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CN106909716B - Lithium iron phosphate battery modeling and SOC estimation method considering capacity loss - Google Patents

Lithium iron phosphate battery modeling and SOC estimation method considering capacity loss Download PDF

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CN106909716B
CN106909716B CN201710044564.9A CN201710044564A CN106909716B CN 106909716 B CN106909716 B CN 106909716B CN 201710044564 A CN201710044564 A CN 201710044564A CN 106909716 B CN106909716 B CN 106909716B
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iron phosphate
lithium iron
phosphate battery
battery
soc
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CN106909716A (en
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李军徽
高凤杰
严干贵
穆钢
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Jilin Power Supply Co Of State Grid Jilinsheng Electric Power Supply Co
Northeast Electric Power University
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Northeast Dianli University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
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Abstract

本发明的一种计及容量损耗的磷酸铁锂电池建模及SOC估计的方法是基于现有磷酸铁锂电池工作状态受温度，电流，循环次数、放电深度等诸多因素的影响，使建模过程非常复杂而提出来的，本发明基于戴维南等效电路，对磷酸铁锂电池进行建模工作，给出模型开路电压、电阻电容值辨识方法，并考虑到磷酸铁锂电池生命周期内的容量的损耗，建立容量估计数学模型，提高磷酸铁锂电池模型的输出精度；同时用扩展卡尔曼滤波算(EKF)法来解决不确定性噪声带来的磷酸铁锂电池SOC估计问题。具有方法简便、科学合理，适用价值高，效果佳等优点。

Figure 201710044564

A method for modeling and SOC estimation of a lithium iron phosphate battery considering capacity loss of the present invention is based on the fact that the working state of an existing lithium iron phosphate battery is affected by many factors such as temperature, current, cycle times, depth of discharge, etc. The process is very complicated and proposed. Based on the Thevenin equivalent circuit, the present invention models the lithium iron phosphate battery, gives the model open circuit voltage, resistance and capacitance value identification methods, and considers the capacity of the lithium iron phosphate battery during its life cycle. At the same time, the extended Kalman filter (EKF) method is used to solve the SOC estimation problem of lithium iron phosphate battery caused by uncertainty noise. The method has the advantages of simple method, scientific and reasonable, high applicable value and good effect.

Figure 201710044564

Description

Lithium iron phosphate battery modeling and SOC estimation method considering capacity loss
Technical Field
The invention relates to the technical field of power supply application, in particular to a method for modeling and SOC (state of charge) estimation of a lithium iron phosphate battery considering capacity loss.
Background
Electrochemical energy storage represented by a lithium battery has the advantages of high controllability and high module degree, so that the energy density is high and the conversion efficiency is high on the whole, and the electrochemical energy storage is generally researched and applied in the field of new energy power generation. At present, a plurality of lithium battery energy storage demonstration projects are established in China, such as Zhang Jiakozhou north county in Hebei (a lithium phosphate battery device with 14MW/63WMh and a liquid flow energy storage device with 2MW/8 MWh), Shenzhen Baoqing energy storage power station (a 4MW/16MW lithium iron phosphate battery energy storage system is installed), and the like. According to relevant domestic policies and documents, the domestic energy storage market shows a rapid development trend, the lithium battery energy storage field mainly deals with the lithium battery energy storage technology with high safety, low cost and long service life, and the experimental demonstration of the technology is realized later, so that the development and the application of the lithium battery technology are greatly promoted.
Around the key problems of modeling, control strategy design, capacity configuration and the like of the lithium battery energy storage system, scholars at home and abroad obtain some research achievements. In the aspect of energy storage modeling research, the battery consists of a positive electrode, a negative electrode and an electrolyte, the charging and discharging process is an electrochemical process, and the voltage and the current of the battery are related to factors such as resistance, polarization, temperature and the like of active substances in the battery and are very complex. In the whole life cycle of the working operation of the lithium battery, the capacity of the lithium battery can generate corresponding loss along with the continuous charging and discharging, and the aging phenomenon of the lithium battery can occur. Therefore, the capacity evaluation of the lithium battery is also necessary, and the working state of the battery can be timely adjusted by workers. And at present, the price of battery energy storage is generally expensive, and how to establish an effective battery model for analyzing the technical-economic characteristics of an energy storage system when the battery model is applied to new energy is a very critical problem.
Disclosure of Invention
The invention aims to solve the technical problem of providing a lithium iron phosphate battery modeling and SOC state estimation method considering battery capacity loss, which is characterized by comprising the following steps of:
1) mathematical model of lithium iron phosphate battery equivalent circuit
Adopting a Thevenin equivalent circuit model, and establishing a model state equation as a formula (1) according to a second-order RC equivalent circuit model and by kirchhoff's theorem:
Figure GDA0002254928570000011
in the formula: u shapebFor the load terminal voltage of lithium iron phosphate batteries, CuseIs the effective capacity of the iron phosphate battery, i.e. the available capacity of the lithium iron phosphate battery, IbIs the operating current of the lithium iron phosphate battery, SOC is the state of charge, U, of the lithium iron phosphate batteryocThe open-circuit voltage of the lithium iron phosphate battery is a nonlinear function of SOC and is represented by a controllable voltage source RsThe ohmic resistance of the lithium iron phosphate battery, two RC links, R1、C1And R2、C2Respectively represents the electrochemical polarization and concentration polarization processes in the operation of the lithium iron phosphate battery, U1，U2Indicating its corresponding voltage valueη is the charge-discharge efficiency of the lithium iron phosphate battery;
the equivalent circuit model of the lithium iron phosphate battery shows that the left and right circuit networks are coupled through SOC (state of charge), SOC is an important factor for connecting the two parts, and the state equation (1) of the model shows that the output voltage of the lithium iron phosphate battery is determined by the open-circuit voltage and the polarization voltage of the lithium iron phosphate battery, wherein the polarization voltage of the lithium iron phosphate battery is directly related to the corresponding resistance, capacitance and current value, and the real-time available capacity (C) of the lithium iron phosphate battery is accurately determineduse) Estimating SOC, an open-circuit voltage value, a resistance value and a capacitance value is basic work of iron phosphate lithium battery modeling;
2) identification of relevant parameters of lithium iron phosphate battery model
Because the working state of the lithium iron phosphate battery is influenced by factors such as discharge depth, cycle times, capacity attenuation and the like, and the equivalent circuit model parameters of the lithium iron phosphate battery change along with the changes of loads and external environments, in order to obtain a more reliable model, the lithium iron phosphate battery needs to be tested under the condition of multiple factors during off-line modeling, and a parameter data relational expression is established;
SOC is the most important influence factor of all parameters of a resistance-capacitance model, the determination of the functional relation between impedance parameters and SOC is the most basic and important part of resistance-capacitance modeling work under the standard running state condition of the lithium iron phosphate battery, and the lithium iron phosphate battery U in the normal working environmentocThe corresponding relation with SOC is stable and is slightly influenced by temperature, therefore, UocIs uniquely determined by SOC, and the relation is obtained by fitting a function;
resistance-capacitance parameters in the model can be obtained by the following method, under different SOC, the initial value can be set to be 0.2, the step length is 0.05, no-load loading discharge and charge experiments are carried out on the resistance-capacitance parameters, when the lithium iron phosphate battery carries out discharge experiments by no-load state actions, the voltage of the lithium iron phosphate battery can generate a period of abrupt drop, the change of the polarization voltage of the lithium iron phosphate battery is very small and ignored at the moment, and the main reason for causing the change is the ohmic resistance R of the lithium iron phosphate batterysVoltage drop caused by this data change to ohm inside the batteryThe internal resistance is estimated, and the terminal voltage of the battery enters an exponential-like change period because of the polarization voltage U on the RC circuit of the battery1，U2The slow decrease results in a period of time that is considered to correspond to a zero state, described by equation (2):
Figure GDA0002254928570000021
wherein U isbRepresents the terminal voltage, U, of a lithium iron phosphate batteryARepresenting the terminal voltage a, b of the lithium iron phosphate battery at the point A, which are parameters to be fitted, and fitting the formula (2) to obtain corresponding a, b, tau1，τ2And estimating and calculating the resistance and the capacitance of the RC circuit by using the value, wherein the value is specifically represented by formula (3):
Figure GDA0002254928570000031
Ibrepresents the operating current, tau, of a lithium iron phosphate battery1，τ2Is a parameter to be fitted, two RC links, R1、C1And R2、C2Respectively representing electrochemical polarization and concentration polarization processes in the operation of the lithium iron phosphate battery;
accordingly, the corresponding resistance and capacitance in the charging process are estimated by using the formula (4), the capacitance and the resistance of the lithium iron phosphate battery under different SOC are obtained by analogy, the R, C values under different states are obtained by carrying out spline interpolation on the capacitance and the resistance,
Figure GDA0002254928570000032
3) evaluation of available capacity of lithium iron phosphate battery
The service life of the lithium iron phosphate battery is limited, and with the continuous action of charging and discharging in the life cycle of the lithium iron phosphate battery, the loss of lithium ions and the decline of active materials in the lithium iron phosphate battery can cause the irreversible capacity loss in the lithium iron phosphate battery and directly influence the service life of the lithium iron phosphate battery, so that the real-time capacity evaluation of the lithium iron phosphate battery is carried out, the real-time state of the lithium iron phosphate battery can be correctly known, and the method has a positive effect on the estimation of the state of the lithium iron phosphate battery at a certain,
according to the maximum charge-discharge cycle number N corresponding to the operation of the lithium iron phosphate battery at delta SOC ═ xm|ΔSOC＝xFitting the relation of the data, wherein the fitting function is a formula (5), and calculating the maximum charge-discharge cycle number of the lithium iron phosphate battery under a certain charge-discharge cycle depth in the life cycle of the lithium iron phosphate battery according to the formula (5)
The fitting function of the maximum charge-discharge cycle times of the lithium iron phosphate battery when the lithium iron phosphate battery operates at different delta SOC is as follows (5):
Figure GDA0002254928570000033
wherein: Δ SOC ═ x, Nm|ΔSOC＝xRepresents the maximum number of charge-discharge cycles;
evaluating the available capacity in the life cycle of the lithium iron phosphate battery to obtain that the maximum charging and discharging cycle times of the lithium iron phosphate battery corresponding to the life cycles of different delta SOCs are different, the charging and discharging cycle times of the lithium iron phosphate battery under the shallow charging and shallow discharging environment are more, and the cycle charging and discharging cycle times of each delta SOC in the charging and discharging process of the lithium iron phosphate battery are converted according to the formula (6) corresponding to the cycle times under the full charging and discharging;
Figure GDA0002254928570000034
in the formula: n is a radical ofm(x) The maximum cycle number of the lithium iron phosphate battery is when the charging and discharging depth of the lithium iron phosphate battery is equal to x, wherein x belongs to (0, 1); n is a radical ofm(1) α (x) represents the equivalent cycle depth for the maximum number of cycles for a lithium iron phosphate battery when the lithium iron phosphate battery has a charge-discharge depth equal to 1.
Setting n times of charge and discharge at a certain time, and the depth of charge and discharge is x0、x1、…、xnAnd adding the equivalent charge-discharge coefficients under different charge-discharge depths to obtain the lithium iron phosphate batteryThe equivalent number of charge and discharge times is as follows (7):
Figure GDA0002254928570000041
wherein Nm' represents an equivalent charge-discharge coefficient;
the state of health (SOH) of a lithium iron phosphate battery, also referred to as the state of life of the lithium iron phosphate battery, is defined as the ratio of the capacity of the lithium iron phosphate battery discharged from a full charge state to a cut-off voltage at a certain rate to its nominal capacity, reflecting the life status of the lithium iron phosphate battery, and is defined as formula (8):
Figure GDA0002254928570000042
in the formula, CCapicityIndicates the nominal capacity, C, of the lithium iron phosphate batteryuseRepresenting the available capacity of the lithium iron phosphate battery;
the available capacity of the lithium iron phosphate battery at the time t is measured by equation (9):
Figure GDA0002254928570000043
gamma is a constant, which means the percentage of the maximum value of the capacity loss allowed by the normal work of the lithium iron phosphate battery, namely the maximum value of SOH, is 0.3, the SOH reflects the health state of the lithium iron phosphate battery, represents the aging degree of the lithium iron phosphate battery, the change range is 0-100%, when the SOH is reduced to 20-30%, the function of the lithium iron phosphate battery basically fails, and the basic charge and discharge tasks cannot be completed;
4) state estimation of SOC using EKF algorithm
From steps 1) -3), SOC is an important parameter in the running process of the lithium iron phosphate battery, and the state of charge estimation of the lithium iron phosphate battery is the guarantee of safe and reliable running of a lithium iron phosphate battery pack in an energy storage device, so that the real-time SOC of the lithium iron phosphate battery is accurately estimated, and the real-time control strategy of the lithium iron phosphate battery is conveniently adjusted;
the Kalman filtering algorithm is composed of a state equation, an output equation and statistical characteristics of system process noise and observation noise, states or parameters needing to be estimated are obtained according to the state equation and the output equation of the system, the SOC of the lithium iron phosphate battery can be optimally estimated in the minimum variance, prediction and estimation of the lithium iron phosphate battery at a certain future moment are facilitated, the Kalman filtering algorithm is a state equation utilizing a linear system, the lithium iron phosphate battery is a nonlinear model, the nonlinear model of the lithium iron phosphate battery is subjected to Kalman filtering algorithm (EKF) expansion, and the real-time SOC state quantity of the battery is estimated by adopting EKF:
based on the equivalent mathematical model of the lithium iron phosphate battery, establishing a Kalman filtering state equation and an output equation of the lithium iron phosphate battery:
equation of state (10):
Figure GDA0002254928570000051
output equation (11):
ub(k)＝uoc(k)-i(k)×Rs(k)-u1(k)-u2(k)+v(k) (11)
corresponding to the general form (12) of the Kalman filtering equation of state, respectively
Figure GDA0002254928570000052
In the formula: u shapebFor the load terminal voltage of lithium iron phosphate batteries, CuseIs the effective capacity of the lithium iron phosphate battery, i.e. the available capacity of the lithium iron phosphate battery, IbIs the operating current of the lithium iron phosphate battery, SOC represents the state of charge of the lithium iron phosphate battery, UocThe open-circuit voltage of the lithium iron phosphate battery is a nonlinear function of SOC and is represented by a controllable voltage source RsThe ohmic resistance of the lithium iron phosphate battery, two RC links, R1、C1And R2、C2Respectively representing operation of lithium iron phosphate batteriesElectrochemical and concentration polarization process, U1，U2Representing the corresponding voltage value, η representing the charging and discharging efficiency of the lithium iron phosphate battery, w (k) representing the system error, v (k) representing the empirical error;
carrying out SOC estimation in real time:
where k | k-1 represents the result of the last state prediction, k-1| k-1 represents the optimal result at the last time, P (k), Q (k), R (k) corresponds to the covariance of X (k), w (k), v (k),
the Kalman filtering start must select a good initial value, which includes three state parameters, SOC (k), U1(k)，U2(k) SOC (k) is obtained from the last time of last operation as an initial value, while the lithium iron phosphate battery has little effect immediately after operation, and the polarization voltage is considered to be 0, and for the covariance q (k), r (k), defined as:
Figure GDA0002254928570000061
further comprises the following steps:
Figure GDA0002254928570000062
Figure GDA0002254928570000063
R(0)＝0.001。
the invention relates to a lithium iron phosphate battery modeling and SOC estimation method considering capacity loss, which is provided based on the fact that the working state of the existing lithium iron phosphate battery is influenced by various factors such as temperature, current, cycle frequency, discharge depth and the like, so that the modeling process is very complicated; meanwhile, an Extended Kalman Filter (EKF) method is used for solving the SOC estimation problem of the lithium iron phosphate battery brought by uncertain noise. Has the advantages of simple, scientific and reasonable method, high application value, good effect and the like.
Drawings
FIG. 1 is a model of an equivalent circuit of a lithium iron phosphate battery;
FIG. 2 is a curve of a constant-current no-load loading discharge and charge experiment of a lithium iron phosphate battery;
FIG. 3 is a graph of the relationship between different Δ SOC and the maximum number of charge and discharge cycles;
FIG. 4 is a flow chart of a Kalman filtering algorithm;
FIG. 5 is a graph showing the relationship between the open-circuit voltage and the SOC of a lithium iron phosphate battery;
FIG. 6 discharge curves after different cycle numbers;
FIG. 71000 cycles later without considering the variation after capacity loss and verification;
FIG. 8 is a graph of partial current versus time;
fig. 9 is a graph of terminal voltage versus time for a lithium iron phosphate battery;
figure 10 lithium iron phosphate battery SOC versus time curves.
Detailed Description
The lithium iron phosphate battery modeling and SOC estimation method taking capacity loss into consideration according to the present invention will be further described with reference to the drawings and examples.
The invention relates to a lithium iron phosphate battery modeling and SOC state estimation method considering battery capacity loss, which comprises the following steps of:
1) mathematical model of lithium iron phosphate battery equivalent circuit
Because the energy storage of the lithium iron phosphate battery is an electrochemical reaction process, the lithium iron phosphate battery is difficult to describe in detail by adopting a conventional physical model, the modeling of an energy storage system is based on an application scene, a simple model cannot reflect the characteristics of the lithium iron phosphate battery, an excessively complex model can greatly increase the complexity of solving and applying a control strategy, and a more modeling method used in the existing system carries out equivalent circuit modeling according to the dynamic characteristics and the external special effect performance in the lithium iron phosphate battery.
External characteristic equivalent circuit modeling is a simple and effective method for modeling electrochemical cells. The equivalent circuit model simulates the transient-stable characteristic of the battery to the outside by forming a circuit network through electric elements such as a voltage source, a capacitor, a resistor, an inductor and the like, has the advantages of simple modeling method, easy parameter identification, high precision, convenient fusion of various factors, easy mathematical analysis, strong general applicability and the like, and is the most widely applied modeling method in the field of electrical engineering.
As shown in fig. 1, a davinan equivalent circuit model is adopted, and according to a second-order RC equivalent circuit model, a model state equation is established by kirchhoff's theorem as formula (1):
Figure GDA0002254928570000071
in the formula: u shapebFor the load terminal voltage of lithium iron phosphate batteries, CuseIs the effective capacity of the iron phosphate battery, i.e. the available capacity of the lithium iron phosphate battery, IbIs the operating current of the lithium iron phosphate battery, SOC is the state of charge, U, of the lithium iron phosphate batteryocThe open-circuit voltage of the lithium iron phosphate battery is a nonlinear function of SOC and is represented by a controllable voltage source RsThe ohmic resistance of the lithium iron phosphate battery, two RC links, R1、C1And R2、C2Respectively represents the electrochemical polarization and concentration polarization processes in the operation of the lithium iron phosphate battery, U1，U2The corresponding voltage value is shown, and η is the charge-discharge efficiency of the lithium iron phosphate battery;
the equivalent circuit model of the lithium iron phosphate battery shows that the left and right circuit networks are coupled through SOC (state of charge), SOC is an important factor for connecting the two parts, and the state equation (1) of the model shows that the output voltage of the lithium iron phosphate battery is determined by the open-circuit voltage and the polarization voltage of the lithium iron phosphate battery, wherein the polarization voltage of the lithium iron phosphate battery is directly related to the corresponding resistance, capacitance and current value, and the real-time available capacity (C) of the lithium iron phosphate battery is accurately determineduse) Estimating SOC, an open-circuit voltage value, a resistance value and a capacitance value is basic work of iron phosphate lithium battery modeling;
2) identification of relevant parameters of lithium iron phosphate battery model
Because the working state of the lithium iron phosphate battery is influenced by factors such as discharge depth, cycle times, capacity attenuation and the like, and the equivalent circuit model parameters of the lithium iron phosphate battery change along with the changes of loads and external environments, in order to obtain a more reliable model, the lithium iron phosphate battery needs to be tested under the condition of multiple factors during off-line modeling, and a parameter data relational expression is established;
SOC is the most important influence factor of all parameters of a resistance-capacitance model, the determination of the functional relation between impedance parameters and SOC is the most basic and important part of resistance-capacitance modeling work under the standard running state condition of the lithium iron phosphate battery, and the lithium iron phosphate battery U in the normal working environmentocThe corresponding relation with SOC is stable and is slightly influenced by temperature, therefore, UocIs uniquely determined by SOC, and the relation is obtained by fitting a function;
as shown in fig. 2, the resistance-capacitance parameters in the model can be obtained by setting the initial value to 0.2 and the step length to 0.05 under different SOCs, and performing no-load charging and discharging experiments on the parameters, wherein when the lithium iron phosphate battery performs the discharging experiments in the no-load state, the voltage of the lithium iron phosphate battery generates a steep drop period (OA period), the change of the polarization voltage of the lithium iron phosphate battery is very small and negligible, and the main cause of the change is the ohmic resistance R of the lithium iron phosphate batterysThe voltage drop caused by the voltage drop is used for estimating the internal ohmic internal resistance of the battery according to the data change, and then the terminal voltage of the battery enters an exponential-like change period (AB period) because of the polarization voltage U on the RC circuit of the battery1，U2The slow decrease results in a period of time that is considered to correspond to a zero state, described by equation (2):
Figure GDA0002254928570000081
wherein U isbRepresents the terminal voltage, U, of a lithium iron phosphate batteryADenotes the terminal voltage of lithium iron phosphate battery at point A, a, b, τ1，τ2Is to be fitted toParameter, fitting formula (2) to obtain corresponding a, b, tau1，τ2And estimating and calculating the resistance and the capacitance of the RC circuit by using the value, wherein the value is specifically represented by formula (3):
Figure GDA0002254928570000091
Ibrepresenting the running current of the lithium iron phosphate battery, two RC links, R1、C1And R2、C2Respectively representing electrochemical polarization and concentration polarization processes in the operation of the lithium iron phosphate battery;
accordingly, the corresponding resistance and capacitance in the charging process are estimated by using the formula (4), the capacitance and the resistance of the lithium iron phosphate battery under different SOC are obtained by analogy, the R, C values under different states are obtained by carrying out spline interpolation on the capacitance and the resistance,
Figure GDA0002254928570000092
3) evaluation of available capacity of lithium iron phosphate battery
The service life of the lithium iron phosphate battery is limited, and with the continuous action of charging and discharging in the life cycle of the lithium iron phosphate battery, the loss of lithium ions and the decline of active materials in the lithium iron phosphate battery can cause the irreversible capacity loss in the lithium iron phosphate battery and directly influence the service life of the lithium iron phosphate battery, so that the real-time capacity evaluation of the lithium iron phosphate battery is carried out, the real-time state of the lithium iron phosphate battery can be correctly known, and the method has a positive effect on the estimation of the state of the lithium iron phosphate battery at a certain,
according to the maximum charge-discharge cycle number N corresponding to the operation of the lithium iron phosphate battery at delta SOC ═ xm|ΔSOC＝xFitting the relation of the data, wherein the fitting function is a formula (5), and calculating the maximum charge-discharge cycle number of the lithium iron phosphate battery under a certain charge-discharge cycle depth in the life cycle of the lithium iron phosphate battery according to the formula (5)
As shown in fig. 3, the fitting function of the maximum number of charge and discharge cycles of the lithium iron phosphate battery when operating at different Δ SOCs is as follows:
Figure GDA0002254928570000093
wherein: Δ SOC ═ x, Nm|ΔSOC＝xRepresents the maximum number of charge-discharge cycles;
according to fig. 3, the available capacity in the life cycle of the lithium iron phosphate battery is evaluated to obtain that the maximum charging and discharging cycle times of the lithium iron phosphate battery corresponding to the life cycles of different delta SOCs are different, the charging and discharging cycle times of the lithium iron phosphate battery under the shallow charging and shallow discharging environment are more, and the cycle charging and discharging cycle times under each delta SOC in the charging and discharging process of the lithium iron phosphate battery are converted according to the formula (6) corresponding to the cycle times under the full charging and discharging;
Figure GDA0002254928570000101
in the formula: n is a radical ofBESS(x)The maximum cycle number of the lithium iron phosphate battery is when the charging and discharging depth of the lithium iron phosphate battery is equal to x (x belongs to (0, 1)); n is a radical ofBESS(1)α (x) represents the equivalent cycle depth for the maximum number of cycles for a lithium iron phosphate battery when the lithium iron phosphate battery has a charge-discharge depth equal to 1.
Setting n times of charge and discharge at a certain time, and the depth of charge and discharge is x0、x1、…、xnAnd accumulating the equivalent charge and discharge coefficients under different charge and discharge depths to obtain the equivalent charge and discharge frequency of the lithium iron phosphate battery as the following formula (7):
Figure GDA0002254928570000102
wherein Nm' represents an equivalent charge-discharge coefficient;
the state of health (SOH) of a lithium iron phosphate battery, also referred to as the state of life of the lithium iron phosphate battery, is defined as the ratio of the capacity of the lithium iron phosphate battery discharged from a full charge state to a cut-off voltage at a certain rate to its nominal capacity, reflecting the life status of the lithium iron phosphate battery, and is defined as formula (8):
Figure GDA0002254928570000103
in the formula, CCapicityIndicates the nominal capacity, C, of the lithium iron phosphate batteryuseRepresenting the available capacity of the lithium iron phosphate battery;
the available capacity of the lithium iron phosphate battery at the time t is measured by equation (9):
Figure GDA0002254928570000104
gamma is a constant, which means the percentage of the maximum value of the capacity loss allowed by the normal work of the lithium iron phosphate battery, namely the maximum value of SOH, is 0.3, the SOH reflects the health state of the lithium iron phosphate battery, represents the aging degree of the lithium iron phosphate battery, the change range is 0-100%, when the SOH is reduced to 20-30%, the function of the lithium iron phosphate battery basically fails, and the basic charge and discharge tasks cannot be completed;
4) state estimation of SOC using EKF algorithm
From steps 1) -3), SOC is an important parameter in the running process of the lithium iron phosphate battery, and the state of charge estimation of the lithium iron phosphate battery is the guarantee of safe and reliable running of a lithium iron phosphate battery pack in an energy storage device, so that the real-time SOC of the lithium iron phosphate battery is accurately estimated, and the real-time control strategy of the lithium iron phosphate battery is conveniently adjusted;
the Kalman filtering algorithm is composed of a state equation, an output equation and statistical characteristics of system process noise and observation noise, states or parameters needing to be estimated are obtained according to the state equation and the output equation of the system, the SOC of the lithium iron phosphate battery can be optimally estimated in the minimum variance, prediction and estimation of the lithium iron phosphate battery at a certain future moment are facilitated, the Kalman filtering algorithm is a state equation utilizing a linear system, the lithium iron phosphate battery is a nonlinear model, the nonlinear model of the lithium iron phosphate battery is subjected to Kalman filtering algorithm (EKF) expansion, and the real-time SOC state quantity of the battery is estimated by adopting EKF:
based on the equivalent mathematical model of the lithium iron phosphate battery, establishing a Kalman filtering state equation and an output equation of the lithium iron phosphate battery:
equation of state (10):
Figure GDA0002254928570000111
output equation (11):
ub(k)＝uoc(k)-i(k)×Rs(k)-u1(k)-u2(k)+v(k) (11)
corresponding to the general form (12) of the Kalman filtering equation of state, respectively
Figure GDA0002254928570000112
In the formula: u shapebFor the load terminal voltage of lithium iron phosphate batteries, CuseIs the effective capacity of the lithium iron phosphate battery, i.e. the available capacity of the lithium iron phosphate battery, IbIs the operating current of the lithium iron phosphate battery, SOC represents the state of charge of the lithium iron phosphate battery, UocThe open-circuit voltage of the lithium iron phosphate battery is a nonlinear function of SOC and is represented by a controllable voltage source RsThe ohmic resistance of the lithium iron phosphate battery, two RC links, R1、C1And R2、C2Respectively represents the electrochemical polarization and concentration polarization processes in the operation of the lithium iron phosphate battery, U1，U2Representing the corresponding voltage value, η representing the charging and discharging efficiency of the lithium iron phosphate battery, w (k) representing the system error, v (k) representing the empirical error;
according to a block diagram 4, estimating the SOC in real time:
where k | k-1 represents the result of the last state prediction, k-1| k-1 represents the optimal result at the last time, P (k), Q (k), R (k) corresponds to the covariance of X (k), w (k), v (k),
the Kalman filtering start must select a good initial value, which includes three state parameters, SOC (k), U1(k)，U2(k)，SOc (k) as an initial value, the SOC obtained from the last moment of last operation, while the lithium iron phosphate battery has little effect right after operation, considering that the polarization voltage is 0, and for the covariance q (k), r (k), defined as:
Figure GDA0002254928570000121
further comprises the following steps:
Figure GDA0002254928570000122
Figure GDA0002254928570000123
R(0)＝0.001。
the method comprises the steps of adopting a domestic lithium iron phosphate battery with the rated capacity of 40AH and the rated voltage of 3.2V to carry out experiment data acquisition, identifying relevant parameters of a model by combining the contents of the previous sections, modeling in Matlab/Simulink, and comparing output changes of the lithium iron phosphate battery after 500-1000 cycle times. And the SOC is estimated by EKF under a certain current and voltage working condition, and the validity of the SOC is verified.
The measured relation between the open-circuit voltage of the lithium iron phosphate battery and the SOC is shown in fig. 5, the curve in fig. 5 shows that an obvious nonlinear relation exists between the open-circuit voltage of the lithium iron phosphate battery and the SOC, the fitting curve can well reflect the change relation between the open-circuit voltage and the SOC, the fitting function is as shown in formula (13), and the open-circuit voltage of the lithium iron phosphate battery under different SOC levels is estimated according to the fitting function:
UOC＝-0.7644e-26.6346×SOC+3.2344+0.4834×SOC-1.2057×SOC2+0.9641×SOC3
according to the following method, discharge experiments are carried out on different new and old lithium iron phosphate batteries under the same experimental conditions.
According to the fact that the lithium iron phosphate battery runs in a state that delta SOC is x and the maximum charge-discharge cycle number Nm corresponding to the delta SOC is the number of the cells in the furnaceΔSOC＝xExperimental data of (a) to (b), on whichFitting the relation, wherein the fitting function is as shown in formula (5), and the maximum charge-discharge cycle number under a certain charge-discharge cycle depth in the life cycle of the lithium iron phosphate battery can be calculated according to the formula (5)
The maximum charge-discharge cycle number of the lithium iron phosphate battery when the lithium iron phosphate battery operates at different delta SOC is shown in figure 3, and the fitting function of the lithium iron phosphate battery is as follows (5):
according to the invention, the available capacity in the life cycle of the lithium iron phosphate battery is evaluated according to the graph 3, and it can be seen that the maximum charge-discharge cycle times of the life cycle corresponding to different delta SOCs are different, and the charge-discharge times of the lithium iron phosphate battery under the shallow charging and shallow discharging environment are more. The invention converts the cycle charge and discharge times under each delta SOC to the cycle times under full charge and discharge in the process of charging and discharging the lithium iron phosphate battery according to the formula 6.
Setting n times of charge and discharge at a certain time, and the depth of charge and discharge is x0、x1、…、xnAnd accumulating the equivalent charge and discharge coefficients under different charge and discharge depths to obtain the equivalent charge and discharge times of the lithium iron phosphate battery according to the formula (7).
Fig. 6 is a discharge curve of a lithium iron phosphate battery after 500 cycles, 1000 cycles, and 1500 cycles. The curve shows that after the lithium iron phosphate battery is subjected to different cycle times, under the same discharge rate and after a period of time, the voltage is obviously different, the terminal voltage is reduced in different ranges, and the discharge cut-off voltage is reached within the shortest time after 1000 times.
Further comparison did not take into account the difference in the change in terminal voltage of the lithium iron phosphate batteries at different SOC levels after the lithium iron phosphate batteries were verified, as shown in fig. 7.
The comparison curve shows that the lithium iron phosphate battery does not consider capacity loss and considers that the estimation of the front period and the rear period of the SOC generates a non-negligible error after the verification, and the error becomes larger along with the increase of the cycle number. The output voltage of the lithium iron phosphate battery under different SOC levels can also show obvious difference, which can seriously affect the accuracy of modeling and the estimation of the output voltage of the lithium iron phosphate battery.
Statistically, the error rates of the two compared to the actual curve are shown in Table 1.
TABLE 11000 Voltage error between different SOC intervals after cycle number
Figure GDA0002254928570000131
It can be seen from the table that the calculation error difference before and after the capacity verification is large, the error difference between different SOC intervals is large, and the error is larger under the low SOC level and the high SOC level and cannot be ignored. If the capacity of the lithium iron phosphate battery does not account for the capacity loss, the calculation error is about 0-11.2% after 1000 times of cycle times, the error is about 0-3.8% at the later stage of capacity correction, and the calculation error is greatly reduced. Obviously, the output accuracy of the model is higher after the capacity loss is considered, so that the estimation of the capacity of the current lithium iron phosphate battery is very necessary, and the improvement of the modeling accuracy of the lithium iron phosphate battery and the accurate estimation of the running state of the lithium iron phosphate battery are facilitated.
Because when the lithium iron phosphate battery energy storage system is applied to the new energy field, the charge-discharge characteristic that shows "random", the electric current of lithium iron phosphate battery is not single unchangeable, and the change of in-process electric current can be very violent, utilizes traditional ampere-hour measurement method to lead to the error very big under this condition, utilizes this problem of solution that the extended Kalman filtering algorithm can be fine, uses the model of building as the basis, according to having surveyed the electric voltage, can converge to the more accurate SOC of battery fast.
If the partial current working condition of the lithium iron phosphate battery is shown in fig. 8, and the voltage of the lithium iron phosphate battery is shown in fig. 9, the EKF can obtain the SOC change, specifically, the formula (10), the formula (11) and the formula (12):
and establishing a Kalman filtering state equation and an output equation of the lithium iron phosphate battery based on the equivalent mathematical model of the lithium iron phosphate battery.
Next, the SOC is estimated in real time according to the block diagram 4, which is shown in fig. 10.
The terms, diagrams, tables and the like in the embodiments of the present invention are used for further description, are not exhaustive, and do not limit the scope of the claims, and those skilled in the art can conceive of other substantially equivalent alternatives without inventive step in light of the teachings of the embodiments of the present invention, which are within the scope of the present invention.

Claims (1)

1.一种计及电池容量损失的磷酸铁锂电池建模及SOC状态估计方法，其特征在于,它包括以下内容：1. a lithium iron phosphate battery modeling and SOC state estimation method considering battery capacity loss, is characterized in that, it comprises the following content: 1)磷酸铁锂电池等效电路的数学模型1) Mathematical model of the equivalent circuit of lithium iron phosphate battery 采用戴维南等效电路模型，根据二阶RC等效电路模型，由基尔霍夫定理，建立模型状态方程为式(1)：Using the Thevenin equivalent circuit model, according to the second-order RC equivalent circuit model and Kirchhoff's theorem, the model state equation is established as formula (1):
Figure FDA0002254928560000011
Figure FDA0002254928560000011
 式中：Ub为磷酸铁锂电池负载端电压，Cuse为磷酸铁电池的有效容量，亦即磷酸铁锂电池的可用容量，Ib为磷酸铁锂电池的运行电流，SOC为磷酸铁锂电池的荷电状态，Uoc磷酸铁锂电池开路电压，是SOC的非线性函数，由可控电压源表示，Rs为磷酸铁锂电池的欧姆电阻，两个RC环节，R1、C1和R2、C2分别表示磷酸铁锂电池运行中的电化学极化和浓差极化过程，U1，U2表示其对应的电压值，η为磷酸铁锂电池充放电效率；In the formula: U b is the load terminal voltage of the lithium iron phosphate battery, C use is the effective capacity of the iron phosphate battery, that is, the available capacity of the lithium iron phosphate battery, I b is the operating current of the lithium iron phosphate battery, and SOC is the lithium iron phosphate battery. The state of charge of the battery, U oc the open circuit voltage of the lithium iron phosphate battery, is a nonlinear function of the SOC, represented by a controllable voltage source, R s is the ohmic resistance of the lithium iron phosphate battery, two RC links, R 1 , C 1 and R 2 and C 2 respectively represent the electrochemical polarization and concentration polarization process in the operation of the lithium iron phosphate battery, U 1 and U 2 represent the corresponding voltage values, and η is the charge and discharge efficiency of the lithium iron phosphate battery; 由磷酸铁锂电池的等效电路模型看出，左右两侧电路网络通过SOC耦合，SOC是联系两部分的重要因子，而从模型的状态方程式(1)看出，磷酸铁锂电池的输出电压由磷酸铁锂电池的开路电压和极化电压共同决定，其中磷酸铁锂电池的极化电压与其相对应的电阻、电容值和电流值大小直接相关，精确地对磷酸铁锂电池实时的可用容量(Cuse)，SOC，开路电压值和电阻值、电容值进行估计是磷酸铁锂电池建模的基础性工作；It can be seen from the equivalent circuit model of the lithium iron phosphate battery that the circuit networks on the left and right sides are coupled through SOC, and the SOC is an important factor connecting the two parts. From the state equation (1) of the model, it can be seen that the output voltage of the lithium iron phosphate battery It is determined by the open circuit voltage and polarization voltage of the lithium iron phosphate battery, in which the polarization voltage of the lithium iron phosphate battery is directly related to its corresponding resistance, capacitance and current value, which can accurately determine the real-time available capacity of the lithium iron phosphate battery. (C use ), SOC, open circuit voltage value, resistance value, capacitance value estimation is the basic work of lithium iron phosphate battery modeling; 2)磷酸铁锂电池模型相关参数辨识2) Identification of relevant parameters of lithium iron phosphate battery model 因磷酸铁锂电池工作状态受到放电深度、循环次数和容量衰减等因素的影响，其等效电路模型参数随负载和外部环境的变化而变化，因此，为得到更可靠的模型，离线建模时需在多因素条件下对磷酸铁锂电池进行实验，并建立参数数据关系表达式；Because the working state of the lithium iron phosphate battery is affected by factors such as the depth of discharge, the number of cycles, and the capacity decay, its equivalent circuit model parameters change with the load and external environment. Therefore, in order to obtain a more reliable model, offline modeling It is necessary to carry out experiments on lithium iron phosphate batteries under multi-factor conditions, and to establish parameter data relationship expressions; SOC是阻容模型所有参数最为重要的影响因子，在磷酸铁锂电池标准运行状态条件下确定阻抗参数与SOC的函数关系是阻容建模工作最基本也是最重要的部分，正常工作环境中磷酸铁锂电池Uoc与SOC对应关系稳定，受温度影响甚微，因此Uoc是由SOC唯一决定的，其关系通过拟合函数得到；SOC is the most important factor affecting all parameters of the RC model. Determining the functional relationship between the impedance parameters and SOC under the standard operating conditions of the lithium iron phosphate battery is the most basic and most important part of the RC modeling work. The corresponding relationship between U oc and SOC of Fe-Li battery is stable, and is little affected by temperature, so U oc is uniquely determined by SOC, and its relationship is obtained by fitting function; 模型中的电阻电容参数可以通过以下方式得到，在不同SOC下，可设置初始值为0.2，步长为0.05，对其进行空载加载放电和充电实验，磷酸铁锂电池由空载状态动作进行放电实验时，磷酸铁锂电池电压会发生一个陡降的时期，此时磷酸铁锂电池的极化电压的变化很小忽略不计，引起这种变化的主要原因是磷酸铁锂电池欧姆电阻Rs上引起的压降，由这段数据变化对电池内部的欧姆内阻进行估计，接下来电池的端电压会进入一个类指数的变化期，这是因为电池RC电路上的极化电压U1，U2缓慢减少导致，此时段认为是一个零状态相应的时段，用式(2)进行描述：The resistance and capacitance parameters in the model can be obtained in the following ways. Under different SOC, the initial value can be set to 0.2 and the step size is 0.05, and no-load loading, discharging and charging experiments can be performed on it. The lithium iron phosphate battery is operated in no-load state. During the discharge experiment, the voltage of the lithium iron phosphate battery will drop sharply. At this time, the change of the polarization voltage of the lithium iron phosphate battery is very small and negligible. The main reason for this change is the ohmic resistance R s of the lithium iron phosphate battery. The ohmic resistance inside the battery is estimated from this data change, and then the terminal voltage of the battery will enter an exponential change period, this is because the polarization voltage U 1 on the battery RC circuit, Due to the slow decrease of U 2 , this period is considered to be a period corresponding to a zero state, which is described by formula (2):
Figure FDA0002254928560000021
Figure FDA0002254928560000021
 其中Ub表示磷酸铁锂电池的端电压，UA表示A点处的磷酸铁锂电池端电压，a，b是待拟合的参变量，对式(2)进行拟合得到对应的a，b，τ1，τ2值，并用其对RC电路上的电阻电容进行估计计算，具体为式(3)：where U b represents the terminal voltage of the lithium iron phosphate battery, U A represents the terminal voltage of the lithium iron phosphate battery at point A, a and b are the parameters to be fitted, and the corresponding a and b are obtained by fitting formula (2). , τ 1 , τ 2 values, and use them to estimate and calculate the resistance and capacitance on the RC circuit, specifically formula (3):
Figure FDA0002254928560000022
Figure FDA0002254928560000022
 Ib表示磷酸铁锂电池的运行电流，τ1，τ2是待拟合的参变量，两个RC环节，R1、C1和R2、C2分别表示磷酸铁锂电池运行中的电化学极化和浓差极化过程；I b represents the operating current of the lithium iron phosphate battery, τ 1 , τ 2 are the parameters to be fitted, two RC links, R 1 , C 1 and R 2 , C 2 represent the current of the lithium iron phosphate battery during operation, respectively Chemical polarization and concentration polarization processes; 据此，利用式(4)对充电过程中的相应电阻电容进行估计，以此类推得到磷酸铁锂电池在不同SOC下的电容、电阻值，对其进行样条插值得到不同状态下的R、C值，According to this, the corresponding resistance and capacitance in the charging process are estimated by formula (4), and the capacitance and resistance values of the lithium iron phosphate battery under different SOCs are obtained by analogy, and spline interpolation is performed on them to obtain R, C value,
Figure FDA0002254928560000023
Figure FDA0002254928560000023
 3)磷酸铁锂电池可用容量的评估3) Evaluation of the available capacity of lithium iron phosphate batteries 磷酸铁锂电池寿命是有限的，随着磷酸铁锂电池的生命周期的不断动作充放电，磷酸铁锂电池内部锂离子损失和活性材料衰退，会引起磷酸铁锂电池内部不可逆的容量损失，直接影响到磷酸铁锂电池的使用寿命，所以对磷酸铁锂电池进行实时容量评估，有利于正确的认识磷酸铁锂电池的实时状态，对于预估磷酸铁锂电池未来某一时刻的状态有积极作用，The life of lithium iron phosphate battery is limited. With the continuous action of charging and discharging in the life cycle of lithium iron phosphate battery, the loss of lithium ions inside the lithium iron phosphate battery and the decline of active materials will cause irreversible capacity loss inside the lithium iron phosphate battery. It affects the service life of the lithium iron phosphate battery, so the real-time capacity evaluation of the lithium iron phosphate battery is conducive to a correct understanding of the real-time status of the lithium iron phosphate battery, and has a positive effect on estimating the status of the lithium iron phosphate battery at a certain moment in the future. , 根据磷酸铁锂电池运行在ΔSOC＝x与其所对应的最大充放电循环次数Nm|ΔSOC＝x的实验数据，对其关系进行拟合，拟合函数为式(5)，由式(5)计算磷酸铁锂电池寿命周期内在某充放电循环深度下的最大充放电循环次数According to the experimental data of the lithium iron phosphate battery operating at ΔSOC=x and its corresponding maximum number of charge and discharge cycles N m | ΔSOC=x , the relationship is fitted. Calculate the maximum number of charge and discharge cycles at a certain depth of charge and discharge cycles within the life cycle of a lithium iron phosphate battery 磷酸铁锂电池运行在不同ΔSOC时最大充放电循环次数拟合函数如式(5)：The fitting function of the maximum number of charge-discharge cycles for lithium iron phosphate batteries operating at different ΔSOC is shown in formula (5):
Figure FDA0002254928560000031
Figure FDA0002254928560000031
 其中：ΔSOC＝x，Nm|ΔSOC＝x表示最大充放电循环次数；Where: ΔSOC=x, N m | ΔSOC=x represents the maximum number of charge-discharge cycles; 对磷酸铁锂电池生命周期内的可用容量进行评估，得出不同ΔSOC对应生命周期的最大充放电循环次数不同，浅充浅放环境下磷酸铁锂电池的充放电次数更多，对磷酸铁锂电池充放电过程中各个ΔSOC下的循环充放电次数对应于满充满放下的循环次数按式(6)进行折算；The available capacity in the life cycle of the lithium iron phosphate battery is evaluated, and it is concluded that the maximum number of charge and discharge cycles in the life cycle corresponding to different ΔSOC is different. During the charging and discharging process of the battery, the number of cycles of charging and discharging at each ΔSOC corresponds to the number of cycles when the battery is fully charged and discharged, and is converted according to formula (6);
Figure FDA0002254928560000032
Figure FDA0002254928560000032
 式中：Nm(x)为当磷酸铁锂电池充放电深度等于x时磷酸铁锂电池的最大循环次数，其中x∈(0,1)；Nm(1)为当磷酸铁锂电池充放电深度等于1时磷酸铁锂电池的最大循环次数，α(x)表示等效的循环深度；In the formula: N m (x) is the maximum number of cycles of the lithium iron phosphate battery when the charging and discharging depth of the lithium iron phosphate battery is equal to x, where x∈(0,1); The maximum number of cycles of the lithium iron phosphate battery when the depth of discharge is equal to 1, α(x) represents the equivalent cycle depth; 设某一时刻进行了n次充放电次数，充放电深度分别为x0、x1、…、xn，将不同充放电深度下等效充放电系数累加，则可得磷酸铁锂电池等效充放电次数如下式(7)：Assuming that n times of charge and discharge are performed at a certain time, the charge and discharge depths are x 0 , x 1 , ..., x n , respectively, and the equivalent charge and discharge coefficients under different charge and discharge depths are accumulated to obtain the equivalent of lithium iron phosphate battery. The number of charge and discharge times is as follows (7):
Figure FDA0002254928560000033
Figure FDA0002254928560000033
 其中，Nm’表示等效充放电系数；Among them, Nm' represents the equivalent charge-discharge coefficient; 磷酸铁锂电池的健康状态(state of health，SOH),也称为磷酸铁锂电池的寿命状态，定义为磷酸铁锂电池从满充状态以一定的倍率放电到截止电压所放出的容量与其标称容量的比值，反应了磷酸铁锂电池的寿命状况，定义为式(8)：The state of health (SOH) of the lithium iron phosphate battery, also known as the life state of the lithium iron phosphate battery, is defined as the capacity released by the lithium iron phosphate battery from the fully charged state at a certain rate to the cut-off voltage and its standard. The ratio of the capacity, which reflects the life of the lithium iron phosphate battery, is defined as formula (8):
Figure FDA0002254928560000034
Figure FDA0002254928560000034
 式中，CCapicity表示磷酸铁锂电池的标称容量，Cuse表示磷酸铁锂电池的可用容量；In the formula, C Capicity represents the nominal capacity of the lithium iron phosphate battery, and C use represents the available capacity of the lithium iron phosphate battery; 则t时刻磷酸铁锂电池的可用容量用式(9)进行衡量：Then the available capacity of the lithium iron phosphate battery at time t is measured by formula (9):
Figure FDA0002254928560000035
Figure FDA0002254928560000035
 γ为一常量，含义为磷酸铁锂电池正常工作允许出现的容量损失最大值的百分比，即SOH最大值，取0.3，SOH的大小反映了磷酸铁锂电池的健康状态，表示磷酸铁锂电池老化程度，变化范围为0～100％，当SOH减小到20％～30％时，磷酸铁锂电池功能基本失效，不能完成基本的充放电任务；γ is a constant, which means the percentage of the maximum capacity loss allowed by the normal operation of the lithium iron phosphate battery, that is, the maximum value of SOH, which is 0.3. The size of the SOH reflects the health status of the lithium iron phosphate battery, indicating the aging of the lithium iron phosphate battery. When the SOH is reduced to 20% to 30%, the function of the lithium iron phosphate battery basically fails, and the basic charge and discharge tasks cannot be completed; 4)用EKF算法对SOC进行状态估计4) Using the EKF algorithm to estimate the state of the SOC 由步骤1)-3)，SOC是磷酸铁锂电池运行过程重要的参变量，而且磷酸铁锂电池的荷电状态估计是储能装置中磷酸铁锂电池组安全、可靠运行的保证，精确地对磷酸铁锂电池实时SOC进行估计，便于对磷酸铁锂电池的实时控制策略进行调整；From steps 1)-3), SOC is an important parameter in the operation process of the lithium iron phosphate battery, and the estimation of the state of charge of the lithium iron phosphate battery is the guarantee for the safe and reliable operation of the lithium iron phosphate battery pack in the energy storage device. Estimate the real-time SOC of the lithium iron phosphate battery, which is convenient to adjust the real-time control strategy of the lithium iron phosphate battery; 卡尔曼滤波法算法是由状态方程、输出方程以及系统过程噪声与观测噪声的统计特性一起构成的，根据系统的状态方程和输出方程求出需要估算的状态或参数，能够对磷酸铁锂电池SOC做出最小方差上的最优估算，便于对磷酸铁锂电池未来某一时刻进行预测和估计，卡尔曼滤波算法是一种利用线性系统的状态方程，而磷酸铁锂电池是一种非线性模型，将磷酸铁锂电池的非线性模型进行卡尔曼滤波算法(EKF)扩展，采用EKF对电池的实时SOC状态量进行估计：The Kalman filter algorithm is composed of the state equation, the output equation, and the statistical characteristics of the system process noise and observation noise. According to the state equation and output equation of the system, the state or parameters to be estimated can be obtained. Make the optimal estimation on the minimum variance, which is convenient for predicting and estimating the lithium iron phosphate battery at a certain time in the future. The Kalman filter algorithm is a state equation that uses a linear system, while the lithium iron phosphate battery is a nonlinear model. , the nonlinear model of the lithium iron phosphate battery is extended by the Kalman filter algorithm (EKF), and the EKF is used to estimate the real-time SOC state quantity of the battery: 以磷酸铁锂电池等效数学模型为基础，建立磷酸铁锂电池的卡尔曼滤波状态方程和输出方程：Based on the equivalent mathematical model of lithium iron phosphate battery, the Kalman filter state equation and output equation of lithium iron phosphate battery are established: 状态方程式(10)：State equation (10):
Figure FDA0002254928560000041
Figure FDA0002254928560000041
 输出方程式(11)：Output equation (11): ub(k)＝uoc(k)-i(k)×Rs(k)-u1(k)-u2(k)+v(k) (11)u b (k)=u oc (k)-i(k)×R s (k)-u 1 (k)-u 2 (k)+v(k) (11) 对应于卡尔曼滤波状态方程的一般形式式(12)，分别令Corresponding to the general form of the Kalman filter state equation (12), let
Figure FDA0002254928560000051
Figure FDA0002254928560000051
 式中：Ub为磷酸铁锂电池负载端电压，Cuse为磷酸铁锂电池的有效容量，也即磷酸铁锂电池的可用容量，Ib为磷酸铁锂电池的运行电流，SOC表示磷酸铁锂电池的荷电状态，Uoc磷酸铁锂电池开路电压，是SOC的非线性函数，由可控电压源表示，Rs为磷酸铁锂电池的欧姆电阻，两个RC环节，R1、C1和R2、C2分别表示磷酸铁锂电池运行中的电化学极化和浓差极化过程，U1，U2表示其对应的电压值，η为磷酸铁锂电池充放电效率，w(k)表示系统误差，v(k)表示经验误差；In the formula: U b is the load terminal voltage of the lithium iron phosphate battery, C use is the effective capacity of the lithium iron phosphate battery, that is, the available capacity of the lithium iron phosphate battery, I b is the operating current of the lithium iron phosphate battery, and SOC represents the iron phosphate The state of charge of the lithium battery, U oc the open circuit voltage of the lithium iron phosphate battery, is a nonlinear function of the SOC, represented by a controllable voltage source, R s is the ohmic resistance of the lithium iron phosphate battery, two RC links, R 1 , C 1 and R 2 and C 2 represent the electrochemical polarization and concentration polarization process of the lithium iron phosphate battery, respectively, U 1 and U 2 represent the corresponding voltage values, η is the charge and discharge efficiency of the lithium iron phosphate battery, w (k) represents the systematic error, v(k) represents the empirical error; 实时进行SOC估计：SOC estimation in real time: 其中k|k-1表示上一状态预测的结果，k-1|k-1表示上一时刻的最优结果，P(k)，Q(k)，R(k)对应于X(k)，w(k)，v(k)的协方差，Where k|k-1 represents the result of the previous state prediction, k-1|k-1 represents the optimal result at the previous moment, P(k), Q(k), R(k) correspond to X(k) , w(k), covariance of v(k), 卡尔曼滤波启动必须选定好初值，包含三个状态参数，分别为SOC(k)，U1(k)，U2(k)，SOC(k)根据上一次工作的最后时刻得到的SOC作为初值，而磷酸铁锂电池刚工作时几乎效应并不明显，认为极化电压为0，而对于协方差Q(k)，R(k)，定义为：Kalman filter startup must select the initial value, including three state parameters, namely SOC (k), U 1 (k), U 2 (k), SOC (k) according to the SOC obtained at the last moment of the previous work As the initial value, the effect of the lithium iron phosphate battery is not obvious when it is just working, and the polarization voltage is considered to be 0. For the covariance Q(k), R(k), it is defined as:
Figure FDA0002254928560000052
Figure FDA0002254928560000052
 进一步为：Further as:
Figure FDA0002254928560000053
Figure FDA0002254928560000053
 R(0)＝0.001。R(0)=0.001.
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