1 Introduction

At the same time, electric vehicles are driven in ambient temperature changes, power demand changes in a wide range and high frequency of operating conditions, which brings greater difficulties for power battery model construction, parameter estimation and testing. The working condition method is the first experimental method to evaluate the emission status and economy of traditional vehicles [1], and distinguish the test of light vehicles and heavy vehicles. GB/T 38146.1-2019 China Vehicle Driving Conditions Part 1: Light Duty Vehicles [2] and GB/T 38146.2-2019 China Vehicle Driving Conditions Part 2: Heavy Duty Commercial Vehicles [3] provide the latest standards to suit the driving conditions of domestic vehicles.

GB/T 31467.2-2015 Lithium-ion Power Battery Packs and Systems for Electric Vehicles Part 2 Test Procedure for High Energy Applications [4] provides for the simulation of working conditions discharge and charging constant charge/discharge test methods for power batteries. The test method is to test the power battery cells for cyclic constant current conditions.

However, in the course of road driving, electric vehicles are affected by the environment and work under the transition of starting, accelerating, braking, maintaining relatively constant speed and idling conditions. The battery modules and cells in the power battery system are regulated by electrical excitation and battery balancing management, and work under cyclic transformations of randomly varying currents for discharge and energy recovery [5]. The model construction and evaluation of key parameters of the power battery under dynamic operating conditions requires the use of simulated operating conditions for relevant tests [6, 7].

Depending on the road conditions and driver habits of each country [8], different driving conditions are constructed, and the variability of the discharge and energy recovery characteristics of the battery cells, modules and systems are also different after transformation by the EV simulation software [9, 10].

2 Battery Simulation Data Selection and Segmentation

2.1 Battery Simulation Data Selection

The power battery simulated working condition discharge and energy recovery power-time schedule mainly consists of two types: (1) vehicle simulation software, input vehicle driving working condition speed-time schedule, output battery system power-time schedule, such as New Europe Driving Cycle (NEDC), The Federal Urban Driving (FUDS) (2) cycle-shifted multiplier discharge and charging processes at various operating currents, such as Dynamic Stress Test (DST), Beijing Dynamic Stress Test (BJDST). In this paper, we use the working condition test data at different temperatures from the University of Maryland battery test dataset.

Figure 36.1 shows the speed-time diagram for the driving conditions of the electric vehicle and Fig. 36.2 shows the power-time diagram for the power cell under simulated driving conditions of the electric vehicle.

Fig. 36.1
figure 1

Electric vehicle driving conditions US06 speed-time diagram

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Fig. 36.2
figure 2

Power battery unit power-time diagram under EV driving simulation

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2.2 Segmentation

In this paper, we first segment multiple sets of vehicle driving condition speed-time-table data (US06, NEDC, Highway, FTP75), and also segment battery power-time under simulated dynamic conditions (FUDS, US06, DST, BJDST) of the power battery. The condition segmentation transforms the condition engineering into a process of inter-transfer between states and analyses the effect of the frequency of state changes on the battery simulation condition testing. In this regard, the length of time and division of the velocity–time data time segments are given by the following equations.

$$T = t_{end} - t_{start}$$
(36.1)

where T is the single state time length, tstart is the start time of that state and tend is the end time of that state.

2.3 Feature Parameter Construction

The characteristic parameters of the analysed segments were constructed, and the segmented segments were statistically and analytically divided. Table 36.1 shows the selected driving conditions’ feature parameters, which are mainly divided into the total time share of the fragment, the fragment speed and state transition frequency acceleration amount and the state transition frequency feature parameters.

Table 36.1 Calculation of battery discharge and energy recovery operating conditions
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Where the total segment time share includes uniform speed Travel time T1, Acceleration travel time T2, Braking time T3, Idling time T4 and start time T5. Slice speed versus Amount of acceleration includes average speed Vaverage, Maximum velocity Vmax, maximum acceleration amax and maximum deceleration abreak. State transitions Frequency includes Start to accelerate, acceleration to constant speed, uniform to braking, acceleration to braking, brake to idle, braking to standstill. Frequency to time ratio of state transitions includes Start to accelerate f1, Acceleration to constant speed f2, Uniform to braking f3, Acceleration to braking f4, Brake to idle f5, Braking to standstill f6, Frequency to time ratio of state transitions r.

The total time share of selected simulated electric vehicle driving condition segments and state transition frequencies are calculated by (36.2) and (36.3) as follows.

$$f_i = \frac{n_i }{{\sum_{j = 1}^6 {n_j } }}(i = 1,2,...,6)$$
(36.2)
$$T_i = \frac{{\sum_{k = 1}^m {T_{k,i} } }}{{\sum_{j = 1}^5 {\sum_{k = 1}^m {T_{k,j} } } }}(i = 1,2,...,n)$$
(36.3)

where fi is the frequency of state transitions in the driving condition of the electric vehicle, ni is the number of 6 state shifts in the driving condition process; Ti is the total time share of the electric vehicle driving condition state fragment; Tk,j indicates the time length of the single state of the kth time slice in state j; m indicates the number of times state j appears. The selected simulated electric vehicle driving condition fragment speed and acceleration quantity calculation formula (36.4) is as follows.

$$V_{average} = \frac{1}{{m_{{\text{total}}} }}\sum_{i = 1}^{m_{{\text{total}}} }\left( {\frac{1}{T_i }\int\limits_{t_{i,start} }^{t_{i,end} } {V_i (t)} dt} \right)$$
(36.4)

where Vaverage is the total average speed of the segments of the electric vehicle driving condition; mtotal is the total number of time segments; Ti is the time length of a single state of segment i in the condition; tstart is the start time of the segment state and tend is the end time of the segment state; Vi is the amount of time variation within the segment.

$$r = \frac{{m_{total} }}{{T_{total} }} \times 100\%$$
(36.5)

where r is the state transition frequency as a percentage of total time; mtotal is the total number of time segments; Ttotal is the total length of the driving condition time state end time; Vi is the amount of time change within the segment.

The power battery power state change in the process of simulated power battery discharge and energy recovery is divided and the characteristic quantity is extracted, and the power battery discharge and energy recovery conditions are mainly divided into continuous discharge segment, continuous energy recovery segment and stationary segment.

Where the total segment time share includes Uniform discharge time t1, Accelerated, Discharge time t2, energy recovery time t3 and resting time t4. Slice power variables include Average output power Paverage, Maximum output Power Pmax, Maximum power climb rate Pcmax and Maximum power drop rate Pdmax. State transitions Frequency includes Standstill to acceleration F1, Acceleration to energy recovery F2, Uniform discharge to energy recovery F3, Accelerated discharge to standstill F4, Frequency to time ratio of state transitions R.

The total time share of the selected simulated power cell discharge and energy recovery segments and the state transition frequency are calculated in (36.5) and (36.6) as follows.

$$F_i = \frac{N_i }{{\sum_{j = 1}^3 {N_j } }}(i = 1,2,3)$$
(36.6)
$$t_i = \frac{{\sum_{k = 1}^m {t_{k,i} } }}{{\sum_{j = 1}^5 {\sum_{k = 1}^m {t_{k,j} } } }}(i = 1,2,...,n)$$
(36.7)

where Fi is the power battery state transition frequency, Ni is the power battery working condition power 5 state transfer times; ti is the power battery working condition power state fragment total time share; tk,j indicates the state j in the kth time piece to maintain a state time length; m indicates the state j appear times. The average output power Paverage in the simulated power condition of the power cell is calculated as follows.

$$P_{average} = \frac{1}{{m_{{\text{total}}} }}\sum_{i = 1}^{m_{{\text{total}}} }\left( {\frac{1}{T_i }\int\limits_{t_{i,start} }^{t_{i,end} } {P_i (t)} dt} \right)$$
(36.8)

3 Principal Component Analysis and Battery Equivalent Circuit Model Construction

Let there be K working conditions, each with p characteristic parameters, denoted as X = (x1, x2, …, xp). Let the mean value of the random variable X be μ and the covariance matrix ∑. After normalising the data in the working conditions by (x1 − μ)/σ and normalising X, the covariance matrix ∑ of x is equal to its correlation coefficient matrix. The principal component is the problem of linearly combining p characteristic parameters. A linear transformation of X generates a new composite indicator, the principal component, denoted y1, y2, …, yp. The covariance matrix is used to find the eigenvalues λ1, λ2,…, λp (λ1 ≥ λ2 ≥ … ≥ λp) and the corresponding eigenvectors A as in (36.9).

$$A = \left[ {\begin{array}{*{20}c} {a_{1,1} } & {a_{1,2} } & {...} & {a_{1,p} } \\ {a_{2,1} } & {a_{2,2} } & {...} & {a_{2,p} } \\ {...} & {...} & {...} & {...} \\ {a_{p,1} } & {a_{p,1} } & {...} & {a_{p,p} } \\ \end{array} } \right]$$
(36.9)

Then each principal component of the characteristic parameters x1, x2,…, xp after the orthogonal transformation can be expressed as (36.10)

$$\left\{ \begin{gathered} y_1 = a_{1,1} x_1 + a_{1,2} x_2 + ... + a_{1,p} x_p \hfill \\ y_2 = a_{2,1} x_1 + a_{2,2} x_2 + ... + a_{2,p} x_p \hfill \\ ... \hfill \\ y_p = a_{p,1} x_1 + a_{p,2} x_2 + ... + a_{p,p} x_p \hfill \\ \end{gathered} \right.$$
(36.10)

where y1, y2, …, yp are called the principal components, respectively.

An equivalent circuit model is constructed [11], with the equivalent power cell unit as a second-order equivalent circuit. Figure 36.3 shows the power cell Thevenin second-order equivalent circuit model. R0 is the internal resistance of the power cell; Et is the open-circuit voltage potential; R1 is the electrochemical polarisation internal resistance, R2 is the concentration polarisation internal resistance; C1 is the electrochemical polarisation capacitance, C2 is the concentration polarisation capacitance; Ud is the measurable terminal voltage; U1, U2 are the battery polarisation internal resistance voltages and i(t) is the real-time battery operating current.

Fig. 36.3
figure 3

Thevenin equivalent circuit model of the power cell

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The power cell unit model is built by Simulink. Figure 36.4 shows a schematic diagram of the Simulink equivalent circuit model of the power cell unit.

Fig. 36.4
figure 4

Simulink equivalent circuit model of power battery unit

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The HPPC test is carried out on the power cell, and the OCV-SOC curve and R0, R1, R2, C1 and C2 equivalent circuit model parameters of the battery cell are identified by the HPPC condition. Finally, the current in various battery discharging and energy recovery conditions is used as model input to observe the error between the simulated voltage output and the actual observed voltage in the power cell simulation model, and the characteristic quantities with high contribution to the battery are compared with the error values.

4 Discussion

Multiple sets of vehicle speed-timeline data (US06, NEDC, Highway, FTP75) were segmented and the results of the selected driving condition segmentation feature parameters were calculated. Table 36.1 shows calculation of battery discharge and energy recovery operating conditions. Table 36.2 shows variation of response error of the simulated cell model under different operating conditions. Table 36.3 shows battery discharging and energy recovery working condition principal component score table.

Table 36.2 Variation of response error of the simulated cell model under different operating conditions
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Table 36.3 Battery discharging and energy recovery working condition principal component score table
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The analysis of the battery discharge and energy recovery working condition principal component score table, with the battery simulation model under this discharge and energy recovery working condition, shows that the prediction error of the power battery model is positively correlated with the high contribution of the characteristic parameters in the principal component analysis of the battery discharge and energy recovery working condition that it is subjected to.

5 Conclusion

In this paper, we select and segment the data of various types of electric vehicle driving conditions and the simulated working condition data used to simulate the power battery, extract the relevant characteristic parameters in the working condition data, and analyse the simulated working condition data of the power battery and the electric vehicle driving condition data by using the principal component analysis method. The typical working conditions of the simulated power battery working condition data and the electric vehicle driving working condition US06 are selected to analyse and compare the principal components of the two types of working conditions and to analyse the influence of the working conditions on the construction of the power battery model.