# How do I calculate power plant capacity loss over 25 years?

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• clearway
In summary, the conversation discusses two methods for calculating the production capacity of a power plant over a 25-year period, in which it loses 0.5% of its capacity each year. The first method involves multiplying the previous year's capacity by (100%-0.5%), while the second method subtracts 0.5% from the previous year's capacity. Both methods result in the same calculation, but it is important to note that the losses are cumulative. This means that in year 25, the production capacity will be 99.95% of the original capacity, or 24 if the plant runs at full capacity in the first year.
clearway
TL;DR Summary
Plant capacity degradation calculation
Hello,

I have a simple question and am hoping someone can help. I have a power plant that loses 0.5% production capacity per year for 25 years. When working with the plant capacity in terms of percentages, year 0 is defined as 100% capacity. For year 1 and each subsequent years, is it correct to take the current plant capacity percentage, and multiply it by (100%-0.5%)? Or do I subtract the 0.5% from the previous year?

Plant capacity:
Method 1:
Year 0 = 100%
Year 1 = Year 0 * (100%-0.5%)
Year 2 = Year 1 * (100%-0.5%)
etc

Method 2:
Year 0 = 100%
Year 1 = Year 0 - 0.5%
Year 2 = Year 1 - 0.5%

Thanks.

Percentage means only "divided by ##100##". So ##100\%=\frac{100}{100}=1##.

Now Year 1 = Year 0 ## \cdot (100\%-0.5\%)=##Year 0 ## \cdot (1-\frac{0.5}{100})=## Year 0 ## \cdot 1 - ##Year 0 ##\cdot \frac{1}{200}## which is what I think you meant by method 2. However, you haven't said from which quantity you want to take ##0.5\%## in method 2. The methods are the same if you subtract ##0.5\%## from Year 0, which makes sense as you lose this amount already in the first year.

What you also haven't said is, that the losses are cumulative, which your calculation is. For a constant loss you simply have ##99.95 \cdot ##Total every year.

In year ##25## you will have ##\operatorname{capacity}(25)=\operatorname{capacity}(0)\cdot (1-\frac{1}{200})^{25}## or ##24## if it runs on full capacity the first year.

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