The hot spot of a transformer winding is the point where the winding temperature is highest during transformer operation. If the hot spot temperature is too high, it will accelerate insulation aging and shorten the transformer's lifespan; if the hot spot temperature is too low, the transformer's capacity will not be fully utilized, reducing economic efficiency.
Depending on the method of obtaining the temperature, there are two main methods for obtaining the temperature of the internal windings of a transformer: direct measurement and indirect measurement.
1. Direct measurement method
Due to the complex internal structure of transformers, which generate significant microwave and electromagnetic interference during operation, traditional temperature measurement methods struggle to obtain accurate results. Fiber optic temperature sensors, with their excellent electrical insulation, strong resistance to electromagnetic interference, and superior reliability, are ideally suited for temperature measurement within transformers. The direct measurement method involves placing a fiber optic temperature sensor near the windings or within the winding coils to directly obtain the hot spot temperature of the transformer windings. The reason for using fiber optic temperature sensors is that their received signals are less susceptible to interference from electromagnetic fields and other environmental factors within the transformer, resulting in more accurate measurements.
Direct measurement yields the most accurate results, but embedding sensors within the winding places high demands on the insulation design, potentially affecting transformer operation. Furthermore, since the location of hot spots in the winding is uncertain, the sensor's placement point may not be the hottest spot, and the measurement result may not accurately reflect the winding's hot spot temperature. To overcome this, a common approach is to install multiple temperature sensors in the vicinity of the winding's hot spot, measuring the temperature at multiple locations to approximate the hot spot temperature. Another solution is to use distributed fiber optic temperature sensors.
Significant progress has been made in the application of fiber optic sensing technology to the direct measurement of hot spot temperatures in transformer windings, but improvements are still needed in terms of stability, economy, and practicality.
2. Indirect Calculation Measurement Method
Indirect measurement methods are those that estimate the hot spot temperature of the transformer winding without directly measuring it. These methods include thermal simulation using physical models, numerical calculations using heat transfer theory, thermal circuit model methods derived from thermoelectric analogy, and calculation methods recommended by national standards.
① Thermal simulation method
The thermal simulation measurement method calculates the hot spot temperature by simulating the temperature rise of the winding relative to the top oil temperature in the transformer's top layer region. This method is based on the formula tk = KΔtwo + t0, where Δtwo is the copper-oil temperature difference, t0 is the top oil temperature, and K is the hot spot coefficient. The test system in Figure 1 uses a current transformer to obtain a current Iw (proportional to the load), which flows through a specially designed heating element inside the temperature bulb to obtain Δtwo. Adding t0 gives the winding hot spot temperature.
Figure 1. Configuration diagram for "thermal simulation"
1. Current transformer 2. Heating element 3. Temperature bulb 4. Capillary tube
The thermal simulation method relies on the premise that the oil temperatures at the top layer of the transformer tank, the top layer of the winding, and the transformer oil temperature are approximately the same. This is unsuitable for transformers in multi-circuit systems. Furthermore, although the additional temperature rise Δtwo generated by the simulation has been calibrated, the temperature rise process of the operating winding is not entirely the same as the simulation, resulting in a large error. The French power grid has discontinued the use of this temperature measuring device.
② Thermal circuit model calculation method
The thermal circuit model calculation method starts from the perspective of heat transfer, simplifies the heat conduction process inside the transformer using a circuit model, and simplifies the internal heat conduction process of the transformer into a thermoelectric analogy of the circuit model. This allows for the acquisition of a thermal circuit model that directly reflects the physical process, ultimately leading to the calculation formula for the hot spot temperature of the transformer.
③ National Standard Recommended Calculation Method
The mathematical model for the internal temperature distribution of oil-immersed transformer windings given in the national standard GB1094.2-1996 "Temperature Rise of Power Transformers" (equivalent to IEC76.2-1993) is currently the most commonly used model. This model makes the following assumptions:
1) The oil temperature inside the winding increases linearly from bottom to top, regardless of the cooling method.
2) The temperature rise of the winding at any position along the height increases linearly from bottom to top. This straight line is parallel to the oil temperature rise line, and the difference between the two parallel lines is a constant g (g is the difference between the average temperature rise of the winding and the average temperature rise of the oil measured by the resistance method).
3) The temperature rise at the hot spot is higher than the average temperature at the top of the winding because eddy current losses are often concentrated near the upper part of the winding, and special electrical insulation may be required, thus increasing the heat insulation level. Therefore, the temperature difference between the conductor and the oil in this part is higher. Assuming the temperature rise at the hot spot is Hg higher than the temperature at the top of the oil, the hot spot factor H = 1.1~1.5. H is related to the transformer capacity, short-circuit impedance, and winding structure. For distribution transformers, we take 1.1, and for large and medium-sized transformers, we take 1.3. The hot spot factor H takes into account that the temperature rise at the winding end is slightly higher than the linear increase due to the influence of leakage flux.
As shown in Figure 2, hot spot temperature rise = top oil temperature rise + Hg × average oil temperature rise
Figure 2 Temperature model of oil-immersed transformer windings
The winding hotspot temperature calculation model in the national standard can basically reflect the actual heat conduction process of a transformer. However, the model's calculation of the transformer winding hotspot temperature is only a simple estimate, and its model is relatively crude. It does not adequately respond to the nonlinear characteristics of the transformer, and it does not cover all the important factors affecting the distribution of transformer winding hotspot temperature in the thermal circuit. Furthermore, some calculation parameters in the formula are derived empirically, and the selection of the hotspot coefficient has a certain degree of randomness, resulting in weak universality and insufficient accuracy of the calculation results. When applied to the hotspot estimation of actual operating transformers, this leads to a large error compared to the actual situation.
④ Numerical calculation method
The numerical calculation method, based on heat conduction and fluid mechanics theories, establishes a set of differential equations for convective heat transfer within the transformer. These equations include mass conservation equations, momentum conservation equations, and energy conservation equations. By setting boundary conditions using software, the temperature field of the windings and the flow field of the oil region are solved. Since the numerical calculation method solves for the actual thermal and flow fields, the temperature values and locations of hot spots in the transformer windings can be determined.
Disclaimer: This article is a reprint. If it involves copyright issues, please contact us promptly for deletion (QQ: 2737591964 ) . We apologize for any inconvenience.
