A 50,000-cfm CV air-handling unit is to be converted to a VAV system. The motor for the existing supply fan is rated at 35 hp with 90 percent efficiency. The fan is operated for 3,500 hours/year according to the following load profile:

Question

100 percent l • oad, 10 percent of the time
• 80 percent load, 40 percent of the time
• 60 perent load, 40 percent of the time
• 40 percent load, 10 percent of the time

Three options for variable air volume controls have been considered:
(a) Outlet dampers at a cost of $,3,500
(b) Variable inlet vanes at a cost of $8,000
(c) Variable speed drive at a cost of 9,000
Determine the best option for the fan control using simple payback period analysis. Assume that electricity costs $0.05/kWh.

Accepted Answer

The electrical energy input of the supply fan motor is first determined for each control option by calculating a weighted average fan horse power rating using the fan performance curves given in Table 7.6.

TABLE 7.6 Percent Reduction of Fan Power as a Function of the Percent Reduction in Air Volume for the Three Control Options

Fan Air Volume (in % of Maximum Flow)				Fan Control Option
40%	60%	80%	100%	Fan Control Option
77	88	96	100	Outlet dampers
51	61	78	100	Variable inlet vanes
				Variable speed drives:
16	36	64	100	Actual performance
6	22	51	100	Theoretical performance

For the outlet dampers:

[latex]k\overline{W} ^{OD}_{e.fan} =35 Hp *(1.0 * 0.1+ 0.96 * 0.4 + 0.88 * 0.40 + 0.77 * 0.1) = 31.95 Hp[/latex]

For the variable inlet vanes:

[latex]k\overline{W} ^{VIV}_{e.fan} =35 Hp *(1.0 * 0.1+0.78 * 0.4 + 0.61* 0.40 + 0.51 * 0.1) = 24.76 Hp[/latex]

The electrical energy input of the supply fan motor is first determined for each control option by calculating a weighted average fan horse power rating using the fan performance curves given in Table 7.6.

For the outlet dampers:

[latex]k\overline{W} ^{OD}_{e.fan} =35 Hp *(1.0 * 0.1+0.96 * 0.4 + 0.88* 0.40 + 0.77 * 0.1) = 31.95 Hp[/latex]

For the variable inlet vanes:

[latex]k\overline{W} ^{VIV}_{e.fan} =35 Hp *(1.0 * 0.1+0.78 * 0.4 + 0.61* 0.40 + 0.51 * 0.1) = 24.76 Hp[/latex]

For the variable speed drives, both the actual and the theoretical fan performance curves are considered. The actual fan performance leads to:

[latex]k\overline{W} ^{VSD}_{e.fan} =35 Hp *(1.0 * 0.1+0.64 * 0.4 + 0.36* 0.40 + 0.064 * 0.1) = 18.06 Hp[/latex]

and the theoretical fan performance gives:

[latex]k\overline{W} ^{VSD}_{e.fan} =35 Hp *(1.0 * 0.1+0.51 * 0.4 + 0.22* 0.40 + 0.064 * 0.1) = 13.99 Hp[/latex]

The total number of hours for operating the fan for one year is [latex]N_{f,h}[/latex] =3,500 hours for all fan types including the constant volume fan (used as a base case for the payback analysis). First, the electrical energy use for each fan control option is estimated.
For the existing constant volume fan:

[latex]kWh^{CV}_{e.fan}=(\frac {35 Hp * 0.647 kWh/yr}{0.90})*3500hrs=101,539 kWh/yr[/latex]

For the outlet dampers (OD):

[latex]kWh^{OD}_{e.fan}=(\frac {31.95 Hp * 0.647 kWh/yr}{0.90})*3500hrs=92.690 kWh/yr[/latex]

For the variable inlet vanes (VIV):

[latex]kWh^{OD}_{e.fan}=(\frac {24.76 Hp * 0.647 kWh/yr}{0.90})*3500hrs=71.832 kWh/yr[/latex]

For the actual performance of the variable speed drives (VSD):

[latex]kWh^{OD}_{e.fan}=(\frac {18.06 Hp * 0.647 kWh/yr}{0.90)}*3500hrs=52,394 kWh/yr[/latex]

For the theoretical performance of the variable speed drives:

[latex]kWh^{OD}_{e.fan}=(\frac {13.99 Hp * 0.647 kWh/yr}{0.90})*3500hrs=40,587 kWh/yr[/latex]

It is clear from the results of the economic analysis presented above, that the fan equipped with a variable speed drive is the most cost-effective option.

Simple Payback Period (yrs)	Annual Cost Savings ($/yr)	Annual Energy Cost ($/yr)	Annual Energy Use (kWh/yr)	Fan Control Option
−	0	5,077	101,539	CV
7.9	442	4,635	92,690	OD
5.4	1,485	3,592	71,832	VIV
3.7	2,457	2,620	52,394	VSD (act.)
3.0	3.048	2.029	40,587	VSD (th.)

Question 7.2: A 50,000-cfm CV air-handling unit is to be converted to a VA...

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