MULTI-OBJECTIVE SIMULTANEOUS CHARGING METHOD FOR LITHIUM-ION BATTERY PACKS

Abstract

Disclosed in the present invention is a multi-target simultaneous charging method for a lithium battery pack: converting energy loss and charging current into a lithium battery pack charging cost model with a charging weight coefficient, and using an interior point method for solving and processing to acquire a preset charging current sequence; on the basis of the preset charging current sequence, calculating the charging time required when charging the lithium battery pack, and adjusting the charging weight coefficient in the lithium battery pack charging cost model by means of an adaptive momentum gradient descent algorithm to obtain the charging weight coefficient with the shortest charging time; using the charging weight coefficient to optimize the lithium battery pack charging cost model to acquire a new preset charging current sequence; and using the new preset charging current sequence to implement charging, thereby implementing optimized multi-target simultaneous charging of the lithium battery pack.

Claims

1. A multi-target simultaneous charging method for a lithium battery pack, wherein considering constraints of a charging current when charging a lithium battery, a charging weight coefficient is added to convert an energy loss and the charging current into a lithium battery pack charging cost model having the charging weight coefficient, an interior point method is adopted for solution processing to obtain a preset charging current sequence; next, according to the preset charging current sequence, a charging time required for charging the lithium battery pack is calculated, and the charging weight coefficient in the lithium battery pack charging cost model is adjusted through an adaptive momentum gradient descent algorithm to obtain the charging weight coefficient within a shortest charging time, the charging weight coefficient is utilized to optimize the lithium battery pack charging cost model to acquire a new preset charging current sequence, the new preset charging current sequence is adopted to implement charging, thereby implementing optimized multi-target simultaneous charging of the lithium battery pack.

2. The multi-target simultaneous charging method for the lithium battery pack according to claim 1, wherein a process of the method is as follows: step 1: the lithium battery pack is composed of n independent single cells, according to basic dynamic characteristics of the lithium battery, an equivalent circuit model of the lithium battery pack is established, and model parameters are determined by using experimental data; step 2: a charging target comprising an estimated charging time and a preset charging SOC (state of charge) is set, the lithium battery pack charging cost model comprising the preset charging SOC, a battery temperature and a battery balance is established; step 3: a quadratic programming solution method is adopted to solve the lithium battery pack charging cost model to obtain a preset charging current u.sub.i,k of each of the single cells at each moment under the estimated charging time and the preset charging SOC, thereby forming an optimal charging current sequence, and the lithium battery pack is controlled with the optimal charging current sequence for charging; step 4: real-time detection of a SOC x.sub.j,k of each of the single cells in a real-time state of a charging process is performed under the control of step 3, a convergence time T.sub.1(ε.sub.1) and a charging time T.sub.2(ε.sub.2) are obtained according to the following formula, and a simultaneous charging time function is established as follows: $\underset{x}{\min }{f}_4\left(x\right)=\max \left\{T_1\left({\epsilon }_1\right),T_2\left({\epsilon }_2\right)\right\}{T}_1\left({\epsilon }_1\right)=\min \left\{\tau .Math.x_i\left(k\right)-x_i\left(k\right).Math.\le {\epsilon }_1,\forall k\ge \tau /T,\forall i,j\right\}{T}_2\left({\epsilon }_2\right)=\min \left\{\tau .Math.x\left(k\right)-{\chi }_d.Math.\le {\epsilon }_2,\forall k\ge \tau /T\right\}$ wherein, T.sub.1(ε.sub.1), T.sub.2(ε.sub.2) represent the convergence time and the charging time, respectively, x.sub.i(k) and x.sub.j(k) represent a value of the SOC of the i-th single cell of the lithium battery pack at a time k, ε.sub.1 and ε.sub.2 represent a cut-off error of a convergence process and a charging process, respectively, T represents a sampling time, τ represents a time variable, i and j represent ordinal numbers of the single cells in the lithium battery pack, and χ.sub.d represents a column vector of an expected value of the SOC of the single cell, which is a n×1 column vector composed of the expected value of the SOC of the single cell, the adaptive momentum gradient descent algorithm is adopted to process the simultaneous charging time function, optimize a first weight coefficient α and a second weight coefficient β in the lithium battery pack charging cost model, and return to step 2 for update, an updated expression of the first weight coefficient α and the second weight coefficient β is: $\mathrm{\Delta \alpha }\left(k\right)=-\omega \left(k\right)\left(1-\theta \right)\nabla T\left(k\right)+\mathrm{\theta \Delta \alpha }\left(k-1\right)\mathrm{\Delta \beta }\left(k\right)=-\omega \left(k\right)\left(1-\theta \right)\nabla T\left(k\right)+\mathrm{\theta \Delta \beta }\left(k-1\right)\omega \left(k+1\right)=\{\begin{array}{c}\mathrm{\lambda \omega }\left(k\right),\nabla T\left(k\right)\ge \mu \nabla T\left(k-1\right)\\ 1/\lambda \omega \left(k\right),\nabla T\left(k\right)\le 1/\mu \nabla T\left(k-1\right)\\ \omega \left(k\right),\mathrm{Other}\mathrm{conditions}\end{array}$ wherein Δα(k), Δα(k−1) represent increments of α at times k and k−1, respectively, Δβ(k), Δβ(k−1) represent increments of β at times k and k−1, respectively, ∇T(k), ∇T(k−1)represent increments of a simultaneous charging time T at the times k and k−1, respectively, wherein the simultaneous charging time T=max {T.sub.1(ε.sub.1), T.sub.2(ε.sub.2)}, θ represents a momentum factor, ω(k) represents an adaptive learning rate; and step 3 is repeated for processing, and an optimal charging current sequence obtained after update is adopted to control charging of the lithium battery pack.

3. The multi-target simultaneous charging method for the lithium battery pack according to claim 2, wherein in the step 1, a single cell equivalent circuit is established for each of the single cells of the lithium battery pack, and the single cell equivalent circuit comprises a capacitor Cb, a constant voltage source Vsoc, a voltage controlled voltage source Voc and an internal resistance R.sub.0, wherein the voltage-controlled voltage source Voc is an SOC equivalent circuit composed of the capacitor Cb and the constant voltage source Vsoc arranged in parallel, the SOC equivalent circuit is configured to simulate a SOC change of the single cell; the voltage-controlled voltage source Voc and the internal resistance R.sub.0 are connected in series to form a voltage equivalent circuit, and the voltage equivalent circuit is configured to simulate a voltage change of the single cell.

4. The multi-target simultaneous charging method for the lithium battery pack according claim 2, wherein in the step 1, the equivalent circuit model of the single cell of the lithium battery pack is expressed by the following formula: $V_{{\mathrm{SOC}}_i}\left(k+1\right)=V_{{\mathrm{SOC}}_i}\left(k\right)-\frac{\eta {\mathrm{TI}}_{B_i}\left(k\right)}{Q}{V}_{B_i}\left(k\right)=V_{{\mathrm{OC}}_i}\left(k\right)-R_0{I}_{B_i}\left(k\right)$ wherein V.sub.SOC.sub.i(k+1) and V.sub.SOC.sub.i(k) represent a value of the SOC of the i-th single cell of the lithium battery pack at times k+1 and k, respectively, η represents a charging efficiency, T represents the sampling time, and I.sub.B.sub.i(k) represents a charging current value of the i-th single cell at the time k, Q represents a capacity of the single cell of the lithium battery pack, R.sub.0 represents an internal resistance of the single cell of the lithium battery pack, V.sub.B.sub.i(k) and V.sub.OC.sub.i(k) represent an output terminal voltage and an open circuit voltage of the i-th single cell at the time k, respectively.

5. The multi-target simultaneous charging method for the lithium battery pack according to claim 2, wherein in the step 2, the following lithium battery pack charging cost model is established: $\underset{x}{\min }F\left(x\right)=f_1\left(x\right)+\alpha f_2\left(x\right)+\beta f_3\left(x\right)f_1\left(x\right)=\underset{k=1}{\overset{m}{.Math.}}\underset{j=1}{\overset{n}{.Math.}}\underset{i=1}{\overset{n}{.Math.}}{\left(x_{i,k}-x_{j,k}\right)}^2{f}_2\left(x\right)=\underset{k=1}{\overset{m}{.Math.}}\underset{i=0}{\overset{n-1}{.Math.}}{R_0\left(u_{i,k}-d_k\right)}^2{f}_3\left(x\right)=\underset{k=1}{\overset{m}{.Math.}}\underset{i=1}{\overset{n}{.Math.}}{\left(x_{i,k}-x_d\right)}^2$ wherein, F(x) represents a vector of the lithium battery pack charging cost model, f.sub.1(x) represents a sum of SOC deviations between the single cells; f.sub.2(x) represents the energy loss generated due to an internal resistance inside the lithium battery during the charging process, f.sub.3(x) represents a sum of deviations of the respective single cells charged to the same value, f.sub.4(x) represents the charging time; α represents the first weight coefficient, β represents the second weight coefficient, x.sub.i,k represents the SOC of the i-th single cell at the time k, x.sub.j,k represents the SOC of the j-th single cell at the time k, u.sub.i,k represents a charging current of the i-th single cell at the time k, d.sub.k represents a disturbance current at the time k, x.sub.d represents an expected value of the SOC of the single cell, i and j represent ordinal numbers of the single cell in the lithium battery pack, n is a total number of the single cells in the lithium battery pack, and m is the number of charging steps; the constraints in the charging process are established, comprising: (1) a SOC column vector SOC(k) of batteries connected in series in the lithium battery pack at the time k satisfies:
SOC(k)≤SOC.sub.u wherein SOC(k) and SOC.sub.u are both column vectors of a length n, and SOC.sub.u represents an upper limit value of the SOC of the lithium battery pack; (2) a charging current column vector I(k) of each of the single cells in the lithium battery pack at the time k satisfies:
I(k)≤I.sub.M wherein I(k) and I.sub.M are both the column vectors of the length n, and I.sub.M represents an upper limit value of the charging current of each of the single cells in the lithium battery pack; (3) a terminal voltage column vector U(k) of each of the single cells in the lithium battery pack at the time k satisfies:
U(k)≤U.sub.M wherein U(k) and U.sub.M are both the column vectors of the length n, and U.sub.M represents an upper limit value of a terminal voltage of each of the single cells of the lithium battery pack.

6. The multi-target simultaneous charging method for the lithium battery pack according to claim 2, wherein during the charging process of the method, a terminal voltage of each of the single cells in the lithium battery pack is detected in real time, if the terminal voltage of the single cell exceeds a preset maximum open circuit voltage of a battery, the preset charging current in the optimal charging current sequence obtained in step 3 is reduced.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0035] FIG. 1 is a schematic diagram of a simultaneous charging structure of lithium batteries in the present disclosure.

[0036] FIG. 2 is a graph showing a state of charge variation under a given weight coefficient in an embodiment of the present disclosure.

[0037] FIG. 3 is a graph showing the variation of an actual value of a charging current under a given weight coefficient in an embodiment of the present disclosure.

[0038] FIG. 4 is a graph showing a state of charge variation optimized by an adaptive momentum gradient descent algorithm in an embodiment of the present disclosure.

[0039] FIG. 5 is a graph showing the variation of an actual value of a charging current optimized by the adaptive momentum gradient descent algorithm in an embodiment of the present disclosure.

[0040] FIG. 6 is a graph showing the change curves of simultaneous charging time and two weight coefficients optimized by the adaptive momentum gradient descent algorithm in an embodiment of the present disclosure.

DESCRIPTION OF THE EMBODIMENTS

[0041] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0042] Embodiments implemented according to the method of the present disclosure are as follows:

[0043] The lithium battery pack for this experiment consists of four lithium batteries. The capacity and nominal voltage of the battery are 3100 mAh and 3.7V, respectively. The current operating range of the battery is [−1 A, 0], the sampling time is T=1 s, and the upper and lower limits of the SOC are set to 100% and 5%. The initial SOC of each battery in the battery pack is:

SOC.sub.1(0)=51%, SOC.sub.2(0)=60%, SOC.sub.3(0)=50%, SOC.sub.4(0)=62%.

[0044] In this embodiment, through the global optimization control setting, if the SOC difference between any two single cells is less than 0.1%, the battery charging process will stop.

[0045] 2. Experimental Results

[0046] In this embodiment, the preset charging current sequence is obtained by real-time calculation to charge the lithium battery pack. The abscissa represents the time (unit of measurement is seconds), the ordinate represents the SOC of the battery, and the four lines with marks respectively represent the real-time SOC of the four single cells, which are respectively denoted as battery 1 . . . battery 4.

[0047] FIG. 2 and FIG. 3 respectively show the change of SOC and the change of charging current of the lithium battery pack obtained through quadratic programming under the given first weight coefficient α and second weight coefficient β, and α=2, β=10.sup.−4. Under the circumstances, the charging time is close to 10000 seconds, the convergence time is 9562 seconds, and the relative error is close to 5%.

[0048] FIG. 4 and FIG. 5 show the changes in the SOC and charging current of the lithium battery pack after the adaptive momentum gradient descent algorithm is adopted to optimize the first weight coefficient α and the second weight coefficient β. The charging time and the convergence time are 5583s and 5533s, respectively. Therefore, during the charging process, the charging time and the convergence time are significantly shortened. In the meantime, the relative time error between the charging time and the convergence time is also minimized by less than 1%, so that it may be ensured that the lithium battery pack is fully charged simultaneously and the required time is the shortest. In this way, batch charging of lithium battery packs is realized, the charging current of lithium batteries is limited in the shortest charging time, so that protection for lithium batteries may be achieved.

[0049] FIG. 6 shows that under the optimization of the adaptive momentum gradient descent algorithm, the simultaneous charging time is significantly shortened, and also shows the corresponding change of the first weighting coefficient α and second weighting coefficient β. It can be seen from FIG. 6 that under the effect of the adaptive momentum gradient descent algorithm, the two weight coefficients are continuously updated to appropriate values to shorten the simultaneous charging time, and the adaptive adjustment term is added to the gradient descent algorithm to ensure the convergence speed of the algorithm. As shown in FIG. 6, the convergence process has been completed under the number of iterations not exceeding 20 steps.