# Case Study of Holistic Energy Management Using Genetic Algorithms in a Sliding Window Approach

^{*}

## Abstract

**:**

## 1. Introduction

- Comparison of real-world drives and driving cycles in regard to the EMS
- Application of a GA to an automotive EMS
- Analysis of the optimization results
- Critical assessment of the use of a GA for an EMS

## 2. Related Work

**Thermal management system:**This includes systems that only consider the powertrain and those that combine powertrain and heating, ventilation, and air conditioning (HVAC). The variables are typically the energy that is used for thermal management and the internal states of the system.**Hybrid energy-storage system:**The considered literature deals with an EMS for storage comprising a lithium-ion battery and super-capacitors. All of these strategies aim to optimize the power split between the two sources.**Variable gear ratio:**Here, the focus lies on a gear-shifting schedule in order to minimize energy consumption.**Multiple electric machines:**The literature cited on this row describes EMS for the use of multiple electric machines. All sources focus on optimizing the power split between the machines.**Variable voltage:**Here, the EMS for the variable intermediate circuit voltage is considered. Only one source is found that focuses on the EMS and not on the overall system. The reason for this is that the optimal voltage for the machine can be computed analytically. Therefore, the focus is on the modeling of the machine.**HVAC:**HVAC constitutes the second largest energy consumer. Therefore, it provides leverage for the EMS. The variable that is adapted is the power consumed by the HVAC. In addition to the energy consumption, the thermal comfort of the passengers is taken into account.**Driving strategies:**Here, the literature on the development of driving strategies aiming to minimize energy consumption is cited. This is achieved by adapting the velocity profile.

## 3. Basics of Multi-Objective Optimization

## 4. Approach

## 5. Results

- ${E}_{bat}$ is the total electric energy provided by the battery. ${E}_{bat}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{E}_{batEff}+{E}_{batLoss}$.
- ${E}_{batEff}$ is the electrical energy taken from the battery that can be used by the auxiliary consumers and the drivetrain.
- ${E}_{batLoss}$ is the electrical energy that is lost in the battery. It is computed as: ${E}_{batLoss}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{R}_{internalBat}\xb7{I}_{bat}^{2}$ with ${R}_{internalBat}$ being the internal resistance of the battery dependent on current, temperature, and state-of-charge.
- ${E}_{heat}$ is the electrical energy used to heat the cabin. Because it can be computed as ${E}_{heat}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{\int}_{0}^{{t}_{max}}{P}_{heater}\left(t\right)dt$, it is directly influenced by the optimization algorithm.
- ${E}_{tract}$ is the total mechanical energy needed for driving. It can be computed as ${E}_{tract}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{E}_{air}+{E}_{roll}+{E}_{acc}+{E}_{recu}+{E}_{sail}$.
- ${E}_{acc}$ is the mechanical energy that is used for accelerating the vehicle. Only the positive acceleration is considered in this value. ${E}_{acc}\sim a$.
- ${E}_{brake}$ is the mechanical energy needed to decelerate the vehicle. Because $v(t=0)\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}v(t\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{t}_{max})\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}0$, it follows that ${E}_{brake}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}-{E}_{acc}$.
- ${E}_{sail}$ is the mechanical energy that is used during the deceleration of the vehicle to overcome the roll and the air resistance. Like ${E}_{brake}$, ${E}_{sail}$ is negative.
- ${E}_{recu}$ is the electrical energy that can be recuperated into the battery. Like ${E}_{brake}$, ${E}_{recu}$ is negative.
- ${E}_{roll}$ is the mechanical energy needed to overcome the rolling resistance. ${E}_{roll}\sim v$.
- ${E}_{air}$ is the mechanical energy needed to overcome the air resistance. ${E}_{air}\sim {v}^{2}$.

^{2}, while ${a}_{mean}$ of the recorded drive was 0.24 m/s

^{2}. The higher ${E}_{acc}$ led to a higher ${E}_{brake}$. This means that more energy could be retrieved: The retrieved energy was expressed as ${E}_{sail}$ and ${E}_{recu}$.

- The proposed approach led to a significant reduction in the total consumed energy, while keeping the driving time nearly constant and the cabin temperature within acceptable limits.
- The holistic approach considering $v\left(x\right(t\left)\right)$ and ${P}_{heat}\left(t\right)$ at the same time had an impact on the battery losses, by avoiding to store the energy in the battery, using it directly for heating instead.
- The execution of the model took about 95% of the total optimization time. This made the GA very dependent on the run time of the simulation model.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BEV | Battery electric vehicle |

EMS | Energy management system |

GA | Genetic algorithm |

HEV | Hybrid electric vehicle |

HVAC | Heating, ventilation and air conditioning |

NEDC | New European Driving Cycle |

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**Figure 1.**Example for the requirements and the subsystem managed by an energy management system (EMS) in a battery electric vehicle (BEV).

**Figure 2.**Overview of the classification of EMS (refer to [2]).

**Figure 3.**To the left: ${v}_{x,tar}\left(t\right)$-curve; to the right: ${v}_{x,tar}\left(x\left(t\right)\right)$-curve of the NEDC.

**Figure 5.**Comparison of the energy components for the recorded drive and the NEDC. All values are expressed as % of ${E}_{bat}$ of the respective driving cycle.

**Figure 6.**Comparison of the energy components for the recorded drive unoptimized and optimized. All values are expressed as % of ${E}_{bat}$ of the unoptimized drive.

**Figure 7.**Comparison of optimized and unoptimized time series of the variables $v\left(t\right)$ and ${P}_{heat}\left(t\right)$, as well as the components of the objective function ${E}_{bat}\left(t\right)$ and $\Delta {T}_{cab}\left(t\right)$.

Component | Optimization-Based | Heuristic | ||
---|---|---|---|---|

Online | Offline | Derived from Optimization | Not Derived from Optimization | |

Thermal management system | [4] | - | - | [5,6] |

Hybrid energy storage | [7] | [8] | [9,10,11] | [12,13,14,15] |

Variable gear ratio | - | [16,17] | [18,19] | [20] |

Multiple electric machines | - | [21] | [22,23,24] | [25] |

Variable voltage | - | - | - | [26] |

HVAC | [27] | - | - | [28] |

Driving strategies | [29,30,31] | [32,33,34] | [35] | - |

Holistic EMS | [36] | - | [3] | - |

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

Population size | $1.5\xb7$ (number of parameters per section l) |

Number of max. generations | 50 |

Crossover-fraction | $0.80$ |

Mutation rate | feasible adaption |

Elitism | $0.05\xb7$ population size |

Selection | rank-based |

Discretization step of time-dependent optimization parameters | 5 s [43] |

Discretization step of space-dependent optimization parameters | 400 m |

**Table 3.**Comparison of traveling time and energy demand ${E}_{bat}$ for different decision-maker priority vectors $\theta $.

Configuration | Reduction of Energy Consumption | Time Relative to Original Traveling Time |
---|---|---|

Recorded Drive | ||

${\theta}_{1}=\left(20\phantom{\rule{3.33333pt}{0ex}}50\phantom{\rule{3.33333pt}{0ex}}30\right)$ | $15.2\phantom{\rule{3.33333pt}{0ex}}\%$ | $112\phantom{\rule{3.33333pt}{0ex}}\%$ |

${\theta}_{2}=\left(20\phantom{\rule{3.33333pt}{0ex}}30\phantom{\rule{3.33333pt}{0ex}}50\right)$ | $10.7\phantom{\rule{3.33333pt}{0ex}}\%$ | $106\phantom{\rule{3.33333pt}{0ex}}\%$ |

${\theta}_{3}=\left(10\phantom{\rule{3.33333pt}{0ex}}15\phantom{\rule{3.33333pt}{0ex}}75\right)$ | $3.39\phantom{\rule{3.33333pt}{0ex}}\%$ | $100\phantom{\rule{3.33333pt}{0ex}}\%$ |

NEDC | ||

${\theta}_{1}=\left(20\phantom{\rule{3.33333pt}{0ex}}50\phantom{\rule{3.33333pt}{0ex}}30\right)$ | $9.79\phantom{\rule{3.33333pt}{0ex}}\%$ | $106\phantom{\rule{3.33333pt}{0ex}}\%$ |

${\theta}_{2}=\left(20\phantom{\rule{3.33333pt}{0ex}}30\phantom{\rule{3.33333pt}{0ex}}50\right)$ | $8.20\phantom{\rule{3.33333pt}{0ex}}\%$ | $101\phantom{\rule{3.33333pt}{0ex}}\%$ |

${\theta}_{3}=\left(10\phantom{\rule{3.33333pt}{0ex}}15\phantom{\rule{3.33333pt}{0ex}}75\right)$ | $3.27\phantom{\rule{3.33333pt}{0ex}}\%$ | $97.4\phantom{\rule{3.33333pt}{0ex}}\%$ |

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**MDPI and ACS Style**

Minnerup, K.; Herrmann, T.; Steinstraeter, M.; Lienkamp, M.
Case Study of Holistic Energy Management Using Genetic Algorithms in a Sliding Window Approach. *World Electr. Veh. J.* **2019**, *10*, 46.
https://doi.org/10.3390/wevj10020046

**AMA Style**

Minnerup K, Herrmann T, Steinstraeter M, Lienkamp M.
Case Study of Holistic Energy Management Using Genetic Algorithms in a Sliding Window Approach. *World Electric Vehicle Journal*. 2019; 10(2):46.
https://doi.org/10.3390/wevj10020046

**Chicago/Turabian Style**

Minnerup, Katharina, Thomas Herrmann, Matthias Steinstraeter, and Markus Lienkamp.
2019. "Case Study of Holistic Energy Management Using Genetic Algorithms in a Sliding Window Approach" *World Electric Vehicle Journal* 10, no. 2: 46.
https://doi.org/10.3390/wevj10020046