This paper presents the numerical models underlying the implementation of a novel harmonic balance compressible Navier-Stokes solver with low-speed preconditioning for wind turbine unsteady aerodynamics. The numerical integration of the harmonic balance equations is based on a multigrid iteration, and, for the first time, a numerical instability associated with the use of such an explicit approach in this context is discussed and resolved. The harmonic balance solver with low-speed preconditioning is well suited for the analyses of several unsteady periodic low-speed flows, such as those encountered in horizontal axis wind turbines. The computational performance and the accuracy of the technology being developed are assessed by computing the flow field past two sections of a wind turbine blade in yawed wind with both the time-and frequency-domain solvers. Results highlight that the harmonic balance solver can compute these periodic flows more than 10 times faster than its time-domain counterpart, and with an accuracy comparable to that of the time-domain solver.