In water distribution network (WDN) steady-state modelling, tanks and reservoirs are modelled as nodes with known heads. As a result, the tank levels are upgraded after every steady-state simulation (snapshot) using external mass balance equations in extended period simulation (EPS). This approach can give rise to numerical instabilities, especially when tanks are in close proximity. In order to obtain a stable EPS model, an unsteady formulation of the WDN model has recently introduced. This work presents an extension of the steady-state WDN model, both for demand-driven and pressure-driven analyses, allowing the direct prediction of head variation of tank nodes with respect to an initial state. Head variations at those nodes are introduced as internal unknowns in the model, the variation of tank levels can be analyzed in the single steady-state simulation and EPS can be performed as a sequence of simulations without the need for external mass balances. The extension of mass balance at tank nodes allows the analysis of some technically relevant demand components. Furthermore, inlet and outlet head losses at tank nodes are introduced and large cross-sectional tank areas are allowed by the model and reservoirs become a special case of tanks. The solution algorithm is the generalized-global gradient algorithm (G-GGA), although the proposed WDN model generalization is universal.

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