Abstract: District heating system (DHS) is an important part in integrated energy systems (IES). As the second paper in this series, this paper focuses on the quality regulated DHS and constructs its mathematical model in the form of partial differential-algebraic equations under certain assumptions, subsequently deriving an analytical solution for the model. First, the pipeline model described by a first-order linear hyperbolic partial differential equation is transformed into an intersection of initial value and boundary value problems. A bilateral method of characteristics is then proposed to derive the analytical expression of the pipeline model, which undergoes theoretical validation. Furthermore, by dividing the transfer paths, the analytical solution is extended from a single pipeline to the network level, thereby establishing a source-load two-port model for the quality-regulated DHS. Case studies show that the proposed analytical method outperforms the traditional numerical methods in terms of efficiency. Specially, the analytical method can significantly improve the accuracy and efficiency over the finite difference method.