Non-iterative Calculation of Quasi-Dynamic Energy Flow in the Heat and Electricity Integrated Energy Systems

TL;DR

This paper introduces a non-iterative, explicit algorithm for quasi-dynamic energy flow calculation in integrated heat and electricity systems, significantly improving efficiency and robustness over traditional iterative methods.

Contribution

The paper proposes a novel non-iterative algorithm transforming nonlinear equations into linear recursive forms, reducing computational costs and enhancing stability in energy flow simulations.

Findings

Requires only one matrix factorization per step

Achieves consistent and small time costs regardless of load levels

Demonstrates high accuracy and robustness in case studies

Abstract

Quasi-dynamic energy flow calculation is an indispensable tool for the heat and electricity integrated energy system (HE-IES) analysis. One solves the nonlinear partial differential algebraic equations to obtain thermal, hydraulic and electric variations. However, mainstream iteration solvers face the challenges of inefficiency and bad robustness. For one thing, the frequent update and factorization of Jacobian matrices utilize high CPU time. For another, the per-step iteration numbers grow exponentially as the system loading level creeps up. This paper presents a novel non-iterative algorithm for the quasi-dynamic energy flow calculation. The kernel of the proposed algorithm is to transform these nonlinear equations into linear recursive ones, by solving which, we obtain explicit closed-form solutions of unknown variables. In each step, the proposed algorithm requires only one matrix factorization and fixed times of arithmetic operations regardless of the loading levels, so that it achieves small and consistent per-step time costs. A semi-discrete scheme is used in PDE solution to avoid dissipative and dispersive errors that are often overlooked in previous literature. To ensure convergence, we also propose to control the temporal step sizes adaptively by estimating the simulation errors. Case studies showed that the proposed method manifested efficient and robust time performance compared with the iterative algorithms, and meanwhile preserved high accuracy.