Energy manegement using fuzzy controller for hybrid electrical vehicles

Abstract

In electric vehicles, the battery is exposure to an excessive stress because of continuously charging and discharging. In this paper, a hybrid energy storage system (HESS) combined of supercapacitors (SC) and batteries is deployed. An energy management strategy based on fuzzy logic controller (FLC) and rule based controller (RBC) are proposed to mitigate the high stress problem and increase the battery lifetime. The battery and SC sizes are optimized based on a power demand profile. Based on simulation results, three different HESSs along with FLC and RBC are compared, in their SC voltages and battery currents viewpoints, and the best one is introduced. FLC has advantageous to alleviate battery current fluctuations in comparison with RBC, but RBC has higher battery lifetime.

Keywords

Hybrid energy storage system (HESS)fuzzy logic controller (FLC)electric vehicles energy management strategy

1 Introduction

Hybrid electric vehicles (HEVs) are becoming ever more popular and show promising future. One of the biggest benefit of HEVs is the fact that they have been reduced our dependence on fossil fuel and the fluctuation markets that go along with it. These vehicles can significantly reduce pollution.

Although technology of HEVs have considerable progress, they have been faced with technical problems. For example, batteries used in HEVs are often faced with the power demand continually, so they tend to repeated charge and discharge operations, which has an adverse effect on battery life. This is one of the main reasons that people are discouraged of using electric vehicles. Recently, some researches have been done for extending the battery life [1 –4]. One possible solution is to use a hybrid energy storage systems, which combines features of supercapacitors and batteries. In this case, they will absorb regenerative energy and collaborate during dischargingstage.

Generally, hybrid energy storage system (HESS) can be classified into three types: passive, semi-active, and fully-active [1 , 6]. In passive HESSs, the battery and SC packs are connected in parallel and directly coupled to the DC bus. In the fully-active HESS, two DC/DC converters and one additional control circuit are used to decouple the battery and SC from the DC bus. The semi-active HESS, which only employ one DC/DC converter [1 , 8].

The passive HESS is the least-cost topology; however, in this topology the SC is not used effectively to achieve a satisfactory performance and there is still stress on the battery. The fully-active HESS has the best performance because it offers more control levers. The semi-active HESS has a good balance with reasonable cost [1 , 10].

Different controllers for HESSs have been designed and examined [1]. Song et al. are presented fuzzy logic controller (FLC), rule-based controller (RBC), filtration based controller (FBC), and predictive controller (MPC) for electric vehicles with a hybrid energy storage system [1, 11]. Trovão presented rule based controller for an electric vehicle based on power demand and different state of charges (SOCs) of battery and SC [12]. Jaafar described the energy management strategy based on a filtration based controller (FBC) for hybrid locomotive [13]. Ferreira proposed fuzzy logic controller for electric vehicles with hybrid energy storage system included battery, supercapacitor, and fuel cells [14].

In this paper, an energy management strategy is employed in HESS. The system consists of a battery and a supercapacitor (SC). Extending battery life and reducing energy storage system life cycle costs are the main purposes of using HESS.

Fuzzy logic controller (FLC) and rule based controller are employed in three different topologies of HESS and achieved results are compared. Three topologies, as shown in Fig. 1, are named DCBATSC (two DC/DC converters and one additional control circuit are involved to decouple the battery and SC with the DC bus), DCBAT (one DC/DC converter connected to the battery in series), and DCSC (one DC/DC converter connected to the SC in series). In the aforementioned topologies, the battery and SC sizes will be optimized based on the desired minimal mileage and a power demand profile, respectively. The demand profile has been borrowed from China Bus Driving Cycle (CBDC) [1]. The aim applying the optimum size algorithm, based on a dynamic programming technique, is to obtain the number of battery cells in the battery pack and number of capacitor modules in the SC pack (connected in series and parallel).

In the simulations, current and voltage diagrams of the battery and supercapacitor of three topologies are compared to choose the proper topology. After selecting the best topology, performances of fuzzy logic and rule based controllers in this topology are compared.

This paper is organized as follows: Section 2 introduces three HESS topologies, SC, battery, and city bus models. Section 3 indicates the proposed optimal sizing of the HESS. Fuzzy logic and rule based controllers are explained in Sections 4 and 5, respectively. Section 6 compares and analyzes the simulation results of different topologies. Section 7 is dedicated to applying two controllers for DCBATSC topology. Finally, Section 8 describes some conclusions and future works.

2 Different topologies of HESS modeling

Three different topologies, DCSC, DCBAT, and DCBATSC used in this article are shown in Fig. 1, respectively. In the figure, the first two topologies are semi-active and the last one is a fully active topologies. In DCSC topology one DC/DC converter connected to the SC in series, and in DCBAT topology, one DC/DC converter connected to the battery in series, while in DCBATSC topology, two DC/DC converters and one additional control circuit are involved to decouple the battery and SC with the DC bus.

In the following sections, the performances of three topologies will be evaluated. Also, fuzzy logic controller will be designed for the best topology.

2.1 SC model

The SC pack is composed of some SC modules that are grouped via N_sc series and M_sc parallel connections. The parameters of one SC module in the SC pack are listed in Table 1 [15].

The following equations can be expressed for SC [1]: $C_{sc} = M_{SC} C_{M} / N_{SC}$ (1) $R_{SC, ch} = N_{SC} R_{SC_M, ch} / M_{SC}$ (2) $R_{SC, disch} = N_{SC} R_{SC_M, disch} / M_{SC}$ (3) $V_{sc} = V_{SC_M} N_{SC}$ (4) where C_sc is the capacity of the SC pack, C_M is the capacity of the module, R_sc,ch is the charge resistance of the SC pack, R_sc,disch is the discharge resistance of the SC pack, R_{sc_M,ch} is the charge resistance of the SC module, R_{sc_M,disch} is the discharge resistance of the SC module, N_SC/M_SC are the series/parallel numbers of the SC module within the SC pack, V_{SC_M} is the open circuit voltage of the module, and V_SC is the open circuit voltage of the SC pack.

The state of charge of the SC pack is as follows [1]: ${SOC}_{SC} = \frac{V_{SC}}{V_{SC, \max}}$ (5) where V_SC,max is the maximum voltage of the SC pack.

In this paper, a RC circuit is used to model SC, as shown in Fig. 2, where R_SC and C_SC are internal resistance and capacitance of the SC, respectively. This model has sufficient accuracy and simplicity [11 , 15–17].

2.2 Battery model

The battery that is chosen in this paper is Lifepo4. It has some outstanding characteristics, such as high voltage, exceptional specific capacity, and long cycle life [1, 18]. The parameters of LiFePO4 cell are listed in Table 2 [1].

The battery pack is consisted in form of N_bat series and M_bat parallel connections. The following equations express the battery pack model [1]: $C_{bat} = M_{bat} N_{bat} C_{bat_cell}$ (6) $R_{bat, ch} = N_{bat} R_{bat_cell, ch} / M_{bat}$ (7) $R_{bat, disch} = N_{SC} R_{bat_cell, disch} / M_{bat}$ (8) $V_{bat} = V_{bat_cell} N_{bat}$ (9) where C_{bat_cell} is the capacity of the battery cell, C_bat is the capacity of the battery pack, R_bat,ch is the charge resistance of the battery pack, R_bat,disch is the discharge resistance of the battery pack, R_{bat_cell,ch} is the charge resistance of the battery cell, R_{bat_cell,disch} is the discharge resistance of the battery cell, N_bat/M_bat are the series/parallel numbers of the battery cells within the battery pack, V_{bat_cell} is the open circuit voltage of the cell, and V_bat is the open circuit voltage of the battery pack. The model of the battery is shown in Fig. 3 [11 , 15–17].

2.3 City bus model

The vehicle dynamic model is given by the following equations [1, 18]: $\begin{matrix} mgfucos α + 0.5 C_{D} A ρ u^{3} + mu \frac{du}{dt} + mguSin α \\ = P_{demand} η_{T} η_{md} (P_{demand} > 0) \end{matrix}$ (10) $\begin{matrix} mgfucos α + 0.5 C_{D} A ρ u^{3} + mu \frac{du}{dt} + mguSin α \\ = P_{demand} / η_{r} (P_{demand} \leq 0) \end{matrix}$ (11) where m is the vehicle mass, g is the gravity acceleration, f is the rolling resistance coefficient, u is the vehicle velocity, α is the climbing angle, C_D is the air drag coefficient, A is the front area, ρ is the air density, P_m is the input electric power of the DC/AC inverter required for the electric motor to drive the vehicle, is the transmission efficiency, η_md is the drive efficiency of the electric motor, and η_r is the average efficiency of the regenerative braking process.

The equations of the power balance in a hybrid powertrain are expressed in (12) and (13) [1, 18]: $P_{bat} + P_{sc} η_{DC / DC} = P_{m} / η_{HESS} (P_{demand} > 0)$ (12) $P_{bat} + P_{sc} η_{DC / DC} = P_{m} η_{HESS} (P_{demand} \leq 0)$ (13) where P_sc is the output power of the SC pack, P_bat is the output power of the battery pack, η_HESS is the average efficiency of HESS, and η_DC/DC is the average efficiency of the DC/DC converter, which sets to 85% in this paper [19]. The parameters of the city bus are listed in Table 3 [1, 18].

3 Sizing of HESS

In order to achieve the optimal number of battery cells and SC modules in HESS, a sizing algorithm is used. Sizes can be optimized according to the requested minimal mileage and a power demand profile of a driving cycle, respectively.

For the demand profile and as a benchmark test, in this paper a typical China Bus Driving Cycle (CBDC) is chosen [1]. This demand profile will be shown in the simulation section.

The functional form of the battery life model that expresses as percentage of the battery capacity loss (Q_loss) is [1 , 21]: $Q_{loss} = {Ae}^{- (\frac{E_{a} + B \times C_Rate}{R T_{Bat}})} (A_{h})^{z}$ (14) where C _ Rate is the battery discharge rate, A is the pre-exponential factor which depends on C _ Rate, E_a is the activation energy (J), B is the compensation factor of C _ Rate, R is the gas constant (is 8.314 (J/(mol K)), T_Bat is the absolute temperature (K), z is the power law factor, and A_h is the Ah-throughput which is expressed as [20, 21]: $A_{h} = cycle number \times DOD \times full cell capacity$ (15) where DOD is the depth of discharge.

Based on the experimental results of Song et al. [1] the battery capacity loss (14) is expressed as: $Q_{loss} = 0.0032 e^{- (\frac{15162 - 1516 C_Rate}{R T_{Bat}})} (A_{h})^{0.824}$ (16)

Following modeling equations, one can deduce: $(0.5 C_{D} A ρ u_{0}^{2} + mgf) (\frac{L}{η_{T} η_{md} η_{HESS}}) \leq E_{HESS}$ (17)

The SC can be neglected here, because the energy stored in the SC is much less than that stored in the battery, thus one can deduce:

$\begin{matrix} (\frac{C_{D} A ρ u_{0}^{2}}{2} + mgf) \frac{L}{η_{T} η_{md} η_{HESS}} \frac{L}{3600 C_{{bat}_{cell}} V_{{bat}_{cell}}} \\ \leq M_{bat} N_{bat} \end{matrix}$ (18) where L is the desired minimal mileage of more than 100 [km], obtained at a constant cruising speed u₀ (50 [km/h]) on a flat road.

By putting values into the equation, one can obtain the following equation: $605 \leq M_{bat} N_{bat}$ (19) Thus: $M_{bat} N_{bat} = 600$ (20)

As a result, 600 battery cells are used in battery pack, N_bat and M_bat are set to 120 and 5.

To solve the above optimization problem, the dynamic programming (DP) algorithm is used. DP algorithm is a recursive method for achieving the optimal solution in sequential decision problems [23]. In terms of mathematical optimization, DP usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time.

Using DP algorithm, N_SC and M_SC are calculated as 25 and 2, respectively [1 , 22].

4 Fuzzy logic controller

Fuzzy logic is a method for implementation a smart routine based on human brain decisions. Fuzzy logic controller because of its simplicity, flexibility, and good performance is used in hybrid vehicles.

Fuzzy logic controller is applied to DCSC topology, that it includes three inputs: V_SC, P_demand, and battery C_Rate, and one output that is the power-split ratio (α₀) between the battery power demand P_{bat_demand} and P_demand. This ratio is defined as follows [1]: $α_{0} = \frac{P_{bat_demand}}{P_{demand}}$ (21) $P_{demand} = P_{bat_demand} + P_{SC_demand}$ (22)

A schematic scheme for the fuzzy logic controller with its inputs and outputs are shown in Fig. 4.

Using MATLAB fuzzy logic toolbox, fuzzy logic inference systems can be created and edited via the graphical tools and command line functions.

Initially, the entire system shown in Fig. 5 in the form of a block diagram. Membership functions maps every point of the input and output to a value between 0 and 1. The triangular membership functions are chosen for inputs and output as shown in Fig. 6.

The proposed fuzzy logic controller is included 17 rules that are listed in Table 4 [1]. The first 15 rules are not intended the discharge rate. C _ Rate is considered only in rules 16 and 17 in the two modes, and the law first and second are intended only V_SC.

The relationship between V_SC, P_demand, α₀, and C _ Rate are shown in Figs. 7 and 8.

Based on Figs. 7 and 8, when the power demand and supercapacitor voltage are high, controller angle α₀ is small, therefore the battery and supercapacitor tend to supply less and higher power, respectively. When the power demand or supercapacitor voltage are low, the battery tends to discharge.

5 Rule based controller

The inputs and outputs of the rule based controller are shown in Fig. 9. In this controller, power portions of the battery (P_Bat) and SC (P_SC) for satisfying the input demand will be determined based on their inputs and supercapacitor voltage.

The flowchart of rule based controller along with its pseudocode are shown Fig. 10. The code is included SC voltage hysteresis controller to adjust the supercapacitor voltage [12, 23].

According to the flowchart, power demand, as an input of the rule based controller, is divided between the battery and SC. The split power depends on the power demand P_d, the battery power threshold P_min, and the charging power sending from battery to SC, P_ch. Therefore, these parameters should be carefully tuned based on the specific type and size of the vehicle.

6 Simulation

DCSC, DCBAT, and DCBATSC topologies with two different controllers, i.e., fuzzy logic and rule based controllers are simulated in this section. The simulations are performed in Matlab/Simulink environment. The supercapacitor and battery currents and voltages are illustrated and analyzed.

A schematic scheme for the control strategy is shown in Fig. 11, where the fuzzy logic controller has received the supercapacitor voltage, power demand, and battery discharge rate. The controller outputs are power-split ratios between the battery power demand P_Bat and supercapacitor power demand. As shown in the scheme, the capacitor current calculates from the supercapacitor power and then compares with the supercapacitor mainstream current. The output signal will pass through PI and PWM blocks to produce switching signals for DC/DC converter.

In the simulation, the initial SOC of the battery and SC are set to 70% and 90%, and operation temperature of the battery is considered 15°C. The simulation of one CBDC is performed in 335 second. the battery power threshold P_min and power sending from battery to SC P_ch are set to 34 kW and 10 kW [1].

The Power demand profile of CBDC is illustrated in Fig. 12 [1].

The SC voltage for three different hybrid energy storage system topologies with Fuzzy logic and rule based controllers during CBDC are shown in Figs. 13 and 14, respectively.

The battery current for three different hybrid energy storage system topologies with fuzzy logic and rule based controllers during CBDC are shown in Figs. 14 and 15, respectively.

In addition, the SC current for three different hybrid energy storage system topologies with Fuzzy logic and rule based controller during CBDC is represented in Figs. 17 and 18, respectively.

Based on the above figures, one can conclude the following issues:

In battery current profiles, although two peak values occur about 127 s and 312 s due to the low V_sc and high P_demand, these two peaks values are not high and happen in a short time, so will not damage the battery.

Considering the battery current fluctuations in the DCBATSC topology, they are lower than two other topologies.

Considering SC voltage profiles, among all topologies, the DCBATSC topology uses the SC in the widest range, which means an effective use of SCs.

Evaluating current and voltage profiles, DCBAT and DCSC topologies have current and voltage profiles very close together.

DCBATSC topology including fuzzy controller has better performance in energy management point of view. This results in less stress and higher lifetime for the battery.

Considering current profiles, current fluctuations in the DCBAT topology is less and resulting better battery current in compared to DCSC topology due to less transient fluctuations.

Considering voltage profile, SC voltage in the DCBAT topology has greater range and this means better use of capacitors in compared to DCSC topology.

7 Comparison fuzzy logic controller with rule based controller

As aforementioned in the previous section, comparing the three topologies, in overall DCBATSC has better performances. In this section, result of applying of fuzzy logic and rule based controllers for DCBATSC will be studied in detail.

The SC voltage for DCBATSC topology with fuzzy logic controller and rule based controller during CBDC are illustrated in Fig. 19.

Also, the battery current for DCBATSC topology with fuzzy logic controller and rule based controller during CBDC are represented in Fig. 20.

In addition, SC current for the DCBATSC topology with fuzzy logic controller and rule based controller during CBDC are shown in Fig. 21.

Above figures show that the performances of two controllers are close together, but by comparing accurately, one can deduce the following points:

•
In the current profiles, current fluctuations in DCBATSC topology with fuzzy logic controller are less compared with rule based controller and therefore battery current with fuzzy logic controller is better due to less transient fluctuations.

In the voltage profiles, SC voltage in DCBATSC topology with rule based controller has greater range (better SOC) compared with Fuzzy logic controller, this means better use of capacitors in this topology.

8 Conclusion

In this paper, a proper topology of a hybrid energy storage system and its controller was introduced to mitigate the battery stresses. Three hybrid energy storage system, named DCSC, DCBAT and DCBATSC with fuzzy logic controller and rule based controller were compared, in battery current fluctuations and SOC of SC points of view. Simulation results revealed that DCBATSC topology had less current stress on battery current, resulting in higher lifetime.

Fuzzy logic controller and rule based controller for DCBATSC topology was compared. FLC had less current fluctuations, but the topology based on RBC, SC voltage had better SOC.

Future works of this research will concentrate on comparing costs of different HESS topologies, controllers, and converters.

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