Modeling and Energy Flow Calculation of Integrated Energy System Based on Partial Differential Equation Model

Abstract

This paper discusses the modeling and energy flow calculation method of integrated energy system based on partial differential equation model. By constructing a model that integrates power, heat, and natural gas networks, we analyze in detail the process of energy transmission, conversion, and storage in the system. In the process of modeling, the influence of compressor in constant compression ratio, constant outlet pressure and constant natural gas flow is specially considered, and the accuracy of the model is verified by specific data. In terms of energy flow calculation methods, we compare the performance of the unified solution method and the decomposition solution method. Data analysis shows that the non-gradient descent iterative method, gradient descent iterative method and decomposition solution method show consistency in calculation accuracy, that is, the calculation results of the three methods are the same. However, in terms of computational efficiency, the gradient descent iterative method shows significant advantages. Specifically, under identical computing conditions, our analysis reveals that the gradient descent iterative method exhibits a convergence rate approximately 30% faster than the decomposition solution method, resulting in a notable reduction of around 25% in computational time. This pivotal observation serves as a solid foundation for selecting a more computationally efficient approach in practical applications. To further enhance the computational efficiency, we have delved into deriving the Jacobian matrix of the model and subsequently proposed an advanced gradient descent iterative calculation technique. Through the actual test, this method not only improves the calculation speed, but also ensures the stability and accuracy of the calculation. The research in this paper not only provides a strong theoretical support for the optimal operation of the integrated energy system, but also provides a valuable reference for future research in related fields. Through specific data analysis, we prove the effectiveness and practicability of the proposed method, laying a solid foundation for the sustainable development of integrated energy systems.