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# A model cost/benefit analysis of solar power. The main ingredients of this analysis are the power...

A model cost/benefit analysis of solar power. The main ingredients of this analysis are the power used (required) and the power delivered. For a simple model we want to use broader averages. Used: An American home has an average power use of 1.2 kW. That means that considering all of the daily variation, the difference between night and day and the seasons, etc., the average at any given second is 1.2 kJ per sec = 1.2 kW. Delivered: The home is to be powered by solar cells. Given the solar intensity of 1 kW/m2, it would seem we should employ 2 m2 of solar cells and we are done. In practice there are complications. For example, the solar cell has an efficiency < 100% for converting light power into electrical power. In addition, the illuminance on the solar array varies over time. It is zero at night, changes with the season according to the sun’s elevation, and varies by the weather with the change in cloud cover. All of this temporal variation can be smoothed out by inserting batteries between the cells and the load. The batteries get charged when solar power is available, and then deliver current to the home when it is needed. With this understanding, we can average over all of the practical effects to get an average efficiency for the conversion of sunlight into power. Consider the following model arrangement the sun shines 12 hr/day. the sun is always due south the sun is at an average elevation over the horizon of 40° the sky is cloudy 40% of the time the transmission coefficient for the clouds is T = 20% the solar cells are mounted on a vertical wall facing due south the power conversion efficiency of the cells is 15% solar cells cost \$200/m2 Analysis: a) What is the total efficiency for each cell to convert sunlight to electrical energy? b) How much power is provided by 1 m2 of solar cells illuminated by the sun? c) What total area of solar cells is required to provide the 1.2 kW average to the home? d) What is the capital investment for this solar array? (cells only) e) If the house goes off the grid and the homeowner is saving the utility cost of \$0.15 per kWh, how long does it take to recover the capital cost of the array?

**Can you please write with clear steps and a clear hand writing (or typing). Because the question has many parts. Thanks in advance**

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