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## Q. 13.2

Consider a 60-kW cogeneration system that produces electricity and hot water with the following efficiencies: (a) 26 percent for the electricity generation, and (b) 83 percent for the combined heat and electricity generation. Determine the annual savings of operating the cogeneration system compared to a conventional system that consists of purchasing electricity at a rate of $0.08/kWh and producing heat from a boiler with 70 percent efficiency. The cost of fuel is$5/MMBtu. The maintenance cost of the cogeneration system is estimated at $1.00 per hour of operation. Assume that all the generated thermal energy and electricity are utilized during 6,500 hrs/year. Determine the payback period of the cogeneration system if the installation cost is$2,500/kW.

## Verified Solution

First, the cost of operating the cogeneration system is compared to that of the conventional system on an hourly basis:
(a) Cogeneration System: For each hour, 60-kW of electricity is generated (at an efficiency of 26 percent) with fuel requirements of 0.787 MMBtu [(= 60 kW * 0.003413 MMBtu/kW/0.26). At the same time, a thermal energy of 0.449 MMBtu (= 0.787 MMBtu * 0.83 – 0.26) is obtained. The hourly flow of energy for the cogeneration system is summarized in the  diagram below:

Thus, the cost of operating the cogeneration on an hourly basis can be  estimated as follows:

 $3.93/hr 0.787 MMBtu/hr *$ 5/MMBtu = Fuel Cost: $1.00/hr Maintenance Cost:$4.93/hr Total Cost:

(b) Conventional System: For this system, the 60 kW electricity is directly purchased from the utility, and the 0.449 MMBtu of hot water is generated using a boiler with an efficiency of 0.65. Thus the costs associated with utilizing a conventional system are as follows:

 $4.80/hr 60 kWh/hr * 0.08 = Electricity Cost:$3.45/hr (0.449 MMBtu/hr)/0.65 * $5/MMBt Fuel Cost (Boiler):$8.25/hr Total Cost:

Therefore, the annual savings associated with using the cogeneration system are:

ΔCost = ($8.25/hr −$4.93/hr)*6500hr/yr = \$21,580/yr

Thus, the simple payback period for the cogeneration system:

$SPB=\frac {\2500/kW*60kW}{\21,580}=7 years$

A life-cycle cost analysis may be required to determine if the investment on the cogeneration system is really warranted.