The arithmetic mirrors the spark-spread but uses coal futures and a coal plant's heat rate, which is typically higher because coal units are less efficient. Where carbon allowances are priced, the "clean dark spread" subtracts the cost of emissions permits as well.
The spread against the spark spread decides which fuel runs. When gas is cheap relative to coal, the spark spread beats the dark spread and generators switch, which is the main short-run driver of gas demand in power.
Example: power $45/MWh, coal $70/tonne, heat rate 9.5 MMBtu/MWh and 25 MMBtu per tonne means fuel cost of 9.5/25 x 70 = $26.60. Dark spread = $18.40/MWh, below the $21.00 spark spread above, so gas runs first.
Related: spark-spread, natural-gas-futures, crack-spread, seasonality, intercommodity-spread