A homeowner in Allentown, PA installs a 60° south-facing solar collector that (on the average over the year) replaces $1 \mathrm {~kW}$ of electric heat (purchased from the public utility at $\$ 0.11$ per $\mathrm { kWh }$ ). The homeowner is considering adding a tracking mechanism to maintain perpendicular alignment of the collector with the solar insolation. If the payback period for the upgrade is expected to be five years, what should the homeowner be willing to pay for the tracking device? Comment on this plan.

Question

Quizplus · Accepted Answer

The Answer is The total savings per year for the current system is

\left( \$ 0.11 \mathrm { kWh } ^ { - 1 } ight) imes ( 1 \mathrm {~kW} ) imes ( 24 \mathrm {~h} / \mathrm { d } ) imes ( 365 \mathrm {~d} / \mathrm { y } ) = \$ 964 ext { per year }

We need to determine how much insolation is received for the current system and how much additional insolation would be obtained with a tracking system. From Table

8.2

we summarize the relevant data as follows.

\begin{array}{rrrrrr} ext { month } & ext { days } & \begin{array}{r} ext { tilted } \\mathrm{MJ} / \mathrm{m}^{2} ext { per } \ ext { day }\end{array} & \begin{array}{r} ext { tilted } \\mathrm{MJ} / \mathrm{m}^{2} ext { per } \ ext { month }\end{array} & \begin{array}{r} ext { tracking } \\mathrm{MJ}^{2} / \mathrm{m}^{2} ext { per } \ ext { day }\end{array} & \begin{array}{r} ext { tracking } \\mathrm{MJ} / \mathrm{m}^{2} ext { per } \ ext { month }\end{array} \\hline ext { Jan } & 31 & 11.2 & 347.2 & 13.7 & 424.7 \ ext { Feb } & 28 & 14.0 & 392 & 16.9 & 473.2 \ ext { Mar } & 31 & 16.2 & 502.2 & 20.2 & 626.2 \ ext { Apr } & 30 & 18.0 & 540 & 23.0 & 690 \ ext { May } & 31 & 18.7 & 579.7 & 25.2 & 781.2 \ ext { Jun } & 30 & 19.4 & 582 & 27.0 & 810 \ ext { Jul } & 31 & 19.4 & 601.4 & 27.0 & 837 \ ext { Aug } & 31 & 19.1 & 592.1 & 25.2 & 781.2 \ ext { Sep } & 30 & 17.6 & 528 & 21.6 & 648 \ ext { Oct } & 31 & 15.1 & 468.1 & 18.4 & 570.4 \ ext { Nov } & 30 & 10.8 & 324 & 13.0 & 390 \ ext { Dec } & 31 & 9.4 & 291.4 & 11.2 & 347.2 \& & & & & \ ext { annual } & 365 & - & 5748.1 & & 7379.1 \\hline\end{array}

The tracking collector will have insolation which is

\left(7379 \mathrm{MJ} / \mathrm{m}^{2} ight) /\left(5748 \mathrm{MJ} / \mathrm{m}^{2} ight)=1.28

times as much as the tilted collector. Thus it will replace

1.28 \mathrm{~kW}

of heat or

0.28 \mathrm{~kW}

additional. Over the course of 1 year this additional

0.28 \mathrm{~kW}

of heat will provide a savings

\left( \$ 0.11 \mathrm { kWh } ^ { - 1 } ight) imes ( 0.28 \mathrm {~kW} ) imes ( 24 \mathrm {~h} / \mathrm { d } ) imes ( 365 \mathrm {~d} / \mathrm { y } ) = \$ 270

per year
For a payback period of 5 years the capital cost must be less than

5 imes \$ 270 = \$ 1350

. Feasibility may be marginal.

A Homeowner in Allentown, PA Installs a 60° South-Facing Solar 1 kW1 \mathrm {~kW}1 kW

A Homeowner in Allentown, PA Installs a 60° South-Facing Solar $1 \mathrm {~kW}$