CN111914394B - Super capacitor parameter online estimation method based on double least square method - Google Patents
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Abstract
The invention discloses a super capacitor parameter online estimation method based on a double least square method, which comprises the following steps: setting system parameter estimates
And an estimated initial value of the correction gain P (k) for state estimation; estimation of equivalent series internal resistance value R of super capacitor by adopting recursive and augmented least square method with forgetting factor ESR (ii) a Judging the equivalent series internal resistance value R ESR Whether the estimation precision meets the precision requirement or not, and when the estimation precision meets the precision requirement, estimating the capacitance parameter C of the super capacitor by using a recursive and augmented least square method 0 And k c Determining the fixed capacitance value C 0 And the coefficient k of capacitance variation with voltage c Whether the precision requirement is met or not, and when the precision requirement is met, finishing R ESR 、C 0 And k c Online estimation of three parameters. The invention has the characteristics of high identification precision, simple algorithm and capability of realizing on-line realization of a microprocessor, and can identify R ESR 、C 0 And k is c And the three parameters are suitable for online estimation of states of the super capacitor SOC, the SOH and the like.
Description
Technical Field
The invention relates to a super-capacitor parameter online estimation method, in particular to a super-capacitor parameter online estimation method based on a double least square method, and belongs to the field of super-capacitor management and state estimation.
Background
The super capacitor as a power type energy storage device has the characteristics of long cycle life, high power density, wide temperature range and the like, and has wide application prospect in the fields of traffic, electric power, national defense and the like. In the super capacitor energy storage system, online monitoring of states of State of Charge (SOC) and State of Health (SOH) of a super capacitor monomer has important significance for use, maintenance, service life prolonging technology and the like of the energy storage system. Super-superThe first-order RC equivalent circuit model of the stage capacitor is shown in FIG. 1 and consists of a series equivalent resistor R ESR And a voltage-dependent capacitance C (C = C) 0 +k c u c1 ；C 0 Is a fixed capacitance value, k c A coefficient of capacitance as a function of voltage).
It is generally recommended that the capacitance value of the super capacitor be attenuated to 80% of the factory value, i.e. the super capacitor is considered to be out of service. According to this suggested monomer SOH value can be expressed as formula (1). However, the capacitance of the super capacitor varies with voltage, and the IEC International electrotechnical Commission recommends 0.4U N ～0.8U N (U N Rated voltage) as the capacitance value of the super capacitor. The capacitance value C of the super capacitor is obtained by adopting a first-order RC equivalent circuit model shown in figure 1 and combining with the proposal of IEC real Can be represented by the formula (2). For super capacitor model parameter C 0 And k c And (3) carrying out online estimation, then obtaining the average value of the super capacitor according to the formula (2), and further combining the formula (1) to estimate the SOH value of the monomer online. The super capacitor SOC value can be expressed as shown in formula (3), and a model parameter C is identified 0 、k c And equivalent series internal resistance value R ESR I.e. online estimation of SOC can be achieved. In order to realize online estimation of SOC and SOH states, equivalent series internal resistance values R are required ESR A fixed capacitance value C 0 And the coefficient k of capacitance variation with voltage c And carrying out online identification on the three model parameters.
In the formula C EOL Is the end-of-life capacitance value, C EOL ＝0.8C new ，C new Capacitance value, C, at factory shipment real Real-time capacitance values.
In the formula of U N The rated voltage of the super capacitor.
In the formula u c1 Is the first RC branch capacitance voltage u c1 ＝V SC -iR ESR ，V SC Is the voltage at the end of the super capacitor, i is the current value of the super capacitor, R ESR The equivalent series internal resistance of the super capacitor.
Chaoui H., gualous H in the article "on line Lifetime Estimation of Supercapacitors", the capacitance parameter is estimated on line by using the adaptive rate based on Lyapunov, so that the stability of parameter identification is improved. In an article of "one conditioning monitoring and fault detection of large superparameter banks in electric circuits applications", authors such as Naseri F, farjah E, allahbakhshi M, etc., recursive expansion recursive two-multiplication is adopted to realize real-time estimation of capacitance parameters, and the calculated amount is small. In an article "Online supercapacitive diagnostic for Electric Vehicle Applications", authors such as Mejdoubi A, oukaour A, chaoui H, etc., an extended Kalman filter is adopted to realize Online estimation of capacitance parameters, so that the method has strong robustness on measurement noise. In an article "on line Parameter Identification for supercapacitive State-of-Health Diagnosis for capacitive Applications", authors such as Mejdoubi A, chaoui H, gualous H, and the like, a sliding mode observer is adopted to identify capacitance parameters on line, so that the stability and precision of estimation are improved. The above four articles all realize on-line estimation of capacitance parameters, but the estimated capacitance value varies with voltage, i.e. only the total capacitance value C is estimated, and the fixed capacitance value C is not estimated 0 And the coefficient of variation of capacitance with voltage k c The SOC and SOH states of the super capacitor cannot be estimated from the changed capacitance parameters. In an article, "A Generalized Extended State Observer for Supercapacitor State of Energy Estimation with Online Identified Model", by authors of Zhou Y, huang Z, li H, etc., an Extended State Observer is used to estimate a fixed capacitance value C 0 And the coefficient of variation of capacitance with voltage k c However, the method is complex and has a large calculation amount, and is not easy to realize on line by adopting a microprocessor. King of unknown personRain, royal and royal hui adopted a nonlinear least square method to estimate a fixed capacitance value C in the article "super capacitor equivalent circuit model parameter identification by nonlinear least square method" of royal hui 0 And the coefficient of variation of capacitance with voltage k c However, this method requires a period of standing and is not suitable for real-time online estimation of parameters. By combining the above analysis, the conventional super capacitor parameter identification method mainly has the following defects: 1. the fixed capacitance value C cannot be estimated 0 And the coefficient of variation of capacitance with voltage k c (ii) a 2. The algorithm is complex and is not easy to realize on line by a microprocessor; 3. special test procedures are needed, the energy storage system needs to be interrupted, and online implementation cannot be achieved. The above disadvantages will cause that the current parameter estimation method cannot be realized on line by adopting a microprocessor, and cannot complete the on-line estimation of the SOC and SOH states of the super capacitor single body.
Disclosure of Invention
Aiming at the prior art, the invention aims to provide a method for identifying the equivalent series internal resistance R in a super capacitor model on line, which has small calculated amount and can be realized by an on-line microcontroller ESR A fixed capacitance value C 0 And the coefficient k of capacitance variation with voltage c The super capacitor parameter online estimation method based on the double least square method meets the requirements of state online estimation of super capacitors SOC, SOH and the like on model parameter identification.
In order to solve the technical problem, the invention discloses a super-capacitor parameter online estimation method based on a double least square method, which comprises the following steps of:
s1: the super capacitor is equivalent to an equivalent series resistor R ESR And a voltage-dependent capacitance C, C = C 0 +k c u c1 ，C 0 At a fixed capacitance value, k c Setting system parameter estimated value for capacitance variation coefficient with voltage
And an estimated initial value of the correction gain P (k) of the state estimation,
P(0)＝P 0 ；
s2: estimation of equivalent series internal resistance value R of super capacitor by adopting recursive and augmented least square method with forgetting factor ESR ；
S3: judging equivalent series internal resistance value R ESR Estimating whether the precision meets the precision requirement, and executing the step S4 when the precision meets the precision requirement; otherwise, returning to S2;
s4: method for estimating capacitance parameter C of super capacitor by adopting recursive augmented least square method 0 And k c ；
S5: determining a fixed capacitance value C 0 And the coefficient k of capacitance variation with voltage c Whether the precision requirement is met or not, and when the precision requirement is met, finishing R ESR 、C 0 And k c Online estimation of three parameters; otherwise, returning to S4;
the invention also includes:
s2, estimating the equivalent series internal resistance R of the super capacitor by adopting a recursive augmented least square method with forgetting factors ESR The method specifically comprises the following steps:
the state equation used is:
wherein y (k) = V SC (k)-V SC (k-1) is the system output quantity,
is a system state quantity, theta T ＝[1/C，R ESR ，d]D is an error coefficient, V, for a system parameter SC (k) I (k) is the current value of the super capacitor observed at the kth time,
in order to output the error for the system,
system parameters for the k-1 th estimation;
introducing a forgetting factor lambda, wherein lambda is more than 0 and less than or equal to 1, and the recursive and augmented least square algorithm with the forgetting factor comprises the following steps:
in the formula
y(k)、
P (k) is the system state, system output, system parameter estimation value and correction gain of state estimation of the k-th observation respectively,
P(0)＝P 0 ，
y(0)＝0。
s3, judging the equivalent series internal resistance value R ESR Whether the estimation precision meets the precision requirement is specifically as follows:
when in use
When the situation is met, the estimation precision meets the requirement;
wherein x =1,2, \ 8230;, h 1 ；y＝1,2,…,h 1 ；ε 1 Given a corresponding R ESR Error value of (d), h 1 Is the number of consecutive estimations.
3.S4, estimating superelevation by adopting recursive-augmentation least square methodCapacitance parameter C of stage capacitor 0 And k c The method specifically comprises the following steps:
the state equation used is:
wherein Q is 0 Is the initial value of the charge of the super capacitor,
is an estimated value of the voltage at two ends of the capacitor C changing along with the voltage during the k-th observation, d is an error coefficient,
in order to output the error for the system,
system parameters estimated for the k-1 st time;
the recursive augmented least square method specifically comprises the following steps:
in the formula
y(k)、
P (k) is respectively the system state, system output, system parameter estimation value and correction gain of state estimation of the k-th observation,
P(0)＝P 0 ，
y(0)＝0。
s5, judging fixed capacitance value C 0 And the coefficient k of capacitance variation with voltage c Whether the accuracy requirement is met is specifically as follows:
when the temperature is higher than the set temperature
Then C is 0 The estimation precision meets the requirement;
wherein x =1,2, \ 8230;, h 2 ；y＝1,2,…,h 2 ；ε 2 For a given error value, h 2 Is the number of consecutive estimations.
When the temperature is higher than the set temperature
Then k is c The estimation precision meets the requirement;
wherein x =1,2, \ 8230;, h 3 ；y＝1,2,…,h 3 ；ε 3 For a given error value, h 3 Is the number of consecutive estimations.
The invention has the beneficial effects that: the invention adopts a double least square method to realize the online estimation of the super capacitor parameters, and the method has small calculated amount, can be realized on line by a microprocessor and can identify the fixed capacitance value C 0 And the coefficient of variation of capacitance with voltage k c The method is suitable for online estimation of the SOC and SOH states of the super capacitor. Compared with the prior art:
the invention adopts two Recursive extended least square methods (RELS), wherein one RELS realizes the equivalent internal resistance R of the super capacitor ESR After it has stabilized, the estimated R is taken into account ESR As known quantity, the online estimation of the capacitance parameter is realized by combining with RELS, and the equivalent internal resistance R is solved ESR With a fixed capacitance value C 0 And the coefficient k of capacitance variation with voltage c The three are mutually coupled, canRealization of R ESR 、C 0 And k c Accurate online estimation of. The parameter identification method has the characteristics of high identification precision, simple algorithm and capability of realizing on-line realization of a microprocessor, and can identify R ESR 、C 0 And k c And three parameters lay a foundation for the online estimation of states such as super capacitor SOC, SOH and the like.
Drawings
FIG. 1 is a first-order RC equivalent circuit model of a super capacitor;
FIG. 2 is a super capacitor bank parameter online identification method based on a double least square method;
fig. 3 is an implementation block diagram of a super capacitor parameter identification method based on a double least square method.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
The least square method has the characteristics of simple algorithm, good convergence, no need of system prior statistical information and the like, and can be applied to online identification of the parameters of the super capacitor. The first order RC model of the super capacitor can be expressed as shown in equation (4). Equivalent series internal resistance R ESR And C 0 ，k c The parameters should be decoupled if there is a coupling relationship. If u is to be c1 As a known quantity, R is firstly identified on line by using a least square method ESR R is to be ESR As a known quantity, it can then be based on the terminal voltage V SC To estimate u c1 And then u will be c1 By combining with least square method 0 ，k c So that R can be realized ESR And C 0 ，k c The decoupling identification of (2).
Where i is the input current, V SC Terminal voltage u for the super capacitor bank c1 Is the first RC branch capacitance voltage u c10 Is the initial voltage of the super capacitor bank.
The invention adopts a double recursion augmentation least square method (Recur)Passive extended least square, RELS) to achieve the estimation of the model parameters of the super capacitor. The recursive augmented least square method takes the noise model into consideration at the same time, and under the condition that the expected value of the noise is nonzero, unbiased estimation can be realized. Firstly, realizing equivalent internal resistance R of super capacitor by adopting a RELS ESR After it has stabilized, the estimated R is estimated ESR The capacitance parameter online estimation is realized by combining the known quantity with another RELS, and the equivalent internal resistance R is solved ESR With a fixed capacitance value C 0 And the coefficient k of capacitance variation with voltage c The problem of mutual coupling of the three is solved, and the super capacitor parameter online identification block diagram shown in figure 2 is obtained.
Firstly, the equivalent internal resistance value R of the super capacitor is estimated ESR The adopted system state equation is shown as the formula (5). In the formula, C is a capacitance value of the super capacitor, changes with voltage, is a slow variable, and needs to introduce a forgetting factor λ (λ is greater than 0 and less than or equal to 1), a large λ value can be set for a slowly time-varying system parameter, a small λ value can be set for a rapidly time-varying system parameter, and λ =0.98 can be selected.
Wherein y (k) = V SC (k)-V SC (k-1) is the output quantity of the system,
is a system state quantity, theta T ＝[1/C，R ESR ，d]Is a system parameter, d is an error coefficient,
in order to output the error for the system,
for the k-1 estimated system parameters, Q (k) is the amount of charge observed at the k-th time.
Then, the resistance value R in the equivalent series ESR After the estimation reaches the steady state, the capacitor parameters can be identified online by RELS. System equation adoptedAs shown in equation (6).
In the formula Q 0 Is the initial value of the charge of the super capacitor, d is the error coefficient,
in order to output the error for the system,
the system parameters for the k-1 th estimation.
The equivalent series internal resistance R can be realized by substituting the state equation into a recursive and augmented least square algorithm ESR A fixed capacitance value C 0 And the coefficient of variation of capacitance with voltage k c Accurate online estimation of three parameters.
The super capacitor model adopts a first-order RC equivalent circuit model as shown in figure 1. An implementation block diagram of the super-capacitor parameter identification method based on the double least square method is shown in fig. 3. The specific description of the implementation process is as follows:
firstly, setting an initial parameter estimation value theta 0 ，P 0 . There are two ways to set the initial value, the first is to observe several groups of data and calculate theta by non-recursion least square method 0 And P 0 (ii) a Second one directly taking theta 0 ＝0，P 0 ＝aI n And a is a very large real number.
And then, estimating the equivalent series internal resistance value of the super capacitor by adopting an RELS algorithm with a forgetting factor. The state equation adopted by the estimation algorithm is shown in formula (5), and the RELS algorithm with the forgetting factor is shown in formula (7). Equivalent internal resistance R of standby super capacitor ESR And after the estimation precision meets the requirement, estimating the capacitance parameter. For the determination of the estimation accuracy, the determination criterion shown in the formula (8) may be selected. In the formula, any one of n system parameters is estimated for h times, the ratio of the deviation between any two times of estimation to the average value of the two times of estimation is less than a proper small number epsilon, and the system parameter is considered to reachAnd (5) precision requirement.
In the formula
y(k)、
P (k) is respectively the system state, system output, system parameter estimation value and correction gain of state estimation of the k-th observation,
P(0)＝P 0 ，
y (0) =0, λ (λ is more than 0 and less than or equal to 1) is a forgetting factor, and in the invention, A (k-1), A (k) and A (k + 1) respectively represent values of the physical quantity A in the k-1 th observation, the k-th observation and the k +1 th observation.
In the formula a i Is the ith parameter of the system; i =1,2, \8230;, n; x =1,2, \ 8230;, h; y =1,2, \8230;, h; ε is a suitably small number.
Equivalent internal resistance R of super capacitor ESR And after the estimation precision meets the requirement, estimating the capacitance parameter of the super capacitor by adopting an RELS algorithm. The estimation algorithm uses a state equation as shown in equation (6), and the RELS algorithm is shown in equation (9). The judgment basis shown in the formula (8) can be selected to judge two parameters C of the super capacitor 0 And k is c And whether the estimation precision requirement is met or not is judged.
In the formula
y(k)、
P (k) is respectively the system state, system output, system parameter estimation value and correction gain of state estimation of the k-th observation,
P(0)＝P 0 ，
y(0)＝0。
to-be-measured capacitance parameter C 0 And k is c The super capacitor model R is completed after the estimation precision is reached ESR 、C 0 And k c Online estimation of three parameters.
Claims (3)
1. A super capacitor parameter online estimation method based on a double least square method is characterized by comprising the following steps:
s1: the super capacitor is equivalent to an equivalent series resistor R ESR And a voltage-dependent capacitance C, C = C 0 +k c u c1 ，C 0 At a fixed capacitance value, k c Setting system parameter estimated value for capacitance variation coefficient with voltage
And an estimated initial value of the correction gain P (k) of the state estimation,
P(0)＝P 0 ；
s2: estimation of equivalent series internal resistance value R of super capacitor by adopting recursive augmented least square method with forgetting factor ESR The method specifically comprises the following steps: the state equation used is:
wherein y (k) = V SC (k)-V SC (k-1) is the system output quantity,
is a system state quantity, theta T ＝[1/C，R ESR ，d]For system parameters, d is the error coefficient, V SC (k) I (k) is the current value of the super capacitor observed at the kth time,
in order to output the error for the system,
system parameters for the k-1 th estimation;
introducing a forgetting factor lambda, wherein lambda is more than 0 and less than or equal to 1, and the recursive and augmented least square algorithm with the forgetting factor comprises the following steps:
in the formula
y(k)、
P (k) is respectively the system state, system output and system of the k-th observationThe parameter estimation value and the correction gain of the state estimation,
P(0)＝P 0 ，
y(0)＝0；
s3: judging equivalent series internal resistance value R ESR Estimating whether the precision meets the precision requirement, and executing the step S4 when the precision meets the precision requirement; otherwise, returning to S2;
s4: method for estimating capacitance parameter C of super capacitor by adopting recursive augmented least square method 0 And k c The method specifically comprises the following steps:
the state equation used is:
wherein Q 0 Is the initial value of the charge of the super capacitor,
is the estimated value of the voltage at two ends of the capacitor C changing with the voltage during the k-th observation, d is an error coefficient,
in order to output the error for the system,
system parameters estimated for the k-1 st time;
the recursive augmented least square method specifically comprises the following steps:
in the formula
y(k)、
P (k) is respectively the system state, system output, system parameter estimation value and correction gain of state estimation of the k-th observation,
P(0)＝P 0 ，
y(0)＝0；
s5: determining a fixed capacitance value C 0 And the coefficient k of capacitance variation with voltage c Whether the precision requirement is met or not, and when the precision requirement is met, finishing R ESR 、C 0 And k c Online estimation of three parameters; otherwise, return to S4.
2. The double least square method-based supercapacitor parameter online estimation method according to claim 1, characterized in that: s3, judging the equivalent series internal resistance value R ESR Whether the estimation precision meets the precision requirement is specifically as follows:
when in use
When the situation is met, the estimation precision meets the requirement;
wherein x =1,2, \8230;, h 1 ；y＝1,2,…,h 1 ；ε 1 Given a corresponding R ESR Error value of (d), h 1 Is the number of consecutive estimations.
3. The supercapacitor parameter online estimation method based on the double least square method according to claim 2, characterized in that: s5, judging fixed capacitance value C 0 And the coefficient k of capacitance variation with voltage c Whether the accuracy requirement is met is specifically as follows:
when in use
Then C is 0 The estimation precision meets the requirement;
wherein x =1,2, \ 8230;, h 2 ；y＝1,2,…,h 2 ；ε 2 For a given error value, h 2 Is the number of consecutive estimations;
when in use
Then k is c The estimation precision meets the requirement;
wherein x =1,2, \ 8230;, h 3 ；y＝1,2,…,h 3 ；ε 3 For a given error value, h 3 Is the number of consecutive estimations.
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