  We present cosmic microwave background (CMB) power spectra from recent
numerical simulations of cosmic strings in the Abelian Higgs model and compare
them to CMB power spectra measured by Planck. We obtain revised constraints on
the cosmic string tension parameter $G\mu$. For example, in the $\Lambda$CDM
model with the addition of strings and no primordial tensor perturbations, we
find $G\mu < 2.0 \times 10^{-7}$ at 95% confidence, about 20% lower than the
value obtained from previous simulations, which had 1/64 of the spatial volume.
We investigate the source of the difference, showing that the main cause is an
improved treatment of the string evolution across the radiation-matter
transition. The increased computational volume also makes possible to simulate
fully the physical equations of motion, in which the string cores shrink in
comoving coordinates. This, and the larger dynamic range, changes the amplitude
of the power spectra by only about 10%, demonstrating that field theory
simulations of cosmic strings have now reached the required dynamic range for
CMB calculations.
