# Towards Optimal Power Management of Hybrid Electric Vehicles in Real-Time: A Review on Methods, Challenges, and State-Of-The-Art Solutions

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## Abstract

**:**

## 1. Introduction

#### 1.1. Problem Statement

#### 1.2. Contribution and Novelty

## 2. Rule-Based Methods

#### 2.1. Deterministic Rule-Based Methods

#### 2.1.1. Thermostat (on/off) Control Strategy

#### 2.1.2. Power Follower (Baseline) Control Strategy

#### 2.1.3. Modified Power Follower—Adaptive RB (ARB)

#### 2.1.4. Frequency-Based Approach

#### 2.1.5. Optimal Points Tracking

#### 2.2. Fuzzy Rule-Based Methods

#### 2.2.1. Basic Fuzzy

#### 2.2.2. Adaptive Fuzzy

#### 2.2.3. Predictive Fuzzy

## 3. Optimization-Based Methods

#### 3.1. Global Optimization

#### 3.1.1. Linear Programming

#### 3.1.2. Dynamic Programming (DP)

#### 3.1.3. Genetic Algorithm (GA)

#### 3.1.4. Optimal Control Theory

#### 3.1.5. Particle Swarm Optimization (PSO)

#### 3.1.6. Further Methods

#### 3.2. Real-time Optimization

#### 3.2.1. ECMS

#### 3.2.2. Pontryagin’s Minimum Principle (PMP)

#### 3.2.3. Model Predictive Control (MPC)

#### 3.2.4. Adaptive Dynamic Programming (ADP)

#### 3.2.5. Extremum Seeking (ES)

#### 3.2.6. Robust Control (RC)

## 4. Towards Optimality in Real-time

#### 4.1. Subsidiary Adaptation Tools

#### 4.2. Integration to Power Management Methods

#### 4.3. Insight Into Optimal Real-Time Methods

#### 4.4. Evaluation and Discussion

## 5. Summary and Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Engine on/off rules for power follower strategy (according to [14]).

**Figure 5.**Frequency-based decomposition of power demand into low, medium, and high-frequency components.

**Figure 7.**Working principle of MPC based on the “moving horizon” approach [66].

**Figure 8.**Basic ES scheme for a static map according to [81].

Auxiliary Tools | Types | Conducted by | Integrated to | Achievement/Output |
---|---|---|---|---|

Rules optimization | - qualitative - quantitative | Static optimization | Rule-based | Robustnes of RB methods |

Multi-rate computing | - fixed rate - adaptive rate | - case-based - parallel computing | Opt-based | Computational time reduction |

Pattern recognition | - driving patterns - route/road type | - machine learning - fuzzy logic/NN | Rule-based & opt-based | Case-based optimized solutions |

Prediction/estimation | - driving conditions - $SoC$ estimation | - statistics/HMM - observers/filter | Opt-based | Priori knowledge of future drive conditions |

Intelligent traffic systems (ITS) | - V2V - V2I | Communication technologies | Rule-based & opt-based | - current traffic conditions - next refuelling options |

* | DRB | FRB | ECMS | PMP | DP | MPC |
---|---|---|---|---|---|---|

1 | [44,86] | [87,96] | [89] | [54] | – | – |

2 | – | – | – | – | [76,77] | [71,97] |

3 | [44,88] ${}^{+}$ [77,98] ${}^{++}$ | [25,99,100] ${}^{+}$ [101] ${}^{++}$ | [57,102] ${}^{+}$ [103] ${}^{++}$ | [104] ${}^{+}$ [105,106] ${}^{++}$ | [25] ${}^{+}$ [77,107] ${}^{++}$ | [108] ${}^{+}$ [109] ${}^{++}$ |

4 | [92] ${}^{\u2020}$ [91] ${}^{\u2020\u2020}$ | [99] ${}^{\u2020}$ [110] ${}^{\u2020\u2020}$ [111] ${}^{\u2021}$ [112] ${}^{\mathrm{K}}$ | [93] ${}^{\u2021,+}$ | [113] ${}^{\u2020\u2020,+}$ [106] ${}^{\mathrm{A}}$ [64] ${}^{\xfc}$ | [114] ${}^{\u2020,+}$ [115] ${}^{\mathrm{N}}$ | [116] ${}^{\u2020}$ [94] ${}^{\mathrm{K}}$ [117] ${}^{\xfc}$ |

5 | [118] | [119] | [120,121] | – | – | [122] |

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**MDPI and ACS Style**

Ali, A.M.; Söffker, D. Towards Optimal Power Management of Hybrid Electric Vehicles in Real-Time: A Review on Methods, Challenges, and State-Of-The-Art Solutions. *Energies* **2018**, *11*, 476.
https://doi.org/10.3390/en11030476

**AMA Style**

Ali AM, Söffker D. Towards Optimal Power Management of Hybrid Electric Vehicles in Real-Time: A Review on Methods, Challenges, and State-Of-The-Art Solutions. *Energies*. 2018; 11(3):476.
https://doi.org/10.3390/en11030476

**Chicago/Turabian Style**

Ali, Ahmed M., and Dirk Söffker. 2018. "Towards Optimal Power Management of Hybrid Electric Vehicles in Real-Time: A Review on Methods, Challenges, and State-Of-The-Art Solutions" *Energies* 11, no. 3: 476.
https://doi.org/10.3390/en11030476