The pH framework may face challenges and limitations when handling non-linear couplings or non-local interactions between different network components in energy systems. One challenge is the complexity of modeling non-linear interactions, especially in systems with feedback loops or highly non-linear behavior. Ensuring the stability and convergence of the numerical methods in the presence of strong non-linearities can be a significant challenge.
Another limitation is the scalability of the pH framework to large-scale energy networks with numerous interconnected components. As the number of network nodes and edges increases, the computational complexity of solving the coupled pH equations grows, requiring efficient parallelization strategies and model reduction techniques to maintain computational tractability.
Handling non-local interactions, where the effects of one component propagate over long distances in the network, can also pose challenges. Incorporating delayed or distributed interactions into the pH formulation may require advanced modeling techniques and numerical algorithms to accurately capture the dynamics of the system.
Overall, while the pH framework offers advantages in preserving the structure and energy properties of network systems, addressing non-linear couplings and non-local interactions effectively requires careful consideration of the model assumptions, numerical methods, and computational resources available.