CN112379270B - Rolling time domain estimation method for state of charge of power battery of electric automobile - Google Patents
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- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 description 2
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 description 2
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- 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
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
- B60L58/00—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles
- B60L58/10—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles for monitoring or controlling batteries
- B60L58/12—Methods or circuit arrangements for monitoring or controlling batteries or fuel cells, specially adapted for electric vehicles for monitoring or controlling batteries responding to state of charge [SoC]
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- 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]
- G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
- G01R31/3842—Arrangements for monitoring battery or accumulator variables, e.g. SoC combining voltage and current measurements
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- Y02T10/60—Other road transportation technologies with climate change mitigation effect
- Y02T10/70—Energy storage systems for electromobility, e.g. batteries
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Abstract
The invention discloses a rolling time domain estimation method for the state of charge of a power battery of an electric automobile, which comprises the following steps: step one: establishing an equivalent circuit model of the battery; step two: describing battery open circuit voltage U with piecewise linear function oc Relationship with SOC; step three: describing the piecewise linear function relation in the second step by using a mixed logic model; step four: taking physical constraint of the power battery into consideration, establishing mathematical description of the SOC estimation problem; step five: and a rolling time domain estimation strategy is designed to realize estimation of the SOC of the power battery. The method has the characteristics of high calculation efficiency, simple model and low requirement on the precision of the battery model, can explicitly process the physical constraint of each variable in the power battery, and can reduce estimation errors caused by model parameter perturbation, thereby improving the precision and reliability of SOC estimation.
Description
Technical Field
The invention belongs to the technical field of automobile control, relates to a rolling time domain estimation method for the state of charge of an electric automobile power battery, and in particular relates to a method for estimating the state of charge of the electric automobile power battery by utilizing hybrid logic modeling and rolling time domain estimation.
Background
New energy automobiles are an important direction for transformation and upgrading of the automobile industry. In recent years, lithium ion batteries have become a major choice for batteries for electric vehicles because of a series of advantages such as high energy density, high output power, and long charge-discharge life. Because of the great demand of automobiles for electric quantity, a plurality of single batteries are usually selected to form a large-sized battery pack, and the safety problem caused by the large-sized battery pack is also gradually highlighted. For safety reasons, the range of battery power used by most electric vehicles is limited to a 10% -90% State of Charge (SOC) range or even less. It follows that at least one fifth of the battery power is left inactive and not effectively utilized. The unused power not only increases the cost of the battery, but also shortens the cruising ability of the battery. Therefore, if the method is used for accurately acquiring the charge state of the battery, more electric energy of the automobile battery can be fully utilized, and the method has very important effects of increasing the endurance capacity of the battery, prolonging the service life of the battery and reducing the cost of the battery pack of the electric automobile.
In the existing method, battery charge state estimation based on an ampere-hour integration method faces an error accumulation problem; the open-circuit voltage method needs to carry out shelving detection on the automobile battery, and cannot meet the SOC estimation requirement in the running process of the automobile; the model-based SOC estimation method combines an algorithm with a model, and is easy to obtain higher estimation precision compared with the former two methods, but improving the robustness and instantaneity of the algorithm is always a difficult problem in the field of SOC estimation.
CN110161423a discloses a power lithium battery state joint estimation method based on a multidimensional coupling model, which is to build an electric-thermal-aging coupling model of a battery, test the charge and discharge quantity of the battery to estimate SOH (State of Health) value of the battery, correct model parameters and estimate the SOC of the battery by combining a rolling time domain estimation strategy. However, the method requires a large amount of experimental data when a coupling model is built, so that the algorithm implementation difficulty is increased, and a relation between the SOC and the open-circuit voltage is modeled by adopting a sixth-order polynomial, so that the complexity of the model is increased, and the timeliness of the algorithm is reduced.
CN104773086a discloses a method and system for estimating battery impedance parameters using rolling time domain regression analysis, by measuring battery input and output, estimating parameters in a circuit model. However, this method estimates the SOC by estimating the open circuit voltage, which may cause the estimation accuracy of the SOC to be seriously dependent on the relationship between the SOC and the open circuit voltage, thereby affecting the estimation accuracy and robustness of the SOC.
CN108318823a discloses a lithium battery state of charge estimation method based on noise tracking, which estimates the battery SOC by constructing a nonlinear state space equation of the battery and combining a nonlinear rolling time domain estimation strategy. However, the method uses a high-order polynomial description for the nonlinear relation between the SOC and the open-circuit voltage, and the introduced nonlinearity can increase the complexity of the algorithm, so that the real-time performance of the algorithm is reduced.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a rolling time domain estimation method for the state of charge of a power battery of an electric automobile. The method has the characteristics of high calculation efficiency, simple model and low requirement on the precision of the battery model, can explicitly process the physical constraint of each variable in the power battery, and can reduce estimation errors caused by model parameter perturbation, thereby improving the precision and reliability of SOC estimation.
The invention aims at realizing the following technical scheme:
the rolling time domain estimation method for the state of charge of the power battery of the electric automobile comprises the following steps:
step one: establishing an equivalent circuit model of the battery;
step two: describing battery open circuit voltage U with piecewise linear function oc Relationship with SOC:
U oc ＝k i SOC+d i ；
wherein k is i 、d i For each linear function coefficient, i=1, 2,..n, n is the minimum number of segments meeting the error requirement, each segment being bounded above by [ a ] 1 ... a n ]The lower bound is [ b ] 1 ... b n ]；
Step three: describing the piecewise linear function relation in the second step by using a mixed logic model:
wherein z is i For each segment a corresponding open circuit voltage OCV, delta i As a logical variable, M corresponds to the parameter (k i 、d i ) All z under the condition i Maximum among the maximum values that can be reached, m corresponds to all z i The minimum of the minimum values that can be reached;
step four: taking physical constraints of the power battery into consideration, establishing mathematical description of SOC estimation problem, namely using measurable battery terminal voltage U based on a battery dynamics equation and constraint conditions thereof L (y in mathematical model) and charge-discharge current i L (u in mathematical model), the system state X including the battery SOC is estimated:
C' k ＝[1 -1 -1 Θ]；
D' k ＝[-R 0 ]；
y＝U L ；
u＝i L ；
the constraint condition given in the third step and the physical constraint of the battery variable are met;
wherein X is represented by all z i And delta i Battery polarization voltage U pa And U pc The optimal variable composed of the battery SOC, y is the output voltage of the battery, W is the system noise, V is the measurement noise, Θ is a matrix or vector with proper dimension, and all elements are 0;
step five: the rolling time domain estimation strategy is designed to realize the estimation of the SOC of the power battery, and the specific steps are as follows:
(1) According to the battery model and the measurement data, initialized parameters Q, P are set 0 R, initial estimated stateAnd the length N of the rolling time domain, wherein Q is a process noise covariance matrix, R is a measurement noise covariance matrix, and P 0 A covariance initial matrix for estimating errors;
(2) When the scroll estimated time T does not exceed N, the optimization problem is solved using the following equation:
the battery dynamics equation and the constraint condition thereof are met;
the obtained optimization solution is as follows:
according to the estimation result, calculating the estimation value of the current state through a recursive formula of the state:
wherein W is k V is system noise k For measuring noise;
(3) When the scroll estimated time T exceeds N, the optimization problem is solved using the following equation:
the battery dynamics equation and the constraint condition thereof are met;
wherein P is T-N Calculated by recursion of:
P j+1 ＝BQB -1 +A(P j -P j C T (R+CP j C T ) -1 CP j )A T ；
the obtained optimization solution is as follows:
according to the estimation result, calculating the estimation value of the current state through a recursive formula of the state:
(4) A priori estimates of the next time state are calculated using the following equation:
(5) After the new data set is obtained, the data is returned to (2) or (3) again according to the size relation between the rolling estimation time T and the rolling estimation length N, and the cyclic calculation is carried out.
Compared with the prior art, the invention has the following advantages:
1. the invention is easy to realize, does not need an additional sensor, and has lower cost;
2. the invention utilizes the piecewise linearization method and combines the mixed logic model to describe the nonlinear relation between the SOC and the open-circuit voltage, thereby effectively simplifying the battery model and having better algorithm timeliness;
3. the invention can explicitly process the physical constraint of the battery state, so that the estimation result is more reasonable;
4. the invention can effectively improve the estimation precision of the battery SOC through reconstructing the system disturbance.
Drawings
FIG. 1 is an equivalent circuit model of a power cell;
FIG. 2 is a graph of the nonlinear relationship between SOC and OCV;
FIG. 3 is a flow chart of a rolling horizon estimation strategy of the present invention;
FIG. 4 is an experimental result of the algorithm of the present invention corresponding to an ambient temperature of 40 ℃;
fig. 5 is an experimental result of the algorithm of the present invention corresponding to an ambient temperature of 10 c.
Detailed Description
The following description of the present invention is provided with reference to the accompanying drawings, but is not limited to the following description, and any modifications or equivalent substitutions of the present invention should be included in the scope of the present invention without departing from the spirit and scope of the present invention.
The invention provides a rolling time domain estimation method for the state of charge of a power battery of an electric automobile, which comprises the following steps:
step one: and establishing an equivalent circuit model of the power battery.
The method selects a second-order equivalent circuit, namely a double RC model to simulate the charge and discharge characteristics of the lithium ion battery by comprehensively considering the precision of the model and the complexity of the model. It should be noted that the method of the present invention is not limited to the second-order equivalent circuit model, and is also suitable for equivalent circuit models of other orders and other forms.
As shown in fig. 1, U oc And U L OCV (open circuit voltage) and terminal voltage of the battery, respectively; resistor R 0 The ohmic internal resistance of the battery is used for describing the charge and discharge energy loss of the battery; r is R pa 、R pc 、C pa 、C pc Respectively representing polarization resistance and capacitance; u (U) pa And U pc Terminal voltage of the corresponding polarized capacitor; i.e L The current through the battery is indicated, with positive discharge and negative charge.
From the model, the relationship between the element voltages can be described as:
U L (t)＝U pc (t)-U pa (t)-i L (t)R 0 (1)；
the dynamic voltage between the polarized capacitances can be described as:
and SOC may be expressed as:
wherein C is N The rated capacity of the battery, η is coulombic efficiency.
Thus, the system state can be defined as:
the output is:
y＝U L ；
the input is:
u＝i L 。
by combining the above formulas, it can be derived that:
wherein:
wherein x is 1 Is U (U) pa ，x 2 Is U (U) pc ，x 3 The SOC is the SOC, w (t) is the external noise, and v (t) is the measurement noise. h ((x (t), u (t)) comprises the open circuit voltage of the battery, and the values of the open circuit voltage and the SOC (i.e., x) 3 ) The second step will be described in detail.
Step two: the battery open circuit voltage versus SOC is described by a piecewise linear function.
To measure the relationship between the open circuit voltage (Open Circuit Voltage, OCV) and SOC of the battery, the battery is first charged to a cutoff voltage in a constant current, constant voltage manner. After the battery is kept stand for a period of time, the current is continuously discharged to a specific SOC (state of charge) at a certain multiplying power, the battery is kept stand for a period of time, and the operation is repeated until the battery is discharged to a cut-off voltage. In the whole discharging process, the battery terminal voltage and the load current are synchronously collected at the frequency of 10 HZ. Based on the SOC at each rest point and the corresponding open circuit voltage measurement value, the relationship between open circuit voltage and SOC as shown in fig. 2 can be obtained.
As can be seen from fig. 2, the OCV and SOC relationship is significantly nonlinear, which is processed piecewise linearly for simplicity of the model and precision assurance. When in segmentation, firstly, an allowable error upper bound is set, and the minimum number of segments meeting the error requirement is searched by calculating a fitting error and is recorded as n. The upper boundary of each segment is [ a ] 1 ... a n ]The lower bound is [ b ] 1 ... b n ]It is possible to obtain:
U oc ＝k i SOC+d i (7)；
wherein k is i 、d i For each linear function coefficient, i=1, 2.
In connection with the piecewise linear description of SOC-OCV above, the battery measurement equation in step one may be rewritten as:
h((x(t),u(t))＝k i x 3 +d i -x 1 -x 2 -uR 0 (8)；
on the basis, discretizing the state space equation (5) to obtain a discrete state space equation of the RC model, wherein the discrete state space equation is as follows:
wherein:
C ik ＝[-1 -1 k i ] (12)；
D k ＝[-R 0 ] (13)。
step three: describing the piecewise linear function relation in the second step by using a mixed logic model.
Since the relationship between the open circuit voltage and the SOC at this time is a piecewise linear function, the switching of the multiple modes is involved, which is described as a hybrid logic model, the estimation model can be simplified.
The piecewise linear function of SOC-OCV is first converted to the linear constraint problem of hybrid logic.
Setting a logic variable delta i When it is equal to 1, it means that the SOC-OCV curve is on the i-th interval of the corresponding segment, as shown in formula (14):
let the open circuit voltage OCV corresponding to each segment be z i Then z is at this time i The calculation formula of (2) is as follows:
z i ＝(k i SOC+d i )δ i (15)。
meanwhile, the open circuit voltage OCV has the expression:
from this, it can be derived about the variable z i Delta i The linear constraint of (2) is:
wherein M corresponds to the parameter (k i 、d i ) All z under the condition i Maximum among the maximum values that can be reached, m corresponds to all z i The minimum of the minimum values that can be reached.
SOC (i.e. x in the variable x 3 ) And logic variable delta i The linear logic constraint of (2) is:
δ i the constraints of the self are:
and delta i It needs to be a non-negative integer, i.e. it may take on values of 0 and 1.
Based on the above analysis, the piecewise linear relation between open circuit voltage and SOC described by equation (7) can be converted into a relation z described by equations (17) to (19) i 、δ i 、x 3 Linear constraints are described.
Further, the battery measurement equation may be described as
Step four: a mathematical description of the SOC estimation problem is established taking into account the physical constraints of the power cell.
On this basis, the physical constraints of the individual variables themselves are considered. SOC ranges from 0 to 1 for U according to physical definition pa And U pc The range is set to U in consideration of the charge and discharge characteristics of the battery min V～U max V, wherein positive value represents discharge, negative value represents charge, U min And U max Can be determined experimentally. The physical constraint of the final obtained variable is
And (3) selecting a new variable by combining a measurement equation described by the mixed logic model given in the step (III):
X＝[z x δ] (22)。
new state space equations and constraints can be derived as follows:
wherein:
C' k ＝[1 -1 -1 Θ] (26)；
D' k ＝[-R 0 ] (27)；
where Θ is a matrix or vector of appropriate dimensions, all elements are 0.
The state space mathematical model of the hybrid logic is built up, and given by equations (23) - (27) and constraints (17), (18), (19) and (21), an estimator is required to be designed to estimate the unmeasurable SOC using the measurable battery terminal voltage (y in mathematical model) and the charge-discharge current (u in mathematical model), and meet the requirements of estimation accuracy, instantaneity and robustness.
Step five: and a rolling time domain estimation strategy is designed to realize estimation of the SOC of the power battery.
In combination with the previously built model, the initial state of systemization is set as x 0 At time T, all measurement data areThe interference sequence is->Then:
setting the objective function as
Wherein Q is a process noise covariance matrix, R is a measurement noise covariance matrix, and P 0 The constraints that need to be satisfied in order to estimate the covariance initial matrix of the error are equations (17), (18), (19) and (21).
The solving of the constraint estimation problem is to estimate the initial state of the system in the current time domain and the disturbance acting on the system by minimizing the objective function on the premise of meeting the constraint condition, and calculate the estimated value of the current state of the system by the dynamic equation of the system.
Supplementing the latest measurement data at each sampling time into a measurement output sequence according to the principle of rolling optimizationThe optimization problem is then solved again online.
Assume that there is an optimal solution to the optimization problem at time T, noted as
Over time, the value of T becomes larger and larger, and the data required by the method is too much, so that the calculated amount is too large, and the calculated amount of the system is reduced by adopting approximate rolling time domain estimation.
The window length N is set, namely, the method only considers the latest N groups of data, so that the problem of excessive data of full-information rolling time domain estimation is effectively avoided.
Dividing the problem into two parts, and respectively processing the parts with the number of information not reaching N and exceeding N, wherein for the part exceeding N, the objective function can be updated as follows:
defining an arrival cost function as:
typically, to narrow down the data, selectWherein P is T-N Calculated by recursion of:
P j+1 ＝BQB -1 +A(P j -P j C T (R+CP j C T ) -1 CP j )A T ；
the problem can be described again as a quadratic programming problem:
the optimal solution is recorded asThe state estimate for the system at time T is:
in summary, the implementation steps of the present invention are shown in fig. 3, and include:
1. establishing a mathematical model of the battery;
2. performing piecewise linear fitting on the SOC-OCV curve;
3. converting the piecewise linear fit curve into linear constraints of the hybrid logic model;
4. according to the battery model and the measurement data, initialized parameters Q, P, R and initial estimated states are setThe length N of the rolling time domain;
5. when the scroll estimation time does not exceed N, solving the optimization problem using equation (30) yields an optimization solution of:
according to the estimation result, calculating the estimation value of the current state through a recursive formula of the state:
6. when the scroll estimation time exceeds N, solving the optimization problem using equation (32) yields an optimization solution of:
according to the estimation result, calculating the estimation value of the current state through a recursive formula of the state:
7. a priori estimates of the next time instant are calculated using the following equation:
8. after the new data set is obtained, the step 5 or step 6 data updating is returned again according to the size relation between the rolling estimation time T and the rolling estimation length N, and the cyclic calculation is carried out.
Finally, battery data of 40 ℃ and 10 ℃ are selected for experimental verification, the two groups of experimental temperatures have larger difference, but the same SOC-OCV model and parameters are adopted, the operation results are shown in fig. 4 and 5, the method has higher accuracy on SOC estimation, battery parameter deviation caused by different environment temperatures does not have obvious influence on the SOC estimation result, and the robustness of the method on model parameter change is verified.
Claims (2)
1. The method for estimating the state of charge of the power battery of the electric automobile in a rolling time domain is characterized by comprising the following steps:
step one: establishing an equivalent circuit model of the battery;
step two: describing battery open circuit voltage U with piecewise linear function oc Relation to SOC, the open circuit voltage U of the battery oc The relation with SOC is:
U oc ＝k i SOC+d i ；
wherein k is i 、d i For each linear function coefficient, i=1, 2,..n, n is the minimum number of segments meeting the error requirement, each segment being bounded above by [ a ] 1 ...a n ]The lower bound is [ b ] 1 ...b n ]；
Step three: describing the piecewise linear function relation in the second step by using a mixed logic model:
wherein z is i For each segment a corresponding open circuit voltage OCV, delta i As a logical variable, M corresponds to the parameter k at each segment i 、d i All z under the condition i Maximum among the maximum values that can be reached, m corresponds to all z i The minimum of the minimum values that can be reached;
step four: taking physical constraints of the power battery into consideration, establishing mathematical description of SOC estimation problem, namely using measurable battery terminal voltage U based on a battery dynamics equation and constraint conditions thereof L And charge-discharge current i L Estimating a system state X including a battery SOC, wherein the system state X including the battery SOC is:
C' k ＝[1-1-1Θ]；
D' k ＝[-R 0 ]；
y＝U L ；
u＝i L ；
the constraint condition given in the third step and the physical constraint of the battery variable are met;
wherein X is represented by all z i And delta i Battery polarization voltage U pa And U pc The optimal variable composed of the battery SOC, y is the output voltage of the battery, W is the system noise, V is the measurement noise, Θ is a matrix or vector with proper dimension, and all elements are 0;
step five: and a rolling time domain estimation strategy is designed to realize estimation of the SOC of the power battery.
2. The method for estimating the state of charge in rolling time domain of the power battery of the electric automobile according to claim 1, wherein the specific steps of the fifth step are as follows:
(1) According to the battery model and the measurement data, initialized parameters Q, P are set 0 R, initial estimated stateAnd the length N of the rolling time domain, wherein Q is a process noise covariance matrix, R is a measurement noise covariance matrix, and P 0 A covariance initial matrix for estimating errors;
(2) When the scroll estimated time T does not exceed N, the optimization problem is solved using the following equation:
the battery dynamics equation and the constraint condition thereof are met;
the obtained optimization solution is as follows:
according to the estimation result, calculating the estimation value of the current state through a recursive formula of the state:
wherein W is k V is system noise k For measuring noise;
(3) When the scroll estimated time T exceeds N, the optimization problem is solved using the following equation:
the battery dynamics equation and the constraint condition thereof are met;
wherein P is T-N Calculated by recursion of:
P j+1 ＝BQB -1 +A(P j -P j C T (R+CP j C T ) -1 CP j )A T ；
the obtained optimization solution is as follows:
according to the estimation result, calculating the estimation value of the current state through a recursive formula of the state:
(4) A priori estimates of the next time state are calculated using the following equation:
(5) After the new data set is obtained, the data is returned to (2) or (3) again according to the size relation between the rolling estimation time T and the rolling estimation length N, and the cyclic calculation is carried out.
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