is used as the alarm threshold, and ME = 6 is set for detecting faults. The same algorithm can be applied to the temperature difference. If the difference between the two methods is 4 • or more for the top-oil or radiator, the temperature distribution inside the transformer or radiator is abnormal, and there may be a fault in the transformer. Furthermore, if the temperature difference between the two methods for the top-oil or radiator is 6 • or more, the fault has occurred inside the transformer and its cooling system [6,14,18,46]. Figure 11 shows the temperature difference between the two methods, where its vertical axis and horizontal are temperatures ( • C) and time (min) respectively. Since the difference is less than 4 • , the transformer is healthy [6,14,18,46].
The last possibility as the feature of the proposed method is using the temperature gradient along with the transformer tank for fault detection. The temperature gradient between the radi-ator and the top cover can be obtained from the thermal model and thermography imaging. If they are far apart, it is an indicator of the fault within the transformer. It is noteworthy that adding the radiator thermal point makes it possible to implement this method for fault detection. In summary, this criterion can also be used for fault detection.

CONCLUSION
This paper uses a new advanced thermal model, infrared imaging, and image processing to predict and detect thermal faults in the transformer. The proposed thermal model consists of the ambient temperature, radiator temperature, top-oil temperature, and the winding temperature. All heat transfer phenomena inside and outside the transformer are modelled by a set of nonlinear thermal resistors between the points mentioned above. These nonlinear thermal resistances show the temperature differences between the two thermal points in the transformer.
The main feature of this model is that it considers the thermal point of the radiator. This and other points were used to predict and detect the fault in the transformer. Besides, the model is used to calculate the temperature of the radiator and top-oil. By careful analysis of thermal images using image processing, it is possible to find the temperature distribution and determine the coordinates and temperature of the hot spots of the radiator and top-oil. The thermal fault is detected in the transformer by comparing the radiator temperature or top-oil temperature obtained by these two methods (advanced thermal model and thermography imaging).

NOMENCLATURE
Emissivity factor of the transformer tank = 0.95.

re f
Fluid constant density (kg/m 3 ). Shear stress ∆T to Top-oil temperature rise over ambient temperature (K). ∆T w Winding temperature gradient (K).
T a Ambient temperature ( 0 C). air Ambient Rconv Nonlinear natural convection thermal resistance (K/W). Aconv The surface area of convection heat transfer (m 2 ).
cp Specific heat (W⋅s/ (kg⋅K)). Re Reynolds number. g Gravitational acceleration = 9.8 (m/s 2 ). g r The temperature gradient between the winding and the oil at rated load (K). h Heat transfer coefficient of natural convection (W/ (m 2 ⋅K)). I Matrix of measured data. i & j Time step. Indices K Load factor (%). Ploss Total losses (W). T m Measured temperature ( 0 C).