  We theoretically identify the noise-induced coherent contribution to the
ergotropy of a four-level quantum heat engine coupled to a unimodal quantum
cavity. We utilize a protocol where the passive state's quasiprobabilities can
be analytically identified from the population-coherence coupled reduced
density matrix. The reduced density matrix elements are evaluated using a
microscopic quantum master equation formalism. Multiple ergotropies within the
same coherence interval, each characterized by a positive and pronounced
coherent contribution, are observed. These ergotropies are a result of
population inversion as well as quasiprobability-population inversion,
controllable through the coherence measure parameters. The optimal flux and
power of the engine are found to be at moderate values of ergotropy with
increasing values of noise-induced coherence. The optimal power at different
coherences is found to possess a constant ergotropy.
