As the number of distributed energy resources in today’s energy distribution grids is growing, measures must be taken to keep the voltage magnitudes in the grid within the operational limits. One prevalent way of doing this is to use voltage dependent reactive power provisioning, so-called Q(V )-control, where a Q(V )-characteristic prescribes how much reactive power is used to stabilise the node voltage. However, due to their interconnection by the power grid, the combined Q(V )-controls of several plants may become unstable. The first part of this paper revisits an existing stability criterion from the literature, based on a discrete-time model of Q(V )-control but limited to radial topologies, in order to assess how steep the slopes can be chosen. In the second part, this criterion is
extended to grids with arbitrary topologies by introducing a more general grid model which explicitly takes the current operating point of the grid into account. Furthermore, an optimisationbased procedure is presented to exploit this new criterion for the direct maximisation of the slopes of the Q(V )-characteristics while guaranteeing stability of the system. Finally, both criteria are compared by applying them on selected benchmark grids.