Operating Cost Calculator

Detailed Description

This calculator quantifies the annual electricity cost of a compressor that cycles between two states under a load/unload control strategy:

• Loaded – the compressor delivers air at full capacity. The motor draws full-load power proportional to the nameplate brake horsepower (BHP).
• Unloaded – the compressor is unloaded but the motor continues to idle. Power consumption drops to a fraction of full-load BHP (the unloaded BHP percentage).

Load/unload control is one of the most common strategies for industrial compressors. It is energy-efficient at high utilization but wastes electricity at low utilization because the motor idles continuously rather than shutting Quantifying both cost components helps engineers evaluate whether a different control strategy is economically justified.

The four calculation outputs are:

1. Run Time Unloaded – percent of the time the compressor is unloaded.
2. Loaded Cost – annual electricity cost while delivering air.
3. Unloaded Cost – annual electricity cost while idling (no air delivery).
4. Total Annual Cost – sum of the loaded and unloaded costs.

Relevant formulas are documented below.

Run Time Unloaded

---

Percentage of total operating time the compressor runs in the unloaded state.

The loaded and unloaded run times are complementary: the compressor is either fully loaded or fully unloaded at any instant. The unloaded percentage is therefore the arithmetic complement of the loaded percentage.

\begin{equation}\label{eq:operating-cost-run-time-unloaded} f_{unloaded} = 100 - f_{loaded} \end{equation}

Symbols

\(f_{unloaded}\)	Percentage of operating time the compressor runs unloaded \([\unit{ \percent}]\)
\(f_{loaded}\)	Percentage of operating time the compressor runs loaded (input) \([\unit{ \percent}]\)

Loaded Annual Cost

---

Annual electricity cost while the compressor delivers air at full load.

When loaded, the compressor draws electrical power equal to the full-load shaft power ( \(P_{motor}\)) converted to kilowatts via \(k_{BHP}\), divided by the motor efficiency to account for electrical-to-mechanical conversion losses. This power is paid for over the fraction of annual hours that the machine actually runs loaded.

\begin{equation}\label{eq:operating-cost-loaded} C_{loaded} = \frac{P_{motor} \cdot k_{BHP} \cdot H_{annual} \cdot f_{loaded} \cdot c_{elec}}{\eta_{loaded}} \end{equation}

Symbols

\(C_{loaded}\)	Annual electricity cost in the loaded condition \([\unit{ \dollar\per\year}]\)
\(P_{motor}\)	Full-load motor brake horsepower \([\unit{ \bhp}]\)
\(k_{BHP}\)	BHP-to-kilowatt conversion factor (0.746) \([\unit{ \kilowatt\per\bhp}]\)
\(H_{annual}\)	Total compressor operating hours per year \([\unit{ \hour}]\)
\(f_{loaded}\)	Run-time loaded fraction (input ÷ 100) \([\unit{ \percent}]\)
\(c_{elec}\)	Electricity unit cost \([\unit{ \dollar\per\kilowatt\hour}]\)
\(\eta_{loaded}\)	Motor efficiency in the loaded condition (input ÷ 100) \([\unit{ \percent}]\)

Note

The run-time and efficiency inputs are entered on a 0–100 percentage scale and divided by 100 internally to obtain dimensionless fractions. Because both the loaded run-time fraction and the loaded efficiency fraction are expressed the same way (percent ÷ 100), the formula is algebraically equivalent to using dimensionless fractions throughout. The result is in dollars per year.

Unloaded Annual Cost

---

Annual electricity cost while the compressor runs unloaded (motor idling).

In the unloaded state the compressor draws only a fraction of its full-load BHP. That fraction, \(f_{bhp,unloaded}\), represents the residual mechanical work (friction, windage, valve actuation) absorbed by the unloaded compressor. The motor efficiency in this state, \(\eta_{unloaded}\), may differ from the loaded value because motors are less efficient at light loads.

\begin{equation}\label{eq:operating-cost-unloaded} C_{unloaded} = \frac{P_{motor} \cdot k_{BHP} \cdot H_{annual} \cdot f_{bhp,unloaded} \cdot f_{unloaded} \cdot c_{elec}}{\eta_{unloaded}} \end{equation}

Symbols

\(C_{unloaded}\)	Annual electricity cost in the unloaded condition \([\unit{ \dollar\per\year}]\)
\(P_{motor}\)	Full-load motor brake horsepower \([\unit{ \bhp}]\)
\(k_{BHP}\)	BHP-to-kilowatt conversion factor (0.746) \([\unit{ \kilowatt\per\bhp}]\)
\(H_{annual}\)	Total compressor operating hours per year \([\unit{ \hour}]\)
\(f_{bhp,unloaded}\)	Percentage of full-load BHP consumed when unloaded (input ÷ 100) \([\unit{ \percent}]\)
\(f_{unloaded}\)	Run-time unloaded fraction (= (100 - f_{loaded}) ÷ 100) \([\unit{ \percent}]\)
\(c_{elec}\)	Electricity unit cost \([\unit{ \dollar\per\kilowatt\hour}]\)
\(\eta_{unloaded}\)	Motor efficiency in the unloaded condition (input ÷ 100) \([\unit{ \percent}]\)

Note

The unloaded BHP percentage, \(f_{bhp,unloaded}\), is a compressor nameplate or measured value that varies by machine type. Reciprocating compressors typically unload to 15–25 % of full-load BHP; rotary screw compressors with inlet modulation may be 25–40 %. A lower value indicates a more efficient unloaded state.

Total Annual Cost

---

Total annual electricity cost for a compressor operating in load/unload mode.

The total annual cost is the simple sum of the loaded and unloaded components. This value represents the baseline against which energy efficiency improvements (VSD drives, pressure setpoint optimization, compressor staging) can be compared.

\begin{equation}\label{eq:operating-cost-total} C_{total} = C_{loaded} + C_{unloaded} \end{equation}

Symbols

\(C_{total}\)	Total annual electricity cost \([\unit{ \dollar\per\year}]\)
\(C_{loaded}\)	Annual electricity cost in the loaded condition \([\unit{ \dollar\per\year}]\)
\(C_{unloaded}\)	Annual electricity cost in the unloaded condition \([\unit{ \dollar\per\year}]\)

Modules
	Run Time Unloaded Formula
	Percentage of total operating time the compressor runs in the unloaded state.
	Loaded Annual Cost Formula
	Annual electricity cost while the compressor delivers air at full load.
	Unloaded Annual Cost Formula
	Annual electricity cost while the compressor runs unloaded (motor idling).
	Total Annual Cost Formula
	Total annual electricity cost for a compressor operating in load/unload mode.

Files
file	operating_cost.h
	Declarations for compressed air compressor annual operating cost calculations.

Namespaces
namespace	operating_cost
	Compressed air compressor annual operating cost calculations.

Classes
struct	operating_cost::Input
	Input parameters for the annual compressor operating cost calculation. More...
struct	operating_cost::Result
	Result of the annual compressor operating cost calculation. More...