Baseline
Average power = installed kW × load factor
Annual energy = average power × operating hours
Annual cost = annual energy × tariff
System flow = average power / specific power [CFM]
Pressure reduction
Rather than the usual “7% per bar” rule of thumb, we use the adiabatic specific-power ratio, which is the physics the rule of thumb approximates:
saving fraction = 1 − [ (P_target / P_amb)^0.286 − 1 ] / [ (P_current / P_amb)^0.286 − 1 ]pressures absolute, P_amb = 1.01325 bar, exponent (k−1)/k = 0.286 for air
At 7 bar(g) this works out at roughly 8% per bar, slightly more than the 6–7% rule of thumb, because the rule of thumb is a linearised average across a wider pressure range. Pressure savings apply to the whole system and are not reduced by the control factor, since the compressor genuinely does less work per cubic metre.
Leak repair
saving = (current leak % − target leak %) × annual energy × control factor
The control factor is the honest part. Cutting demand only saves energy if the compressor can actually turn down. A VSD or a well-sequenced multi-machine system converts almost all of it; an inlet-modulating machine with no unloading converts about half, because it keeps drawing significant power at reduced output. This is the single most over-claimed number in compressed air proposals, which is why it is an input here rather than a hidden assumption.
Zero-loss condensate drains
air lost = number of timer/manual drains × loss per drain [CFM]
saving = air lost × specific power × hours × tariff × control factor
Timer drains discharge air on every cycle whether or not condensate is present, and a stuck-open manual drain leaks continuously. Zero-loss electronic level-sensing drains open only when there is condensate to remove.
Payback
simple payback (months) = investment / (annual saving / 12)
5-year net benefit = 5 × annual saving − investment
Simple payback ignores the time value of money, energy price escalation and maintenance savings. All three usually work in your favour, so treat this as the pessimistic case.