optimisation-based energy management of series hybrid ... · results of the proposed energy...

Int. J. Alternative Propulsion, Vol. 1, No. 1, 2006 79

Copyright © 2006 Inderscience Enterprises Ltd.

Optimisation-based energy management of series hybrid vehicles considering transient behaviour

B. He and M. Yang* State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, PR China E-mail: [email protected] E-mail: [email protected] *Corresponding author

Abstract: This paper presents a real-time implementable optimisation-based energy management strategy for a series Hybrid Electric Vehicle (HEV). On the basis of the introduction of a transient fuel consumption model of the diesel Auxiliary Power Unit (APU) and a battery equivalent fuel consumption model incorporating a charge-sustaining strategy, a novel Semi-Global Optimisation (SGO) problem is formulated to minimise the vehicle fuel consumption, which is defined over a relatively shorter time horizon characterised by the quasi-steady-state time constant of the diesel engine. A two-stage real-time optimisation algorithm is developed to solve this problem, including the precomputed Static Instantaneous Optimisation (SIO) to obtain the basic power distribution map, and the online adaptive dynamic compensation optimisation considering the transient loss of the diesel APU. Computer simulation work is carried out to evaluate the proposed energy management strategy.

Keywords: series hybrid vehicles; energy management; fuel economy; optimisation; optimal control.

Reference to this paper should be made as follows: He, B. and Yang, M. (2006) ‘Optimisation-based energy management of series hybrid vehicles considering transient behaviour’, Int. J. Alternative Propulsion, Vol. 1, No. 1, pp.79–96.

Biographical notes: B. He received his BS in Automotive Engineering from Tsinghua University, China, in 2001. Currently, he is a PhD candidate in Power Mechanical Engineering at Tsinghua University. His research interests are modelling and control of hybrid vehicles.

M. Yang received his PhD in Mechanical Engineering from the Technical University of Denmark, Denmark, in 1993. Currently, he is a Professor with the Department of Automotive Engineering, Tsinghua University. His research interests include new energy vehicles, automotive power trains, engine control systems, transportation energy strategy and policy.

80 B. He and M. Yang

1 Introduction

The growing worldwide concern about environmental and energy issues caused by transportation has brought about an increased demand for cleaner and more energy efficient vehicles. As a near-term solution, series Hybrid Electric Vehicles (HEVs) have attracted much attention from the automotive companies and research institutes, especially for heavy-duty applications. Reports in Kelly and Eudy (2000) show that most of the heavy-duty hybrid vehicles are in series designs.

The series HEV investigated in this paper has two power sources: the primary power source is an efficient diesel Auxiliary Power Unit (APU) while the assistant power source is a NiMH type battery with high power-to-energy ratio. This hybrid configuration raises the question of coordinating the operation of the hybrid power sources, which is usually called energy management strategy, to achieve system-level performance objectives such as vehicle high fuel economy and polluting emissions restriction while satisfying the performance constraints.

In recent years, many studies have been carried out in the field of energy management strategies for HEVs. Generally, control strategies proposed in the literature can be categorised into the following three types: rule-based strategy (Andersson et al., 1999; Aoyagi et al., 2001; Jalil et al., 1997), instantaneous optimisation strategy (Guezennec et al., 2003; Oh et al., 2004; Paganelli et al., 2002) and global optimisation strategy (Brahma et al., 2000; Lin et al., 2003). Rule-based strategy is based on heuristics and can be easily implemented for the in-vehicle application. It can be further improved by extracting near-optimal rules from the optimisation strategies (Lin et al., 2003). Instantaneous optimisation strategy weighs the electrical energy consumption of the battery using the equivalent fuel consumption concept. A static optimal power distribution can be obtained from the minimisation of the system instantaneous fuel consumption. Global optimisation strategy minimises a cost function over a whole driving cycle. Dynamic programming technique is commonly used for its numerical solution. Because it is based on a priori knowledge of the future driving conditions, in general, it could not be applied in real time. However, it can be used as a benchmark for the evaluation of other control strategies.

These control strategies have been investigated for both series hybrid and parallel hybrid vehicles, which shows that there are many common characteristics of energy management strategies for hybrid vehicles. However, still there are some special characteristics for different type hybrid vehicles. Compared to the parallel hybrid, the series hybrid shields the engine from the transient operating conditions associated with the delivery of power directly to the vehicle. This originates the idea of the simple On/Off control strategy (Andersson et al., 1999; Jalil et al., 1997), where the engine operates in an optimum point, and it is shut off or put to idling when the battery State-of-Charge (SOC) reaches a maximum charge level. But test results show that driver power-dependent optimised rule-based strategy can achieve much improvement on fuel economy compared to the On/Off strategy (Abthoff et al., 1998); hence, how to optimise the engine operation in view of system-level optimisation is essential to take full advantage of this special characteristic of series hybrid. In Barsali et al. (2004), from the starting point of On/Off strategy, an optimisation strategy was proposed, considering that the diesel APU power is composed of an average value and a time-varying instantaneous value. Analytical solution to the optimisation problem was obtained based on a very simple battery model.

Optimisation-based energy management of series hybrid vehicles 81

On the other hand, engine transient operation loss was seldom explicitly considered in the optimisation-based energy management strategies, which at the most was roughly considered as a constraint to the change rate of engine power (Guezennec et al., 2003). Recent studies in Pelkmans et al. (1998) and Lindgren (2005) have shown that engine transient operation can be important contributors to the vehicle fuel economy and exhaust emissions.

In this paper, we present a novel optimisation-based energy management strategy for the series HEVs. It’s based on a transient fuel consumption model of the diesel APU and an equivalent fuel consumption model of the battery that incorporates a charge-sustaining strategy and gives no assumption of the average efficiencies of the battery. Different from the instantaneous and global optimisation strategies, the optimisation problem is formulated over a relatively shorter time horizon characterised by the quasi-steady-state time constant of the diesel engine. To some extent, it can be called a Semi-Global Optimisation (SGO) strategy. To obtain a real-time implementable solution to this problem, a two-stage optimisation procedure is proposed. A preliminary solution is obtained from the Static Instantaneous Optimisation (SIO) and it’s further adaptively filtered to optimise the diesel APU operation using the dynamic compensation optimisation. Simulation tests are done to validate the proposed energy management strategy.

The rest of this paper is organised as follows: the system model is described in Section 2. In Section 3, a SGO problem of energy management is formulated and its real-time solution strategy is presented. Section 4 shows the simulation results of the proposed energy management strategy. Finally, conclusions are given in Section 5.

2 System modelling

Figure 1 presents a schematic representation of the series hybrid power train considered in this study. Two power sources are combined to provide traction power for the AC induction motor. One is the diesel APU that consists of diesel engine, synchronous generator and three-phase diode rectifier. The other one is the NiMH type battery characterised by its high power-to-energy ratio. The series hybrid vehicle uses a simple two-speed manual transmission, which is connected with a final reduction gear. A two-level hierarchical architecture is used for the vehicle control system. On the regulatory level, each subcontroller regulates its corresponding power train component. The supervisory controller on the supervisory level provides the regulatory level set points based on the driver commands and feedback signals of the power train components. It mainly concerns the energy management of hybrid power sources and drive force control of the traction motor.

In this paper, we focus on the supervisory energy management of hybrid power sources. For the development of our model-based optimal strategy and also its simulation validation, a suitable physical model of the overall system is essential. Different from the modelling approach for the controller design on the regulatory level, which usually involves a detailed analysis of the physical process, for the upper level supervisory controller design, the system model is commonly based on a quasi-static approach (Rizzoni et al., 1999). The details are given below.


Figure 1 Schematic representation of the series HEV

2.1 Diesel APU model

The diesel APU is a complex non-linear integrated system of mechanical, electrical and power-electronic devices. Its main dynamics are ignored in this study. The system fuel consumption model is our focus.

The static specific fuel consumption of the diesel engine and the power efficiency of the generator-rectifier sets are both functions of the engine speed and the engine output torque, which are denoted as τe ( ),C n, τg ( ),h n, respectively. In the series hybrid

vehicles, the engine speed is decoupled from the vehicle speed, so it can operate along an optimal fuel consumption curve. This optimal fuel consumption curve can be obtained from the solution of the optimisation problem given below:

( )s apu n,

apug

e,max

min

( )

0

e

g

C (n, )C P

(n, )

n n, P

n P

τ

τη τ

τ η ττ

=

× × =

≤ × ≤

(1)

where Papu is the output power of the diesel APU, Cs is the best specific fuel consumption of the diesel APU and Pe,max is the maximum engine power. The optimal hourly fuel consumption curve Capu is apu apu s apu apu( ) = ( )C P C P P .

Owing to the lack of test data, η τg ( , )n is assumed to be 1.0. Then the optimal fuel

consumption can be well interpolated by a quadratic function with the interpolating parameters c0, c1 and c2.

( ) = 2apu apu 0 1 apu 2 apu+ +C P c c P c P (2)

while the corresponding optimal speed curve is interpolated by a cubic function with the interpolating parameters n0, n1, n2 and n3.

( ) 2 3apu 0 1 apu 2 apu 3 apu= + + +N P n n P n P n P (3)


Figure 2 shows the optimal fuel consumption curve of the diesel APU with a TDI 1.9 l diesel engine used in our study.

Figure 2 The optimal operation curve of diesel APU

The developed fuel consumption model is a steady-state-based one. In actual operation, the diesel engine operates in a widely, changing operation range to satisfy the vehicle load demand. In fast transients, measured fuel consumption is perhaps much higher than that of the calculated from the above static model. In Lindgren (2005), a transient fuel consumption model was developed by improving the static model with a transient correction factor for both the changes in engine speed and torque

t s t( , ) (1 ( ))Z Z n R n, ,n,τ τ τ= × + (4)

where Zt is the transient fuel consumption, Zs is the static fuel consumption and Rt is a dimensionless transient correction function, ,n τ are the change rate of engine speed and torque, respectively. Here, this transient fuel consumption model is extended to our application. For the diesel APU that operates along the predefined curve in (3), using the test data in Pelkmans et al. (1998), the transient fuel consumption model is given by

( ) ( ) ( )= + + × +2 2apu apu apu 0 1 apu 2 apu apu, 1C P P c c P c P k P (5)

where the transient correction coefficient k = 7 × 10−4 (kW/s)−2.

2.2 Battery model

The battery was modelled with an equivalent circuit, which was expressed as an open circuit voltage in series with a resistor (Lin et al., 2003). Figure 3 shows the charge and discharge characteristics of the NiMH battery with the maximum capacity 80 Ahr.


From the test data, the open circuit voltage and internal resistance of the battery are interpolated as a function of the battery SOC, which are shown in Figure 4. Owing to the lack of test data, temperature effect is not considered. The equivalent circuit equation can be written in the following mathematical form as

bat oc bat

bat bat bat

dis bat

chg bat

= –

=

0=

< 0

V V I R

P V I

R PR

R P

≥

(6)

where the open circuit voltage Voc, and the discharge and charge internal resistance Rdis and Rchg are functions of the battery SOC, Ibat, Vbat and Pbat are respectively the battery terminal current, voltage and power, Pbat ≥ 0 (<0) means discharge (charge). From (6), the battery terminal current Ibat is given by

− −=

2oc oc bat

bat

4

2

V V R PI

R (7)

while the battery discharge and charge efficiencies can be written respectively as

dis batdis

oc

1

chg batchg

oc

41 11

2 2

41 11

2 2

R P

V

R P

V

η

η−

= + −

= + −

(8)

The battery SOC is evaluated from the state equation

2oc oc batbat

b b

4dSOC

d

V V R PI

t Q 2R Q

− −= − = − (9)

where Qb is the maximum battery capacity.

Figure 3 NiMH battery charge and discharge characteristics under 2 °C. Left figure: under charge currents of 24, 50, 55, 60, 80, 120 and 160 A; Right figure: under discharge currents of 24, 50, 80, 120, 160 and 240 A


Figure 4 NiMH battery model. Left figure: open circuit voltage; Right figure: internal resistance under charge (dotted) and discharge (solid)

2.3 Series hybrid vehicle simulator

A full vehicle simulator was developed to evaluate the energy management strategies. Besides, the models of hybrid power sources mentioned above, the simulator includes the models of driver behaviour, traction motor, transmission and vehicle dynamics. The driver model is treated as a PID controller for tracking the reference of the vehicle speed. As the approach in ADVISOR (National Renewable Energy Lab, 2001), the static efficiency characteristic is considered in the traction motor model, which is a function of motor speed and torque. In the two-speed manual transmission model, gear shifting was simply done with a hysteresis algorithm according to the vehicle speed. For the vehicle dynamics, a point-mass model is adopted, which considers the vehicle rolling resistance force, aerodynamic drag force and road slope (Lin et al., 2001). The simulator was implemented in the Matlab-Simulink software platform using the components data obtained from bench tests, as shown in Figure 5. The essential vehicle parameters are given in Table 1.

Figure 5 Matlab-Simulink model of the series hybrid vehicle simulator

Table 1 Vehicle parameters

Vehicle Mass 10500 kg Tire radius 0.509 m Transmission Type Two-speed manual Gear ratio 3.002, 1.862 Final reduction gear ratio 6.83 Traction motor Maximum power 160 kW Maximum torque 765 Nm


3 SGO algorithm

The objective of the energy management as considered in this paper is to control the hybrid power sources so that high fuel economy can be achieved, while the drivability is satisfactory and power train components are maintained within the operating limits. To put it simply, diesel engine pollutant emissions are not considered in our study. In this section, after the development of the equivalent fuel consumption concept, we formulate the control objective as an optimisation problem, and a real-time optimisation algorithm is proposed for its solution.

3.1 The equivalent fuel consumption concept

The concept of equivalent fuel consumption was proposed by Paganelli et al. (2002), Oh et al. (2004) and Guezennec et al. (2003) for the development of the instantaneous optimisation energy management strategy. In hybrid vehicles, both fuel energy and electrical energy can be used. To make them comparable, the electrical energy consumption of the battery is transformed into equivalent fuel consumption.

The power flow of the series hybrid vehicle is shown in Figure 6. The motor power demand Pdem is represented as

= +dem apu batP P P (10)

Figure 6 Power flow of series hybrid vehicle

From Figure 6, we can see that, there is a variety of choices to satisfy a given power demand Pdem. The battery can act as either positive or negative, while the diesel APU can also provide the traction power or operate in an idle state. To evaluate these choices, at each time t, an associated instantaneous cost Jt is defined as

( ) ( )t apu apu apu apu apu batt bat, ,SOC ( , ) ,SOCJ P P C P P C P= + (11)

where Cbatt is the battery equivalent fuel consumption. In Paganelli et al. (2002), the average charge and discharge efficiencies are considered in converting electrical energy consumption to equivalent fuel consumption, where Cbatt is given by

( ) λ

ηλη

=

≥

= <

bat bat bat bat

chg,avgbat

bat,avgbat

dis,avg bat,avg bat

0

0

C P P

CP

C P

(12)


where ηbat, avg is the battery average round trip charge and discharge efficiency, Cchg, avg, Cdis, avg are respectively the average specific fuel consumption rate for the charge and discharge case.

Here it is slightly improved based on the development of the detailed battery model. It will be explained below for the battery discharge process. The battery is assumed to discharge some power Pbat at the sample time t. From (8), we can see that this gives the electrical energy utilisation efficiency ηdis. To maintain the SOC, the battery will have to be recharged using the energy provided by the diesel engine, which implies an extra fuel consumption. This recharge is supposed to be done in the future. Because the operating points of components are not yet known, the battery mean charge efficiency ηchg,avg under the current SOC state is used. Now, the equivalent fuel consumption for the discharge case can be written as

( )η

−

= + −

1

chg,avg dis batbat bat bat

chg,avg oc

41 1,SOC 1

2 2

C R PC P P

V (13)

For the battery, model parameters are all functions of the battery SOC, the equivalent fuel consumption above is a function of the battery power Pbat and SOC.

Similarly, for the battery charge process, the equivalent fuel consumption is given by

( ) η−

= + −

1

chg batbat bat dis,avg dis,avg bat

oc

41 1,SOC 1

2 2

R PC P C P

V (14)

The practical operation of hybrid vehicles usually requires that energy management strategy should be charge-sustaining to maintain the battery SOC. In this paper, a linear penalty function is added to the cost function (11) to accomplish the charge-sustaining operation, which biases the battery equivalent fuel consumption up or down depending on the SOC deviation from the target. The SOC normalised deviation ∆SOC is defined as

− +∆ = =−

SOC SOC SOCH SOCLSOC 2 , SOC

SOCH SOCL 2

where SOCH, SOCL represent respectively the high and low SOC limits (SOCH = 0.7, SOCL = 0.3). ∆SOC = 1 implies that the current SOC hits the upper bound while ∆SOC = −1 the lower bound. The penalty function is given as the form (1−β∆SOC), where β is a constant, which can be adjusted to reflect the battery charge and discharge characteristics. Now the instantaneous cost function (11) is improved by

( ) ( ) ( )t apu apu apu apu apu bat bat, ,SOC , (1 SOC) ,SOCJ P P C P P C P= + − ∆β (15)


3.2 Optimisation problem formulation

From the above equivalent fuel consumption concept, defining the diesel APU power Papu as the control variable and the battery SOC as the system state, an energy management optimisation problem is formulated over a time horizon length Ts

( )= ∫sapu

t apu apumin , ,SOC dTP

J J P P t (16)

s.t. State Equation (9); Power flow balance constraint (10); Components operating constraints:

≤ ≤apu apu,max0 P P

≤ ≤bat,min bat bat,maxP P P

≤ ≤SOCL SOC SOCH

≤ ∆apu apu,maxP P

Comparing this with the optimisation problem considered in the previous work, the formulated problem here has some distinctive characteristics. The transient loss of the diesel APU is considered with the transient fuel consumption model (5) and the change rate constraint of the diesel APU power.

Another important point is the determination of the time horizon length Ts. If Ts is chosen as the whole length of a driving cycle, then it becomes a global optimisation problem. In general, the global optimisation cannot offer an online implementable solution, as it assumes that the future driving cycle is entirely known. Here, we propose a short-term optimisation concept, which is called ‘SGO’. The time horizon length Ts is considered as the quasi-steady-state time constant of the diesel APU. Over this time horizon, the diesel APU operates in a quasi-steady-state behaviour. Nevertheless, within this time horizon, the dynamic behaviour of the diesel APU will be optimised.

Because the term Pdem is versatile and non-convex, and the gradient of control command apuP is explicitly included in the objective function, the optimisation

problem (16) is difficult to be solved exactly in real time. Even if the exact solution can be found to obtain an online implementable strategy, a reliable prediction algorithm over the time horizon Ts has to be developed, which is still an open problem. In Section 3.3, an effective approximate optimisation algorithm will be developed to approach this problem.

3.3 Real-time optimisation algorithm

As mentioned above, in series hybrid vehicles, the engine speed is decoupled from the vehicle speed. This allows the diesel APU to operate in a very efficient manner: it can operate along an optimal fuel consumption curve, and involves less transient behaviour. But, on the other hand, the diesel APU is the main power source and the battery only acts as a power-assisting one. It has to compensate some part of the dynamic


power demand under some vehement driving cycles. To account for the contradictive objectives, a viable way is to adaptively identify the required dynamic behaviour of the diesel APU.

On the basis of this idea, here we propose a novel alternative optimisation algorithm to this problem, which is achieved by a two-stage optimisation procedure: the usual instantaneous optimisation considering only the static fuel consumption (2), and the dynamic compensation optimisation considering the dynamic characteristic time constant Tf of the diesel APU. The details will be given below in mathematical forms.

Within the shorter time horizon length Ts, the variation of battery SOC from the state Equation (9) is relatively small due to the battery’s larger capacity (for a battery with the capacity 80 Ahr, assume it discharges at a 2C discharge rate, and Ts = 20 sec, the SOC variation is about 2 × 80 × 20/80/3600 ≈ 0.9%). When the state equation is neglected, the optimisation problem (16) with the static fuel consumption (2) is simplified to an instantaneous optimisation problem at each time t. As the solution approach in Paganelli et al. (2002) and Oh et al. (2004), a static optimal solution is obtained as a function of power demand and battery SOC, which is stored as a static map

( )=apu dem ,SOCP f P (17)

For the trajectories Pdem(t), t ∈ [0, Ts], we denote the corresponding static optimal diesel APU power as apu ( ).P t

Now, to compensate the transient fuel loss of the diesel APU, we reconsider the whole optimisation problem based on the above-mentioned approximate solution. The improved solution is assumed to be in the following form

[ ]f

apu apu sf

1( ) ( )d 0,

t

t TP t P t T

Tτ τ

−= ∈∫ (18)

In fact, it is a moving average value of the instantaneous solution characterised by the time constant Tf. The time constant lies in the range f s ,t T T∆ ≤ ≤ where ∆t is the

sampling period. When Tf = ∆t, Papu(t) is equal to τapu ( ),P while Tf = Ts, the diesel APU

operates in a steady-state manner. To consider the change rate constraint of the diesel APU power in (16), a minimum allowed diesel APU dynamic time constant Tmin is defined, which is approximated as min apu,max apu,max/ .T P P= ∆ The time constant Tf is further

restricted in the range

≤ ≤min f sT T T (19)

If Tf is assumed to be constant over the period Ts, then the change rate of diesel APU power can be obtained from (18)

( )( )= − −apu apu apu ff

1( ) ( )P t P t P t T

T (20)


In real-time applications, Tf is updated at each period Ts; hence the switching behaviour of Tf between successive periods has to be considered. The following S-shape function is adopted to describe the switching behaviour

( ) [ ]= + − ∈f f 0 f1 f 0 s( ) ( ) 0T t T T T f t t ,T (21)

where Tf0 is the known optimised time constant at the previous period, Tf1 is the optimisation variable at the current period, the S-shape function is

µ−=+

1( )

1 tf t

e (22)

where µ is a large constant µ = 103. Now we will derive the term apuP under the Tf trajectory (21). From Equations (18),

(21) and (22), the derivatives of associated functions are respectively given below:

µ∂ = −∂

( ) ( )(1 ( ))f t f t f tt

(23)

( )∂ ∂= −∂ ∂f f1 f 0( ) ( )T t T T f tt t

(24)

( )( )∂ = − −∂ apu apu apu f

f f

1( ) ( )P t P t P t T

T T (25)

Then, from (20), (23), (24) and (25), the derivative of apu ( )P t can be obtained

as follows:

( )( ) ( )

( )( ) )

apu apu apu f f1 f 0f

apu apu ff

1( ) ( )

1 ( ) ( )(1 ( )

P t P t P t T T TT

P t P t T f t f tT

µ= − − + −

− − − (26)

Substituting the associated Equations (21), (26) into the objective function in (16), an optimal control problem associated with the control parameter Tf1 is obtained

( )= ∫sf1

t f1min ,SOC dTT

J J T t (27)

The constraints are almost the same as in (16), except that the condition ≤ ∆apu apu,maxP P

is replaced by (19). Because the objective function J is continuous as a function of the parameter Tf1,

and the parameter lies in a compact set (19), there exists a global solution to this problem.

For optimal control problems, gradient-based optimisation methods such as SQP (Nocedal and Wright, 1999) are widely used, which requires the gradient of the objective function. Here the terms apu (t)P and Cbatt in the objective function J are

non-differential functions. Although we can use some smoothing techniques to overcome this (Mayne and Polak, 1984), but still there is another difficult issue. This optimal control problem is non-convex, for the driver power demand Pdem is


versatile. The objective function may have many local minima that are not of interest. Figure 7 shows the objective function value assuming a sine-wave driver power demand, in which three local optimal solutions can be found.

Figure 7 Objective function value as a function of the parameter Tf1 for a sine-wave power demand

Recently, intelligent optimisation methods such as genetic algorithm have also been much investigated in control parameter optimisation (Campos-Delgado et al., 2003). It has an advantage to be less sensitive to the presence of local minima. It is an efficient tool for the multiobjective multiparameter optimisation problems.

For our problem, there is only one optimisation parameter Tf1 lying in a small compact set. On the basis of the above-mentioned discussions, the simple enumeration method is used. The global solution is obtained by griding the parameter space and evaluating the objective function at each discrete grid point. Practical applications show that it can satisfy the real-time requirement completely.

Finally, a summary is given to the application of our developed operation algorithm in real-time control.

1 precompute the static optimal power distribution map (17)

2 according to the battery SOC SOC(t0) and the power demand Pdem(t0) at the current time t0, the static optimal diesel APU power apu 0( )P t is interpolated from

the power distribution map (17)

3 update the dynamic characteristic constant Tf at each period Ts by the solution of the optimal control problem (27)

4 assuming that the statistical property of the required diesel APU dynamic behaviour at the current period is similar to that at the previous period, the outcome of the previous optimisation is used in the current real-time control. The current diesel APU power command apu 0( )P t is obtained

from (18).


4 Simulation results

The proposed energy management strategy is implemented on the series hybrid vehicle simulator. The evaluation process is performed by comparing the simulation results of the following strategies as given below:

• On/Off strategy: the diesel APU operates in the optimum point or in the idle state according to the logic control of battery SOC (Jalil et al., 1997).

• SIO: SIO algorithm with the constraint to the maximum change rate of diesel

APU power, ≤ ∆apu apu,max .P P It was ever applied to fuel cell powered series

hybrid vehicles in Guezennec et al. (2003).

• SGO: SGO algorithm proposed in this paper.

In contrast to the On/Off strategy, the latter two energy management strategies belong to the optimised power following strategies. Their difference is that the dynamic behaviour of the diesel APU is optimised in the SGO strategy whereas it is only considered as a gradient constraint in the SIO strategy.

According to the test procedure of heavy-duty hybrid vehicles in Lin et al. (2003), the chassis-based driving cycle for heavy-duty vehicles (UDDSHDV) is adopted for measuring the vehicle fuel economy performance. For the maximum speed of our series hybrid vehicle is designed to be 80 km/hr, the original UDDSHDV is scaled as shown in Figure 8. In addition, in the simulation, it is assumed that the diesel engine is in the fully warm-up state and cold-start effect is not considered, and when the diesel APU power is set to zero it is put to idling.

Figure 8 The UDDSHDV driving cycle

Figures 9 and 10 show respectively the simulation results of the SIO and SGO strategies. The initial condition of the battery SOC is both set to 0.5. From the battery SOC trajectories, it can be seen that the two strategies have the similar charge-sustaining feature. The battery SOC variation is very small in this most efficient operating region. The average battery power is 1.7 and 1.5 kW, respectively.


The battery acts well as a power-assisting power source in the case of transient or heavy vehicle power demand. But the two strategies have different APU operation schemes. In the SIO strategy, the diesel APU responses to the vehicle power demand within the allowable change rate range. While in the SGO strategy, to reduce the transient loss, an online adaptive strategy is used to capture the required dynamics of the diesel APU. The dynamic characteristic constant Tf over the driving cycle is also shown in Figure 10. It generally well represents the vehicle dynamic behaviour. But in some cases such as switching from stop state into normal operation, it fails to capture it in time. This is caused by the one-period delay in the real-time implementation. However, it will not affect much the overall performance of the strategy. In addition, it should be pointed out that in the vehicle stop state or other absolute steady states, the time constant Tf does not have any effect on the control performance; hence its value at the previous period is maintained.

Figure 9 SIO algorithm results

To further confirm the charge-sustaining strategy, simulations with different initial SOC values are carried out under the SGO strategy. Figure 11 shows the corresponding sequences of the SOC with the two initial SOC values 0.3 and 0.7. The variation in SOC is very small, because of the larger capacity of the battery. But it is still much larger than the SOC variation in Figure 10, and we can see clearly the tendency of battery SOC towards the optimum operating point.


Figure 10 SGO algorithm results

The control performance of the three strategies is summarised in Table 2. The terms include the equivalent miles per gallon (eMPG), diesel fuel usage and the final battery SOC reached. In this cycle, the On/Off strategy tends to charge the battery to the maximum level, and its fuel usage is almost twice as that of the SIO strategy, while achieving much higher the final SOC value. Under this condition, the eMPG value better represents the real control performance. The SIO strategy achieves about 7% improvement on equivalent fuel economy as compared with the On/Off strategy, whereas the SGO strategy achieves about 14% improvement. As the final SOC value is almost the same in the SIO and SGO strategy, the eMPG and fuel usage consistently show that the proposed SGO strategy has better fuel economy performance than the SIO strategy.


Figure 11 Battery SOC with different initial SOC values under the SGO strategy

Table 2 Control performance comparison over the UDDSHDV cycle with initial SOC 0.5

Strategy eMPG (mi/gal) Fuel usage (kg) Final SOC

On/Off 10.398 (100%) 3.348 (100%) 0.622

SIO 11.125 (107.0%) 1.765 (52.7%) 0.490

SGO 11.860 (114.1%) 1.597 (47.7%) 0.491

5 Conclusions

A novel optimisation-based energy management strategy is developed for series hybrid vehicles based on the following two facts:

• the engine transient operation is an important contributor to the vehicle fuel economy and exhaust emissions

• the engine speed is decoupled from the vehicle speed in series hybrid vehicles.

The first one is taken into account by a transient engine fuel consumption model. The second one allows the engine to operate in an optimal curve and in a less transient manner, which provides the feasibility to optimise the engine dynamics.

The optimal energy management strategy is formulated over a shorter time horizon characterised by the quasi-steady-state time constant of diesel engine. The real-time solution strategy includes the preliminary SIO and adaptive optimisation of the time constant of engine dynamics. The proposed strategy has been validated by simulations. It achieves much improvement in vehicle fuel economy in comparison with other strategies.

This study is restricted to minimising vehicle fuel consumption. But, we think that the methods used here can be improved by taking into account emissions, especially the transient emissions, which are the topics of our future work. In addition, the proposed strategy for series hybrid vehicles can be well extended to fuel cell powered hybrid


vehicles due to similar configurations of the two. In fact, as stated in Guezennec et al. (2003), the transient behaviour of fuel cell engine affects both its performance and life period.

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