Research on energy management of hybrid energy storage system for electric bus

Abstract

This article presents an energy management approach for the hybrid energy storage system in an electric bus at different temperatures. An electric bus equipped with a semi-active hybrid energy storage system is considered as the research object. According to the urban climatic characteristics of the vehicle running, the convex optimization approach considering temperature factors is proposed. The purpose of this study is to minimize the energy loss and maximize the discharge and charge depth of the super capacitor. Simulation results show that the comprehensive energy efficiency of the proposed method is 83.31% and the comprehensive energy efficiency is improved by 2.42% at 25°C, which is compared with the rule-based power allocation method based on urban driving cycle in Harbin, China. When the ambient temperature is −5°C, the comprehensive energy efficiency of the proposed method is 81.03%. This result is improved by 1.45% and the battery power variance at −5°C is reduced by 20.11% compared with the rule-based power allocation method. Therefore, the proposed power distribution method can effectively improve the functioning of an electric bus at different temperatures.

Keywords

Electric bus hybrid energy storage system power distribution temperature convex optimization

Introduction

The functioning of a lithium-ion battery in an electric vehicle is significantly affected by the ambient temperature. With a decrease in the temperature, the ohm resistance, internal resistance, and total internal resistance of the battery will increase.¹ For instance, the charging ohm resistance is five times the normal temperature resistance. When the temperature is below −10°C, the battery will show significant power loss and capacity loss.² The functioning of the power battery of an electric vehicle in Harbin, a city in the north of China, changes at different temperatures because the temperature of the city is different in summer and winter. Although the research results demonstrate that the use of an electric vehicle hybrid energy storage system (HESS) could improve the working ability of the electric vehicle and extend the life of the power battery at low temperature, the methods to optimize the size and power split of an HESS are the key technical problems in the application of electric vehicles.^3,4

There are several researches in the field of HESS. The HESS energy management strategies can be divided into on-line and off-line. On-line energy management strategies mainly include rule-based energy management strategies, energy management strategies based on model predictions and energy management strategy of fuzzy control.^5,6 Off-line energy management strategies mainly includes Pontryagin’s minimum principle, dynamic programming (DP), convex optimization, and other methods.⁷ In Song et al.,⁸ aiming at a semi-active HESS with different structures, a DP method to solve the problem of optimization of semi-active HESS was presented. In Song et al.,⁹ a new semi-active HESS was proposed, and a DP method to optimize size of the semi-active HESS was used to minimize the operating costs and battery capacity loss. In Hu et al.,¹⁰ convex optimization method was used to optimize the size of battery and super capacitor (SC) in a fuel cell hybrid vehicle with a semi-active HESS.

Wang et al.⁵ and Azib et al.¹¹ used a kind of rule-based energy management approach for semi-active HESS. In Garcia et al.,¹² the energy management strategy of fuzzy control was used to allocate energy to the HESS. In Romaus et al.,¹³ stochastic DP was proposed. In Romaus et al.,¹³ there were two objects whose purpose was to reduce the power loss of the HESS and to ensure that the SC voltage was close to the reference voltage. Torreglosa et al.¹⁴ proposed a model predictive control of the HESS for energy management. In order to reduce the power loss of HESS, Laldin et al.,¹⁵ used a prediction algorithm to distribute the power of the storage system. Vinot and Trigui¹⁶ used Pontryagin’s minimum principle to reduce the root mean square value of the battery current. In Moreno et al.,¹⁷ a neural network was applied to reduce the power loss. Although the aforementioned power optimization methods can achieve good results under normal temperature or fixed working conditions, the influence of temperature was neglected.

This study is concerned with energy management of semi-active HESS in an electric bus. In this article, a convex approach is proposed combined with the climatic characteristics of Harbin, whose optimization objective is to minimize the energy loss and maximize discharge and charge depth of the SC. The proposed method will realize the efficient and stable operation of HESS at different temperatures.

Analysis of configuration and working modes of HESS

There are three configurations of HESS: passive, fully active, and semi-active.¹⁸

The configuration of a passive composite energy storage system is shown in Figure 1, where an SC and battery are connected in parallel with a drive motor. The SC acts as a low-pass filter to reduce the impact of frequent output power changes on the power batteries. This structure has the characteristics of high efficiency and low cost. However, this parallel approach requires the two energy sources to have the same voltage, thus limiting the use of SCs; moreover, it cannot achieve control of the two energy sources.

Figure 1.

Passive parallel configuration.

The configuration of a fully active composite energy storage system is shown in Figure 2. The configuration applies to two chopper circuits. Through the control of the two chopper circuits, the energy distribution of the SC and battery is flexibly realized. However, the structure of the composite energy storage system is relatively complex in terms of control. Moreover, the two chopper circuit structures reduce the system efficiency and increase the costs.

Figure 2.

Fully active configuration.

Battery/SC configuration is shown in Figure 3. The battery is connected to the DC bus, via a DC/DC converter, with the SC in parallel. The main feature of this structure is its ease of control, but the SC directly connected to the DC bus causes the problem of bus voltage instability.

Figure 3.

Battery/SC configuration.

SC/battery configuration is shown in Figure 4. The SC is connected to the DC bus via a bi-directional DC/DC converter. Compared with the fully active composite energy storage system, this structure reduces the costs. Compared with battery/SC configuration, the bus voltages is more stable. Therefore, this study selected this structure as the research object. In general, for such a composite energy storage system, the bi-directional DC/DC converter is turned off when the output power of the power battery can satisfy the power demand of the electric vehicle. When the output power of the power battery is not sufficient to satisfy the requirements of the electric vehicle, the bi-directional DC/DC converter is opened, and the output power of the SC and the battery satisfy the power demand of the electric vehicle. Under braking conditions, the bi-directional DC/DC converter is opened to ensure the use of SC to absorb the feedback energy. When the SC cannot satisfy the feedback energy requirements, the power battery will be used to feedback energy.

Figure 4.

SC/battery configuration.

Power system modeling

Traction modeling

When a passenger is traveling on the road, the traction motor should overcome the running resistance (F_t), including the rolling resistance (F_f), air resistance (F_w), slope resistance (F_i), and acceleration resistance (F_j), to satisfy the following equations¹⁹

F_{t} = F_{f} + F_{w} + F_{i} + F_{j}

(1)

F_{f} = fmg \cos α

(2)

F_{i} = mg \sin α

(3)

F_{w} = 1 / 2 C_{d} A ρ u_{a}^{2}

(4)

F_{j} = ma

(5)

where f is the rolling resistance coefficient, m is the mass of the electric bus, g is the gravitational acceleration (assumed to be 9.8 m/s²), and α is the slope of the road. In this study, α = 0, C_d is the air resistance coefficient, A is the windward area of the electric vehicle, ρ is the air density, and u_a is the motor speed.

According to the pure electric bus power balance characteristics, at time t, the following relationship should be satisfied

P_{m} + P_{mloss} + P_{aux} = P_{bt} + P_{sct} η_{dc}

(6)

where P_m is the output power of the motor, which is equal to the multiplication of F_t and speed v; P_mloss is the loss power of the motor; P_aux is the power of the electric air conditioner, electric power steering, and other electric auxiliary systems; P_bt is the output power of the battery port; P_sct is the output power of the SC port; and η_dc is the bi-directional DC/DC converter efficiency.

HESS modeling

The SC model is shown in Figure 5, where R_sc is the equivalent series resistance of the SC.

Figure 5.

The equivalent model of SC.

The state of charge (SOC) and open circuit voltage of the SC have the following relationship

u_{sc} = bso c_{sc} + u_{sc 0}

(7)

where u_sc is the open voltage of the SC, soc_sc is the SOC of the SC, and u_sc₀ is the open circuit voltage of the SC when its SOC is equal to 0, and its value is 0. Furthermore, b is the amount associated with du_sc/dsoc_sc, and it can be obtained by fitting the data. According to the SC model shown in Figure 5, the following relationship exists

P_{sct} = P_{sc} - P_{scloss}

(8)

where P_sct is the output power of the SC port, P_sc is the output power of the SC in the ideal state, and P_scloss is the total power dissipated in the equivalent series resistance of the SC. The SC satisfies the following relationship

E_{sc} = \frac{n_{sc} C_{sc}}{2} (u_{sc}^{2} - u_{sc 0}^{2})

(9)

where E_sc is the energy of the SC, n_sc is the number of SCs, and C_sc is the capacitance of the SC. The output power of the SC satisfies the following relationship

P_{nsc} = u_{sc} i_{sc}

(10)

where P_nsc is the output power of the SC and i_sc is the current of the SC. According to equation (10), the single current flowing through the SC is

i_{sc} = \frac{P_{nsc}}{u_{sc}}

(11)

According to equations (9) and (11), the total power P_scloss that can be dissipated in the equivalent series resistance of the SC satisfies the following equation

P_{scloss} = \frac{R_{sc} C_{sc} P_{sc}^{2}}{2 E_{sc} + u_{sc 0}^{2} C_{sc} n_{sc}}

(12)

where R_sc is the equivalent series resistance of the SC. The relationship between the energy E_sc and power P_sc of the SC is

\frac{d E_{sc}}{dt} = - P_{sc}

(13)

The SC single current i_sc ∈ [I_sc_min, I_sc_max], where I_sc_min is the minimum value of the output current of the SC and I_sc_max is the maximum value of the output current of the SC; therefore, the power of the SC P_sc satisfies the following equation

\begin{matrix} I_{sc min} \sqrt{n_{sc} (\frac{2 E_{sc}}{C_{sc}} + u_{sc 0}^{2} n_{sc})} \\ \leq P_{sc} \leq I_{sc max} \sqrt{n_{sc} (\frac{2 E_{sc}}{C_{sc}} + u_{sc 0}^{2} n_{sc})} \end{matrix}

(14)

The SOC of SC satisfies [SOC_sc_min, SOC_sc_max], where SOC_sc_min is the minimum value of the SOC of the SC and SOC_sc_max is the maximum value of the SOC of the SC. Hence, the energy of the SC has the following constraints

\begin{matrix} \frac{C_{sc} n_{sc}}{2} (u_{sc}^{2} (so c_{sc min}) - u_{sc 0}^{2}) \\ \leq E_{sc} \leq \frac{C_{sc} n_{sc}}{2} (u_{sc}^{2} (so c_{sc max}) - u_{sc 0}^{2}) \end{matrix}

(15)

In order to ensure that the energy of the SC remains the same as its initial value, the following constraints are set

E_{SC} (t_{0}) = E_{SC} (t_{f})

(16)

where t₀ and t_f are the initial time and final time of a cyclic condition, respectively. The battery cell model is shown in Figure 6. In the figure, R_bat is the equivalent series resistance of the battery.

Figure 6.

The equivalent model of power battery.

The relationship between the open circuit voltage and the SOC of lithium iron phosphate batteries at different temperatures is shown in Figure 7.

Figure 7.

The relationship between SOC and battery open circuit voltage.

From Figure 7, it can be observed that the battery SOC and open circuit voltage can be approximated by the following linear relationship when the SOC is in the range of 10%–100%

u_{b} = aso c_{b} + u_{b 0}

(17)

where u_b is the open circuit voltage of the battery, soc_b is the SOC of the battery, u_b₀ is the open circuit voltage when the SOC of the battery is equal to 0, a is the amount associated with du_b/dsoc_b, and u_b₀ can be obtained by fitting the data.

According to the equivalent model of the power cell in Figure 6, we can observe that the relationship between the power P_b and the power of the port output P_bt is not considered when the equivalent series resistance R_bat is considered

P_{bt} = P_{b} - P_{bloss}

(18)

where P_bt is the battery output power, P_b is the ideal state under the conditions of the battery output power, and P_bloss is the loss of power in the battery resistance. The stored energy of the power battery E_b satisfies

E_{b} = \frac{n_{b} C_{b}}{2} (u_{b}^{2} - u_{b 0}^{2})

(19)

where n_b is the number of batteries used, C_b is the capacitance of the battery, u_b is the open circuit voltage of the battery, and u_b₀ is the open circuit voltage when the battery SOC is equal to zero. The output power of the battery cell satisfies the following relationship

P_{nb} = u_{b} i_{b}

(20)

where P_nb is the output power of the battery cell and i_b is the current of the battery cell. According to equation (20), the battery cell current is

i_{b} = \frac{P_{nb}}{u_{b}}

(21)

According to equations (19) and (21), the power loss P_bloss in the battery resistance can be obtained as

P_{bloss} = n_{b} i_{b}^{2} R_{b} = \frac{R_{b} C_{b} P_{b}^{2}}{2 E_{b} + u_{b 0}^{2} C_{b} n_{b}}

(22)

where R_b is the internal resistance of the battery and C_b is the capacity of the battery. The relationship between the energy E_b and power P_b of the battery is as follows

\frac{d E_{b}}{dt} = - P_{b}

(23)

Owing to the battery cell current i_b ∈ [I_b_min, I_b_max], where I_b_min is the minimum value of the output current of the battery cell and I_b_max is the maximum value of the current that the battery cell can output, the battery power P_b satisfies

I_{b min} \sqrt{n_{b} (\frac{2 E_{b}}{C_{b}} + u_{b 0}^{2} n_{b})} \leq P_{b} \leq I_{b max} \sqrt{n_{b} (\frac{2 E_{b}}{C_{b}} + u_{b 0}^{2} n_{b})}

(24)

Owing to the battery SOC∈[SOC_b_min, SOC_b_max], where SOC_b_min is the minimum value of the SOC of the battery and SOC_b_max is the maximum value of the SOC of the battery, the battery energy E_b satisfies

\frac{C_{b} n_{b}}{2} (u_{b}^{2} (so c_{b min}) - u_{b 0}^{2}) \leq E_{b} \leq \frac{C_{b} n_{b}}{2} (u_{b}^{2} (so c_{b max}) - u_{b 0}^{2})

(25)

Power distribution approach based on convex optimize

Convex optimization is a kind of optimization problem approach where the objective function is a convex function. Compared with the traditional global optimization algorithm, it has the characteristics of fast operation.^20–22 The standard form of convex optimization is

\begin{matrix} minimize f_{0} (x) \\ \begin{matrix} subject to & \begin{matrix} f_{i} (x) \leq 0, & i = 1, \dots, m \\ a_{i}^{T} x = b_{i}, & i = 1, \dots, p \end{matrix} \end{matrix} \end{matrix}

where f₀, …, f_m are convex functions. The equation constraint function $h_{i} (x) = a_{i}^{T} x - b_{i}$ must be affine. In this study, the output power P_b of the battery in the ideal state, output power P_bt of the battery port, energy E_b of the battery, output power P_sc of the SC in the ideal state, output power P_sct of the SC port, and energy E_sc of the SC are set as the optimization variables. Therefore, according to the standard form of convex optimization, in the modeling process, equations (13)–(16) and (23)–(25) all satisfy the convex optimization requirement. However, equations (8) and (18) do not satisfy the requirement of constraints of convex optimization. Since P_bloss in equation (18) is the loss in the equivalent series resistance, $P_{bt} = P_{b} - P_{bloss} - Δ_{1}$ , where Δ₁ is the loss of the rest of the resistor, which exists when we consider that there are other losses such as the polarization loss of the power battery. Therefore, in the ideal state, the output power P_b of the battery, output power P_bt of the battery port, and power loss P_bloss of the series resistance have the following relationship

P_{bt} \leq P_{b} - P_{bloss}

(26)

This inequality satisfies the requirement of inequality in the standard form of convex optimization. Similarly, the SC power exists as follows to satisfy the inequality conditions of the convex optimization

P_{sct} \leq P_{sc} - P_{scloss}

(27)

Therefore, the constraint condition of the convex optimization problem is as follows

{\begin{matrix} P_{m} + P_{mloss} + P_{aux} = P_{hess} \\ P_{bt} \leq P_{b} - P_{bloss} \\ \frac{d E_{b}}{dt} = - P_{b} \\ I_{b min} \sqrt{n_{b} (\frac{2 E_{b}}{C_{b}} + u_{b 0}^{2} n_{b})} \leq P_{b} \leq I_{b max} \sqrt{n_{b} (\frac{2 E_{b}}{C_{b}} + u_{b 0}^{2} n_{b})} \\ \frac{C_{b} n_{b}}{2} (u_{b}^{2} (so c_{b min}) - u_{b 0}^{2}) \leq E_{b} \leq \frac{C_{b} n_{b}}{2} (u_{b}^{2} (so c_{b max}) - u_{b 0}^{2}) \\ P_{sct} \leq P_{sc} - P_{scloss} \\ \frac{d E_{sc}}{dt} = - P_{sc} \\ I_{sc min} \sqrt{n_{sc} (\frac{2 E_{sc}}{C_{sc}} + u_{sc 0}^{2} n_{sc})} \leq P_{sc} \leq I_{sc max} \sqrt{n_{sc} (\frac{2 E_{sc}}{C_{sc}} + u_{sc 0}^{2} n_{sc})} \\ \frac{C_{sc} n_{sc}}{2} (u_{sc}^{2} (so c_{sc min}) - u_{sc 0}^{2}) \leq E_{sc} \leq \frac{C_{sc} n_{sc}}{2} (u_{sc}^{2} (so c_{sc max}) - u_{sc 0}^{2}) \\ E_{SC} (t_{0}) = E_{SC} (t_{f}) \end{matrix}

(28)

In order to reduce the energy consumption of the electric bus during operation, we accept the factor $\int_{t_{0}}^{t_{f}} P_{b} + P_{sc} dt$ as a part of the objective function, where t₀ is the initial time of the driving cycle and t_f is the time of termination. Since the SC has good low-temperature characteristics, under low-temperature conditions, the SC is fully used. Therefore, another part of the objective function is $\int_{t_{0}}^{t_{f}} | V_{sc} - V_{ref} | dt$ , where V_ref is as follows²³

{\begin{matrix} \begin{matrix} V_{ref} = V_{min} & P \geq 0 \end{matrix} \\ \begin{matrix} V_{ref} = V_{max} & P < 0 \end{matrix} \end{matrix}

(29)

where V_min is 0 and V_max is the maximum value of the open circuit voltage of the SC. Therefore, the objective function is

j = a_{1} \int_{t_{0}}^{t_{f}} | V_{sc} - V_{ref} | dt + a_{2} \int_{t_{0}}^{t_{f}} (P_{b} + P_{sc}) dt

(30)

where a₁ and a₂ are the weight values, and they can be selected according to the actual demand. In this study, the values of a₁ and a₂ are shown in equation (31)

{\begin{matrix} \begin{matrix} a_{1} = 0, a_{2} = 1 & T \geq T_{0} \end{matrix} \\ \begin{matrix} a_{1} = 1, a_{2} = 0 & T < T_{0} \end{matrix} \end{matrix}

(31)

where T is the environment and T₀ is the set temperature threshold. In this study, T₀ is 0°C.

By the convex optimization method, the basic flow of the energy distribution of the HESS of the electric vehicle is shown in Figure 8.

Figure 8.

Power allocation process of the power source.

Simulation results

In order to verify the validity of the method proposed in this article, an electric bus with a HESS is considered as the research object, as shown in Table 1. Furthermore, the bus road conditions of Harbin city are selected as the cycle conditions, as shown in Figure 9.²⁴ In Figure 9, P_dem is power demand under the bus road conditions of Harbin city. Under the conditions of −5°C and 25°C, the optimal power distribution of the power battery and the SC of the electric bus with the composite energy storage system was determined by the convex optimization method. Moreover, the results of the optimal allocation are compared with the rule-based power allocation method proposed in Peng et al.²⁵

Table 1.

Parameters of electric vehicle with semi-active HESS.

	Parameter	Value
Vehicle	Vehicle weight, m (t)	13
	Frontal area, A (m²)	7.83
	Air resistance coefficient, C_d	0.75
	Rolling resistance coefficient, f	0.007
	Air density, ρ (kg/m³)	1.1839
	Wheel radius, r (m)	0.512
	Vehicle auxiliary power, P_aux (kW)	5
	Final gear, i₀	6.2
	Average annual mileage, s (km)	50,000
Battery	Nominal battery capacity, Q_b (Ah)	180
	Nominal battery voltage u_b (V)	3.2
	Maximum battery discharge, I_b_max (A)	540
SC	Nominal capacity, C_s (F)	2000
	Nominal voltage, u_sc (V)	2.7
	Maximum battery discharge, I_sc_max (A)	1500
	Nominal voltage, V_max (V)	2.7

HESS: hybrid energy storage system; SC: super capacitor.

Figure 9.

Harbin city driving cycle.

The rule-based power allocation strategy, which is compared with the method presented in this article, is shown in Figure 10. When the electric bus functions in the driving mode, the output power P_b of the power battery and the output power P_sc of the SC can be expressed as equation (32)

\begin{matrix} P_{b} (t) = {\begin{matrix} P_{d} & P_{d} \leq P_{min} \\ P_{min} & (P_{d} > P_{min}) and (SO C_{s} > 0.5) \\ P_{d} & (P_{d} > P_{min}) and (SO C_{s} \leq 0.5) \end{matrix} \\ P_{sc} (t) = {\begin{matrix} 0 & P_{d} \leq P_{min} \\ P_{d} - P_{min} & (P_{d} > P_{min}) and (SO C_{s} > 0.5) \\ 0 & (P_{d} > P_{min}) and (SO C_{s} \leq 0.5) \end{matrix} \end{matrix}

(32)

where SOC_s are the SOCs of SC, P_d is the power demand under this condition, and P_min is the power threshold.

Figure 10.

Rule-based optimization method.

According to the rule-based power allocation strategy described in Figure 10, when the pure electric bus is in the braking state, that is, P_d < 0, the output power of the power battery P_b and the output power of the SC P_sc can be expressed as equation (33)

\begin{matrix} P_{b} (t) = {\begin{matrix} P_{d} & SO C_{S} \geq 0.9 \\ 0 & SO C_{S} < 0.9 \end{matrix} \\ P_{sc} (t) = {\begin{matrix} 0 & SO C_{S} \geq 0.9 \\ P_{d} & SO C_{S} < 0.9 \end{matrix} \end{matrix}

(33)

where SOC_s are the SOCs of SC and P_d is the power demand under this condition.

The results of the power distribution of the SC and the power battery are shown in Figures 11 and 12, where bottom image is an enlarged view of the red box, in the case of 25°C and −5°C, respectively. It can be observed from Figure 11 that, at the ambient temperature of 25°C, the maximum output power of the power battery is 80.47 kW and that of the SC is 80.49 kW. Thus, SC can effectively achieve power balance. From Figure 12, at the ambient temperature of −5°C, the maximum output power of the battery is 73.58 kW and that of the SC is 87.47 kW. The output power of the SC is improved relative to the optimization result in Figure 11. Because, at low-temperature conditions, the optimization method highlights the utilization of SC in terms of providing power.

Figure 11.

Power distribution of battery and super capacitor at 25°C.

Figure 12.

Power distribution of battery and super capacitor at −5°C.

The power allocation strategy based on the rule is shown in Figure 13 where bottom image is an enlarged view of the red box. The comparison of the SC power and the battery distribution power between the two strategies is shown in Figure 14. From Figure 14, when P_d < 0, the power allocation method proposed in this article is more effective than the rule-based power allocation strategy, and the use of SC achieves a balance of power and optimizes the functioning of the battery at −5°C. Therefore, the proposed method of power distribution at −5°C can effectively extend the life of the battery.

Figure 13.

Rule-based allocation power.

Figure 14.

The comparison of the two strategies.

In order to compare the optimization effect of the power allocation strategy, according to Hu et al.,²⁶ the calculation method of the comprehensive energy efficiency of the electric vehicle is shown in equation (34)

η = \frac{E_{d}}{E_{ele}}

(34)

where η is the comprehensive energy efficiency of the electric vehicle, E_d is the energy output of the electric vehicle under a working condition cycle, and E_ele is the electric energy consumed in a working cycle. E_d and E_ele are calculated as shown in equation (35)

{\begin{matrix} E_{d} = \int_{t_{0}}^{t_{f}} P_{d} dt \\ E_{ele} = \int_{t_{0}}^{t_{f}} P_{b} + P_{sc} dt \end{matrix}

(35)

where t₀ is the initial time of the operating condition, t_f is the end time of the operating condition, P_d is the power demand of the electric bus under this condition, P_b is the output power of the power battery in the HESS, and P_sc is the output power of the SC.

According to the calculation results of Figures 12 –14, the comprehensive energy efficiency of HESS under different temperature conditions can be obtained by combining the calculations of equations (34) and (35) as shown in Figure 15.

Figure 15.

Comprehensive energy efficiency of composite energy storage systems under different temperature conditions.

It can be observed from Figure 15 that the comprehensive energy efficiencies of the convex optimization and the rule-based power allocation method are 83.31% and 80.89% at 25°C, respectively. Compared with the rule-based power allocation method, the energy efficiency of the proposed power allocation method is improved by 2.42%. When the temperature is −5°C, the comprehensive energy efficiencies of the convex optimization and the rule-based power allocation method are 81.03% and 79.58%, respectively. At −5°C, compared with the rule-based power allocation method, the energy efficiency of the proposed power allocation method increased by 1.45%.

The energy flow diagram of the power system is shown in Figures 16 and 17 with the convex optimization method and the rule-based power distribution method at 25°C and −5°C, respectively. In the electric vehicle running process, power loss mainly contains the SC loss, battery loss, motor loss, and bi-directional DC/DC loss. From Figures 16 and 17, compared to the rule-based power allocation method, the battery power loss of the convex optimization allocation strategy in the ambient temperature of 25°C and −5°C are reduced by 27.3% and 19.25%, respectively. Although the SC loss is relatively increased, the functioning of the battery is optimized. The power system achieves a reduction in the comprehensive energy consumption.

Figure 16.

At 25°C, energy flow diagram of the two power distribution methods: (a) power allocation method based on convex optimization and (b) power allocation method based on rule.

Figure 17.

At −5°C, energy flow diagram of the two power distribution methods: (a) power allocation method based on convex optimization and (b) power allocation method based on rule.

In some studies,^27–29 the increase (or decrease) in the battery power amplitude and variance can lead to an increase (or decrease) in the battery life attenuation. For the optimal power distribution at −5°C, according to the method of evaluation of the energy management strategy in Choi et al.,³⁰ combined with equation (36), the mean square error s of the battery power is calculated as

s = \sqrt{\frac{{\sum_{t_{0}}^{t_{f}} (P_{b} (t) - P_{avg})}^{2}}{t_{f} - t_{0}}}

(36)

where s is the mean square deviation of the battery power, P_b(t) is the battery power at time t, P_avg is the average of the battery power at each time, t₀ is the initial time of a condition, and t_f is the termination time of a condition. According to the aforementioned mean square error calculation method, the mean square errors of the proposed method and the rule-based method at −5°C are obtained, as shown in Figure 18.

Figure 18.

Comparison of the mean square error of the battery power.

As evident from Figure 18, the mean square error of the battery power based on the convex-optimized power distribution method is 8.66 kW. Compared with the rule-based power allocation strategy, the battery power variance is reduced by 20.11%. The main reason for this result is that, at low temperatures, the proposed optimization method is more focused on the use of SCs to reduce the frequent changes in the power the battery.

The comparison of the power allocation method and the rule-based power allocation method is shown in Table 2. According to the results in Table 2, the maximum output power of the battery in the proposed power distribution method is 80.47 and 73.58 kW at 25°C and −5°C, respectively. Compared with the rule-based power distribution method, the maximum output power of the power battery is reduced by 46.00% and 50.62 %, respectively. Therefore, the proposed power distribution method effectively reduces the capacity loss of the power battery.

Table 2.

Simulation results.

	Proposed power allocation method	Rule-based power allocation method
25°C maximum battery power (kW)	80.47	149.02
−5°C maximum battery power (kW)	73.58	149.02
−5°C Battery power variance (kW)	8.66	10.84
25°C comprehensive energy efficiency (%)	83.31	80.89
−5°C comprehensive energy efficiency (%)	81.03	79.58

It can be observed from the simulation and analysis results that the proposed power distribution method can effectively extend the life of the power battery of an electric vehicle under low-temperature conditions. Simultaneously, the power distribution method proposed at −5°C and 25°C effectively increases the comprehensive energy efficiency of the electric vehicle. According to the above analysis, the power allocation method based on convex optimization improves the running characteristics of electric vehicles under different temperature conditions.

Conclusion

In this article, an electric bus system equipped with a semi-active composite energy storage system is considered as the object of study. Combined with the urban climate status at the area where the vehicle operates, the minimum energy consumption of the power system and the maximum discharge and charge depth of the SC are considered as the optimization targets. A convex optimization approach considering the influence of temperature is proposed, which realizes the optimization of the working conditions of the electric bus HESS under different ambient temperature conditions. The urban driving cycles in Harbin are considered as the cyclic conditions, and the approach was compared with the rule-based power distribution method at 25°C and −5°C. The simulation results show that the comprehensive energy efficiency of the dynamic system is 83.31% at 25°C, and compared with the rule-based power allocation method, the energy efficiency is improved by 2.42%. When the ambient temperature is −5°C, the comprehensive energy efficiency of the power system is 81.03%, and the comprehensive energy efficiency is improved by 1.45% compared with the rule-based power allocation method. The proposed method effectively improves the comprehensive energy efficiency of the electric vehicle integrated with an energy storage system at different temperatures. At 25°C and −5°C, under the premise of satisfying the vehicle power demand, the maximum output power of the proposed power distribution method is 80.47 and 73.58 kW, respectively. Compared with the rule-based power distribution method, the maximum output power of the power battery is reduced by 46.00% and 50.62%, respectively. The battery power variance is reduced by 20.11%. The proposed power distribution method effectively prolongs the service life of the battery and effectively improves the functioning of the electric bus HESS at different temperatures.

Footnotes

Handling Editor: Hamid Reza Karimi

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the State Key Laboratory of Automotive Safety and Energy under Project No. KF16062 and Natural Science Foundation of Heilongjiang Province, No. E201451.

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