An analytical calculation method for hot spot temperature of high-frequency transformer

Abstract

The present invention discloses an analytical calculation method for solving the hotspot temperature according to the thermal equivalent model of a high-frequency transformer. The method includes obtaining the structure and electrical parameters of the high-frequency transformer, obtaining the temperature difference between the hotspot and the environment under rated conditions, and the initial temperature of the primary / secondary windings, and then obtaining the dynamic value of the hotspot temperature of the high-frequency transformer according to the load factor of the actual working condition. The calculation method of the present invention, on the one hand, is accurate in the calculation model, and the calculation method takes into account the nonlinear characteristics of the change of convection thermal resistance with temperature, so that the calculation model is suitable for operating conditions with different temperature conditions and different load factors; on the other hand, the calculation method is simple and the calculation amount is small. The thermal circuit equivalent model of the high-frequency transformer is generally complex, with a high order of differential equations, many calculation nodes, and a large amount of calculation. The calculation method of the present invention can reduce the number of differential equations, and it is not necessary to calculate the core loss of the high-frequency transformer in real time, which provides the possibility of calculating the hotspot temperature of the high-frequency transformer on a microprocessor.

Description

Technical Field

[0001] The invention relates to the field of high-frequency transformers, and in particular to a calculation method for determining a thermal resistance that varies with temperature in a dynamic thermal equivalent model of a high-frequency transformer and a simplified calculation method for solving a hot spot temperature. Background Art

[0002] High-frequency transformers are an indispensable part of building a new power system based on new energy sources, and their life management and optimization design have received extensive attention. Hot spot temperature rise is the main factor restricting the operation of transformers and the main parameter for evaluating the insulation life loss of high-frequency transformers. Therefore, it is very important to study the hot spot temperature of high-frequency transformers.

[0003] The hot spot temperature calculation methods of high-frequency transformers can be roughly divided into three categories, namely, empirical formula, finite element simulation method, and thermal network model method. Among them, the empirical formula method can only calculate the overall temperature rise of the transformer, but cannot obtain the hot spot temperature rise of the transformer. However, the main factor affecting the insulation life of the transformer is the hot spot temperature rise, so this method is only applicable to engineering temperature rise estimation. Under specific load conditions, the finite element simulation method also takes a long time to obtain a final solution. Therefore, the use of numerical methods to predict hot spot temperatures cannot meet the requirements for real-time monitoring of hot spot temperature parameters during the actual operation of the power system. At present, the analytical calculation model of the scheme using the thermal equivalent model is relatively complex, and the method for determining the important process parameters involved in the model is not clear enough, which leads to certain difficulties in practical application. Moreover, parameters such as thermal resistance are nonlinear functions of temperature. The analytical calculation method of the thermal circuit model currently proposed generally regards the thermal resistance parameter as a constant, and does not consider its nonlinear characteristics with temperature. Therefore, it is necessary to find a relatively simple and practical analytical calculation model that can characterize nonlinear parameters to calculate the hot spot temperature of high-frequency transformers. Summary of the invention

[0004] The purpose of the present invention is to propose an analytical calculation method for the hot spot temperature of a high-frequency transformer. The method is based on the thermal circuit equivalent model of the high-frequency transformer, takes into account the nonlinear characteristics of the convection thermal resistance changing with temperature, makes the thermal resistance parameters closer to reality, and simplifies the calculation process. It only needs to extract the load factor and ambient temperature to calculate the dynamic value of the hot spot temperature in real time.

[0005] The technical solution for implementing the present invention is as follows:

[0006] A temperature analytical calculation method based on a high-frequency transformer hot spot model, wherein the hot spot model includes a magnetic core thermal capacitance C core , primary winding heat capacity C pri , secondary winding heat capacity C sec ; Primary winding hot spot temperature T p , secondary winding hot spot temperature Ts , core hot spot temperature T c and ambient temperature T a ; Core loss P core , primary winding loss P pri , secondary winding loss P sec ; Thermal resistance R between the core and the primary winding cp , thermal resistance between the core and the secondary winding R cs , thermal resistance between the core and the environment R ca , thermal resistance between primary winding and environment R pa , thermal resistance between secondary winding and environment R sa .

[0007] The hotspot temperature resolution algorithm consists of the following steps:

[0008] S1: Obtain the known high-frequency transformer related structure and physical parameters;

[0009] S2: Calculate thermal circuit equivalent parameters based on the hot spot equivalent model of the high-frequency transformer;

[0010] S3: Considering the influence of temperature on the convective heat transfer coefficient, the method for determining the convective heat transfer thermal resistance parameters is improved;

[0011] S4: Write down the equations for hot spot temperature based on the thermal circuit model;

[0012] S5: Simplify the hotspot temperature dynamic solution equation and obtain an analytical expression to reduce the amount of calculation while ensuring high accuracy.

[0013] The physical parameters of the S1 medium and high frequency transformer include the characteristic length of the heat dissipation surface, the height of the winding, the volume expansion coefficient, the aerodynamic viscosity, the Prandtl number, the air fluid density, the rated working current of the high frequency transformer, the rated working capacity, the hot spot temperature difference under rated working conditions, the DC and AC equivalent resistance of the high frequency transformer winding, the starting temperature of the hot spot temperature, the core loss coefficient, etc.

[0014] When calculating the parameters of the heat circuit model constructed in S2, the heat dissipation mode of the high-frequency transformer is mainly considered to be convection heat dissipation, wherein the calculation formula of the convection heat transfer thermal resistance is as follows:

[0015]

[0016] Where h c is the convection coefficient, A c is the convection area; the convection heat transfer area of ​​the magnetic core is determined by the following formula:

[0017]

[0018] In the formula, H cis the core height, H r is the winding height, W c is the core width, K 1 is the core area coefficient, which is 0.0069, x is the distance from the winding to the core, and d is the wire diameter; the convection coefficient h c The expression is as follows:

[0019]

[0020] Where ρ is the fluid density, ΔT is the temperature difference, λ is the thermal conductivity, D is the surface characteristic length, g is the gravitational acceleration, and c is the p is the isobaric specific heat capacity, β is the volume expansion coefficient, Pr is the Prandtl number, and μ is the dynamic viscosity, which is determined by the following formula:

[0021]

[0022] In the formula, t and t 0 Respectively represent time, μ 0 t 0 Moment dynamic viscosity.

[0023] The improved convective heat transfer thermal resistance coefficient formula in S3 is as follows:

[0024]

[0025] Where, T hk , T ak They represent the hot spot temperature and ambient temperature under rated load conditions, I represents the current working current, and I k It represents the rated load current, m is an empirical constant, which is equal to 0.8 under natural cooling conditions and equal to 1 under forced air cooling conditions.

[0026] The differential equation in S4 is written as follows using the three-node hot spot temperature:

[0027]

[0028]

[0029]

[0030] The S5 simplifies the hotspot temperature dynamic solution equation and obtains an analytical expression, reducing the amount of calculation while ensuring high accuracy. The obtained hotspot temperature dynamic solution differential equation is as follows:

[0031]

[0032] Where, T x Can represent the hot spot temperature T of the core and primary and secondary windingsc , T p and T s , R x It can be expressed as the thermal resistance R of the core and the primary and secondary windings c , R p and R s ; C x It can be expressed as the heat capacity C between the core and the primary and secondary windings core , C pri and C sec ; R ac and R dc represents AC resistance and DC resistance respectively; K represents load factor; A is a constant related to thermal resistance and AC and DC resistance. The analytical solution of the change of hot spot temperature over time is as follows:

[0033]

[0034] Where, T x_st represents the initial hot spot temperature, and t represents time. According to the analytical formula, substituting the data into the data, the dynamic process of the hot spot temperature changing with time under different load factors can be obtained.

[0035] Compared with the prior art, the beneficial effect of the present invention is that compared with the traditional oil-immersed transformer, it is difficult to determine the hot spot temperature of the high-frequency transformer. On the one hand, it is difficult to measure and monitor, and on the other hand, the working conditions are complex and fluctuate greatly. In order to realize the hot spot temperature modeling and calculation of the high-frequency transformer, it is necessary to solve the difficulties in two aspects. First, the parameters of the thermal equivalent circuit model are very difficult to quantify accurately; second, the analytical calculation model is complex and the calculation amount is large, and it is difficult to realize the dynamic calculation and monitoring of the hot spot model on the underlying microprocessor. Therefore, the advantages of the present invention are mainly concentrated in the following three aspects: 1. The convection heat transfer thermal resistance takes into account the nonlinear characteristics of temperature change, which is closer to the actual operating conditions of the high-frequency transformer, and can more accurately characterize the thermal equivalent model under different temperatures and different load factors; 2. The calculation process is simplified, and the solution model of multiple differential equations is equivalently replaced by the calculation of a differential equation solution model, which greatly reduces the calculation amount; 3. The calculation process is equivalent to replacing the real-time calculation of the core loss, and only two real-time data of the load factor and the ambient temperature are needed to realize the real-time monitoring of the hot spot temperature, and the calculation efficiency is greatly increased. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart for analyzing and calculating the hot spot temperature of a high-frequency transformer.

[0037] Figure 2 This is a structural diagram of a hot spot model of a large-capacity high-frequency transformer.

[0038] Figure 3 for Figure 2 This is a three-dimensional magnetic core and winding structure diagram of a large-capacity high-frequency transformer.

[0039] In the figure:

[0040] C core , C pri , C sec are the core heat capacity, primary winding heat capacity and secondary winding heat capacity respectively; T p , T s , T c , T a They are primary winding hot spot temperature, secondary winding hot spot temperature, magnetic core hot spot temperature and ambient temperature respectively; P core , P pri , P sec They are core loss, primary winding loss, and secondary winding loss respectively; R cp , R cs , R ca , R pa , R sa They are the thermal resistance between the magnetic core and the primary winding, the thermal resistance between the magnetic core and the secondary winding, the thermal resistance between the magnetic core and the environment, the thermal resistance between the primary winding and the environment, and the thermal resistance between the secondary winding and the environment. DETAILED DESCRIPTION

[0041] In order to enable those skilled in the art to better understand and utilize the technical solution of the present invention, the implementation process is described in detail below in conjunction with the specific drawings. The drawings are only for ease of understanding and illustration, and do not represent the actual size, structure and position relationship of the high-frequency transformer. The use of the drawings of the present invention or the contents of the examples of the present invention that are equivalent to the contents of the present invention are all within the protection scope of the present invention.

[0042] The present invention aims to provide an analytical calculation method based on a high-frequency transformer hotspot model, taking into account the nonlinear characteristics of the convection thermal resistance changing with temperature, and can realize real-time monitoring of the hotspot temperature through two data, load coefficient and ambient temperature, thereby improving the calculation efficiency and providing an effective method for the heat dissipation design of the high-frequency transformer.

[0043] The technical solution for implementing the present invention is as follows:

[0044] A temperature analytical calculation method based on a high-frequency transformer hot spot model, wherein the hot spot model includes a magnetic core thermal capacitance C core , primary winding heat capacity C pri , secondary winding heat capacity C sec ; Primary winding hot spot temperature T p , secondary winding hot spot temperature T s , core hot spot temperature T c and ambient temperature T a ; Core loss Pcore , primary winding loss P pri , secondary winding loss P sec ; Thermal resistance R between the core and the primary winding cp , thermal resistance between the core and the secondary winding R cs , thermal resistance between the core and the environment R ca , thermal resistance between primary winding and environment R pa , thermal resistance between secondary winding and environment R sa .

[0045] The hotspot temperature resolution algorithm consists of the following steps:

[0046] S1: Obtain the known high-frequency transformer related structure and physical parameters;

[0047] S2: Calculate thermal circuit equivalent parameters based on the hot spot equivalent model of the high-frequency transformer;

[0048] S3: Considering the influence of temperature on the convective heat transfer coefficient, the method for determining the convective heat transfer thermal resistance parameters is improved;

[0049] S4: Write down the equations for hot spot temperature based on the thermal circuit model;

[0050] S5: Simplify the hotspot temperature dynamic solution equation and obtain an analytical expression to reduce the amount of calculation while ensuring high accuracy.

[0051] The physical parameters of the S1 medium and high frequency transformer include the characteristic length of the heat dissipation surface, the height of the winding, the volume expansion coefficient, the aerodynamic viscosity, the Prandtl number, the air fluid density, the rated working current of the high frequency transformer, the rated working capacity, the hot spot temperature difference under rated working conditions, the DC and AC equivalent resistance of the high frequency transformer winding, the starting temperature of the hot spot temperature, the core loss coefficient, etc.

[0052] When calculating the parameters of the heat circuit model constructed in S2, the heat dissipation mode of the high-frequency transformer is mainly considered to be convection heat dissipation, wherein the calculation formula of the convection heat transfer thermal resistance is as follows:

[0053]

[0054] In the formula, h c is the convection coefficient, A c is the convection area; the convection heat transfer area of ​​the magnetic core is determined by the following formula:

[0055]

[0056] In the formula, H c is the core height, H r is the winding height, W c is the core width, K 1is the core area coefficient, which is 0.0069, x is the distance from the winding to the core, and d is the wire diameter; the convection coefficient h c The expression is as follows:

[0057]

[0058] Where ρ is the fluid density, ΔT is the temperature difference, λ is the thermal conductivity, D is the surface characteristic length, g is the gravitational acceleration, and c is the p is the isobaric specific heat capacity, β is the volume expansion coefficient, Pr is the Prandtl number, and μ is the dynamic viscosity, which is determined by the following formula:

[0059]

[0060] In the formula, t and t 0 Respectively represent time, μ 0 t 0 Moment dynamic viscosity.

[0061] The improved convective heat transfer thermal resistance coefficient formula in S3 is as follows:

[0062]

[0063] Where, T hk , T ak They represent the hot spot temperature and ambient temperature under rated load conditions, I represents the current working current, and I k It represents the rated load current, m is an empirical constant, which is equal to 0.8 under natural cooling conditions and equal to 1 under forced air cooling conditions.

[0064] The differential equation in S4 is written as follows using the three-node hot spot temperature:

[0065]

[0066]

[0067]

[0068] Furthermore, after entering the steady state, the relationship between hotspot temperature, loss and thermal resistance is as follows:

[0069] R pa R cp P pri =R cp (T p -T a )+R pa (T p -T c )

[0070] Rcp R cs R ca P core =R cs R ca (T c -T p )+R cp R ca (T c -T s )+R cp R cs (T c -T a )

[0071] R cs R sa P sec =R sa (T s -T c )+R cs (T s -T a )

[0072] The S5 simplifies the hotspot temperature dynamic solution equation. Taking the primary winding hotspot temperature and the core hotspot temperature as examples, the calculation amount is reduced while ensuring high accuracy. From the steady-state relationship and the improved convection thermal resistance relationship, it can be obtained:

[0073]

[0074] Further, simplify the above formula:

[0075]

[0076] The differential equation for the hotspot temperature dynamics solution is as follows:

[0077]

[0078] In the formula, T x Can represent the hot spot temperature T of the core and primary and secondary windings c , T p and T s , R x It can be expressed as the thermal resistance R of the core and the primary and secondary windings c , R p and R s ; C x It can be expressed as the heat capacity C between the core and the primary and secondary windings core , C pri and C sec ; R ac and R dcThey represent AC resistance and DC resistance respectively; K represents load factor; A is a constant related to thermal resistance and AC and DC resistance.

[0079] Furthermore, the analytical solution of the hotspot temperature variation over time is as follows:

[0080]

[0081] Where, T x_st represents the initial hot spot temperature, and t represents time. According to the analytical formula, the dynamic process of hot spot temperature changing with time under different load factors is obtained by substituting the data.

[0082] High-frequency transformers used in new energy grid-connected converters are generally controlled by microprocessors. Due to the limited computing resources of microprocessors, it is difficult to support relatively complex calculations and solutions. Using the calculation method proposed by the invention, it is only necessary to input the initial hot spot temperature, time constant, winding DC / AC resistance, rated load current and equivalent thermal resistance value of the thermal network before normal operation, and then sample the ambient temperature and load factor in real time according to the actual working conditions to quickly calculate the hot spot temperature of the current high-frequency transformer for real-time monitoring and protection.

Claims

1. A method for calculating the hot spot temperature of a high-frequency transformer is based on the hot spot equivalent model of the high-frequency transformer. The nonlinear characteristics of the convection thermal resistance changing with temperature are considered to make the thermal resistance parameters closer to the actual operating conditions. At the same time, the calculation process is simplified. The dynamic value of the hot spot temperature can be calculated in real time by extracting the load factor and the ambient temperature. The hotspot model includes the core thermal capacitance C core , primary winding heat capacity C pri , secondary winding heat capacity C sec ; Primary winding hot spot temperature T p , secondary winding hot spot temperature T s , core hot spot temperature T c and ambient temperature T a ; Core loss P core , primary winding loss P pri , secondary winding loss P sec ; Thermal resistance R between the core and the primary winding cp , thermal resistance between the core and the secondary winding R cs , thermal resistance between the core and the environment R ca , thermal resistance between primary winding and environment R pa , thermal resistance between secondary winding and environment R sa ; The temperature analytical calculation method based on the hot spot model The following steps are involved: S1: Obtain known physical parameters of the high-frequency transformer; S2: Calculate the thermal circuit equivalent parameters based on the hot spot equivalent model of the high-frequency transformer, considering that the heat dissipation method of the high-frequency transformer is convection heat dissipation, where the calculation formula of the convection heat transfer thermal resistance is as follows: In the formula, h c is the convection coefficient, A c is the convection area; the convection heat transfer area of ​​the magnetic core is determined by the following formula: In the formula, H c is the core height, H r is the winding height, W c is the core width, K 1 is the core area coefficient, which is 0.0069, x is the distance from the winding to the core, and d is the wire diameter; the convection heat transfer coefficient h c The expression is as follows: Where ρ is the fluid density, ΔT is the temperature difference, λ is the thermal conductivity, D is the surface characteristic length, g is the gravitational acceleration, and c is the p is the isobaric specific heat capacity, β is the volume expansion coefficient, Pr is the Prandtl number, and μ is the dynamic viscosity, which is determined by the following formula: In the formula, t and t 0 Respectively represent time, μ 0 t 0 Momentary dynamic viscosity; S3: Considering the influence of temperature on the convection heat transfer coefficient, the method for determining the convection heat transfer thermal resistance parameters is improved; S4: Write down the equations for hot spot temperature based on the thermal circuit model; S5: Simplify the hotspot temperature dynamic solution equation and obtain an analytical expression to reduce the amount of calculation while ensuring high accuracy.

2. According to the steps of a high-frequency transformer hot spot temperature analysis method described in claim 1, It is characterized in that The physical parameters in S1 include the characteristic length of the heat dissipation surface, the height of the winding, the volume expansion coefficient, the aerodynamic viscosity, the Prandtl number, the air fluid density, the rated working current of the high-frequency transformer, the rated working capacity, the hot spot temperature difference under rated working conditions, the DC and AC equivalent resistances of the high-frequency transformer winding, the starting temperature of the hot spot temperature, and the core loss coefficient.

3. According to the steps of the method for analyzing the hot spot temperature of a high-frequency transformer as described in claim 1, It is characterized in that The improved convective heat transfer thermal resistance coefficient formula in S3 is as follows: Where, T hk , T ak They represent the hot spot temperature and ambient temperature under rated load conditions, I represents the current working current, and I k It represents the rated load current, m is an empirical constant, which is equal to 0.8 under natural cooling conditions and equal to 1 under forced air cooling conditions.

4. According to the steps of a high-frequency transformer hot spot temperature analysis method as described in claim 1, It is characterized in that The differential equation in S4 is written as follows using the three-node hot spot temperature:

5. According to the steps of the method for analyzing the hot spot temperature of a high-frequency transformer as described in claim 1, It is characterized in that The S5 simplifies the hotspot temperature dynamic solution equation and obtains an analytical expression, reducing the amount of calculation while ensuring high accuracy. The obtained hotspot temperature dynamic solution differential equation is as follows: Where, T x Can represent the hot spot temperature T of the core and primary and secondary windings c , T p and T s , R x It can be expressed as the thermal resistance R of the core and the primary and secondary windings c , R p and R s ; C x It can be expressed as the heat capacity C between the core and the primary and secondary windings core , C pri and C sec ; R ac and R dc They represent AC resistance and DC resistance respectively; K represents load factor; A is a constant related to thermal resistance and AC and DC resistance.

6. According to the steps of the method for analyzing the hot spot temperature of a high-frequency transformer as described in claim 1, It is characterized in that The analytical solution of the differential equation in S6 is as follows: Where, T x_st represents the initial hot spot temperature, and t represents time. According to the analytical formula, by substituting the data, the dynamic process of the hot spot temperature changing with time under different load factors can be obtained.

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