Optimal energy management of a hybrid electric powertrain system using improved particle swarm optimization

Applied Energy 160 (2015) 132–145

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Optimal energy management of a hybrid electric powertrain system using improved particle swarm optimization Syuan-Yi Chen a, Yi-Hsuan Hung b,⇑, Chien-Hsun Wu c, Siang-Ting Huang b a

Department of Electrical Engineering, National Taiwan Normal University, Taipei 106, Taiwan Department of Industrial Education, National Taiwan Normal University, Taipei 106, Taiwan c Department of Vehicle Engineering, National Formosa University, Yunlin 63201, Taiwan b

h i g h l i g h t s
Online sub-optimal energy management using IPSO.
A second-order HEV model with 5 major segments was built.
IPSO with equivalent-fuel fitness function using 5 particles.
Engine, rule-based control, PSO, IPSO and ECMS are compared.
Max. 31+% fuel economy and 56+% energy consumption improved.

a r t i c l e

i n f o

Article history: Received 25 May 2015 Received in revised form 27 August 2015 Accepted 10 September 2015

Keywords: Energy management Hybrid vehicle Particle swarm optimization (PSO) Online control

a b s t r a c t This study developed an online suboptimal energy management system by using improved particle swarm optimization (IPSO) for engine/motor hybrid electric vehicles. The vehicle was modeled on the basis of second-order dynamics, and featured five major segments: a battery, a spark ignition engine, a lithium battery, transmission and vehicle dynamics, and a driver model. To manage the power distribution of dual power sources, the IPSO was equipped with three inputs (rotational speed, battery state-of-charge, and demanded torque) and one output (power split ratio). Five steps were developed for IPSO: (1) initialization; (2) determination of the fitness function; (3) selection and memorization; (4) modification of position and velocity; and (5) a stopping rule. Equivalent fuel consumption by the engine and motor was used as the fitness function with five particles, and the IPSO-based vehicle control unit was completed and integrated with the vehicle simulator. To quantify the energy improvement of IPSO, a four-mode rule-based control (system ready, motor only, engine only, and hybrid modes) was designed according to the engine efficiency and rotational speed. A three-loop Equivalent Consumption Minimization Strategy (ECMS) was coded as the best case. The simulation results revealed that IPSO searches the optimal solution more efficiently than conventional PSO does. In two standard driving cycles, ECE and FTP, the improvements in the equivalent fuel consumption and energy consumption compared to baseline were (24.25%, 45.27%) and (31.85%, 56.41%), respectively, for the IPSO. The CO2 emission for all five cases (pure engine, rule-based, PSO, IPSO, ECMS) was compared. These results verify that IPSO performs outstandingly when applied to manage hybrid energy. Hardware-in-the-loop (HIL) implementation and a real vehicle test will be conducted in the near future. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction To reduce the increasing number of environmental concerns, green transportation has become increasingly used because of favorable characteristics such as high well-to-wheel efficiency, ⇑ Corresponding author at: 162, He-ping East Road, Section 1, Taipei 10610, Taiwan. Tel.: +886 2 77343377; fax: +886 2 23929449. E-mail address: [email protected] (Y.-H. Hung). http://dx.doi.org/10.1016/j.apenergy.2015.09.047 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

low (zero) pollutant emission, high output performance, and outstanding fuel economy [1,2]. The concept of hybridization has been widely applied in designs for hybrid electric vehicles (HEVs), plug-in HEVs (PHEVs), multi-energy source (fuel cell/battery/supercapacitor) electric vehicles, and in-wheel motors [3,4]. Hybridization maximizes the advantages of power (energy) sources and minimizes the inherent drawbacks. For instance, the powertrain in an HEV drives the vehicle with the motor to avoid the low-efficiency, high-pollutant operation of the engine, and

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133

Nomenclature Af Cd c1, c2, c3 E F G i FIT k m _ m N P RR r r1, r2, r3 T t V v x

a g gmin

area, m2 air drag coefficient acceleration factor energy, J force, N global solution for IPSO ith particle fitness function kth iteration for IPSO mass, g mass flow rate, g/s rotational speed, rpm power, W or population size reduction ratio radius, m uniform random number torque, N m time, s vehicle speed, kph or voltage, V particle velocity particle position power split ratio efficiency, % lower bound of particle position or velocity

powers the engine at a medium speed with favorable fuel economy to extend the mileage. The engine/motor hybrid mode optimizes the output performance (such as acceleration and gradeability) for heavy load or high-power requirements. In addition to the hybrid configurations, the control strategies of the vehicle control unit (VCU) are the keys for appropriately managing the power allocation and increasing the efficiency of dual power/energy sources. According to relevant literature, rulebased control, theoretical control, and rule/theoretical integration control are three main types of control strategies. Rule-based control is characterized by rapid rule design and easy implementation in VCUs. ‘‘If–Else” rules are based on the engineering intuition that the operation modes can be determined quickly [5]. In [6], fuzzy rules from the expert system were used to construct multidimensional tables for power management. However, these rules cannot be applied to manage complicated systems with various designed variables. By contrast, for theoretical energy management, dynamic programming (DP) is an absolute optimization method for determining the energy distribution during determined driving cycles [7]. The Pontryagin Minimum Principle (PMP), as another theoretical analysis tool for optimal energy management of HEVs, was compared to DP in [8] and was found that the solution was very close to that of DP. A genetic algorithm (GA) is another method for cooperating with the hybrid powertrain [9]. These methods can be used to calculate the optimal power management offline. However, when the results are implemented in VCUs, rule extraction is difficult. The third type, rule/theoretical integration control, is characterized by easy VCU implementation and provides suboptimal power (energy) management. Methods of this type typically include stochastic dynamic programming (SDP) and the equivalent consumption minimization strategy (ECMS). In SDP, the advantages of offline DP optimization are incorporated with the concept of probability distribution for online energy management [10]. In ECMS, the consumed electricity is regarded as the equivalent engine fuel, and the appropriate allocation of the hybrid power distribution is globally searched according to the minimized equivalent fuel [11]. Meanwhile, a proposed Approximate Pontryagin Minimization Principle was used to deal with the

gmax q r f

upper bound of particle position or velocity air density, kg/m3 learning factor inertia weight

Subscripts a actual BEST best solution b battery brk brake CO2 emission CO2 d demand or dimension of the particle e engine m motor oc open circuit roll rolling resistance t transmission tot total tq torque v vehicle w wheel wind wind force

sub-optimal energy management for plug-in PHEVs in [12]. On the basis of the aforementioned studies, this study employed another effective optimization method for the online control of hybrid powertrain, called improved particle swarm optimization (IPSO), which incorporates both online VCU strategies and theoretical calculation for power management optimization. PSO, a population-based optimization method, has attracted increasing attention because it is highly efficient and can search for global optimal solutions in scientific and engineering domains [13,14]. The PSO method is based on simulating the social behaviors and self-adaptive characteristics of animals. Compared with the GA, which no longer considers previous knowledge after each evolution, PSO can remember satisfactory solutions by using all particles [15]. Moreover, the evolution of the GA is based on reproduction, crossover, and mutation. Therefore, a high computation load is required. By contrast, because the unique information diffusion and interaction mechanisms of PSO are comparably simple, a low computational burden is required, and the PSO is suitable for use in various applications such as control [16,17], system identification [18], network optimization [19], and electric power systems [20]. The aforementioned studies have revealed that PSO is a rapid and reliable tool for designing an optimal strategy and can outperform other evolutionary algorithms. Many variants of PSO have been proposed to further enhance the particle learning and reasoning ability over the past decade [20–23]. An adaptive elite-based particle swarm optimization (EPSO) applied to VAR optimization in electric power systems was proposed in [20]. Mean value appending and particle pruning/cloning are two elite strategies used in EPSO, which facilitates the iterative process to coordinate between global and local searches. In [21], a self-adaptive learning-based PSO with inherent four velocity updating strategies was proposed to improve the universality and robustness of PSO. Moreover, a cellular automata mechanism was integrated in a cellular PSO to prevent the particle from being trapped in the local optimum [22]. Furthermore, the worst experience component is included in improved PSO (IPSO) to provide additional exploration capability.

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Only a few studies on PSO have been used for advanced vehicles. In [24], the fuel economy fitness function and PSO were used to design the control parameters of the plug-in HEV (PHEV). Without sacrifice of the driving performance, the fuel economy was improved. Optimal control parameters for different driving cycles and the various numbers of driving cycles have been studied. In [25], similar to in [24], for the real-time control of PHEVs, the artificial neural network method was used after the designed parameters in PSO were derived. In [26], PSO was used for optimizing the parameters of both the powertrain and the control strategy, thereby reducing the fuel consumption, exhaust emissions, and manufacturing costs of the HEV. In [27], PSO and GA were used for an optimal design that minimized the mass, cost, and occupied volume of the fuel cell and supercapacitor in a fuel cell HEV. According to these aforementioned studies, the main contributions of the present study can be summarized as follows: (1) IPSO was used instead of PSO to efficiently search the optimal control with fewer iteration numbers. (2) The energy-based improvement was discussed from the viewpoint of equivalent fuel economy and total energy consumption; the CO2 emission was also analyzed. (3) Totally five cases (traditional vehicle, rule-based, PSO, IPSO and ECMS) were compared in this study.

2. Powertrain architecture and system modeling 2.1. Hybrid powertrain configuration Fig. 1 illustrates the configuration of the hybrid powertrain. The driving cycle sends the demanded speed (Vd(t)) to the driver. According to comparison of Vd and the actual feedback speed (Va(t)), the demanded hybrid torque (Td(t)) is calculated and sent to the VCU. Combined with the transmission rotational speed (Nt(t)) and the battery state-of-charge (SOC), the two outputs, demanded engine torque (Te(t)) and motor torque (Tm(t)), are determined by IPSO and sent to the dual power sources to calculate the fuel economy and the battery current. The hybrid torque is then delivered to the transmission. On the other hand, two electric clutches, located between the power sources and the transmission, are controlled by the VCU with rule-based control for determining the operation mode (system ready, motor, engine, and hybrid). The hybrid torque is then transferred to the transmission and the vehicle dynamics for accelerating or decelerating the vehicle body. 2.2. System modeling Five major segments (subsystems and operation scenario) are modeled for the low-order hybrid vehicle dynamics. 2.2.1. Dual power sources Because of the rapid response compared to the vehicle mass dynamics, the spark ignition engine and the traction motor are assumed to be steady and are represented by a two-dimensional brake specific fuel consumption (BSFC) map and a twodimensional efficiency map. The engine BSFC (g/kW h) can be determined by the engine speed and torque as follows:

BSFCðtÞ ¼ f ðT e ðtÞ; Ne ðtÞÞ

ð1Þ

Table 2 Rule-based operation modes. Mode

Condition

Action

(1) (2) (3) (4)

Td = 0 Td > 0 Td > 0 Td > 0

Tm = 0, Te = 0 Tm = Td, Te = 0 Tm = 0, Te = Td Tm = 0.3Td, Te = 0.7Td

System ready Motor only Engine only Hybrid mode

& & & &

Nt = 0 0 < Nt < 2770 2400 6 N t < 3550 N t P 3100

Fig. 1. Engine/motor hybrid powertrain system with control.

Table 1 Parameter values of targeted vehicle model. Parameter

Value

Gtq Gbrk Kp KI RRt

100 1200 0.5 0.2 7.0 95% 0.36 1.6 m2 1.225 kg/m3 0.014 1460 kg 9.81 m/s2 0.27 m 80% 295 g/kW h

gt

Cd Af

q l

Mv g rw SOCint BSFC LHV Qmax

43,070 J/g 40 A h

Fig. 2. Movement of one particle in one iteration.

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The fuel rate (g/s) is then calculated:

_ e ðtÞ ¼ BSFCðtÞ=1000=3600  T e ðtÞNe ðtÞ m

ð2Þ

The motor efficiency is a function of the motor speed and torque and is represented as

gm ðtÞ ¼ f ðT m ðtÞ; Nm ðtÞÞ

ð3Þ

The efficiencies for charge and discharge conditions are assumed to be the same. 2.2.2. Lithium battery module First-order dynamics contribute to the battery model because of the slow variation of battery SOC, which can be calculated using the charge accumulation method. A lithium battery is modeled using a simple inner resistance model, in which the system is regarded as an equivalent circuit with an open circuit voltage (Voc) and an equivalent inner resistance (Rb) [28]. Therefore, the battery current and SOC can be formulated as follows:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ib ¼ ðV oc ðSOCÞ  V 2oc ðSOCÞ  4Rb ðSOCÞPb Þ=2Rb Z

ð4Þ

t

SOCðtÞ ¼ SOC init 

Ib ðtÞdt=Q max

ð5Þ

0

where Pb denotes the battery power; and SOCinit and Qmax are the initial battery SOC and maximal electric capacity of the battery, respectively. According to the charge and discharge conditions, separately, Pb can be evaluated from the motor power (Pm) as (up for discharge, down for charge):

Pb ¼ Pm =gm ¼ T m Nm =gm

ð6Þ

Pb ¼ Pm  gm ¼ T m Nm  gm

2.2.3. Longitudinal vehicle dynamics, driver model and the driving cycle A transmission is a pair of reduction gears with a reduction ratio (RRt) that properly modifies the transmission torque (Tt) and speed (Nt) according to the wheel torque (Tw) and rotational speed (Nw), respectively, as follows:

T w ðtÞ ¼ T t ðtÞ  RRt  gt ¼ ½T e ðtÞ þ T m ðtÞ  RRt  gt

ð7Þ

Nt ðtÞ ¼ Ne ¼ Nm ¼ Nw  RRt

ð8Þ

where gt is the efficiency of transmission. For the longitudinal vehicle dynamics, it can be formulated as follows:

mv dVðtÞ=dt ¼ T w =rw  F brk  F wind  F roll ¼ T w =rw  F brk  0:5C d qAf V 2  lmv g;

where Fbrk, Fwind and Froll represent the braking force, wind and rolling resistances, respectively. Symbols rw, Cd, q, Af, and l denote wheel radius, the air drag coefficient, air density, vehicle frontal area, and the rolling resistance coefficient, respectively. A driver model is selected as a proportional-integral (PI) control, in which the input is the vehicle speed error between Vd and Va, and the output is the demanded hybrid torque:

  Z t T d ðtÞ ¼ Gtq K p ðV d ðtÞ  V a ðtÞÞ þ K I ðV d ðtÞ  V a ðtÞÞdt

Particle 2

Particle n

α1

α2

αn

Initialization

Determination of Fitness Function

Selection and Memorization Update Local Best, Local Worst & Global Best Modification of Velocity and Position Update Velocity & Position

No

where Gtq, Kp, and KI represent a constant gain for the traction torque, the proportional gain, and the integral gain, respectively. If the value of Td is negative, then the vehicle is in the braking mode, and the braking force can be written as:

A driving cycle is a standard test scenario that the demanded vehicle speed with respect to time is fixed (Vd = Vd(t)). Therefore, specific driving cycles are used for evaluating the output performance (pollutant emission, fuel consumption, electricity usage, energy consumption, etc.) of specific types of vehicles (light-duty vehicles, trucks, motorcycles, EVs). In this research, two standard driving cycles: ECE and FTP are selected for the target vehicle. The ECE cycle is for low-speed (torque) test with more steady-state (constant speed) conditions, while FTP cycle is for high-speed (torque) test with more transient conditions. The target vehicle was based on our previous study in [29]. It is a 1500 kg four-wheel vehicle modified from a commercial PHEV: Chevrolet Volt. Therefore, the selection of key components as well as the parameter values was reasonable. The parameter values are listed in Table 1.

Table 3 Parameter values of IPSO control. Parameter

Value

P

5 1 0.5 0.5 0.5 1 0 1 1 30 1 0.005

w

Yes

c1 c2 c3

Update Power Split Ratio α Fig. 3. IPSO procedure.

ð11Þ

0

Finished?

Update Controlled Variable

ð10Þ

0

  Z t F brk ðtÞ ¼ Gbrk K p ðV d ðtÞ  V a ðtÞÞ þ K I ðV d ðtÞ  V a ðtÞÞdt Particle 1

ð9Þ

gamax gamin gvmax gvmin kmax f

r

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Fig. 4. Simulator of engine/motor hybrid powertrains with vehicle control unit.

3. Energy management control strategies 3.1. Energy management using baseline control strategy The ‘‘If–Else” baseline control strategy consists of four modes. The designed philosophy is to operate the motor at a low rotational speed to achieve high output torque (favorable vehicle acceleration). The engine activates at a medium speed to extend traveling mileage. In addition, the engine operates efficiently in this zone (with higher BSFC). At a high rotational speed, when the maximal engine torque drops, the motor functions as a power-assist source, and the system enters hybrid mode. Table 2 presents a summary of the four modes of If–Else rules. According to the concept of thermostat control, to avoid frequent power source switching, the rotational speeds for the mode switch are of different values. For instance, when the mode switches from ‘‘motor only” to ‘‘engine only,” the switch timing is N t P 2770. However, to switch from the engine-only mode to the motor-only mode, the switch speed is 2400 rpm.

3.2.1. Design of power split ratio The power split ratio, a, is the controlled variable for energy management, which is defined as follows:

ð12Þ

According to Eq. (8), because the engine rotational speed is the same as the transmission speed, the power split ratio is the same as the torque split ratio. Therefore, the demanded engine torque and demanded motor torque can be rewritten as

T e ¼ a  T d ; T m ¼ ð1  aÞ  T d

v di ðk þ 1Þ ¼ fv di ðkÞ þ c1  r1  ðPdbest;i  xdi ðkÞÞ þ c2  r2  ðGdbest  xdi ðkÞÞ þ c3  r3  ðxdi ðkÞ  Pdworst;i Þ

3.2. Energy management using IPSO control strategy

a  Pe =Pd ¼ T e Ne =T d Nt ¼ T e =T d

3.2.2. Basic principle of improved particle swarm optimization PSO, an evolutionary optimization method used for minimizing an objective, reflects the behavior of a flock of flying birds or a school of fish. A particle swarm optimizer composed a population of particles and iteratively updates the empirical information regarding a search space. The population consists of many individuals that represent potential solutions to a problem and are modeled as particles moving in a w-dimensional search space. In a general PSO algorithm, each particle adjusts its position according to its experience and the experiences of its neighbors, including the current velocity, position, and the most favorable previous position. To improve the convergent efficiency of PSO, IPSO includes the worst experience of each particle to obtain additional exploration capacity for the swarm [23]. Because the particle remembers its worst experience, it can explore the search space more effectively to identify the promising solution region. Thus, the position and velocity of each particle are updated using the IPSO algorithm as follows [18,23]:

ð13Þ

xdi ðk þ 1Þ ¼ xdi ðkÞ þ rv di ðk þ 1Þ

ð14Þ ð15Þ

where v di ðkÞ is the current velocity of the ith particle, i = 1, . . ., P, in which P is the population size; k represents the kth iteration; superscript d = 1, . . ., w is the dimensions of the particle; Pbest,i is the best previous position of the ith particle; Pworst,i is the worst previous position of the ith particle; Gbest is the best previous position among all the particles in the swarm; xdi ðkÞ is the current position of the ith particle; c1, c2, and c3 are the acceleration factors; r1, r2, and r3 are the uniform random numbers between 0 to 1; and r is the learning factor. The designed inertia weight f is used to copy the previously

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Fig. 5. Iterative performances of PSO, IPSO and ECMS during: (a) ECE driving cycle at the 20th second and (b) FTP driving cycle at the 40th second.

updated feature to the next iteration. If a greater f is selected, then the preceding v di ðkÞ strongly affects v di ðk þ 1Þ. Fig. 2 illustrates the moving principle of particles in one iteration. Note that the PSO algorithm in Eq. (14) is without the last term (effect of worst case) on the right side. 3.2.3. Procedure of energy management achieved using improved particle swarm optimization To optimize energy management of an engine/motor hybrid electric powertrain system, the IPSO algorithm was adopted in this study to adjust the power split ratio a online for energy optimiza-

tion. The procedure of the IPSO algorithm (Fig. 3) is described as follows [18,23]: (1) Initialization: The initial position xdi and velocity v di for the particles, which are the potential optimal power split ratio a and its variation, respectively, are randomly generated. Because only one dimension was considered in this study, the superscript d is omitted here for easy representation. Therefore, the initial position xdi was considered as ai in this study. The initial position ai and its velocity vi are randomly generated as follows:

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Speed (km/hr)

ECE driving cycle 100

Vdemamded

50 0

0

20

40

60

80

100

Vactual

120

140

160

180

200

120

140

160

180

200

140

160

180

200

140

160

180

200

140

160

180

200

140

160

180

200

Mode (n)

Engine only 4 2 0

0

20

40

60

80

100

Mode (n)

Rule-based Control 4 2 0

0

20

40

60

80

100

120

Alpha (%)

PSO Control 1 0.5 0

0

20

40

60

80

100

120

Alpha (%)

IPSO Control 1 0.5 0

0

20

40

60

80

100

120

Alpha (%)

ECMS Control 1 0.5 0

0

20

40

60

80

100

120

Elapsed Time (s) Fig. 6. Speed profiles, mode of rule-based control, and a of PSO, IPSO, and ECMS control during ECE driving cycle at SOCinit = 80%.

Torque (Nm)

Rule-based Control 80 Tv

60

Te

40

T

m

20 0

Torque (Nm)

0

20

40

60

80

100

120

140

160

180

200

IPSO Control

80

Tv

60

Te

40

Tm

20 0

SOCb (%)

80

0

20

40

60

80

100

120

140

160

180

200

Rule-based Control IPSO Control

79.5

79 0

20

40

60

80

100

120

140

160

Elapsed Time (s) Fig. 7. Torque and battery SOC of baseline and IPSO control during ECE driving cycle.

180

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139

engine fuel consumption rate is calculated according to Eq. _ b Þ is calcu(2), whereas the battery fuel consumption rate ðm lated after the average BSFC of the engine and battery power are obtained using Eq. (6):

_ b ¼ BSFC  Pb =3600=1000 m

ð20Þ

where BSFC is the average BSFC of the engine for battery power. Again in Eq. (18), W(SOC) is a weighting function related to the battery SOC. When the SOC value is high, W (SOC) decreases to increase the period of electricity usage, and vice versa. W(SOC) can balance the SOC throughout the entire driving cycle. The effectiveness of IPSO is demonstrated by the gradual increase in the fitness function during the optimization process. In other words, only the optimal power split ratio can result in the maximum fitness value. The equivalent fuel consumption as shown in Eq. (18) is the inverse of the sum of engine fuel consumption and battery power consumption. Thus, the higher equivalent fuel consumption results in lower fitness value in which the highest one and the lowest one during the optimization process can be considered as the best and the worst own positions of the specified particle, respectively. Since each particle moves from its initial position to promising positions based on its velocity, its best own position, its worst own position, and the particle swarm’s global best position, the optimal power split ratio which can obtain the highest fitness value, i.e. the lowest equivalent fuel consumption can be found after complete evolution.

Fig. 8. Operation points for (a) engine and (b) motor during ECE driving cycle.

ai  U½gamin ; gamax 

ð16Þ

v i  U½gvmin ; gvmax 

ð17Þ

where U½gmin ; gmax  designates the outcome of uniformly distributed random variables within the given lower and upper bounded values, gmin and gmax, respectively. (2) Determination of fitness function: To improve the system efficiency, a suitable fitness function was designed to calculate the fitness value of the particle. The reciprocal of equiv_ eq Þ principally based on [11] was alent fuel consumption ðm used for calculating the fitness value because the maximum fitness value (lowest equivalent fuel consumption) is defined as the optimal solution. It is formulated as

_ eq þ b ¼ 1=½m _ e ðT e ; Ne Þ þ WðSOCÞm _ b þ b FIT ¼ 1=m

ð18Þ

where FIT is the fitness value. To avoid an impractical phenomenon from occurring, constraints must be provided by a penalty value b. If any of the two conditions is violated, then b is set as a high negative value (i.e., b = 106); otherwise, b = 0.

0 6 T e < T e;max ðNÞ; 0 6 T m < T m;max ðNÞ

ð19Þ

Te and Tm are evaluated according to Eqs. (12) and (13). When the value of b is considered, the optimal a can be searched without violating the physical constraints. The

(3) Selection and memorization: Each ai memorizes its corresponding fitness value and chooses the best maximum value, Pbesti. Moreover, the best fitness value among all Pbesti is set as the global best, Gbest. Furthermore, each ai is set directly as Pbesti in the first iteration. (4) Modification of velocity and position: The modification of each ai is based on Eqs. (14) and (15). (5) Stopping rule: Steps 2–4 are repeated until the best fitness value for the Gbest is obviously improved or a set count of the generation is reached. The solution with the highest fitness value is chosen as the optimal power slip ratio of the energy management system. Note that in this study, the ECMS was coded with three-for-loop structure for the three parameters (SOC, xt, and Pd). It is regarded as the optimal target due to the offline global search. After the same process in [3,4], a three-dimensional table for a can be derived. Therefore, the comparison can be conducted. 4. Simulation results and discussion 4.1. Simulator and settings The simulator was constructed on the MATLAB/Simulink platform (Fig. 4). The blocks described in Section 2 were interconnected by transition lines. The fixed sampling time is 0.1 s, and the numerical method used was the Runge–Kutta method. For the VCU portion, the parameter values of IPSO control described in Sections 3.2.2 and 3.2.3 are listed in Table 3; these values can be used in Eqs. (14)–(17). It was coded as an S-function at the rear of the driver model. 4.2. Comparison of baseline, PSO, and IPSO controls Compared with conventional PSO, the worst position of the particle is added in IPSO to achieve a faster iterative process and a more effective search space (last term in Eq. (14)). The different

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Speed (km/hr)

FTP driving cycle 150 100 50 0

Vdemamded 0

200

400

600

800

Vactual

1000

1200

1400

1000

1200

1400

1000

1200

1400

1000

1200

1400

1000

1200

1400

1000

1200

1400

Mode (n)

Engine only 4 2 0

0

200

400

600

800

Mode (n)

Rule-based Control 4 2 0

0

200

400

600

800

Alpha (%)

PSO Control 1 0.5 0

0

200

400

600

800

Alpha (%)

IPSO Control 1 0.5 0

0

200

400

600

800

Alpha (%)

ECMS Control 1 0.5 0

0

200

400

600

800

Elapsed Time (s) Fig. 9. Speed profiles, mode of rule-based control, and a of PSO, IPSO, and ECMS control during FTP driving cycle at SOCinit = 80%.

performances of PSO and IPSO were investigated, and the best position of each particle Pbest (P1–P5), the best position of all particles Gbest, and the fitness value of best position Gbset during ECE and FTP driving cycles at a specified time are shown in Fig. 5. Meanwhile, the solutions from ECMS were added as the optimal targets. To compare the different methods fairly, all five particles had the same initial positions, a1–5 = [0.32, 0.25, 0.15, 0.63, 0.87], and initial velocities, v1–5 = [0.65, 0.34, 0.67, 0.21, 0.76]. At the 20th second during the ECE driving cycle (Fig. 5(a)) and at the 40th second during the FTP driving cycle (Fig. 5(b)), where the situation is at a constant vehicle speed (power), the best position Pbest of each particle varies in the optimization process to search for the global best solution during the iterations. Moreover, because of the additional consideration of the worst position in IPSO, the number of required iterations can be mitigated and a higher fitness values can be determined effectively. For example, the fitness functions converge in a higher value (15.5329) at the 10th iteration and in a lower value (15.5315) at the 19th iteration when IPSO and PSO are used, respectively (Fig. 5(a)). Similarly, the fitness functions converge in a higher value (7.5146) at the 10th iteration and in a lower value (7.5136) at the 11th iteration when IPSO and PSO are used, respectively (Fig. 5(b)). Therefore, compared with the conventional PSO method, the IPSO method yields swifter and more stable convergence performance when searching for the optimal solution. Hence, IPSO was used for the following simulation. Moreover, as the solution of ECMS is regarded as the optimal target, it shows that both the best solutions of PSO and IPSO move toward the ECMS solution.

Figs. 6–8 present the simulation results during the ECE driving cycle at SOCinit = 80%. In Fig. 6, the first row shows the standard driving cycle for the testing scenario. Because of the appropriate selections of PI control gains for the driver model in Eqs. (10) and (11), the speed tracking was excellent (within ±0.5 kph), which implies that the following simulation results are convincible. The second row shows the case of traditional vehicle, which only used the engine (mode 3). At the third row for rule-based control at an idle condition (Td = 0), the operation mode was 1, according to Table 2. During acceleration, the operation mode switches to mode 2 (motor only) and to mode 3 (engine only) when a larger Vd (medium speed) is required. The fourth row shows the PSO simulation results based on the fitness function in Eq. (18) During acceleration, a increases, indicating that the engine provides the main power, according to Eqs. (12) and (13), to save electricity. During deceleration, since Td (or Pd) is zero, the value of searched a will not influence the energy distribution. However, in stable (constant _ e . The fifth speed) areas or when Pd is low, a drops to decrease m row is for the five-step IPSO procedure. It shows that the simulation profile is similar to that of PSO. However, the simulation speed is faster according to Fig. 5. The last row is for ECMS, which is regarded as the optimal solution for a. It indicates that the profile is similar to those of PSO and IPSO. Nevertheless, at the deceleration period with Td = 0 (or Pd = 0), a might be different with the reason as mentioned above. Rows 1 and 2 in Fig. 7 show a comparison of torques in baseline and IPSO cases. The motor primarily activates in the low-tomedium speed area, and the engine only activates in the high-

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Fig. 10. (a) Torque and battery SOC of baseline and IPSO control during FTP driving cycle, and (b) zoom-in of first 300 s.

speed area. By contrast, in the IPSO case, the engine is in charge of the high torque (power) area, and the motor activates to reduce the engine fuel consumption in the constant speed areas. After a 195-s simulation, the difference of battery SOCs between these cases was minimal. Fig. 8(a) illustrates the efficient operation of engine during the IPSO control. During the rule-based control, the engine operated in an inefficient area, in which the BSFC was mostly within 350–500 g/kW h. Under IPSO control, the engine operated in a more efficient area, in which the BSFC was approximately within 270–400 g/kW h. In Fig. 8(b), the operation points of the motor for IPSO were in similar locations as those in the baseline case. Therefore, by combining the operation points of dual power sources, IPSO conserves more energy.

Figs. 9–11 demonstrate the simulation results obtained during the FTP driving cycle. In Fig. 9, frequent acceleration and deceleration periods with a higher Td are apparent. Similar to Fig. 6, the driver model precisely tracks the vehicle speed within ±0.5 kph. The second row represents the traditional vehicle with only mode 3: engine mode. The third row shows the variation of the four mode operation under baseline control. According to Table 1, a similar tendency is apparent between the mode number and Vd. The mode reaches 4 (hybrid mode) at a high speed area. The fourth and fifth rows depict the dynamics of a in the online calculation of PSO and the five-step IPSO, and reveals a sharper variation compared with the profile of the ECE driving cycle. Meanwhile, it also indicates that the operation points of the engine and motor vary more

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Fig. 10(a) shows a comparison of the torques under baseline and IPSO control. Similar to the results shown in Fig. 7, the motor activates in the low-to-medium speed area, and the engine solely operates in the high-speed area under baseline control (see the first 300 s in Fig. 10(b)). The engine under IPSO control is responsible for the high torque (power) area. After a 1370-s simulation, the battery SOC between these cases was nearly 2%, indicating that baseline control conserves more electricity. However, fuel consumption should be considered for system efficiency. According to the results shown in Fig. 11, the engine still operates in the inefficient area under rule-based control, and the motor operates more extended in the high-speed area. Under IPSO control, the engine operates in the efficient zone; however, the motor operation points are located more in the area with comparatively low efficiency (80–85%). Therefore, the SOC drops more than that under baseline control.

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4.3. Fuel economy, energy improvement and CO2 emission

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This section discusses the improvement in fuel economy and energy consumption for five cases (engine-only, rule-based, PSO, IPSO, and ECMS), as well as the CO2 emission. Fig. 12 shows the accumulated equivalent fuel consumption in terms of the fitness function expressed in Eq. (18) during the ECE driving cycle, that Rt _ eq ðtÞdt. For the traditional vehicle case (engine-only), is, meq ¼ 0 m

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the gasoline is the only choice for driving the vehicle so that the equivalent fuel usage is the highest. For rule-based control, initially, during the driving cycle, because the rule-based control was in mode 1 (the motor only mode) and the high initial SOC was 80% with a smaller value of W(SOC), the equivalent fuel was less. Therefore, the two profiles of these control strategies vary closely. After the 140th second, because the engine mode was switched on under rule-based control, when the IPSO control was in hybrid mode, the difference in meq gradually increased until the simulation ended. For the comparison with PSO and ECMS, since the profiles of a are similar (especially at the high power (energy) areas), the profiles of accumulated meq are similar. The energy consumption in five cases was defined as the summation of the theoretical heat stored in the gasoline and the energy drawn from the battery set (Eb):

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Fig. 11. Operation points for (a) engine and (b) motor during FTP driving cycle.

Fuel Consump. (g)

rapidly to achieve more satisfactory energy consumption. The last row was the profile of the ECMS. Similar to ECE case, the profile compared to PSO and IPSO was different due to the zero or low power (torque) requirement. The value of a will be different due to the slight variation of fitness function.

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where LHV represents the low heating value of the fuel. Fig. 12(b) shows that the energy consumption under engine-only mode is still the highest value due to the sole power source. Comparing IPSO and rule-based cases, Etot for IPSO was slightly higher than that under rule-based control before 140th second. This result is because the _ eq and not for Etot. However, after optimization was aimed for m the 140th second, the consumed energy greatly increased because more fuel was consumed under rule-based control. Comparing IPSO to PSO and ECMS, similar to the variation of meq, the final values of energy consumption are more closed than those of engine-only and rule-based cases. Fig. 13 shows the simulation results obtained during the FTP driving cycle. In Fig. 13(a), the demanded speed (power) (Fig. 9) is higher than that in the ECE cycle, indicating that more equivalent and energy are required. Similar to Fig. 12, the engine-only case consumed more equivalent fuel and energy. For rule-based case compared to IPSO, from Table 1, more time is required for mode 3 (engine only) and mode 4 (hybrid). Hence, the difference of meq becomes greater after the 50th second. Furthermore, for the accumulated energy consumption in Fig. 13(b), the profile has the proportional tendency to meq. The difference of the total energy between these two controls gradually increased. Comparing profiles of meq of PSO and ECMS to IPSO, similar to Fig. 12, the three curves are closer than those of engine-only and rule-based case. And, the profiles of the total energy consumption are similar. Table 4 summarizes the energy improvement with five cases. During the ECE cycle, the final values of meq (g) under engine only, rule-based, PSO, IPSO, ECMS were: [50.34, 37.91, 28.99, 27.96, 28.13]. Comparing rule-based control and IPSO, the fuel consumption improvement was 24.25%. It is interesting that meq for ECMS is slightly higher than that of IPSO. It is because the learning factor (r) in Eq. (15) of optimal search (a) for IPSO is only 0.005 (see Table 3). Contrarily, the discretization increment of parameters in

ECMS was limited due to the system memory. For the accumulated energy consumption, the values of Etot (kJ) under five cases were: [675.47, 611.09, 441.56, 416.47, 381.35]. The energy improvement of IPSO compared to rule-based case significantly increased (45.27%). During the FTP driving cycle, the accumulated meq under rule-based (IPSO) control was 611 g (416 g). The fuel consumption improvement was 31.85%, greater that the improvement during the ECE cycle because of the longer operation period for the engine during the FTP cycle. Similarly, for the accumulated energy consumption, the Etot under rule-based (IPSO) control was 21,512 kJ (9376 kJ). The energy improvement increased to 56.41%, indicating that more than half of the energy consumed under rule-based control was conserved under IPSO control. The superior fuel and energy conservation confirms that the proposed IPSO can effectively manage the energy flow of hybrid powertrains. Another critical issue to evaluate the vehicle output performance is the pollutant emission, especially for the CO2. In this study, CO2 emission is regarded as a two-dimensional T-N table _ CO2 ðT e ; xe ÞÞ which was integrated with the engine model _ CO2 ¼ m ðm described in Section 2.2.1. Fig. 14 illustrates the comparison of CO2 emission during ECE cycle and FTP cycle under engine only, rulebased, PSO, IPSO, and ECMS control. The values of CO2 emission (g) for ECE cycle were sequentially listed as: [78.48, 21.60, 18.56, 18.20, 14.36], while CO2 emission for FTP cycle were sequentially listed as: [823.01, 539.41, 288.83, 212.14, 135.68]. It shows that the CO2 production at ECMS case is with the smallest value, then IPSO, PSO, finally rule-based control compared to the engine-only case under both driving cycles. It is interesting that due to EV mode of rule-based control approximately before the 130th second, the CO2 emission is zero. After that, the engine mode largely increases the CO2 emission. To evaluate the online calculation of VCU, the operation time for both driving cycles and one iteration to derive a were recorded.

Table 4 Equivalent fuel and energy improvement during two driving cycles. Equivalent fuel consumption (g)

Engine Rule-based PSO IPSO ECMS

Energy consumption (kJ)

Energy improvement compared to baseline case (%)

ECE

FTP

ECE

FTP

ECE

FTP

50.34 36.91 28.99 27.96 28.13

675.47 611.09 441.56 416.47 381.35

2168.1 1014.60 608.73 555.32 515.22

29,093 21,512 12,076 9376 6729

36.39/113.7 – 21.45/40.00 24.25/45.27 23.80/49.22

10.54/35.24 – 27.74/43.86 31.85/56.41 37.60/68.72

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The comparison between the theoretical analysis: DP or Pontryagin Minimum Principle will be conducted. A HIL platform for VCU designs and a real vehicle test will be implemented in future studies.

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Acknowledgements

40 30

The authors would like to thank the Ministry of Science and Technology of the Republic of China, Taiwan, for financial support for this research under Contract No. 103-2221-E-003-022- and MOST 103-2218-E-150-002-MY2.

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Elapsed Time (s) Fig. 14. CO2 emission during (a) ECE driving cycle and (b) FTP driving cycle under engine only, rule-based, PSO, IPSO, and ECMS control.

The simulation was conducted in a PC with an Intel Core i7-3770 3.4 GHz CPU and 8 GB RAM. For ECE cycle, 43 s was recorded in real time for the 195 s test with 1 Hz control frequency; and 296 s in real time for the 1370 s FTP driving cycle with 1 Hz control frequency. For one iteration to determine a, it spent only 0.13 s. In other words, the power split ratio can be determined to control the dual power sources for at least 7 times in one second. It proves that the IPSO for VCU will be implemented in the HIL and a real hybrid vehicle in the future. 5. Conclusion In this study, online hybrid energy management was implemented using an IPSO approach for HEVs. A control-oriented vehicle model of five major segments was constructed first, while the five-step IPSO was then developed and integrated with the vehicle model. The industrial and academic contributions are summarized as follows: (1) Four-mode rule-based control: The modes of the rule-based control are system ready, motor only, engine only, and hybrid mode; these modes are determined according to the engine’s rotational speed. The demanded engine torque and motor torque are the two outputs. (2) Energy improvement of IPSO: IPSO searches for the optimal solution more quickly than does the PSO. During ECE and FTP driving cycles, the improvements in equivalent fuel consumption and energy consumption are [24.25%, 45.27%] and [31.85%, 56.41%], respectively. This confirms that the IPSO control performs outstandingly for hybrid powertrains. (3) Five case comparisons: detailed comparisons including the energy management control, equivalent fuel consumption, have been simulated for the cases of traditional vehicle, rule-based, PSO, IPSO and ECMS.

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