**Simple Calculations & a self-test Quiz**

To accompany this lesson, there’s another simple online calculator (click below and it’ll open in a new window):

Make sure you read the “READ THIS” tab of the calculator before you use it, in order to be clear about the various inputs and outputs. Then, to illustrate some outcomes around efficiency and energy resources, use the calculator and try the self-test quiz below.

**Test Your Understanding…**

**Q1.**

In a sunny country, where the solar panels will receive 2,000kWh on each square metre each year, and 300,000 MWh of electricity needs to be generated each year, at minimum how many more square km of land will be needed, if 15% efficient panels are chosen over 20% efficient ones.

**Q2.**

For the same energy target (300,000 MWh) and 15% efficient panels, what is the minimum difference in land requirements between an area receiving primary solar irradiation of 2,000 kWh on each square metre over a year and one receiving only 1,200 kWh?

**Q3.**

Looking again at the previous calculations: using 15% efficient panels, how has the reduction in primary solar resource from 2,000 to 1,200 kWh/m^{2}/yr impacted the cost of building a project capable of producing 300,000 MWh of energy per year, assuming an installed cost of $2 per Watt?

**Q4.**

In the low resource area (1,200 kWh/m^{2}/yr) a project using 15% efficiency panels can be built for $1.25 per W, whereas one with 20% efficient panels would cost $1.75 per W. Assume the same 300,000 MWh energy target as before, an actual land use area that is three times that of the collector area, and a land purchase cost of $10m per km^{2}. What is the difference in investment required between the two projects?

**Q5.**

A 100MW open-cycle gas power plant operates only at peak times (achieving a capacity factor of 10%) and with an average efficiency of just 35%. It cost $0.6 per W to build and can sell its peak-time electricity at $100/MWh. If natural gas costs $5/MMBtu, how many years will it take for its sales revenue to pay back its investment and fuel costs? (ignoring any other costs or financial considerations).

**Q6.**

Taking the previous scenario*, how much longer would the simple payback period be if the plant was built in a market where gas cost closer to $10/MMBtu?

(*A 100MW plant, capacity factor of 10%, average efficiency of 35%, cost $0.6 per W to build, electricity price at $100/MWh, natural gas costs $5/MMBtu)

**Q7.**

With this $10/MMBtu gas price, the plant modelled previously has an opportunity to generate more often, beyond the very peak times, achieving a capacity factor of 25%. In doing so, it will be able to operate more efficiently – at 40%. However in selling outside the very peak times, the average sale price of its electricity will drop to $55/MWh. Should it take this opportunity?

**Back to:** Power Generation Efficiency, Fuel & Capacity Factor

**Next Lesson:** Why Does Energy Density Matter?

**Return to:** Course Index