## 1 Introduction  
Transformer is the core equipment of power systems, and its safe operation is of great significance to the stability of the power supply. The failure of a large power transformer often leads to a blackout in an entire area, causing huge economic losses. As such real-time dynamic monitoring of the online transformer status has aroused wide interest [1; 2; 3]. The internal temperature of a transformer, especially the winding hotspot, has a direct influence on the insulation performance and its service life. Overheating during operation will decrease the life expectancy of the insulated materials and thus threaten the safety of the local grid, while running at a lower temperature means less load and the sacrifice of economic benefits [4]. Hence, the optimal balance between safety and economy requires actual data-based criterion to grasp. Moreover, the dynamic capacity-increasing and energy-saving control of the transformers are both empirical models, still lacking quantitative, reliable support [5]. It is therefore necessary to obtain the real time temperature distribution inside the transformer. Currently, the traditional transformer temperature monitoring methods can be primarily divided into four types: empirical formula method [6; 7], numerical simulation, infrared measurements [8; 9]and contact measurements (including thermocouples, fiber Bragg grating (FBG) and fluorescence optical fiber, etc.) [10; 11]. Among them, the empirical formula method has gradually become mature after many amendments since it was first proposed in 1911 and has been widely applied in actual operations [12]. In IEC 60076 standard, different coefficients are suggested for transformers with different heat dissipation modes, which can be directly used for the temperature calculation of transformer hotspots under different load conditions and operating conditions [13]. This method can reflect the relationship between the hotspot temperature and the transformer operating state. It is simple and thus has a wide range of applications [6]. However, it has been proved that in some cases, the calculation result holds a large error compared with the actual measurements [14]. Meanwhile, it is also difficult to keep pace with the instantaneous load changes, which inevitably leads to the lack of real-time response [15]. Therefore, the empirical formula based detecting method is more suitable for a rough but fast calculation. However, the method above only focuses on the hotspot temperature, lacking the thermal information of the entire internal area. The numerical simulation, which establishes the partial differential equations for the internal convective heat exchange process according to the fluid mechanics, could solve this problem theoretically through a global computing by relevant algorithms [16]. [PERSON] and [PERSON] were the first to make great progress in this area through a 2D thermodynamic modelling of an oil-immersed transformer [17; 18]. Then, [PERSON] further obtained a more detailed 3D temperature distribution by combining genetic algorithms with the multi-physics coupling [19]. In order to reduce the modelling complexity, [PERSON] furtherly simplified the transformer heat source and boundary conditions, and hereby proposed an equivalent calculation model [20]. However, limited by the inevitable simplifications and the convergence of algorithms, the simulation result usually has deviations in reflecting the real state of a transformer, and in most cases, it only serves as a theoretical reference [21]. Besides the aforesaid calculation methods, direct detection usually stands out for its simple and intuitive properties. The remote non-contact measurement with infrared camera is convenient for people to operate, but it can be easily affected by the ambient temperature, electromagnetic signals or the shooting position, bringing inevitable measurement errors [8]. Moreover, this camera-based method is also unable to measure the internal temperature distribution of a transformer in real time.