CN112858920B - SOC estimation method of all-vanadium redox flow battery fusion model based on adaptive unscented Kalman filtering - Google Patents

SOC estimation method of all-vanadium redox flow battery fusion model based on adaptive unscented Kalman filtering Download PDF

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CN112858920B
CN112858920B CN202110139746.0A CN202110139746A CN112858920B CN 112858920 B CN112858920 B CN 112858920B CN 202110139746 A CN202110139746 A CN 202110139746A CN 112858920 B CN112858920 B CN 112858920B
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孟青
冯娜
张文
陈昌鑫
贺养慧
牛慧芳
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Shanxi Guorun Energy Storage Technology Co ltd
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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]
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Abstract

The invention provides a method based on self-adaptationThe SOC estimation method of the unscented Kalman filtering all-vanadium redox flow battery fusion model comprises the following steps: s10, establishing an equivalent circuit of the all-vanadium redox flow battery fusion model; s20, establishing a state of charge (SOC) equation according to the equivalent circuit; s30, establishing a state space equation and a nonlinear system model equation of the vanadium cell according to the ampere-hour integral calculation model and the SOC equation of the battery to be tested; s40, taking the SOC value of the vanadium battery as the state variable x of the system state equation k Charging and discharging current I of the battery d System input u as system state equation k Terminal voltage U of battery d Variable y as an observation equation for a system k Estimating the SOC of the battery through a self-adaptive unscented Kalman filtering algorithm; the invention has better response speed and robustness and is suitable for the field of batteries.

Description

SOC estimation method of all-vanadium redox flow battery fusion model based on adaptive unscented Kalman filtering
Technical Field
The invention relates to the technical field of batteries, in particular to an SOC estimation method of an all-vanadium redox flow battery fusion model based on self-adaptive unscented Kalman filtering.
Background
The all-vanadium redox flow battery is a green energy storage battery, and the charging and discharging of the battery are realized mainly through the conversion of the valence state of vanadium ions in the positive and negative electrolytes of the battery.
The physical quantity of state of charge (SOC) can reflect the state of storage and release of electric energy of the battery electrolyte, so that people can know and master the stored or residual electric quantity of the battery more effectively.
The state of charge estimation is a main component of a battery management system, provides an important basis for control decision of the management system, not only can the output capacity of the battery be predicted and estimated in advance, but also the running state of the battery can be fed back, and the battery protection effect is achieved. Therefore, when the SOC of the all-vanadium redox flow battery is estimated, the characteristics of the following aspects are considered and guaranteed: the method comprises the following steps that firstly, in the process of estimating the SOC of the vanadium redox flow battery, the normal operation of the battery is not influenced, and secondly, the estimated SOC result can accurately reflect the state of the residual power of the battery; and thirdly, the SOC estimation process can reflect the battery residual capacity in real time and can provide dynamic data for predicting the vanadium redox battery.
The state estimation of the all-vanadium redox flow battery has nonlinearity, so experts mostly adopt Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) to perform SOC estimation.
The extended Kalman filtering is to adopt a battery state space model, and convert the battery state space model into a Jacobian matrix through linearization treatment by carrying out recursion iteration on the SOC of the battery; in the process of processing the nonlinear problem, the method has the defects of complex calculation, narrow application range, long time and reduction of the estimation precision of the SOC; when the extended kalman filter is employed, the accuracy of the model has a large influence on the estimation accuracy.
The unscented Kalman filtering algorithm is subjected to linearization processing through sampling statistics, so that the calculation complexity is reduced, the error of SOC estimation is reduced, and compared with the extended Kalman filtering algorithm, the unscented Kalman filtering algorithm is simple and easy to implement; however, the accuracy of SOC estimation is susceptible to battery model.
Disclosure of Invention
Aiming at the defects in the related technology, the technical problem to be solved by the invention is as follows: the SOC estimation method of the all-vanadium redox flow battery fusion model based on the adaptive unscented Kalman filtering has good response speed and robustness.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a SOC estimation method of an all-vanadium redox flow battery fusion model based on adaptive unscented Kalman filtering comprises the following steps:
s10, establishing an equivalent circuit of the all-vanadium redox flow battery fusion model;
s20, establishing a state of charge (SOC) equation according to the equivalent circuit;
s30, establishing a state space equation and a nonlinear system model equation of the vanadium battery according to the ampere-hour integral calculation model and the state of charge (SOC) equation of the battery to be tested;
s40, taking the SOC value of the vanadium battery as the state variable x of the system state equation k Charging and discharging current I of the battery d System input u as system state equation k Terminal voltage U of battery d Variable y as an observation equation for a system k And estimating the SOC of the battery through an adaptive unscented Kalman filtering algorithm.
Preferably, in step S30, the expression of the ampere-hour integral calculation model of the battery to be tested is as follows:
Figure GDA0003762926910000021
wherein: SOC 0 Is the state of charge at the start of charging and discharging of the battery; c N Is the rated capacity; i is t Is the charge-discharge current at time t; η is the battery charge-discharge efficiency.
Preferably, in step S30, the expressions of the state space equation and the nonlinear system model equation of the vanadium redox battery are:
Figure GDA0003762926910000022
Figure GDA0003762926910000023
wherein: SOC (system on chip) k SOC estimated value of the battery at the k moment of charging and discharging; SOC (system on chip) k-1 The SOC estimation value at the k-1 moment of battery charging and discharging is obtained; c N Is the rated capacity; i is k-1 Is the charge-discharge current at time k-1; w is a k-1 Is the system noise at time k-1; v k Is the observed noise at time k; Δ T is the time interval;
U dk is the terminal voltage of the vanadium redox battery at the moment k; n is a series connection of single batteriesThe number of the particles; e 0 Is the equilibrium potential of the vanadium cell in the standard state; r is a gas constant; t is the temperature; f is a Faraday constant; r is res Ohmic internal resistance in the internal resistance loss of the pile of the all-vanadium redox flow battery;
x k is a state variable of a state equation of the system; u. of k Is an input variable of the state equation of the system;
f(x k-1 ,u k-1 ) Is a state function; y is k Is an observed variable of an observed equation of the system; h (x) k ,u k ) Is an observation function.
Preferably, in step S40, the estimating the SOC of the battery by the adaptive unscented kalman filter algorithm specifically includes:
s401, initializing a system state quantity and an error variance matrix;
s402, reading the current epoch data, carrying out UT conversion, and obtaining a Sigma point and a Sigma weight;
s403, predicting based on the Sigma points and the weight of the Sigma to obtain a predicted value of the state variable and the error variance matrix;
s404, predicting value U based on state prediction, covariance matrix prediction, Kalman filtering coefficient and system original output variable k Updating the predicted values of the state variable and the error variance matrix;
s405, correcting the predicted values of the state variables and the error variance matrix through adaptive factors to obtain an SOC estimated value at the k +1 moment;
s406, judging whether the k epochs are settled: if not, returning to the step S401 to carry out the next cycle; otherwise, the operation is ended.
Preferably, in step S403, the specific process of obtaining the predicted values of the state variables and the error variance matrix is as follows: according to the state equation of the system, and the state variable x at the moment k k And system input u k For the state variable x at time k +1 k+1 ' making a prediction; and according to the error variance matrix P of the k time k Calculating an error variance matrix P at time k +1 k+1 ′；
Shape of the pair of k +1 timeState variable x k+1 ' making a prediction, specifically:
state variable x k+1 The predictive expression of' is:
x k+1 '＝A k *x k +B k *u k formula (4.1);
the error variance matrix P for the k +1 time k+1 ' making a prediction, specifically:
error variance matrix P k+1 The predictive expression of' is:
Figure GDA0003762926910000031
wherein: a. the k A state transition matrix for the system; b is k Inputting a matrix for control of the system; x is the number of k Is the state variable of the system at the time k; q k Is the system noise W k The covariance matrix of (a); p k Is measuring the noise V k The error variance matrix of (2).
Preferably, in the step 404, the predicted values of the state variable and the error variance matrix are updated, and the specific process is as follows: updating a system state variable and an error variance matrix by calculating a measurement difference value, a measurement error covariance value and a Kalman filtering coefficient;
the calculating of the measurement difference value and the measurement error covariance value specifically includes:
the calculation expression of the measurement difference is as follows:
v k '＝y k -C k *x k formula (4.3);
the calculation expression of the covariance of the measurement error is:
Figure GDA0003762926910000041
calculating a Kalman filtering coefficient, and updating a system state variable and an error variance matrix, wherein the method specifically comprises the following steps:
the calculation expression of the Kalman filtering coefficient is as follows:
Figure GDA0003762926910000042
the updating expression of the system state variable is as follows:
X k+1 ＝x k+1 '+K k *v k ' formula (4.6);
the updated expression of the error variance matrix is:
P k+1 ＝(E-K k *C k )*P k+1 ' formula (4.7);
wherein: c k Is a system observation matrix; r is k Is the measurement noise; e is an identity matrix.
Preferably, in step S10, the equivalent circuit of the all-vanadium redox flow battery fusion model includes:
equivalent voltage V s Internal resistance loss simulation circuit, pump loss simulation circuit and equivalent capacitor C e ；
The pump loss analog circuit includes: pump loss current I P And internal resistance R f (ii) a Pump loss current I P One end of is connected in parallel with the internal resistance R f Is respectively connected with the terminal voltage U of the all-vanadium redox flow battery d Positive electrode and equivalent capacitance C e One end of the two ends are connected;
the internal resistance loss analog circuit includes: polarization resistance R rea And ohmic internal resistance R res Said polarization resistance R rea One terminal and equivalent voltage V s Is connected to the negative pole of the said polarization resistor R rea The other end of the resistor is connected in series with ohmic internal resistance R res The back and the pump loss current I P Another end of (1), internal resistance R f The other end of the voltage U of the all-vanadium redox flow battery terminal d Is connected with the cathode; the equivalent capacitance C e Is connected in parallel with the polarization resistor R at the other end rea And ohmic internal resistance R res On the connecting line between them.
Preferably, in step S20, the expression of the state of charge SOC equation is:
Figure GDA0003762926910000043
wherein: v s Is the stack voltage of the all-vanadium redox flow battery; n is the number of the single batteries connected in series; e is the voltage of the cell; r is a gas constant; t is the temperature; f is the Faraday constant.
The invention has the beneficial technical effects that:
according to the equivalent circuit of the fusion model of the all-vanadium redox flow battery, the battery characteristics are simulated by combining engineering practice and an equivalent circuit model on the basis of a chemical model Nernst equation, the internal resistance caused by chemical reaction of the all-vanadium redox flow battery is fully considered by the model, SOC estimation is carried out by utilizing an Nernst equation, pump loss and some mechanical characteristics are comprehensively considered, and the accuracy and the feasibility of the battery model are improved; on the basis of an equivalent circuit of an all-vanadium redox flow battery fusion model, the invention provides an SOC estimation method of the all-vanadium redox flow battery fusion model based on self-adaptive unscented Kalman filtering, so that real-time estimation and error observation of the SOC of an all-vanadium redox flow battery system are realized; compared with the traditional unscented Kalman filtering algorithm, the algorithm has the advantages of fast response, good robustness and the like, and is extremely high in practicability.
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Fig. 1 is a schematic flowchart of an SOC estimation method of an all-vanadium redox flow battery fusion model based on adaptive unscented kalman filtering according to an embodiment of the present invention;
fig. 2 is a schematic circuit structure diagram of an equivalent circuit of an all-vanadium redox flow battery fusion model according to a first embodiment of the present invention;
FIG. 3 is a schematic flow chart of an adaptive unscented Kalman filtering algorithm according to a second embodiment of the present invention;
FIG. 4 is a schematic diagram of a simulation model for SOC estimation by the adaptive unscented Kalman filtering algorithm according to a third embodiment of the present invention;
FIG. 5 is a schematic diagram of a simulation model of an adaptive unscented Kalman filtering algorithm according to a third embodiment of the present invention;
FIG. 6 is a SOC estimation curve of the AUKF algorithm in the third embodiment of the present invention;
fig. 7 is a SOC estimation error curve of the AUKF algorithm in the third embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention; all other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
An embodiment of the SOC estimation method based on the all-vanadium redox flow battery fusion model with the adaptive unscented kalman filter is described in detail below with reference to the accompanying drawings.
Example one
Fig. 1 is a schematic flowchart of an SOC estimation method of an all-vanadium redox flow battery fusion model based on adaptive unscented kalman filtering according to an embodiment of the present invention; as shown in fig. 1, a method for estimating SOC of an all-vanadium redox flow battery fusion model based on adaptive unscented kalman filtering includes the following steps:
s10, establishing an equivalent circuit of the all-vanadium redox flow battery fusion model;
s20, establishing a state of charge (SOC) equation according to the equivalent circuit;
s30, establishing a state space equation and a nonlinear system model equation of the vanadium battery according to the ampere-hour integral calculation model and the state of charge (SOC) equation of the battery to be tested;
s40, taking the SOC value of the vanadium battery as the state variable x of the system state equation k Charging and discharging current I of the battery d System input u as system state equation k Terminal voltage U of battery d Variable y as an observation equation for a system k And estimating the SOC of the battery through an adaptive unscented Kalman filtering algorithm.
The Adaptive Unscented Kalman Filter (AUKF) algorithm combines unscented transformation, Kalman filter algorithm and adaptive filter algorithm, UT transformation is the data preparation link of the algorithm, and then system errors and observation errors are updated in real time according to the Kalman filter algorithm and the adaptive filter algorithm.
The determination of system equations, namely state equations and observation equations, is the key to the application of the Kalman filtering algorithm; in order to obtain an accurate system equation, it is necessary to build a suitable battery model before estimating the SOC using this method.
Fig. 2 is a schematic circuit structure diagram of an equivalent circuit of an all-vanadium redox flow battery fusion model in a first embodiment of the invention; as shown in fig. 2, in the first embodiment, in step S10, the equivalent circuit of the fusion model of the all-vanadium redox flow battery includes:
equivalent voltage V s Internal resistance loss simulation circuit, pump loss simulation circuit and equivalent capacitor C e ；
The pump loss analog circuit includes: pump loss current I P And internal resistance R f (ii) a Pump loss current I P One end of is connected in parallel with the internal resistance R f Is respectively connected with the terminal voltage U of the all-vanadium redox flow battery d Positive electrode and equivalent capacitance C e One end of the two ends are connected;
the internal resistance loss analog circuit includes: polarization resistance R rea And ohmic internal resistance R res Said polarization resistance R rea One terminal and equivalent voltage V s Is connected to the negative pole of the said polarization resistor R rea The other end of the resistor is connected in series with ohmic internal resistance R res The back and the pump loss current I P Another end of (1), internal resistance R f The other end of the battery is the terminal voltage U of the all-vanadium redox flow battery d The negative electrodes are connected; the equivalent capacitance C e Is connected in parallel with the polarization resistor R at the other end rea And ohmic internal resistance R res On the connecting line between them.
As shown in FIG. 2, U d The terminal voltage of the all-vanadium redox flow battery can be collected and measured by an instrument; pump loss is equivalent to pump loss current I P Parallel resistance R f The value of which is related to the selected power and operating voltage of the circulation pump, the battery stack current I stack And SOC; v s Is the stack voltage of the cell, also referred to as the core voltage or open circuit voltage of the cell, depending on the magnitude of the SOC of the cell and U d Related, controlled voltage sources are used instead; the relationship of each parameter in the fusion model of the invention is as follows
Figure GDA0003762926910000071
Wherein: u shape e Is an equivalent capacitance C e The voltage across; i is the ohmic internal resistance R res The current of (a); u shape s Is a V s The voltage across; I.C. A s Is a polarization resistance R rea The current of (a); i is d Is terminal voltage U d The current of (a); i is f Is internal resistance R f The current of (a); i is e Is an equivalent capacitance C e The current of (2).
According to the nernst equation, the cell open-circuit voltage of the all-vanadium flow battery can be expressed as:
Figure GDA0003762926910000072
wherein: e 0 Is the equilibrium potential of the vanadium cell in the standard state; r is a gas constant, R is 8.31J/K/mol; t is temperature in K; f is the faraday constant, 96500C/mol.
As shown in the equation (2-1) and the nernst equation (2-2), in step S20, the expression of the SOC equation is:
Figure GDA0003762926910000073
wherein: v s Is the stack voltage of the all-vanadium redox flow battery; n is the number of the single batteries connected in series; e is the voltage of the cell; r is a gas constant; t is the temperature; f is the Faraday constant.
In the equivalent circuit of the fusion model of the all-vanadium redox flow battery in the first embodiment, the battery characteristics are simulated by combining engineering practice and an equivalent circuit model on the basis of a chemical model Nernst equation, the internal resistance caused by chemical reaction of the all-vanadium redox flow battery is fully considered by the model, SOC estimation is performed by using an Nernst equation, pump loss and some mechanical characteristics are comprehensively considered, and the accuracy and the feasibility of the battery model are improved.
The invention provides an SOC estimation method of an all-vanadium redox flow battery fusion model based on an adaptive unscented Kalman filter on the basis of an equivalent circuit of the all-vanadium redox flow battery fusion model, so that the real-time estimation and error observation of the SOC of an all-vanadium redox flow battery system are realized; compared with the traditional unscented Kalman filtering algorithm, the algorithm has the advantages of fast response, good robustness and the like.
Example two
On the basis of the first embodiment, in step S30, an expression of an ampere-hour integral calculation model of the battery to be measured is as follows:
Figure GDA0003762926910000081
wherein: SOC (system on chip) 0 Is the state of charge at the start of charging and discharging of the battery; c N Is the rated capacity; i is t Is the charge-discharge current at time t; eta is the battery charge-discharge efficiency.
Specifically, according to the formula (2) and the formula (3.1), in the step S30, the expressions of the state space equation and the nonlinear system model equation of the vanadium redox battery are:
Figure GDA0003762926910000082
Figure GDA0003762926910000083
wherein: SOC (system on chip) k SOC estimated value of the battery at the k moment of charging and discharging; SOC k-1 Is the SOC estimated value at the k-1 moment of battery charging and discharging；C N Is the rated capacity; i is k-1 Is the charge-discharge current at time k-1; w is a k-1 Is the system noise at time k-1; v k Is the observed noise at time k; Δ T is the time interval;
U dk is the terminal voltage of the vanadium redox battery at the moment k; n is the number of the single batteries connected in series; e 0 Is the equilibrium potential of the vanadium cell in the standard state; r is the gas constant and T is the temperature K; f is the Faraday constant; r res Ohmic internal resistance in the internal resistance loss of the pile of the all-vanadium redox flow battery;
x k is a state variable of a state equation of the system; u. u k Is an input variable of the state equation of the system; f (x) k-1 ,u k-1 ) Is a state function; y is k Is an observed variable of an observed equation of the system; h (x) k ,u k ) Is an observation function.
FIG. 3 is a schematic flow chart of an adaptive unscented Kalman filtering algorithm according to a second embodiment of the present invention; as shown in fig. 3, in the present embodiment, in the step S40, the estimating the SOC of the battery by the adaptive unscented kalman filter algorithm specifically includes:
s401, initializing a system state quantity and an error variance matrix;
s402, reading the current epoch data, carrying out UT conversion, and obtaining a Sigma point and a Sigma weight;
s403, predicting based on the Sigma points and the weight of the Sigma to obtain a predicted value of the state variable and the error variance matrix;
s404, predicting value U based on state prediction, covariance matrix prediction, Kalman filtering coefficient and system original output variable k Updating the predicted values of the state variable and the error variance matrix;
s405, correcting the predicted values of the state variables and the error variance matrix through adaptive factors to obtain an SOC estimated value at the k +1 moment;
s406, judging whether the k epochs are settled: if not, returning to the step S401 to carry out the next cycle; otherwise, the operation is ended.
In the embodiment, the estimation of the SOC of the vanadium redox battery by using an Adaptive Unscented Kalman Filter (AUKF) is mainly divided into three stages:
firstly, the method comprises the following steps: UT conversion phase
The UT transformation is a previous data processing part of unscented Kalman filtering and is one of key links, the UT transformation is approximate to Gaussian distribution by using a fixed number of parameters, the transformation principle is to sample data points in a known distribution curve according to a certain rule, and the mean value and covariance of a data set obtained by acquisition are kept consistent with the known distribution curve; this transformation process is called Sigma-quantization of the estimator, the collection of points is called Sigma points, and the specific steps are as follows:
a10, constructing Sigma points and corresponding weights
Statistics in conjunction with a known variable x
Figure GDA0003762926910000091
And P x Selecting a Sigma point sampling strategy, and obtaining a Sigma point { x ] of an input variable through transformation i 1, … …, n and corresponding weights
Figure GDA0003762926910000092
And variance weight
Figure GDA0003762926910000093
Figure GDA0003762926910000094
The weight is calculated as:
Figure GDA0003762926910000095
a20, Sigma point nonlinear transformation:
for sampled input variable Sigma point { x i Each Sigma point in the lattice is linearly transformed by f (. -) to obtain a set of transformed points y i }
y i ＝f(x i ) (i ═ 0,1,. 2n) formula (3.13);
a30, set of transformed points { y i Weighting to obtain statistic of output variable y
Figure GDA0003762926910000101
And P y The weight value is obtained in step a10,
Figure GDA0003762926910000102
and P y Is calculated as follows:
y i ＝f(x i ) (i ═ 0,1,. 2n) formula (3.14);
Figure GDA0003762926910000103
in this embodiment, SOC k And P k Respectively the state value and the estimation error at time k. According to SOC k And P k Converting the SOC value at the time k into SOC k1 、SOC k2 、SOC k3 Three values, mean and variance of these values and SOC xk 、P xk Equal; and carrying in (3.12), calculating the average weight corresponding to each SOC value
Figure GDA0003762926910000104
And variance weight
Figure GDA0003762926910000105
And obtaining an optimal transformation function coefficient (2, 0.01, 2) through parameter adjustment.
Secondly, the method comprises the following steps: prediction phase
According to SOC k1 、SOC k2 、SOC k3 And the state equation to calculate the estimated value SOC at the k +1 moment (k+1)1 ′、SOC (k+1)2 ′、SOC (k+1)3 '; according to SOC (k+1)1 ′、SOC (k+1)2 ′、SOC (k+1)3 ' and
Figure GDA0003762926910000106
to calculate the estimated value SOC at the time k +1 k+1 ' and P k+1 '; calculating the terminal voltage and the terminal voltage variance of the observed value at the moment K +1 and the covariance of the SOC and the SOC according to a system observation equation, and finally determining a gain coefficient K k ；
Thirdly, the method comprises the following steps: update phase
For the transformed point set y i Weighting to obtain statistic of output variable y
Figure GDA0003762926910000107
And P y The weight value is obtained in the step (1),
Figure GDA0003762926910000108
and P y Is calculated as follows:
y i ＝f(x i ) (i ═ 0,1,.., 2n) formula (3.16);
Figure GDA0003762926910000109
specifically, in step S403, the specific process of obtaining the predicted values of the state variables and the error variance matrix is as follows: according to the state equation of the system, and the state variable x at the moment k k And system input u k For the state variable x at time k +1 k+1 ' making a prediction; and according to the error variance matrix P of the k time k Calculating an error variance matrix P at time k +1 k+1 ′；
The state variable x at the time of k +1 k+1 ' predict, specifically:
state variable x k+1 The predictive expression of' is:
x k+1 '＝A k *x k +B k *u k formula (4.1);
the error variance matrix P for the k +1 time k+1 ' making a prediction, specifically:
error variance matrix P k+1 The predictive expression of' is:
Figure GDA0003762926910000112
wherein: a. the k A state transition matrix for the system; b is k Inputting a matrix for control of the system; x is the number of k Is the state variable of the system at the time k; q k Is the system noise W k The covariance matrix of (a); p k Is measuring the noise V k The error variance matrix of (2).
Further, in step 404, updating the predicted values of the state variable and the error variance matrix, where the specific process is as follows: updating a system state variable and an error variance matrix by calculating a measurement difference value, a measurement error covariance value and a Kalman filtering coefficient;
the calculating of the measurement difference value and the measurement error covariance value specifically includes:
the calculation expression of the measurement difference is as follows:
v k '＝y k -C k *x k formula (4.3);
the calculation expression of the measurement error covariance is:
Figure GDA0003762926910000113
calculating a Kalman filtering coefficient, and updating a system state variable and an error variance matrix, wherein the method specifically comprises the following steps: the calculation expression of the Kalman filtering coefficient is as follows:
Figure GDA0003762926910000111
the updating expression of the system state variable is as follows:
X k+1 ＝x k+1 '+K k *v k ' formula (4.6);
the updated expression of the error variance matrix is:
P k+1 ＝(E-K k *C k )*P k+1 ' formula (4.7);
wherein: c k Is a system observation matrix; r k Is the measurement noise; and E is an identity matrix.
EXAMPLE III
On the basis of the first embodiment, in the step S405, the predicted values of the state variables and the error variance matrix are corrected by adaptive factors, specifically including updating of system errors and updating of observation errors.
B10, systematic error update
Assuming that the difference between the real value and the estimated value of the system state variable at the time k is:
Δx k ＝x k -x k ' formula (4.51);
the updating of the system error at the time k is to perform weighted average on the difference value between the real value and the estimated value in the previous period, and then add the difference between the real value and the predicted value of the state variable error matrix, as shown in the formula (4.52):
Figure GDA0003762926910000121
in order to increase the calculation speed without affecting the accuracy, the difference value of the first three times is usually selected for calculation.
B20, update of observation error
The difference between the true value of the observation variable at the time k and the estimated value obtained by the Unscented Kalman Filter (UKF) is set as follows:
△y k ＝y k -y k ' formula (4.53);
the observation error at the moment k to be updated can be obtained by subtracting the output error caused by the variance error of the state variable in the system equation from the difference between the real value and the estimated value in the previous period by weighted average:
Figure GDA0003762926910000122
in order to avoid overlarge calculation amount, the first three differences are still selected for calculation, and the accuracy of a system equation and an observation equation is guaranteed by correcting the two errors.
FIG. 4 is a schematic diagram of a simulation model for SOC estimation by an adaptive unscented Kalman filtering algorithm according to a third embodiment of the present invention; FIG. 5 is a schematic diagram of a simulation model of an adaptive unscented Kalman filtering algorithm according to a third embodiment of the present invention; as shown in fig. 4 and fig. 5, in the present embodiment, the adaptive unscented kalman filter model is shown in fig. 4, and mainly includes two modules, namely, a Subsystem module and an ad _ kalman module; subsystem is used for realizing UT transformation of data; the ad-kalman module realizes the self-adaptation and the kalman filtering, and a simulation model schematic diagram of the self-adaptation and the kalman filtering algorithm is shown in fig. 5.
The model experiment takes a 5kW/30kWh all-vanadium redox flow battery produced by Shanxi company as a research object, and model parameters involved in the simulation process are shown in Table 1.
TABLE 1 SOC estimation simulation parameter Table
Figure GDA0003762926910000131
Three working states of discharging, static and charging are set in the whole SOC estimation simulation process; in the embodiment, comparison simulation is performed on the unscented kalman filter and the adaptive unscented kalman filter algorithm.
FIG. 6 is a SOC estimation curve of the AUKF algorithm in the third embodiment of the present invention; as can be seen from fig. 6, the SOC estimation of the nonlinear fusion model by using the AUKF has excellent fast response and robustness; the estimated SOC and the actual SOC curves are basically coincident no matter in any working state.
FIG. 7 is a SOC estimation error curve of the AUKF algorithm in the third embodiment of the present invention; as shown in fig. 7, it can be seen that the error is controlled within ± 7%, which meets the international standard; research shows that certain error exists in the estimation of the SOC of the vanadium redox battery by the AUKF, the error is acceptable, and the problem of online SOC estimation can be well solved.
In conclusion, the invention provides a self-adaptive unscented Kalman filtering algorithm aiming at the problems of low SOC estimation precision and poor operability of the all-vanadium redox flow battery, realizes the SOC estimation of the all-vanadium redox flow battery, and establishes a Simulink simulation model. The AUKF is shown to have better response speed and robustness through comparative analysis of simulation results of unscented Kalman filtering and adaptive unscented Kalman filtering; the self-adaptive unscented Kalman filter established by the method can realize online estimation of SOC, has error control within +/-7 percent and higher precision, conforms to the international standard of vanadium batteries and has feasible engineering application value.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; they may be directly connected or indirectly connected through intervening media, or they may be interconnected within two elements or in a relationship where two elements interact with each other unless otherwise specifically limited. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the foregoing embodiments, the descriptions of the respective embodiments have respective emphasis, and for parts that are not described in detail in a certain embodiment, reference may be made to the related descriptions of other embodiments.
It can be clearly understood by those skilled in the art that, for convenience and brevity of description, the specific working processes of the system and the module described above may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (6)

1. A SOC estimation method of an all-vanadium redox flow battery fusion model based on adaptive unscented Kalman filtering is characterized by comprising the following steps: the method comprises the following steps:
s10, establishing an equivalent circuit of the all-vanadium redox flow battery fusion model;
s20, establishing a state of charge (SOC) equation according to the equivalent circuit;
s30, establishing a state space equation and a nonlinear system model equation of the vanadium battery according to the ampere-hour integral calculation model and the state of charge (SOC) equation of the battery to be tested;
s40, taking the SOC value of the vanadium battery as the state variable x of the system state equation k Charging and discharging current I of the battery d System input u as system state equation k Terminal voltage U of battery d Variable y as an observation equation for a system k Estimating the SOC of the battery through a self-adaptive unscented Kalman filtering algorithm;
in step S30, the expressions of the state space equation and the nonlinear system model equation of the vanadium redox battery are:
Figure FDA0003762926900000011
Figure FDA0003762926900000012
wherein: SOC k SOC estimated value of the battery at k moment of charging and discharging; SOC k-1 The SOC estimation value at the k-1 moment of battery charging and discharging is obtained; c N Is the rated capacity; i is k-1 Is the charge-discharge current at time k-1; w is a k-1 Is the system noise at time k-1; v k Is the observed noise at time k; Δ T is the time interval;
U dk is the terminal voltage of the vanadium redox battery at the moment k; n is the number of the single batteries connected in series; e 0 Is the equilibrium potential of the vanadium cell in the standard state; r is the gas constant and T is the temperature K(ii) a F is the Faraday constant; r is res Ohmic internal resistance in the internal resistance loss of the all-vanadium redox flow battery pile;
x k is a state variable of a state equation of the system; u. of k Is an input variable of the state equation of the system; f (x) k-1 ,u k-1 ) Is a state function; y is k Is an observed variable of an observed equation of the system; h (x) k ,u k ) Is an observation function;
in step S40, the estimating SOC of the battery by the adaptive unscented kalman filter algorithm specifically includes:
s401, initializing a system state quantity and an error variance matrix;
s402, reading the current epoch data, carrying out UT conversion, and obtaining a Sigma point and a Sigma weight;
s403, predicting based on the Sigma points and the weight of the Sigma to obtain a predicted value of the state variable and the error variance matrix;
s404, predicting value U based on state prediction, covariance moment prediction, Kalman filtering coefficient and system original output variable k Updating the predicted values of the state variable and the error variance matrix;
s405, correcting the predicted values of the state variables and the error variance matrix through adaptive factors to obtain an SOC estimated value at the k +1 moment;
s406, judging whether the settlement of the k epochs is finished: if not, returning to the step S401 to carry out the next cycle; otherwise, the operation is ended.
2. The SOC estimation method of the all-vanadium redox flow battery fusion model based on the adaptive unscented Kalman filtering according to claim 1, characterized in that: in step S30, the expression of the ampere-hour integral calculation model of the battery to be tested is:
Figure FDA0003762926900000021
wherein: SOC 0 Is the state of charge at the beginning of the charging and discharging of the battery; c N Is the rated capacity; I.C. A t Is the charge-discharge current at time t; eta is the battery charge-discharge efficiency.
3. The SOC estimation method of the all-vanadium redox flow battery fusion model based on the adaptive unscented Kalman filtering according to claim 1, characterized in that: in step S403, the specific process of obtaining the predicted values of the state variables and the error variance matrix is as follows: according to the state equation of the system, and the state variable x at the moment k k And system input u k For the state variable x at time k +1 k+1 ' making a prediction; and according to the error variance matrix P of the k time k Calculating an error variance matrix P at time k +1 k+1 ′；
The state variable x at the time of k +1 k+1 ' predict, specifically:
state variable x k+1 The predictive expression of' is:
x k+1 '＝A k *x k +B k *u k formula (4.1);
the error variance matrix P for the k +1 time k+1 ' making a prediction, specifically:
error variance matrix P k+1 The predictive expression of' is:
Figure FDA0003762926900000022
wherein: a. the k A state transition matrix for the system; b is k Inputting a matrix for control of the system; x is the number of k Is the state variable of the system at the time k; q k Is the system noise W k The covariance matrix of (a); p k Is measuring the noise V k The error variance matrix of (2).
4. The SOC estimation method of the all-vanadium redox flow battery fusion model based on the adaptive unscented Kalman filtering according to claim 3, characterized in that: in step 404, the predicted values of the state variables and the error variance matrix are updated, and the specific process is as follows: updating a system state variable and an error variance matrix by calculating a measurement difference value, a measurement error covariance value and a Kalman filtering coefficient;
the calculating of the measurement difference value and the measurement error covariance value specifically includes:
the calculation expression of the measurement difference is as follows:
v k '＝y k -C k *x k formula (4.3);
the calculation expression of the covariance of the measurement error is:
Figure FDA0003762926900000031
calculating a Kalman filtering coefficient, and updating a system state variable and an error variance matrix, wherein the method specifically comprises the following steps:
the calculation expression of the Kalman filtering coefficient is as follows:
Figure FDA0003762926900000032
the updating expression of the system state variable is as follows:
X k+1 ＝x k+1 '+K k *v k ' formula (4.6);
the updated expression of the error variance matrix is:
P k+1 ＝(E-K k *C k )*P k+1 ' formula (4.7);
wherein: c k Is a system observation matrix; r k Is the measurement noise; e is an identity matrix.
5. The SOC estimation method of the all-vanadium redox flow battery fusion model based on the adaptive unscented Kalman filtering according to claim 2, characterized in that: in step S10, the equivalent circuit of the all-vanadium redox flow battery fusion model includes:
equivalent voltage V s Internal resistance loss simulation electricityCircuit, pump loss analog circuit and equivalent capacitor C e ；
The pump loss analog circuit includes: pump loss current I P And internal resistance R f (ii) a Pump loss current I P One end of is connected in parallel with the internal resistance R f Is respectively connected with the terminal voltage U of the all-vanadium redox flow battery d Positive electrode and equivalent capacitance C e One end of the two is connected;
the internal resistance loss analog circuit includes: polarization resistance R rea And ohmic internal resistance R res Said polarization resistance R rea One terminal and equivalent voltage V s Is connected to the negative pole of the said polarization resistor R rea The other end of the resistor is connected in series with ohmic internal resistance R res The back and the pump loss current I P Another end of (1), internal resistance R f The other end of the battery is the terminal voltage U of the all-vanadium redox flow battery d The negative electrodes are connected; the equivalent capacitance C e Is connected in parallel with the polarization resistor R at the other end rea And ohmic internal resistance R res On the connecting line between them.
6. The SOC estimation method of the all-vanadium redox flow battery fusion model based on the adaptive unscented Kalman filtering according to claim 5, characterized in that: in step S20, the expression of the state of charge SOC equation is:
Figure FDA0003762926900000041
wherein: v s Is the stack voltage of the all-vanadium redox flow battery; n is the number of the single batteries connected in series; e is the voltage of the cell; r is a gas constant; t is the temperature; f is the Faraday constant.
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