WO2018153116A1 - 计及非线性容量特性的分数阶KiBaM电池模型及参数辨识方法 - Google Patents

计及非线性容量特性的分数阶KiBaM电池模型及参数辨识方法 Download PDF

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WO2018153116A1
WO2018153116A1 PCT/CN2017/106912 CN2017106912W WO2018153116A1 WO 2018153116 A1 WO2018153116 A1 WO 2018153116A1 CN 2017106912 W CN2017106912 W CN 2017106912W WO 2018153116 A1 WO2018153116 A1 WO 2018153116A1
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battery
capacity
fractional
discharge
nonlinear
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English (en)
French (fr)
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张承慧
商云龙
张奇
段彬
崔纳新
周忠凯
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山东大学
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Priority to US16/493,547 priority Critical patent/US11526639B2/en
Publication of WO2018153116A1 publication Critical patent/WO2018153116A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M10/00—Secondary cells; Manufacture thereof
    • H01M10/42—Methods or arrangements for servicing or maintenance of secondary cells or secondary half-cells
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M10/00—Secondary cells; Manufacture thereof
    • H01M10/42—Methods or arrangements for servicing or maintenance of secondary cells or secondary half-cells
    • H01M10/4285—Testing apparatus
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/06—Power analysis or power optimisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2310/00—The network for supplying or distributing electric power characterised by its spatial reach or by the load
    • H02J2310/40—The network being an on-board power network, i.e. within a vehicle
    • H02J2310/48—The network being an on-board power network, i.e. within a vehicle for electric vehicles [EV] or hybrid vehicles [HEV]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J7/00—Circuit arrangements for charging or depolarising batteries or for supplying loads from batteries
    • H02J7/0047—Circuit arrangements for charging or depolarising batteries or for supplying loads from batteries with monitoring or indicating devices or circuits
    • H02J7/0048—Detection of remaining charge capacity or state of charge [SOC]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/10—Energy storage using batteries

Definitions

  • the invention relates to a fractional-order KiBaM battery model and a parameter identification method which take into account nonlinear capacity characteristics.
  • Lithium-ion batteries have become the most widely used power battery for electric vehicles due to their high energy density, long service life, good cost performance and high single-cell voltage.
  • the battery model is of great significance for the rational design and safe operation of the power battery and its battery management system. It is the basis for battery state of charge (SOC) estimation, health status (SOH) estimation, and residual life (RUL) prediction.
  • SOC battery state of charge
  • SOH health status
  • RUL residual life
  • the battery model is developed to the present stage. According to different modeling mechanisms, it can be divided into electrochemical models that represent the internal characteristics of the battery, simplified electrochemical models, thermal models, etc., as well as stochastic models, neural network models, and equivalents that describe the external characteristics of the battery. Circuit model, etc.
  • the electrochemical model uses complex nonlinear differential equations to describe the internal chemical process of the battery.
  • the model is accurate, it is too abstract; the thermal model mainly studies the heat generation and heat transfer process of the battery; the stochastic model mainly focuses on the recovery characteristics of the battery, and the battery
  • the behavior is described as a Markov process, which can describe the pulse discharge characteristics of the battery, but it can not be applied to the variable current situation.
  • the neural network model has good nonlinear mapping ability, fast parallel processing ability, strong self-learning and self-organization. The advantages of ability, but a lot of experiments are needed to obtain training data, and the model error is susceptible to training data and training methods.
  • the equivalent circuit model uses the physical characteristics of the battery, using different physical components such as voltage source, current source, capacitor and resistor to form an equivalent circuit to simulate the IV output characteristics of the battery, because of its simple and intuitive form, and suitable for electrical Design and simulation advantages have become the most widely used model.
  • the equivalent circuit model can accurately describe the external characteristics of the battery's I-V output, it is difficult to express the internal characteristics such as the nonlinear capacity effect of the battery and the running time.
  • the available power of a lithium-ion battery is not like the water in a bucket. How much electricity you use drops, but with some nonlinear characteristics. Therefore, it is impossible to take out all the power of the battery, and the specific amount of electricity is related to the battery load and usage.
  • This nonlinear characteristic is mainly manifested in two aspects: capacity effect and recovery effect.
  • the capacity effect means that the larger the discharge current, the smaller the amount of electricity obtained. For example, the current discharge with 1A is smaller than the total discharge with 0.5A current discharge; the recovery effect means that the battery is no longer discharged. The battery's power will pick up.
  • KiBaM The KiBaM electrochemical model
  • KiBaM fully known as the Kinetic Battery Model
  • the KiBaM electrochemical model is a model based on perceptual knowledge, so the model is intuitive, easy to understand and simple. It is easy to use, which uses a reduced order equation to characterize the nonlinear capacity effect and running time of the battery, which can well describe the discharge characteristics of the battery.
  • the KiBaM electrochemical model takes into account the recovery and capacity effects of the battery and accurately characterizes the internal characteristics of the battery.
  • the internal electrochemical reaction process of the battery is extremely complicated, including conductive ion transfer, internal electrochemical reaction, charge and discharge hysteresis effect, and concentration diffusion effect. It exhibits strong nonlinear characteristics and is more suitable for simulation with fractional model. .
  • the fractional model has more degrees of freedom, greater flexibility and newness in design.
  • fluid motion characteristics, including lithium ion and electrons inside the battery still exhibit strong fractional calculus.
  • the results of the KiBaM electrochemical model using fractional calculus have not been found yet.
  • the present invention proposes a fractional-order KiBaM battery model and parameter identification method that takes into account nonlinear capacity characteristics.
  • the present invention considers the recovery effect and specific capacity effect of the battery, and can accurately describe the nonlinear capacity effect of the battery. And the running time, the discharge characteristics of the battery are well described, and the accurate simulation of the internal characteristics of the power battery is realized, which has high application value. It is difficult to solve the shortcomings and shortcomings of the internal characteristics such as the nonlinear capacity effect of the battery and the running time of the existing battery model.
  • the invention provides a fractional-order KiBaM battery model and parameter identification method which takes into account nonlinear capacity characteristics, and uses a fractional-order calculus principle to generalize the traditional KiBaM battery model to fractional order (non-integer order), so that the model obtains more
  • fractional-order calculus principle to generalize the traditional KiBaM battery model to fractional order (non-integer order)
  • the degree of freedom, greater flexibility and novelty, and the introduction of fractional order have also added many new phenomena and laws, which have the superiority that conventional integer-order battery models cannot achieve.
  • a fractional-order KiBaM battery model that accounts for nonlinear capacity characteristics, including a temporary capacity and a achievable capacity portion for describing a nonlinear capacity characteristic of a battery, the temporary capacity portion indicating a quantity of electricity that can be directly obtained during discharge, The state of charge of the battery SOC; the portion of the available capacity represents the amount of power that cannot be directly obtained, and the two parts are connected.
  • the load current i flows out from the temporary capacity portion, and at the same time, the rate of passage of the volume of the capacity portion is obtained.
  • the non-linear capacity effect and battery recovery effect of the battery are expressed by the ratio of the temporary capacity to the height of the available capacity portion, combined with the size of the battery capacity characteristic fractional order.
  • the sum of the temporary capacity portion and the available capacity portion is the total capacity of the battery.
  • the height of the temporary capacity portion is zero.
  • the temporary capacity is denoted by y 1 and represents the amount of electricity that can be directly obtained during discharge.
  • the height is denoted by h 1 , indicating the state of charge SOC of the battery;
  • the available capacity is denoted by y 2 , indicating that it cannot be directly obtained.
  • the amount of electricity is recorded as h 2 ; and the sum of y1 and y 2 is the total capacity of the battery;
  • c represents the distribution ratio of the battery capacity between the two parts, and the following relationship exists:
  • the temporary capacity is denoted by y 1 , which represents the amount of electricity that can be directly obtained during discharge, and its height is denoted by h 1 , which represents the state of charge SOC of the battery;
  • the available capacity is denoted by y 2 , indicating that it cannot be directly obtained.
  • the amount of electricity is recorded as h 2 ; and the sum of y 1 and y 2 is the total capacity of the battery;
  • c is the distribution ratio of the battery capacity between the two parts;
  • k is the rate coefficient from the temporary capacity flow to the available capacity ;
  • ⁇ represents the size of the battery capacity characteristic fractional order, and has: 0 ⁇ ⁇ ⁇ 1.
  • the state of charge SOC of the power battery is expressed as:
  • the battery's unavailable capacity C unavail is expressed as:
  • the capacity relationship of the power battery is expressed as:
  • C avail (t) C init - ⁇ i bat (t)dt-C unavail (t)
  • c represents the distribution ratio of the battery capacity
  • k represents the rate coefficient from the temporary capacity flow to the available capacity
  • ⁇ represents the battery capacity characteristic
  • An identification method for applying the above-described fractional-order KiBaM battery model includes the following steps:
  • Step 1 Perform a constant current charge and discharge test on the power battery to restore the power battery to a fully charged state as the initial state of the battery;
  • Step 2 Perform a small current constant current discharge test on the power battery to obtain an initial capacity of the power battery C init ;
  • Step 3 Fully charge the power battery and conduct a large current constant current discharge test. Since the discharge current is large, the discharge cutoff voltage is discharged in a short time, and the capacity C 1 of the power battery under a large current is obtained, and the distribution ratio of the battery capacity is calculated. ;
  • Step 4 Perform two sets of constant current discharge tests of different power rates on the power battery, obtain the data of the unusable capacity C unavail and the discharge time t d of the battery under the discharge rate, and calculate the parameter k according to the battery discharge end determination condition. 'and the size of the order ⁇ ;
  • Step 5 Through the above tests and experiments, the parameters of the fractional-order KiBaM electrochemical model of the tested power battery are obtained.
  • the identification method further comprises the step 6: performing a constant current discharge test on the power battery at other magnifications, obtaining the unavailable capacity and the discharge time data of the battery at the discharge rate; and comparing with the unusable capacity and the discharge time calculated by the model , verify the accuracy of the model.
  • the battery discharge end determination condition is:
  • a fractional-order KiBaM electrochemical model of a power battery according to the present invention taking into account the recovery effect and specific capacity effect of the battery, comprehensively considering characteristics such as dynamic characteristics and electrochemical mechanism, and establishing a fractional-order electrochemical model of the power battery. Accurately capture the nonlinear capacity characteristics of the power battery and the battery discharge characteristics; it can well describe the internal characteristics of the battery's nonlinear capacity effect and running time;
  • 1 is a schematic structural view of a fractional-order KiBaM electrochemical model of a power battery of the present invention.
  • the fractional-order KiBaM battery model includes two parts, which can be regarded as two containers having a volume with a connecting path , for example, a well.
  • temporary capacity the non-linear capacity characteristics of the battery, which are called “temporary capacity” and “acquired capacity” respectively;
  • temporary capacity is denoted by y 1 , which indicates the amount of electricity that can be directly obtained during discharge, and its height is recorded as h 1 indicating the SOC state of charge of the battery;
  • available capacity denoted y 2
  • c represents the distribution ratio of battery capacity between the two "wells”, and obviously has the following relationship:
  • the fractional-order KiBaM battery model the relationship between "temporary capacity" y 1 and “available capacity” y 2 and h 1 and h 2 representing the state of charge SOC of the battery can be expressed as:
  • temporary capacity is denoted by y 1 and represents the amount of electricity directly obtainable at the time of discharge, the height of which is denoted by h 1 , which indicates the state of charge SOC of the battery; and the said "obtainable capacity” is denoted by y 2 , indicating The amount of electricity that cannot be directly obtained is recorded as h 2 ; and the sum of y 1 and y 2 is the total capacity of the battery; c represents the distribution ratio of the battery capacity between the two "wells"; k represents the "temporary capacity” The rate coefficient flowing to the "available capacity"; ⁇ represents the size of the battery capacity characteristic fractional order, and has: 0 ⁇ ⁇ ⁇ 1.
  • the battery's unavailable capacity can be expressed as:
  • ⁇ ( ⁇ ) and E ⁇ , ⁇ (z) are the commonly used Gamma functions and Mittag-Leffler functions in fractional calculus calculations;
  • the battery's unavailable capacity C unavail can be expressed as:
  • the capacity relationship of the power battery can be expressed as:
  • C max, C avail, C unavail representing initial capacity of the battery, the capacity of available capacity and unavailable
  • C unavail wherein unavailable capacity SOC represents the nonlinear variable battery characteristics of the battery capacity due to the nonlinear effects
  • the fractional-order KiBaM battery model can obtain the current total battery remaining capacity y(t), available capacity C avail (t), unavailable capacity C unavail (t), and battery state of charge SOC, thereby accurately capturing battery operation Time and power battery nonlinear capacity characteristics.
  • the above-mentioned fractional-order KiBaM battery model and its identification method are known.
  • the battery model shows that the parameter identification mainly includes the initial capacity y 0 of the battery, representing the distribution ratio c of the battery capacity between the two “wells”, indicating the “temporary capacity”.
  • the rate coefficient k flowing to the "capable capacity”; and the size ⁇ indicating the fractional order of the battery capacity characteristics mainly includes the following steps:
  • Step 1 Perform a constant current charge and discharge test on the power battery to restore the power battery to a fully charged state as the initial state of the battery;
  • Step 2 Perform a small current constant current discharge test on the power battery to obtain an initial capacity of the power battery C init ;
  • Step 3 Fully charge the power battery and conduct a large current constant current discharge experiment. Since the discharge current is large, the discharge cutoff voltage is discharged to a short time, and the capacity C 1 of the power battery under a large current is obtained; then the parameters of the battery model
  • Step 4 Perform two sets of constant current discharge tests of different power rates on the power battery, obtain the data such as the unavailable capacity C unavail and the discharge time t d of the battery at the discharge rate; and formula (8) according to the end of the discharge of the battery.
  • the parameter k' and the size ⁇ of the order can be identified;
  • Step 5 Through the above tests and experiments, the parameters of the fractional-order KiBaM electrochemical model of the tested power battery can be obtained;
  • Step 6 Perform constant current discharge test on the power battery at other magnifications, obtain the data such as the unavailable capacity and discharge time of the battery under the discharge rate; and compare with the unusable capacity and discharge time calculated by the model to verify the accuracy of the model. degree.

Abstract

一种计及非线性容量特性的分数阶KiBaM电池模型及参数辨识方法，模型包括用于描述电池的非线性容量特性的临时容量(y 1)与可获得容量(y 2)部分，临时容量(y 1)部分表示放电时可直接获得的电量，表示电池的荷电状态SOC；可获得容量(y 2)部分表示不能直接获取的电量，两部分相连通，当电池放电时，负载电流i从临时容量(y 1)部分流出，同时可获得容量(y 2)部分的电量通过速率系数(k)，利用临时容量(y 1)与可获得容量(y 2)部分的高度比、结合电池容量特性分数阶阶次(ɑ)的大小，表达电池的非线性容量效应和电池恢复效应。计及非线性容量特性的分数阶KiBaM电池模型及参数辨识方法能够很好地描述电池的非线性容量效应及运行时间等内部特征。

Description

计及非线性容量特性的分数阶KiBaM电池模型及参数辨识方法 技术领域
本发明涉及一种计及非线性容量特性的分数阶KiBaM电池模型及参数辨识方法。
背景技术
随着能源危机和环境污染日益严重，电动汽车已成为最具发展前景的汽车产业。目前动力电池是制约电动汽车规模发展的最主要瓶颈，对整车性能至关重要。锂离子电池由于具有能量密度高、使用寿命长、性价比好和单体电压高等诸多优势，逐步成为电动汽车应用最广的一种动力电池。
电池模型对动力电池及其电池管理系统的合理设计和安全运行意义非凡，是电池荷电状态(SOC)估计、健康状态(SOH)估计、剩余寿命(RUL)预测等方法的基础。然而，建立一个精确且结构简单的电池模型绝非易事，究其原因，其内部化学反应十分复杂，具有高度的非线性和不确定性。电池模型发展到现阶段，按照建模机理的不同可以划分为表现电池内部特征的电化学模型、简化的电化学模型、热模型等，以及描述电池外部特征的随机模型、神经网络模型、等效电路模型等。其中，电化学模型使用复杂非线性微分方程描述电池内部化学过程，模型虽然精确，但太过抽象；热模型主要研究电池的生热、传热过程；随机模型主要关注电池的恢复特性，将电池行为描述为一个马尔科夫过程，能够描述电池的脉冲放电特性，但无法适用于变电流情况；神经网络模型具有良好的非线性映射能力、快速的并行处理能力、较强的自学习和自组织能力等优点，但需要大量的实验来获取训练数据，且模型误差易受训练数据和训练方法的影响。等效电路模型根据电池的物理特性，使用不同物理元器件如电压源、电流源、电容和电阻等构成等效电路来模拟电池的I-V输出外特性，因其简单直观的形式，以及适宜于电气设计与仿真等优点，已成为应用最为广泛的一种模型。
然而，等效电路模型虽可以准确描述电池的I-V输出外特性，但难以表现电池的非线性容量效应及运行时间等内部特征。与通常的认识不同，锂离子电池的可用电量并不是像水桶中的水一样，你用多少电量就下降多少，而是带有一定的非线性特性。因此，不可能将电池的所有电量全部取出，具体得到的电量与电池负载及使用情况有关。这种非线性特性主要表现在两个方面：容量效应和恢复效应。其中，容量效应是指放电电流越大，得到的电量越小，比如用1A的电流放电要比用0.5A的电流放电所能得到的总放电量要小；恢复效应是指当电池不再放电时，电池的电量会有所回升。
而KiBaM电化学模型(KiBaM，全称为Kinetic Battery Model)很巧妙的解决了这一难题。不同于其他模型直接用微分方程描述电池的两个特性或对电池的内部物理特点进行严格精确的描述，KiBaM电化学模型是一种比较基于感性认识的模型，因此模型比较直观、易于理解和简单好用，其采用一个降阶方程来表征电池的非线性容量效应及运行时间，能够很好地描述电池的放电特性。KiBaM电化学模型考虑了电池的恢复效应和容量效应，可以准确表现电池的内部特征。
事实上，电池内部电化学反应过程极其复杂，包括导电离子转移、内部电化学反应、充放电迟滞效应以及浓差扩散效应等，表现出较强的非线性特性，更适合用分数阶模型来模拟。对比整数阶模型，分数阶模型在设计上具有更多的自由度、更大的柔性和新意。同时，通过引入分数阶微积分，也增加了许多新的现象和规律，具有常规整数阶电池模型无法实现的优势。实际上，流体运动特性，包括电池内部锂离子、电子等运动特性，仍然表现出很强的分数阶微积分特性。目前还未发现采用分数阶微积分研究KiBaM电化学模型的成果。
发明内容
本发明为了解决上述问题，提出了一种计及非线性容量特性的分数阶KiBaM电池模型及参数辨识方法，本发明考虑了电池的恢复效应和比容量效应，能够精确描述电池的非线性容量效应及运行时间，很好地描述电池的放电特性，实现对动力电池内部特征的精确模拟，具有较高的应用价值。解决现有电池模型难以表现电池的非线性容量效应及运行时间等内部特征的缺点和不足。
本发明提供一种计及非线性容量特性的分数阶KiBaM电池模型及参数辨识方法，采用分数阶微积分原理，将传统KiBaM电池模型推广到分数阶(非整数阶)，使模型获得了更多的自由度、更大的柔性和新意，同时分数阶的引入也增加了许多新的现象和规律，具有常规整数阶电池模型无法实现的优越性。
为了实现上述目的，本发明采用如下技术方案：
一种计及非线性容量特性的分数阶KiBaM电池模型，包括用于描述电池的非线性容量特性的临时容量与可获得容量部分，所述的临时容量部分表示放电时可直接获得的电量，表示电池的荷电状态SOC；所述的可获得容量部分表示不能直接获取的电量，两部分相连通，当电池放电时，负载电流i从临时容量部分流出，同时获得容量部分的电量通过速率系数，利用临时容量与可获得容量部分的高度比、结合电池容量特性分数阶阶次的大小，表达电池的非线性容量效应和电池恢复效应。
所述的临时容量部分与可获得容量部分之和为电池的总容量。
当电池完全放电结束后，临时容量部分的高度为零。
所述的临时容量记为y1，表示放电时可直接获得的电量，其高度记为h1，表示电池的荷电状态SOC；所述的可获得容量记为y2，表示不能直接获取的电量，其高度记为h2；并且，y1与y2之和是电池的总容量；c代表两部分之间电池容量的分配比例，且存在以下关系：
Figure PCTCN2017106912-appb-000001
临时容量y1和可获得容量y2与代表电池荷电状态SOC的h1和h2之间关系表示为：
Figure PCTCN2017106912-appb-000002
式中，临时容量记为y1，表示放电时可直接获得的电量，其高度记为h1，表示电池的荷电状态SOC；所述的可获得容量记为y2，表示不能直接获取的电量，其高度记为h2；并且，y1与y2之和是电池的总容量；c代表两个部分之间电池容量的分配比例；k表示从临时容量流到可获得容量的速率系数；α表示电池容量特性分数阶阶次的大小，且有：0＜α＜1。
通过建立的分数阶KiBaM电池模型，获取当前的电池总剩余容量y(t)、可用容量Cavail(t)、不可用容量Cunavail(t)和电池荷电状态SOC，以捕获电池运行时间和动力电池非线性容量内特征。
动力电池的荷电状态SOC表示为：
Figure PCTCN2017106912-appb-000003
其中，电池的不可用容量Cunavail表示为：
Figure PCTCN2017106912-appb-000004
动力电池的容量关系式表示为：
Cavail(t)＝Cinit-∫ibat(t)dt-Cunavail(t)，c代表电池容量的分配比例；k表示从临时容量流到可获得容量的速率系数；α表示电池容量特性分数阶阶次的大小，且有：0＜α＜1，系数
Figure PCTCN2017106912-appb-000005
SOC0为初始SOC。
一种应用上述分数阶KiBaM电池模型的辨识方法，包括以下步骤：
步骤一：对动力电池进行恒流充放电实验，使动力电池恢复到充满电的状态，作为电池的初始状态；
步骤二：对动力电池进行小电流恒流放电实验，得到动力电池的初始容量Cinit；
步骤三：对动力电池充满电，进行大电流恒流放电实验，由于放电电流很大，很短时间就放电到放电截止电压，得到大电流下动力电池的容量C1，计算电池容量的分配比例；
步骤四：对动力电池进行两组不同倍率的恒流放电测试，获取此放电倍率下电池的不可用容量Cunavail、放电时间td数据，依据电池放电结束判定条件，计算得到可辨识出参数k'和阶次的大小α；
步骤五：通过以上测试和实验，得到被测动力电池的分数阶KiBaM电化学模型的参数。
所述辨识方法，还包括步骤六对动力电池进行其他倍率的恒流放电测试，获取此放电倍率下电池的不可用容量、放电时间数据；并与模型计算得到的不可用容量、放电时间做比较，验证模型的精确度。
电池放电结束判定条件为：
Figure PCTCN2017106912-appb-000006
与现有技术相比，本发明的有益效果为：
(1)本发明涉及的一种动力电池分数阶KiBaM电化学模型，考虑了电池的恢复效应和比容量效应，综合考虑动力学特性、电化学机理等特征因素，建立动力电池分数阶电化学模型，精确捕获动力电池的非线性容量特性和电池放电特性；能够很好地描述电池的非线性容量效应及运行时间等内部特征；
(2)动力电池因其特殊的材料和化学特性，展现出了分数阶动力学行为，用整数阶描述电池特性其精度受到很大的限制，而釆用分数阶微积分描述那些本身带有分数阶特性的对 象时，能更好地描述对象的本质特性及其行为；本发明首次将分数阶微积分应用在KiBaM电化学模型中，见解独到、极具创新；
(3)分数阶微积分具有一定的记忆功能，更符合自然界普遍连续的朴素哲学观点，由于增加了分数阶阶数这一未知参数，模型获得了更多的自由度、更大的柔性和新意，因此动力电池分数阶KiBaM电化学模型获得了更高的精度、更好的动态性能和稳定性，为SOC估计提供了一个精确且易实现的电池模型。
附图说明
构成本申请的一部分的说明书附图用来提供对本申请的进一步理解，本申请的示意性实施例及其说明用于解释本申请，并不构成对本申请的不当限定。
图1为本发明动力电池分数阶KiBaM电化学模型结构示意图。
具体实施方式：
下面结合附图与实施例对本发明作进一步说明。
应该指出，以下详细说明都是例示性的，旨在对本申请提供进一步的说明。除非另有指明，本文使用的所有技术和科学术语具有与本申请所属技术领域的普通技术人员通常理解的相同含义。
需要注意的是，这里所使用的术语仅是为了描述具体实施方式，而非意图限制根据本申请的示例性实施方式。如在这里所使用的，除非上下文另外明确指出，否则单数形式也意图包括复数形式，此外，还应当理解的是，当在本说明书中使用术语“包含”和/或“包括”时，其指明存在特征、步骤、操作、器件、组件和/或它们的组合。
如图1所示为本发明公开的一种动力电池分数阶KiBaM电化学模型；所述分数阶KiBaM电池模型，包含两个部分，可以将其视作两个具有连通路的具有一定容积的容器，例如井。用于描述电池的非线性容量特性，分别叫做“临时容量”和“可获得容量”；所述的“临时容量”记为y1，表示放电时可直接获得的电量，其高度记为h1，表示电池的荷电状态SOC；所述的“可获得容量”记为y2，表示不能直接获取的电量，其高度记为h2；并且，y1与y2之和是电池的总容量；c代表两个“井”之间电池容量的分配比例，显然存在以下关系：
Figure PCTCN2017106912-appb-000007
所述分数阶KiBaM电池模型，当电池放电时，负载电流i从表示“临时容量”的y1右下角 的管道流出，同时“可获得容量”y2的电量通过k慢慢流入y1，且流出的速度要比从y2流入y1的速度快，y1下降更快，y1和y2高度差随之增加；当电池停止放电时，y1的电量会有所回升，直到y1和y2高度相等，是电池恢复效应的体现；同时也说明了当放电电流越大时，所放出的电量就越小，体现了电池的非线性容量效应；
所述分数阶KiBaM电池模型，“临时容量”y1和“可获得容量”y2与代表电池荷电状态SOC的h1和h2之间关系可表示为：
Figure PCTCN2017106912-appb-000008
式中，“临时容量”记为y1，表示放电时可直接获得的电量，其高度记为h1，表示电池的荷电状态SOC；所述的“可获得容量”记为y2，表示不能直接获取的电量，其高度记为h2；并且，y1与y2之和是电池的总容量；c代表两个“井”之间电池容量的分配比例；k表示从“临时容量”流到“可获得容量”的速率系数；α表示电池容量特性分数阶阶次的大小，且有：0＜α＜1。
定义代表两个“井”的高度差为δh(t)，显然：
δh(t)＝h2(t)-h1(t)   (3)
电池的不可用容量可以表示为：
Cunavail(t)＝(1-c)δh(t)   (4)
假设电池“临时容量”y1和“可获得容量”y2初始状态的容量y10和y20分别为：
Figure PCTCN2017106912-appb-000009
式中，C表示电池的总容量。
当首次以电流I对电池进行恒电流放电，且放电时间区间t0≤t≤td，若取初始条件t0＝0，即高度差初始为零，然后静置一段时间td＜t≤tr，则公式(2)经拉氏变换和反拉氏变换，变换过程省略，整理可得：
Figure PCTCN2017106912-appb-000010
式中，Γ(α)和Eα,α(z)分别为分数阶微积分计算里常用的Gamma函数和Mittag-Leffler函数；且系数
Figure PCTCN2017106912-appb-000011
整理可得：
Figure PCTCN2017106912-appb-000012
代入初始条件(2)，可化简为：
Figure PCTCN2017106912-appb-000013
由前面分析可知，电池完全放完电时，高度h1＝0；此时电池的总剩余容量等于不可用容量：
y(t)＝Cunavail(t)＝(1-c)δh(t)   (9)
电池的不可用容量Cunavail可表示为：
Figure PCTCN2017106912-appb-000014
动力电池的容量关系式可表示为：
Cavail(t)＝Cinit-∫ibat(t)dt-Cunavail(t)   (11)
式中，Cmax、Cavail、Cunavail分别代表电池的初始容量、可用容量和不可用容量；其中不可用容量Cunavail代表了由于电池非线性容量特性影响的电池非线性SOC变量；
显然，动力电池的荷电状态SOC可表示为：
Figure PCTCN2017106912-appb-000015
所述分数阶KiBaM电池模型，可以得到当前的电池总剩余容量y(t)、可用容量Cavail(t)、不可用容量Cunavail(t)和电池荷电状态SOC，因此可以精确捕获电池运行时间和动力电池非线性容量内特征。
一种应用上述分数阶KiBaM电池模型及其辨识方法，由电池模型可知，参数辨识主要包括电池的初始容量y0，代表两个“井”之间电池容量的分配比例c，表示从“临时容量”流到“可获得容量”的速率系数k；以及表示电池容量特性分数阶阶次的大小α，主要包括以下步骤：
步骤一：对动力电池进行恒流充放电实验，使动力电池恢复到充满电的状态，作为电池的初始状态；
步骤二：对动力电池进行小电流恒流放电实验，得到动力电池的初始容量Cinit；
步骤三：对动力电池充满电，进行大电流恒流放电实验，由于放电电流很大，很短时间就放电到放电截止电压，得到大电流下动力电池的容量C1；则电池模型的参数
Figure PCTCN2017106912-appb-000016
步骤四：对动力电池进行两组不同倍率的恒流放电测试，获取此放电倍率下电池的不可用容量Cunavail、放电时间td等数据；根据判断电池放电结束的公式(8)
Figure PCTCN2017106912-appb-000017
可辨识出参数k'和阶次的大小α；
步骤五：通过以上测试和实验，可以得到被测动力电池的分数阶KiBaM电化学模型的参数；
步骤六：对动力电池进行其他倍率的恒流放电测试，获取此放电倍率下电池的不可用容量、放电时间等数据；并与模型计算得到的不可用容量、放电时间做比较，验证模型的精确度。
以上所述仅为本申请的优选实施例而已，并不用于限制本申请，对于本领域的技术人员来说，本申请可以有各种更改和变化。凡在本申请的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本申请的保护范围之内。
上述虽然结合附图对本发明的具体实施方式进行了描述，但并非对本发明保护范围的限制，所属领域技术人员应该明白，在本发明的技术方案的基础上，本领域技术人员不需要付出创造性劳动即可做出的各种修改或变形仍在本发明的保护范围以内。

Claims (10)

  1. 一种计及非线性容量特性的分数阶KiBaM电池模型，其特征是：包括用于描述电池的非线性容量特性的临时容量与可获得容量部分，所述的临时容量部分表示放电时可直接获得的电量，表示电池的荷电状态SOC；所述的可获得容量部分表示不能直接获取的电量，两部分相连通，当电池放电时，负载电流i从临时容量部分流出，同时获得容量部分的电量通过速率系数，利用临时容量与可获得容量部分的高度比、结合电池容量特性分数阶阶次的大小，表达电池的非线性容量效应和电池恢复效应。
  2. 如权利要求1所述的一种计及非线性容量特性的分数阶KiBaM电池模型，其特征是：所述的临时容量部分与可获得容量部分之和为电池的总容量。
  3. 如权利要求1所述的一种计及非线性容量特性的分数阶KiBaM电池模型，其特征是：当电池完全放电结束后，临时容量部分的高度为零。
  4. 如权利要求1所述的一种计及非线性容量特性的分数阶KiBaM电池模型，其特征是：所述的临时容量记为y1，表示放电时可直接获得的电量，其高度记为h1，表示电池的荷电状态SOC；所述的可获得容量记为y2，表示不能直接获取的电量，其高度记为h2；并且，y1与y2之和是电池的总容量；c代表两部分之间电池容量的分配比例，且存在以下关系：
    Figure PCTCN2017106912-appb-100001
  5. 如权利要求1所述的一种计及非线性容量特性的分数阶KiBaM电池模型，其特征是：临时容量y1和可获得容量y2与代表电池荷电状态SOC的h1和h2之间关系表示为：
    Figure PCTCN2017106912-appb-100002
    式中，临时容量记为y1，表示放电时可直接获得的电量，其高度记为h1，表示电池的荷电状态SOC；所述的可获得容量记为y2，表示不能直接获取的电量，其高度记为h2；并且，y1与y2之和是电池的总容量；c代表两个部分之间电池容量的分配比例；k表示从临时容量流到可获得容量的速率系数；α表示电池容量特性分数阶阶次的大小，且有：0＜α＜1。
  6. 如权利要求1所述的一种计及非线性容量特性的分数阶KiBaM电池模型，其特征是：通过建立的分数阶KiBaM电池模型，获取当前的电池总剩余容量y(t)、可用容量Cavail(t)、不 可用容量Cunavail(t)和电池荷电状态SOC，以捕获电池运行时间和动力电池非线性容量内特征。
  7. 如权利要求1所述的一种计及非线性容量特性的分数阶KiBaM电池模型，其特征是：动力电池的荷电状态SOC表示为：
    Figure PCTCN2017106912-appb-100003
    其中，电池的不可用容量Cunavail表示为：
    Figure PCTCN2017106912-appb-100004
    动力电池的容量关系式表示为：
    Cavail(t)＝Cinit-∫ibat(t)dt-Cunavail(t)，c代表电池容量的分配比例；k表示从临时容量流到可获得容量的速率系数；α表示电池容量特性分数阶阶次的大小，且有：0＜α＜1，系数
    Figure PCTCN2017106912-appb-100005
  8. 一种应用如权利要求1-7中任一项所述的分数阶KiBaM电池模型的参数辨识方法，其特征是：包括以下步骤：
    步骤一：对动力电池进行恒流充放电实验，使动力电池恢复到充满电的状态，作为电池的初始状态；
    步骤二：对动力电池进行小电流恒流放电实验，得到动力电池的初始容量Cinit；
    步骤三：对动力电池充满电，进行大电流恒流放电实验，由于放电电流很大，很短时间就放电到放电截止电压，得到大电流下动力电池的容量C1，计算电池容量的分配比例；
    步骤四：对动力电池进行两组不同倍率的恒流放电测试，获取此放电倍率下电池的不可用容量Cunavail、放电时间td数据，依据电池放电结束判定条件，计算得到可辨识出参数k'和阶次的大小α；
    步骤五：通过以上测试和实验，得到被测动力电池的分数阶KiBaM电化学模型的参数。
  9. 如权利要求8所述的参数辨识方法，其特征是：还包括步骤六对动力电池进行其他倍率的恒流放电测试，获取此放电倍率下电池的不可用容量、放电时间数据；并与模型计算得 到的不可用容量、放电时间做比较，验证模型的精确度。
  10. 如权利要求8所述的参数辨识方法，其特征是：电池放电结束判定条件为：
    Figure PCTCN2017106912-appb-100006
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