Combinatorial Optimization Algorithm of MIGA and ... - Science Direct

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ScienceDirect Energy Procedia 105 (2017) 2460 – 2465

The 8th International Conference on Applied Energy – ICAE2016

Combinatorial optimization algorithm of MIGA and NLPQL for a Plug-in Hybrid Electric Bus parameters optimization Hongwen Hea,b,* ,Lu Yia,b, Jiankun Penga,b a National Engineering Laboratory for Electric Cehicles, Beijing Institute of Technology,Beijing 100081, China Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing Institute of Technology, Beijing 100081, China

b

Abstract In this paper, the fuel economy is chosen as the optimization target of a Plug-in hybrid electric bus (PHEB). The optimization mathematical model of PHEB powertrain parameters is established, which is based on optimal energy management strategy, and the energy management strategy of this model is formulated by dynamic programming (DP) algorithm. Firstly, PHEB fuel economy is chosen as the objective function of parameter optimization. Then, combinatorial optimization algorithm is designed by Multi-Island genetic algorithm (MIGA) and Sequential Quadratic Programming-NLPQL. MIGA is used for global optimization firstly, and the NLPQL is used for local optimization. Finally, experiments results prove that PHEB fuel consumption per 100 km has reduced to 17.41 L diesel from 18.51 L diesel, and electricity consumption per 100 km remains the same level. © by Elsevier Ltd. Thisby is an open access ©2017 2016Published The Authors. Published Elsevier Ltd.article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). under responsibility ofthe ICAE Selection and/or peer-review Peer-review under responsibility of the scientific committee of 8th International Conference on Applied Energy. Keywords: Parameters optimization; Plug-in Hybrid electric bus; Multi-Island genetic algorithm; Sequential Quadratic Programming-NLPQL

1. Introduction Plug-in hybrid electric vehicle (PHEV) is a new type of Hybrid electric vehicle. PHEV is a complex nonlinear system consisted of engine, motor, power battery and electromechanical coupling device [1]. In practical engineering, different engine powers, motor powers and battery capacity will make PHEV show different dynamic performances and fuel economy. PHEB is a kind of PHEV. To solve the problem of PHRB parameter optimization, Multi-island Genetic algorithm (MIGA) [2], evolutionary algorithms (EAS) [3], Sequential Quadratic Programming-NLPQL [4] and more combinatorial optimization algorithms are widely used in the whole world. MIGA and NLPQL have been widely used in various kinds of optimization problem. MIGA has a better ability on global optimization, but it is slightly weak in local search. At the same time, NLPQL has a strong ability on local search and a high search efficiency [5]. In this paper, NLPQL, which has a good stability to use together with other algorithms, and MIGA are combined. The Multi-Island genetic algorithm (MIGA) is used for global optimization firstly, then the NLPQL was used for local optimization

1876-6102 © 2017 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 scientific committee of the 8th International Conference on Applied Energy. doi:10.1016/j.egypro.2017.03.708

Hongwen He et al. / Energy Procedia 105 (2017) 2460 – 2465

to new population, to get the optimized solution. Finally, the optimization results of combinatorial optimization algorithm can be proved by DP program simulation experiments. 2. PHEB powertrain structure and model building 2.1. PHEB powertrain structure In this paper, the plug-in hybrid bus powertrain adopts series-parallel structure, specifically shown in Figure 1, where the engine and ISG motor are mechanically integrated; the ISG motor is connected to the main drive motor through a clutch, the powertrain structure and initial vehicle parameters of PHEB can reference Ref. [6]. Energy management system Clutch

CAN bus

ECU

Engine

Differential

Traction motor

ISG

Main reducer ISG controller BMS

Power Battery Pack

Traction motor Electric cable controller

High-voltage distribution box

Fig. 1. PHEB Powertrain

2.2. Optimization variables Because of the special requirements to ISG motor by single-axle parallel hybrid system structure of PHEB, the peak power of engine PE _ peak , the peak power of main drive motor PM _ peak , the battery capacity Qb and the reduction ratio ig are optimized in this paper. The results of preliminary matching for PHEB hybrid system structure parameters are chosen as the upper boundary and lower boundary of optimized variables, through rising or falling by 20%, as shown in table 1. Table 1. PHEB Parameters to be optimized Parameters

Maximum

Minimum

Initial value

PE _ peak /kw PM _ peak /kw ig Qb /A*h

117.6

176.4

147

120

170

148

4.26

6.40

5.33

57.6

86.4

72

2.3. Objective function Objective function of parameters optimization is to find with the minimum fuel consumption V fuel under the premise of meeting the constraint conditions.

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min f ( X pt ) U ( X pt )

(1)

U ( X pt ) is fuel consumption per 100km. The equation (1) shows that the engine fuel consumption V fuel is the objective function of the parameter optimization on discrete simulation conditions. 2.4. Constraint conditions According to PHEB parameters optimization problem, it is also the optimization targets that seeking the optimal fuel economy and meeting the demand of vehicle dynamic performance, to maintain stability of the SOC at a constant value at the end of the simulation. So constraint conditions in this paper are vehicle dynamic performance index and SOC final value of power battery. To ensure that each part of PHEB hybrid system (such as engine, ISG motor, main drive motor and power battery, etc.) is normal to run smoothly, this model need to satisfy the following constraints, such as equation (2). SOCmin d SOCk d SOCmax ° I s _ kmin d I s _ k d I s _ kmax ° ° Temin (ne _ k ) d Te _ k d Temin (ne _ k ) ° ° ne _ min d ne _ k d ne _ max ° nISG _ min d nISG _ k d nISG _ max ° ®T ° ISG _ min (nISGk , SOCk ) d TISG _ k d TISG _ max (nISGk , SOCk ) ° nMO _ min d nMO _ k d nMO _ max ° °TMO _ min (nMOk , SOCk ) d TMO _ k d TMO _ max (nMOk , SOCk ) ° Treqk Tek TISGk TMOk Tbrakek / i0 ° ° tanD ! 12% ¯

(2)

In equation (2) the subscript of min/max represent minimum/maximum of corresponding variables; I s _ k is battery current after the loss in the current simulation step, A; Te _ k is engine output torque in the current simulation step, Nm; ne _ k is engine output tachometer in the current simulation step, r/min;

TISG _ k is ISG motor output torque in the current simulation step, Nm; nISG _ k is ISG motor output tachometer in the current simulation step, Nm; nISG _ k is drive motor output torque in the current simulation step, Nm; nMO _ k is drive motor output tachometer in the current simulation step, r/min;

Tbrake _ k is mechanical brake braking torque in the current simulation step, Nm; Treq _ k is aggregate demand torque in the current simulation step, Nm; i0 is final drive ratio; tanα is the maximum climbable gradient. 3. Parameter Optimization In the process of each optimization, the Matlab model with dynamic programming will be used, and each individual will have parameters optimization based on the optimal energy management strategy. The process of combinatorial optimization algorithm of MIGA and NLPQL has been shown as follows: ķInitialization of population P(t), genetic algebra N, amount of island M, k=1; ĸCalculate Current population Fitness U i ĹIndividual Selection, crossover, variation, migration between different islands˗ ĺTermination condition judgment: If k>120, turn to step ļ; If not, k=k+1, turn to step ĸ; ĻInitialization of parameter D 0 , positive definite symmetric matrix B (0) , permissible error H 1 , H 2 ;


ļTo solve Quadratic Programing SUB-problem (QP), and ensure new lagrange multiplier vector and search direction s k ; O ĽTo ensure step factor D k , and solve the new generation point x(k 1) x(k) D k * s(k) ; (k 1)

ľTermination condition judgment: criterion convergence:

ci x k 1 H1 ,?i p ° ° k 1 k f x ® f x H2 ° k ° f x ¯

If situation meet the termination conditions, turn to step Ŀ; or to get correction matrix B (k) , k=k+1, then turn to step ļ; ĿThe current optimal individual can be output, algorithm end. The process of combinatorial optimization algorithm is shown as Fig2. 4. Simulation of PHEB parameters optimization 4.1. Parameter optimization simulation PHEB vehicle parameters can reference Ref. [8]. The initial values of optimization parameters in hybrid system is listed in Table 1. The weight of PHEB is set as full load. The time of a single CTBDC (China Transport Bus Driving Cycle) driving cycle is 1314 s. CTBDC driving cycle has been repeated 19 times as the objective condition, and target travel is 100 km. The working condition figure is shown in Fig.3. 4.2. Optimization results In this paper, optimization process of PHEB fuel economy and corresponding iterative are shown in Fig. 4 and Fig. 5. As Fig. 4 and Fig. 5.shown, PHEB fuel consumption of per hundred kilometer has shown a downward trend with the increase of the number of generation and a trend of convergence gradually. But it still can show a trend of fluctuating gradually, appears ups and downs. It embodies that the combinatorial optimization algorithm has strong ability on global search and local search. MIGA takes the global optimization with a wide range before 130 generations, and NLPQL takes the local optimization in a small range after 40 generations. In MIGA, the objective function has conducted a wide range of search optimization process, and gradually converge to a small range of stable value, to achieve the goal of a wide range of selection. Subsequently, In NLPQL optimization process, the objective function conducted corresponding optimization values on a small scale, then basically stable at the end of the near optimal value, which shows fast convergence speed, and the optimal value is stable. The corresponding curve and the change trend of four optimization parameter also can reflect the results that the combinatorial optimization algorithm has advantages in both global and local search. Before and after optimization, the contrast condition of optimization variables, PHEB fuel consumption and SOC final value are shown in table 2. In practical application, the convenience of components resources and the costs of component should be considered due to the limitation of components resources. Finally, the parameters combination which are close to optimization results is selected. As Fig.6.shown, fuel economy corresponded to the ultimately selected solution has increased by 5.94%, comparing with fuel economy before optimization, and PHEB fuel economy corresponded to optimization results has

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increased by 6.86% than fuel economy before optimization. Final value of SOC remains in the vicinity of 0.3 after optimization, confirming the stability and effectiveness of the hybrid optimization strategy. Take the individual T individualሺܺ ሺܺ݅݇ ሻԢ as the initial

Start

value of NLPQL, k=0;

Initialization parameters of MIGA

NLPQL Initialization of parameter ߙͲ , symmetric

MIGA

MIGA initial group (S), Island ( M)

solve Quadratic Programing SUB-problem (QP)ˈand ensure

ൌͳ

Fitness function ܷ݅ ൌ

matrix ‫ ܤ‬ሺͲሻ , permissible error ߝͳ ˈߝʹ Ǥ

ͳ ͳ൅ܿ൅݂ ሺܺ݅݇ ሻ

new lagrange multiplier vector ߣሺ൅ͳሻ and search direction‫ ݏ‬

to ܺ݅݇ ,

T ensure step factor ߙ݇ , and solve the new To

݂ሺܺ݅݇ ሻ is Objective function to individual i, ൌ ͳǡʹǡ‫ڄڄڄ‬ǡ .

iteration point ‫ ݔ‬ሺ൅ͳሻ ൌ ‫ ݔ‬ሺሻ ൅ ߙ݇ ‫ ݏ כ‬ሺሻ Ǣ Selection, crossover and

migration between ܿ݅ ൫ ሺ൅ͳሻ ൯ ൏ ߝͳ ǡ ൌ ͳǡʹǡ ‫ ڮ‬ǡ ൞ ห݂൫ ሺ൅ͳሻ ൯ െ ݂൫ ሺሻ ൯ห ൏ ߝʹ ȁ݂ሺ ሺሻ ሻȁ

different islands of MIGA; to get offspring ሺܺ݅݇ ሻԢ

൐ ͳʹͲ

No

ൌ൅ͳ

Yes

get

No

൅ ͳ;

Y Yes To get optimal value of object function

݂ሺܺ݅݇ ሻ

in group, and note the ܺ݅݇

Output search results

Fig. 2. Flow chart of Algorithm

Fig. 3. CTBDC driving cycle

Fig. 4. Fuel consumption

Fig .5. (a)Axle ratio (b)Engine peak power (c)Motor peak power (d)Battery capacity

Fig.6. (a)Fuel consumption (b)SOC

correction

matrix ‫ ܤ‬ሺሻ ǡ ൌ


Table 2. Contrast condition of optimization variables Parameters

PE _ peak /kw PM _ peak /kw ig Qb /A*h Fuel economy(L/100km) Final value of SOC

Before optimization 147 148 5.33 72 18.51 0.3024

After optimization 123.7 171.5 5.78 60 17.24 0.2982

Final value 128 166 5.71 60 17.41 0.2931

5. Conclusion In this paper, MIGA and NLPQL are combined to improve the efficiency and quality of optimization process. The combination algorithm makes up for the disadvantages of NLPQL in global optimization, and makes it more effective to optimize the parameters. Simulation experiments prove that PHEB fuel consumption per 100 km has down to 17.41 L from 18.51 Lˈand electricity consumption per 100 km remains the same level. The fuel economy of PHEB has been improved significantly, thus the validity of the combination algorithm for parameters optimization has been proved. 6. Copyright Authors keep full copyright over papers published in Energy Procedia Acknowledgements This work was supported by Beijing Institute of Technology in part. The authors would also like to thank the reviewers for their corrections and helpful suggestions. References [1] Mets K, Verschueren T, Haerick W, et al. Optimizing smart energy control strategies for plug-in hybrid electric vehicle charging[C]//Network Operations and Management Symposium Workshops (NOMS Wksps), 2010 IEEE/IFIP. Ieee, 2010: 293-299. [2] Wang Z, Huang B, Li W, et al. Particle swarm optimization for operational parameters of series hybrid electric vehicle[C]//Robotics and Biomimetics, 2006. ROBIO'06. IEEE International Conference on. IEEE, 2006: 682-688. [3] Li L, Zhang Y, Yang C, et al. Hybrid genetic algorithm-based optimization of powertrain and control parameters of plug-in hybrid electric bus[J]. Journal of the Franklin Institute, 2015, 352(3): 776-801. [4] Yan Y, Liu G, Chen J, et al. NLPQL of control rules for improving fuel economy of a parallel hydraulic hybrid bus[J]. International Journal of Modelling, Identification and Control, 2009, 7(4): 315-320. [5] Zhang B, Chen Z, Mi C, et al. Multi-objective parameter optimization of a series hybrid electric vehicle using evolutionary algorithms[C]//Vehicle Power and Propulsion Conference, 2009. VPPC'09. IEEE. IEEE, 2009: 921-925. [6] Peng J.K, He H, Xiong R. Rule based energy management strategy for a series–parallel plug-in hybrid electric bus optimized by dynamic programming[J]. Applied Energy, 2016.

Biography Hongwen He is currently a Professor with the National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology and a researcher with the Beijing Co-innovation Center for Electric Vehicles. His research interests include power battery modeling and simulation on electric vehicles, design, and control theory of the hybrid power train.

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