# Sizing of a Plug-In Hybrid Electric Vehicle with the Hybrid Energy Storage System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling and Control Strategy

#### 2.1. Vehicle Configuration

#### 2.2. Model

#### 2.2.1. Battery Model

_{b}is the open circuit voltage (OCV), i

_{b}is the current and R

_{b}represents inner resistance. SOC

_{b}represents the remaining capacitor of the battery in the current state:

#### 2.2.2. Supercapacitor Model

_{uc}and R

_{uc}represent the supercapacitor capacity and inner resistance, respectively. U

_{uc}is the supercapacitor OCV, I

_{uc}is the current and P

_{uc}is the supercapacitor output power.

#### 2.3. Hybrid Drive Control Strategy

#### 2.4. Hybrid Energy Storage System Control Strategy

_{req}is the power demand of the motor on the HESS; P

_{bat}is the demand power of the battery; P

_{cap}is the demand power of the supercapacitor; and F

_{1}(s) is the filter function. The control rules are as follows.

_{min}), only the battery supplies power; when the SOC of the supercapacitor is in a normal state and the required power of the motor is less than the threshold value (P

_{p}), the battery provides power for the vehicle, and when the required power of the motor exceeds Pp, the remaining power is supplied by the supercapacitor.

_{max}) and the braking power does not reach the threshold value (P

_{n}), the supercapacitor is charged, and when the braking power exceeds Pn, the battery and supercapacitor are charged at the same time; when the SOC2 reaches its maximum, the battery recovers energy alone.

## 3. PHEV Component Sizing Optimization

_{IC}), the torque scaling factors of the motor (S

_{EM}), the battery modules number (N

_{B}) and the capacity scaling factor (S

_{BC}), supercapacitor modules number (N

_{UC}) and the capacity scaling factor (S

_{UC}) are varied during optimization. The boundary values were estimated from the theoretical analysis. The parameters are shown in Table 2.

_{E}is the engine cost, C

_{M}is the motor cost, C

_{bat_init}is the initial cost of the battery, C

_{uc_init}is the cost of the ultracapacitor, and C

_{bat_rep}is the replacement cost of the battery, which can be expressed as follows [26,27]:

_{E}is the engine peak power in kW, P

_{M}is the motor peak power in kW, C

_{bat}is the battery cost, C

_{uc}is the cost of supercapacitors, and n

_{r}is the number of batteries’ replacement times [28].

_{day}is the daily average ampere–hour circulation of the battery pack in Ah, including the cycling and charging conditions [29]; A

_{life}is the cycling life of the battery in Ah [30,31]; and L

_{day}is the average daily mileage in km.

_{j}(x) and g

_{k}(x) are p-dimensional equality constraints and one-dimensional inequality constraints, respectively. h

_{j}(x) and g

_{k}(x) determine the feasible range of decision variables jointly.

#### PSO Solution

_{1}is the cognitive parameter, c

_{2}is the social parameter, c

_{1}= 0.5, c

_{2}= 2.0. r

_{1}and r

_{2}are random numbers, the range is [0, 1] and it is uniformly distributed. ω is the inertia weight, ω = 0.8. Equation (13) provides the i-th particle’s new velocity. The new position of the i-th particle is determined by Equation (14) at each iteration. The particle will be iteratively updated using these formulas until an optimal solution is obtained or the number of iterations is reached. The optimization flow is shown in Figure 6:

## 4. Optimization Results

#### 4.1. Effect of Supercapacitors on Component Sizing

#### 4.2. Effect of Driving Cycle on Component Sizing

## 5. Conclusions

- (1)
- The drivetrain cost of an HESS with a Ni-MH battery is reduced by up to 12.21% when compared to a HESS with Li-ion battery. Compared to the results from theoretical analysis, the drivetrain cost optimized by PSO is reduced by 8.79%.
- (2)
- After adding the supercapacitor to the energy storage system, the parameters of the engine and motor slightly increased, and the initial cost is higher, but the supercapacitor can extend the battery life and thus the drivetrain cost is reduced by 12.34% compared to an energy storage system without supercapacitors.
- (3)
- In order to study the effect of a drive cycle on component sizing, choose three different drive cycles to optimize. The simulation results show that the parameters of the engine, motor, battery and supercapacitor are increased with the cycle aggressiveness, and the vehicle mass and drivetrain cost are higher.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Hybrid drive control strategy. (

**a**) CDCS strategy; (

**b**) CS mode (flag = 0); and (

**c**) CS mode (flag = 1).

Parameter | Value |
---|---|

Glider mass (kg) | 1150 |

Rolling resistance coefficient | 0.009 |

Air drag coefficient | 0.3 |

Frontal area (m^{2)} | 2.17 |

Engine power (kW) | 41 |

Motor power (kW) | 58 |

Li-ion battery capacity (Ah/module) | 30 |

Li-ion battery voltage (V/module) | 12 |

Ni-MH battery capacity (Ah/module) | 28 |

Ni-MH battery capacity (Ah/module) | 6 |

Supercapacitors capacity (F/module) | 3000 |

Supercapacitors voltage (V/module) | 2.5 |

Optimization Variable | Lower Bound | Upper Bound |
---|---|---|

S_{IC} | 0.8 | 1.8 |

S_{EM} | 0.6 | 1.5 |

N_{B}N _{UC} | 25 65 | 65 120 |

S_{BC} (AER40 km) | 0.7 | 1.4 |

(AER60 km) | 1.0 | 2.0 |

(AER80 km) | 1.4 | 2.7 |

S_{BC} (AER40 km) | 0.8 | 1.8 |

(AER60 km) | 1.1 | 2.1 |

(AER60 km) | 1.4 | 2.5 |

S_{UC} (AER40 km) | 0.3 | 1.1 |

(AER60 km) | 0.4 | 1.2 |

(AER60 km) | 0.5 | 1.3 |

Constraints | Description |
---|---|

Acceleration | 0–97 km/h (0–60 mph) ≤ 12 s |

time | 64–97 km/h (40–60 mph) ≤ 5.3 s |

0–137 km/h (0–85 mph) ≤ 23.4 s 0–48.3 km/h (0–30 mph) ≤ 5 s in motor alone | |

Gradeability | >30% (15 km/h) |

Maximum speed | ≥170 km/h |

Battery Type | AER (km) | S_{IC} | S_{EM} | N_{B} | S_{BC} | N_{UC} | S_{UC} |
---|---|---|---|---|---|---|---|

Li-ion | 40 | 0.9976 | 0.7310 | 32.6252 | 0.9207 | 115.7019 | 0.5414 |

Ni-MH | 40 | 1.0975 | 0.8068 | 49.1521 | 1.3856 | 108.5634 | 0.6382 |

Li-ion | 60 | 1.0463 | 0.8621 | 29.7014 | 1.5304 | 110.2505 | 0.6495 |

Ni-MH | 60 | 1.1926 | 0.9155 | 49.0465 | 2.0753 | 108.0355 | 0.6995 |

Li-ion | 80 | 1.1293 | 0.9052 | 35.0756 | 1.8425 | 102.3658 | 0.7492 |

Ni-MH | 80 | 1.3121 | 0.9810 | 60.8873 | 2.3406 | 108.6984 | 0.8256 |

Battery Type | AER (km) | Mass (kg) | Engine Power (kW) | Motor Power (kW) | Battery Capacity (Ah) | Battery Energy (kWh) | Supercapacitor Energy (Wh) | Drivetrain Cost (CNY) |
---|---|---|---|---|---|---|---|---|

Li-ion | 40 | 1609 | 40.9 | 42.4 | 27.6 | 10.94 | 351 | 118,013 |

Ni-MH | 40 | 1701 | 45.0 | 46.8 | 38.8 | 11.44 | 386 | 101,525 |

Li-ion | 60 | 1680 | 42.9 | 50.0 | 45.9 | 16.53 | 401 | 141,862 |

Ni-MH | 60 | 1804 | 48.9 | 53.1 | 58.1 | 17.08 | 415 | 126,163 |

Li-ion | 80 | 1752 | 46.3 | 52.5 | 55.3 | 23.21 | 432 | 177,401 |

Ni-MH | 80 | 1935 | 53.8 | 56.9 | 65.5 | 23.94 | 499 | 156,829 |

AER | Engine (kW) | Motor Energy (kW) | Battery Energy (kWh) | Supercapacitor Energy (Wh) | Mass (kg) | Drivetrain Cost (CNY) |
---|---|---|---|---|---|---|

40 | 54.2 | 57.0 | 11.26 | 362 | 1671 | 123,706 |

60 | 54.7 | 61.8 | 17.21 | 429 | 1742 | 161,792 |

80 | 55.1 | 64.6 | 23.62 | 458 | 1802 | 193,958 |

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**MDPI and ACS Style**

Tu, J.; Bai, Z.; Wu, X.
Sizing of a Plug-In Hybrid Electric Vehicle with the Hybrid Energy Storage System. *World Electr. Veh. J.* **2022**, *13*, 110.
https://doi.org/10.3390/wevj13070110

**AMA Style**

Tu J, Bai Z, Wu X.
Sizing of a Plug-In Hybrid Electric Vehicle with the Hybrid Energy Storage System. *World Electric Vehicle Journal*. 2022; 13(7):110.
https://doi.org/10.3390/wevj13070110

**Chicago/Turabian Style**

Tu, Jian, Zhifeng Bai, and Xiaolan Wu.
2022. "Sizing of a Plug-In Hybrid Electric Vehicle with the Hybrid Energy Storage System" *World Electric Vehicle Journal* 13, no. 7: 110.
https://doi.org/10.3390/wevj13070110