CN112287597A - Lead-acid storage battery SOH estimation method based on VPGA-GPR algorithm - Google Patents

Lead-acid storage battery SOH estimation method based on VPGA-GPR algorithm Download PDF

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CN112287597A
CN112287597A CN202011001400.6A CN202011001400A CN112287597A CN 112287597 A CN112287597 A CN 112287597A CN 202011001400 A CN202011001400 A CN 202011001400A CN 112287597 A CN112287597 A CN 112287597A
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丁一
王旭东
霍现旭
戚艳
郗晓光
尚学军
张磐
刘盛终
姚程
黄潇潇
于光耀
李谦
郑骁麟
胡志刚
于啸
姜帆
阮琛奂
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State Grid Corp of China SGCC
State Grid Tianjin Electric Power Co Ltd
Electric Power Research Institute of State Grid Tianjin Electric Power Co Ltd
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State Grid Tianjin Electric Power Co Ltd
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Abstract

The invention relates to a lead-acid storage battery SOH estimation method based on a VPGA-GPR algorithm, which comprises the following steps of: step 1, performing a capacity fading experiment on a lead-acid storage battery, and recording the change relation of the actual capacity of the battery along with the cycle number and the time of constant voltage charging and constant current charging in a charging stage; step 2, determining factors which have obvious influence on the SOH of the lead-acid storage battery based on the test result of the step 1, and establishing a Gaussian process regression model; and 3, optimizing the objective function of the Gaussian process regression model established in the optimization step 2 through a variable probability genetic algorithm, and estimating the SOH of the lead-acid storage battery. The method can quickly search the high-quality solution of the training error function, thereby establishing a more accurate Gaussian process regression model and improving the regression performance and the prediction capability of the model.

Description

Lead-acid storage battery SOH estimation method based on VPGA-GPR algorithm
Technical Field
The invention belongs to the technical field of evaluation of running states of running energy storage equipment of a power distribution network, relates to a lead-acid storage battery SOH estimation method, and particularly relates to a lead-acid storage battery SOH estimation method based on Variable Probability Genetic Algorithm (VPGA) -Gaussian Process Regression (GPR).
Background
Lead-acid battery energy storage systems have a wide range of uses in the electric vehicle industry. The novel photovoltaic power generation system is low in price, high in specific power and relatively mature in technology, is still widely applied to an uninterruptible power supply of a power supply system and a large photovoltaic power station at present, and is an important guarantee for power supply continuity and stability. The State of Health (SOH) of a lead-acid Battery is an important reflection index of Battery performance and an important factor of a Battery Management System (BMS). At present, research aiming at the SOH estimation of the lead-acid storage battery is less, and the SOH estimation method mainly comprises a storage battery mechanism-based method and a data-driven method, wherein the storage battery mechanism-based method needs to establish a complex physical and chemical model, and the estimation precision is poor. The latter mainly comprises: a Relevance Vector Machine (RVM), an Artificial Neural Network (ANN), etc., which require a large amount of data as a training set and have a large computational burden; and the generalization and nonlinear approximation capability of the model is weak, and meanwhile, the training error is easy to fall into the local optimal solution.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a lead-acid storage battery SOH estimation method based on a VPGA-GPR algorithm, which can quickly search a high-quality solution of a training error function, thereby establishing a more accurate Gaussian process regression model and improving the regression performance and the prediction capability of the model.
The invention solves the practical problem by adopting the following technical scheme:
a lead-acid storage battery SOH estimation method based on variable probability genetic algorithm-Gaussian process regression comprises the following steps:
step 1, performing a capacity fading experiment on a lead-acid storage battery, and recording the change relation of the actual capacity of the battery along with the cycle number and the time of constant voltage charging and constant current charging in a charging stage;
step 2, determining factors which have obvious influence on the SOH of the lead-acid storage battery based on the test result of the step 1, and establishing a Gaussian process regression model;
and 3, optimizing the objective function of the Gaussian process regression model established in the optimization step 2 through a variable probability genetic algorithm, and estimating the SOH of the lead-acid storage battery.
Moreover, the specific method of step 1 is: firstly, carrying out a cyclic charge-discharge experiment on a lead-acid storage battery, wherein the charge is stage charge, namely constant-current charge is carried out firstly, and constant-voltage charge is kept after the charge cut-off voltage is reached until the charge current is reduced to be below a specified value; constant current discharging is adopted for discharging, terminal voltage current data are recorded to calculate the actual capacity, a plurality of cyclic charging and discharging experiments are carried out, the change relation of the actual capacity of the battery along with the number of cycles is recorded, and the time of constant voltage charging and constant current charging in the charging stage is recorded.
Moreover, the specific method of the step 2 is as follows:
outputting the capacity sequence of the storage battery as a regression model { x }0(k)},T1,T2,T3The sequence is as follows: { xi(k) And (3) calculating the correlation between input and output by using the following formula:
Figure BDA0002694450220000021
in the above formula, T total charging time, T1Constant voltage charging time and T2Constant current charging time;
the result shows that the grey correlation degree of the constant voltage charging time is the highest, so that a Gaussian process regression model of the constant voltage charging time and the battery capacity is established.
Further, the specific steps of step 3 include:
(1) all data points (x)2(k),x0(k) K1, 2.. m is divided into mutually exclusive training sets and independent test sets, and K-fold cross check is carried out on the training sets and is carried out on the training setsAnd dividing the test result into mutually exclusive K groups, wherein one of the K groups is taken as a verification set, and the other K-1 groups are taken as training sets in sequence to train a GPR model. The kernel function of the GPR model is a square exponential kernel function, and the number of the kernel functions is 3 and is respectively sigmap,l,σn
Figure BDA0002694450220000031
The training process is to optimize the following objective function through a Variable Probability Genetic Algorithm (VPGA), namely, the root mean square value of the actual output and the predicted output of the verification set is minimum:
Figure BDA0002694450220000032
(2) implementation of VPGA:
initializing N three-dimensional random vectors, wherein each vector contains hyperparametric information of a GPR kernel function, namely, the ith random vector is (delta)ip,liin) Referred to as an individual; selecting a formula (3) for the fitness value f; calculating fitness values in the formula (3) respectively, and determining and selecting parent individuals according to a roulette method, wherein the probability that individuals with higher fitness are selected is higher; calculating the cross probability and the mutation probability by the following formulas, performing cross operation on the selected parent individuals, and performing mutation operation on the generated filial generations:
Figure BDA0002694450220000033
and (3) adopting an elite storage strategy to store the optimal M individuals of the previous generation to replace the worst M individuals of the next generation, wherein M is determined according to the following formula:
Figure BDA0002694450220000034
repeating the cross variation operation and the elite preservation strategy, knowing that the optimal fitness value is not obviously changed any more for continuous generations;
(3) and selecting an optimal group of results in K rounds of training as the hyperparametric output of the GPR, and taking the result as the SOH estimation result of the lead-acid storage battery.
The invention has the advantages and beneficial effects that:
1. the method adopts Gaussian Process Regression (GPR), has the characteristics of strong nonlinear generalization capability and less required data points and high precision, and is suitable for monitoring and evaluating the health state of the battery. The hyper-parameter determination algorithm comprises the following steps: the Variable Probability Genetic Algorithm (VPGA) has good global optimization characteristics and local fine tuning capacity, has high response speed to fitness change, and can quickly search a high-quality solution of a training error function, so that a more accurate Gaussian process regression model is established, and the regression performance and the prediction capacity of the model are improved.
2. The maximum error of SOH estimation by adopting a Variable Probability Genetic Algorithm (VPGA) -Gaussian Process Regression (GPR) is lower than 2%, and the average calculation time of each training verification is less than 3s, so that the method can meet the requirement of real-time performance and is suitable for the SOH online monitoring of the lead-acid storage battery.
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FIG. 1 is a flow chart of the VPGA-GPR algorithm of the present invention;
FIG. 2(a) is a diagram of the estimated effect of the training set 1 of the present invention;
FIG. 2(b) is a diagram of the estimated effect of the training set 2 of the present invention;
FIG. 2(c) is a diagram of the estimated effect of the training set 3 of the present invention;
FIG. 2(d) is a diagram of the estimated effect of the training set 4 of the present invention;
FIG. 3(a) is a diagram of the SOH estimation effect of the lead-acid battery in the independent test set according to the present invention;
FIG. 3(b) is a graph of percentage of SOH estimation error for lead acid batteries in an independent test set according to the present invention.
Detailed Description
The embodiments of the invention will be described in further detail below with reference to the accompanying drawings:
a lead-acid battery SOH estimation method based on variable probability genetic algorithm-Gaussian process regression is shown in figure 1 and comprises the following steps:
step 1, performing a capacity fading experiment on a lead-acid storage battery, and recording the change relation of the actual capacity of the battery along with the cycle number and the time of constant voltage charging and constant current charging in a charging stage;
the specific method of the step 1 comprises the following steps: firstly, carrying out a cyclic charge-discharge experiment on a lead-acid storage battery, wherein the charge is stage charge, namely constant-current charge is carried out firstly, and constant-voltage charge is kept after the charge cut-off voltage is reached until the charge current is reduced to be below a specified value; constant current discharging is adopted for discharging, terminal voltage current data are recorded to calculate the actual capacity, a plurality of cyclic charging and discharging experiments are carried out, the change relation of the actual capacity of the battery along with the number of cycles is recorded, and the time of constant voltage charging and constant current charging in the charging stage is recorded.
Step 2, determining factors which have obvious influence on the SOH of the lead-acid storage battery based on the test result of the step 1, and establishing a Gaussian process regression model;
the specific method of the step 2 comprises the following steps:
by analyzing the charging process, the total charging time T and the constant voltage charging time T can be known along with the increase of the cycle number and the attenuation of the battery capacity1And constant current charging time T2Obviously reduced and shows good correlation. Outputting the capacity sequence of the storage battery as a regression model { x }0(k)},T1,T2,T3The sequence is as follows: { xi(k) I 1,2,3 is the regression input, k 1,2. Calculating the relevance between input and output by using the formula (1):
Figure BDA0002694450220000051
the grey correlation results are shown in table 1:
TABLE 1
Figure BDA0002694450220000052
The result shows that the gray correlation degree of the constant voltage charging time is the highest, so that a regression model of the constant voltage charging time and the battery capacity is established.
And 3, optimizing the objective function of the Gaussian process regression model established in the optimization step 2 through a variable probability genetic algorithm, and estimating the SOH of the lead-acid storage battery.
The specific steps of the step 3 comprise:
(3) all data points (x)2(k),x0(k) And K is 1,2.. m is divided into mutually exclusive training sets and independent test sets, K-fold cross inspection is carried out on the training sets, the training sets are divided into mutually exclusive K groups, one of the K groups is taken as a verification set, and the rest K-1 groups are taken as training sets to train a GPR model. The kernel function of the GPR model is a square exponential kernel function, as shown in (2), the number of the kernel functions is 3, and the number is respectively sigmap,l,σn
Figure BDA0002694450220000061
The training process is to optimize an objective function (3) through a Variable Probability Genetic Algorithm (VPGA), and the root mean square value of actual output and predicted output of a verification set is minimum.
Figure BDA0002694450220000062
(4) The VPGA is implemented by initializing N three-dimensional random vectors, each vector containing the hyperparametric information of the GPR kernel function, i.e. the ith random vector is (delta)ip,liin) And is referred to as an individual. The fitness value f is expressed by the formula (3). And (4) calculating fitness values in the formula (3) respectively, and determining to select parent individuals according to a roulette method, wherein the probability that individuals with higher fitness are selected is higher. And (4) calculating the cross probability and the mutation probability by using the formula (4), performing cross operation on the selected parent individuals, and performing mutation operation on the generated offspring.
Figure BDA0002694450220000063
And (3) storing the optimal M individuals of the previous generation by adopting an elite storage strategy to replace the worst M individuals of the next generation, wherein M is determined according to the formula (5).
Figure BDA0002694450220000071
And repeating the cross mutation operation and the elite preservation strategy to know that the optimal fitness value does not change obviously for continuous generations. The flow chart of the VPGA algorithm is shown in fig. 1.
(3) And selecting an optimal group of results in K rounds of training as the hyperparameter output of the GPR. In this experiment, K is 4, and the training effect of each training set is shown in fig. 2(a) - (d). And the established GPR model is used for predicting an independent test set, and a predicted value is compared with a true value to test the effectiveness of the lead-acid storage battery SOH estimation method based on a variable probability genetic algorithm-Gaussian process (VPGA-GPR). The prediction effectiveness curves and the prediction error percentages for the independent test sets are shown in fig. 3(a) - (b).
It should be emphasized that the examples described herein are illustrative and not restrictive, and thus the present invention includes, but is not limited to, those examples described in this detailed description, as well as other embodiments that can be derived from the teachings of the present invention by those skilled in the art and that are within the scope of the present invention.

Claims (4)

1. A lead-acid storage battery SOH estimation method based on a VPGA-GPR algorithm is characterized by comprising the following steps: the method comprises the following steps:
step 1, performing a capacity fading experiment on a lead-acid storage battery, and recording the change relation of the actual capacity of the battery along with the cycle number and the time of constant voltage charging and constant current charging in a charging stage;
step 2, determining factors which have obvious influence on the SOH of the lead-acid storage battery based on the test result of the step 1, and establishing a Gaussian process regression model;
and 3, optimizing the objective function of the Gaussian process regression model established in the optimization step 2 through a variable probability genetic algorithm, and estimating the SOH of the lead-acid storage battery.
2. The method for estimating the SOH of the lead-acid storage battery based on the VPGA-GPR algorithm in claim 1, wherein the method comprises the following steps: the specific method of the step 1 comprises the following steps: firstly, carrying out a cyclic charge-discharge experiment on a lead-acid storage battery, wherein the charge is stage charge, namely constant-current charge is carried out firstly, and constant-voltage charge is kept after the charge cut-off voltage is reached until the charge current is reduced to be below a specified value; constant current discharging is adopted for discharging, terminal voltage current data are recorded to calculate the actual capacity, a plurality of cyclic charging and discharging experiments are carried out, the change relation of the actual capacity of the battery along with the number of cycles is recorded, and the time of constant voltage charging and constant current charging in the charging stage is recorded.
3. The method for estimating the SOH of the lead-acid storage battery based on the VPGA-GPR algorithm in claim 1, wherein the method comprises the following steps: the specific method of the step 2 comprises the following steps:
outputting the capacity sequence of the storage battery as a regression model { x }0(k)},T1,T2,T3The sequence is as follows: { xi(k) And (3) calculating the correlation between input and output by using the following formula:
Figure FDA0002694450210000011
in the above formula, T total charging time, T1Constant voltage charging time and T2Constant current charging time;
the result shows that the grey correlation degree of the constant voltage charging time is the highest, so that a Gaussian process regression model of the constant voltage charging time and the battery capacity is established.
4. The method for estimating the SOH of the lead-acid storage battery based on the VPGA-GPR algorithm in claim 1, wherein the method comprises the following steps: the specific steps of the step 3 comprise:
(1) all data points (x)2(k),x0(k) K 1,2.. m is divided into mutually exclusive training sets and independent test sets, and pairsAnd performing K-fold cross inspection on the training set, dividing the training set into mutually exclusive K groups, taking one of the K groups as a verification set and the rest K-1 groups as a training set in sequence, and training a GPR model. The kernel function of the GPR model is a square exponential kernel function, and the number of the kernel functions is 3 and is respectively sigmap,l,σn
Figure FDA0002694450210000021
The training process is to optimize the following objective function through a Variable Probability Genetic Algorithm (VPGA), namely, the root mean square value of the actual output and the predicted output of the verification set is minimum:
Figure FDA0002694450210000022
(2) implementation of VPGA:
initializing N three-dimensional random vectors, wherein each vector contains hyperparametric information of a GPR kernel function, namely, the ith random vector is (delta)ip,liin) Referred to as an individual; selecting a formula (3) for the fitness value f; calculating fitness values in the formula (3) respectively, and determining and selecting parent individuals according to a roulette method, wherein the probability that individuals with higher fitness are selected is higher; calculating the cross probability and the mutation probability by the following formulas, performing cross operation on the selected parent individuals, and performing mutation operation on the generated filial generations:
Figure FDA0002694450210000031
and (3) adopting an elite storage strategy to store the optimal M individuals of the previous generation to replace the worst M individuals of the next generation, wherein M is determined according to the following formula:
Figure FDA0002694450210000032
repeating the cross variation operation and the elite preservation strategy, knowing that the optimal fitness value is not obviously changed any more for continuous generations;
(3) and selecting an optimal group of results in K rounds of training as the hyperparametric output of the GPR, and taking the result as the SOH estimation result of the lead-acid storage battery.
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