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Optimization-based method to develop practical driving cycle for application in electric vehicle power management: A case study in Shenyang, China Zeyu Chen*, Qing Zhang, Jiahuan Lu**, Jiangman Bi School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 March 2019 Received in revised form 14 July 2019 Accepted 15 July 2019 Available online 26 July 2019

In this study, a novel method for the construction of a driving cycle based on a two-layer optimization process is proposed with a case study in Shenyang, China. First, the statistical data is obtained and divided into many micro-trips, namely the speed proﬁles between two successive stops; then, three representative parameters are derived from the vehicular model. Second, the development of the driving cycle is transferred to an optimization problem, and a two-layer optimization method is proposed to construct the typical driving cycle. In the ﬁrst layer, the optimal combination of micro-trips is determined using a genetic algorithm (GA) with varying quantity of micro-trips, whereas in the second layer, the best quantity of micro-trips is determined according to the speedeacceleration probability distribution (SAPD) and average energy consumption (AEC). The results indicate that the proposed method can produce a more representative driving cycle, 2.49% closer to the statistical data than the traditional Markov chain method. Finally, the established driving cycle is applied to power management design with three different vehicle types. The results indicate that the established driving cycle can help in reducing the energy cost by up to 19.8% under the real-world Shenyang driving condition. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Electric vehicle Plug-in hybrid electric vehicle Driving cycle construction Optimal power management Genetic algorithm

1. Introduction Vehicle emission is one of the major contributors to environmental pollution, and it has caused widespread concern [1]. Using electricity as the vehicle power source can reduce global CO2 emissions and offers the possibility to substitute oil in the transportation sector [2]. Therefore, electric vehicles (EVs) have been widely considered a promising solution to environmental pollution and energy crisis [3e5]. A power management system is critical for the development of EVs [6] because it directly impacts the energy saving ability and the reliability of the vehicle [7e11]. Power management aims to obtain an optimal control policy of the vehicle power system. The employed driving cycle is essential for the optimization and evaluation of power management in EVs. The construction of accurate and representative driving conditions is crucial for establishing effective power management strategies.

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Z. Chen), [email protected] edu.cn (J. Lu). https://doi.org/10.1016/j.energy.2019.07.096 0360-5442/© 2019 Elsevier Ltd. All rights reserved.

Unlike the internal combustion engine (ICE)-based vehicle, EVs are more likely to operate in a certain city or along a certain route; hence, the power management design strongly relies on the employed driving cycle. However, real-world urban trafﬁc conditions have conspicuous complexity and randomness; thus, the development of a typical driving cycle from a large quantity of test data statistics remains a technique challenge. To resolve this issue, we present an optimization-based method to establish a representative driving cycle for EV power management applications. The proposed method is implemented with a case study in Shenyang but the method is also suitable for any other city.

1.1. Review of the literature Several driving cycles have been constructed in the past to provide the speed proﬁles of real-world driving conditions [12e16]. Some driving cycles, known as legislative driving cycles, are developed by governments for imposing exhaust emission certiﬁcations; these driving cycles include the FTP-75 in the United States [17], NEDC in the European Union, and Japan-15 in Japan. Other driving cycles [18e20] such as the Hong Kong and Toronto driving

2

Z. Chen et al. / Energy 186 (2019) 115766

Nomenclature

UDDS Pv CD

Symbols Abbreviations EVs electric vehicles SAPD speedeacceleration probability distribution AEC average energy consumption PMS power management strategy NEDC new European driving cycle ECE European Commission of Europe driving cycle EUDC extra urban driving cycle CNY Chinese Yuan FTP-75 Federal Test Procedure ICE internal combustion engine GPS global positioning system SUDC Shenyang urban driving cycle GA genetic algorithm RMSE root mean square error PHEV plug-in hybrid electric vehicle SoC state of Charge CD-E charge depleting electric CD-H charge depleting hybrid CS charge sustaining ADVISOR advanced vehicle simulator AMT automatic mechanical transmission APU auxiliary power unit RE relative error ED experiment data PSO particle swarm optimization

d h

cycles are not developed by governments. Most of the existing driving cycles are developed based on two categories of methods. In the ﬁrst method, acceleration, idle speed, deceleration, and various cruising driving modes are combined to constitute a typical driving cycle [21]. In the second method, the driving cycle is derived from a large quantity of real-world statistical data [22]. In recent publications, the latter method has been widely adopted for driving cycle development because it can provide more accurate information [23,24]; it can be further classiﬁed into the following four categories:

m

tcoas tidli tbrak Dv Da pt,ij pij Dorig Preq g A PL* PH* Pe Pb JE

l

ε1 v C q*

urban dynamometer driving schedule instantaneous power of the vehicle aerodynamic drag factor conversion coefﬁcient of rotating mass transmission efﬁciency vehicle mass time sets of coasting time sets of idling time set of brake segmental interval of velocity segmental interval of acceleration ijth probability of the total statistic data ijth probability of the candidate driving cycle the entire dataset required power gravity frontal area low value of high efﬁciency range of engine high threshold of high efﬁciency range of engine power of engine power of battery cost function energy consumption rate threshold value of SoC quantity of micro-trips constant value characteristic parameter of the real-world statistical data

The clustering method is based on a distance metric for evaluating sample similarities. The micro-trips that are closer to the cluster centers are chosen as representative micro-trips. The clustering method includes the K-means, hierarchical clustering, and fuzzy clustering. Liu [30] investigated the driving cycle of longdistance passenger vehicles based on the clustering algorithm. The clustering algorithm requires less computation than the random method [31,32]; however, the way to determine the best cluster number remains a difﬁcult problem. (3) Statistical-analysis-based method.

(1) Random-selection-based method. The random-selection-based method for cycle synthesis randomly selects micro-trips from the experimental data for developing a representative driving cycle. This method is widely used because of its simplicity. Tsai [25] proposed the motorcycle driving cycle by comparing the emission factor with the European Commission of Europe driving cycle (ECE) to test the validity of the result. Hung [26] proposed the Hong Kong driving cycle utilizing the performance value and speedeacceleration probability distribution (SAPD) to determine the best synthesized driving cycle. Tong [27] proposed the Vietnam driving cycle using a random process based on the statistics of emission tests. Ho [28] proposed the Singapore driving cycle to estimate the energy cost and car emissions. Seer [29] proposed two driving cycles for utility vehicles using a random method. The random selection-based method is easy to implement but the calculation is time-consuming, and the result is not optimal. (2) Clustering method.

To obtain the driving cycle from a large dataset, some analytic methods have also been used. The statistical analysis method can build up the driving cycle correctly, but the mathematical modelling and the theoretical deduction are complicated; hence, only a few studies have adopted this approach. For example, Jing [33] implemented the linear discriminant analysis to build the Tianjin driving cycle and Yu [34] constructed the Changchun driving cycle based on the statistical inference theory. (4) Markov chain method. In this method, we construct the driving cycle by forecasting the future changes of random variables based on their current changes. The Markov method has attracted considerable attention recently [35e39]. Jiang [35] constructed the driving cycle of urban vehicles using the Markov process, Liu [36] synthesized the candidate driving cycle using the Markov chain based on the transition probability matrix, and Silvas [38] proposed an approach based on multidimensional Markov chains to construct a driving cycle considering road slope information. The Markov chain method can

Z. Chen et al. / Energy 186 (2019) 115766

3

reﬂect the variation in velocity but it requires a large amount of data, and the results lack consistency among multiple operations. Qingnian Street

1.2. Motivation and innovation A normative method for developing the driving cycle, especially for EVs, has not been developed yet. Although the aforementioned studies have made considerable contributions to the construction of driving cycles, the existing methodologies for assessing the representativeness of the driving cycle generally lack optimality, thereby leading to differences between the driving cycles and the real-world driving conditions. To address these issues, the main purpose of this study is to propose a novel general design approach for constructing the most representative driving cycle, which will be useful for EV power management investigation. Speciﬁcally, three original contributions are made:

1.3. Outline of the paper

Route selection Velocity record Velocity (km/h)

100

This study is conducted with a case study in Shenyang, China. The test vehicle is driven in a “car following mode,” which means that the test vehicle is driven to randomly follow a vehicle on the road, and experimental data is collected by a global positioning system (GPS) device, which is called the P-box. The total test distance covers 393 km. The Shenyang city is located mainly in a plain area, and the road slope is very small; thus, the impact of the slope is neglected. Two main streets, namely, The Qingnian Street and The Second Ring Road, are chosen as the driving routes, and the devices, driving routes, and statistical data are shown in Fig. 1. The test data is split into multiple micro-trips, each of which is a small speed proﬁle between two consecutive stops, as shown in Fig. 2. Commonly, the driving cycle is a combination of micro-trips with time length between 500 and 3000 s [21]. According to the average speed of each micro-trip, they are subdivided into three categories: 0e18.1 km/h (low speed), 18.1e36.2 km/h (medium speed), and 36.2e54.3 km/h (high speed), which constitute 56%, 34%, and 10% of the total trips, respectively. The proportions of the

2

3

4

5 Time (h)

6

7

8

9

10

Velocity (km/h)

Second ring Road 50

0 0

0.5

1

1.5

2

2.5 Time (h)

3

3.5

4

4.5

5

Fig. 1. Trafﬁc data collection in Shenyang, China.

80 60

35

Original data Smoothed data

30 25

40 2095

100

20 0 0

105

Micro-trip 20

40

60 80 Time (s)

100

120

140

Fig. 2. Example of a micro-trip.

kinematic segments in the sample data are shown in Fig. 3, and they represent the velocity distribution under the actual Shenyang driving environment.

250

Frequency

2.1. Driving environment collection

1

100

The remainder of the paper is organized as follows: data collection, data processing, and driving cycle development method are introduced in Section 2; the result of the practical driving cycle development method, comparison with other methods, and discussions are presented in Section 3; Section 4 illustrates the application of PHEV power management under the established driving cycle, and the conclusion is presented in Section 5. 2. Method

Qingnian Street 50

0 0

Velocity (km/h)

C The driving cycle construction is treated as an optimization problem using three representative characteristic variables and the SAPD. It is veriﬁed that there exists an optimal length for the speed proﬁle to represent the real-world driving condition, and a two-layer optimization is proposed for the construction of driving cycle using a genetic algorithm (GA). C The Shenyang urban driving cycle (SUDC) is developed for the ﬁrst time using the presented method. A comparison between the proposed GA-based method and the Markov chain method is performed. C The optimal power management strategy for a plug-in hybrid electric vehicle (PHEV) is applied under SUDC. With this approach, the effectiveness of the presented driving cycle development method is evaluated and analyzed.

Second Ring Road

P-box

200

56%

150

Low 34%

100 Medium 50 0 0

10% High 10 20 30 40 50 Velocity of micro-trips (km/h) Fig. 3. Average velocity frequency distribution.

60

4

Z. Chen et al. / Energy 186 (2019) 115766

relationships:

2.2. Speed proﬁle characteristic parameters The practical driving cycle is developed for the purpose of the EV power management investigation; thus, it should be constructed considering the power consumption information. The vehicle's power balance equation is described by

Pv ¼

1 dv fmgv þ CD Arv3 þ dmv þ imgv ; 2 dt h

1

ð E ¼ Pv dt ¼

ð t2ttrac ∪tbrak

t

1 dv fmgvðtÞ þ CD ArvðtÞ3 þ dmvðtÞ 2 dt #

þ mgiðtÞvðtÞ dt;

(2)

where E means the energy consumption of the vehicle, ttrac the time sets of positive propulsion, and tbrak the time sets of braking. Therefore, the average energy consumption (AEC) is deﬁned as

E E¼ ; x

(3)

where E is the AEC of the vehicle and x is the mileage. To simplify, the vehicle parameters should be moved beyond the integral symbol. Then, the AEC of the EV can be rewritten as follows:

E ¼ J1 þ J2 þ J3 þ J4 þ J5 þ J6 þ J7 þ J8 8 > > > > 1 > > J1 ¼ fmgq1 ; J2 ¼ CD Arq2 ; J3 ¼ dmq3 > > > 2 > > > > > > < 1 J4 ¼ fmgq4 ; J5 ¼ CD Arq5 ; J6 ¼ dmq6 2 > > > > > > > > > > > > > > > J7 ¼ mg q7 ; J8 ¼ mg q8 :

(4)

wherein the eight characteristic parameters q1eq8 are deﬁned as

8 > 1 > > > q1 ¼ > > x > > > > > > > > < 1 q4 ¼ x > > > > > > > > 1 > > q ¼ > > > 7 x > :

ð vðtÞdt; q2 ¼

1 x

t2ttrac

vðtÞdt; q5 ¼ t2tbrak

t2ttrac

vðtÞ3 dt; q3 ¼

1 x

t2ttrac

ð

ð

ð

vðtÞ3 dt; q6 ¼

t2tbrak

1 iðtÞvðtÞdt; q8 ¼ x

ð aðtÞvðtÞdt

where tcoas and tidli are the time sets of coasting and idling, respectively. Based on the above analysis, the characteristic of the driving condition can be expressed by eight variables. For any given driving cycle, the parameters q1eq8 are subjected to

8 > > 1 > > q1 þ q4 þ > > > x > > > > > > > > 1 > > q2 þ q5 þ > > > x > < > 1 > > q3 þ q6 þ > > > x > > > > > > > > > >q þ q þ 1 > 7 8 > > x > > :

ð vðtÞdt ¼ 1 t2tcoas

ð

vðtÞ3 dt ¼ Const

t2tcoas

(7)

ð

aðtÞvðtÞdt ¼ Const t2tcoas

ð

iðtÞvðtÞdt ¼ Const t2tcoas

In comparison with other events, coasting does not occur often; hence, it is assumed that tcoaszØ. Thus, the representative characteristic variables q1eq3 and q7 are chosen as the main indicators of the driving cycle construction. Once q1eq3 and q7 are given, the indicators to construct the driving cycle can be determined accordingly. The above deduction of the formulation shows that the proposed method is independent of the vehicle parameters, except for parameter t. However, it hardly affects the construction of driving cycle, which has been proved in Ref. [15]. Therefore, the vehicle speciﬁcations and parameters are selected without any qualiﬁcation for the proposed method. The ideal candidate driving cycle also needs to ensure that the SAPD is similar to that of the original data. Here, the root mean square error (RMSE) of the SAPD is used to describe the consistency degree of the distribution. The ranges of vehicle speed and acceleration are expressed as an Ns-by-Na matrix, in which Ns ¼ max (v)/ Dv, Na ¼ {max (a)-min (a)}/Da (a is the acceleration, and Dv and Da are the segmental intervals of the velocity and acceleration, respectively). Thus, the RMSE of the SAPD is deﬁned as

vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ uN N 2 u Ps Pa u pij pt;ij u ti¼1 j¼1 ; lP ¼ Ns Na

(8)

where pij and pt,ij are the ijth probability of the candidate driving cycle and the total statistical data, respectively.

t2ttrac

ð

1 x

(6)

(1)

where Pv stands for the instantaneous power of the vehicle, m is the vehicle mass，v is the vehicle velocity, g is the gravitational acceleration，f is the coefﬁcient of friction, i is the slope of the road, CD is the aerodynamic drag factor，A is the frontal area, r is air density, d is the conversion coefﬁcient of a rotating mass, and h denotes the transmission efﬁciency. Concerning the energy recuperation of the braking process, the energy consumption is integrated over the set ttrac and tbrak, expressed by

"

t ¼ ttrac ∪tbrak ∪tcoas ∪tidli 8 > > > > ttrac ¼ ft2t : Ft ðtÞ > 0g < tbrak ¼ ft2t : Ft ðtÞ < 0g tcoas ¼ ft2t : Ft ðtÞ ¼ 0; vs0g > > > > : tidli ¼ ft2t : Ft ðtÞ ¼ 0; v ¼ 0g

1 x

ð

aðtÞvðtÞdt t2tbrak

ð iðtÞvðtÞdt

t2tbrak

(5) The time sets of the driving cycle have the following

2.3. The two-layer optimization process The ideal candidate driving cycle should have the closest characteristics to the real-world statistical data. Therefore, the driving cycle construction can be treated as a minimization problem where the optimal cycle is formed by a conjunction of micro-trips to reach the minimum difference with the real word driving condition. The candidate driving cycle is denoted as V, which is a collection of several micro-trips. The entire dataset Dorig is composed of three

Z. Chen et al. / Energy 186 (2019) 115766

categories of micro-trips (as shown in Fig. 3), denoted as D1, D2, and D3. To ensure the rationality of the combination, the micro-trips that constitute the candidate driving cycle V are extracted from D1, D2, and D3 proportionately. As the terrain in Shenyang city is ﬂat, the inﬂuence of slope can be neglected and the parameter q7 is accordingly set to zero during the driving cycle construction. The process of the driving cycle construction aims to obtain a suitable combination of V to minimize the difference of characteristic parameters between V and the real-world statistical data, expressed by

number of micro-trips. The number of data segments for constructing the driving cycle has a direct impact on its performance. In the second process, these twenty-ﬁve optimal driving cycles are further compared with each other to ﬁnally determine the best N. The comparison is conducted according to two indexes, namely, the AEC and the RMSE of SAPD (compared with the entire dataset). Having both the closest AEC and the smallest SAPD is regarded as the best-case scenario. The detailed process of this comparison will be demonstrated in Section 3. After the best N is chosen, the driving cycle is established accordingly by connecting the micro-trips serially. 3. Result and discussion

(9)

The optimization results of the proposed GA are represented in Fig. 5. We can see from the results that the optimality of the driving cycle varies with the number of data segments. As the number of

30

where w is the weight coefﬁcient, q* is the characteristic parameter of the real-world statistical data, t is the time length of the driving cycle, tmax and tmin are the upper and lower limits of the time length, v denotes the quantity of micro-trips, and N is the number of micro-trips contained in V, respectively. Fig. 4 shows the ﬂow chart of the presented two-layer optimization-based algorithm. In the ﬁrst layer, a GA is employed to determine the optimal combination of N segments chosen from the entire dataset. The initial number of N is ﬁrst started from N0 ¼ 6, and then the objective function can be used to determine the performance with each combination of candidate micro-trips. In each step, the GA can determine an optimal combination with a number of N, and then the recurrence (N ¼ N þ 1) is carried on to repeat the optimization process until N reaches the maximum value Nmax ¼ 30. Then, we will have twenty-ﬁve “optimal driving cycles” in total; each one represents the best combination with a certain

Objective function value

8 3 > X > > * > wk qk ðVÞ qk þ w4 lP ðVÞ minJðVÞ ¼ > > < k¼1 V ¼ V1 ∪V2 ∪V3 > > > > > V1 4D1 ; V2 4D2 ; V3 4D3 > : D ∪D ∪D ¼ D 1 2 3 orig 8 > > < vðVÞ ¼ N; N2Z s:t: vðV1 Þ : vðV2 Þ : vðV3 Þ ¼ vðD1 Þ : vðD2 Þ : vðD3 Þ > > : tmin tðVÞ tmax

5

25

20

15 N =21 10 5

Fig. 4. Flow chart of driving cycle construction.

10

15 20 25 Number of micro-trips Fig. 5. Objective function value.

30

Z. Chen et al. / Energy 186 (2019) 115766

Table 1 Initialization parameters of GA. Parameter

Value

Population size Crossover function Mutation function Crossover ratio Selection function generation Elite Count Iteration time windows Fitness tolerance

350 Heuristic Uniform 1.2 Uniform 2000 17 50 0

Best fitness value

24

Best fitness value

data segments increases, the objective function value decreases at ﬁrst and then increases gradually. When N is equal to 21, the value of the objective function drops to a minimum. This minimum value of the ﬁtness function means that the former parameters q1eq3 are well chosen, making the characteristics of established driving cycle the closest to that of the overall database. The speciﬁc parameters of the GA are listed in Table 1. Two terminal conditions, the maximum number of iterations and the ﬁtness function tolerance limitation, are set in the process of GA optimization. The optimal ﬁtness of each iteration may change a little, sometimes even below the optimal ﬁtness tolerance limit and the algorithm is triggered to terminate, but the algorithm is not necessarily convergent at this time. The convergence of the algorithm is unconvincing and arbitrary just because the optimal ﬁtness between the two generations is close. Therefore, the GA introduces the iteration time windows to assist the triggering judgment of the optimal ﬁtness tolerance limit. When the change in the average optimal ﬁtness is lower than the tolerance index of ﬁtness under a certain number of time windows, the algorithm can be considered as convergent. The iterative results of the algorithm are shown in Fig. 6. The practical driving cycle is established for the purpose of power management investigation; thus, the AEC of the vehicle on the established driving cycle must be considered. The correlations between the RMSE of the SAPD compared with the entire dataset and the AEC of all the 25 optimal candidates are plotted in Fig. 7, in which the AEC of the overall dataset is marked as the “energy target” line. The distance of the point to this line denotes the difference in energy consumption while the abscissa RMSE of SAPD denotes the consistency with the overall dataset. It can be noted that three points are very close to the “energy target” line, but the two points on the right have a relatively larger RMSE. Similarly, there are four points having a relatively smaller RMSE (less than 0.1), but three of them are far from the “energy target” line. Only the point with N ¼ 21 has both a small RMSE and a close AEC in comparison with the overall dataset. Consequently, the driving cycle with 21 micro-trips is regarded as the best choice and the practical SUDC is established accordingly, as shown in Fig. 8. The vehicle condition of idling has no impact on the power consumption in EVs because the motor can be turned off every time the vehicle comes to a stop, but these idle conditions are still preserved for the integrity of the speed proﬁle. The time range of the established SUDC is 2984 s, and the total length is 23.13 km. The maximum velocity is 74.4 km/h while the average velocity is 27.9 km/h, reﬂecting the operation characteristics of urban driving conditions. Fig. 9 shows a comparison of the SAPD between the established SUDC and the overall statistical dataset. It can be observed that the probability distribution of SUDC is quite identical to the overall dataset.

22 20 18

14 12 10 138

148 158 168 Generations

178

16 14 12

0

50

100

Generations

150

200

Fig. 6. Best ﬁtness value.

Average energy consumption (Wh/km)

6

122.4 122.2 122.0 N =21 121.8 121.6

Energy Target Results Target

121.4 0 0.05 0.1 0.15 0.2 RMSE of velocity acceleration frequency distribution Fig. 7. Distribution of average energy consumption (AEC).

3.1. Consistency evaluation To further analyze the established SUDC and verify its consistency with the real-world statistical data, six commonly used parameters that represent the driving conditions [8,16,22,29] are used to evaluate the constructed SUDC quantitatively: 1) average speed, 2) standard deviation of velocity, 3) average acceleration, 4) average deceleration, 5) standard deviation of acceleration, and 6) proportion of acceleration. The comparison results of these seven parameters along with the AEC are listed in Table 2. The maximum error of these parameters is only 2.7% while the average error is 1.08%, indicating that the established SUDC is very close to the realworld statistical data. In addition, the AEC error is only 0.03%; thus, the established driving cycle is quite suitable for the power management investigation. Given that the driving cycle is established here for the power management investigation, the energy consumption is a critical index. The vehicle type that used in the above analysis of energy consumption is deﬁned as Custom. To verify whether the results are still suitable for other vehicles, four other cars in the Advisor database are utilized to test the energy consumption that applies to the SUDC and the overall dataset [40]. The basic parameters of the vehicles are listed in Table 3. The previous analysis in Section 2.2 shows that the parameters do not have strict restrictions for the driving cycle construction. Here, vehicles with different parameters

Z. Chen et al. / Energy 186 (2019) 115766

7

Velocity (km/h)

80 60 40 20 0 0

500

1000

1500 Time (s)

2000

2500

3000

Fig. 8. The practical driving cycle in Shenyang, China.

5

Probability (%) 10 15

5

1.0 0.5 0 -0.5 -1.0 -1.5 0

(a) 20

40 60 Velocity (km/h)

Probability (%) 10 15

1.5

Overall dataset Acceleration (m/s2)

Acceleration (m/s2)

1.5

20

SUDC

1.0 0.5 0 -0.5 -1.0 -1.5 0

80

20

(b) 20

40 60 Velocity (km/h)

80

Fig. 9. Comparison of SAPD between (a) the overall dataset and (b) the SUDC.

Table 2 Comparison between the SUDC and the overall dataset. Parameter

SUDC

Dataset Relative error (%)

Average speed (km/h) Standard deviation of velocity (km/h) Average acceleration (m/s2) Average deceleration (m/s2) Standard deviation of acceleration (m/s2) Proportion of acceleration (%) Average energy consumption (Wh/km)

27.91 21.74 0.29 0.38 0.45 31.70 122.18

27.99 21.81 0.29 0.37 0.44 32.32 122.22

0.29 0.32 0 2.70 2.27 1.92 0.03

are adopted and the results are presented in Table 4. Compared with the implementation of the real word data, the error in energy consumption from the SUDC is less than 0.0412 Wh/km. It shows that the energy consumption in the established SUDC is quite consistent with the real-world statistical data, even for different types of vehicles, which means that the varying vehicle parameters have a minor inﬂuence on the proposed driving cycle construction method. Therefore, the established driving cycle is suitable for the power management strategy investigation. 3.2. Comparison with the traditional method

Table 3 Basic parameters of different vehicle types. Vehicle parameter

Prius

Focus

Insight

Fiat Seic

Custom

m (kg) A (m2) f CD

1398 1.746 0.015 0.3 1.05

1157 2.06 0.015 0.312 1.05

856 1.9 0.015 0.25 1.05

1200 1.79 0.015 0.34 1.05

1200 2.05 0.015 0.301 1.05

d

Based on the collected real-world trafﬁc data, we also construct a driving cycle using the traditional Markov chain method and compare these different methods to illustrate the optimality of the presented method. The Markov chain method is based on the state transition probability for constructing the driving cycle, and the speciﬁc procedure can be found in Refs. [15,38,41]. Fig. 10 shows the

Table 4 Energy consumption (Wh/km) of vehicles under SUDC. Vehicle

SUDC

Statistical data

error

Prius Focus Insight Fiat SEIC

134.5308 119.7260 88.5579 121.8381

134.5373 119.7672 88.5884 121.8759

0.0065 0.0412 0.0305 0.0378

Velocity (km/h)

80 60 40 20 0

0

200

400

600

800

1000

1200

Time (s) Fig. 10. Driving cycle based on the Markov chain method.

1400

8

Z. Chen et al. / Energy 186 (2019) 115766

Table 5 Comparison with the Markov chain method. Parameters

Actual value

SUDC

RE (%)

Markov-based driving cycle

RE (%)

No.1 (km/h) No.2 (km/h) No.3 (m2/s) No.4 (m2/s) No.5 (m2/s) No.6 (%) AEC(Wh/km) MAE (%)

27.9922 21.8076 0.2871 0.3739 0.4438 32.3187 122.2169 N/A

27.9086 21.7403 0.2900 0.3756 0.4480 31.7024 122.1778 N/A

0.30 0.31 1.01 0.45 0.95 1.91 0.03 0.71

28.0598 21.4167 0.3069 0.3572 0.4597 30.7099 122.7192 N/A

0.24 1.79 6.90 4.47 3.58 4.98 0.41 3.20

result of the driving cycle established using the Markov chain method. The average velocity is 28.1 km/h, which is very close to that of the established SUDC. The comparison of the two driving cycles is presented in Table 5. From the results, it can be noted that the SUDC established by the proposed optimization-based method is nearer to the real-world statistical data than that constructed by the Markov chain method. The mean absolute error (MAE) of SUDC is 2.49% smaller than that of the Markov chain method, and the AEC of SUDC is 0.38% closer to the benchmark than that of the Markov chain method. The results illustrate that the presented GA-based method can result in a more representative driving cycle. The computation time of the GA method is 2112 s, which is longer than Markov chain method (122 s). However, as an ofﬂine algorithm, such computation time is acceptable. 4. Application of the power management strategy The ultimate purpose of establishing the driving cycle is to design and evaluate the power management strategies for EVs. The above investigations are based on the characteristics of the driving conditions to establish the practical driving cycle that is the most representative speed proﬁle of the real-world statistical data. From the viewpoint of power management, a well-designed practical driving cycle should have the following features: 1) for a certain power management strategy, the energy cost of different vehicles driving under the established driving cycle should be equal to that under the real-world driving condition; or 2) the optimal control parameters calculated based on the established driving cycle should still be optimal under the real-world driving condition. Otherwise, the driving cycle does not possess applicability. In this section, an optimal power management strategy for a PHEV is

applied to the established driving cycle. The results of the energy consumption and optimal control policy under the SUDC are analyzed with a comparative study. 4.1. Optimal power management for PHEVs Here, three PHEVs (Custom, Focus, and Prius) with the same series topology are taken as the research targets, in which a 120 kW electric motor is used to drive the vehicle with an automatic mechanical transmission (AMT). The motor is mainly powered by a 26 kWh lithium-ion battery pack, and a 60 kW engine-generator system is used as an auxiliary power unit (APU) for prolongation of the driving range. The vehicle power system conﬁguration and the control strategy are presented in Table 6. The power management algorithm contains three control modes, namely, charge depleting electric (CD-E) driving mode, (2) charge depleting hybrid (CD-H) driving mode, and (3) charge sustaining (CS) driving mode. In the beginning, the ﬁrst choice is the CD-E, in which all the power demand Preq is supplied by the battery pack considering the fact that the cost of electricity is much lower than that of oil fuel. If the battery SoC is lower than a threshold value ε1, the vehicle will operate in the CD-H mode; in this mode, Preq is provided by both the battery pack and APU. When SoC reaches the threshold value ε2, the operation will switch to CS mode, in which only the APU is utilized to provide power. There are only two parameters, namely PL* and PH*, that need to be optimized in the control algorithms. Here, PL* and PH* are two power thresholds that deﬁne a high efﬁciency range of the engine in which the engine power follows Preq. In an ofﬂine global optimization problem, the control policy is a power allocation relationship varying with time. If parameters PL* and PH* are

Table 6 PHEV system conﬁguration and power management strategy. Conﬁguration

Control algorithm

PHEV with series topology:

C CD-E mode: APU is turned off, and the Preq is supplied by the battery pack. 8 > > Pe ¼ P *H ; if Preq > P *H > > < Pe ¼ Preq ; if P *L < Preq < P *H C CD-H mode: (10) > Pe ¼ 0; if Preq < P *L > > > 8 : Pbatt ¼ Preq Pe < Pe ¼ maxf0; Preq g C CS mode: APU works as power source (11) : Pbatt ¼ Preq Pe

Electric transimission

Front

Mechanical transimission Charge

AC/DC converter

Battery Engine G

AC/DC converter

Generator

AC/DC converter

M

AMT

Electric motor

Z. Chen et al. / Energy 186 (2019) 115766

Velocity (km/h)

100

(A)

determined, then the control policy can be deduced based on Table 6. These two parameters are optimized [42] based on the established driving cycle. Thus, the control policy is expressed as u ¼ [PL, PH ], and then the optimization problem can be deﬁned as

Velocity

80 60 40 20 0

0

0.5

1

1.5

2

2.5

ð JE ðu* Þ JE ðuÞJE ðuÞ ¼ lðu; x; tÞdt cu2U 8 > > > > 0 PL < PH maxðPe Þ < minðPbatt Þ Pbatt maxðPbatt Þ s:t: ε2 xð1Þ 1 > > > > : xð2Þ ¼ vD ðtÞ

3 4

x 10

Power (kW)

60

(B)

Battery power

40 20 0 -20

0

0.5

1

1.5

2

2.5

Power (kW)

(C)

where JE is the cost function, l is the energy consumption rate, x ¼ [SoC, v] is the system state, and vD denotes the velocity of the employed driving cycle. The above control algorithm is applied under the SUDC. The thresholds ε1 and ε2 are set as 0.4 and 0.2 in the simulation. Fig. 11 shows the Custom optimization results of the battery power, engine power, battery SoC, and Preq under ten times the SUDC (231.3 km). At the beginning of the simulation, the vehicle is driven in the CD-E mode, so the engine is turned off and the battery pack supplies the power to meet the Preq for a clean driving. When the battery SoC reaches 0.4, the engine starts and the CD-H model is switched on. The engine and battery work together in a hybrid manner.

Engine power

30 20 10 0

0

0.5

1

1.5

2

2.5

3 4

x 10 0.8

Battery SoC

Battery SoC

(D) 0.6 0.4 0.2 0

0

0.5

1

1.5

2

2.5

3 4

x 10

Power (kW)

60

(E)

(12)

3 4

x 10

40

9

Required power

4.2. Analysis of the optimal parameters

40 20

Based on the above simulation study, the energy cost and the optimal parameters are recorded for further analysis. As mentioned, the optimal parameters calculated based on the SUDC should be approaching those under real-world statistical driving conditions. It should be noticed that the optimal control parameters and energy cost are inﬂuenced by the driving distance. Therefore, the distance of the chosen driving cycles and selected experimental data are exactly the same as those of the SUDC for a fair comparison. In total, ten periods of speed proﬁles are selected randomly

0 -20

0

0.5

1

1.5

2

2.5

3

Time(s)

4

x 10

Fig. 11. Simulation of the control results with the Shenyang driving cycles: (A) velocity proﬁle, (B) battery power, (C) engine power, (D) battery SoC, and (E) power requirement.

PL (kW)

7.5

(A)

7.2358

7

6.7653

6.7995

6.7759 6.6554

6.6631 6.723

6.5

6.3208

6 ED1 50

6.3137

SUDC: 6.5491

6.1358

ED2

ED3

ED4

ED5

ED6

ED7

ED8

ED9

42.2047

Average 34.1272

31.471

30 20

ED10

(B)

40

PH (kW)

Average 6.9053

34.1272

25.3878

26.0074

25.7788

10 ED1

20.1426

19.9784

ED2

ED3

20.7832

20.2404

19.9598

ED8

ED9

SUDC: 29.6690 ED4

ED5

ED6

ED7

ED10

Speed profile of experimental data Fig. 12. Comparison of optimal control parameters: (A) parameter PL and (B) parameter PH.

10

Z. Chen et al. / Energy 186 (2019) 115766

Table 7 PL and PH values in the four standard driving cycles. PHEVs

Driving cycles

PL

PH

Relative error (PL)

Relative error (PH)

MAE (%)

Custom

EDmean SUDC LA92 EUDC US06 EDmean SUDC LA92 EUDC US06 EDmean SUDC LA92 EUDC US06

6.6631 6.5491 3.8383 5.6727 4.2070 6.5921 6.4606 4.4573 5.4864 4.7415 6.9950 6.8656 1.4410 5.4184 2.3171

26.0074 29.6690 20.5817 22.7049 35.6616 24.4692 21.2895 20.5090 22.6018 35.0119 27.3540 33.1001 22.4567 18.9881 39.7694

N/A 1.71% 42.39% 14.86% 36.86% N/A 1.99% 32.38% 16.77% 28.07% N/A 1.85% 79.39% 22.54% 66.87%

N/A 14.08% 20.86% 12.70% 37.12% N/A 12.99% 16.18% 7.63% 43.08% N/A 21.00% 17.90% 30.58% 45.39%

N/A 7.90% 31.63% 13.78% 36.99% N/A 7.49% 24.28% 12.2% 35.58% N/A 11.43% 48.65% 26.56% 56.13%

Focus

Prius

(each one has the same length with ten times the SUDC) from the overall real-world experimental data, and are denoted as ED1, ED2, …, ED10. The optimization of PL and PH is repeated under these real-world speed proﬁles, and the results are shown in Fig. 12. It can be found that the optimal control parameters obtained from the SUDC are very close to the mean values of the optimal control

parameters from the actual driving conditions. This indicates that the established SUDC is very representative of the real-world driving conditions. Three typical driving cycles, namely, EUDC, US06, and LA92, are considered to further analyze this issue. When the vehicle is operated in Shenyang, China, if the SUDC does not exist, the

Cost (CNY)

50

(A)

SUDC-based strategy Benchmark

40 30 20 10 0

0

0.5

1

1.5

2

2.5

3

3.5 4

x 10

Cost (CNY)

50

(B)

LA92-based strategy Benchmark

40 30 20 10 0

0

0.5

1

1.5

2

2.5

3

3.5 4

x 10

Cost (CNY)

50

(C)

EUDC-based strategy Benchmark

40 30 20 10 0

0

0.5

1

1.5

2

2.5

3

3.5 4

x 10

Cost (CNY)

50

(D)

US06-based strategy Benchmark

40 30 20 10 0

0

0.5

1

1.5

2

Time(s)

2.5

3

3.5 4

x 10

Fig. 13. Results of the comparison of energy cost. (A) SUDC-based strategy; (B) LA92-based strategy; (C) EUDC-based strategy; (D) US06-based strategy.

Cost (CNY/100km)

18.5

(A) 18.0597

18

17.8283

17.8142

17.7764

17.7597

17.627

17.5 17.3099 17

Cost (CNY/100km)

19

ED4

ED5

ED6

ED7

ED8

ED9

ED10

18.9509

(B)

18.4398

18.5

18.2964

18.1938

17.9474

17.802 18

17.9599 17.5735

17.5

17.7237

17.7203

SUDC-based strategy Average

17 16.9509

22

Cost (CNY/100km)

ED3

ED2

16.5 ED1

ED2

ED3

ED4

(C)

ED5

ED6

ED7

ED8

ED9

ED10

21.2953

21.3955

21.5211

21.5

21.1358

21.2409

21.085 21

20.9675 20.5364 20.7538

20.7553

20.5 20

LA92-based strategy Average

19.9555 19.5 ED1 20

Cost (CNY/100km)

Actual optimal strategy Average

16.5197

16.5 ED1

ED2

ED3

ED4

ED5

(D)

19.5

ED6

ED7

19.8236

ED8

ED9

ED10

19.3457 19.5321

18.9553

19.0962

19.0155

19

18.8545 18.7822

18.18

18.5

18.3553

18

17.4593

EUDC-based strategy Average

17.5 17 ED1

21.5

Cost (CNY/100km)

17.5271

17.3607

17.215

ED2

ED4

ED3

ED5

ED6

ED7

ED8

ED9

ED10

21.3238

(E)

21

21.2185

20.8724 20.9693

20.9486 21.1352 20.7336

20.5

20.5083

20.1697

20.5582

20

US06-based strategy Average

19.6321

19.5 ED1

ED2

ED3

ED4

ED5

ED6

ED7

ED8

ED9

Speed profile of experimental data Fig. 14. Energy cost of (A) experimental data, (B) the Shenyang driving cycle (C) LA92, (D) EUDC, and (E) US06.

ED10

12

Z. Chen et al. / Energy 186 (2019) 115766

Table 8 Comparison of energy cost per 100 km. PHEVs

Driving cycles

EDmean (benchmark)

SUDC-based strategy

LA92-based strategy

EUDC-based strategy

US06-based strategy

Custom

Cost rate (CNY/100 km) Relative error (%) Reduction (%) Cost rate (CNY/100 km) Relative error (%) Reduction (%) Cost rate (CNY/100 km) Relative error (%) Reduction (%)

17.5271 N/A N/A 16.8926 N/A N/A 20.6755 N/A N/A

17.9599 2.47 N/A 17.2750 2.26 N/A 21.1051 2.08 N/A

20.9675 19.63 17.16 19.6377 16.25 13.99 24.9235 20.55 18.74

18.8545 7.57 5.10 18.4823 9.41 7.15 22.5462 9.05 6.97

20.7336 18.29 15.82 19.4303 15.02 12.76 25.2003 21.88 19.80

Focus

Prius

researchers may use other typical driving cycles for the power management investigation. Using these typical driving cycles with three different vehicles, we obtain their optimal control parameters, as listed in Table 7, in which EDmean denotes the mean value of the ten real-world data using a certain vehicle (the purple line in Fig. 12). Apparently, the established SUDC can help achieve the optimal control parameters, which are much closer to the actual optimality under the Shenyang driving condition than when using other typical driving cycles. This shows that an effective method for developing the typical driving cycle is very important and indispensable for power management design considering the short distance and regional driving characteristics of EVs.

4.3. Analysis of the energy cost The energy saving effect is analyzed quantitatively in this section. Using the optimal control parameters of each vehicle in Table 7, we can generate four optimal control strategies, denoted as SUDC-based, LA92-based, EUDC-based, and US06-based strategies. For instance, the LA92-based strategy means the optimal power management strategy in which the control parameters are optimized from the LA92 driving cycle. Then, the simulation study is conducted to evaluate the energy cost with these four control strategies under the real-world driving conditions in Shenyang. The actual optimization result of the energy cost based on the realworld statistical data is used as the benchmark. As mentioned, we have randomly chosen ten periods of experimental data (ED1, ED2, …, ED10). Fig. 13 shows the comparison of energy cost variation in the ED1 (vehicle type: Custom), in which the unit of the energy cost is Chinese Yuan (CNY). We can notice that the energy cost with the SUDC-based power management strategy is the lowest and closest to the actual optimal control result. For the other three strategies, their control policies deviate more or less from the benchmark owing to the difference between the employed driving cycle and the practical driving condition. This further illustrates that the established driving cycle construction method is very effective for studying the power management strategy. The simulation results of the ten situations (ED1, ED2, …, ED10) are shown in Fig. 14, where the energy cost is transferred into the energy cost per hundred kilometers (CNY/100 km) for better illustration. Fig. 14(A) shows the actual optimal results under the experimental data, which is used as the benchmark. Fig. 14(B) shows the energy cost with the SUDC-based strategy. It can be noted that the energy cost under each of the ten periods of realworld experimental data with the SUDC-based strategy is very close to the actual optimal results. The average cost is 17.9599 CNY/ 100 km, which is only 2.47% higher than the actual optimal result. The results of the three other strategies are shown in Fig. 14(C)e(E). Apparently, the energy costs of the power management strategies increase without knowing the exact driving cycle. The speciﬁc comparison results are listed in Table 8. Here, two other vehicle

types (Focus and Prius) are added for obtaining more comprehensive analysis results. For each kind of vehicle type, the SUDC-based strategy can achieve a near optimal control effect under the realworld Shenyang driving condition, in which the energy costs are only 2.47%, 2.26%, and 2.08% higher than the actual optimal result, respectively. Compared with the three optimal strategies obtained from other typical driving cycles, the SUDC-based strategy is evidently closer to the actual optimum. The SUDC-based strategy can signiﬁcantly reduce the energy consumption, by 5.1%e19.8%, under the Shenyang driving condition. 5. Conclusion A novel optimization-based method for practical driving cycle development is presented for EV power management applications. The SUDC is developed under the Shenyang urban trafﬁc condition as a case study. The presented method can achieve a more representative driving cycle that is 2.49% closer to the actual data than the traditional Markov chain method. An optimal power management strategy for PHEVs is applied under the established SUDC. The evaluation results indicate that the established SUDC is very representative of the real-world Shenyang driving conditions. The SUDC-based strategy can achieve a near optimal control effect, with a deviation from the actual optimum of less than 2.47%. The presented SUDC-based power management strategy can further reduce the energy consumption by up to 19.8% in comparison with the strategies without Shenyang trafﬁc information. Acknowledgments This work was supported by the National Natural Science Foundation of China (51607030) and the Fundamental Research Funds for the Central Universities (N160304001). References [1] Fotouhi A, Montazeri-Gh M. Tehran driving cycle development using the kmeans clustering method. Sci Iran 2013;20:286e93. [2] Brady J, Mahony M. Development of a driving cycle to evaluate the energy economy of electric vehicles in urban areas. Appl Energy 2016;177:165e78. [3] Xiong R, Yang R, Chen Z, Shen W, Sun F. Online fault diagnosis of external short circuit for lithium-ion battery pack. IEEE Trans Ind Electron 2019. https://doi.org/10.1109/TIE.2019.2899565. [4] Xiong R, Li L, Tian J. Towards a smarter battery management system: a critical review on battery state of health monitoring methods. J Power Sources 2018;405:18e29. [5] Xiong R, Zhang Y, Wang J, He H, Peng S, Pecht Michael. Lithium-ion battery health prognosis based on a real battery management system used in electric vehicles. IEEE Trans Veh Technol 2019;68:4110e21. [6] Wu J, Zhang C, Cui N. Fuzzy power management strategy for a hybrid electric vehicle based on driving cycle recognition. Int J Automot Technol 2012;13: 1159e67. [7] Xiong R, Yu Q, Shen W, Lin C, Sun F. A sensor fault diagnosis method for a lithium-ion battery pack in electric vehicles. IEEE Trans Power Electron 2019;34:9709e18. https://doi.org/10.1109/TPEL.2019.2893622. [8] Xiong R, Tian J, Shen W, Sun F. A novel fractional order model for state of charge estimation in lithium ion batteries. IEEE Trans Veh Technol 2018.

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