Energy Management of Hydrogen Hybrid Electric Vehicles—OnlineCapable Control
Abstract
:1. Introduction
1.1. Context and Motivation
1.2. Literature Review
 (a)
 The potential for NO${\text{}}_{\mathrm{x}}$ reduction is much larger for H${\text{}}_{2}$HEVs than for conventional dieselpowered HEVs, as well as standard H${\text{}}_{2}$ vehicles.
 (b)
 Although ultralean combustion of hydrogen–air mixtures allows H${\text{}}_{2}$ICEs to emit nearzero NO${\text{}}_{\mathrm{x}}^{\mathrm{eo}}$ emissions, this is a highly delicate process. Small deviations from the chosen operating point of the H${\text{}}_{2}$ICE can increase the instantaneous NO${\text{}}_{\mathrm{x}}^{\mathrm{eo}}$ emissions by over two orders of magnitude.
 (c)
 The mixed hybrid drivetrain architecture is required to achieve consistent NO${\text{}}_{\mathrm{x}}^{\mathrm{eo}}$ reductions across a wide range of challenging driving missions. However, it is more complex than the standard parallel or series hybrid architectures.
1.3. Research Statement
 To the authors’ best knowledge, this publication presents the first onlinecapable EMS controller for a H${\text{}}_{2}$HEV, explicitly accounting for the H${\text{}}_{2}$NO${\text{}}_{\mathrm{x}}^{\mathrm{eo}}$ tradeoff.
 A case study, using the same mixed H${\text{}}_{2}$HEV as discussed in [18], allows for a comparison between the proposed onlinecapable EMS controller and the full theoretically reachable Pareto front obtained by the DP algorithm. The results show that the proposed onlinecapable controller reaches closetooptimal performance on all investigated driving missions, covering a broad range of driving scenarios.
1.4. Paper Structure
2. Modeling
2.1. MapBased Powertrain Model
2.1.1. Driving Modes
2.1.2. Rotational Speeds
2.1.3. EMS Including NO${\text{}}_{\mathrm{x}}^{\mathrm{eo}}$
2.2. Simplified Powertrain Model
2.2.1. Parallel Mode
2.2.2. Series Mode
 Step 1: The generator power and the tradeoff factor ($\psi $) are discretized.
 For each realizable ${P}_{\mathrm{gen}}$, all possible combinations (${\omega}_{\mathrm{e}}$, ${T}_{\mathrm{e}}$) that result in ${P}_{\mathrm{gen}}\left(j\right)$ are identified. By using the mapbased model, the corresponding hydrogen consumption ${\dot{m}}_{f}^{\mathrm{map}}$ and the NO${\text{}}_{\mathrm{x}}^{\mathrm{eo}}$ emissions ${\dot{m}}_{{\mathrm{NO}}_{\mathrm{x}}}^{\mathrm{map}}$ are calculated (steps 3–5).
 By looping over all $\psi $, Equation (19) is used to formulate the extended cost for all identified pairs of (${\omega}_{\mathrm{e}}$, ${T}_{\mathrm{e}}$) and the corresponding tradeoff weight $\psi $ (step 7).
 Minimizing the extended cost function over all previously identified operating points (${\omega}_{\mathrm{e}}$, ${T}_{\mathrm{e}}$) yields the optimal engine operating point (${\omega}_{\mathrm{e}}^{*}$, ${T}_{\mathrm{e}}^{*}$) for the corresponding $\psi $ (step 8).
 Finally, for the generator power (${P}_{\mathrm{gen}}\left(j\right)$) and the tradeoff parameter ($\psi $), the following optimal values are stored for later use: optimal engine power (${P}_{\mathrm{e}}^{*}$), optimal hydrogen consumption (${\dot{m}}_{f}^{*}$), and optimal NO${\text{}}_{\mathrm{x}}^{\mathrm{eo}}$ emissions (${\dot{m}}_{{\mathrm{NO}}_{\mathrm{x}}}^{*}$) (steps 9–11).
Algorithm 1 Preoptimization for series mode. 

2.3. Optimization Parameters
3. ControlOriented Optimization Problem
3.1. Driving Mode Estimation
3.2. Convex Optimization Problem
3.2.1. Cost Function and Dynamics
3.2.2. Power Split
3.2.3. Constraint Relaxations
3.2.4. Battery
3.2.5. Input and State Domains
4. Controller Structure
4.1. LowerLevel Controller
4.2. MPC
4.3. Reference Trajectory Generator
Algorithm 2 RTG iterations. 

5. Case Study
5.1. Driving Missions
5.2. SingleNO${\text{}}_{\mathrm{x}}^{\mathrm{eo}}$Target Adherence
5.3. NO${\text{}}_{\mathrm{x}}^{\mathrm{eo}}$Target Expansion
5.4. Driving Mission Generalization
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
CO${\text{}}_{2}$  carbon dioxide 
$\mathcal{COP}$  convex optimization problem 
DP  dynamic programming 
EMS  energy management system 
EU  European Union 
EV  electric vehicle 
GB  gearbox 
H${\text{}}_{2}$  hydrogen 
H${\text{}}_{2}$ICE  hydrogen combustion engine 
HEV  hybrid electric vehicle 
MPC  model predictive control 
NO${\text{}}_{\mathrm{x}}$  nitrogen oxides 
NO${\text{}}_{\mathrm{x}}^{\mathrm{eo}}$  engineout nitrogen oxides 
OCP  optimal control problem 
PMP  Pontryagin’s minimum principle 
PR  power request (block diagram schematic) 
RTG  reference trajectory generator 
SoC  state of charge 
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Series mode  H${\text{}}_{2}$ICE = ON  clutch = OPEN  $M=1$ 
Parallel mode  H${\text{}}_{2}$ICE = ON  clutch = CLOSED  $M=2$ 
EV mode  H${\text{}}_{2}$ICE = OFF  clutch = OPEN  $M=3$ 
${\mathit{e}}_{{\mathbf{H}}_{2}}^{\mathbf{mean}}$  ${\mathit{e}}_{{\mathbf{H}}_{2}}^{\mathbf{max}}$  

Real driving mission  2.18%  2.47% 
Urban driving mission  4.66%  5.13% 
Mountain driving mission  3.79%  6.62% 
Highway driving mission  4.15%  6.91% 
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Machacek, D.; Yasar, N.; Widmer, F.; Huber, T.; Onder, C. Energy Management of Hydrogen Hybrid Electric Vehicles—OnlineCapable Control. Energies 2024, 17, 2369. https://doi.org/10.3390/en17102369
Machacek D, Yasar N, Widmer F, Huber T, Onder C. Energy Management of Hydrogen Hybrid Electric Vehicles—OnlineCapable Control. Energies. 2024; 17(10):2369. https://doi.org/10.3390/en17102369
Chicago/Turabian StyleMachacek, David, Nazim Yasar, Fabio Widmer, Thomas Huber, and Christopher Onder. 2024. "Energy Management of Hydrogen Hybrid Electric Vehicles—OnlineCapable Control" Energies 17, no. 10: 2369. https://doi.org/10.3390/en17102369