The inconsistency of the battery cell will lead to the different capacity, internal resistance, voltage and electrolyte density of the monomer, and also lead to the battery pack being fully charged and discharged, and the overall capacity of the battery pack will be greatly reduced. In the normal use of the battery, due to the influence of the use environment, self-discharge and other factors, the inconsistency will be further expanded, so that the battery is in an unbalanced state. Therefore, balancing the power of each single cell in the battery pack is an important task to ensure the normal operation of the battery pack.
1 Active intelligent balancing scheme
1.1 Equilibrium scheme analysis
There are two types of equalization methods: active equalization and passive equalization. Passive equalization consumes excess energy of the battery cell through resistance to achieve the consistency of the monomer voltage, and the effect is better when only one battery cell has more power; However, in the case of less power in only one battery unit, it will cause all the remaining battery cells to be discharged, further expanding the inconsistency of power. In contrast, the active balancing method achieves battery energy balancing through energy transfer rather than energy consumption, and actively redistributes excess power, which is a more efficient balancing method. However, the existing technology is still difficult to transfer energy quickly and accurately, and there is an over-equilibrium phenomenon. Therefore, an active intelligent balancing scheme based on model prediction is designed, which can achieve the least number of energy transfers and the highest equilibrium efficiency.
1.2 Active intelligent equalization circuit
The principle of active equalization in this article is shown in Figure 1. Taking the need for discharge of cell 1 as an example, closing the switch G1P, cell 1 starts charging the DC/DC coil, and when the charging current reaches the maximum, the magnetic field energy stored in the inductor reaches the maximum; At this time, disconnect G1P, close G1S, the energy in the inductance is transferred to the coil on the side of the battery pack, charge the battery module (monomer 1~12) by switching G1S, when the charging current drops to 0, disconnect G1S, close G1P, monomer 1 charges DC/DC again, repeat the above process until the energy of monomer 1 returns to the average level.
Figure 1 Schematic diagram of active equalization principle
1.3 Active equalization current model predictive control
In this paper, the model predictive control (MPC) algorithm is used to control the equilibrium current, and the control variable that meets the constraints and the lowest cost is calculated by using the deviation value of the current output and target of the system, the deviation value of the past output and target of the system, and the deviation information of the future output and target of the system in a finite prediction time domain.
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The controlled object is represented by a state-space equation that takes the SOC of each cell as the state variable (); The spatial model takes the difference between () and the mean of all cell SOCs as the objective function (); By modeling the control object, the state-space equation (6) is obtained. As shown in Figure 1, assuming that the battery pack in the bidirectional DC/DC equalization system has a string of cells connected in series, there is a group of equalization channels, the capacity of battery 1~ can be expressed by a diagonal matrix, and the SOC of the battery is defined as (), then the amount of power flowing through each string of cells is
· ()∈
(1)
thereinto
()=[…]
The SOC=0 of the battery means that the battery energy is 0, and SOC=1 means that the battery is fully charged. If the SOC difference between the cells is large, energy transfer is required, and the charge is transferred between channels. If a diagonal matrix is used to represent the maximum equalization current from channel 1 to channel, and () is used to represent the normalized equalization current of each channel, then the actual equalization current can be expressed as
· ()∈
(2)
thereinto
(3)
If the total amount of electricity transferred is 1, each cell in the battery pack (including discharged batteries) gets 1/, so the discharged battery transfers 1/-1, and the other batteries are 1/. Similarly, the battery with the lowest voltage gets the power from the entire battery pack, and if the total amount transferred is 1, each cell in the battery pack (including the charged battery) loses 1/, so the charged battery transfers 1-1/, and the other batteries are -1/. The equalization charge is transferred between the cell cells, and the connection between the string cell and the bank channel can be represented by a matrix ∈×:
(4)
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(5)
By selecting battery capacity () as the state variable, control current () as the input control variable, and () as the system output, the state control equation for the equilibrium process can be expressed as
(6)
When MPC control of the balancing process, the cost function can be expressed as
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The system constraint is ()∈{∈|-1≤≤1}, that is, there is a limit to the equalization current per channel.
The standard equation for MATLAB linear programming is
Figure 2 MPC schematic diagram of active intelligent equalization
Linear programming is a mathematical calculation to find the decision method that minimizes the cost function under constraints. The linear programming problem can be expressed as
(7)
(8)
Represented in matrix form:
min=
(9)
(10)
where = (,,...,), = [...], =[12...] (=1,2,...,),=[...]。
The steps to solve linear programming problems with MATLAB are: by traversing the tried methods, find a feasible solution, and then determine whether it is the optimal solution, if not, continue to iterate until an optimal solution is found, or judged to be no solution.
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min=
(11)
s.t.≤,=,≤≤
(12)
The corresponding MATLAB linear programming function linprog() is as follows:
[,]=linprog(,,,,,,)
(13)
In equation (11) ~ (13), is the objective function coefficient, is the control variable, and is the inequality constraint coefficient, , is the equation constraint coefficient, is the upper and lower limits of the control variable, is the minimum value of the objective function under constraints, and is the value of the control variable when the objective function takes the minimum value under constraints.
where: T is the lower limit value of the logarithmic anomaly calculated (its negative value is the lower limit of the anomaly); X is the logarithmic mean (logarithmic mean after removing the extra high value); S is the logarithmic standard deviation.
min(||+||+…+||)
(14)
To convert this problem to a standard linear programming problem, let =(+|| 2,=(||-)2。 Then, =-,||=+, where > 0 and > 0 hold.
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Then the amount of electricity transferred per unit time Δ can be used =· () Δ is denoted by () >0 for charge, and () < 0 for discharge. The goal of equilibrium is to achieve a minimum difference between the SOC of each cell and the average value of all cell SOCs in the shortest possible time, i.e. () close to the target value of 0.
If remembered:
(15)
Then convert the above question into follows:
(16)
(17)
The constraint function can be further expressed as:
(18)
The solution can be optimized using MATLAB's linpro() function.
2 Equalization effect verification
A battery pack balancing test bench was built to evaluate the equalization control effect based on MPC by comparing the collected equalization current and SOC. The MPC control algorithm and the linear programming solver function written through the S function are used to generate C code through the MATLAB automatic code generation tool. As shown in Figure 3, a battery pack composed of 24 strings of lithium titanate batteries, each slave controller controls 12 strings of batteries, the master and slave controllers communicate through a daisy chain, the use of multi-channel Hall current sensor to measure the size of the equalization current, PC1 is used to debug the BMS main control board, the control slave controller 1 and 2 realize the battery equalization function, PC2 is used to record the collected current value.
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Figure 3 Active equalization test bench
Under the initial conditions, the SOC maximum and SOC minimum values differ by 52%, corresponding to a voltage difference of about 0.5 V for the battery. The equalization current collected by the NI data acquisition system is shown in Figure 4.
Figure 4 Equalization current comparison between MPC control and normal control
It can be seen from Figure 4 that the equalization method based on ordinary control rules does not decouple the entire equalization process, resulting in frequent changes in the direction of the equalization current, which adversely affects the life of the battery and increases the time consumed by equalization; During the whole equalization process, except for the equalization current of monomer 1, which did not change direction, the other five currents changed direction frequently. Based on the equalization method of MPC control rules, the overall analysis of the balancing process of the battery pack is carried out, and the mutual influence between the equalization cells is considered, and the decoupling of the equalization process is realized, and the equalization current of all batteries does not change direction. Each equalization current is controlled by a duty cycle over a control cycle, and the duty cycle is adjusted to 1 (monomer 6) when it is necessary to operate with maximum balancing capability. After comparison, it is found that under the same initial conditions, the equilibrium time of ordinary control is 1 030 s. The equalization time of MPC control is 710 s, which is a 31% reduction in equalization time.
3 Concluding remarks
In this paper, an active equalization control scheme based on model prediction is designed, MPC algorithm is used to control battery pack equalization, and linear programming is used to solve the minimum equilibrium time to achieve the optimal control of series equilibrium. Experiments show that the MPC algorithm can avoid unnecessary energy transfer and reduce the equilibrium time by 31%, which verifies the rationality of the equilibrium strategy proposed in this paper.