Table 3 Comparison of different modeling methods for integrated energy systems

Commercial & open-source tools

Commercial software (Aspen Plus, EnergyPlus, APROS, etc.)

High-fidelity simulations based on physical equations for specific energy domains

Power plant thermodynamics, building energy analysis, network hydraulics

High precision, user-friendly interfaces

Closed architecture, expensive, slow for large systems

Open-source modeling frameworks (Oemof, pyPSA, EnergyPLAN, etc.)

Modular, Python-based platforms for custom energy system models

Energy planning, multi-energy system optimization, algorithm research

Free and transparent, strong community

Steep learning curve, lacks polished GUIs, and usability varies

Mechanism-based theories

Energy hub model (EH)

A multi-input, multi-output model for energy conversion, storage, and distribution

District energy, multi-energy buildings, industrial hubs

Simple and scalable, easily extensible

Steady-state model, Oversimplifies conversion processes

Generalized energy flow models (EFM)

Uses circuit theory analogies to model multi-energy networks dynamically

Electricity-gas-heat network analysis, stability, flexibility studies

Captures dynamic behavior, Integrates multi-energy flows

Computationally intensive, relies on linear assumptions

AI-based Hybrid Models

Physics-informed neural networks (PINN)

Neural networks that integrate physical laws into their learning process

State estimation and parameter identification in physical systems

Data-efficient, physically consistent solutions, Handles ill-posed problems

Struggles with complex networks, Training stability issues

Graph neural networks (GNN)

Learns from graph-structured data, capturing network relationships

Spatio-temporal prediction, power grid optimization

Manages topology, faster, robust to missing data

Hard to interpret dynamics, Issues with unseen topologies