Power battery voltage simulation method based on successive nearest neighbor interpolation

Author profile: Zhang Jin (1994-), male, from Taiyuan, Shanxi, master student at Hunan University of Technology, main research direction is power battery simulation. E-mail: 1498641264@qq.com.

0 Preface

As the pressure of energy crisis and environmental pollution increases, new energy vehicles, especially pure electric vehicles, have become a solution supported by government policies and vigorously developed by various automobile manufacturers[1]. The governments of the United Kingdom, Germany and other countries have announced that they will completely ban the sale of traditional fuel vehicles between 2025 and 2040. At the China Automotive Industry Development International Forum held in September 2017, the relevant person in charge of the Ministry of Industry and Information Technology stated that my country has also launched a plan to withdraw traditional fuel vehicles.

The test platform uses a power battery simulation power supply to overcome the high cost and inconvenience of directly using power batteries , and solves the problem that ordinary voltage-stabilized power supplies cannot simulate power battery characteristics. Therefore, the power battery simulation power supply is an indispensable equipment for electric vehicle test platforms. The battery model is the key factor for the simulation power supply to achieve high-fidelity battery volt-ampere characteristics, which directly affects the effect of the power supply simulating the battery. The main task of establishing a battery model is to give the reference voltage of the output port of the simulation power supply according to the battery SOC  and load current. The existing simulation power battery model establishment methods mainly include: ① using the existing standard battery model to obtain battery characteristic parameters; ② using segmented fitting of the battery volt-ampere characteristic curve [4]; ③ table lookup method. Among them, method ① uses the battery model to obtain the characteristic curve with high accuracy, but the model contains exponential functions, which is difficult to implement in the chip, requires a lot of calculations and has high requirements for the chip, and is not suitable for dynamic systems. Although method ② reduces the amount of calculation, the error is also significantly increased. If a high-order equation is used, the accuracy can be improved. However, under the condition of large-scale changes in the working current, multiple curves need to be fitted, which has a large amount of calculation and a long algorithm time, and cannot keep up with the real-time dynamic response of the system. Method ③ requires obtaining the VI characteristic curve first, and then obtaining the required data by discretizing the curve, which requires less calculation [2].

In order to obtain sufficient simulation accuracy, the table lookup method often requires the use of large data samples, but this will place high demands on the system capacity. In order to reduce the data capacity, the table lookup method generally uses an interpolation algorithm, while traditional methods such as the nearest neighbor interpolation algorithm and the bilinear interpolation algorithm are either not accurate enough or the algorithm calculation is large, making system implementation difficult. In order to reduce the data samples and the amount of calculation while meeting the output accuracy requirements, this paper proposes a method for giving the output voltage of a power battery simulation system based on the successive nearest neighbor difference algorithm by improving the nearest neighbor difference algorithm, and proves the effectiveness of this method through simulation experiments.

1 Background

1.1 Power battery simulation system

A typical power battery simulation system includes a bidirectional PWM rectifier and a bidirectional DC/DC converter [3], as shown in Figure 1.

1.2 Common interpolation methods

The battery model table is similar to the pixel grayscale table in digital image processing. Therefore, the battery model table lookup can refer to the interpolation algorithm in image processing. Common interpolation algorithms include the nearest neighbor interpolation algorithm and the bilinear interpolation algorithm. The nearest neighbor interpolation algorithm [4] maps the actual coordinate value to the coordinate in the model table based on the principle of shortest distance, and uses the voltage value of the coordinate in the model table as the voltage output by the battery. As shown in Figure 2, point U is the output voltage to be obtained during operation, and U1(1), U2(1), U3(1), and U4(1) are the voltage values ​​corresponding to the four coordinates of point U in the model table. Since the coordinate position of U1(1) is the shortest distance from point U, the value of U1(1) is assigned to point U as the output voltage value of the simulated battery.

2 Successive nearest neighbor interpolation algorithm

2.1 System workflow

Figure 3 is a flow chart of the voltage setting method of the power battery simulation system in this paper. It can be seen from the figure that the system includes  three parts: SOC estimation, power battery model table and interpolation algorithm. Among them, SOC  estimation is based on the initial value SOC* and the collected load current i, and the ampere-hour method is used to estimate the SOC value of the power battery.

Considering that the output voltage of the power battery changes rapidly when the SOC is large or small, the power battery model table is divided into three sub-tables, namely: when SOC ≥ 85%, it is called model sub-table 1; when 85%>SOC ≥ 20%, it is called model sub-table 2; when SOC<20%, it is called model sub-table 3. Because the VI characteristic curve of the power battery fluctuates greatly in the SOC value range of 5%~20% and 85%~100%, which makes the voltage value between two adjacent coordinates after discretization differ greatly; while the VI characteristic curve in the 20%~85% range does not change much. Therefore, sub-table 1 and sub-table 3 use the model table with a smaller SOC resolution dSOC, while sub-table 2 uses the model table with a larger SOC resolution dSOC. At the same time, the change of current has little effect on voltage, so the resolution di of the load current i in the three model tables is the same.

As can be seen from Figure 3, after selecting the corresponding power battery model sub-table according to different SOCs, the estimated SOC and the collected current i can be used to determine the four adjacent voltage values ​​of the output voltage to be determined in the model sub-table. The successive nearest neighbor interpolation algorithm proposed in this paper is used to iteratively calculate these four voltage values, continuously update the coordinates and corresponding voltage values, and finally output the given voltage value U*.

2.2 Principle of Successive Nearest Neighbor Interpolation Algorithm

As can be seen from the previous section, the successive nearest neighbor interpolation algorithm searches the power battery model subtable according to the estimated SOC and the sampled load current i, and then obtains four adjacent voltage values ​​U1~U4, namely points U1(1), U2(1), U3(1), and U4(1). These four points are regarded as a square, and the successive nearest neighbor interpolation algorithm is implemented according to the following steps.

1) Divide the square into four small squares or four zones according to the partition criteria in Table 1, and set m=1.

2) Take Ux(m) (x is one of 1 to 4) which is in the same region as the point U to be solved as an invariant point.

3) Use Table 2 to update the four vertices U1(m+1), U2(m+1), U3(m+1), and U4(m+1) in the region where the point U is located.

4) Update the partition basis using equations (6) to (10).

5) Let m=m+1. If m

The update formulas (1) to (5) in Table 2 are:

Formulas (1) to (5) describe the voltage update methods for the left, right, top, bottom, and diagonal points of the invariant point, respectively.

After each iteration, the coordinates SOC and i need to be updated according to the partition. The update formulas for zones 1 to 4 are formulas (6) to (9) respectively.

The update method of SOC and i resolution is based on formula (10):

When m=M, the output voltage given value U* of the power battery simulation system, i.e. the mean value of Ux(m), is calculated using formula (5).

3 Experiments and analysis

3.1 Determination of model table capacity

The table lookup method often requires large data samples, but this places high demands on system capacity. While ensuring the output voltage accuracy, minimizing the data capacity of the model table can reduce table lookup time and lower system costs.

3.2 Comparison with Nearest Neighbor Interpolation

The standard power battery model in MATLAB & Simulink is used to generate the benchmark table data, and the bilinear interpolation algorithm is used to look up the benchmark table to obtain the benchmark value. The D2 extraction table and the benchmark table are used as data samples, and the nearest neighbor difference algorithm and the method in this paper are used to calculate the given voltage of the battery simulation system, and the absolute value of the absolute error between the given voltage and the benchmark value obtained by the two methods is analyzed. Experiments are carried out with fixed SOC (random values ​​of 5% ≤ SOC ≤ 100%) and different currents (100 values ​​randomly generated from -100 A ≤ i ≤ 100 A). The absolute value of the absolute error between the given voltage and the benchmark voltage obtained by the two methods is shown in Figure 5.

As can be seen from Figure 5a, under the condition of SOC of 13.7%, the absolute error of the reference table lookup of the proposed method is less than 0.000 4, while the absolute error of the nearest neighbor method under the same conditions is within 1.2. For the D2 extraction table, the absolute error of the proposed method is less than 0.03, while the absolute error of the nearest neighbor method is within 1.7. Therefore, under the same table lookup conditions, the proposed method has higher accuracy. At the same time, the result shows that because the SOC value of 13.7% is in the interval where the power battery characteristic curve changes greatly, the voltage values ​​between the two adjacent coordinates after discrete extraction differ greatly, which causes the table lookup error of the nearest neighbor method to increase. The proposed method corrects the error caused by the reduction of the data table resolution through successive approximation.