Multi-objective Optimal Energy Management Strategy ... - Science Direct

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ScienceDirect Energy Procedia 88 (2016) 814 – 820

CUE2015-Applied Energy Symposium and Summit 2015: Low carbon cities and urban energy systems

Multi-objective Optimal Energy Management Strategy and Economic Analysis for an Range-Extended Electric Bus Jun-qiu Lia,*, Xin Jina, Rui Xionga a

Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing Institute of Technology, Beijing, 100081,China.

Abstract An optimal energy management strategy is proposed to match engine fuel consumption and battery SOH of REEB. Models of APU fuel consumption and battery SOH loss are established and multi-objective performance function is provided. DP algorithm is adopted to solve the optimization problem. Under the conditions of different drive cycles, different SOH penalty coefficients are analyzed to reveal its effects. Considering the total life-cycle costs, simulations prove that when battery is not to be replaced, and the capacity configuration and SOH penalty coefficient of battery are both taken the minimum, the best economical results can be achieved. © 2016 by Elsevier Ltd. This an openLtd. access article under the CC BY-NC-ND license © 2015Published The Authors. Published by is Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review under responsibility of CUE Peer-review under responsibility of the organizing committee of CUE 2015

Keywords: energy management; multi-objective optimization; dynamic programming; range-extended electric vehicle

Nomenclature REEB SOH SOC APU DP MNEDC CTUDC CD-CS

Range-Extended Electric Bus State of Health State of Charge Auxiliary Power Unit Dynamic Programming Modified New European Drive Cycle Chinese Typical Urban Drive Cycle Charge Depleting-Charge Sustaining

* Corresponding author. Tel.:086-010-68940589; fax:086-010-68914842. E-mail address: [email protected].

1876-6102 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of CUE 2015 doi:10.1016/j.egypro.2016.06.133

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Jun-qiu Li et al. / Energy Procedia 88 (2016) 814 – 820

1.

Introduction

Pure electric vehicles are faced with many disadvantages such as short driving range, long charging time, short battery life and high prices. To solve these disadvantages, REEB are designed with APU and small-capacity battery pack. Due to REEB has both pure electric drive model and hybrid power drive model, it is gradually becoming a development trend of electric vehicle products[1]. Energy management strategy is critical for REEB to extend driving ranges and reduce the engine fuel consumption[2]. There are two main controlling strategies: Blend and CD-CS. CD-CS control strategy with the goal of reducing emissions and improving fuel efficiency has the working condition of pure electric drive and is popular for REEB. Therefore, this paper adopts the CD-CS. Energy management strategies on the basis of rule control, instantaneous optimal control, global optimization control and adaptive control[5]. Usually, the global optimization control strategy with the DP algorithm can be adopted to obtain optimal fuel consumption in known conditions and evaluate control effect of other online energy management in practical applications[6]. However, the majority of existing practices often focus on minimizing the fuel consumption, while ignoring the battery aging. Thus, SOH of battery need to be considered. In order to find the appropriate tradeoff between fuel economy and battery life, optimization design between the battery configuration and SOH penalty coefficient is conducted in the DP-based control strategy, and the results can provide an important basis for initial parameters design and energy management strategies. 2.

Compositions of Power System

The basic parameters of the REEB are shown in Table 1. The power system structure, which consists of APU system, battery system and motor-transmission system, is shown in Fig.1. APU system adopts diesel engine which is coaxial with the permanent magnet synchronous generator. Voltage matching can be achieved by DC-DC convertor between battery and APU systems. Wheel 0RWRU FRQWURO OHU

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Fig. 1. Configuration of the REEB Table 1. Vehicle Parameters Parameter

value

Vehicle total mass

14500kg

Transmission ratio of the final drive

6.5

Transmission ratio of the 2-speed

1 and 3.5

APU

80kW

Battery Patch

140Ah

permanent magnet synchronous motor

170kW

DC Voltage

400V

816


3.

System Modeling

In this paper, the engine fuel consumption is only related with the engine torque and speed ignored of engine dynamic effects. The differential equation of engine speed can be gained by the formula (1). ng (k 1)

ng (k )

'T *(Teng (k ) T f (k ) Tg (k ))

(0.1047*( J e J g ))

(1) In the formula, Teng denotes engine output torque, Tm is the generator electromagnetic torque, Tf (k) is the connection resistance torque for the engine and generator, Je+Jg are rotational inertia with both engine and generator, ng and is the speed of the engine. Based on the above differential equationˈthe engine fuel consumption mf (k) can be a checked through fuel consumption MAP of engine. Then we get the formula (2).

m f (k )

fe (ng (k ), Teng (k ))

(2) In order to establish the relationship between the engine and the DC bus power, the equivalent circuit method is adopted as shown in the Fig.2. In the formula, ¹P denotes the engine and the generator speed, Tm is electromagnetic torque of the generator; Keng is the equivalent electromotance of generator, Kxng is the equivalent impedance, Udc and Idc represent the output voltage and output current of the rectifier, Pb is the battery power,¨m is the comprehensive efficiency of the generator and rectifier bridge, and¨DC-DC represents the battery voltage of DC-DC converter efficiency. Kxng Idc ng

Keng

Tg

Udc

U dc (k ) K e n g (k ) K x n g (k ) I g (k ) °T (k ) ( K I (k ) K I 2 (k )) /K e g x g m ® g ° P (k ) U (k ) I (k ) P (k ) / K dc g b DC - DC ¯ dc

Fig. 2. Diagram of Equivalent Circuit and Equations of Generator-rectifier

As a state variable of energy management optimization, battery SOC is usually considered the most critical factor among the influential factors on battery energy management strategies. Therefore, RINT model is used , and the battery SOC state control is realized based on DC-DC duty cycle which can be described as the formula (3)~(6). Pb (k ) ( Pdc (k ) Pg (k )) / KDC DC (3) I b (k )

U oc (k ) U oc2 (k ) 4Pb (k ) Rb (k )

SOC (k 1) SOC (k )

D (k )

2 Rb (k )

(4)

'T * Ib (k )

3600C Udc(k ) /(U oc( k ) Ib (k ) Rb (k ))

(5)

(6) In the formulaˈUoc is the open circuit voltage, Rb is the internal resistance of the battery in relation with SOC, Ib is the current in battery and the regulation is that the charging current direction is negative and the discharging current direction is positive. C is battery capacity. Battery aging models are mainly divided into three types[7], and Ah-throughput-aging model is adopted and defined as follows: SOH (n 'T ) SOH 0

n 1 1 ¦ | Pb (k 'T ) | 'T 2 Q0 (0) k 1 N ( Pb (k 'T ))

(7)

817


Where SOH0 is the initial state-of-health which is set to 1; N is the total number of cycles before endof-life; Q0(0) is the initial energy capacity of the battery and the Pb(´) is the internal power of the battery at time´. For each time step, 1 represents the SOH loss during T (T =1second in 1 | Pi (k 'T ) | 'T 2 Q0 (0) N ( Pi (k 'T ))

this paper), which means it is theSOH [8]. Clearly it can be incorporated into the cost function as an indication of battery capacity degradation. As for the influence of battery power Pb on number of cycles to battery end-of-life for the battery cell used in this paper is shown in Fig. 3. Additionally, the relationship between Pb and SOH is shown in the figure using the red line. -5

x 10 1

d SOH / dt

Number of cycles

2000

1000

0

0

100

200 300 Battery internal power (W)

400

0 500

Fig. 3. Influence of Battery Power on the Number of Cycles and Battery Cell Degradation

4.

Multi-Objective Optimization of Engine Fuel Consumption and Battery SOH

The optimal control problem can be stated as minimize the total amount of fuel consumption and battery SOH loss over the whole drive cycle as show: J

k N ½ min ® ¦ m f (k ) w u 'SOH (k ) ¾ ¯k 0 ¿

U

(8) Where mf (k) is the fuel consumption rate determined by engine operation point and S is the weighting factor of the battery SOH. Due to the order of magnitude of SOH is small and the conversion relation between SOH with the rate of fuel consumption is 10^7, S is used to represent the penalty coefficient conversion value of SOH. The state variables are SOC and engine speed while the control variable is DC-DC ratio. Based on the mechanical and electrical properties of the vehicle devices, Eq.(8) is subjected to the following constrained equations: | SOC ( N ) SOC (0) | 'SOC °n ° eng _ idle neng (k ) neng _ max ° n (k 1) n (k ) 'n eng ° eng ® (9) ° I b _ max_ char I bat (k ) I b _ max_ disch °0 I ( k ) I g g _ max ° °U dc _ min U dc U dc _ max ¯

818


DP is a powerful tool to solve dynamic optimal control problem. The overall problem of dynamic optimization can be decomposed into a sequence of simpler minimization problems as follows[7]: Step N-1˖ J N* 1 ( x( N 1)) min[ L( x( N 1), u( N 1)) G( x( N ))] u ( N 1)

Step kˈfor 0İk 6, the curve decreases pretty slowly, which sacrifices a large amount of fuel to get a tiny battery health improvement. It is not recommended to do so due to the cost of the fuelˈas it will overwhelm the battery wear. Therefore, analyzing the vehicle cost in running cycle, vehicle fuel consumption and capacity decline of battery SOH, the parameters of battery capacity configuration and parameters of control can be holistically optimized.

Fig. 5. Effect of Penalty Coefficient on Fuel Consumption and of per 100 km

Considering the basic parameters of 35Ah battery cell, we make an optimization design on the battery capacity configuration of 70Ah, 105Ah, 140Ah and 175Ah. In order to simplify the research,, cost analysis are conducted on the assumption that the vehicle runs in charge sustaining stage of CD-CS way


and actual service life is 240,000km. In order to reflect the various road conditions, the simulation conditions adopt MNEDC. According to the different configuration and SOH penalty coefficient of battery, cost of fuel consumption and Battery can be acquired in Fig.6.

(a)Cost of fuel consumption

(b) Cost of battery

Fig. 6. Cost of battery and fuel consumption with Different Capacity Configurations

From Fig. 6, appropriately selecting the value of S will help the vehicle run at the most economical point and reduce the cost of fuel consumption. However, if the battery capacity, under the same driving condition, is configured too low, the aging recession speed of the battery may be hastened greatly and replacement cost will be raised; the fuel consumption is more sensitive to battery SOH penalty coefficient, and the fuel consumption increases more quickly as penalty coefficient rises. But if the battery capacity is configured too high, the battery will not be fully used; and there will be too much capacity unused beyond the whole life-cycle. It is preferable to choose the battery capacity with no need to be replaced, so that the battery can be fully utilized as much as possible. Setting penalty coefficient s of Battery SOH as the abscissa ordinate and the total cost as the vertical ordinate, the curve of total cost is shown in Fig. 7. In the selection of penalty coefficient S, it is critical to ensure that the value should be moderateˈbecause the large value of S will lead to high fuel consumption. If the value of S is too large, it will lead to high fuel costs. However, if the value of S is too small, recession of battery SOH will be speeded up, the battery life will be shortened and the battery needs to be replaced. Fig. 7 indicates that in the MNEDC cycle, the lowest and the most reasonable total cost of REEB can be obtained when capacity configuration of the battery pack is 140Ah and the battery SOH penalty coefficient is 3.

Fig. 7. Total Cost for REEB with Different Capacity Configurations and Battery SOH Penalty Coefficient

6.

Conclusion

The fuel consumption of APU system and battery SOH loss models are established and selected as the optimization objectives of energy management strategies with DP algorithm. In consideration of mileage requirements for REEB within its whole life cycle, we obtain the optimal methods of energy management

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strategies when an REEB has the optimal battery capacity configuration, and optimal results have been achieved when battery capacity configuration and penalty coefficients of battery SOH are taken the minimum value at the same time. Copyright Authors keep full copyright over papers published in Energy Procedia. Acknowledgement The authors would like to thank the Collaborative Innovation Center of Electric Vehicles in Beijing Institute of Technology for the support of this research project. Reference [1]Tate E.D, Harpster M.O, Savagian P.J. The Electrification of the Automobile: From Conventional Hybrid, to Plug-in Hybrids, to Extended-Range Electric Vehicles[C]. SAE Paper, 2008, pp 156-166. [2]S. Barsali, C. Miulli, and A. Possenti, “A control strategy to vehicles,” IEEE Trans. Energy Convers., vol. 19, no. 1, pp. 187– 195, 2004.. [3]Qi ZHANG,Hao YANG,Yuguang WEI et al.Selection of Destination Ports of Inland-Port-Transferring RHCTS Based on Sea-Rail Combined Container Transportation[C]. ISMR. September 20-21, 2012, Nanchang, China.2012:675-680. [4]Theo Hofman,Maarten Steinbuch,Roell van Druten et al.Rule-based energy management strategies for hybrid vehicles[J].International Journal of Electric and Hybrid Vehicles,2007,1(1):71-94. [5]B. Wu, C.-C. Lin, Z. Filipi, H. Peng, and D. Assanis, “Optimal power management for a hydraulic hybrid delivery truck,” Veh. Syst. Dyn., vol. 42, no. 1–2, pp. 23–40, 2004. [6]D.U.Sauer,H. Wenzl.Comparison of different approaches for lifetime prediction of electrochemical systems—Using lead-acid batteries as example[J]. Journal of Power Sources 176 (2008) 534–546 [7]D. P. Bertsekas, Dynamic Programming and Optimal Control. Belmont, MA: Athena Scientific, 1995. [8]Ebbesen, S, Elbert. P, Guzzella. L. “Battery State-of-Health Perceptive Energy Management for Hybrid Electric Vehicles” [J], IEEE Transactions on Vehicular Technology, vol. 61, 2012.

Biography Junqiu Li, Doctor of Engineering, associate professor, engaged in the researches of energy management and control strategy for electric vehicles. Used to take charge of a national defense fund project, win a second prize of National Technology Invention Award and a second prize of Technology Invention Award of the Commission of Science.