  In this paper, we concentrate on power dilation systems
$\{f(z^k)\}_{k\in\mathbb{N}}$ in Dirichlet-type spaces $\mathcal{D}_t\
(t\in\mathbb{R})$. When $t\neq0$, we prove that $\{f(z^k)\}_{k\in\mathbb{N}}$
is orthogonal in $\mathcal{D}_t$ only if $f=cz^N$ for some constant $c$ and
some positive integer $N$. We also give complete characterizations of
unconditional bases and frames formed by power dilation systems for
Drichlet-type spaces.
