A lithium battery low-temperature self-heating power optimization method with analytical solution

Abstract

A lithium battery low-temperature self-heating power optimization method with an analytical solution, in the method, the low-temperature discharge capacity of the lithium battery and various battery parameter data are acquired; according to the acquired battery low-temperature discharge related data, a dischargeable capacity Q a is fitted out as a function of temperature T and state of charge SOC, a simplified battery low-temperature discharge model is established; according to the established physical model, a lithium battery low-temperature self-heating optimization model P is established with the minimum power consumption of the battery heating driving process under the driving range requirement of the electric vehicle as the optimization target; according to the established optimization model, a solution model with inequality constraints corresponding to the optimization model is established, the heating problem of the optimal power consumption is solved by an analytical method, and the heating strategy under the driving range requirement of this time is output. The present application can be applied to the improvement of the low-temperature performance of the lithium battery, the formulation of the driving strategy of the electric vehicle in winter, the driving range arrangement of the electric vehicle in winter, and the low-power warning of the electric vehicle.

Description

Technical Field

[0001] This invention belongs to the field of electric vehicle low-temperature driving strategy and power optimization technology, and in particular, it is a method for optimizing the power consumption of lithium battery self-heating at low temperatures with analytical solution. Background Technology

[0002] With the continuous development and popularization of domestically produced electric vehicles, lithium batteries have initially developed into mature products. Due to their advantages in safety and cycle life, they have become one of the main energy storage media in electric vehicle applications. However, in practical use, lithium batteries are limited in their ability to provide sufficient power, especially when operating in cold weather (i.e., below 0°C), where the discharge capacity is significantly reduced. Studies have shown that in cold weather, the driving range of electric vehicles is reduced by about 40%.

[0003] Currently, existing solutions for low-temperature driving of electric vehicles do not fully leverage the performance advantages of lithium-ion batteries. While some academic research includes optimization models for battery preheating strategies at low temperatures, given current battery temperatures and capacities, no effective low-temperature self-heating strategy has yet been developed to balance the constraints between battery self-heating and energy optimization, and to provide suitable heating and driving solutions under different actual driving mileage requirements.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of the present invention, and therefore may contain information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention proposes an analytical solution for optimizing the power consumption of lithium batteries at low temperatures and for self-heating. Based on function fitting of the discharge capacity of the power battery at different temperatures and SOC values, the heating strategy and discharge state of the lithium battery at different temperatures are modeled. The model is solved using Karush-Kuhn-Tucker (KKT) conditions, yielding the optimal heating strategy for drivers to choose when different mileage requirements are met at the current temperature and power level, thus optimizing the driving performance of electric vehicles at low temperatures.

[0006] The objective of this invention is achieved through the following technical solution: a method for optimizing the power consumption of lithium batteries at low temperatures with analytical solutions includes the following steps.

[0007] Step 1: Obtain the low-temperature discharge capacity and battery parameter data of the lithium battery, including temperature T and state of charge (SOC);

[0008] Step 2: Fit the discharge capacity Q based on the low-temperature discharge capacity and battery parameter data. aThe functional relationship between temperature T and state of charge (SOC) is established, and a low-temperature discharge model for lithium batteries is built based on this functional relationship.

[0009] Step 3: Based on the low-temperature discharge model of lithium batteries, and with the goal of minimizing the power consumption during the battery heating process to meet the driving range requirements of electric vehicles, establish a low-temperature self-heating optimization model P for lithium batteries.

[0010] Step 4: Based on the self-heating optimization model P, establish a solution model with inequality constraints corresponding to the optimization model, solve the heating problem with optimal power consumption using analytical methods, and output the heating strategy under the required driving mileage.

[0011] The method described includes battery parameter data such as the battery discharge capacity variation curve data with temperature at different temperatures, battery mass, equivalent specific heat capacity, average output voltage value, and heat transfer efficiency of external heater.

[0012] In the method described, the lithium battery low-temperature discharge model uses an ideal voltage source connected in series with an equivalent internal resistance, and the external heater is equivalent to a heating resistor.

[0013] In the method described above, step 3, the modeling process of the lithium battery low-temperature self-heating optimization model P is as follows:

[0014] The objective function is determined to be min z0-z2(1)

[0015] Where z0 is the initial SOC value of the lithium battery, and z2 is the remaining SOC value after the battery has been heated to the required mileage for driving.

[0016] The power constraint for introducing an external battery heater for self-heating: Q a (T0, z0)-Q h =Q a (T1, z1) (2), where T0 and T1 are the initial temperature and the temperature after heating of the battery, respectively, and z0 and z1 are the initial SOC value and the SOC value after heating of the battery, respectively. Q a (T0, z0), Q a (T1, z1) represent the discharge capacity of the battery at states T0, z0, T1, and z1, respectively. h The amount of electricity consumed by the battery for heating;

[0017] Introducing a power constraint on the discharge rate of the battery during normal driving after it has been heated:

[0018] Q a (T1, z1)-Q d =Q a (T1, z2) (3)

[0019] Where z2 is the SOC value of the battery after it has been heated and discharged for normal driving, and Q is... d To provide the battery with the necessary power for the driving range;

[0020] Temperature rise constraints when using an external battery heater for heating:

[0021]

[0022] Where α is the heating efficiency of the external heater, U is the output voltage provided by the battery to the heater, c is the equivalent specific heat capacity of the battery, and m is the mass of the battery.

[0023] Introducing constraints on the change in SOC value after battery discharge:

[0024]

[0025] Among them, Q N This refers to the battery's rated capacity.

[0026] Introduce constraints on the relationship between battery discharge capacity and driving range requirements:

[0027] Q a (T1, z2)≥0 (7)

[0028] Introduce initial state constraints:

[0029] z0, z1, z2 ∈ [0, 1] (8)

[0030] T0, T1∈[-30, 30] (9)

[0031] The battery temperature variation range is set to -30℃ to 30℃.

[0032] In summary, the following optimization model P for low-temperature self-heating of lithium batteries is established:

[0033] (P)min z0-z2 (10)

[0034] st(2)-(9).

[0035] In the method described above, step 4, the solution method for the analytical solution model containing inequality constraints includes:

[0036] Define the decision variable as u = Q h State variable s = (T i , z j ) i＝0，1；j＝0，1，2Once the low-temperature self-heating optimization model P is determined, the state change of the battery discharge after heating is determined by selecting decision variables. A generalized Lagrange multiplier λ is introduced to the inequality constraints, transforming the original constrained optimization problem into an equivalent unconstrained optimization problem. The Lagrangian function is defined as follows:

[0037] L(Q h ,λ)=f(Q h )+λg(Q h (11)

[0038] Where, f(Q) h For optimizing the objective function, g(Q) h Let λ be the constraint function and λ be the defined Lagrange multiplier. From equations (5) and (6), we get...

[0039]

[0040] From equations (3) and (7), we get

[0041]

[0042] The constraint inequality (13) is called the original feasibility, and the feasible region K = {Q} is defined accordingly. d |g(Q h Assume )≤0}, To find the optimal solution that satisfies the constraints, we will discuss two separate cases:

[0043] (1)g(Q h If K < 0, the optimal solution lies inside K, and is called an internal solution. In this case, the constraints are invalid, and the problem degenerates into an unconstrained problem. satisfy And λ = 0;

[0044] (2)g(Q h If K < 0, the optimal solution lies on the boundary of K, and is called the boundary solution. In this case, the constraints are valid, which can be proven. Occurred in That is, there exists λ * Make

[0045] Therefore, whether it is an internal solution or a boundary solution, The condition that holds true consistently is the complementary relaxation condition.

[0046] In summary, for the optimal solution There exists λ * This makes the following condition true:

[0047]

[0048]

[0049] λ * ≥0 (16)

[0050]

[0051] By simultaneously solving equations (14-17), we can find the optimal solution that satisfies the conditions using analytical methods. and the corresponding multiplier λ * This represents the amount of electricity consumed by the battery for heating under the current temperature and SOC value.

[0052] In the method described, step 4 divides battery heating and driving into two stages, and obtains the state variable T for each stage. i , z j With decision variable Q d The relationship.

[0053] In the method described above, in step 4, the current dischargeable capacity Q is obtained based on the initial state T0 and z0. a (T0, z0), according to equation (2), the optimal state Q that the battery discharge capacity can reach when only considering the power consumption of heating is taken into account. a (T1, z1) max And the battery level Q required by the user's driving range. d The comparison is divided into three cases for discussion: if Q d ≤Q a (T0, z0) means that the current battery charge is sufficient for this trip, and the battery does not need to self-heat. If Q d >Q a (T1, z1) max This means that even after heating, the current battery level is insufficient for this driving requirement, and there is no solution to this problem; the user needs to charge the battery. If Q... a (T0, z0) < Q d ≤Q a (T1, z1) max That is, the heating strategy can ensure that the battery's available power meets the requirements of this driving, and then continue to solve the optimal energy consumption model.

[0054] Compared with existing technologies, this invention has the following advantages: It provides a physical model of how the discharge capacity of an electric vehicle battery changes with temperature and SOC value at low temperatures, and proposes a corresponding optimization model for battery self-heating at low temperatures. This improves the low-temperature discharge state of lithium batteries, increases battery energy utilization, and provides different heating strategies for different driving mileages, offering practical reference value for electric vehicle driving. Based on nonlinear problem-solving methods in operations research, it overcomes the high complexity of general nonlinear problems by utilizing problem characteristics and designing ingenious models and algorithms. It ensures the minimization of power consumption during electric vehicle operation and satisfies the physical constraints of battery temperature and SOC value changes. Furthermore, this method is flexible, allowing for the prioritization of heating and power consumption by setting different driving mileages. This invention has broad application prospects in the field of low-temperature electric vehicle operation, including: improving the low-temperature performance of lithium batteries, formulating winter electric vehicle driving strategies, scheduling winter electric vehicle driving mileage, and providing low battery warnings for electric vehicles. Attached Figure Description

[0055] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0056] In the attached diagram:

[0057] Figure 1 This is a flowchart of the steps of an optimal strategy for low-temperature self-heating energy of lithium batteries based on analytical solutions provided by the present invention.

[0058] Figure 2 This is a simplified equivalent circuit model diagram of a lithium battery for low-temperature self-heating discharge provided by the present invention;

[0059] Figure 3 This is a flowchart of a battery heating decision and electric vehicle driving strategy scheme based on the initial state of the battery and the user's driving mileage requirements provided by the present invention;

[0060] Figure 4 This is a graph showing the battery voltage and capacity variation curves at different temperatures in an embodiment of the present invention.

[0061] Figure 5 This is a diagram of the test equipment in an embodiment of the present invention;

[0062] Figure 6 This is a schematic diagram of the equivalent circuit of the test experiment in the embodiment of the present invention;

[0063] Figure 7 This is a three-dimensional surface plot of the battery voltage and capacity change curve data under different temperatures in the embodiments of the present invention, which is a function fit.

[0064] Figure 8 This is a diagram illustrating the effect of the battery heating decision and electric vehicle driving strategy proposed by the algorithm in this embodiment of the invention, based on the initial state of the battery and the user's driving mileage requirements.

[0065] The present invention will be further explained below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0066] Specific embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the invention and to fully convey the scope of the invention to those skilled in the art.

[0067] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0068] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0069] For better understanding, in one embodiment, such as Figures 1 to 8 As shown, the low-temperature self-heating power consumption optimization method for lithium batteries with analytical solutions includes the following steps:

[0070] Step 1: Obtain the low-temperature discharge capacity and battery parameter data of the lithium battery, including temperature T and state of charge (SOC);

[0071] Step 2: Fit the discharge capacity Q based on the low-temperature discharge capacity and battery parameter data. aThe functional relationship between temperature T and state of charge (SOC) is established, and a low-temperature discharge model for lithium batteries is built based on this functional relationship.

[0072] Step 3: Based on the low-temperature discharge model of lithium batteries, and with the goal of minimizing the power consumption during the battery heating process to meet the driving range requirements of electric vehicles, establish a low-temperature self-heating optimization model P for lithium batteries.

[0073] Step 4: Based on the self-heating optimization model P, establish a solution model with inequality constraints corresponding to the optimization model, solve the heating problem with optimal power consumption using analytical methods, and output the heating strategy under the required driving mileage.

[0074] In a preferred embodiment of the method, the battery parameter data also includes data on the change curve of the battery's discharge capacity with temperature at different temperatures, the battery's mass, equivalent specific heat capacity, average output voltage, and heat transfer efficiency of the external heater.

[0075] In a preferred embodiment of the method, in the low-temperature discharge model of the lithium battery, the lithium battery is represented by an ideal voltage source connected in series with an equivalent internal resistance, and the external heater is represented by an equivalent heating resistor.

[0076] In a preferred embodiment of the method, the modeling process of the lithium battery low-temperature self-heating optimization model P in step 3 is as follows:

[0077] The objective function is determined to be min z0-z2 (1)

[0078] Where z0 is the initial SOC value of the lithium battery, and z2 is the remaining SOC value after the battery has been heated to the required mileage for driving.

[0079] The power constraint for introducing an external battery heater for self-heating: Q a (T0, z0)-Q h =Q a (T1, z1) (2), where T0 and T1 are the initial temperature and the temperature after heating of the battery, respectively, and z0 and z1 are the initial SOC value and the SOC value after heating of the battery, respectively. Q a (T0, z0), Q a (T1, z1) represent the discharge capacity of the battery at states T0, z0, T1, and z1, respectively. h The amount of electricity consumed by the battery for heating;

[0080] Introducing a power constraint on the discharge rate of the battery during normal driving after it has been heated:

[0081] Q a (T1, z1)-Q d =Q a (T1, z2) (3)

[0082] Where z2 is the SOC value of the battery after it has been heated and discharged for normal driving, and Q is... d To provide the battery with the necessary power for the driving range;

[0083] Temperature rise constraints when using an external battery heater for heating:

[0084]

[0085] Where α is the heating efficiency of the external heater, U is the output voltage provided by the battery to the heater, c is the equivalent specific heat capacity of the battery, and m is the mass of the battery.

[0086] Introducing constraints on the change in SOC value after battery discharge:

[0087]

[0088] Among them, Q N This refers to the battery's rated capacity.

[0089] Introduce constraints on the relationship between battery discharge capacity and driving range requirements:

[0090] Q a (T1, z2)≥0 (7)

[0091] Introduce initial state constraints:

[0092] z0, z1, z2 ∈ [0, 1] (8)

[0093] T0, T1∈[-30, 30] (9)

[0094] The battery temperature variation range is set to -30℃ to 30℃.

[0095] In summary, the following optimization model P for low-temperature self-heating of lithium batteries is established:

[0096] (P)min z0-z2 (10)

[0097] st(2)-(9).

[0098] In a preferred embodiment of the method, step 4, the method for solving the analytical solution model containing inequality constraints, includes:

[0099] Define the decision variable as u = Q h State variable s = (T i , z j ) i＝0，1；j＝0，1，2Once the low-temperature self-heating optimization model P is determined, the state change of the battery discharge after heating is determined by selecting decision variables. A generalized Lagrange multiplier λ is introduced to the inequality constraints, transforming the original constrained optimization problem into an equivalent unconstrained optimization problem. The Lagrangian function is defined as follows:

[0100] L(Q h ,λ)=f(Q h )+λg(Q h (11)

[0101] Where, f(Q) h For optimizing the objective function, g(Q) h Let λ be the constraint function and λ be the defined Lagrange multiplier. From equations (5) and (6), we get...

[0102]

[0103] From equations (3) and (7), we get

[0104]

[0105] The constraint inequality (13) is called the original feasibility, and the feasible region K = {Q} is defined accordingly. d |g(Q h Assume )≤0}, To find the optimal solution that satisfies the constraints, we will discuss two separate cases:

[0106] (1)g(Q h If K < 0, the optimal solution lies inside K, and is called an internal solution. In this case, the constraints are invalid, and the problem degenerates into an unconstrained problem. satisfy And λ = 0;

[0107] (2)g(Q h If K < 0, the optimal solution lies on the boundary of K, and is called the boundary solution. In this case, the constraints are valid, which can be proven. Occurred in That is, there exists λ * Make

[0108] Therefore, whether it is an internal solution or a boundary solution, The condition that holds true consistently is the complementary relaxation condition.

[0109] In summary, for the optimal solution There exists λ * This makes the following condition true:

[0110]

[0111]

[0112] λ * ≥0 (16)

[0113]

[0114] By simultaneously solving equations (14-17), we can find the optimal solution that satisfies the conditions using analytical methods. and the corresponding multiplier λ * This represents the amount of electricity consumed by the battery for heating under the current temperature and SOC value.

[0115] In a preferred embodiment of the method, step 4 divides battery heating and driving into two stages, and obtains the state variable T for each stage. i , z j With decision variable Q d The relationship.

[0116] In a preferred embodiment of the method, in step 4, the current dischargeable capacity Q is obtained based on the initial state T0 and z0. a (T0, z0), according to equation (2), the optimal state Q that the battery discharge capacity can reach when only considering the power consumption of heating is taken into account. a (T1, z1) max And the battery level Q required by the user's driving range. d The comparison is divided into three cases for discussion: if Q d ≤Q a (T0, z0) means that the current battery charge is sufficient for this trip, and the battery does not need to self-heat. If Q d >Q a (T1, z1) max This means that even after heating, the current battery level is insufficient for this driving requirement, and there is no solution to this problem; the user needs to charge the battery. If Q... a (T0, z0) < Q d ≤Q a (T1, z1) max That is, the heating strategy can ensure that the battery's available power meets the requirements of this driving, and then continue to solve the optimal energy consumption model.

[0117] In one embodiment, the method includes the following steps:

[0118] Step 1: Obtain the low-temperature discharge capacity and various battery parameter data of the lithium battery, including the discharge capacity change curve data of the battery at different temperatures, the battery mass, equivalent specific heat capacity, average output voltage value, and heat transfer efficiency of the external heater.

[0119] Step 2: Based on the battery low-temperature discharge data obtained in Step 1, fit the discharge capacity Q. a Based on the functional relationship between temperature T and state of charge (SOC), a simplified low-temperature discharge model of the battery is established, and its equivalent circuit diagram is shown below. Figure 2 As shown, the lithium battery uses an ideal voltage source connected in series with an equivalent internal resistance, and the external heater uses an equivalent heating resistor.

[0120] It should be noted that the solution algorithm for the above model and subsequent steps is only applicable in situations such as... Figure 3 This heating decision is used in one scenario. When the other two scenarios occur—namely, low mileage or low battery charge—the battery low-temperature self-heating strategy is not employed. However, considering the energy-optimal model and subsequent solution algorithm is meaningful only when heating is required and the mileage requirement can be met.

[0121] Step 3: Based on the equivalent circuit model established in Step 2, and with the goal of minimizing the power consumption during battery heating during driving under the constraint of electric vehicle mileage requirements, establish a low-temperature self-heating optimization model P for lithium batteries.

[0122] The optimization objective of model P is to minimize the electricity consumed during battery heating while meeting user driving needs. Therefore, the objective function of the model can be described as follows:

[0123] min z0-z2 (1)

[0124] Where z0 is the initial SOC value of the lithium battery, and z2 is the remaining SOC value after the battery is heated to drive the required mileage.

[0125] The constraints of the established optimization model P include:

[0126] Battery power constraints for self-heating via external heater:

[0127] Q a (T0, z0)-Q h =Q a (T1, z1) (2)

[0128] Where T0 and T1 are the initial temperature and the temperature after heating of the battery, respectively; z0 and z1 are the initial SOC value and the SOC value after heating of the battery, respectively; and Q... a (T0, z0), Q a (T1, z1) represent the discharge capacity of the battery at states T0, z0, T1, and z1, respectively. h The amount of electricity consumed by the battery for heating;

[0129] Battery discharge limit for normal driving after heating:

[0130] Q a (T1, z1)-Q d =Q a (T1, z2) (3)

[0131] Where z2 is the SOC value of the battery after it has been heated and discharged for normal driving, and Q is... d To provide the battery with the necessary power for the driving range;

[0132] Temperature rise constraints when using an external battery heater:

[0133]

[0134] Where α is the heating efficiency of the external heater, U is the output voltage provided by the battery to the heater, c is the equivalent specific heat capacity of the battery, and m is the mass of the battery.

[0135] Constraints on SOC value change after battery discharge:

[0136]

[0137]

[0138] Among them, Q N This refers to the battery's rated capacity.

[0139] Constraints on the relationship between battery discharge capacity and driving range requirements:

[0140] Q a (T1, z2)≥0 (7)

[0141] Battery initial state constraints

[0142] z0, z1, z2 ∈ [0, 1] (8)

[0143] T0, T1∈[-30, 30] (9)

[0144] The battery temperature range is set to -30℃ to 30℃. Considering the actual driving conditions of electric vehicles and the issue of lithium battery performance degradation at high temperatures, setting the temperature range to -30℃ to 30℃ ensures that the battery is not damaged by excessively low or high temperatures, while also conforming to the actual usage scenarios of electric vehicles. This ensures that the optimization model is more realistic and maximizes the performance of lithium batteries at low temperatures.

[0145] In summary, the following optimization model P for low-temperature self-heating of lithium batteries is established:

[0146] (P)min z0-z2 (10)

[0147] st(2)-(9)

[0148] Step 4: Based on the optimization model established in Step 3, establish a solution model for the analytical solution containing inequality constraints corresponding to the optimization model, solve the problem of the heating method with optimal power consumption, and output the heating strategy under the required driving mileage.

[0149] The optimization problem P is an analytical problem with multiple equality and inequality constraints. Generally, due to the complexity of the analytical solution function, solving analytical problems is much more difficult than solving linear programming problems. Moreover, unlike linear programming, which has general methods such as the simplex method, there is currently no general algorithm suitable for solving all types of problems; each method has its own specific scope of application. To overcome these difficulties, considering the relationship between the problem constraints and the optimal value function, this invention proposes a Lagrange multiplier method, utilizing Karush-Kuhn-Tucker (KKT) conditions to solve the optimization problem. First, the state variables and decision variables are determined; then, the Lagrange multiplier λ is introduced to simplify the model to an unconstrained form; finally, the KKT conditions are used to formulate the conditional expressions and obtain the analytical solution to the problem.

[0150] First, define the decision variable as u = Qh, and the state variable as s = (T i , z j ) i＝0，1；j＝0，1，2 Once the low-temperature self-heating optimization model P is determined, the state change of the battery discharge after heating is determined by selecting decision variables.

[0151] Introducing the generalized Lagrange multiplier λ to the inequality constraints transforms the original constrained optimization problem into an equivalent unconstrained optimization problem. The Lagrangian function is defined as follows:

[0152] L(Q h ,λ)=f(Q h )+λg(Q h (11)

[0153] From equations (5) and (6), we get

[0154]

[0155] From equations (3) and (7), we get

[0156]

[0157] The constraint inequality (13) is called the original feasibility, and the feasible region K = {Q} is defined accordingly. d |g(Q h )≤0}. Assume To find the optimal solution that satisfies the constraints, we will discuss two separate cases:

[0158] (1)g(Q h If K < 0, the optimal solution lies inside K, and is called an internal solution. In this case, the constraints are invalid, and the problem degenerates into an unconstrained problem. satisfy And λ = 0;

[0159] (2)g(Q h If K < 0, the optimal solution lies on the boundary of K, and is called the boundary solution. In this case, the constraints are valid, which can be proven. Occurred in That is, there exists λ * Make

[0160] Therefore, whether it is an internal solution or a boundary solution, If this condition holds true, it is a condition of complementary relaxation.

[0161] In summary, for the optimal solution There exists λ * This makes the following condition true:

[0162]

[0163]

[0164] λ * ≥0 (16)

[0165]

[0166] By simultaneously solving equations (14-17), we can find the optimal solution that satisfies the conditions using analytical methods. and the corresponding multiplier λ * This refers to the amount of electricity consumed by the battery for heating under the current temperature and SOC value.

[0167] In equation (13) of step 4, battery heating and driving are divided into two stages, thus deriving the state variable T for different stages. i , z j With decision variable Q d The relationship simplifies the solution model.

[0168] Before solving the model in step 4, the current dischargeable capacity Q is obtained based on the initial state T0 and z0. a (T0, z0), according to equation (2), the optimal state Q that the battery discharge capacity can reach when only considering the power consumption of heating is taken into account. a (T1, z1) max And the battery level Q required by the user's driving range. d The comparison is divided into three cases for discussion: if Q d ≤Qa (T0, z0) means that the current battery charge is sufficient for this trip, and the battery does not need to self-heat. If Q d >Q a (T1, z1) max This means that even after heating, the current battery level is insufficient for this driving requirement, and there is no solution to this problem; the user needs to charge the battery. If Q... a (T0, z0) < Q d ≤Q a (T1, z1) max That is, the heating strategy can ensure that the battery's available power meets the requirements of this driving, and then continue to solve the optimal energy consumption model.

[0169] In summary, after determining the initial battery state, this algorithm can provide the actual available battery power in the current state to meet different user driving mileage requirements, offering a reference for driving strategies. In heating decisions, it accurately solves the analytical solution of the nonlinear optimization model using KKT conditions, providing users with a precise energy-optimal heating strategy. In terms of both time complexity and algorithm accuracy, it outperforms some existing battery low-temperature preheating algorithms.

[0170] Example

[0171] To enable those skilled in the art to better understand the present invention, this embodiment uses a 26650 type lithium iron phosphate battery to conduct a low-temperature heating experiment to verify the reliability of the model establishment, and obtains data from the battery voltage and capacity change curves at different temperatures, such as... Figure 4 The algorithm is used to fit the functional relationship between battery discharge capacity and battery temperature and SOC value. Finally, under different initial conditions, the algorithm outputs the optimal decision for different driving mileage requirements, and the rationality of the final heated driving scheme is analyzed.

[0172] First, to verify the reliability of the model, a low-temperature heating experiment of the battery was designed, and the experimental equipment was tested, such as... Figure 5 The equivalent circuit diagram of the experiment is as follows: Figure 6 The experiment involved discharging the battery at both low and room temperature. The experimental data are shown in the table below. This verifies the significant decrease in lithium battery discharge capacity at low temperatures and the real-time improvement in lithium battery discharge performance upon temperature increase, laying the experimental foundation for model establishment.

[0173] Table 1. Basic Discharge Experiment Test Data

[0174]

[0175] Table 2 Test data of temperature rise and discharge experiment

[0176]

[0177] Figure 7 A three-dimensional surface plot is shown, which uses the algorithm of this invention to perform function fitting on the battery voltage and capacity variation curves at different temperatures. The quadratic polynomial fitting method is used, and its analytical expression is as follows:

[0178] Q a (T, z)=93.937+0.4373T-0.2119T 2 +2965.998z -403.775z 2 +39.1056T·z(18)

[0179] As shown in the figure, the battery discharge capacity decreases as the temperature decreases, which is particularly noticeable at 0°C.

[0180] Figure 8 The figure shows the effect of the proposed battery heating decision and electric vehicle driving strategy based on the initial battery state and user driving range requirements. If Q... d ≤Q a (T0, z0) means that the current battery charge is sufficient for this trip, and the battery does not need to self-heat. If Q d >Q a (T1, z1) max This means that even after heating, the current battery power is insufficient to meet the driving requirements, which also makes... If Q a (T0, z0) < Q d ≤Q a (T1, z1) max The optimal heating power is obtained by the optimization algorithm. The lower the initial battery temperature and the more charge it has, the longer the decision-making range can accommodate different driving mileage requirements, and the better the improvement in battery discharge performance. The more charge used for driving, the more heating power is required to meet driving requirements; however, the optimization model shows that this minimizes the overall power consumption. In summary, the optimal heating decision is found while meeting driving mileage requirements, providing car users with an accurate and complete energy-optimal heating driving strategy.

[0181] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A method for optimizing the power consumption of lithium batteries at low temperatures for self-heating, characterized by having an analytical solution, It includes the following steps, Step 1: Obtain the low-temperature discharge capacity and parameter data of the lithium battery. The lithium battery parameter data includes temperature. and state of charge (SOC); Step 2: Fit the discharge capacity based on the low-temperature discharge capacity and lithium battery parameter data. With temperature The functional relationship of state of charge (SOC) is used to establish a low-temperature discharge model for lithium batteries. Step 3: Based on the low-temperature discharge model of lithium battery, and with the goal of minimizing the power consumption of lithium battery heating during driving while meeting the driving range requirements of electric vehicles, establish a low-temperature self-heating optimization model P for lithium battery. Step 4: Based on the lithium battery low-temperature self-heating optimization model P, establish a corresponding solution model with inequality constraints, use analytical methods to solve the heating problem with optimal power consumption, and output the heating strategy under the required driving range. In step 3, the modeling process of the lithium battery low-temperature self-heating optimization model P is as follows: The objective function is determined as follows: (1) in, This represents the initial SOC value of the lithium battery. The remaining state of charge (SOC) value after the required mileage for driving with the lithium battery heated; The power constraint of introducing an external heater for self-heating of the lithium battery: (2) in, These are the initial temperature and the temperature after heating of the lithium battery, respectively. These are the initial SOC value and the SOC value after heating of the lithium battery, respectively. Lithium batteries and Discharge capacity under certain conditions This refers to the amount of electricity consumed by the lithium battery for heating. Introducing the power constraint of lithium battery discharge during normal driving after heating: （3） in, This refers to the SOC value of a lithium battery after it has been heated and discharged for normal driving. To meet the power requirements of lithium batteries for driving range; Temperature rise constraints when using an external heater for heating lithium batteries: （4） in, The heating efficiency of the external heater. The output voltage provided to the heater for the lithium battery. Let m be the equivalent specific heat capacity of the lithium battery, and m be the mass of the lithium battery. Introducing constraints on the SOC value change after lithium battery discharge: (5) （6） in, This refers to the rated capacity of the lithium battery. Introduce constraints on the relationship between discharge capacity and driving range requirements: （7） Introduce initial state constraints: （8） （9） The temperature range of the lithium battery is set to -30℃ to 30℃. In summary, the following optimization model P for low-temperature self-heating of lithium batteries is established: （10） 。 2. The method as described in claim 1, characterized in that, The lithium battery parameter data also includes the curve data of the discharge capacity of the lithium battery at different temperatures as a function of temperature, the mass of the lithium battery, the equivalent specific heat capacity, the average output voltage value, and the heat transfer efficiency of the external heater.

3. The method as described in claim 1, characterized in that, In the low-temperature discharge model of lithium batteries, the lithium battery is represented by an ideal voltage source connected in series with an equivalent internal resistance, and the external heater is represented by an equivalent heating resistor.

4. The method as described in claim 1, characterized in that, In step 4, the solution method for the analytical solution model containing inequality constraints includes: Define decision variables as State variables Once the low-temperature self-heating optimization model P is determined, the state changes of the lithium battery after heating are determined by selecting decision variables. A generalized Lagrange multiplier λ is introduced to the inequality constraints, transforming the original constrained optimization problem into an equivalent unconstrained optimization problem. The Lagrangian function is defined as follows: （11） in, To optimize the objective function, For constraint functions, For the defined Lagrange multipliers, from equations (5) and (6) we get （12） From equations (3) and (7), we get （13） The constraint inequality (13) is called the original feasibility, and the feasible region is defined accordingly. Assuming To find the optimal solution that satisfies the constraints, we will discuss two separate cases: (1) The optimal solution lies inside K, and is called an internal solution. In this case, the constraints are invalid, and the problem degenerates into an unconstrained problem. satisfy ; (2) The optimal solution lies on the boundary of K, and is called the boundary solution. In this case, the constraints are valid, which can be proven. Occurred in That is, it exists. Make ; Therefore, whether it is an internal solution or a boundary solution, The condition that holds true consistently is the complementary relaxation condition. In summary, for the optimal solution ,exist This makes the following condition true: （14） （15） （16） （17） By combining the conditional equations (14-17), the optimal solution satisfying the conditions can be obtained analytically. and the corresponding multiplier This represents the amount of electricity consumed by the lithium battery for heating under the current temperature and SOC value.

5. The method as described in claim 4, characterized in that, In step 4, the heating of the lithium battery and driving are divided into two stages, and the state variables of different stages are obtained. With decision variables The relationship.

6. The method as described in claim 4, characterized in that, In step 4, based on the initial state Determine the current discharge capacity According to equation (2), the optimal state of discharge capacity can be achieved when only the power consumption for heating is considered. and the amount of electricity required for the user's driving mileage. The comparison is divided into three cases for discussion: If This means the current battery charge is sufficient for this trip, and the lithium battery does not require self-heating. ;like This means that even after heating, the current battery capacity is insufficient for this driving requirement, and the user needs to charge the lithium battery; if This means using a heating strategy to ensure that the available power of the lithium battery meets the driving requirements.

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