1. Introduction

A transit bus is a prime commuting tool for city residents, which consumes lots of fuel every year and produces a huge amount of poisonous emissions [1]. Electrification of transit bus is a good solution for these problems. Normally, the energy storage device consists of batteries [2]. The supercapacitor is a newly developed high-power electrochemical energy storage component [3, 4]. Farkas and Bonert have predicted that a supercapacitor is a good solution for hybrid vehicles [5]. Recently, many researches were performed to study the characteristics of supercapacitors as the energy storage system (ESS) of a hybrid electric vehicle (HEV) [6, 7].

Supercapacitors have a large surface area of electrode materials, which normally are activated carbons, and a very thin electrolytic separator leading to a very high capacitance. They store energy electrostatically. For automotive applications, most of them are electrochemical double-layer capacitors (EDLCs) [8]. Supercapacitors have a very high power density, which is over 10 times than batteries and can be charged or discharged up to 1,000,000 times which is significantly larger than lithium-ion batteries. They also have a very long life time and a wide operation temperature range [9].

velocity and has a huge computation load. Therefore, it is infeasible for a practical

Performance Evaluation and Control Strategy Comparison of Supercapacitors for a Hybrid…

In this chapter, a series hybrid transit bus powered by a compressed natural gas (CNG) engine and supercapacitors is studied. The energy conversion characteristics of the designed series hybrid powertrain are analyzed using a mathematical model. First, two rule-based control strategies—the thermostatic control and the power follower control—are designed and compared. Later, the maximum potential of energy savings is estimated using an optimal control strategy based on dynamic programming. Finally, the operation characteristics of the series hybrid powertrain using the different control strategies are discussed. The results of this study provide a demonstration on how to design an ESS for an electric vehicle or hybrid electric

The designed series hybrid powertrain for a transit bus is described as follows. A CNG engine is directly connected with a permanent magnetic synchronous generator (PMSG). A high-voltage power line is connected to the generator and the ESS as well as a permanent magnetic synchronous motor (PMSM). The PMSM connected to the final drive is a specially designed low-speed and high-power PMSM. The engine is a Yuchai 6.5 L CNG engine whose rated power is 140 kW. Both the PMSG and the PMSM are developed by Jing-Jin Electric Technologies (Beijing) Co., Ltd. The PMSG is a low-speed and high-efficiency electric machine whose rated power is 135 kW. The rated power of the PMSM is slightly greater than that of the PMSG. These two high-power electric machines have already been applied to several different types of hybrid vehicles successfully. The ESS includes three parallel groups of supercapacitors, and each group consists of 13 units of Maxwell 48 V module connected in series. The total energy capacity of the ESS is 2.115 kWh, and the rated voltage is 624 V. To keep the supercapacitors from overdischarging, the minimum

The working principle of the designed series hybrid powertrain can be explained by an energy flow diagram shown in Figure 1. When the series hybrid transit bus is running, four different operation modes are defined according to the working conditions. Two modes are used for the driving conditions, and the other two modes are for the regenerative braking conditions. For the driving mode A, the

real-time vehicle system.

DOI: http://dx.doi.org/10.5772/intechopen.80948

vehicle from the systematic level.

operation voltage of the ESS is set to 300 V.

Energy flow diagram of the series hybrid transit bus.

2. System description

Figure 1.

119

Because supercapacitors have a high power density and can be charged or discharged in a short time, they can be used as a sole ESS for transit bus, which undergoes a frequent acceleration and deceleration processes. The first known transit bus powered by supercapacitors alone is Capabus operating in Shanghai since 2010. The buses were manufactured by Sunwin Bus Co., Ltd., and the supercapacitors were provided by Shanghai Aowei Co., Ltd. The transit bus can run 8–10 km each time after being fully charged. A total mileage of several million kilometers has been achieved, and the average energy consumption is close to 0.98 kWh/km [10]. Many other bus manufacturers also developed their products. Higer Bus Co., Ltd. together with an Israeli-Bulgarian bus company designed a transit bus with 20 kWh supercapacitors named as Chariot e-bus [10].

Supercapacitors have a low energy density of up to 10 Wh/kg. However, batteries especially lithium-ion batteries take advantage of high energy density which can be over 180 Wh/kg. For most automotive applications such as a plug-in hybrid electric vehicle (PHEV) or electric vehicle (EV), the ESS should guarantee a driving distance of more than 50 km normally, which can cover over 80% of people's daily travel in Beijing. Therefore, supercapacitors are combined together with batteries as a hybrid energy storage system (HESS). The batteries provide average energy, while the supercapacitors absorb energy during regenerative braking or discharge energy during acceleration. As a result, the high-rate working conditions of the batteries are avoided, and their life spans are extended. On the other hand, the internal resistance of a supercapacitor is much lower than that of a battery; the energy efficiency of a vehicle with an HESS is also improved compared with only batteries. Moreover, the size of the ESS can be decreased if supercapacitors are used. Accordingly, the cost can be reduced. There are mainly three kinds of topologies for HESS: passive, semi-active, and active [11]. Currently, supercapacitor semi-active topology shows a better performance considering efficiency, size, cost, and complexity [12]. Many studies were carried out to determine the size of HESS and optimize the energy management [13–16].

Control strategy design of a hybrid transit bus has important impact on system performance. The control strategy can be categorized as rule-based and optimization-based strategies [17, 18]. Rule-based control strategy specifies the power distribution between the auxiliary power unit (APU) and the ESS based on a set of rules according to the power demand of a vehicle and the state of charge (SOC) of ESS. Thermostatic control, power follower control, and fuzzy logic control are three types of rule-based control strategies [19–23]. Because these strategies do not need information of future driving conditions and have a low computation load, they are appropriate for real-time control application. Optimization-based control strategy splits the power demand based on an optimal algorithm and a mathematical model of the hybrid powertrain. They require the details of the entire driving profile. Normally, they are a kind of global optimization method such as dynamic programming [24], optimal control strategy [25–27], and neural network control [28]. Optimization-based control strategy can be used to estimate the theoretical maximum energy efficiency. However, it requires future information of the driving Performance Evaluation and Control Strategy Comparison of Supercapacitors for a Hybrid… DOI: http://dx.doi.org/10.5772/intechopen.80948

velocity and has a huge computation load. Therefore, it is infeasible for a practical real-time vehicle system.

In this chapter, a series hybrid transit bus powered by a compressed natural gas (CNG) engine and supercapacitors is studied. The energy conversion characteristics of the designed series hybrid powertrain are analyzed using a mathematical model. First, two rule-based control strategies—the thermostatic control and the power follower control—are designed and compared. Later, the maximum potential of energy savings is estimated using an optimal control strategy based on dynamic programming. Finally, the operation characteristics of the series hybrid powertrain using the different control strategies are discussed. The results of this study provide a demonstration on how to design an ESS for an electric vehicle or hybrid electric vehicle from the systematic level.

### 2. System description

Supercapacitors have a large surface area of electrode materials, which normally are activated carbons, and a very thin electrolytic separator leading to a very high capacitance. They store energy electrostatically. For automotive applications, most of them are electrochemical double-layer capacitors (EDLCs) [8]. Supercapacitors have a very high power density, which is over 10 times than batteries and can be charged or discharged up to 1,000,000 times which is significantly larger than lithium-ion batteries. They also have a very long life time and a wide operation

Science,Technology and Advanced Application of Supercapacitors

Because supercapacitors have a high power density and can be charged or discharged in a short time, they can be used as a sole ESS for transit bus, which undergoes a frequent acceleration and deceleration processes. The first known transit bus powered by supercapacitors alone is Capabus operating in Shanghai since 2010. The buses were manufactured by Sunwin Bus Co., Ltd., and the supercapacitors were provided by Shanghai Aowei Co., Ltd. The transit bus can run 8–10 km each time after being fully charged. A total mileage of several million kilometers has been achieved, and the average energy consumption is close to 0.98 kWh/km [10]. Many other bus manufacturers also developed their products. Higer Bus Co., Ltd. together with an Israeli-Bulgarian bus company designed a transit bus with 20 kWh supercapacitors named as

Supercapacitors have a low energy density of up to 10 Wh/kg. However, batteries especially lithium-ion batteries take advantage of high energy density which can be over 180 Wh/kg. For most automotive applications such as a plug-in hybrid electric vehicle (PHEV) or electric vehicle (EV), the ESS should guarantee a driving distance of more than 50 km normally, which can cover over 80% of people's daily travel in Beijing. Therefore, supercapacitors are combined together with batteries as a hybrid energy storage system (HESS). The batteries provide average energy, while the supercapacitors absorb energy during regenerative braking or discharge energy during acceleration. As a result, the high-rate working conditions of the batteries are avoided, and their life spans are extended. On the other hand, the internal resistance of a supercapacitor is much lower than that of a battery; the energy efficiency of a vehicle with an HESS is also improved compared with only batteries. Moreover, the size of the ESS can be decreased if supercapacitors are used. Accordingly, the cost can be reduced. There are mainly three kinds of topologies for HESS: passive, semi-active, and active [11]. Currently, supercapacitor semi-active topology shows a better performance considering efficiency, size, cost, and complexity [12]. Many studies were carried out to determine the size of HESS and

Control strategy design of a hybrid transit bus has important impact on system

optimization-based strategies [17, 18]. Rule-based control strategy specifies the power distribution between the auxiliary power unit (APU) and the ESS based on a set of rules according to the power demand of a vehicle and the state of charge (SOC) of ESS. Thermostatic control, power follower control, and fuzzy logic control are three types of rule-based control strategies [19–23]. Because these strategies do not need information of future driving conditions and have a low computation load, they are appropriate for real-time control application. Optimization-based control strategy splits the power demand based on an optimal algorithm and a mathematical model of the hybrid powertrain. They require the details of the entire driving profile. Normally, they are a kind of global optimization method such as dynamic programming [24], optimal control strategy [25–27], and neural network control [28]. Optimization-based control strategy can be used to estimate the theoretical maximum energy efficiency. However, it requires future information of the driving

performance. The control strategy can be categorized as rule-based and

temperature range [9].

Chariot e-bus [10].

118

optimize the energy management [13–16].

The designed series hybrid powertrain for a transit bus is described as follows. A CNG engine is directly connected with a permanent magnetic synchronous generator (PMSG). A high-voltage power line is connected to the generator and the ESS as well as a permanent magnetic synchronous motor (PMSM). The PMSM connected to the final drive is a specially designed low-speed and high-power PMSM. The engine is a Yuchai 6.5 L CNG engine whose rated power is 140 kW. Both the PMSG and the PMSM are developed by Jing-Jin Electric Technologies (Beijing) Co., Ltd. The PMSG is a low-speed and high-efficiency electric machine whose rated power is 135 kW. The rated power of the PMSM is slightly greater than that of the PMSG. These two high-power electric machines have already been applied to several different types of hybrid vehicles successfully. The ESS includes three parallel groups of supercapacitors, and each group consists of 13 units of Maxwell 48 V module connected in series. The total energy capacity of the ESS is 2.115 kWh, and the rated voltage is 624 V. To keep the supercapacitors from overdischarging, the minimum operation voltage of the ESS is set to 300 V.

The working principle of the designed series hybrid powertrain can be explained by an energy flow diagram shown in Figure 1. When the series hybrid transit bus is running, four different operation modes are defined according to the working conditions. Two modes are used for the driving conditions, and the other two modes are for the regenerative braking conditions. For the driving mode A, the

Figure 1. Energy flow diagram of the series hybrid transit bus.

CNG engine is running, and the APU together with the ESS supplies electric power to the motor. This driving mode is activated if the required driving power is high or the SOC is low. When the SOC is high and the required driving power is less than a certain value, the ESS provides electric energy to the motor alone as the driving mode B shows. If the series hybrid bus is braking, the regenerative energy output from the motor is supplied to the ESS. Meanwhile, the APU can be activated or deactivated denoted by the braking modes A and B, respectively.

## 3. Mathematical model

A mathematical model is established according to the working principle of the designed series hybrid powertrain. The corresponding parameters of the hybrid transit bus are listed in Table 1. The tractive force acting on a rear-wheel-driven two-axle vehicle can be determined according to the corresponding longitudinal dynamic equation expressed as

$$F = mg\cos a \left(f\_1 + f\_2 v\right) + \frac{1}{2}\rho A C\_D v\_r^2 + mg\sin a + \delta m \frac{dv}{dt}.\tag{1}$$

The wheel and axle model first calculates the front axle load and the rear axle load according to the technical parameters of the series hybrid transit bus. Then, the tractive force coefficient of the rear tires can be determined. The slip of the tires can be modeled as a function of the tractive force coefficient. Finally, the angular speed of the rear tire can be obtained [29].

If the transit bus is operating at the regenerative braking process, the required braking force Fb can be determined according to the deceleration of the vehicle. Then the regenerative braking force of the rear axle Fbr is obtained based on the following force distribution equation:

$$F\_{bf} = \beta\_1 F\_{b\text{\textquotedblleft}b\text{\textquotedblright}} \tag{2}$$

ω<sup>m</sup> ¼ i0ω, (5)

Tmr ¼ Tm þ Jmdωm=dt: (6) Pm ¼ fð Þ ωm; Tmr : (7)

dt : (8)

, (9)

� 100%: (10)

� 100%: (11)

Ter ¼ Te þ Jedωe=dt: (12)

me ¼ f ω<sup>e</sup> ð Þ ; Ter : (13)

where Tw is the output torque of the final drive and Tm and ω<sup>m</sup> are the input

Performance Evaluation and Control Strategy Comparison of Supercapacitors for a Hybrid…

The mathematical model of the generator is similar to the motor.

<sup>i</sup> <sup>¼</sup> dQ

<sup>i</sup> <sup>¼</sup> Uc �

<sup>η</sup>dch <sup>¼</sup> <sup>1</sup> � Rsi

For charging process, the energy efficiency ηch is expressed as

<sup>η</sup>ch <sup>¼</sup> <sup>1</sup> � Rsi

relation between the current i and the voltage Uc is expressed as

the current is obtained by

ciency ηdch is calculated as

map measured by an engine test bench.

block:

diesel fuel ρ<sup>f</sup> :

121

If the detailed physical mechanism of supercapacitors is studied, an electrochemical model or a high-order equivalent circuit model must be adopted [30]. In this study, we only consider the systematic performance of the ESS. Therefore, the RC equivalent circuit model is built using Advisor. The internal series resistance Rs and capacitance C can be obtained according to the capacitor test procedure. The

dt <sup>¼</sup> <sup>C</sup>dUc

With regard to the energy conversion processes during charging or discharging,

2Rs

where PL is the output power of the ESS. During discharging, the energy effi-

PL þ Rsi 2

� �

2

2 PL � �

The CNG engine model computes the requested torque Ter according to the engine output torque Te and the engine speed ω<sup>e</sup> determined by the control strategy

Subsequently, the instantaneous fuel consumption me is determined from a 2D

Then, the equivalent fuel consumption Qe can be obtained according to the integral values of the fuel consumption and the driving distance using the density of

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U2

<sup>c</sup> � 4RsPL

The electric motor model determines the requested torque Tmr according to the motor inertia Jm and the output torque Tm. Then the input power Pm is calculated based on a two-dimensional (2D) lookup table measured from a motor test bench.

torque and speed of the final drive, respectively.

DOI: http://dx.doi.org/10.5772/intechopen.80948

$$F\_{br} = (1 - \beta\_1 - \beta\_2) F\_b. \tag{3}$$

The model of the final drive takes into account the friction loss Tl0, and the inertia of rotating parts J<sup>0</sup> and is expressed as

$$T\_m = T\_w/i\_0 + T\_{l0} + i\_0 l\_0 d o/d t,\tag{4}$$


Table 1.

Technical parameters of the series hybrid transit bus.

Performance Evaluation and Control Strategy Comparison of Supercapacitors for a Hybrid… DOI: http://dx.doi.org/10.5772/intechopen.80948

$$
\rho\_m = i\_0 \rho\_\text{\prime} \tag{5}
$$

where Tw is the output torque of the final drive and Tm and ω<sup>m</sup> are the input torque and speed of the final drive, respectively.

The electric motor model determines the requested torque Tmr according to the motor inertia Jm and the output torque Tm. Then the input power Pm is calculated based on a two-dimensional (2D) lookup table measured from a motor test bench.

$$T\_{mr} = T\_m + f\_m d
o
o\_m/dt.\tag{6}$$

$$P\_m = f(o\_m, T\_{mr}).\tag{7}$$

The mathematical model of the generator is similar to the motor.

If the detailed physical mechanism of supercapacitors is studied, an electrochemical model or a high-order equivalent circuit model must be adopted [30]. In this study, we only consider the systematic performance of the ESS. Therefore, the RC equivalent circuit model is built using Advisor. The internal series resistance Rs and capacitance C can be obtained according to the capacitor test procedure. The relation between the current i and the voltage Uc is expressed as

$$i = \frac{dQ}{dt} = \mathcal{C}\frac{dU\_c}{dt}.\tag{8}$$

With regard to the energy conversion processes during charging or discharging, the current is obtained by

$$i = \frac{U\_{\varepsilon} - \sqrt{U\_{\varepsilon}^{2} - 4R\_{\varepsilon}P\_{L}}}{2R\_{\varepsilon}},\tag{9}$$

where PL is the output power of the ESS. During discharging, the energy efficiency ηdch is calculated as

$$
\eta\_{dch} = \left(\mathbf{1} - \frac{R\_i \dot{i}^2}{P\_L + R\_i \dot{i}^2}\right) \times \mathbf{10096.}\tag{10}
$$

For charging process, the energy efficiency ηch is expressed as

$$
\eta\_{ch} = \left(\mathbf{1} - \frac{R\_s i^2}{P\_L}\right) \times \mathbf{100\%}.\tag{11}
$$

The CNG engine model computes the requested torque Ter according to the engine output torque Te and the engine speed ω<sup>e</sup> determined by the control strategy block:

$$T\_{cr} = T\_e + f\_e d o\_e / d\text{t.}\tag{12}$$

Subsequently, the instantaneous fuel consumption me is determined from a 2D map measured by an engine test bench.

$$m\_{\epsilon} = f(o\_{\epsilon}, T\_{\epsilon r}). \tag{13}$$

Then, the equivalent fuel consumption Qe can be obtained according to the integral values of the fuel consumption and the driving distance using the density of diesel fuel ρ<sup>f</sup> :

CNG engine is running, and the APU together with the ESS supplies electric power to the motor. This driving mode is activated if the required driving power is high or the SOC is low. When the SOC is high and the required driving power is less than a certain value, the ESS provides electric energy to the motor alone as the driving mode B shows. If the series hybrid bus is braking, the regenerative energy output from the motor is supplied to the ESS. Meanwhile, the APU can be activated or

A mathematical model is established according to the working principle of the designed series hybrid powertrain. The corresponding parameters of the hybrid transit bus are listed in Table 1. The tractive force acting on a rear-wheel-driven two-axle vehicle can be determined according to the corresponding longitudinal

> 1 2

The wheel and axle model first calculates the front axle load and the rear axle load according to the technical parameters of the series hybrid transit bus. Then, the tractive force coefficient of the rear tires can be determined. The slip of the tires can be modeled as a function of the tractive force coefficient. Finally, the angular speed

If the transit bus is operating at the regenerative braking process, the required braking force Fb can be determined according to the deceleration of the vehicle. Then the regenerative braking force of the rear axle Fbr is obtained based on the

The model of the final drive takes into account the friction loss Tl0, and the

Parameter Value Unit Vehicle mass excluding pack 9000 kg Cargo mass 3200 kg Dimensions 8.995 � 2.42 � 3.085 m � m � m Rolling resistance coefficient 0.0094 — Aerodynamic drag coefficient 0.79 — Vehicle frontal area 7.466 m<sup>2</sup> Wheel radius 0.506 m Final gear 5.833 —

ρACDv<sup>2</sup>

<sup>r</sup> þ mg sin α þ δm

Fbf ¼ β1Fb, (2)

Fbr ¼ 1 � β<sup>1</sup> � β<sup>2</sup> ð ÞFb: (3)

Tm ¼ Tw=i<sup>0</sup> þ Tl<sup>0</sup> þ i0J0dω=dt, (4)

dv

dt : (1)

deactivated denoted by the braking modes A and B, respectively.

Science,Technology and Advanced Application of Supercapacitors

<sup>F</sup> <sup>¼</sup> mg cos <sup>α</sup> <sup>f</sup> <sup>1</sup> <sup>þ</sup> <sup>f</sup> <sup>2</sup><sup>v</sup> <sup>þ</sup>

3. Mathematical model

dynamic equation expressed as

of the rear tire can be obtained [29].

following force distribution equation:

Table 1.

120

inertia of rotating parts J<sup>0</sup> and is expressed as

Technical parameters of the series hybrid transit bus.

Science,Technology and Advanced Application of Supercapacitors

$$Q\_{\epsilon} = \frac{\int\_{0}^{t\_f} m\_{\epsilon} dt}{\rho\_f \int\_{0}^{t\_f} \nu dt},\tag{14}$$

engine is shown in Figure 4a. The blue contour denotes the engine power in kW. The black contour is the brake-specific fuel consumption (bsfc) in g/kWh. It can be seen that the minimum bsfc of the CNG engine is 196 g/kWh, which is better than that of a diesel engine. The effective thermal efficiency map of the CNG engine shown in Figure 4b is obtained based on the performance map of Figure 4a. The maximum engine efficiency achieves 36.8%, and in most of the operation regions, the effective thermal efficiency of the CNG engine is greater than 30%. The efficiency map of the PMSG is given in Figure 4c, where the highest energy efficiency is 94.5%. In most of the operation regions, the generator efficiency is greater than

Performance Evaluation and Control Strategy Comparison of Supercapacitors for a Hybrid…

89%. The efficiency decreases obviously if the generator speed is less than

close to the point with a maximum of engine torque.

control strategy.

123

Figure 3.

The designed power follower control strategy.

DOI: http://dx.doi.org/10.5772/intechopen.80948

500 r/min. According to the results of Figure 4b and c, the energy efficiency map of the APU is obtained as the product of the efficiencies of the CNG engine and the generator. The engine speed ranges from 900 to 2500 r/min, and the maximum engine torque is 650 Nm, which can be covered completely by the generator's operation domain. The results are given in Figure 4d. In this figure, the x-axis is the engine speed, and the y-axis is the engine torque. The blue contour represents the APU output power in kW. The black contours denote the energy efficiency of APU, which decreases with the engine torque and is greater than 30% over the regions of middle and high engine torques. The maximum efficiency is 34.06% located very

Subsequently, the OOL is determined according to the efficiency map of the APU. The efficiency for each point of the OOL is the maximum at each power contour. The result is shown as the green line in Figure 4d. The OOL is the same with the external profile when the engine speed is greater than 1600 r/min. Meanwhile, the engine speed of the OOL remains at 900 r/min if the APU power is less than 50 kW. The OOL appears to have a U shape when the APU power is between 50 and 100 kW. Finally, the parameters of the rule-based control strategies must be optimized. The maximum energy efficiency of the APU is 34.06%. This point is denoted as point P in Figure 8. The corresponding engine speed and torque are 1543 r/min and 650 Nm, respectively, which are specified as the operation point of the thermostatic control strategy. The lower and upper bounds of the SOC is set to 0.58 and 0.99. The other parameters are also optimized for the power follower

where tf is the final time of the driving cycle.
