Pump operating costs are calculated using the following formula:

Operating Costs=(0.7457) × (Q×H×ρ) × time × (energy costs/kWh)/(247,000) × (effP×effM)

where:
0.7457 converts hp to kW
Q = pump flow rate
H = pump total head
ρ = fluid density
effP = pump efficiency
effM = motor efficiency

In Figure 1 below, two pumps are operated in parallel to supply makeup water to four different stock chests at various flow rates throughout the year. The customer wants to compare the annual operating costs of their existing fixed speed pumps with the cost to operate the pumps using variable frequency drives (VFD).  

Figure 1. Pumping Cost Calculation System

After drawing the system, separate lineups are created to simulate the operating conditions at each flow rate using fixed speed (FS) pumps, as well as to simulate the pump operation using a VFD. The lineups in the PIPE-FLO model are as shown in Table 1 below:

PIPE-FLO already calculates the pump flow rate and uses the pump curve to find the total head and pump efficiency, so the only information needed to perform the cost analysis is the amount of time spent operating at each condition (lineup) and the power cost per kWh.

To perform an Operating Cost Analysis, the Operating Cost Calculator button is selected on the tool bar and the dialog box shown in Figure 2 is opened.

Figure 2. Operating Cost Calculator dialog box

In this dialog box, enter the Analysis Period and select the units of time (hours, days, weeks, or years). Also select the Operating Load input time (as units of Time or % of Time). Also, using the drop down list under "Lineup", you can select the lineup to be used and enter the "Energy Cost" and amount of operating time at that condition (as percent or in units of the analysis period). The amount of time in the analysis period that is unaccounted for is shown in the "Remaining Time" block.Click the "Add" button to add additional lineups that will be used in the analysis period and enter the Energy Costs and Operating Time for each lineup (Figure 3).

Figure 3. Operating Cost Calculator dialog box with all Fixed Speed lineups defined

When all lineups for the analysis are defined, click on the "Calculate" button to view the Operating Cost Calculator Results (Figure 4).

Figure 4. Operating Cost Calculator Results using Fixed Speed pumps

Each lineup is listed along with the energy costs used in the calculation, the total operating cost for each lineup, and the operating cost for each pump in the lineup. A summary at the bottom of the box shows the analysis period, the amount of time, and the total cost for operating the system (sum of each lineup costs).

To analyze the system operation using Variable Frequency Drives on the pumps, you can change lineups to the ones that have the pumps operating at variable speed and enter the energy cost and operating time at each lineup (Figure 5). Select the calculate button to view the results (Figure 6).

Figure 5. Operating Cost Calculator dialog box with all Variable Speed Pump lineups defined

Figure 6. Operating Cost Calculator Results using VFD pumps

The total operating cost for fixed speed operation is $27,245/year. With the implementation of VFDs, the operating cost is reduced to $15,063/year.