# Modelica-Based Energy Management of PEMFC Hybrid Power System of Vehicle
## 1 Introduction  
The proton exchange membrane fuel cell (PEMFC) is a clean power conversion device that generates electrical and thermal energy through the electrochemical reaction of hydrogen and oxygen [1]. It has been widely applied in mobile power sources, automobiles, drones, and other devices. The power generation process produces virtually no noise and realizes no carbon emissions. However, fuel cells have relatively smooth output characteristics and may not provide sufficient power for instantaneous demands [2]. As a result, they often require supplementary power sources, such as lithium-ion batteries. A system composed of fuel cells and lithium-ion batteries forms a fuel cell hybrid power system. Vehicles equipped with fuel-cell hybrid power systems have a better range compared to traditional vehicles [3]. However, the highly nonlinear nature of power systems composed of multiple energy sources presents design challenges for energy management strategies (EMS), particularly regarding adaptability and control robustness under various driving conditions [4]. Under this premise, advanced EMSs have a considerable effect on releasing the energy-saving potential of hybrid power systems. Many experts and researchers have already designed various hybrid power systems and studied their energy management [5, 6]. Currently, there are two mainstream types ofEMS: rule-based EMS and optimization-based EMS [7]. Rule-based EMS uses deterministic or fuzzy logic strategies and is widely favored in the industry due to its simple structure and easy implementation [8]. Nevertheless, rule-based methods heavily rely on expert experience and practical operating constraints, which lack flexibility, especially when facing with complex driving conditions. Typically, rule-based methods allocate the power between the fuel cell and lithium-ion battery according to different power demand phases. This approach primarily considers the operation of a single battery, to some extent leading to fuel waste. Optimization-based methods effectively address such issues by setting different objectives to constrain and allocate the power between the fuel cell and the lithium-ion battery [9]. Some indicators, such as the lithium battery SOC, stack temperature, and the hydrogen mass flow rate, are used as optimization objectives to balance the power distribution in hybrid power systems. Through a review of the latest research literature, global optimized-based EMS and instantaneous optimization-based EMS offer superior economic performance. The globally optimized-based EMS mainly includes dynamic programming (DP) [10], Pontryagin's minimum principle (PMP) [11], and heuristic algorithms such as genetic algorithms (GA) [12] and differential evolution (DE) [13]. These methods intend to obtain the optimal control sequence based on known driving information. However, these strategies are limited by their computational complexity and heavy reliance on prior driving information. This makes it difficult for them to be applied in practice. In contrast, instantaneous optimization-based EMS, such as the equivalent consumption minimization strategy (ECMS) [14] and Model Predictive Control (MPC) [15], offer satisfactory control performance and have the potential for real-time applications. ECMS uses an equivalent factor to minimize the instantaneous equivalent fuel consumption by equating power consumption with fuel consumption. However, the inability to automatically adjust internal parameters limits its adaptability to different driving conditions. Recently, [PERSON] et al. [16] proposed a preferred variant called adaptive ECMS (A-ECMS). A-ECMS adapts the equivalent factor in ECMS by obtaining several ideal driving conditions, thus enhancing robustness. However, external disturbances are not considered, making it difficult to apply in real-world, complex, and dynamic driving environments. MPC generates the optimal control input signal by defining a prediction horizon for rolling optimization, demonstrating its flexibility under different driving conditions.