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Energy management strategies can improve fuel cell hybrid electric vehicles’ dynamic and fuel economy, and the strategies based on model prediction control show great advantages in optimizing the power split effect and in real time. In this paper, the influence of prediction horizon on prediction error, fuel consumption, and real time was studied in detail. The framework of energy management strategy was proposed in terms of the model prediction control theory. The radial basis function neural network was presented as the predictor to obtain the short-term velocity in the future. A dynamic programming algorithm was applied to obtain optimized control laws in the prediction horizon. Considering the onboard controller’s real-time performance, we established a simple fuel cell vehicle mathematical model for simulation. Different prediction horizons were adopted on UDDS and HWFET to test the influence on prediction and energy management strategy. Simulation results showed the strategy performed well in fuel economy and real-time performance, and the prediction horizon of around 20 s was appropriate for this strategy.

The transportation industry is one of the primary sources of energy consumption and exhaust emissions. Many technologies on NEVs (new energy vehicles) have high fuel efficiency and fewer emissions. As one of the most popular NEVs, FCVs (fuel cell vehicles) have huge development space in transportation, depending on their zero emission and high efficiency.

The vehicle with fuel cell stack as the single energy source has a poor dynamic response, and the practical solution is to add a short-term storage system to assemble a hybrid vehicle, thus improving the vehicle’s drivability and dynamic. The most common short-term storage systems include battery and supercapacitor—the former can store more electricity due to its higher specific energy, and the latter has high power density. The hybrid vehicle’s dynamic performance and fuel economy are related to the architecture, the components, and the energy management strategy of the vehicle [

The vehicle propulsion system’s power split is optimized by the energy management strategy when the dynamic vehicle performance is satisfied. Depending on the control method, energy management strategies include optimization-based and rule-based ones.

Current energy management strategies are mostly based on certain/fuzzy logic rules. Certain rule-based strategies are first presented to solve the power split for hybrid electric vehicles, and these strategies have been extensively applied to real vehicles such as Toyota’s Mirai and Hyundai’s Nexo. Fuzzy logic-based strategies, relying on the fuzzy processing of control variables and the threshold value, are more robust and adaptive than those based on specific rules.

Buntin et al. first proposed a switching logic control system for hybrid vehicles [

Optimization-based strategies can be decided into instantaneous optimization, global optimization, and MPC-based (model-predictive-control-based) ones. The most popular instantaneous optimization strategy is ECMS (equivalent consumption minimization strategy), wherein the equivalent consumption of hydrogen in the fuel cell is changed into that of fuel in the battery, and the strategy is used to minimize the equivalent fuel consumption at each sampling time [

In this paper, a MPC-based energy management strategy for fuel cell vehicles was proposed, and the influence of prediction horizon was studied in detail. In the built MPC framework, a radial basis function (RBF) neural network was adopt as predictor to obtain the prediction speed, dynamic programming algorithm was employed as the solver to get the optimal trajectory of SOC, and different prediction horizons were tested in terms of prediction error, fuel consumption, and real-time performance. This work is based on fuel cell vehicles, but the method is applicable to other vehicles with two energy sources.

The remainder of this paper is organized as follows. The fuel cell vehicle power system’s mathematical model is established in Section

Figure

Structure of FCV. The red and black lines represent the electrical and mechanical connections of FCV, respectively.

When the impacts of lateral dynamics and rotating mass are ignored, the traction force

Parameters of the fuel cell vehicle.

Parameters | Value |
---|---|

Vehicle total mass (kg) | 1380 |

Air density (kg/m^{3}) | 1.2 |

Aerodynamic drag coefficient | 0.335 |

Vehicle frontal area (m^{2}) | 2 |

Wheel radius (m) | 0.282 |

Gear ratio | 6.67 |

Transmission efficiency (%) | 0.95 |

Rolling resistance coefficient |

With the calculated traction force and velocity, the torque

It is defined that the motor power demand

A 50 kW fuel cell system is chosen as the primary energy source of the vehicle. A complete onboard fuel cell system [

The hydrogen consumption rate

The net power is a function of the stack current, and the hydrogen consumption rate can be described as a function of the net power. Figure

Curve of hydrogen consumption rate.

The efficiency

Figure

Equivalent circuit of the battery.

The open-circuit voltage and the internal resistance are the functions of the SOC and the temperature. The test can be used to obtain internal resistance and the relationship between the open-circuit voltage and SOC (see Figure

Curves of open-circuit voltage and internal resistance of the battery.

The change rate of SOC is defined as the ratio of the terminal current and the battery capacity:

Every single battery has a capacity of 6 Ah and a peak voltage of 3.8 V. A battery pack is constituted with 87 cells in series and three battery packs formed by the parallel connection for simulation.

With the transformation of global optimization into a series of suboptimizations, MPC can obtain the optimal local control laws based on model prediction, rolling optimization, and feedback correction. In Figure

Predict the vehicle’s future short-term velocity through the constructed prediction model.

Obtain the optimal control rules in the short-term drive cycle by minimizing the cost function.

Apply the optimal control rules in the first time step of the prediction horizon to vehicles’ control system. Repeat the above steps until the drive cycle ends.

Structure of MPC-based energy management strategy.

The whole system is discretized into constrained optimization problems in the finite time domain, and DP algorithm [

The fuel consumption is employed as the cost function:

For the structure of fuel cell vehicle, a terminal constraint is implemented to the SOC at every control horizon

Other parameters under constraints are shown in equation (

The neural networks can respond to the nonlinear relationship between inputs and outputs through training the black-box model. In this work, a neural network of the radial basis function is trained to predict the velocity.

In Figure

Structure of neural network predictor.

Here, a RBF-neural network with the structure of 10-50-

The simulation was performed at MATLAB 2018b on a laptop with the configurations of Inter Core i3-3227U CPU @ 1.90 GHz. Seven drive cycles were used to train the network, the other two was used to test the performance of the network and the MPC-based energy management strategy. It was defined that the sampling time

In fact, with the structure of MPC, the final SOC for the global time horizon is practically impossible to have

To evaluate the performance of the constructed controllers, DP-based energy management strategy is employed as the benchmark of the simulation. It should be noted that unlike the DP algorithm mentioned in Section

Different prediction horizons are tested in this work to explore the effect of the prediction horizon on fuel economy. Figure

Prediction results for UDDS in three horizons.

Prediction results for HWFET in three horizons.

Figures

SOC trajectories of DP and MPC for UDDS.

SOC trajectories of DP and MPC for HWFET.

To explore the relationship between prediction error, prediction horizon, and fuel consumption, the hydrogen consumption at different prediction horizons for UDDS and HWFET is shown in Tables

Simulation results at different horizons of MPC for UDDS.

SOC (N) | |||||
---|---|---|---|---|---|

10 | 5 | 2.1279 | 0.602 | 0.071 | 140.95 |

10 | 10 | 3.9320 | 0.604 | 0.120 | 119.14 |

10 | 15 | 6.0122 | 0.604 | 0.168 | 111.39 |

10 | 20 | 7.5998 | 0.604 | 0.213 | 110.34 |

10 | 25 | 9.0285 | 0.604 | 0.267 | 109.58 |

Simulation results at different horizons of MPC for HWFET.

SOC (N) | |||||
---|---|---|---|---|---|

10 | 5 | 1.3259 | 0.6035 | 0.073 | 130.66 |

10 | 10 | 2.4245 | 0.6063 | 0.127 | 129.58 |

10 | 15 | 4.1004 | 0.6099 | 0.169 | 126.99 |

10 | 20 | 5.7272 | 0.6098 | 0.207 | 122.86 |

10 | 25 | 7.3255 | 0.6102 | 0.247 | 125.77 |

H_{2} consumption for the different prediction horizons.

As an onboard controller, the real-time performance of strategy should also be considered. The simulation time at laptop is 0.213 s with the prediction horizon 20 s; this data shows that the MPC-based energy management strategy has a real-time basis. In this work, considering the requirements of energy management strategy on fuel consumption and real-time performance, the prediction horizon is selected to be 20 s. The following analysis is established in the selected horizon. Table

Comparison of MPC and DP for two drive cycles.

Type | SOC (N) | Normalized average (%) | |||
---|---|---|---|---|---|

UDDS-MPC | 20 | 0.6046 | 0.2132 | 110.34 | 87.42 |

UDDS-DP | — | 0.6 | 113.60 | 98.01 | 100 |

HWFET-MPC | 20 | 0.6098 | 0.207 | 122.86 | 90.09 |

HWFET-DP | — | 0.6 | 65.44 | 111.79 | 100 |

Based on the simple vehicle model, the RBF-based predictor, and the DP-based solving algorithm, the work presented an MPC-based energy management strategy on a fuel cell vehicle. Models with different prediction horizons were built to study the influence of the prediction time steps.

Simulation results showed that the fuel economy performed best with 25 s as the prediction horizon for UDDS, while for HWFET the best fuel economy appeared at 20 s. In addition, large prediction horizon led to the longer optimizing time. In fact, to a real vehicle, in addition for energy management strategy, the onboard controller also needs to process a lot of real-time data from other components, which may result in much greater actual processing time than simulation. With this in mind, the prediction horizon of around 20 s is appropriate for the onboard MPC-based energy management strategy.

Although the structure of MPC-based energy management strategy is studied in this work, the results are based on the single prediction model with RBF neural network as the frame. In the future, prediction models with multiple algorithms will be studied to obtain the batter predictor.

The dataset and codes of this paper for the simulation are available from the corresponding author if requested.

The authors declare that there is no conflict of interest regarding the publication of this paper.

The study was supported by the Innovation-Driven Development Special Fund Project of Guangxi (Guike AA18242033), Liuzhou Science Research and Planning Development Project (2020GAAA0403 and 2019AD10203), Liudong Science and Technology Project (20200108), and Innovation Project of Guet Graduate Education (2019YCXS008).