  Modern battery materials can contain many elements with substantial site
disorder, and their configurational state has been shown to be critical for
their performance. The intercalation voltage profile is a critical parameter to
evaluate the performance of energy storage. The application of commonly used
cluster expansion techniques to model the intercalation thermodynamics of such
systems from \textit{ab-initio} is challenged by the combinatorial increase in
configurational degrees of freedom as the number of species grows. Such
challenges necessitate efficient generation of lattice models without
over-fitting and proper sampling of the configurational space under charge
balance in ionic systems. In this work, we introduce a combined approach that
addresses these challenges by (1) constructing a robust cluster-expansion
Hamiltonian using the sparse regression technique, including
$\ell_0\ell_2$-norm regularization and structural hierarchy; and (2)
implementing semigrand-canonical Monte Carlo to sample charge-balanced ionic
configurations using the table-exchange method and an ensemble-average
approach. These techniques are applied to a disordered rocksalt oxyfluoride
Li$_{1.3-x}$Mn$_{0.4}$Nb$_{0.3}$O$_{1.6}$F$_{0.4}$ (LMNOF) which is part of a
family of promising earth-abundant cathode materials. The simulated voltage
profile is found to be in good agreement with experimental data and
particularly provides a clear demonstration of the Mn and oxygen contribution
to the redox potential as a function of Li content.
