  The strong coupling in the effective quark mass was usually taken as a
constant in a quasiparticle model while it is, in fact, running with an energy
scale. With a running coupling, however, the thermodynamic inconsistency
problem appears in the conventional treatment. We show that the renormalization
subtraction point should be taken as a function of the summation of the
biquadratic chemical potentials if the quark's current masses vanish, in order
to ensure full thermodynamic consistency. Taking the simplest form, we study
the properties of up-down ($ud$) quark matter, and confirm that the revised
quasiparticle model fulfills the quantitative criteria for thermodynamic
consistency. Moreover, we find that the maximum mass of an $ud$ quark star can
be larger than two times the solar mass, reaching up to $2.31M_{\odot}$, for
reasonable model parameters. However, to further satisfy the upper limit of
tidal deformability $\tilde{\Lambda}_{1.4}\leq 580$ observed in the event
GW170817, the maximum mass of an $ud$ quark star can only be as large as
$2.08M_{\odot}$, namely $M_{\text{max}}\lesssim2.08M_{\odot}$. In other words,
our results indicate that the measured tidal deformability for event GW170817
places an upper bound on the maximum mass of $ud$ quark stars, but which does
not rule out the possibility of the existence of quark stars composed of $ud$
quark matter, with a mass of about two times the solar mass.
