# A Multi-Stage Approach to a Hybrid Lead Acid Battery and Supercapacitor System for Transport Vehicles

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## Abstract

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## 1. Introduction

_{2}emission, better fuel consumption, and advanced electrical drive capabilities. With supercapacitors, recapturing and re-use of power in regenerative braking is possible [5]. Energy management control is the most important part in hybrid energy storage systems (HESS) for transport vehicles. In the work of [6], a combination of parallel-active system comprising of lithium ion and a supercapacitor has been studied, it is claimed that integrating both energy storage technologies provides an energy storage system with high energy availability combined with high power density. However, the parallel-active topology is not suitable for use in transport vehicles (TVs), because the supercapacitor tends to charge from the battery when the system is not operational.

## 2. Materials and Methods

#### 2.1. Lead Acid Battery

- Open circuit voltage of 12.2733 V.
- Internal Resistance of 0.0016 Ω.
- Performance factors K of 0.0047651, A of 0.81645, and B of 12.

#### 2.2. Supercapacitor

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Describes the nomenclature used | |

DC | Direct Current |

DC/DC | Direct Current-to-Direct Current |

EDLC | Electric Double Layer Capacitor |

EVs | Electric Vehicles |

HESS | Hybrid Energy Storage System |

HEVs | Hybrid Electric Vehicles |

IGBTs | Insulated Gate Bipolar Transistors |

LABs | Lead Acid Batteries |

MATLAB/Simulink | Matrix Laboratory |

PHEVs | Plug-in Hybrid Electric Vehicles |

PID | Proportional plus Integral plus Derivative |

PWM | Power Width Modulation |

RAM | Random Access Memory |

SOC | State-of-Charge |

TVs | Transport Vehicles |

VRLABs | Valve Regulated Lead Acid Batteries |

Describes the mathematical expressions used in this paper | |

${E}_{m}$ | Battery Electromotive Energy |

${I}_{battery}\left(t\right)$ | Battery current as function of time |

${I}_{sc}$ | Supercapacitor current |

${K}_{e}$ | Electron constant |

$K,AB$ | Battery performance factors |

${P}_{sc}$ | Supercapacitor power |

$\rho $ | PID compensation factor |

${Q}_{battery}$ | Battery charge |

$Q$ | Charge |

${R}_{in.battery}$ | Battery internal resistance |

$RC$ | Resistance and capacitance |

${T}_{b}$ | Battery operating temperature |

${V}_{oc}\left(t\right)$ | Open circuit voltage as a function of time |

${V}_{sc}\left(t\right)$ | Supercapacitor voltage as a function of time |

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**Figure 1.**Matrix Laboratory (MATLAB)/Simulink lead acid battery (LAB)/supercapacitor hybrid system based on two direct current-to-direct current (DC/DC) converters. PWM—power width modulation.

**Figure 2.**Boost DC/DC converter for the LAB and control strategy. PID—proportional-plus-derivative-plus-integral.

**Figure 8.**Describes the simulation procedure of the developed model. EDLC—electro double layer capacitor.

**Figure 11.**Typical power delivered by the LAB/supercapacitor hybrid system versus the required power of the hybrid transport vehicle.

Lead Acid Battery | Supercapacitor |
---|---|

Output voltage = 12.2733 V | Rated Voltage = 12 V |

Capacity = 75 Ah | Rated Capacitance = 500 F |

Initial SOC = 100% | Number of series capacitance = 6 |

Temperature = 25 °C | Initial Voltage = 16 V |

Temperature = 25 °C |

**Table 2.**Mean results of supercapacitor and lead acid battery (LAB) power, voltage, current, and state-of-charge (SOC).

SC Power (W) | LAB Power (W) | SC Current (A) | LAB Current (A) | SC Voltage (V) | LAB Voltage (V) | SC SOC (%) | LAB SOC (%) |
---|---|---|---|---|---|---|---|

114.7985 | 779.9167 | 13.4772 | 55.8535 | 7.9157 | 11.9350 | 58.1388 | 96.9880 |

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**MDPI and ACS Style**

Lencwe, M.J.; Chowdhury, S.P.; Olwal, T.O.
A Multi-Stage Approach to a Hybrid Lead Acid Battery and Supercapacitor System for Transport Vehicles. *Energies* **2018**, *11*, 2888.
https://doi.org/10.3390/en11112888

**AMA Style**

Lencwe MJ, Chowdhury SP, Olwal TO.
A Multi-Stage Approach to a Hybrid Lead Acid Battery and Supercapacitor System for Transport Vehicles. *Energies*. 2018; 11(11):2888.
https://doi.org/10.3390/en11112888

**Chicago/Turabian Style**

Lencwe, Mpho J., Shyama P. Chowdhury, and Thomas O. Olwal.
2018. "A Multi-Stage Approach to a Hybrid Lead Acid Battery and Supercapacitor System for Transport Vehicles" *Energies* 11, no. 11: 2888.
https://doi.org/10.3390/en11112888