CN113361165B - Battery pack temperature field online acquisition method based on distributed parameter thermal resistance model - Google Patents

Battery pack temperature field online acquisition method based on distributed parameter thermal resistance model Download PDF

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CN113361165B
CN113361165B CN202110626743.XA CN202110626743A CN113361165B CN 113361165 B CN113361165 B CN 113361165B CN 202110626743 A CN202110626743 A CN 202110626743A CN 113361165 B CN113361165 B CN 113361165B
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CN113361165A (en
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吕超
朱世怀
宋彦孔
王立欣
葛亚明
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Harbin Institute of Technology
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Abstract

A battery pack temperature field online acquisition method based on a distributed parameter thermal resistance model belongs to the field of lithium ion battery pack thermal management. The invention aims to solve the problems of poor applicability and low precision of a method for calculating a temperature field on line. The method comprises the steps of dividing the whole battery pack into a plurality of cubic areas, calculating the thermal resistance between every two adjacent cubic areas by adopting a Fourier heat conduction law, calculating the average value of the thermal resistance of nodes in the corresponding cubic areas for the thermal resistance between each cubic area on the outer surface of the battery pack and the external environment to obtain a steady state or transient state equation of each cubic area, and establishing a steady state space equation set of the whole battery pack or a transient state space equation set of the whole battery pack according to the steady state or transient state equation of each cubic area to obtain a temperature field of the battery pack. It is used to obtain the battery temperature field.

Description

Battery pack temperature field online acquisition method based on distributed parameter thermal resistance model
Technical Field
The invention relates to an online calculation method of a temperature field of a lithium ion battery pack, belonging to the field of thermal management of the lithium ion battery pack.
Background
The lithium ion battery is widely applied to energy storage units of new energy automobiles due to the advantages of high voltage, high power density, high energy density, long cycle life and the like.
The continuous development of new energy vehicles puts strict requirements on battery thermal management systems. Because the battery system is a complex distributed parameter system, the temperature change has great hysteresis, and the internal structure of the automobile limits the use of temperature measuring equipment, an efficient and accurate thermal model of the battery system is needed to calculate the temperature field data of the battery system on line.
At present, the most accurate method for calculating the battery temperature field is finite element simulation, however, the calculation scale of the finite element simulation is huge, the calculation time is too long, and the finite element simulation cannot be used for calculating the temperature field on the automobile on line. Compared with finite element simulation, the application range and the precision of many online temperature field calculation methods which are proposed at present are severely limited.
Disclosure of Invention
The invention aims to solve the problems of poor applicability and low precision of a method for calculating a temperature field on line, and provides a method for acquiring the temperature field of a battery pack on line based on a distributed parameter thermal resistance model.
The battery pack temperature field online acquisition method based on the distributed parameter thermal resistance model comprises the following steps:
step 1, dividing a battery pack into a node map consisting of a plurality of nodes by adopting finite element software, and obtaining the heat flux density between each node on the outer surface of the battery pack and the external environment and the temperature of each node on the outer surface of the battery pack;
step 2, obtaining the thermal resistance of each node on the outer surface of the battery pack according to the heat flux density between each node on the outer surface of the battery pack and the external environment, the temperature of each node on the outer surface of the battery pack and a thermal resistance formula;
step 3, establishing a three-dimensional region model of the battery pack, wherein the battery pack is divided into a plurality of cubic regions in the model, the cubic regions comprise cubic regions inside the battery pack and cubic regions on the outer surface of the battery pack, and the heat transfer area between every two adjacent cubic regions and the heat transfer area between each cubic region on the outer surface of the battery pack and the external environment are obtained;
step 4, obtaining the thermal resistance between each cubic region in the battery pack and the cubic regions in the adjacent 6 directions and the thermal resistance between each cubic region on the outer surface of the battery pack and the adjacent cubic region according to the heat transfer area between every two adjacent cubic regions, and averaging the thermal resistance of nodes in each cubic region on the outer surface of the battery pack to obtain the thermal resistance between each cubic region on the outer surface of the battery pack and the external environment;
step 5, establishing a steady state or transient state equation of each cubic region according to the heat transfer area between every two adjacent cubic regions obtained in the step 3, the heat transfer area between each cubic region on the outer surface of the battery pack and the external environment and all the heat resistances obtained in the step 4;
and 6, obtaining a steady state space equation set of the whole battery pack or a transient state space equation set of the whole battery pack according to the steady state or transient state equation set of each cubic region obtained in the step 5, obtaining a battery pack temperature column vector under the transient state according to the transient state space equation set of the whole battery pack, and obtaining a steady state battery pack temperature column vector according to the steady state space equation set of the whole battery pack.
Preferably, in step 2, the thermal resistance of each node is expressed as:
Figure BDA0003101551630000021
in the formula, T1Temperature, T, of each node on the outer surface of the battery pack simulated by the finite element software0The external environment temperature is shown, W represents the heat flow density between each node of the outer surface of the battery pack and the external environment simulated by the finite element software, and R1 is the thermal resistance of each node.
Preferably, in step 4, the thermal resistance between each cubic region inside the battery pack and the adjacent cubic regions in the 6 directions and the thermal resistance between each cubic region on the outer surface of the battery pack and the adjacent cubic region are obtained according to the heat transfer area between each two adjacent cubic regions and the fourier heat conduction law, and the nodes in each cubic region on the outer surface of the battery pack are averaged to serve as the thermal resistance between each cubic region on the outer surface of the battery pack and the external environment.
Preferably, the fourier thermal conduction law is expressed as:
Figure BDA0003101551630000022
wherein λ is the thermal conductivity coefficient of the battery material, l is the distance between the center points of two adjacent cubic regions, S is the heat transfer area between two adjacent cubic regions, and R2 is the thermal resistance between each two adjacent cubic regions.
Preferably, in step 5, the equation of state of the transient state of each cubic region is expressed as:
Figure BDA0003101551630000023
in the formula, mi,j,kC is the mass of the cubic region, R is the specific heat capacity of the cubic region, R is R1 or R2, R is the thermal resistance of the cubic region in 6 directions, S is the heat transfer area of the cubic region in 6 directions, V is the volume of the corresponding node of the cubic region, Q is the heating power density of the cubic region, T is the time, and delta T is the timei，j，k(t) is a temperature change amount of the cubic region between time t and time t +1, and (i, j, k) is coordinates of the corresponding cubic region, and S and R parameters denoted by (i +1, j, k), (i-1, j, k), (i, j +1, k), (i, j-1, k), (i, j, k +1), (i, j, k-1) at lower corners are a heat transfer area and a heat resistance in 6 directions of the region having the coordinates (i, j, k), respectively;
transform equation 3 to:
Figure BDA0003101551630000031
in the formula (I), the compound is shown in the specification,
Figure BDA0003101551630000032
the steady state equation for each cubic region is expressed as:
Figure BDA0003101551630000033
wherein:
Figure BDA0003101551630000034
preferably, in step 6, the transient state space equation system of the whole battery pack is expressed as:
Figure BDA0003101551630000035
wherein H is a heat transfer coefficient matrix, T (T) is a battery temperature column vector at time T, D is a heat generation distribution matrix, T (T +1) is a battery temperature column vector at time T +1, Δ T is a time step between time T +1 and time T,
T(t)＝[T0,0,0(t) T0,0,1(t) … Ti,j,k(t)…]T，Ti,j,k(t) is the temperature of the cubic region with coordinates (i, j, k) at time t,
Figure BDA0003101551630000036
Figure BDA0003101551630000037
preferably, in step 6, the steady state space equation set of the whole battery pack is expressed as:
0 is DQ + HE formula 7,
where H is the heat transfer coefficient matrix, E is the steady state battery pack temperature column vector, and E ═ E0,0,0 E0,0,1 … Ei,j,k…]T，Ei,j,kIs the steady state temperature of the cubic region with coordinates (i, j, k), D is the heat generation distribution matrix, and Q is the heat generation power density of the cubic region.
The invention has the beneficial effects that:
the whole battery pack is divided into a plurality of cubic areas, the thermal resistance between every two adjacent cubic areas can be calculated by adopting the Fourier heat conduction law, the thermal resistance between each cubic area on the outer surface of the battery pack and the external environment can be calculated by averaging the thermal resistances of nodes in the corresponding cubic areas, so that the thermal resistance of the whole battery pack can be calculated by adopting the method, a steady state or transient state equation of each cubic area is obtained, and a steady state space equation set of the whole battery pack or a transient state space equation set of the whole battery pack is established according to the steady state or transient state equation of each cubic area, so that the temperature field of the battery pack is obtained. According to the method and the device, the battery pack temperature field with unknown adjacent moments can be obtained according to the known battery pack temperature field. The battery pack temperature field obtaining method is simple and high in applicability; compared with finite element simulation, the method has the advantages of small calculation error and greatly improved calculation speed.
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FIG. 1 is a flow chart of a battery pack temperature field online acquisition method based on a distributed parameter thermal resistance model;
FIG. 2 is a diagram of a battery partitioned into a plurality of cubic regions, wherein each dot in FIG. 2 represents each cubic region;
FIG. 3 is a graph of the contact area of two adjacent cubic areas;
FIG. 4 is a three-dimensional model diagram of a battery pack consisting of 5 battery cells;
fig. 5 is a division view of each battery cell in the three-dimensional model of the battery pack in fig. 4 into a plurality of cubic regions, with a plurality of dots in fig. 5 being the center points of each cubic region;
FIG. 6 is a node diagram of a battery pack divided into a plurality of nodes by using finite element software;
FIG. 7 is a graph of the thermal resistance distribution of each node in FIG. 6;
FIG. 8 is a cut-away view of one of the faces of FIG. 7;
FIG. 9 is a cell monomer model;
FIG. 10 is a battery model;
fig. 11 is a comparison graph of battery cell temperature simulation, in which reference numeral 1 represents a temperature simulation result of the distributed parameter thermal resistance model on the line2 in fig. 9, reference numeral 2 represents a temperature simulation result of a finite element simulation on the line2 in fig. 9, reference numeral 3 represents a temperature simulation result of the distributed parameter thermal resistance model on the line1 in fig. 9, reference numeral 4 represents a temperature simulation result of a finite element simulation on the line1 in fig. 9, reference numeral 5 represents a temperature simulation result of a finite element simulation on the line3 in fig. 9, and reference numeral 6 represents a temperature simulation result of the distributed parameter thermal resistance model on the line3 in fig. 9;
fig. 12 is a comparison graph of battery pack temperature simulation, in which reference numeral 7 represents the temperature simulation result of the finite element simulation on the line1 in fig. 10, reference numeral 8 represents the temperature simulation result of the distributed parametric thermal resistance model on the line1 in fig. 10, reference numeral 9 represents the temperature simulation result of the distributed parametric thermal resistance model on the line3 in fig. 10, reference numeral 10 represents the temperature simulation result of the finite element simulation on the line3 in fig. 10, reference numeral 11 represents the temperature simulation result of the distributed parametric thermal resistance model on the line2 in fig. 10, and reference numeral 12 represents the temperature simulation result of the finite element simulation on the line2 in fig. 10.
Detailed Description
The first embodiment is as follows: the embodiment is described with reference to fig. 1 to 3, and the method for acquiring a battery pack temperature field on line based on a distributed parameter thermal resistance model according to the embodiment includes the following steps:
step 1, dividing a battery pack into a node map consisting of a plurality of nodes by adopting finite element software, and obtaining the heat flux density between each node on the outer surface of the battery pack and the external environment and the temperature of each node on the outer surface of the battery pack;
step 2, obtaining the thermal resistance of each node on the outer surface of the battery pack according to the heat flux density between each node on the outer surface of the battery pack and the external environment, the temperature of each node on the outer surface of the battery pack and a thermal resistance formula;
step 3, establishing a three-dimensional region model of the battery pack, wherein the battery pack is divided into a plurality of cubic regions in the model, the cubic regions comprise cubic regions inside the battery pack and cubic regions on the outer surface of the battery pack, and the heat transfer area between every two adjacent cubic regions and the heat transfer area between each cubic region on the outer surface of the battery pack and the external environment are obtained;
step 4, obtaining the thermal resistance between each cubic region in the battery pack and the cubic regions in the adjacent 6 directions and the thermal resistance between each cubic region on the outer surface of the battery pack and the adjacent cubic region according to the heat transfer area between every two adjacent cubic regions, and averaging the thermal resistance of nodes in each cubic region on the outer surface of the battery pack to obtain the thermal resistance between each cubic region on the outer surface of the battery pack and the external environment;
step 5, establishing a steady state or transient state equation of each cubic region according to the heat transfer area between every two adjacent cubic regions obtained in the step 3, the heat transfer area between each cubic region on the outer surface of the battery pack and the external environment and all the heat resistances obtained in the step 4;
and 6, obtaining a steady state space equation set of the whole battery pack or a transient state space equation set of the whole battery pack according to the steady state or transient state equation set of each cubic region obtained in the step 5, obtaining a battery pack temperature column vector under the transient state according to the transient state space equation set of the whole battery pack, and obtaining a steady state battery pack temperature column vector according to the steady state space equation set of the whole battery pack.
In this embodiment, fig. 6 is a node diagram drawn by dividing the battery pack into a plurality of nodes and extracting nodes on the surface of the battery pack by using the finite element software mentioned in the step one. The thermal resistance between the cubic region divided inside the battery pack and the adjacent cubic region is well calculated by adopting formula 2, and for each cubic region on the outer surface of the battery pack, the average value of the thermal resistances of all nodes in the region is used as the thermal resistance between the corresponding cubic region on the outer surface and the adjacent external environment. In the first embodiment, the thermal resistance of the positive and negative electrodes of the battery in fig. 6 is not included. The difference in the gradation depths in fig. 7 and 8 represents the difference in the thermal resistance values.
In this embodiment, the transient battery pack temperature column vector refers to a transient battery pack temperature field, and the steady battery pack temperature column vector refers to a steady battery pack temperature field; in addition, the battery temperature column vector in the transient state refers to T (T +1) in equation 6, and the equation of equation 6 is to find the battery temperature column vector at an adjacent unknown time according to the battery temperature column vector at the known time. The steady state battery temperature column vector is E in equation 7, and because it is steady state, the battery temperature column vector is time independent.
The second embodiment is as follows: in this embodiment, as for the method for acquiring a battery pack temperature field on line based on a distributed parameter thermal resistance model described in the first embodiment, in step 2, the thermal resistance of each node is represented as:
Figure BDA0003101551630000061
in the formula, T1Temperature, T, of each node on the outer surface of the battery pack simulated by the finite element software0The external environment temperature is shown, W represents the heat flow density between each node of the outer surface of the battery pack and the external environment simulated by the finite element software, and R1 is the thermal resistance of each node.
In this embodiment, the reason why the decision formula of selecting formula 1 to calculate the thermal resistance of each node instead of selecting the thermal resistance is to calculate the thermal resistance of the node is as follows: selecting a certain constant heating power, respectively performing steady-state simulation at different cooling fluid inlet flow rates, respectively extracting the heat flux density on the surface of the battery and the temperature parameters of the surface of the battery and the external atmospheric environment after simulation, and utilizing the definition formula of thermal resistance
Figure BDA0003101551630000062
And calculating the thermal resistance parameter between the surface of the battery and the external atmospheric environment. Determined by the thermal resistance
Figure BDA0003101551630000063
It can be known that the value of the thermal resistance is independent of the temperature, and since the structure of the battery cooling system is not changed during the use, it can be concluded that the change of the thermal resistance of the battery surface to the outside in the battery pack is only related to the flow rate of the cooling fluid inlet. Therefore, the thermal resistance parameters under different inlet flow rates can be summarized into a table for storage, and the corresponding thermal resistance parameters are called according to the inlet flow rates in the calculation process, so that the on-line operation function of the finite element simulation can be realized.
The third concrete implementation mode: in step 4, according to a heat transfer area between every two adjacent cubic areas and a fourier heat conduction law, heat resistance between each cubic area inside the battery pack and the adjacent cubic areas in 6 directions and heat resistance between each cubic area on the outer surface of the battery pack and the adjacent cubic area are obtained, and an average value of nodes in each cubic area on the outer surface of the battery pack is obtained to be used as the heat resistance between each cubic area on the outer surface of the battery pack and the external environment.
In this embodiment, the thermal resistances between the cubic region on the outer surface of the battery pack and the adjacent external environment are all determined by the average value of the nodes in the cubic region corresponding to the outer surface, and for the outer surface of the battery pack in fig. 8, the thermal resistance between a certain cubic region on the face and the external environment is 1-direction thermal resistance, the thermal resistance between a certain cubic region on the side line and the external environment is 2-direction thermal resistance, and the thermal resistance between a certain cubic region on the apex and the external environment is 3-direction thermal resistance.
The fourth concrete implementation mode: in this embodiment, for the method for acquiring the temperature field of the battery pack on line based on the distributed parameter thermal resistance model described in the third embodiment, the fourier transform law of thermal conductivity is expressed as:
Figure BDA0003101551630000071
wherein λ is the thermal conductivity coefficient of the battery material, l is the distance between the center points of two adjacent cubic regions, S is the heat transfer area between two adjacent cubic regions, and R2 is the thermal resistance between each two adjacent cubic regions.
The fifth concrete implementation mode: in this embodiment, for the method for acquiring a battery pack temperature field on line based on a distributed parameter thermal resistance model in the fourth embodiment, in step 5, a transient state equation of each cubic region is expressed as:
Figure BDA0003101551630000072
in the formula, mi,j,kC is the mass of the cubic region, R is the specific heat capacity of the cubic region, R is R1 or R2, R is the thermal resistance of the cubic region in 6 directions, S is the heat transfer area of the cubic region in 6 directions, V is the volume of the corresponding node of the cubic region, Q is the heating power density of the cubic region, T is the time, and delta T is the timei，j，k(t) is a temperature change amount of the cubic region between time t and time t +1, and (i, j, k) is coordinates of the corresponding cubic region, and S and R parameters denoted by (i +1, j, k), (i-1, j, k), (i, j +1, k), (i, j-1, k), (i, j, k +1), (i, j, k-1) at lower corners are a heat transfer area and a heat resistance in 6 directions of the region having the coordinates (i, j, k), respectively;
transform equation 3 to:
Figure BDA0003101551630000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003101551630000082
the steady state equation for each cubic region is expressed as:
Figure BDA0003101551630000083
wherein:
Figure BDA0003101551630000084
in this embodiment, an example of selecting the coordinate axis direction and the origin is shown in fig. 2, and fig. 2 is a three-dimensional region model of the battery cell, which is created, and divides the battery pack into a plurality of cubic regions, where the plurality of cubic regions include a cubic region into which the battery case is divided, a cubic region into which the battery interior is divided, and 2 cubic regions into which the positive and negative electrodes of 2 batteries are respectively divided. Each dot in fig. 2 represents each of the cubic regions into which the battery case is divided, each of the cubic regions into which the battery inside is divided, and the cubic regions representing the positive and negative electrodes of the battery are respectively represented by three gray scale depths in fig. 2. The values of the cubic area number of the battery in three directions can be selected according to actual conditions.
Fig. 3 is a graph of the distance between the center points of two adjacent cubic regions and the contact area, and the thermal resistance R2 between each two adjacent cubic regions can be obtained according to equation 2.
Fig. 4 is a battery pack three-dimensional node model assembled according to the established single battery models. Taking a battery pack consisting of 5 batteries as an example, a three-dimensional model thereof is shown in fig. 4; the three-dimensional region model is shown in fig. 5, and the gray dots in fig. 5 represent the center point of each cubic region. The adjacent batteries are isolated by the insulating plate, and the thermal resistance and the heat transfer area between the battery areas corresponding to the two sides of the insulating plate are determined.
Fig. 6 is a node diagram of a battery pack obtained by finite element simulation, and fig. 7 is a thermal resistance distribution diagram of each node. Fig. 8 is a view taken through one of the faces of fig. 7, and the following describes a process of determining the thermal resistance between each cubic region of the outer surface of the battery pack and the external environment: fig. 8 shows a node on one surface of the battery pack and corresponding thermal resistance distribution, and for obtaining the thermal resistance between each cubic region on the outer surface of the battery and the external environment established by the distributed parameter thermal resistance model, the average value of the thermal resistances of the nodes established by finite element software included in each cubic region on the outer surface of the battery is taken as the thermal resistance between each cubic region and the external environment.
The sixth specific implementation mode: in this embodiment, for the method for acquiring a temperature field of a battery pack based on a distributed parameter thermal resistance model in the fifth embodiment, in step 6, a transient state space equation set of the whole battery pack is expressed as:
Figure BDA0003101551630000091
wherein H is a heat transfer coefficient matrix, T (T) is a battery temperature column vector at time T, D is a heat generation distribution matrix, T (T +1) is a battery temperature column vector at time T +1, Δ T is a time step between time T +1 and time T,
T(t)＝[T0,0,0(t) T0,0,1(t) … Ti,j,k(t)…]T，Ti,j,k(t) is the temperature of the cubic region with coordinates (i, j, k) at time t,
Figure BDA0003101551630000092
Figure BDA0003101551630000093
in the present embodiment, T (T +1) is the temperature field of the battery pack to be determined in the first embodiment, and T (T +1) is also referred to as a battery pack temperature sequence vector at time T +1 because the temperature field of the battery pack changes with time in a transient state.
The seventh embodiment: in this embodiment, as for the method for acquiring a temperature field of a battery pack on line based on a distributed parameter thermal resistance model in the first embodiment, in step 6, a steady state space equation set of the whole battery pack is expressed as:
0 is DQ + HE formula 7,
where H is the heat transfer coefficient matrix, E is the steady state battery pack temperature column vector, and E ═ E0,0,0 E0,0,1 … Ei,j,k …]T，Ei,j,kIs the steady state temperature of the cubic region with coordinates (i, j, k), D is the heat generation distribution matrix, and Q is the heat generation power density of the cubic region.
In this embodiment, E in equation 7 is the temperature field of the battery pack to be determined in the first embodiment, and the battery pack temperature field is constant in the steady state.
The specific implementation mode is eight: in this embodiment, as to the method for acquiring a battery pack temperature field on line based on a distributed parameter thermal resistance model in the first embodiment, step 3 further includes: representing the anode and the cathode of the battery pack by a cubic area respectively, and obtaining the heat transfer area between the anode and the cathode of the battery pack represented by each cubic area and the adjacent cubic area and the heat transfer area between the anode and the cathode of the battery pack represented by each cubic area and the external environment;
step 4 also includes: obtaining the thermal resistance between the anode and the cathode of the battery pack represented by each cubic region and 1 adjacent cubic region according to the heat transfer area between the anode and the cathode of the battery pack represented by each cubic region and the adjacent cubic region, and averaging the thermal resistance of nodes in the anode and the cathode of the battery pack represented by each cubic region to obtain the thermal resistance between the anode and the cathode of the battery pack represented by each cubic region and the external environment in 5 directions;
step 5 also includes: establishing a steady state or transient state equation of the anode and the cathode of the battery pack for the anode and the cathode of the battery pack represented by the cubic area according to the heat transfer area obtained in the step 3 and the thermal resistance obtained in the step 4;
the step 6 specifically comprises the following steps: according to the steady state or transient state equation of each cubic area of the battery pack and the steady state or transient state equation of the anode and the cathode of the battery pack, a steady state space equation set or a transient state space equation set of the whole battery pack is obtained, battery pack temperature column vectors at all moments in a transient state are obtained according to the transient state space equation set of the whole battery pack, and a steady state battery pack temperature field is obtained according to the steady state space equation set of the whole battery pack.
In this embodiment, the thermal resistances of the positive and negative electrodes of the battery pack may be included in this embodiment.
The specific implementation method nine: in this embodiment, for the method for acquiring a temperature field of a battery pack based on a distributed parameter thermal resistance model described in the eighth embodiment, the process of thermal resistance between the positive and negative electrodes of the battery pack and the external environment in 5 directions, which is represented by each cubic region, is as follows:
the thermal resistances of the nodes in each cubic region representing the positive and negative poles of the battery pack were averaged as the thermal resistances between the positive and negative poles of the battery pack represented by each cubic region and the external environments in the adjacent 5 directions.
The detailed implementation mode is ten: in this embodiment, for the method for acquiring a temperature field of a battery pack on line based on a distributed parameter thermal resistance model according to the eighth embodiment, the thermal resistance between the positive and negative electrodes of the battery pack and the adjacent cubic region, which are represented by each cubic region, is obtained according to the fourier transform law of thermal conductivity.
The effect of this application is verified:
to verify the effectiveness of the proposed method, the model was used in the simulation of a cell model and a battery model, respectively, fig. 9 is a cell model, fig. 10 is a battery model, the size of the battery is 148mm long, 92mm wide and 147mm high, and the heating power of the battery is 8 × 104W/m3And 1X 105W/m3The cooling liquid inlet flow rates were 1m/s and 0.5m/s, respectively, and the atmospheric temperature and the cell initial temperature were 300K. Compiling distributed parameter thermal resistance model simulation codes by utilizing Matlab, calculating steady-state temperatures of the two models, and comparing with the results of finite element simulation, wherein FIG. 11 is a comparison graph of temperatures obtained by compiling a single battery multi-node thermal model by utilizing Matlab and simulating the single battery by adopting finite elements, FIG. 12 is a comparison graph of temperatures obtained by compiling a battery multi-node thermal model by utilizing Matlab and simulating the battery by adopting finite elements,
the maximum relative error (absolute error/temperature rise at point) is shown in the following table:
line1 line2 line3
battery monomer 4.8％ 2.0％ 1.7％
Battery pack 9.8％ 3.8％ 2.4％
At the calculation speed, the cell and pack calculation times were 0.013s and 0.048s, respectively. The result shows that the distributed parameter thermal resistance model meets the requirement of on-line calculation.

Claims (8)

1. The battery pack temperature field online acquisition method based on the distributed parameter thermal resistance model is characterized by comprising the following steps of:
step 1, dividing a battery pack into a node map consisting of a plurality of nodes by adopting finite element software, and obtaining the heat flux density between each node on the outer surface of the battery pack and the external environment and the temperature of each node on the outer surface of the battery pack;
step 2, obtaining the thermal resistance of each node on the outer surface of the battery pack according to the heat flux density between each node on the outer surface of the battery pack and the external environment, the temperature of each node on the outer surface of the battery pack and a thermal resistance formula;
step 3, establishing a three-dimensional region model of the battery pack, wherein the battery pack is divided into a plurality of cubic regions in the model, the cubic regions comprise cubic regions inside the battery pack and cubic regions on the outer surface of the battery pack, and the heat transfer area between every two adjacent cubic regions and the heat transfer area between each cubic region on the outer surface of the battery pack and the external environment are obtained;
step 4, obtaining the thermal resistance between each cubic region in the battery pack and the cubic regions in the adjacent 6 directions and the thermal resistance between each cubic region on the outer surface of the battery pack and the adjacent cubic region according to the heat transfer area between every two adjacent cubic regions, and averaging the thermal resistance of nodes in each cubic region on the outer surface of the battery pack to obtain the thermal resistance between each cubic region on the outer surface of the battery pack and the external environment;
step 5, establishing a steady state or transient state equation of each cubic region according to the heat transfer area between every two adjacent cubic regions obtained in the step 3, the heat transfer area between each cubic region on the outer surface of the battery pack and the external environment and all the heat resistances obtained in the step 4;
step 6, obtaining a steady state space equation set of the whole battery pack or a transient state space equation set of the whole battery pack according to the steady state or transient state equation set of each cubic region obtained in the step 5, obtaining a battery pack temperature column vector under the transient state according to the transient state space equation set of the whole battery pack, and obtaining a steady state battery pack temperature column vector according to the steady state space equation set of the whole battery pack;
in step 2, the thermal resistance of each node is represented as:
Figure FDA0003520908760000011
in the formula, T1Temperature, T, of each node on the outer surface of the battery pack simulated by the finite element software0Representing the temperature of the external environment, W representing the heat flow density between each node on the outer surface of the battery pack and the external environment simulated by the finite element software, and R1 being the thermal resistance of each node;
in step 5, the transient state equation of each cubic region is expressed as:
Figure FDA0003520908760000021
in the formula, mi,j,kC is the mass of the cubic region, R is the specific heat capacity of the cubic region, R is R1 or R2, R is the thermal resistance of the cubic region in 6 directions, S is the heat transfer area of the cubic region in 6 directions, V is the volume of the corresponding node of the cubic region, Q is the heating power density of the cubic region, T is the time, and delta T is the timei,j,k(t) is the cube region at time t and time t +1The temperature change amount between (i, j, k) is the coordinate of the corresponding cubic region, and the S and R parameters with lower corner labels of (i +1, j, k), (i-1, j, k), (i, j +1, k), (i, j-1, k), (i, j, k +1), (i, j, k-1) are the heat transfer area and the thermal resistance in 6 directions of the region with the coordinate of (i, j, k), respectively;
transform equation 3 to:
Figure FDA0003520908760000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003520908760000023
the steady state equation for each cubic region is expressed as:
0＝Vi,j,kQi,j,k-Ji,j,kTi,j,k+Si+1,j,kRi+1,j,kTi+1,j,k+Si-1,j,kRi-1,j,kTi-1,j,k+Si,j+1,kRi,j+1, kTi,j+1,k+Si,j-1,kRi,j-1,kTi,j-1,k+Si,j,k+1Ri,j,k+1Ti,j,k+1+Si,j,k-1Ri,j,k-1Ti,j,k-1equation 5, where:
Ji,j,k＝Si+1,j,kRi+1,j,k+Si-1,j,kRi-1,j,k+Si,j+1,kRi,j+1,k+Si,j-1,kRi,j-1,k+Si,j,k+1Ri,j,k+1+Si,j,k- 1Ri,j,k-1。
2. the method for acquiring the battery pack temperature field on line based on the distributed parameter thermal resistance model according to claim 1, wherein in the step 4, the thermal resistance between each cubic region inside the battery pack and the cubic regions in the adjacent 6 directions and the thermal resistance between each cubic region on the outer surface of the battery pack and the adjacent cubic region are acquired according to the heat transfer area between each two adjacent cubic regions and the Fourier heat conduction law, and the node in each cubic region on the outer surface of the battery pack is averaged to be used as the thermal resistance between each cubic region on the outer surface of the battery pack and the external environment.
3. The method for acquiring the temperature field of the battery pack on line based on the distributed parameter thermal resistance model according to claim 2,
the fourier thermal conduction law is expressed as:
Figure FDA0003520908760000031
wherein λ is the thermal conductivity coefficient of the battery material, l is the distance between the center points of two adjacent cubic regions, S is the heat transfer area between two adjacent cubic regions, and R2 is the thermal resistance between each two adjacent cubic regions.
4. The method for acquiring the temperature field of the battery pack on line based on the distributed parameter thermal resistance model according to claim 3, wherein in the step 6, the transient state space equation set of the whole battery pack is expressed as:
Figure FDA0003520908760000032
wherein H is a heat transfer coefficient matrix, T (T) is a battery temperature column vector at time T, D is a heat generation distribution matrix, T (T +1) is a battery temperature column vector at time T +1, Δ T is a time step between time T +1 and time T,
T(t)＝[T0,0,0(t)T0,0,1(t)…Ti,j,k(t)…]T，Ti,j,k(t) is the temperature of the cubic region with coordinates (i, j, k) at time t,
Figure FDA0003520908760000033
5. the method for acquiring the temperature field of the battery pack on line based on the distributed parameter thermal resistance model according to claim 1, wherein in the step 6, a steady state space equation set of the whole battery pack is expressed as:
0 DQ + he (t) formula 7,
wherein H is a heat transfer coefficient matrix, E is a steady-state battery pack temperature column vector, and E (t) [ E ]0,0,0(t)E0,0,1(t)…Ei,j,k(t)…]T，Ei,j,kAnd (t) is the steady-state temperature of the cubic region with coordinates (i, j, k) at the time t, D is a heat generation distribution matrix, and Q is the heat generation power density of the cubic region.
6. The method for acquiring the temperature field of the battery pack on line based on the distributed parameter thermal resistance model according to claim 1, wherein the step 3 further comprises the following steps: representing the anode and the cathode of the battery pack by a cubic area respectively, and obtaining the heat transfer area between the anode and the cathode of the battery pack represented by each cubic area and the adjacent cubic area and the heat transfer area between the anode and the cathode of the battery pack represented by each cubic area and the external environment;
step 4 also includes: obtaining the thermal resistance between the anode and the cathode of the battery pack represented by each cubic region and 1 adjacent cubic region according to the heat transfer area between the anode and the cathode of the battery pack represented by each cubic region and the adjacent cubic region, and averaging the thermal resistance of nodes in the anode and the cathode of the battery pack represented by each cubic region to obtain the thermal resistance between the anode and the cathode of the battery pack represented by each cubic region and the external environment in 5 directions;
step 5 also includes: establishing a steady state or transient state equation of the anode and the cathode of the battery pack for the anode and the cathode of the battery pack represented by the cubic area according to the heat transfer area obtained in the step 3 and the thermal resistance obtained in the step 4;
the step 6 specifically comprises the following steps: according to the steady state or transient state equation of each cubic area of the battery pack and the steady state or transient state equation of the anode and the cathode of the battery pack, a steady state space equation set or a transient state space equation set of the whole battery pack is obtained, battery pack temperature column vectors at all moments in a transient state are obtained according to the transient state space equation set of the whole battery pack, and a steady state battery pack temperature field is obtained according to the steady state space equation set of the whole battery pack.
7. The method for acquiring the temperature field of the battery pack on line based on the distributed parameter thermal resistance model according to claim 6, wherein the thermal resistance between the positive and negative electrodes of the battery pack and the external environment in 5 directions, which is represented by the cubic region, is obtained by the following steps:
the thermal resistances of the nodes in each cubic region representing the positive and negative poles of the battery pack were averaged as the thermal resistances between the positive and negative poles of the battery pack represented by each cubic region and the external environments in the adjacent 5 directions.
8. The method for acquiring the temperature field of the battery pack on line based on the distributed parameter thermal resistance model according to claim 6, wherein the thermal resistance between the anode and the cathode of the battery pack and the adjacent cubic region, which are represented by the cubic regions, is acquired according to the Fourier heat conduction law.
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