# A new, systematic approach to determine the global energy optimum of a hybrid vehicle

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## Abstract

Hybridization is one of the key technologies to reduce the fuel consumption of a vehicle with internal combustion engine (ICE) significantly. Using at least one electric motor (EM), the kinetic energy of the vehicle can be recuperated and the ICE can operate more efficiently. The control strategy (CS) coordinates the torque of the ICE and the EM. If the driving cycle is known, the coordination of the drive units can be adjusted for every point in time, therefore the fuel consumption based on the entire cycle is minimal. Dynamic programming, for example, can be used, but computation time is long and it offers only a few degrees of freedom to evaluate the potential of hybrid drives. For this reason, a new method to identify the global energy optimum in a particularly systematic and transparent way was developed at the Institute of Automotive Engineering. It is therefore a globally optimal control strategy. At the same time, the approach is efficient in terms of computation time and inherently SOC neutral, therefore allowing a very good comparability of results.

### Keywords

Control strategy Global optimum Hybrid drive Efficiency Consumption Energy## 1 Introduction

Control strategy comparison regarding memory and calculation effort [1]

Control Strategy | Memory effort | Calculation effort | Calculation time (s) |
---|---|---|---|

ECMS | 1 | | 1/40 |

DP | | | 60 |

Although the ECMS leads to very good fuel consumption, it will not provide a theoretical energy optimum. Instead, it does enable relatively short simulation durations which are important for case studies or online optimization of a vehicles’ control strategy. The new globally optimal control strategy presented in this paper was developed to achieve simulation times on the same level as the ECMS [4, 5, 6].

In addition, the results of known strategies like DP or the ECMS often evade the intuition so they are difficult to understand and lack transparency. As a consequence, it can be very difficult to figure out the reasons for efficiency advantages or disadvantages for different hybrid concepts. The approach presented in this paper determines the global energy optimum gradually and systematically within multiple steps. Therefore, the powertrain can be evaluated in terms of pure mechanical efficiency (no use of the battery), recuperation, pure electric driving and the sensitivity and efficiency regarding load point shift. This makes the new strategy demonstrative and, at the same time, efficient in terms of computational time.

## 2 Basics

Parameters of the P2 hybrid vehicle

Compact size hybrid vehicle | ||
---|---|---|

| (kg) | 1450 |

| (m | 0.59 |

| (-) | 1.03 |

| (N) | 45 |

| (-) | 8·10 |

The powertrain consists of a 120 kW internal combustion engine (ICE), an 80 kW electric machine (EM), and a 7-speed dual clutch transmission (DCT). The vehicle mass includes the mass of the powertrain. Compared to a conventional vehicle, an additional mass of 150 kg was considered for electrification. Stationary maps are used to represent the efficiency of energy as well as torque and speed converters. Since efficiency maps can cause numerical inaccuracy during interpolation especially at low loads, absolute losses were used to calculate energy consumption.

The simulation model is quasi-stationary which means that dynamic effects (e.g., turbo lag) are not considered. Additionally, the battery is assumed to have unlimited capacity. Its efficiency depends on the battery power but dependencies to the state of charge (SOC) are neglected. Since the influence of the SOC on the battery efficiency is usually very small in a relatively wide SOC range, this assumption can be made without sacrificing too much accuracy. Furthermore, no criteria of drivability, comfort or NVH are considered [7].

To evaluate the fuel consumption for an HEV properly, SOC neutrality is important. The presented control strategy is inherent SOC neutral therefore no parameter iterations are needed which also saves computation time. Nevertheless, a blended charge sustaining operation (for Plug-In HEV) is also possible if a certain ΔSOC will be defined as a constraint.

The functionality of the globally optimal control strategy (GOCS) is explained at first based on the NEDC because the synthetic speed profile makes it easier to understand. The principals of the GOCS apply to each and every driving cycle. In this respect, a boost functionality is not implemented yet, but will be in the future. For the presented driving cycles in this paper boosting is not relevant though. After explaining the functionality in NEDC, customer use will be investigated with the GOCS.

## 3 Global optimum without auxiliary consumers

For a first description and explanation of the hybrid drive, it is not appropriate to take the power demand of the auxiliaries into account. They will therefore not be considered in the following but later on.

### 3.1 Conventional ICE operation (battery neutral operation)

The driving cycle is completed first with ICE only. For this reason, the battery is not used to accelerate or decelerate the vehicle. If the EM cannot be disconnected from the drivetrain, which is the case for the presented P2 hybrid, occurring drag losses are taken into account.

*P*

_{tank}) for each and every time step. Based on the above-mentioned vehicle parameters, it results in a consumption of 5.3 l/100 km. In Fig. 2, the phases in which the ICE is driving can be identified as the red areas. In the thrust phase it is dragged or disabled. Thus, there is no consumption (white areas).

### 3.2 Recuperation

The recuperated energy is now available to the powertrain again. To maximize its efficiency, the electric energy is used to achieve the greatest fuel savings. This is the case where the ratio of electric energy and fuel consumption is minimal. Basically, the electric energy can be deployed to decrease the engine load or to disable the engine and drive electrically. For the presented vehicle in the NEDC, the highest fuel savings are achieved through electric driving. The operating points with the lowest powertrain efficiency (engine and transmission combined) are replaced and the gear selection for electric operation is also carried out with optimum efficiency. In contrast to heuristic operation strategies, there is no static threshold for electric driving like [8] has described. Instead the presented control strategy optimizes the fuel saving for a given amount of electrical energy.

### 3.3 Recuperation and electric driving as driving resistance

### 3.4 Load point shift (LPS)

To minimize the losses of LPS operation, the electric energy for the additional electrical operating points has to be recharged in an optimal way. For this purpose, all time steps are taken into account where the ICE is still active. All torque combinations for all gears of ICE and EM are considered for each operation point. The control strategy calculates the ratio of battery charging power and fuel tank power for each possible operation point. The point with the maximum of recharged electric energy in relation to additional fuel consumption is selected. This ensures that the necessary recharging is associated with minimal additional consumption. SOC neutrality is also ensured because the engine does only recharge the electrical energy needed for electric driving or load decrease applied beforehand.

### 3.5 LPS and electric driving as driving resistance

## 4 Consideration of auxiliary consumers

In the previous approach, the auxiliary consumers were not taken into account to make their consideration in the following more plausible. Without taking them into account, the recuperated energy was directly used for electric driving. Additional electric driving due to the LPS further improved the efficiency.

## 5 Optimal control strategy in costumer use

Lower ICE power limits in 3D city cycles with and without load point shift (LPS)

| | |
---|---|---|

Mild | 2.8 | 8.4 |

Average | 3.9 | 9.3 |

Sporty | 20.6 | 20.6 |

## 6 Summary

In this paper, a new approach to systematically determine the global energy optimum of a hybrid electric vehicle was introduced. The method can be used to gradually identify the potential of different hybrid modes. It allows a particularly transparent analysis of the consumption behavior of a hybrid concept. Compared to other methods, the approach is also very efficient in terms of computing time and can therefore also be used for parameter studies of hybrid vehicles. The systematic approach with regard to the use of the different hybrid modes was described and explained based on the NEDC. Furthermore, the potential of the hybrid modes recuperation and LPS was quantified and illustrated with reference to driving resistances. It was shown that reducing the fuel consumption of hybrid vehicles is based on a combination of reduction of driving resistance and increase in efficiency. The developed control strategy was then applied to three different types of drivers in an urban driving environment according to the 3D method. The results revealed that the operation range of the engine and the electric motor is quite different if an optimum result has to be achieved. A limitation compared to other methods currently is the fact that battery SOC limits are not taken into account. It can, however, be deduced from the results what battery size would be optimal. In case of the considered city cycles, a battery with comparatively low energy capacity is sufficient.

## 7 Outlook

A parallel hybrid with P2 topology was used to illustrate the approach to determine the global energy optimum presented in this paper. Since the approach is based on fundamental energetic considerations, it can also be extended to systems with several EM and different powertrain topologies. Additionally, the boost functionality will be implemented for cases where ICE power alone is not sufficient. Furthermore, it is possible to take constraints into account, e.g., specific phases of a driving cycle that require electric driving. This, for instance, could be zero emission zones in cities. Particularly in view of real vehicle use, the question arises how the driving cycle can be predicted to calculate the energy optimum. This could be done using the 3D method in combination with the driving style identifier developed at the Institute of Automotive Engineering. Using the driving style identifier and taking a number of parameters into account, the driving style of the driver can be determined while driving (mild, average or sporty). The present driving environment and the slope profile can be determined using navigation data. Together with the driving style it results in a representative speed profile, which can be used as a constraint for the optimization of the control strategy. When the driving cycle is known, the presented operation strategy can be used to adapt the operation strategy parameters of the vehicle. Therefore, the results are analyzed and parameters are derived out of these to tune the implemented control strategy of the vehicle. For instance, for a sporty city driver the implemented operation strategy parameters can be modified to realize electric driving at higher loads without recharging the battery through LPS too much [12, 13, 14].

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