CN105116346A - Series-connected battery system and method for estimating state of charge thereof - Google Patents

Abstract

The invention discloses a series-connected battery system and a method for estimating the state of charge (SOC) thereof. The series-connected battery system is formed by N battery lithium ion single bodies connected in series. The method comprises the steps of: establishing a SOC-based equivalent circuit model of the series-connected battery system; establishing a space state equation of the series-connected battery system in combination with the implication of the SOC; estimating the SOC of the series-connected battery system by means of unscented Kalman filter and updating a gain matrix by comparing the online-detected output voltage of the battery system with a voltage estimated value so as to obtain the estimated value of the SOC of the series-connected battery system by means of such recursion. Compared with an extended Kalman filter algorithm, the method for estimating the SOC of the series-connected battery system is better in accuracy and robustness and is suitable for series-connected battery systems and other types of batteries such as lead-acid cells and nickel-cadmium cells.

Description

A kind of tandem type lithium-ion battery systems and state-of-charge method of estimation thereof

Technical field

The invention belongs to the design of MW level battery energy storage system and control technology field in intelligent grid, relate to a kind of tandem type lithium-ion battery systems and state-of-charge method of estimation thereof.

Background technology

Along with the regenerative resource such as wind-powered electricity generation, photovoltaic generation and electrical network is intelligentized greatly develops, battery system, as the main carriers of battery energy storage system stored energy, is subject to concern and the application of countries in the world more and more.The continuous expansion of regenerative resource scale simultaneously and the quick growth of power load, also battery system will be impelled to high capacity (MW level) future development, the expansion of battery capacity can be realized by the series connection of multiple battery cell, i.e. tandem type lithium-ion battery systems (Series-connectedBatterySystem, SBS).But, because the complicacy (as level and smooth in level fluctuating power second, a contour dynamic case of high frequency) of applied environment and battery electric quantity such as directly can not to measure at the factor, accurate estimation battery system state-of-charge (StateofCharge, SOC) not only directly determine that can battery system safe, reliable, efficiently run, and battery system is distributed rationally, design and controls etc. most important.

Traditional SOC algorithm for estimating mainly contains: ampere-hour method, impedance method, open-circuit voltage method etc., has in succession occurred the advanced algorithms such as neural network, fuzzy logic method, support vector machine and standard Kalman filter method, EKF in recent years.Ampere-hour method, because of advantages such as its algorithm are simple, easy, has been used widely, but there is the shortcoming such as self open loop, error time accumulation, and its precision is limited; Under open-circuit voltage method is applicable to stable state, SOC estimates, is unsuitable for On-line Estimation; The advanced algorithm such as neural network, fuzzy logic under being suitable for constant load, constant current charge-discharge state dissimilar battery SOC estimate but have that amount of training data is large, training method affects large limitation to evaluated error; Standard Kalman filter method has the advantages such as robustness is high, Ability of Resisting Disturbance is strong, and the SOC being suitable for linear system estimates, but battery system is a kind of nonlinear and time-varying system, and its precision is still limited; For this reason, for the battery system of nonlinear time-varying, often adopt EKF at present, and obtain good effect, but there is self calculation of complex, ignore the problems such as higher order term due to EKF, must certain error be produced, make the SOC estimated accuracy of battery still treat further research.

Summary of the invention

The problem that the present invention solves is to provide a kind of based on Unscented kalman filtering (UnscentedKalmanFilter, UKF) tandem type lithium-ion battery systems state-of-charge method of estimation, solve that tandem type lithium-ion battery systems performance parameter affects by SOC, EKF method calculation of complex, precision is not high and cause battery system SOC to be difficult to the problem being accurately, estimating, reaches the object of accurately estimation tandem type lithium-ion battery systems SOC.

The present invention seeks to be achieved through the following technical solutions:

The invention provides a kind of tandem type lithium-ion battery systems, this system is in series by N number of lithium-ion battery monomer, and wherein N is the natural number being greater than 1.

A kind of tandem type lithium-ion battery systems state-of-charge method of estimation based on Unscented kalman filtering provided by the invention is as follows: according to known lithium-ion battery monomer performance parameter, utilize the relation of parallel circuit operating characteristic and charge/discharge operation characteristic determination tandem type lithium-ion battery systems performance parameter and battery cell performance parameter, determine battery system output end voltage equation in conjunction with Kirchhoff's law KVC again, set up tandem type lithium-ion battery systems equivalent model (1); Using the terminal voltage of 2 RC parallel circuits in the state-of-charge SOC of tandem type lithium-ion battery systems and equivalent model as state variable, using the electric current of battery system and output voltage as system input quantity and output quantity, in conjunction with tandem type lithium-ion battery systems equivalent-circuit model, obtain tandem type lithium-ion battery systems state-space equation (2); Using the state variable of the terminal voltage of the battery system SOC in tandem type lithium-ion battery systems state-space equation (2), 2 RC parallel circuits as Unscented kalman filtering algorithm UKF; Using the input state space equation of tandem type lithium-ion battery systems state-space equation (2), output voltage state space equation as UKF algorithm nonlinear state equation and measure equation; The battery terminal voltage estimated value obtained by actual value and the UKF algorithm of voltage sensor measurement tandem type lithium-ion battery systems terminal voltage (4) upgrades gain matrix (5), last by UKF algorithm through loop iteration, thus obtain the estimated value of battery system SOC in real time.

Described tandem type lithium-ion battery systems equivalent-circuit model (1) is second order equivalent-circuit model, and model main circuit is by 2 RC parallel circuits, controlled voltage source U _s0and internal resistance of cell R (SOC) _sdeng composition.Set up the relation that the key of battery system equivalent-circuit model is accurately how to determine according to battery working characteristic battery system performance parameter and battery cell performance parameter.In the present invention, tandem type lithium-ion battery systems performance parameter and battery cell performance parameter relational expression are:

$\left\{\begin{array}{c}{U}_{s0}\left(t\right)=\underset{i=1}{\overset{n}{\Σ}}{U}_{i0}\left(t\right)\\ R_s\left(t\right)=\underset{i=1}{\overset{n}{\Σ}}{R}_i\left(t\right)\\ R_{ss}\left(t\right)=\underset{i=1}{\overset{n}{\Σ}}{R}_{is}\left(t\right)\\ \frac{1}{C_{ss}\left(t\right)}=\underset{i=1}{\overset{n}{\Σ}}\frac{1}{C_{is}\left(t\right)}\\ R_{s1}\left(t\right)=\underset{i=1}{\overset{n}{\Σ}}{R}_{i1}\left(t\right)\\ \frac{1}{C_{s1}\left(t\right)}=\underset{i=1}{\overset{n}{\Σ}}\frac{1}{C_{i1}\left(t\right)}\end{array}\right.$

In formula, R _ss, R _s1, C _ss, C _s1represent resistance and the electric capacity of 2 RC parallel circuits in battery system model respectively; Subscript i represents i-th battery cell; U _i0, R _irepresent the open-circuit voltage of battery cell, internal resistance respectively; R _is, R _i1, C _is, C _i1represent resistance and the electric capacity of 2 RC parallel circuits in battery cell model respectively; U _i0, R _i, R _is, R _i1, C _is, C _i1all relevant with SOC, SOC is defined as: wherein, SOC ₀for battery cell SOC initial value, be generally the constant of 0 ~ 1; Q _ut () is the unavailable capacity of battery cell, Q ₀for battery cell rated capacity.U _i0(SOC), R _is, R _i1and C _is, C _i1, R _icalculating respectively as follows: $U_{i0}\left(SOC\right)=a_0{e}^{-a_{1}SOC\left(t\right)}+a_2+a_{3}SOC\left(t\right)-a_4{\mathrm{SOC}}^2\left(t\right)+a_5{\mathrm{SOC}}^3\left(t\right),$ $R_{is}\left(t\right)=c_0{e}^{-c_{1}SOC\left(t\right)}+c_2,C_{is}\left(t\right)=d_0{e}^{-d_{1}SOC\left(t\right)}+d_2,R_{i1}\left(t\right)=e_0{e}^{-e_{1}SOC\left(i\right)}+e_2,$ $C_{i1}\left(t\right)=f_0{e}^{-f_{1}SOC\left(t\right)}+f_2,R_i\left(t\right)=b_0{e}^{-b_{1}SOC\left(t\right)}+b_2+b_{3}SOC\left(t\right)-b_4{\mathrm{SOC}}^2\left(t\right)+b_5{\mathrm{SOC}}^3\left(t\right),$ Wherein, a ₀~ a ₅, c ₀~ c ₂, d ₀~ d ₂, e ₀~ e ₂, f ₀~ f ₂, b ₀~ b ₅be model coefficient, can be obtained through matching by battery measurement data.

The foundation of described tandem type lithium-ion battery systems state-space equation (2) is as follows: a, with the state-of-charge SOC of battery system _sand in equivalent model the terminal voltage of 2 RC parallel circuits as state variable, with the electric current I of battery system _sfor system input quantity, setting up cell system space state equation according to equivalent-circuit model is

$\left[\begin{array}{c}SO{C}_{s,k+1}\\ U_{ss,k+1}\\ U_{s1,k+1}\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& \exp \left(-\mathrm{\Δ}t/{\mathrm{\τ}}_1\right)& 0\\ 0& 0& \exp \left(-\mathrm{\Δ}t/{\mathrm{\τ}}_2\right)\end{array}\right]\×\left[\begin{array}{c}SO{C}_{s,k}\\ U_{ss,k}\\ U_{s1,k}\end{array}\right]+\left[\begin{array}{c}\frac{-\mathrm{\η}\mathrm{\Δ}t}{Q_N}\\ R_{ss}\[1-\exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_1)\]\\ R_{s1}\[1-\exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_2)\]\end{array}\right]I_{s,k}+w_k$

In formula, U _ss, U _s1be 2 RC parallel circuit terminal voltages, R _ss, R _s1be the resistance of 2 RC parallel circuits, Q _nfor battery system specified electric quantity, τ ₁, τ ₂for time constant, w _kfor systematic perspective process noise, Δ t is the sampling period, k be greater than 1 natural number; B, according to Kirchhoff's second law, in conjunction with battery system equivalent-circuit model, can obtain battery system output voltage equation state-space equation is: $U_{s,k+1}\left(t\right)=U_{s0,k+1}\left(t\right)-R_{s,k+1}\left(t\right)I_{s,k+1}\left(t\right)-\[\begin{array}{ccc}0& 1& 1\end{array}\]\×\left[\begin{array}{c}SO{C}_{s,k+1}\\ U_{ss,k+1}\\ U_{s1,k+1}\end{array}\right],$ In formula, U _sfor battery system terminal voltage, R _sfor battery system internal resistance.

The key step of described Unscented kalman filtering algorithm UKF is: 1) init state variable x average E () and square error P ₀: ${\hat{x}}_0=E\left(x_0\right),{\hat{P}}_0=E\[(x_0-{\hat{x}}_0){(x_0-{\hat{x}}_0)}^T\];$ 2) sampled point x is obtained _iand respective weights ω: $\left\{\begin{array}{c}{x}_{0,k-1}={\hat{x}}_{k-1}\\ x_{i,k-1}={\hat{x}}_{k-1}+{\left(\sqrt{\left(n+\mathrm{\γ}\right)P_{i,k-1}}\right)}_i,i=1,2,\mathrm{...},n\\ x_{i+n,k-1}={\hat{x}}_{k-1}+{\left(\sqrt{\left(n+\mathrm{\γ}\right)P_{i,k-1}}\right)}_i,i=n+1,n+2,\mathrm{...},2n\end{array}\right.,$ $\left\{\begin{array}{c}{\mathrm{\ω}}_0^m=\mathrm{\λ}/(n+\mathrm{\λ})\\ {\mathrm{\ω}}_0^c=\mathrm{\λ}/(n+\mathrm{\λ})+(1+\mathrm{\β}-{\mathrm{\α}}^2)\\ {\mathrm{\ω}}_i^m={\mathrm{\ω}}_i^c=1/2(n+\mathrm{\λ}),i\≠0\end{array}\right.$ In formula, λ=α ²(n+h)-n; 3) time of state estimation and square error upgrades: the state estimation time is updated to $\left\{\begin{array}{c}{x}_{i,k/k-1}=f_{k-1}\left(x_{i,k-1}\right)+q_{k-1},i=0,1,...,2n\\ {\hat{x}}_{k/k-1}=\underset{i=0}{\overset{2n}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^m{f}_{k-1}\left(x_{i,k-1}\right)+q_{k-1}\end{array}\right.,$ The square error time is updated to $P_{k/k-1}=\underset{i=0}{\overset{2n}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^c(x_{i,k/k-1}-{\hat{x}}_{k/k-1}){(x_{i,k/k-1}-{\hat{x}}_{k/k-1})}^T+Q_{k-1},$ System output time is updated to $\left\{\begin{array}{c}{\mathrm{\χ}}_{i,k/k-1}=g_{k-1}\left(x_{i,k-1}\right)+r_{k-1}\\ {\hat{y}}_{k/k-1}=\underset{i=0}{\overset{2n}{\Σ}}{\mathrm{\ω}}_i^m{g}_{k-1}\left(x_{i,k-1}\right)+r_{k-1}\end{array}\right.$ In formula, g _k-1() is for measuring equation; 4) calculated gains matrix (5): in formula, $\left\{\begin{array}{c}{P}_{y,k}=\underset{i=0}{\overset{2n}{\Σ}}{\mathrm{\ω}}_i^c({\mathrm{\χ}}_{i,k/k-1}-{\hat{y}}_{k/k-1}){({\mathrm{\χ}}_{i,k/k-1}-{\hat{y}}_{k/k-1})}^T\\ P_{xy,k}=\underset{i=0}{\overset{2n}{\Σ}}{\mathrm{\ω}}_i^c(x_{i,k/k-1}-{\hat{x}}_{k/k-1}){({\mathrm{\χ}}_{i,k/k-1}-{\hat{y}}_{k/k-1})}^T\end{array}\right.;$ 5) measurement updaue of state estimation and square error: state estimation measurement updaue is square error measurement updaue is $P_k=P_{k/k-1}-L_k{P}_{y,k}{L}_k^T.$

Carry out compared with tandem type lithium-ion battery systems SOC estimates with employing expanded Kalman filtration algorithm EKF, the present invention has following useful technique effect: one is whole discharge process, it is higher that UKF algorithm of the present invention carries out UKF estimated accuracy when tandem type lithium-ion battery systems SOC estimates than EKF algorithm, especially discharge the initial stage and latter stage effect more obvious; Two be adopted UKF algorithm than EKF algorithm can more rapid convergence be in experimental data, robustness is better.

Accompanying drawing explanation

The state-of-charge method of estimation implementing procedure block diagram of Fig. 1 tandem type lithium-ion battery systems

Fig. 2 is tandem type lithium-ion battery systems structural representation;

Fig. 3 is the tandem type lithium-ion battery systems structural representation containing 6 battery cells;

Fig. 4 is the tandem type lithium-ion battery systems equivalent-circuit model figure containing 2 RC parallel circuits;

Fig. 5 is Unscented kalman filtering algorithm flow chart;

Fig. 6-1 ~ Fig. 6-4 is SOC ₀battery constant-current discharge characteristic time different, wherein Fig. 6-1 is SOC ₀sOC situation of change when=1, Fig. 6-2 is SOC ₀battery system terminal voltage situation of change when=1, Fig. 6-3 is SOC ₀sOC situation of change when=0.8, Fig. 6-4 is SOC ₀battery system terminal voltage situation of change when=0.8;

Fig. 7-1 ~ Fig. 7-4 is SOC ₀cell pulse discharge characteristic time different, wherein Fig. 7-1 is SOC ₀sOC situation of change when=1, Fig. 7-2 is SOC ₀battery system terminal voltage situation of change when=1, Fig. 7-3 is SOC ₀sOC situation of change when=0.8, Fig. 7-4 is SOC ₀battery system terminal voltage situation of change when=0.8.

Embodiment

Below in conjunction with concrete example, the present invention is described in further detail, and described is explanation of the invention instead of restriction.

The concrete implementing procedure block diagram of state-of-charge method of estimation of a kind of tandem type lithium-ion battery systems provided by the invention as shown in Figure 1.

1, tandem type lithium-ion battery systems and equivalent-circuit model (1) thereof

1.1 tandem type lithium-ion battery systems

Tandem type lithium-ion battery systems is in series by by N number of lithium-ion battery monomer, and its structural drawing as shown in Figure 2.For ease of analyzing, suppose tandem type lithium-ion battery systems in this example by 6 battery cells through being in series, i.e. 6 × 1 tandem type lithium-ion battery systems, as shown in Figure 3.In tandem type lithium-ion battery systems, the rated voltage of each battery cell is 3.2V, and rated capacity is 25Ah, and discharge cut-off voltage is 2.5V.

1.2 tandem type lithium-ion battery systems equivalent-circuit models (1)

Tandem type lithium-ion battery systems equivalent-circuit model (1) is second order equivalent-circuit model, and model main circuit is by 2 RC parallel circuits, controlled voltage source U _s0and internal resistance of cell R (SOC) _sdeng composition, as shown in Figure 4.Tandem type lithium-ion battery systems performance parameter, by obtaining with the relation of battery cell performance parameter, is specifically calculated as follows:

$\left\{\begin{array}{c}{U}_{s0}\left(t\right)=\underset{i=1}{\overset{6}{\Σ}}{U}_{i0}\left(t\right)\\ R_s\left(t\right)=\underset{i=1}{\overset{6}{\Σ}}{R}_i\left(t\right)\\ R_{ss}\left(t\right)=\underset{i=1}{\overset{6}{\Σ}}{R}_{is}\left(t\right)\\ \frac{1}{C_{ss}\left(t\right)}=\underset{i=1}{\overset{6}{\Σ}}\frac{1}{C_{is}\left(t\right)}\\ R_{s1}\left(t\right)=\underset{i=1}{\overset{6}{\Σ}}{R}_{i1}\left(t\right)\\ \frac{1}{C_{s1}\left(t\right)}=\underset{i=1}{\overset{6}{\Σ}}\frac{1}{C_{i1}\left(t\right)}\end{array}\right.$

In above formula, battery cell performance parameter U ₀(t), R _s(t), R ₁(t) and C _s(t), C ₁t the calculating of () is as follows respectively: $U_0\left(t\right)=a_0{e}^{-a_{1}SOC\left(t\right)}+a_2+a_{3}SOC\left(t\right)-a_4{\mathrm{SOC}}^2\left(t\right)+a_5{\mathrm{SOC}}^3\left(t\right),R_s\left(t\right)=c_0{e}^{-c_{1}SOC\left(t\right)}+c_2,$ $C_s\left(t\right)=d_0{e}^{-d_{1}SOC\left(t\right)}+d_2,R_1\left(t\right)=e_0{e}^{-e_{1}SOC\left(t\right)}+e_2,C_1\left(t\right)=f_0{e}^{-f_{1}SOC\left(t\right)}+f_2,$ $R\left(t\right)=b_0{e}^{-b_{1}SOC\left(t\right)}+b_2+b_{3}SOC\left(t\right)-b_4{\mathrm{SOC}}^2\left(t\right)+b_5{\mathrm{SOC}}^3\left(t\right),$ Wherein, a ₀~ a ₅value is respectively-0.602 ,-10.365,3.395,0.267 ,-0.202,0.105, c ₀~ c ₂value is respectively 0.1058 ,-59.96,0.0036, d ₀~ d ₂value is respectively-196 ,-142,295, e ₀~ e ₂value is respectively 0.00697 ,-60.8,0.0022, f ₀~ f ₂value is respectively-2996 ,-175,5122, b ₀~ b ₅value is respectively-0.0558 ,-29.96,0.0055,0.0062,0.0121,0.0066.

2, tandem type lithium-ion battery systems state-space equation (2)

A, with the state-of-charge SOC of tandem type lithium-ion battery systems _sand the terminal voltage U of 2 RC parallel circuits in equivalent model _ss, U _s1as state variable, with the electric current I of tandem type lithium-ion battery systems _sfor system input quantity, setting up tandem type lithium-ion battery systems input state space equation according to equivalent-circuit model (1) is

$\left[\begin{array}{c}SO{C}_{s,k+1}\\ U_{ss,k+1}\\ U_{s1,k+1}\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& \exp \left(-\mathrm{\Δ}t/{\mathrm{\τ}}_1\right)& 0\\ 0& 0& \exp \left(-\mathrm{\Δ}t/{\mathrm{\τ}}_2\right)\end{array}\right]\×\left[\begin{array}{c}SO{C}_{s,k}\\ U_{ss,k}\\ U_{s1,k}\end{array}\right]+\left[\begin{array}{c}\frac{-\mathrm{\η}\mathrm{\Δ}t}{Q_N}\\ R_{ss}\[1-\exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_1)\]\\ R_{s1}\[1-\exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_2)\]\end{array}\right]I_{s,k}+w_k$

In formula, U _ss, U _s1be 2 RC parallel circuit terminal voltages, R _ss, R _s1be the resistance of 2 RC parallel circuits, Q _nfor battery system specified electric quantity, τ ₁, τ ₂for time constant, w _kfor systematic perspective process noise, Δ t is the sampling period, k be greater than 1 natural number.

B, according to Kirchhoff's second law, in conjunction with tandem type lithium-ion battery systems equivalent-circuit model, can obtain tandem type lithium-ion battery systems output voltage equation is: $U_{s,k+1}\left(t\right)=U_{s0,k+1}\left(t\right)-R_{s,k+1}\left(t\right)I_{s,k+1}\left(t\right)-\[\begin{array}{ccc}0& 1& 1\end{array}\]\×\left[\begin{array}{c}SO{C}_{s,k+1}\\ U_{ss,k+1}\\ U_{s1,k+1}\end{array}\right],$ In formula, U _sfor battery system terminal voltage, R _sfor battery system internal resistance, k be greater than 1 natural number.

3, Unscented kalman filtering method (3)

Using the state variable x of the terminal voltage of the battery system SOC in tandem type lithium-ion battery systems state-space equation, 2 RC parallel circuits as Unscented kalman filtering algorithm UKF; Using the input state space equation of tandem type lithium-ion battery systems, output voltage state space equation as the nonlinear state Equation f of UKF algorithm _k-1() and measurement equation g _k-1(); The actual value y of battery system terminal voltage (4) is measured by voltage sensor _kthe battery terminal voltage estimated value obtained with UKF algorithm upgrade gain matrix (5), finally carry out loop iteration by UKF algorithm, as shown in Figure 5, in an iterative process, state variable x initial value is [100] to idiographic flow, and α value is 1, β value be 2, h value is 0; The last estimated value SOC obtaining tandem type lithium-ion battery systems SOC in real time _k.

4, system emulation result and Contrast on effect

L-G simulation test mainly comprises constant current and pulse two kinds of operating modes, and one is constant current operating mode, and namely battery is outwards powered with current constant mode (25A); Two is pulse operations, namely outwards supplies discharge of electricity with impulse current system, is specially: first with 25A constant current operation 600s, after leaving standstill 600s, then with 25A constant current operation 600s, so circulates.For verifying the high robust of UKF, in constant current and pulse two kinds of operating modes respectively with SOC ₀be 1,0.8 two kind of situation be analyzed.Fig. 6-1 ~ Fig. 6-4 is SOC ₀battery constant-current discharge characteristic time different, wherein Fig. 6-1 is SOC ₀sOC situation of change when=1, Fig. 6-2 is SOC ₀battery system terminal voltage situation of change when=1, Fig. 6-3 is SOC ₀sOC situation of change when=0.8, Fig. 6-4 is SOC ₀battery system terminal voltage situation of change when=0.8; From Fig. 6-1 and Fig. 6-2, in whole discharge process, EKF and UKF can predict the change of battery system SOC and terminal voltage thereof well, but UKF is higher in the precision of electric discharge latter stage (3000s), proves that UKF is more accurate than EKF under constant current operating mode.From Fig. 6-3 and Fig. 6-4, UKF electric discharge the initial stage (before 500s) and electric discharge latter stage (after 3000s) precision higher, and converge on experimental data at the electric discharge initial stage quickly than EKF, to demonstrate under constant current operating mode UKF than EKF precision and robust all good.

Fig. 7-1 ~ Fig. 7-4 is SOC ₀cell pulse discharge characteristic time different, wherein Fig. 7-1 is SOC ₀sOC situation of change when=1, Fig. 7-2 is SOC ₀battery system terminal voltage situation of change when=1, Fig. 7-3 is SOC ₀sOC situation of change when=0.8, Fig. 7-4 is SOC ₀battery system terminal voltage situation of change when=0.8.From Fig. 7-1 and Fig. 7-2, in whole discharge process, UKF is higher than EKF precision of prediction, especially at electric discharge latter stage (after 3000s).From Fig. 7-3 and Fig. 7-4, in whole discharge process, UKF and EKF all can follow experimental data change fast, but when the initial stage of electric discharge, because UKF is less than EKF calculated amount, its speed of convergence is faster, and discharging latter stage, because EKF itself ignores higher order term, UKF closer to experimental data, to demonstrate under pulse operation UKF higher and robustness is better than EKF estimated accuracy than EKF simulation result further.

Claims (5)

1. the present invention discloses a kind of tandem type lithium-ion battery systems and state-of-charge method of estimation thereof, and it is characterized in that described tandem type lithium-ion battery systems is in series by N number of lithium-ion battery monomer, wherein N is the natural number being greater than 1.

Said method comprising the steps of:

According to known lithium-ion battery monomer performance parameter, utilize the relation of parallel circuit operating characteristic and charge/discharge operation characteristic determination tandem type lithium-ion battery systems performance parameter and battery cell performance parameter, determine battery system output end voltage equation in conjunction with Kirchhoff's law KVC again, set up tandem type lithium-ion battery systems equivalent model (1).

Using the terminal voltage of 2 RC parallel circuits in the state-of-charge SOC of tandem type lithium-ion battery systems and equivalent model as state variable, using the electric current of battery system and output voltage as system input quantity and output quantity, in conjunction with tandem type lithium-ion battery systems equivalent-circuit model, obtain tandem type lithium-ion battery systems state-space equation (2).

Using the state variable of the terminal voltage of the battery system SOC in tandem type lithium-ion battery systems state-space equation (2), 2 RC parallel circuits as Unscented kalman filtering algorithm UKF; The input state space equation of tandem type lithium-ion battery systems state-space equation (2), output voltage state space equation respectively as UKF algorithm nonlinear state equation and measure equation; The battery terminal voltage estimated value obtained by actual value and the UKF algorithm of voltage sensor measurement tandem type lithium-ion battery systems terminal voltage (4) upgrades gain matrix (5), last by UKF algorithm through loop iteration, thus obtain the estimated value of tandem type lithium-ion battery systems SOC in real time.

2. a kind of tandem type lithium-ion battery systems according to claim 1 and state-of-charge method of estimation thereof, is characterized in that set up tandem type lithium-ion battery systems model (1) is the second order equivalent-circuit model containing 2 RC parallel circuits.

3. a kind of tandem type lithium-ion battery systems according to claim 1 and state-of-charge method of estimation thereof, is characterized in that described tandem type lithium-ion battery systems state-space equation (2) is as follows: system state space equation and system output equation are respectively $\left[\begin{array}{c}{\mathrm{SOC}}_{p,k+1}\\ U_{ps,k+1}\\ U_{pl,k+1}\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& \exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_1)& 0\\ 0& 0& \exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_2)\end{array}\right]\×\left[\begin{array}{c}{\mathrm{SOC}}_{p,k}\\ U_{ps,k}\\ U_{pl,k}\end{array}\right]+\left[\begin{array}{c}\frac{-\mathrm{\η}\mathrm{\Δ}t}{Q_N}\\ R_{ps}\[1-\exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_1)\]\\ R_{pl}\[1-\exp (-\mathrm{\Δ}t/{\mathrm{\τ}}_2)\]\end{array}\right]I_{p,k}+w_k$ , [U _{p, k}]=U _{p0, k}-R _{p, k}i _{p, k}-U _{ps, k}-U _{p1, k}+ v _k, SOC in formula _pfor tandem type lithium-ion battery systems state-of-charge, U _ps, U _p1be 2 RC parallel circuit terminal voltages, R _ps, R _p1be the resistance of 2 RC parallel circuits, τ ₁, τ ₂for time constant, v _k, w _kbe respectively systematic observation noise and process noise, Δ t is the sampling period, U _p, U _p0be respectively battery system terminal voltage and open terminal voltage, R _p, I _pbe respectively battery system internal resistance and electric current, Q _nfor battery system specified electric quantity, k be greater than 1 natural number.

4. a kind of tandem type lithium-ion battery systems according to claim 1 and state-of-charge method of estimation thereof, is characterized in that described Unscented kalman filtering UKF algorithm steps is as follows: 1) init state variable x average E () and square error P ₀; 2) sampled point x is obtained _iand respective weights ω; 3) time of state estimation and square error upgrades; 4) calculated gains matrix; 5) measurement updaue of state estimation and square error.

5. a kind of tandem type lithium-ion battery systems according to claim 1 and state-of-charge method of estimation thereof, it is characterized in that described state-of-charge method of estimation is not only applicable to tandem type lithium-ion battery systems, also can be applicable to other types battery, as plumbic acid, nickel-cadmium battery etc.