4. Control strategy design

#### 4.1 Rule-based control strategy

To evaluate the performance of the designed series hybrid powertrain, a simulation program is developed according to the established mathematical model with MATLAB/Simulink and Advisor. Advisor is a modeling and simulation tool for hybrid electric vehicle based on MATLAB and Simulink developed by the US National Renewable Energy Laboratory [31]. The designed program is shown in Figure 2. Using a backward-facing method, the performance and fuel consumption of the series hybrid transit bus can be calculated. First, the driving force is determined based on the longitudinal dynamic equation. The rotating speed and driving torque of the rear axle are computed according to the tire model. Subsequently, the input torque and speed are determined for the final drive, and the input power of the motor is obtained. Then, the control strategy decides the power distribution between the ESS and the APU. As a result, both the output powers of the ESS and the APU are specified by the power bus. The supercapacitor model calculates the current and energy loss of the ESS. Moreover, the control strategy determines the operation torque and speed of the CNG engine according to the output power of the APU. Then, the fuel consumption is determined based on the performance maps of the CNG engine and the PMSG.

Rule-based control strategy takes advantage of a small computation load, which is very suitable for real-time applications. Therefore, two rule-based control strategies—the thermostatic control and the power follower control—are set up, respectively. The thermostatic control is adopted first for hybrid electric vehicles due to its simple logic. When the HEV is running, if the SOC value drops to a lower bound, the engine starts and operates at a fixed point until the SOC value reaches to an upper bound. The operation condition of the engine is set to the point with the highest effective thermal efficiency.

Large current variation in the ESS may occur for the thermostatic control strategy which results in high energy loss. Therefore, a more sophisticated power follower control is developed. According to this strategy, if the engine state is on, the output power of the APU follows the power demand of the transit bus along an optimal operation line (OOL). Hence, the output power of the APU is decreased, and the operation current of the ESS can be alleviated. The designed power follower control strategy is shown in Figure 3. The decision algorithm for the engine state is designed using Stateflow.

Since the power follower control needs to define an OOL, the energy efficiency characteristics of the APU must be studied first. The performance map of the CNG

Figure 2. The analysis program of the series hybrid powertrain. Performance Evaluation and Control Strategy Comparison of Supercapacitors for a Hybrid… DOI: http://dx.doi.org/10.5772/intechopen.80948

Figure 3. The designed power follower control strategy.

Qe ¼

where tf is the final time of the driving cycle.

Science,Technology and Advanced Application of Supercapacitors

4. Control strategy design

4.1 Rule-based control strategy

the CNG engine and the PMSG.

highest effective thermal efficiency.

The analysis program of the series hybrid powertrain.

designed using Stateflow.

Figure 2.

122

Ðtf <sup>0</sup> medt

<sup>0</sup> vdt , (14)

ρf Ðtf

To evaluate the performance of the designed series hybrid powertrain, a simulation program is developed according to the established mathematical model with MATLAB/Simulink and Advisor. Advisor is a modeling and simulation tool for hybrid electric vehicle based on MATLAB and Simulink developed by the US National Renewable Energy Laboratory [31]. The designed program is shown in Figure 2. Using a backward-facing method, the performance and fuel consumption of the series hybrid transit bus can be calculated. First, the driving force is determined based on the longitudinal dynamic equation. The rotating speed and driving torque of the rear axle are computed according to the tire model. Subsequently, the input torque and speed are determined for the final drive, and the input power of the motor is obtained. Then, the control strategy decides the power distribution between the ESS and the APU. As a result, both the output powers of the ESS and the APU are specified by the power bus. The supercapacitor model calculates the current and energy loss of the ESS. Moreover, the control strategy determines the operation torque and speed of the CNG engine according to the output power of the APU. Then, the fuel consumption is determined based on the performance maps of

Rule-based control strategy takes advantage of a small computation load, which is very suitable for real-time applications. Therefore, two rule-based control strategies—the thermostatic control and the power follower control—are set up, respectively. The thermostatic control is adopted first for hybrid electric vehicles due to its simple logic. When the HEV is running, if the SOC value drops to a lower bound, the engine starts and operates at a fixed point until the SOC value reaches to an upper bound. The operation condition of the engine is set to the point with the

Large current variation in the ESS may occur for the thermostatic control strategy which results in high energy loss. Therefore, a more sophisticated power follower control is developed. According to this strategy, if the engine state is on, the output power of the APU follows the power demand of the transit bus along an optimal operation line (OOL). Hence, the output power of the APU is decreased, and the operation current of the ESS can be alleviated. The designed power follower control strategy is shown in Figure 3. The decision algorithm for the engine state is

Since the power follower control needs to define an OOL, the energy efficiency characteristics of the APU must be studied first. The performance map of the CNG 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 89%. The efficiency decreases obviously if the generator speed is less than 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 close to the point with a maximum of engine torque.

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 control strategy.

Neither the target function nor the state equation of the designed series hybrid powertrain can be expressed as an explicit equation. Therefore, the analytic solution of this optimal problem cannot be obtained. However, a numerical optimal solution can be determined by a discrete optimal model translated from the aforementioned

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

N�1 k¼1

x kð Þ¼ þ 1 Fkð Þ x kð Þ; u kð Þ; k

x kð Þ∈ ½ � SOCmin; SOCmax u kð Þ<sup>∈</sup> <sup>0</sup>; Papu,max � �

Based on the established model of the series hybrid powertrain, the numerical solution of this discrete optimization problem can be determined. The solution approximates a theoretical minimum of the continuous model if the discrete computational grids for the state and input variables are fine enough. In this study, the discretization steps for the SOC and the APU output power are set to 0.005 and 1 kW, respectively. Since the total driving time of the CTBCDC is 1305 s, a time step

The optimization problem for the designed series hybrid powertrain contains the final state constraint, which can be translated to a problem without constraint via a penalty function. Sundstrom et al. have successfully applied this method to optimize the energy management problem of a parallel hybrid electric vehicle [32]. In this research, the penalty function for the state variable xi at time stage k is

Φkð Þ¼ xið Þk θð Þ xið Þ� k S<sup>0</sup>

A program is developed in MATLAB based on the designed optimal algorithm, and its working principle can be explained by Figure 5. The entire driving cycle is discretized along the time horizon from stage 1 to stage N shown as the yellow dashed lines. For time stage k, the state variable is discretized from SOCmin to SOCmax in a step of 0.005 and is expressed by xi(k), i = 1, 2, …, 79. At each state variable xi(k), the value of the cost-to-go function is denoted by Ji(k), and the corresponding penalty function is Φi(k). The input variable is discretized from 0 to

Papu,max in a step of 1 kW and is denoted by uj(k), j = 1, 2, …, 136. The fuel

consumption from stage k to stage k + 1 at the state xi(k) is denoted by the function mi(k). The initial and final states are constrained to the two red points S<sup>0</sup> shown in

The algorithm first calculates the penalty function JN at the last stage for the

mkð Þ x kð Þ; u kð Þ; k , (15)

(16)

(18)

:

2

m xið Þ<sup>k</sup> ; ujð Þ<sup>k</sup> ; <sup>k</sup> � � <sup>þ</sup> Jkþ<sup>1</sup> Fk xið Þ<sup>k</sup> ; ujð Þ<sup>k</sup> ; <sup>k</sup> � � � � � � <sup>þ</sup> <sup>Φ</sup>kð Þ xið Þ<sup>k</sup> :

: (17)

designed program:

subject to

of 1 s is used.

defined as

Figure 5.

125

state vector xi:

Jkð Þ¼ xið Þ<sup>k</sup> min ujð Þ<sup>k</sup> <sup>∈</sup> U kð Þ

min

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

8 >>>>>><

>>>>>>:

Accordingly, the cost-to-go function is defined by

u kð Þ Juk ð Þ¼ ð Þ <sup>∑</sup>

xð Þ¼ 0 s<sup>0</sup> x Nð Þ¼ s<sup>0</sup>

Figure 4. Performance maps of the APU.

#### 4.2 Optimal control using dynamic programming

In order to evaluate the maximum potential of energy savings, the theoretical minimum fuel consumption of the designed series hybrid powertrain is calculated using an optimal control algorithm based on dynamic programming. Dynamic programming is a static backward-facing optimal algorithm according to Bellman's principle of optimality. The boundary conditions of the optimal algorithm are the same with the thermostatic control.

The optimization target is the total fuel consumption based on the Chinese Transit Bus City Driving Cycle (CTBCDC). The SOC of the ESS is used as the state variable, and the output power of the APU is used as the input variable. If the output power of the APU keeps constant, the fuel consumption achieves the minimum when the CNG engine operates along the OOL. Therefore, the corresponding engine output torque and speed are determined. The target function calculates the instantaneous fuel consumption at time t and is denoted by m(x(t), u(t), t). Function F(x(t), u(t), t) is the state equation determining the SOC for the next time. The initial and final states of the SOC are set to the same values as a constraint. Moreover, the SOC and the output power of the APU must be limited within the allowable ranges all the time.

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

Neither the target function nor the state equation of the designed series hybrid powertrain can be expressed as an explicit equation. Therefore, the analytic solution of this optimal problem cannot be obtained. However, a numerical optimal solution can be determined by a discrete optimal model translated from the aforementioned designed program:

$$\min\_{u(k)}\ J(u(k)) = \sum\_{k=1}^{N-1} m\_k(\boldsymbol{\omega}(k), u(k), k), \tag{15}$$

subject to

$$\begin{cases} \varkappa(k+1) = F\_k(\varkappa(k), \mu(k), k) \\ \varkappa(\mathbf{0}) = \varkappa\_0 \\ \varkappa(N) = \varkappa\_0 \\ \varkappa(k) \in [\mathrm{SOC}\_{\mathrm{min}}, \mathrm{SOC}\_{\mathrm{max}}] \\ u(k) \in \left[\mathbf{0}, \mathrm{P}\_{\mathrm{app}, \mathrm{max}}\right] \end{cases} \tag{16}$$

Based on the established model of the series hybrid powertrain, the numerical solution of this discrete optimization problem can be determined. The solution approximates a theoretical minimum of the continuous model if the discrete computational grids for the state and input variables are fine enough. In this study, the discretization steps for the SOC and the APU output power are set to 0.005 and 1 kW, respectively. Since the total driving time of the CTBCDC is 1305 s, a time step of 1 s is used.

The optimization problem for the designed series hybrid powertrain contains the final state constraint, which can be translated to a problem without constraint via a penalty function. Sundstrom et al. have successfully applied this method to optimize the energy management problem of a parallel hybrid electric vehicle [32]. In this research, the penalty function for the state variable xi at time stage k is defined as

$$\Phi\_k(\varkappa\_i(k)) = \theta(\varkappa\_i(k) - \mathbb{S}\_0)^2. \tag{17}$$

Accordingly, the cost-to-go function is defined by

$$J\_k(\mathbf{x}\_i(k)) = \min\_{\boldsymbol{u}\_j(k) \in U(k)} \left\{ m\left(\mathbf{x}\_i(k), \boldsymbol{u}\_j(k), k\right) + f\_{k+1}\left[\boldsymbol{F}\_k\left(\mathbf{x}\_i(k), \boldsymbol{u}\_j(k), k\right)\right] \right\} + \Phi\_k(\mathbf{x}\_i(k)).\tag{18}$$

A program is developed in MATLAB based on the designed optimal algorithm, and its working principle can be explained by Figure 5. The entire driving cycle is discretized along the time horizon from stage 1 to stage N shown as the yellow dashed lines. For time stage k, the state variable is discretized from SOCmin to SOCmax in a step of 0.005 and is expressed by xi(k), i = 1, 2, …, 79. At each state variable xi(k), the value of the cost-to-go function is denoted by Ji(k), and the corresponding penalty function is Φi(k). The input variable is discretized from 0 to Papu,max in a step of 1 kW and is denoted by uj(k), j = 1, 2, …, 136. The fuel consumption from stage k to stage k + 1 at the state xi(k) is denoted by the function mi(k). The initial and final states are constrained to the two red points S<sup>0</sup> shown in Figure 5.

The algorithm first calculates the penalty function JN at the last stage for the state vector xi:

4.2 Optimal control using dynamic programming

Science,Technology and Advanced Application of Supercapacitors

same with the thermostatic control.

Figure 4.

Performance maps of the APU.

able ranges all the time.

124

In order to evaluate the maximum potential of energy savings, the theoretical minimum fuel consumption of the designed series hybrid powertrain is calculated using an optimal control algorithm based on dynamic programming. Dynamic programming is a static backward-facing optimal algorithm according to Bellman's principle of optimality. The boundary conditions of the optimal algorithm are the

The optimization target is the total fuel consumption based on the Chinese Transit Bus City Driving Cycle (CTBCDC). The SOC of the ESS is used as the state variable, and the output power of the APU is used as the input variable. If the output power of the APU keeps constant, the fuel consumption achieves the minimum when the CNG engine operates along the OOL. Therefore, the corresponding engine output torque and speed are determined. The target function calculates the instantaneous fuel consumption at time t and is denoted by m(x(t), u(t), t). Function F(x(t), u(t), t) is the state equation determining the SOC for the next time. The initial and final states of the SOC are set to the same values as a constraint. Moreover, the SOC and the output power of the APU must be limited within the allowScience,Technology and Advanced Application of Supercapacitors

$$J\_N(\mathfrak{x}\_i) = \mathfrak{G}(\mathfrak{x}\_i - \mathfrak{S}\_0)^2. \tag{19}$$

5. Result analysis

follower strategy.

Figure 6.

127

System performance of the thermostatic control strategy.

5.1 Comparison of rule-based control strategies

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

The system performance and fuel economy of the series hybrid transit bus are evaluated using the CTBCDC driving cycle. The performances of the thermostatic control and the power follower control are compared. The results of the thermostatic control strategy are given in Figure 6. Figure 7 shows the results of the power

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

The target vehicle speed and the achievable vehicle speed are given in Figures 6a and 7a, which are denoted by the blue and magenta lines, respectively. The achievable vehicle speeds for both of the rule-based strategies can trace the target one perfectly. Therefore, both can satisfy the requirements of drivability. Figure 6b shows the input power of the PMSM as the blue lines and the output power of the CNG engine by the red lines. Figure 7b shows the results of the power

Then taking into account each state variable of stage N � 1, a state vector at the next time stage is computed corresponding to the input variable vector based on the state equation. This process is described by a group of lines from one state point of stage N � 1 to different positions of stage N. Because the calculated state vector for stage N may not locate exactly at the computational grid points, a linear interpolation is used to determine the values of the corresponding cost-to-go function. Meanwhile, the fuel consumption function for each state variable is calculated. As a result, the values of cost-to-go function at time stage N � 1 is obtained according to Eq. (18). The optimal path for each state variable is represented by a blue line in Figure 5. The above recurrence calculation process is repeated along the time horizon one by one until to the first time stage. Finally, an optimal map of the costto-go function for all the time stages and the state variables is obtained.

In order to determine the optimal policy, a forward calculation process is performed based on the optimal map. The following equation is used to compute the minimum fuel consumption from the initial state S<sup>0</sup> to the same final state, and the corresponding input variable is recorded:

$$M(k) = \min\_{\boldsymbol{\mu}\_{j}(k) \in \boldsymbol{U}(k)} \left\{ m\left(\mathbf{x}\_{op}(k), \boldsymbol{u}\_{j}(k), k\right) + \boldsymbol{I}\_{k+1}\left[\boldsymbol{F}\_{k}\left(\mathbf{x}\_{op}(k), \boldsymbol{u}\_{j}(k), k\right)\right] \right\}.\tag{20}$$

where xop(k) is the optimal state variable at stage k. The optimal state value for the next time stage is determined by

$$\varkappa\_{op}(k+1) = \varkappa\_{op}(k) + \frac{(P\_m(k) - \mathfrak{u}(k))\mathcal{C}(k)}{U\_0^2 \varkappa\_{op}(k)},\tag{21}$$

where U<sup>0</sup> is the rated voltage of the ESS. Repeating the calculation process until the last time stage, an optimal policy is obtained shown as the green line in Figure 5. The algorithm uses a weighting factor θ for the penalty function whose value specifies the importance of the SOC deviation relative to the fuel consumption. In order to make the final state of the optimal path converge to S0, various values of θ are tried. Finally, a value of 120 is specified, and the relative error of the SOC at the last state is 0.44%.

Figure 5. Principle of the optimal algorithm based on dynamic programming.

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

## 5. Result analysis

JNð Þ¼ xi θð Þ xi � S<sup>0</sup>

Science,Technology and Advanced Application of Supercapacitors

to-go function for all the time stages and the state variables is obtained.

the corresponding input variable is recorded:

M kð Þ¼ min ujð Þ<sup>k</sup> <sup>∈</sup> U kð Þ

last state is 0.44%.

Figure 5.

126

Principle of the optimal algorithm based on dynamic programming.

the next time stage is determined by

In order to determine the optimal policy, a forward calculation process is performed based on the optimal map. The following equation is used to compute the minimum fuel consumption from the initial state S<sup>0</sup> to the same final state, and

where xop(k) is the optimal state variable at stage k. The optimal state value for

where U<sup>0</sup> is the rated voltage of the ESS. Repeating the calculation process until the last time stage, an optimal policy is obtained shown as the green line in Figure 5. The algorithm uses a weighting factor θ for the penalty function whose value specifies the importance of the SOC deviation relative to the fuel consumption. In order to make the final state of the optimal path converge to S0, various values of θ are tried. Finally, a value of 120 is specified, and the relative error of the SOC at the

xopð Þ¼ <sup>k</sup> <sup>þ</sup> <sup>1</sup> xopð Þþ <sup>k</sup> ð Þ Pmð Þ� <sup>k</sup> u kð Þ C kð Þ

Then taking into account each state variable of stage N � 1, a state vector at the next time stage is computed corresponding to the input variable vector based on the state equation. This process is described by a group of lines from one state point of stage N � 1 to different positions of stage N. Because the calculated state vector for stage N may not locate exactly at the computational grid points, a linear interpolation is used to determine the values of the corresponding cost-to-go function. Meanwhile, the fuel consumption function for each state variable is calculated. As a result, the values of cost-to-go function at time stage N � 1 is obtained according to Eq. (18). The optimal path for each state variable is represented by a blue line in Figure 5. The above recurrence calculation process is repeated along the time horizon one by one until to the first time stage. Finally, an optimal map of the cost-

2

m xopð Þ<sup>k</sup> ; ujð Þ<sup>k</sup> ; <sup>k</sup> <sup>þ</sup> Jkþ<sup>1</sup> Fk xopð Þ<sup>k</sup> ; ujð Þ<sup>k</sup> ; <sup>k</sup> : (20)

U2

: (19)

<sup>0</sup>xopð Þ<sup>k</sup> , (21)

#### 5.1 Comparison of rule-based control strategies

The system performance and fuel economy of the series hybrid transit bus are evaluated using the CTBCDC driving cycle. The performances of the thermostatic control and the power follower control are compared. The results of the thermostatic control strategy are given in Figure 6. Figure 7 shows the results of the power follower strategy.

The target vehicle speed and the achievable vehicle speed are given in Figures 6a and 7a, which are denoted by the blue and magenta lines, respectively. The achievable vehicle speeds for both of the rule-based strategies can trace the target one perfectly. Therefore, both can satisfy the requirements of drivability. Figure 6b shows the input power of the PMSM as the blue lines and the output power of the CNG engine by the red lines. Figure 7b shows the results of the power

Figure 6. System performance of the thermostatic control strategy.

The output power of the ESS for the thermostatic control is shown in Figure 6f, where the positive values mean discharging and the negative values denote charging (this expression is used for the following figures). Figure 7f shows the results of the power follower control. Both output powers vary all the time except for the stopping conditions. Furthermore, the variation magnitude of the thermostatic control is obviously greater than that of the power follower control. The maximum discharging power for the thermostatic control is 126.8 kW, while this value reduces to 95.68 kW for the power follower control. By contrast, the maximum charging power of the ESS for the thermostatic control is 202.8 kW, while this value reduces significantly to 106.6 kW for the power follower control. The profiles of the SOC are given in Figures 6g and 7g, respectively. In terms of the thermostatic control, the SOC shows an alternative variation process that first decreases slowly then increases rapidly. However, the SOC of the power follower control shows a relative slow augmentation process, which is in favor of the life

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

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

The energy efficiencies of the ESS are obtained according to Eqs. (10) and (11). The results are given in Figures 6h and 7h. The average discharging and charging efficiencies of the power follower control are 99.1 and 98.5%. As a contrast, these two values are 99.1 and 98.4% for the thermostatic control. The results indicate that the energy efficiency of the power follower control is slightly higher than the thermostatic control. The energy efficiency of supercapacitor will decrease obviously if the operation temperature is too high. Therefore, a temperature control system for the ESS is required in practice. The voltage profiles are given in Figures 6i and 7i. Both of them operate within the constraint range. The average voltage for the power follower control is 450 V, while the average voltage is 505 V for the thermostatic control. Enhancement of the operation voltage is helpful to improve the energy efficiency of the electric motor. Because the SOC value has a linear relation with the operation voltage, the variation tendency of the SOC

is consistent with that of the voltage. The current profiles are given in

Figures 6j and 7j. The maximum discharging and charging currents for the power follower control are 247 and 269 A. However, these two values are increased significantly to 300 and 471 A for the thermostatic control. Although supercapacitors can work with a high power rate, a lower current will be in favor of their life span. Therefore, it seems that the power follower control strategy is better than the

Table 2 gives the equivalent fuel consumptions of these strategies. The equivalent fuel consumption is 17.32 L/100 km for the power follower strategy, while it equals 17.51 L/100 km for the thermostatic control strategy. In contrast to a conventional vehicle powered solely by the same CNG engine, the fuel consumptions of the two rule-based strategies are decreased by 52%. Figure 8 is used to explain the reason from a viewpoint of energy efficiency. The OOL is displayed as the green line. Point P is the operation point of the thermostatic control whose energy efficiency is 34.06%. Because most of the APU output power of the thermostatic control first charges to the ESS and then outputs to the power line, the overall energy efficiency of the series hybrid powertrain decreases slightly to 33.2%, which is denoted by a blue contour L in Figure 8. The operation points of the power follower control are described by the cyan points. Most of the APU output power is delivered directly to the power line for the power follower strategy. The energy efficiencies for the thermostatic control approximate the line L, while the energy efficiencies of the power follower control remain at the cyan points. Therefore, the fuel economy of the power follower control is a little higher than that of the

span of the ESS.

thermostatic control.

thermostatic control.

129

Figure 7. System performance of the power follower control strategy.

follower strategy. The engine operation time of the thermostatic control is less than that of the power follower strategy, which is 141 s for the thermostatic control while 151 s for the power follower control. The engine power keeps constant for the thermostatic control. However, the engine power of the power follower control varies along the OOL within a small range. The results of the engine state for these two control strategies are shown in Figures 6c and 7c, where the engine state ON is represented by 1, and the engine state OFF is denoted by 0. The engine demonstrates a regular alternative start and stop for the thermostatic control, whereas the engine starts more frequently for the power follower control, which will worsen the engine emissions. The engine speed and torque are shown in Figure 6d and e for the thermostatic control. Compared to the results of the power follower control given in Figure 7d and e, the engine can operate more stably for the thermostatic control, which will be beneficial for the engine working life.

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

The output power of the ESS for the thermostatic control is shown in Figure 6f, where the positive values mean discharging and the negative values denote charging (this expression is used for the following figures). Figure 7f shows the results of the power follower control. Both output powers vary all the time except for the stopping conditions. Furthermore, the variation magnitude of the thermostatic control is obviously greater than that of the power follower control. The maximum discharging power for the thermostatic control is 126.8 kW, while this value reduces to 95.68 kW for the power follower control. By contrast, the maximum charging power of the ESS for the thermostatic control is 202.8 kW, while this value reduces significantly to 106.6 kW for the power follower control. The profiles of the SOC are given in Figures 6g and 7g, respectively. In terms of the thermostatic control, the SOC shows an alternative variation process that first decreases slowly then increases rapidly. However, the SOC of the power follower control shows a relative slow augmentation process, which is in favor of the life span of the ESS.

The energy efficiencies of the ESS are obtained according to Eqs. (10) and (11). The results are given in Figures 6h and 7h. The average discharging and charging efficiencies of the power follower control are 99.1 and 98.5%. As a contrast, these two values are 99.1 and 98.4% for the thermostatic control. The results indicate that the energy efficiency of the power follower control is slightly higher than the thermostatic control. The energy efficiency of supercapacitor will decrease obviously if the operation temperature is too high. Therefore, a temperature control system for the ESS is required in practice. The voltage profiles are given in Figures 6i and 7i. Both of them operate within the constraint range. The average voltage for the power follower control is 450 V, while the average voltage is 505 V for the thermostatic control. Enhancement of the operation voltage is helpful to improve the energy efficiency of the electric motor. Because the SOC value has a linear relation with the operation voltage, the variation tendency of the SOC is consistent with that of the voltage. The current profiles are given in Figures 6j and 7j. The maximum discharging and charging currents for the power follower control are 247 and 269 A. However, these two values are increased significantly to 300 and 471 A for the thermostatic control. Although supercapacitors can work with a high power rate, a lower current will be in favor of their life span. Therefore, it seems that the power follower control strategy is better than the thermostatic control.

Table 2 gives the equivalent fuel consumptions of these strategies. The equivalent fuel consumption is 17.32 L/100 km for the power follower strategy, while it equals 17.51 L/100 km for the thermostatic control strategy. In contrast to a conventional vehicle powered solely by the same CNG engine, the fuel consumptions of the two rule-based strategies are decreased by 52%. Figure 8 is used to explain the reason from a viewpoint of energy efficiency. The OOL is displayed as the green line. Point P is the operation point of the thermostatic control whose energy efficiency is 34.06%. Because most of the APU output power of the thermostatic control first charges to the ESS and then outputs to the power line, the overall energy efficiency of the series hybrid powertrain decreases slightly to 33.2%, which is denoted by a blue contour L in Figure 8. The operation points of the power follower control are described by the cyan points. Most of the APU output power is delivered directly to the power line for the power follower strategy. The energy efficiencies for the thermostatic control approximate the line L, while the energy efficiencies of the power follower control remain at the cyan points. Therefore, the fuel economy of the power follower control is a little higher than that of the thermostatic control.

follower strategy. The engine operation time of the thermostatic control is less than that of the power follower strategy, which is 141 s for the thermostatic control while 151 s for the power follower control. The engine power keeps constant for the thermostatic control. However, the engine power of the power follower control varies along the OOL within a small range. The results of the engine state for these two control strategies are shown in Figures 6c and 7c, where the engine state ON is represented by 1, and the engine state OFF is denoted by 0. The engine demonstrates a regular alternative start and stop for the thermostatic control, whereas the engine starts more frequently for the power follower control, which will worsen the engine emissions. The engine speed and torque are shown in Figure 6d and e for the thermostatic control. Compared to the results of the power follower control given in Figure 7d and e, the engine can operate more stably for the thermostatic

control, which will be beneficial for the engine working life.

System performance of the power follower control strategy.

Science,Technology and Advanced Application of Supercapacitors

Figure 7.

128

#### Figure 8.

Comparison of energy efficiencies of different control strategies.


#### Table 2.

Results of fuel consumption.

#### 5.2 Results of optimal control

The optimal performance of the series hybrid powertrain is shown in Figure 9. Figure 9a is the velocity profile of the CTBCDC cycle. The corresponding input power required by the PMSM is shown in Figure 9b, where the positive values are used for the driving mode and the negative values are used for the regenerative braking mode. These two profiles are used as input parameters for the optimal algorithm. The optimal results of the output power of the APU are given in Figure 9c, which demonstrates a series of short impulse when the transit bus undergoes an acceleration process. Furthermore, the number of the impulse increases as the power demand of the motor rises. The APU stops if the power demand of the motor is negative. The corresponding engine output torque and speed are shown in Figure 9d and e, respectively. The optimal engine speed and torque remain around 1500 r/min and 600 Nm. The reason for such an optimal trajectory can be explained as follows. The operation points of the CNG engine for the optimal control are described by the red points in Figure 8. These red points are very close to the point P where the energy efficiency is the highest. Therefore, an overall minimum of the fuel consumption is realized. On the other hand, the

internal series resistance of the ESS consumes part of the energy during the charging or discharging process, especially for large current conditions. To avoid too much energy loss of the ESS, the optimal policy will try to use the APU power to satisfy the power demand of the PMSM exactly. In other words, the optimal policy is obtained if the APU operates at the maximum energy efficiency point and the amount of the output power equals to the power demand of the PMSM, leading to

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

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

The output power of the supercapacitors is given in Figure 9f. Generally, the variation tendency of the output power is similar to that of the power follower control shown in Figure 7f. However, a series of impulses occur under the driving modes due to the same reason for the output power of the APU. The SOC profile is given in Figure 9g. The optimal SOC remains within a small interval around the initial valleys. Only two valleys occur at the high-velocity condition with rapid braking. The energy loss of the ESS is decreased if the current of the ESS is limited

the energy supply in the form of a series of impulse.

System performance of the optimal control by dynamic programming.

Figure 9.

131

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

Figure 9. System performance of the optimal control by dynamic programming.

internal series resistance of the ESS consumes part of the energy during the charging or discharging process, especially for large current conditions. To avoid too much energy loss of the ESS, the optimal policy will try to use the APU power to satisfy the power demand of the PMSM exactly. In other words, the optimal policy is obtained if the APU operates at the maximum energy efficiency point and the amount of the output power equals to the power demand of the PMSM, leading to the energy supply in the form of a series of impulse.

The output power of the supercapacitors is given in Figure 9f. Generally, the variation tendency of the output power is similar to that of the power follower control shown in Figure 7f. However, a series of impulses occur under the driving modes due to the same reason for the output power of the APU. The SOC profile is given in Figure 9g. The optimal SOC remains within a small interval around the initial valleys. Only two valleys occur at the high-velocity condition with rapid braking. The energy loss of the ESS is decreased if the current of the ESS is limited

5.2 Results of optimal control

Results of fuel consumption.

Hybrid bus using the power follower

Relative to the conventional bus with a CNG engine.

control

Figure 8.

a

130

Table 2.

The optimal performance of the series hybrid powertrain is shown in Figure 9. Figure 9a is the velocity profile of the CTBCDC cycle. The corresponding input power required by the PMSM is shown in Figure 9b, where the positive values are used for the driving mode and the negative values are used for the regenerative braking mode. These two profiles are used as input parameters for the optimal algorithm. The optimal results of the output power of the APU are given in Figure 9c, which demonstrates a series of short impulse when the transit bus undergoes an acceleration process. Furthermore, the number of the impulse increases as the power demand of the motor rises. The APU stops if the power demand of the motor is negative. The corresponding engine output torque and speed are shown in Figure 9d and e, respectively. The optimal engine speed and torque remain around 1500 r/min and 600 Nm. The reason for such an optimal trajectory can be explained as follows. The operation points of the CNG engine for the optimal control are described by the red points in Figure 8. These red points are very close to the point P where the energy efficiency is the highest. Therefore, an overall minimum of the fuel consumption is realized. On the other hand, the

(L/100 km)

17.32 52.7

Energy reduction (%)a

Powertrain Fuel consumption

Science,Technology and Advanced Application of Supercapacitors

Hybrid bus using the thermostatic control 17.51 52.2

Hybrid bus using optimal control 15.72 57.1

Conventional bus using a CNG engine 36.60

Comparison of energy efficiencies of different control strategies.

within a small range. Thus, the fuel consumption can be reduced. The calculated energy efficiencies of the ESS are shown in Figure 9h. The average energy efficiency is very close to the results of the rule-based strategies. The output voltage and current are given in Figures 9i and j, respectively. The output voltage is proportional to the SOC. The optimal current demonstrates a similar tendency as that of the power follower control. However, more spikes occur at the driving conditions.

Acronyms

APU auxiliary power unit

CNG compressed natural gas

ESS energy storage system EV electric vehicle

SOC state of charge

Conflict of interest

Author details

Enhua Wang<sup>1</sup>

Beijing, China

133

bsfc brake-specific fuel consumption

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

HESS hybrid energy storage system HEV hybrid electric vehicle OOL optimal operation line

PHEV plug-in hybrid electric vehicle

The authors declare no conflict of interest.

\*, Minggao Ouyang<sup>2</sup>

provided the original work is properly cited.

\*Address all correspondence to: enhua.wang@yahoo.com

, Fujun Zhang<sup>1</sup> and Changlu Zhao<sup>1</sup>

1 School of Mechanical Engineering, Beijing Institute of Technology, Beijing, China

2 State Key Laboratory of Automotive Safety and Energy, Tsinghua University,

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

CTBCDC Chinese Transit Bus City Driving Cycle EDLC electrochemical double-layer capacitor

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

PMSG permanent magnetic synchronous generator PMSM permanent magnetic synchronous motor

The optimal equivalent fuel consumption is 15.72 L/100 km listed in Table 2. Compared to the conventional transit bus, the optimal fuel consumption of the hybrid bus can be decreased by 57% if the quantity of fuel consumed during the starting processes is ignored. In practice, the fuel consumption including starting process will be increased slightly. Taking the optimal result as a reference, the fuel consumptions of the rule-based control strategies are increased by approximate 1.7 L/100 km.
