# Adaptive-Energy-Sharing-Based Energy Management Strategy of Hybrid Sources in Electric Vehicles

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## Abstract

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## 1. Introduction

_{2}emissions. The requirement for high-power charging stations is the reason why the development of charging infrastructure heavily constrains the adoption of electric vehicles. Since the battery is the single source available to handle sudden and fluctuating load demands in BEVs due to varying driving profiles, alternate strategies are necessary to ensure optimal battery operation [16].

- Design and modelling of an Intelligent Hybrid-Source Energy Management Strategy (IHSEMS) for a Battery–SC–PV hybrid-source EV based on absolute energy sharing to ensure an effective and optimal power allocation without any complex modelling and data collection.
- Investigation of EV technical and economic parameters of proposed IHSEMS compared with BEVs and standard EMS.
- Stabilization of DC bus voltage and minimization of fluctuations during varying driving and environmental conditions.
- Contrary to the existing EMSs (SMC [41] and FDS [42]), the proposed work is highly adaptive and effective towards different driving and environmental conditions. It improves the SC utilization and reduces the RMS battery current with a downsized battery capacity, without compromising the vehicle range.

## 2. Energy Management System and Strategies

#### 2.1. Dynamics of Electric Vehicle

_{r}the rolling resistance coefficient, $\alpha $ the gradeability, $\rho $ the air density, A${}_{f}$ the frontal area of the vehicle, ${C}_{D}$ the drag coefficient, V the velocity of the vehicle, $\lambda $ the rotational inertia constant ${\eta}_{R}$ the regenerative braking efficiency, ${\eta}_{HESS}$ the hybrid system efficiency, ${\eta}_{T}$ the transmission efficiency, and ${\eta}_{M}$ the motor drive efficiency.

#### 2.2. Properties of Hybrid Sources

#### 2.3. Proposed Energy Management Strategy

#### 2.4. Technical Evaluation

- (a)
- Battery peak power reduction (${B}_{PPR}$): The peak battery power demand (${B}_{P}$) increases the battery C-rates (${I}_{B}$/${C}_{B}$) and reduces the life (Equation (22)) [13,44]. The percentage reduction in battery peak power is expressed as follows:$${B}_{PPR}\phantom{\rule{4pt}{0ex}}(\%)=\left(\frac{{B}_{P}-{B}_{PEMS}}{{B}_{P}}\right)\xb7100$$
- (b)
- Battery capacity reduction (${B}_{CR}$): Describes the percentage reduction in battery capacity (${B}_{C}$) [52].$${B}_{CR}\phantom{\rule{4pt}{0ex}}(\%)=\left(\frac{{B}_{C}\phantom{\rule{4pt}{0ex}}-\phantom{\rule{4pt}{0ex}}{B}_{CEMS}}{{B}_{C}}\right)\xb7100$$
- (c)
- Battery di/dt reduction (${B}_{IR}$): Rate of change of battery current ($di/dt$) and the percentage reduction are expressed in Equations (16) and (17), respectively, which determines the stress on the battery.$$di/dt\phantom{\rule{4pt}{0ex}}(A/s)=\frac{{I}_{max}\phantom{\rule{4pt}{0ex}}-\phantom{\rule{4pt}{0ex}}{I}_{min}}{{t}_{max}-{t}_{min}}$$$${B}_{IR}\phantom{\rule{4pt}{0ex}}(\%)=\left(\frac{di/d{t}_{BEV}\phantom{\rule{4pt}{0ex}}-\phantom{\rule{4pt}{0ex}}di/d{t}_{EMS}}{di/d{t}_{BEV}}\right)\xb7100$$
- (d)
- Battery RMS current reduction (${B}_{RIR}$): Battery RMS current reduction % can be calculated using Equation (18), and its reduction extends the battery life [30]. RMS current is a vital factor that affects battery life and gives a rough estimation of the battery ohmic losses [55]. The system’s overall losses and efficiency highly depend on the RMS current. ${B}_{RIR}$, by employing the suitable hybrid source in EVs, decelerates battery capacity degradation.$${B}_{RIR}(\%)=\left(\frac{{B}_{RI}\phantom{\rule{4pt}{0ex}}-\phantom{\rule{4pt}{0ex}}{B}_{RIEMS}}{{B}_{RI}}\right)\xb7100$$
- (e)
- Battery capacity loss (${B}_{CL}$): Instantaneous battery capacity loss, battery capacity loss, and total capacity losses are evaluated with Equations (19)–(21), respectively [44,56].$${B}_{\delta {Q}_{loss}\left(k\right)}\phantom{\rule{4pt}{0ex}}=9.78\times {10}^{-4}\xb7\left(\frac{Abs\left({I}_{B,k}\right)\xb7\phantom{\rule{4pt}{0ex}}{T}_{s}\xb7\phantom{\rule{4pt}{0ex}}ex{p}^{\frac{(-15162+1516\xb7{C}_{rate,k})}{(0\xb7849\xb7R\xb7T)}}\xb7{Q}_{loss,(k-1)}^{-0.1779}}{3600}\right)$$$${B}_{{Q}_{loss}}=F\left(\right)open="("\; close=")">{C}_{rrate}\xb7T\xb7{A}_{h}\xb7N\xb7DOD\xb7exp{p}^{\frac{\left(\right)}{-}}(R\xb7T)$$$${B}_{{Q}_{loss}\left(k\right)}=0.0032\xb7\phantom{\rule{4pt}{0ex}}exp(\frac{(-15162+1516\xb7\phantom{\rule{4pt}{0ex}}Crate(k\left)\right)}{R\xb7\phantom{\rule{4pt}{0ex}}(T+273)}\xb7\phantom{\rule{4pt}{0ex}}Ah{\left(k\right)}^{z};$$The capacity loss of a lithium-ion battery determines the life of the battery. Reduction in capacity from the initial capacity (100%) must be less than 20% to achieve optimal battery operation for EV applications. The end of life (EOL) of a battery is defined as whenever the battery capacity reaches less than 80% of its initial capacity [57]. The Arrhenius degradation model [58] is used to depict the battery degradation, and the model explains how the battery temperature, depth of discharge (DOD), current rate ${C}_{rate}$, RMS current, and BIR ($di/dt$) highly deteriorate the battery life and increase the BDC Equation (28) [13,30].
- (f)
- Battery lifespan (${B}_{LS}$): The significant impact on battery life is due to the battery capacity loss, as expressed in Equation (22) for a lithium-ion battery [44].$${B}_{LS}=\left(\frac{20\%}{{Q}_{lossD}\xb7\phantom{\rule{4pt}{0ex}}{D}_{day}\xb7\phantom{\rule{4pt}{0ex}}365}\right)$$
- (g)
- DC bus voltage fluctuations($D{C}_{BVF}$): Equation (23) expresses the percentage variation of the peak-to-peak DC bus voltage fluctuation [27] as follows:$$D{C}_{BVF}\phantom{\rule{4pt}{0ex}}(\%)=\left(\frac{{V}_{max}\phantom{\rule{4pt}{0ex}}-\phantom{\rule{4pt}{0ex}}{V}_{min}}{{V}_{bus}}\right)\xb7100$$
- (h)
- Optimum battery size (${B}_{OS}$): The battery size provides a standard driving range to run a vehicle without PV irradiance for a day. The ${n}_{sBc}$ and ${n}_{pBc}$ are selected as 10 and 58, respectively, to meet the required average power demand and nominal voltage.$${B}_{OS},\phantom{\rule{4pt}{0ex}}{n}_{sBc}\xb7{n}_{pBc}>=\frac{(\rho \xb7{A}_{f}\xb7{C}_{D}\xb7{V}^{2}+2\xb7M\xb7g\xb7{f}_{r})\xb7D}{2\xb7{\eta}_{HESS}\xb7{\eta}_{T}\xb7{\eta}_{M}\xb73600\xb7{C}_{Bc}\xb7{V}_{Bc}-(2\xb7{M}_{Bc}\xb7g\xb7{f}_{r})}$$The battery size of HSEVs can be reduced by 26.72% compared to BEVs available in the market, as shown in Table 2. The derived battery size from Equation (1) and expressed in Equation (24) would provide the standard driving range even under adverse conditions. Additionally, the proposed vehicle can accommodate a PV panel. The output power ratings of PV are analyzed analytically in Section 3.1, considering different weather conditions.
- (i)
- Battery State of charge (${B}_{SOC}$): Charge levels in the battery are decided by the SOC. Improvement in energy economy is reflected in the battery SOC levels.$${B}_{SOC}={B}_{SOC0}-\int \frac{{I}_{B}}{{B}_{C}}$$
- (j)
- SC State of charge ($S{C}_{SOC}$): SCs operate with higher efficiency at higher SOC. In order to achieve a better SC performance, SOC should not go below 40% and over 100%. The relationship between $S{C}_{SOC}$ and voltage is shown in Equation (26) [14].$$S{C}_{SOC}={({U}_{SC}/{V}_{SC})}^{2}$$
- (k)
- PV range (PVR): As per the Indian electric 3W standard test case, the average driving range is 100 km per day [59]. PV energy per day directly impacts both the range and battery energy savings.$$P{V}_{Range}=\frac{{E}_{PVday}}{ECR}$$

#### 2.5. Economy Evaluation

- (a)
- EV Battery degradation cost (BDC) is the measure of battery replacement and maintenance cost from its capacity and instantaneous capacity loss (Equation (19)) [44,60].$$BDC=\frac{{B}_{C}\phantom{\rule{4pt}{0ex}}\xb7{V}_{B}\xb7\phantom{\rule{4pt}{0ex}}Pric{e}_{BAT}\xb7\phantom{\rule{4pt}{0ex}}{B}_{\delta {Q}_{loss}\left(k\right)}}{\left(1000\right)\xb7\phantom{\rule{4pt}{0ex}}\left(0.2\right)}\left(INR\right)$$
- (b)
- EV Electricity cost (EC) is the cost associated with energy utilized (${E}_{source}$) during the battery’s charging. EC depends on the per unit cost (kWh), the battery size (Ah), and SOC (%) as expressed below [61]:$$EC\phantom{\rule{4pt}{0ex}}=\frac{{E}_{source}\xb7\phantom{\rule{4pt}{0ex}}Pric{e}_{kWh}}{\left(1000\right)}\left(INR\right)$$
- (c)
- EV Total operation cost (TOC) describes the cost associated with battery degradation with time and energy usage. The battery degradation cost (BDC) and electricity cost (EC) of EVs determine the total operation cost of the vehicle.$$TOC\phantom{\rule{4pt}{0ex}}=BDC\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}EC\left(INR\right)$$

## 3. Results and Discussions of EMS

#### 3.1. Impact of PV Power

^{2}[49,64]. It is evident from Figure 13b that PV energy generation is highest during March (143.63 kWh) and lowest during November (103.12 kWh). The yearly average PV energy production at Bangalore is 1455.07 kWh under a fixed panel arrangement. However, PV energy consumed by vehicles is significantly lower due to the shading on roads and parking spaces which reduces solar irradiance. Centeno et al. (2021) reported the annual average irradiance loss of 20% and 50% during driving and parking due to shading, respectively [65]. Three cases with different PV irradiance and vehicle drive conditions were examined to show the significance of PV energy in HSEV. Scheduling of the daily NYCC driving cycle of electric 3W energy management is shown in Table 3. The daily standard 100 km driver’s driving cycle needs to drive 53 times that of the NYCC driving cycle [44].

^{2}at t = 221 s, and a decrease from 1000 to 0 W/m

^{2}at t = 257 s verify sudden PV power variations. The power allocation of IHSEMS described in Figure 14a includes the load power, battery power, SC power, and PV power. IHSEMS took care of the load demand at t = 221s, where PV irradiance and regenerative braking excess power were at the bus. SC consumed this excess power at that instant by consuming more power (-ve rise shows the sudden increase in SC charge power) to avoid disturbances in battery power. At t = 257s, the PV irradiance suddenly reduced to zero, and traction operation demanded a dip in power at the bus. The SC delivered more power (+ve rise shows the sudden increase in SC discharge power) to avoid fluctuations in battery power. This strategy ensures a smooth battery operation during rising and falling PV irradiance and load variations. Similarly, Figure 14b shows the same load fluctuation as discussed in Figure 14a. However, the PV power is considered zero to analyze the impact of energy management during the same load fluctuations but with different environmental conditions. Under zero PV irradiance, the SC does not take additional charge or discharge currents as in the case of Figure 14a. Three different driving cases were considered based on the instant of the driving time in a day, and are as follows:

**Case I:**Where daily average PV irradiance is available for charging;**Case II:**Where half of daily average PV irradiance is available for charging;**Case III:**Where zero daily average PV irradiance is available for charging.

#### 3.2. Techno-Economic Analysis

#### 3.2.1. Technical Performance Comparison of EMSs

#### 3.2.2. Economy Analysis of EMSs

## 4. Conclusions

- The battery’s stress reduces in IHSEMS by reducing RMS current by 46.60%, 37.88%, and 17.03% compared with BEV, SMC, and FDS methods.
- The battery peak power reduces in IHSEMS by 50.2%, 30.74%, and 3.71% compared with BEV, SMC, and FDS methods.
- Compared to BEV, the battery capacity reduces in IHSEMS by 26.72% (7.37 kWh to 5.4 kWh).
- The IHSEMS exhibits a reduction in battery peak power, RMS current, and continuous charge–discharge cycles, which improves the battery lifespan by 92.68%, 80.22%, and 32.40% compared with BEV, SMC, and FDS EMS, respectively.
- Economic analysis of IHSEMS shows a reduction of 60%, 43.9%, and 23.68% in total operation cost compared to BEV, SMC, and FDS, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BEV | Battery Electric vehicles |

BMS | Battery management systems |

DP | Dynamic programming |

ECMS | Equivalent consumption minimization strategy |

EV | Electric vehicle |

EM | Energy Management |

EMS | Energy management strategies |

FCEV | Fuel cell electric vehicles |

GA | Genetic algorithm |

HSEV | Hybrid source electric vehicles |

IHSEMS | Intelligent Hybrid Source Energy Management Strategy |

MPC | Model predictive control |

NDC | Nationally Determined Contribution |

NYCC | New York city cycle |

PSO | Particle swarm optimization |

PV | Photovoltaic |

RMS | Root mean square |

STEPS | Stated Policies Scenario |

SC | Supercapacitor |

SDS | Sustainable Development Scenario |

3W | Three-wheeler |

WLTP | Worldwide Harmonized Light Vehicles Test Procedure |

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**Figure 13.**PV energy generation (kWh). (

**a**) Map of selected location for the analysis (Bangalore-12.9716° N, 77.5946° E). (

**b**) PV energy generation (kWh) at Bangalore, India throughout the year.

**Figure 14.**Power allocation of IHSEMS for sudden variation in solar irradiance (

**a**) at zero PV power; (

**b**) under NYCC driving cycle.

**Figure 15.**Comparison of BEV, SMC, FDS, and IHSEMS in terms of battery current (

**a**) and battery capacity loss (

**b**) under NYCC driving cycle.

**Figure 16.**Comparison of BEV, SMC, FDS, and proposed IHSEMS under NYCC driving cycle. (

**a**) Comparison of peak battery power for NYCC driving cycle (510 s–599 s). (

**b**) Comparison of power fluctuations for NYCC driving cycle (400 s–520 s).

**Figure 18.**Comparison of $D{C}_{BVF}$ bus voltage fluctuations with SMC, FDS, and IHSEMS under NYCC driving cycle.

Sl No | Parameters | Symbols | Values |
---|---|---|---|

1 | Vehicle category | L5M auto | |

2 | Seating capacity | Driver + 3 seaters | |

3 | Kerb weight | ${M}_{0}$ | 450 kg |

4 | Gross weight (with full capacity) | M | 800 kg |

5 | Gradability | $\alpha $ | 10° |

6 | Average velocity | V | 40 km/h |

7 | Frontal area | ${A}_{F}$ | 2 m^{2} |

8 | Rolling coefficient | ${f}_{r}$ | 0.01 |

9 | Drag coefficient | ${C}_{D}$ | 0.5 |

10 | Air density | $\rho $ | 1.225 kg/m^{3} |

11 | Roof area | ${A}_{R}$ | 5 m^{2} |

12 | Acceleration due to gravity | g | 9.81 m/s^{2} |

13 | Efficiency of hybrid system (%) | ${\eta}_{HESS}$ | 95 |

14 | Transmission efficiency (%) | ${\eta}_{T}$ | 90 |

15 | Motor drive efficiency (%) | ${\eta}_{M}$ | 85 |

Sl No | Components | Parameters | Values | Values |
---|---|---|---|---|

1 | Lithium-ion battery | Cell type | 3.2 V, 2.6 Ah, LFP cell | |

2 | Battery capacity | ${C}_{B}$ | 5.4 kWh | |

3 | Rated voltage | ${V}_{B}$ | 36 V | |

4 | Specific energy | ${e}_{B}$ | 151 Wh/kg | |

5 | Supercapacitor | Module ratings | 32 V, 250 F | |

6 | Maximum current | ${I}_{SCmax}$ | 1900 A | |

7 | Specific energy | ${e}_{SC}$ | 3.65 Wh/kg | |

8 | Solar PV | PV array power | 965.6 W | |

9 | Voltage at maximum power | ${V}_{PV}$ | 34 V | |

10 | Current at maximum power | ${I}_{PV}$ | 28.4 A | |

11 | Total panel area | ${A}_{PV}$ | 4.8 m^{2} |

Sl no | Parameters | Case-I | Case-II | Case-III |
---|---|---|---|---|

1 | Daily energy demand (Wh) | 3445 | 3445 | 3445 |

2 | Monthly energy demand (Wh) | 124,020 | 124,020 | 124,020 |

3 | Monthly PV energy generation (Wh) | 63,600 | 31,800 | 0 |

4 | Monthly battery energy consumption (Wh) | 60,420 | 92,220 | 124,020 |

5 | Daily 3W EV drive distance(km) | 100 | 100 | 100 |

6 | Daily PV range (km) | 60 | 30 | 0 |

Sl no | Parameters | BEV | SMC | FDS | IHSEMS |
---|---|---|---|---|---|

1 | Battery Peak Power (kW) | 10.93 | 7.96 | 5.64 | 5.44 |

2 | Battery capacity (kWh) | 7.37 | 5.4 | 5.4 | 5.4 |

3 | Battery di/dt (A/s) | 113 | 98 | 61 | 26.8 |

4 | Battery RMS current (A) | 64 | 54.95 | 41.14 | 34.13 |

5 | Battery Capacity Loss | 4.20 × 10${}^{-5}$ | 3.92 × 10${}^{-5}$ | 2.88 × 10${}^{-5}$ | 2.18 × 10${}^{-5}$ |

6 | Battery Life Span Improvement (%) | - | 6.91% | 45.50% | 92.68% |

7 | DC bus voltage fluctuations (%) | 13.19% | 10.40% | 5.20% | 2.05% |

8 | Total Operational Cost (INR.) | 18.54 | 12.942 | 9.50 | 7.25 |

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## Share and Cite

**MDPI and ACS Style**

Sidharthan, V.P.; Kashyap, Y.; Kosmopoulos, P.
Adaptive-Energy-Sharing-Based Energy Management Strategy of Hybrid Sources in Electric Vehicles. *Energies* **2023**, *16*, 1214.
https://doi.org/10.3390/en16031214

**AMA Style**

Sidharthan VP, Kashyap Y, Kosmopoulos P.
Adaptive-Energy-Sharing-Based Energy Management Strategy of Hybrid Sources in Electric Vehicles. *Energies*. 2023; 16(3):1214.
https://doi.org/10.3390/en16031214

**Chicago/Turabian Style**

Sidharthan, Vishnu P., Yashwant Kashyap, and Panagiotis Kosmopoulos.
2023. "Adaptive-Energy-Sharing-Based Energy Management Strategy of Hybrid Sources in Electric Vehicles" *Energies* 16, no. 3: 1214.
https://doi.org/10.3390/en16031214