  The $r^{-n}$ interaction energy, $1\leq n< 3$, for a infinitely periodic
system with explicit charges and a neutralizing, uniform background charge
density is derived. An Ewald based expression for this energy has an extra term
proportional to the square of the total explicit charges of the system. This
expression may be useful for simulations in which explicit charge neutrality
does not hold or for which the total explicit charges is a fluctuating
quantity.
