This report describes different methods for modelling of pressurized water supply networks with consideration of pressure dependent demands (PDM: Pressure Driven Modelling) in combination with flow constraints. For that purpose, the PDM model described in D 4.1 is extended by additional bounds for the link flows that refer to closed or failed links (equality conditions) and the operation of more sophisticated and automated flow control devices such as check valves and flow control valves (inequality constraints). In contrast to the pure PDM model where the proof of the Linear Constraint Qualification (LICQ) to hold was simple (only assumption is connectivity of the network) the same is not true for general flow bounded problems. A simple example is given by the case where two valves are closed in a path disconnecting at least one node from the rest of the system. If the disconnected node is a demand node then in DDM the problem would have no solution. In contrast, PDM allows to reduce the outflow to zero such that a solution exists. Adding the two flow constraints with q = 0 for the closed valves to the continuity equation results in linear dependency of the constraints, which in turn leads to a singular Jacobian. Because of the singularity, there is non-uniqueness of equation, with infinity of solutions for nodal heads and minor losses of active flow control devices (the Lagrangian multipliers associated with the problem constraints). In this report, it will be shown that almost all problems of non- convergence are related to the problem of linear dependent constraints and the resulting singularity of the system. Consequently, the central problem of the robust solver is the prevention of linear dependent constraints or the derivation of methods that deal explicitly with non-unique multipliers. The content of the deliverable is as follows. After a brief introduction that summarizes the problem of modelling disconnected systems a relevant Literature about flow and pressure control modelling in hydraulic system analysis is reviewed. In the main part the extended PDM model for flow controlled problems is derived and the appearance of non-unique pressure heads is discussed, Then, different approaches for avoiding singularities in the network equations are summarized and compared as to their robustness, efficiency and practical applicability.