  We characterise simplicity of twisted C*-algebras of row-finite k-graphs with
no sources. We show that each 2-cocycle on a cofinal k-graph determines a
canonical second-cohomology class for the periodicity group of the graph. The
groupoid of the k-graph then acts on the cartesian product of the infinite-path
space of the graph with the dual group of the centre of any bicharacter
representing this second-cohomology class. The twisted k-graph algebra is
simple if and only if this action is minimal. We apply this result to
characterise simplicity for many twisted crossed products of k-graph algebras
by quasifree actions of free abelian groups.
