Fractional Order Adaptive Integral Hierarchical Sliding Mode Controller for Energy Management System in Electric Vehicles

The majority of the world's 1 billion passenger automobilesare powered by crude oil-derived fuel. By 2025, the population will have risen to 1.2 billion. To meet India's transportation demands, around 90 lakh liters of petrol and 4 lakh 50 thousand gallons of diesel are consumed annually [1]. Fossil fuel energy is the major source of greenhouse gas emissions, which has a significant impact on people and ecosystems all over the world. Automobiles are a big contributor to global warming, which has a negative influence on the planet's ecosystem [1]. Electric vehicles have piqued the interest of automakers and researchers in recent decades due to its efficiency in terms of power maintenance and emission reduction.

Electric vehicles (EV) depend heavily on energy management systems (EMS) to maximise fuel efficiency (energy optimisation control), increase battery life, and increase range. The energy management system, in general, tries to reduce power consumption while functioning inside the system without affecting driving compatibility. Traditional energy management techniques can result in a variety of pollution. Acid rain, greenhouse gases, and air pollution are a few of the more prevalent ones. Chemicals and particles are discharged into the atmosphere during the burning of fossil fuels. In electric vehicles, the accumulator is serious in distributing the essential energy to the electric motor for transit. The online monitoring and assessment of battery states is critical for the harmless and consistent functioning of batteries in electric cars. A Battery Management System can help with this (BMS). Aside from the BMS, the proper power flow between the converters, battery and other sections of the vehicle should be controlled. Energy Management System is the name of this control (EMS).

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Figure 1. Growth of electric vehicle in India

Figure 1 depicts the growth of electric vehicles in India. The EMS' primary job is to connect with exterior mechanisms such as a power charger/inverter, environment-controlling devices, and controllers of systems. Among these interaction interfaces give users admittance to EMS data about the state and diagnostics, as well as the ability to change switching constraints. Apart from future developments in battery substantial and strategy, on-board energy management takes a critical role in achieving the intended cost, safety, performance, and trustworthiness standards. This contributes to electric vehicles' profitable achievement. An acceptable energy management system was proposed by C. Kothai Andal et al. [1] and integrated into a suitable platform. A significant benefit of this work is energy management in relation to IoT, including real-time device monitoring and control data processing. This project is using the Internet of Things to construct a smart control system that will remotely monitor power generated and consumed in order to manage produced energy across many Nano grids. A collection of multi-purpose sensors collect real-time data wirelessly, and they also transfer that data over a "Internet Connection" to numerous cloud servers where they are formatted appropriately. Achikkulath Prasanthi and coworkers[2], A non-inverted buck-boost H-bridge is suggested as the source side converter for effectively recovering the braking energy when connecting a parallel arranged multi-source system. For effective control of the EV, a detailed control design for the traction motor and converter is also offered. Additionally, the total control system incorporates an adaptive energy management method that takes into account power profile and dynamic source characteristics.

A real-time energy management system and electric vehicle optimisation technique based on deep long-term and short-term memory neural networks are proposed by Wenqi Zhu [3]. To manage large-scale electric vehicles in layers and regions, a three-tier architecture consisting of the power grid layer, regional energy management systems, and charging station energy management systems is first built. Next, a region station interaction strategy based on deep long-term and short-term memory neural networks is then proposed. A multi-criteria framework is created by Moein Moeini-Aghtaie et al. [4]to coordinate the charging habits of PHEVs on an energyhub platform. In this case, the ideal charging profiles are firstnoted and reported to the PHEVs Coordinator Entity (PCE)from the perspectives of both hub managers and PHEVowners. The PCE then employs an optimisation frameworkthat considers a number of factors, such as the comfort ofPHEV owners, the financial success of the energy hub, and thetechnical performance of the distribution grid, to produce thePHEVs' ideal charging schedules. When all the typical aspectsof vehicle operation are incorporated to the reinforcementlearning algorithm, the model will have a certain degree ofgeneralizability, according to the initial analysis.

Chunyang Qi et al. [5] proposed from the state values ofreinforcement learning in the state selection. Then, with theaid of the auxiliary agent, KL-divergence can be used toincrease the reinforcement learning's reward value. Zhou,Huayanran, and others [6], This research proposes a machinelearning approach based on a long short-term memory(LSTM) recurrent neural network (RNN) to arrange thecharging and discharging of many EVs in prosumers ofcommercial buildings. The suggested system control structureallows for the separation of the offline and online stages of theLSTM algorithm. The LSTM is used to map states (inputs) todecisions (outputs) based on network training during theoffline stage. Arian Zahedmanesh and colleagues [7], It is proposed to operate an integrated system as a virtual energy hub (VEH) that includes an electric transportation system with a battery-powered bus [electric bus (eBus)] charging station and an EV parking lot, integrated with solar photovoltaic (PV) generation, combined with a battery storage system (BSS), and powered by solar energy. A novel three-stage cooperative control system is used to schedule the active and reactive power flows as well as the economic functioning of the VEH in a cooperative decision-making (CDM) strategy. Agents are used in the development of a supervisory control system to implement the VEH's scheduled CDM and assign control parameters for the delivery of ancillary services. Based on the existing research, this paper examines the development of electric vehicles, batteries and energy management systems, different anode and cathode compounds being used battery packs, the parts of the powertrain and how they work, as well as a potential energy management system with Fractional Order Adaptive Integral Hierarchical Sliding Mode Controller (FOAIHSM).

The contribution of the paper includes:

i) To develop a better energy management system toassure a maximum lifetime of the battery.

ii) The energy management system involves the closemonitoring of the individual battery modules of thebattery pack to assure appropriate charging anddischarging conditions.

iii) Demonstrate that the suggested controller respondsquickly and robustly even when there is modeluncertainty.

iv) Using MATLAB/Simulink to validate the proposedcontroller.

Paper is organized as follows, The first section explains why this project is needed and introduces the topic. The second section contains proposed method of this paper. Third section explains about mathematical modeling of Energy Management System. Section 4 contains the results of simulation studies as well as a discussion of the findings. Finally, Section 5 has the conclusion.

3.1 Battery model

The Energy Management System (EMS) and the batteries which are known as Energy Storage System. For the creation of updated battery packs, advanced composite technologies and sources of energy are needed. Electric automobiles' acceleration and operating range are constrained as hydrocarbon fuel has a higher energy density than battery packs. They must operate on very little power, so an EMS is required to switch the flow of power and keep tolerable energy stores in the storing elements. There will be tactics used for the processes of creation, preservation, dissemination, and consumption of electric power. Since deep-cycle batteries are designed to supply electricity for longer durations, electric vehicle battery packs differ from beginning, lights, and ignition (SLI) packs. Lighter and smaller batteries are favoured because they reduce vehicle mass and hence improve efficiency; Electric car batteries stand out thanks to their ratio between power and mass, greater specific energy and high - power density. Modern battery topologies often have a lower specific energy than liquid fuels, which affects the possible all-electric range of the vehicles. An electric car is powered by a battery. If the battery is entirely discharged without being charged, the vehicle's performance suffers. Although EVs have battery monitoring systems, and just keep track of the battery's ability and do not optimise power utilisation. This research tries to reduce the amount of electricity used by the battery to power all of the vehicle's components.

Knowing the current and voltage readings of the vehicle's devices allows you to determine the battery's state of charge. The following relationship is used to calculate the battery's state of charge:

$\operatorname{SOE}(t)=\operatorname{SOE}(t 0) \int_{t 0}^t\left(P_e+P_d\right)$           (13)

Where, Pe denotes the instantaneous power transferred from the accumulator to the electric motor, Pd denotes the power drawn by the vehicle's devices, and "t" is the time period during which the devices are operational. The battery pack state of charge (SOC) is defined as a discrete state variable along the distance as follows:

$\operatorname{SOC}(K+1)=\operatorname{SOC}(K)-\frac{P(K)}{E_{\text {Battery }}} \Delta t(K)$           (14)

P is battery power, while $E_{\text {battery }}$ is the total energy of the battery pack. When the battery is discharging, $P$ is positive (negative) (charging).

Because BEVs are propelled by an electric motor that works on energy deposited in a battery, practically all of the equipment in an EV relies on battery power to operate, as it does not have an internal combustion engine. Several factors influence vehicle energy consumption, which can be categorized into two groups [7, 8]: (a) inner factors related to the vehicle and (b) external factors related to driving conditions. The impact of all elements must be thoroughly investigated in order to construct an exact EV energy consumption estimation model, because slope of road, for example, has a significant effect. External factors show a wide range of variability when it comes to real-world driving situations. Based on their both uncertainty and flexibility, they are categorised into three groups: stable, dynamic but forecastable, and tough to anticipate. Figure 3 shows a hierarchical map of the variables that affect how much energy an EV uses.

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Figure 3. EV energy consumption's impacting aspects are depicted in a hierarchy

The energy consumed, $E_{\text {cons }}$ is intended as a unit of distance (Wh/m) using the output power of $\left(P_{b a t}\right)$

$E_{c o n s}=\frac{E_{b a t}}{d}$           (15)

$E_{\text {bat }}=\left(P_{b_{\text {out }}}(\tau) d r-P_{b_{\text {in }}}(\tau) d r\right) \cdot \frac{1}{3600}$           (16)

$P_{b_{\text {out }}}=\frac{R_{\text {Total }} \cdot V_{\text {vehicle }}}{\eta_{\text {powertrain }}}$ and $P_{b_{\text {in }}}=\alpha . P_{\text {regan }}$           (17)

where, $R_{\text {Total }}$ is the total resistance to vehicle motion in ( N ), $V_{\text {vehicle }}$ is the vehicle speed in $(\mathrm{m} / \mathrm{s})$, Distance travelled in meter is denoted by d, and $E_{b a t}$ is the battery energy output in (Wh). Powertrain efficiency, which includes the electrical motor, transmission, and power electronics, is the proportion of braking energy that can be recovered $(0<a<1)$.

$T_{B r-\text { demanded }}=\frac{X_{B r e g a n} \cdot r_d}{G \cdot \eta_G}$           (18)

$P_{B r-\text { demanded }}=T_{B r-\text { demanded }} \cdot \omega_{\text {motor }}(s)$           (19)

$P_{b_{\text {out }}}$ and $P_{b_{\text {in }}}$ are the power delivered by the battery for vehicle movement and the electricity reproduced to energize the battery in generator mode, taking into account electric motor braking capabilities.

The output power of battery $\left(P_{b a t}\right)$ is split into two parts:

- Vehicle propulsion power ( $P_{b_{o u t}}$ ): In order to overcome resistance and any losses of power throughout the motor vehicle system, the battery must supply this power (Power out).

- Regenerative braking power ( $P_{b_{i n}}$ ): regenerative braking can recover some of the braking energy by running charging the battery while operating in generator mode (Power in).

3.2 Battery pack model

Electric motor must generate driving force $(F M)$ to overcome resistive force $(F v)$ and parallel component of weight on inclination $(F g)$ to cause movement. Equations describing force and speed of vehicle are

$F_{M, k+1}+F_{v, k+1}+F_{B r k, k+1}+F_{G, k+1}=m a_{k+1}$           (20)

$v_{k+1}=v_k+\Delta \mathrm{Ta}_{\mathrm{k}+1}$           (21)

$v_{r e f, k+1}+\Delta v_{k+1}=v_{k+1}$           (22)

Battery voltage can be estimated using equation,

$\begin{aligned} & U_{B, K+1}=U_{B 0}+ R_B I_{B, k+1}+ \\ & A_B e^{-B_B Q_{B, M a x}\left(1-S o C_{B, k+1}\right)} \\ &-\frac{K_B}{\operatorname{Soc}_{B, k+1}}\left(Q_{B, \max }\left(1-\operatorname{SoC}_{B, k+1}\right)\right.\end{aligned}$           (23)

where, $U_{B 0}$ is constant voltage, $R_B$ is internal resistance, $A_B$ is amplitude of exponential zone, $B_B$ is the inverse exponential zone time constant, $Q_{B, \max }$ is maximum capacity, $K B$ is polarisation constant. As battery charge changes slowly over time it is able to replace $S o C_{B, \max }$ in exponential term and in denominator of the last term with $S o C_{B, K}$. State of charge of battery $\left(S o C_B\right)$ can be estimated from current over time increment:

$S o C_{B, K+1}=S o C_{B, K}+\frac{\Delta T}{Q_{B, M a x}} I_{B, k+1}$           (24)

Depth of charge $\left(D S C_B\right)$ is limited to $85 \%$, and maximum discharge and charge rates are 6 and 2 times of specific capacity $\left(Q_{B, M a x}\right)$, respectively.

3.3 Motor driver model

DC machine is used to represent electric drive for the sake of simplicity. Motor voltage is a function of current and speed:

$U_{M, k+1}=R_M I_{M, K+1}+\frac{K_w}{N r_{\text {wheel }}} v_{k+1}$           (25)

where, $k$ is back-EMF constant, $r_{\text {wheel }}$ is effective wheel radius and $N$ is a gear ratio.

Propulsive force is expressed in term of current, linear speed and acceleration:

$F_{M, k+1}=\frac{N}{r_{\text {wheel }}} M_{M, k+1}$           (26)

$F_{M, k+1}=\frac{N}{r_{\text {wheel }}}\left(K_M I_{M, k+1}-\frac{J_M N}{r_{\text {wheel }}} a_{k+1}-\frac{d_M N}{r_{\text {wheel }}} v_{k+1}\right)$         (27)

where, $k_m$ is torque constant which equals $k \omega, J_m$ is inertia, $d_M$ is damping value. Motor voltage is automatically limited by speed limit of EV on optimization level and saturated to maximum voltage $\left(U_{M, \max }\right)$ on component level. Maximum motor current on component level equals the ratio of maximum torque to torque constant $\left(M_{M, M a x} / k_m\right)$.

3.4 Energy management strategies

A centralized power system is necessary after the expansion of BMS and vehicle motor devices to supply the ratio of a wheel's adhesive friction to its outer layer's motive force, such as it is between the road and vehicle’s wheels, and to determine which pack should receive power during regeneration.

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Figure 4. Effective energy transfer between the powertrain elements and the energy management system

The name of the central control programme is “Energy Management”. This EMS establishes an interaction link among the each motor and DC-DC Converter for managing power flow across powertrain mechanisms, as well as a communication link between the batteries to regulate the status of charge of each battery pack. Figure 4 depicts the ideal power flow between the powertrain elements and an EMS. The EMS is used in electric vehicles to properly transfer power throughout the powertrain's modules and increase battery life by enhancing thermal stability. Enhanced power control tactics are needed since large super-capacitors are expensive. These are utilised to regulate the performance and norms of the super-charge/discharge capacitor. Here, it is necessary to know the functioning voltage and current of the battery power, the group of battery power system, the super capacitor's initial charging condition, the super capacitor’s charging current, and the performance of the vehicle. The strategies for control the speed and current, both of which are dependent on the time of the charging and dis-charging of the supercapacitor are discussed in the sections that follow.

3.4.1 Current restrained control strategy

An electric vehicle's load current changes wildly during accelerating, braking, and downgrading. The super-capacitor enhances the battery's working condition and lengthen its operating safety while the load current extends the threshold charging or discharging current that the battery can sustain. The operational current of the battery is:

$I_b=I_L+I_C$           (28)

$I_c$ is supplied by a supercapacitor through a Buck-Boost converter, whereas $I_L$ is the load current. To restrict the operating current of the power battery, the following requirements must be met:

$-I_b^N \leq I_b \leq I_b^p$           (29)

where, $I_b^N$ is the power battery's maximum charging current and $I_b^b$ is its maximum discharging current,

$I_b^N=-K_1 C_n$           (30)

$I_b^p=K_2 C_n$           (31)

where, $C_n$ is the battery's nominal capacity, $\mathrm{A}-\mathrm{h}$ is the maximum charging rate of the battery, and $k_1$ is the maximum dis-charging rate of the battery. Equations (30) and (31) provide the following relationship:

$-I_b^N-I_L \leq I_c \leq I_b^p-I_L$           (32)

The current limitation control strategy uses the Buck-Boost circuit to maintain $I_C$ within the desirable range.

Table 2. Primary attributes of the instance a fluctuating load and a 400 volt-regulated output voltage

3.4.2 Speed restrained control strategy

The speed of the vehicle is also significant since it has an immediate effect on the super-condition capacitor. The ultra-capacitor should be completely energized and permitted to de-energized when the electric car starts up for greater-performance momentum. The ultra- capacitor should have less energy stored because the electric car is moving quickly in order to acquire regenerative power used when braking. Another crucial signal is the rate of the traction battery. The traction battery can only store so much energy after it is fully charged. Throughout real-world driving, current flow from the regenerative cycle is permitted while the ultra-capacitor is not powered up. The amount of energy deposited in the supercapacitor is comparative to the square of the applied voltage (Uultr), which may be changed using the IGBT PWM regulator.

The goal of the energy management approach is to safeguard the suitable quantities of energy are stored in the super-capacitor and that the ultra-capacitor is constantly operating at the correct level of charge. It works like a solid-state flywheel, delivering and absorbing energy in real time to and from the system. The vehicle's current speed and discharge surface are used in all computations for the control strategy (DOD). The control strategy of speed and current are combined in the integrated control strategy.