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.
