  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.
