  A new family of conserved currents for vacuum space-times with a Killing
vector is presented. The currents are constructed from the superenergy tensor
of the Mars-Simon tensor and using the positivity properties of the former we
find that the conserved charges associated to the currents have natural
positivity properties in certain cases. Given the role played by the Mars-Simon
tensor in local and semi-local characterisations of the Kerr solution, the
currents presented in this work are useful to construct non-negative scalar
quantities characterising Kerr initial data (known in the literature as
non-Kerrness) which in addition are conserved charges.
