Energy Management Control Strategy Based on Harris Hawks Optimization Technique for Fuel Cell Hybrid Electric Vehicle ^†

Abstract

The focus and sales of EVs are slowly coming into scope, as the power source of such vehicles is a significant area in which the integration of power systems is becoming a crucial issue. This work involves the use of hybrid sources, batteries as a primary source, fuel cells, and an ultra-capacitor as an auxiliary source. This hybrid system provides the grip of the FCEV. The constraints of fuel cells are the SOC of the battery and the H2 level. These three power sources in hybrid systems are connected to the DC bus via proper DC-to-DC converters. This paper will discuss the combination of Harris Hawks Optimization (HHO) for the energy management and control of these source systems, for the constraint of mandated sources, and to ensure stability. The proposed system provides a satisfactory energy management system for the hybrid system. Using the proposed technique, the fuel consumption settling period is reduced. The proposed method was implemented and validated with and without the HHO technique.

1. Question of Research

Power sources are a primary concern in EVs. Why are only batteries used as power sources, why can other sources not be used, and why are sources not integrated? [1,2,3].

2. Introduction

New hydrogen technology is rapidly emerging for electric vehicle propulsion systems. Fuel cell systems (FCSs) will play an important role in electric vehicles in the coming decades. This energy source has many advantages, from the environment to its efficiency and effectiveness [4]. Because the power response of FCSs is small, PEMFC (proton exchange membrane fuel cell)-powered vehicles may become unstable during sudden load changes.

An energy management system (EMS) is needed to produce the power from the hybrid source to distribute the load. EMSs meet the hybrid resource constraints used to achieve the high recital of the projected method and improve the fuel economy [5,6,7]. Rule-based control and optimization-based control techniques are used in some of the literature. These often have success or reverse the cycle. Ideally, a reduction in hybrid fuel consumption can only be achieved when driving conditions are known to be necessary.

PMEFCs can provide non-stop energy to electric vehicles. As a result, hydrogen-powered PEMFCs are used [8]. This is the best power source and removes conventional fossil fuel usage. Battery (BT)-powered devices and Ultra-capacitors (UCs) are known for their high power. BTs can provide long-term alternative energy. (UCs) are also used to control the energy compared to the battery. The efficiency and power of UCs are high, and their discharging and charging cycles are also increased [9].

Of the hybrid sources that exist, one of the sources is UCs. UCs are electrochemical condenser devices that deliver a very short period of maximum power. UCs consist of an electric motor coated as a double layer. The double coated layer is made up of non-ferrous metals [10,11,12]. An electric motor is a combination of a power source and an engine. Methanol and propane create hydrogen gas through biological processes and the transformation of hydrocarbons. Designing an EMS system consists of the use of hybrid seeds to manage the power required. The proposed EMS is used to provide and improve the electrical load. The hybrid system provides the grip of the fuel cell EV. The fuel cell constraints are the SOC of the battery and the H₂ level. This work selected PI-based HHO control for energy management. This is used to manage and control the energy, consider the multi-source for source limitation, and improve the system’s performance [13]. The workflow of the entire proposed work is described below:

Step 1: The modelling of the battery and analysis of the battery output with/without the HHO technique.

Step 2: The modelling of the fuel cell and analysis of the output with/without the HHO technique.

Step 3: The modelling of the ultra-capacitor and analysis of the output with/without the HHO technique.

Step 4: The integration of the above three sources to see the output of the energy management system for the hybrid system as a whole.

3. Functional Block Diagram of EMS of Fuel Cell Hybrid Electric Vehicle

EMSs (Energy Management Systems) are required by hybrid vehicle systems to achieve good efficiency and performance. According to some control objectives, they determine the energy separation between the system’s different energy sources, considering each source’s characteristics.

Figure 1 shows that the primary source is a battery, whereas fuel cells and ultra-capacitors are used as supplementary sources. A unidirectional DC/DC converter connects the FC and DC bus to improve the voltage. An ultra-capacitor connects the DC bus using a bidirectional DC/DC converter for charging and discharging, and is connected to the DC bus for maintaining bus voltage.

4. Battery Modelling and Analysis

A model of a dynamic equivalent circuit. The diagram in Figure 2 suggests the simulation study. The simulation circuit comprises a direct current voltage source, a series resistance, and two RC parallel circuits. The DC voltage source represents the battery’s open circuit voltage in series networks. R_s denotes the internal DC resistance and the RC parallel denotes the networks, which characterize the transient response of the voltage and current V_t. The rate capacity effect is also deliberated in this model, where the usable capacity is varied, with the current representing the terminal voltage. The SOC of the battery is calculated based on the value of the functional capacity parameters depending on the SOC and current.

V_t = OCV − V₁ − V₂ − V_s

(1)

V_s = I × R_s

(2)

The battery open circuit voltage is denoted as V_oc BAT, the battery’s output voltage is denoted VBAT, and the battery series resistance is represented as R series. The R-C circuit is multiple time constants for the circuit designed. They are τ-hour, τ-sec and τ-min. These parameters are called SOC functions and are also used to model the transient behavior of the battery. The battery state of charge calculation is performed using the following equation.

5. Survey and Case Studies

Migration towards electric vehicles has started globally in India, and the significant adoption of these vehicles began in 2021. The prime reason for accepting these vehicles could be the exorbitant increases in the price of fossil fuel in the past few years. The alternate solution product, the electric vehicle rung cost, is deficient compared to the currently available products.

Comparative study of various types of fossil fuel alongside alternate fuel technology (CNG and EV) vehicles to understand the running cost per km and the cost of ownership of these vehicles.

$$SOC={SOC}_0+\frac{{\eta }_{BAT}}{(3600.C_{BAT})}\int i_{BAT} dt$$

(3)

where the battery’s initial parameters are i_BAT & SOC₀ is the battery’s initial current and sate of charge, and C_BAT is the battery’s capacity.

6. Fuel Modelling and Considerations

As show in the Figure 3, the fuel cell is a type of battery that uses hydrogen and oxygen as fuel. It converts chemical energy directly into electrical energy through an electrode reaction. A simplified model for the fuel cell has been established.

When the load current changes due to the charging effect, the fuel cell generates a gradually changing voltage on the bipolar plate surface. This voltage is accompanied by an equivalent resistance Ra, which is connected in parallel with a capacitor C, as shown in the given diagram of a specific equivalent model.

$$\left[E_{cell}-R.j_{Stack}-A.In\left(j_{Stack}+jl\right)-mexp\left(n j_{Stack}\right)\left(j_{Stack}=I_{Stack}/A_{cell}\right)\right]$$

(4)

where V_FC is the fuel cell voltage; i_FC is the current for the fuel cell; A_cell is each fuel area; E_cell is the fuel cell reversible voltage; N is the fuel cell stack number; j_stack is the density of the FC current; R is the specific resistance of the membrane area; m and n are the two mass transfer coefficients; A is the coefficient of T α; α, β and γ are second-order model approximating coefficients; I_stack is the fuel stack current; and i_FC is the output current of the fuel cell.

7. Ultra-Capacitor Modelling and Consideration

A fuel cell is a device that uses hydrogen and oxygen as fuel through an electrode reaction that directly converts chemical energy into electrical energy. At present, a simplified model concerning the model has been established.

When the load current changes due to the fuel cell’s bipolar plate surface, it produces a slow charging effect in response to the charging effect. The voltage is being changed. The corresponding resistance Ra is linked in parallel with a, as shown in the specific equivalent model diagram of the capacitor C which represented in the Figure 4.

8. Design and Implementation of EMS Controller

8.1. Proportional Term

The proportional time produces an output value proportional to the current error value. The proportional response can be modified by multiplying the error by a constant K_p, called the proportional gain constant. The proportional term is given by the following:

$$P_{out}=K_{p}e\left(t\right)$$

(5)

A high proportional increase causes a significant change in the output for a given change in error. If the proportional increase is too high, the system can become unstable. In contrast, a slight gain results in a small output for a significant input error, and the controller is unresponsive or less responsive. If the gain balance is too low, the control will be too small when responding to internal disturbances. Tuning theory and industrial practice show that the proportional time should contribute to the number of output changes.

8.2. Integral Term

The contribution from the critical point is proportional to both the magnitude of the error and the duration of the error. The key in the PID controller is the number of instantaneous errors over time and provides variables that must be corrected in the past. The excess error is divided by the gain (Ki) and added to the output. The main point is given by the following:

$$I_{out}=Ki{\int }_0^{t}e\left(T\right)dT$$

(6)

The movement of the process is performed by the integral term toward the set point and eliminates the residual steady-state error that occurs with a pure proportional controller. However, since the central term corresponds to accumulated errors from the past, it can cause the current value to exceed the set point value. Which, the complete working block diagram representation in Figure 5.

The PI controller can guarantee a fast response due to proportional action, and the integral action will make the steady-state error zero by adequately selecting the parameters Kc and T_i values. If the error is zero, the previous value of the integral term is retained as an output signal. When the error changes from zero, the proportional term works for correction, and the integral term increases or reduces the output.

9. Implementation of HHO for the Proposed Application

The converter’s switching pulse is generated using the Harris Hawks Optimization technique in a closed-loop operation. Here, the error signal is given to the PI controller. The PI Controller controls the error signal. So, this error signal is considered an objective function problem.

Mathematically, this can be represented as follows:

$$P=K_p{e}_p\left(t\right)+K_p{K}_I{\int }_0^T{e}_p\left(\tau \right)d+P_I\left(0\right)$$

(7)

where

P = PI controller’s output

K_p = Proportional gain

K_I = Integral gain

(t) = Desired value of controlled variable—measured value

(0) = Integral term initial value.

The proposed optimization techniques take this error signal as an objective function.

The tuning of the parameter problem is formulated as an optimization problem, and to identify the optimal, it is applied. The controller parameters have to be tuned for satisfactory plant operations. The objective of the optimization problem is to reduce hydrogen consumption and achieve a quick settling. The figure below shows the flowchart of the tuned PI controller. The following issues must be addressed while applying the HHO for any problem. The same represented in the Figure 6. Tuning of PI controller using HHO

Step_1: The individual population represents the parameters of the PI.

Step_2: HHO searches for the optimal solution by maximizing the fitness function and, therefore, an evaluation function that measures the quality of the problem solution.

Step_3: In the transmission line voltage control process, in terms of the system time constant, the objective is to minimize the Integral Square Error (ISE), which decides the performance of the transmission line. For removing the negative error component controllers, the ISE squares the error to remove.

$$ISE={\int }_0^T{e}^2\left(t\right)dt$$

(8)

Step_4: HHO minimizes the fitness function, and the minimization objective function is transformed into the fitness function = 1/ISE. The ISE is used as the basis of the fitness function. The HHO, however, maximizes the fitness function, whereas the ISE needs to be minimized. The same mentioned in the

Table 1. The parameters considered for HHO optimizers.

Sl.no	Parameter Type	Value Considers
1	Maximum iteration	500
2	Number of Hawks	30

.

For the compensation process, K_p and K_i are the control parameters.

Where

K_i = K_p/τi

(9)

The considered parameters for PI are as follows:

0.1 < K_i < 1

1 < K_p < 3

10. Implementation of the Proposed System

The proposed system was simulated and implemented in MATLAB/Simulink. A controlled voltage source represents the terminal voltage V_ocv of the battery. At the same time, five subsystems control the voltage value of the battery model: SOC calculation, OCV calculation, RC values, voltages of RC parallel networks, and VRS. The I measurement produces the current value for the subsystems. SOC_0 represents the initial SOC, whereas SOCn represents the real-time SOC_n.

Figure 7a,b shows the boost converter obtaining output from the battery. The battery output voltage is DC. The Simulink results are compared without and with the optimization techniques [11,12,13,14,15].

11. Results and Discussion

From the converter results from the Figure 8 and Figure 9, the proposed optimization techniques produce a constant output voltage, and the rise time is low. Without using the optimization techniques, the switching pulse of the converter is given from the pulse generator. But using the proposed optimization techniques, the PI controller is used to generate the pulse of the converter. Here, the PI controller gain values of Kp and Ki are generated through optimization. The objective function of the integral square error is to control the PI controller gain values. The error values are minimized using the proposed optimization technique. Only optimization techniques generate the gain parameter values in the minimized time. Here, the converter’s output voltage is 60 V DC, and the current is 8.6 A. The obtained gain values using HHO are a Kp of 1 and ki of 0.65 which are discussed in

Table 2. Observations with and without HHO technique implementation.

Sl.no	Parameter Type	Without HHO	With HHO
1	Rise time	0.175	0.001
2	Settling time	1.85	0.005

.

Results for Integration of the Sources

Figure 10 and Figure 11 shows the proposed multi-source system simulation model created with MATLAB/Simulink. The current measurement block is used to give the present value of the fuel cell, and the voltage measurement block is used to give the voltage value of the FC. The converter obtains output from the multi-source (battery, fuel cell and ultra capacitor). The multi-source system output voltage is DC. The converter fixed the DC voltage to variable DC voltage. The Simulink results are compared to the optimization techniques along with converter specifications used in the design discussed in

Table 3. Converter design parameters implemented in MATLAB.

Boost Converter
Parameters	Ratings
Inductance	10 mH
Capacitors	0.1 F
Output inductance	5.5 mH
Output load	1 Ω
Fuel cell voltage	103.6 V
Boost converter voltage of fuel cell	150 V
Battery voltage	3.4 V
Boost the converter voltage of the battery	60 V
Supercapacitor voltage	2.56 V
Boost converter voltage of supercapacitor	60 V

.

12. Conclusions

The proposed system provides a satisfactory energy management system for the hybrid system. The simulation results under the control of PI-tuned HHO support the validity of the power control strategy. The control strategy is compared by integrating multiple sources (battery, fuel cell, and ultra-capacitor using HHO and without the HHO algorithm). For this comparison, the converter settling time and rise time performance are improved.