CN104730386A - Supercapacitor charge state estimating method based on Kalman filtering algorithm - Google Patents

Abstract

The invention relates to a supercapacitor charge state estimating method based on the Kalman filtering algorithm, in particular to a charge state estimating method. The charge state estimating method includes the steps of firstly collecting the voltage value and the current value of a supercapacitor in the working state in real time; based on the collected data, carrying out online parameter identification on a supercapacitor model with the least square method; based on the collected data and an obtained circuit model, estimating the charge state of the supercapacitor with the Kalman filtering algorithm. By means of the charge state estimating method, the supercapacitor charge state real-time estimation accuracy can be effectively improved; meanwhile, no large calculation load of a system is caused, and the charge state estimating method has the advantages of being high in stability and reliability and the like. Meanwhile, state variables of the nonlinear system can be accurately estimated through the Kalman algorithm, estimation does not depend on accurate initial value setting, and a system true value can be rapidly approached in the large-deviation original state.

Description

A kind of ultracapacitor charge state estimation method based on Kalman filtering algorithm

Technical field

The present invention relates to a kind of state-of-charge method of estimation, especially relate to a kind of ultracapacitor state-of-charge method of estimation based on Kalman filtering algorithm.

Background technology

Ultracapacitor is a kind of Novel energy storage apparatus based on interfacial electric double layer theory, and compared to traditional energy storage device, as accumulator, it has duration of charging short, the advantage such as long service life, good temp characteristic, economize energy and environmental protection.In recent years, due to the problem such as environmental protection and energy crisis, ultracapacitor is widely used in numerous areas, such as generation of electricity by new energy, electric automobile and urban track traffic Brake energy recovery etc.

In concrete engineering application, for ensureing the safety and reliability of super capacitor energy storage system, its concrete inside state-of-charge (State-of-Charge, SOC) needs by real-time estimation.At present, the evaluation method being applicable to ultracapacitor SOC is less, and being used maximum in actual application is Ah counting method.Ah counting method flows through the electric current of ultracapacitor by Real-Time Monitoring, and then carry out time integral to complete the estimation process of ultracapacitor SOC to this electric current, its process is as follows.

${\mathrm{SOC}}_t={\mathrm{SOC}}_0-\underset{0}{\overset{t}{\∫}}\mathrm{i\τd\τ}$

In above formula, SOC _tthe SOC of t ultracapacitor, SOC ₀be that initial SOC, the i of ultracapacitor flows through in working order the electric current flowing through ultracapacitor, if ultracapacitor electric discharge, then it is just, otherwise is negative.From above formula, Ah counting method in use can produce the accumulation of error, due to its better simply computation process, it is auto modification error mechanism not, so utilize the method can not meet higher accuracy requirement to the estimation of ultracapacitor state-of-charge.

Summary of the invention

The present invention is intended to the problem overcoming the lower estimation precision of prior art, under can not obviously increasing the condition of system operations load, provides a kind of method accurately completing ultracapacitor estimation.

Technical scheme of the present invention is: a kind of ultracapacitor charge state estimation method based on Kalman filtering algorithm, and step is as follows:

1) real-time magnitude of voltage and current value collection are carried out to the ultracapacitor under in running order.

2) based on step 1) magnitude of voltage that collects and current value, utilize discrimination method to carry out on-line parameter identification to ultracapacitor equivalent-circuit model in normal operation.Obtain model for on-line parameter identification, set up the state space equation of this model:

$\left\{\begin{array}{c}\stackrel{\·}{x}=\mathrm{Ax}+\mathrm{Bu}\\ y=\mathrm{Cx}+\mathrm{Du}\end{array}\right.$

X is state space equation state variable and x=[U ₁u ₂sOC], A, B, C, D are the parameter matrixs of state space equation, and u is system input and u=I, y are system output and y=U.

Based on above-mentioned state space equation, complete the identification of ultracapacitor model on-line parameter.Wherein, discrimination method comprises least square method, particle swarm optimization algorithm or differential evolution method.

3) based on step 1) magnitude of voltage that gathers and current value and step 2) model that on-line parameter identification obtains, utilize Kalman filtering algorithm to complete the estimation of ultracapacitor state-of-charge.

As follows according to system state space model inference Kalman filtering algorithm computation process:

${\tilde{x}}_k^{-}=A_{k-1}{\tilde{x}}_{k-1}+B_k{u}_k+w_k$

$P_k^{-}=A_{k-1}{P}_{k-1}{A}_{k-1}^T+Q_{k-1}$

${\mathrm{\κ}}_k=P_k^{-}{C}_k^T{(C_k{P}_k^{-}{C}_k^T+R_k)}^{-1}$

${\tilde{x}}_k={\tilde{x}}_k^{-}+{\mathrm{\κ}}_k(y_k-C_k{\tilde{x}}_k^{-}-D_k{u}_k)$

$P_k=(I-{\mathrm{\κ}}_k{C}_k)P_k^{-}$

In above formula, w _kbe systematic procedure error, its covariance is Q _k, the measuring error covariance of system is R _k, P _kthe all square evaluated error of system, κ _kit is system kalman gain.

Utilize above-mentioned Kalman filtering algorithm, iterative computation is carried out to the state space equation containing ultracapacitor state-of-charge, just can go out the accurate state-of-charge of ultracapacitor by real-time estimation.

Compared with prior art, the present invention has the following advantages: can complete ultracapacitor in working order under real-time state-of-charge accurately estimate, thus efficiency of energy utilization and the mission life of ultracapacitor can be promoted, the safety and reliability of elevator system.Meanwhile, Kalman Algorithm can make accurate estimation to the state variable of nonlinear system, and it is estimated and does not rely on initial value setting accurately, and the original state larger in deviation can approach system actual value fast.

Accompanying drawing explanation

Accompanying drawing is ultracapacitor equivalent model.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.The present embodiment is implemented premised on technical solution of the present invention, give detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

In the present invention, ultracapacitor charge state estimation method comprises the following steps:

1) real-time magnitude of voltage and current value collection are carried out to the ultracapacitor under in running order.

2) based on step 1) experimental data, utilize least square method to carry out on-line parameter identification to ultracapacitor model.

As shown in drawings, set up ultracapacitor equivalent-circuit model in normal operation, and on-line identification is carried out to model parameter.Based on identification model, set up the state space equation of this model:

$\left\{\begin{array}{c}\stackrel{\·}{x}=\mathrm{Ax}+\mathrm{Bu}\\ y=\mathrm{Cx}+\mathrm{Du}\end{array}\right.$

In above formula, x is state space equation state variable and x=[U ₁u ₂sOC], A, B, C, D are the parameter matrixs of state space equation, and u is system input and u=I, y are system output and y=U.In addition, consider that in ultracapacitor model, equivalent parallel resistance resistance is higher, its branch current is less, therefore in above formula output equation y=Cx+Du, ignores the impact of equivalent parallel resistance on model, removed and do not consider.

Therefore, ultracapacitor state space equation is specific as follows:

$\left[\begin{array}{c}{U}_1(k+1)\\ U_2(k+1)\\ \mathrm{SOC}(k+1)\end{array}\right]=\left[\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right]\left[\begin{array}{c}{U}_1\left(k\right)\\ U_2\left(k\right)\\ \mathrm{SOC}\left(k\right)\end{array}\right]+\left[\begin{array}{c}{b}_{11}\\ b_{21}\\ b_{31}\end{array}\right]u$

$y=\left[\begin{array}{ccc}{c}_{11}& c_{12}& 0\end{array}\right]\left[\begin{array}{c}{U}_1\left(k\right)\\ U_2\left(k\right)\\ \mathrm{SOC}\left(k\right)\end{array}\right]+d\·u$

Based on above-mentioned state space equation, complete the identification of ultracapacitor model on-line parameter.Wherein, discrimination method comprises least square method, particle swarm optimization algorithm or differential evolution method.

3) based on step 1 experimental data and step 2 circuit model, Kalman filtering algorithm is utilized to complete the estimation of ultracapacitor state-of-charge.

As follows according to system state space model inference Kalman filtering algorithm computation process:

${\tilde{x}}_k^{-}=A_{k-1}{\tilde{x}}_{k-1}+B_k{u}_k+w_k$

$P_k^{-}=A_{k-1}{P}_{k-1}{A}_{k-1}^T+Q_{k-1}$

${\mathrm{\κ}}_k=P_k^{-}{C}_k^T{(C_k{P}_k^{-}{C}_k^T+R_k)}^{-1}$

${\tilde{x}}_k={\tilde{x}}_k^{-}+{\mathrm{\κ}}_k(y_k-C_k{\tilde{x}}_k^{-}-D_k{u}_k)$

$P_k=(I-{\mathrm{\κ}}_k{C}_k)P_k^{-}$

In above formula, w _kbe systematic procedure error, its covariance is Q _k, the measuring error covariance of system is R _k, P _kthe all square evaluated error of system, κ _kit is system kalman gain.In the setting of Kalman filtering algorithm initial value, the state variable of system can choose at random, but all square evaluated error of system generally elects unit matrix as.

Utilize above-mentioned Kalman filtering algorithm, iterative computation is carried out to the state space equation containing ultracapacitor state-of-charge, just can go out the accurate state-of-charge of ultracapacitor by real-time estimation.

Claims (2)

1., based on a ultracapacitor charge state estimation method for Kalman filtering algorithm, it is characterized in that, step is as follows:

1) real-time magnitude of voltage and current value collection are carried out to the ultracapacitor under in running order;

2) based on step 1) magnitude of voltage that collects and current value, utilize discrimination method to carry out on-line parameter identification to ultracapacitor equivalent-circuit model in normal operation; Obtain model for on-line parameter identification, set up the state space equation of this model:

$\left\{\begin{array}{c}\stackrel{.}{x}=\mathrm{Ax}+\mathrm{Bu}\\ y=\mathrm{Cx}+\mathrm{Du}\end{array}\right.$

X is state space equation state variable and x=[U ₁u ₂sOC], A, B, C, D are the parameter matrixs of state space equation, and u is system input and u=I, y are system output and y=U;

Based on above-mentioned state space equation, complete the identification of ultracapacitor model on-line parameter;

3) based on step 1) magnitude of voltage that gathers and current value and step 2) model that on-line parameter identification obtains, utilize Kalman filtering algorithm to complete the estimation of ultracapacitor state-of-charge;

As follows according to system state space model inference Kalman filtering algorithm computation process:

${\tilde{x}}_k^{-}=A_{k-1}{\tilde{x}}_{k-1}+B_k{u}_k+w_k$

$P_k^{-}=A_{k-1}{P}_{k-1}{A}_{k-1}^T+Q_{k-1}$

${\mathrm{\κ}}_k=P_k^{-}{C}_k^T{(C_k{P}_k^{-}{C}_k^T+R_k)}^{-1}$

${\tilde{x}}_k={\tilde{x}}_k^{-}+{\mathrm{\κ}}_k(y_k-C_k{\tilde{x}}_k^{-}-D_k{u}_k)$

$P_k=(I-{\mathrm{\κ}}_k{C}_k)P_k^{-}$

In above formula, w _kbe systematic procedure error, its covariance is Q _k, the measuring error covariance of system is R _k, P _kthe all square evaluated error of system, κ _kit is system kalman gain;

Utilize Kalman filtering algorithm, carry out iterative computation to the state space equation containing ultracapacitor state-of-charge, just real-time estimation goes out the accurate state-of-charge of ultracapacitor.

2. ultracapacitor charge state estimation method according to claim 1, is characterized in that, described discrimination method comprises least square method, particle swarm optimization algorithm or differential evolution method.