Panel Output After Degradation
Panel power after n years of gradual degradation.
Formula
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Example
P_0=400 W, d=0.005, n=25: P ≈ 353 W
How it works
Solar panels usually do not lose the same number of watts each year; instead, they tend to lose a fixed percentage of their remaining output. This formula captures that compounding effect: each year’s output is the previous year’s output multiplied by (1 - d), so after n years the power is P_0(1 - d)^n. It works because repeated percentage reductions stack multiplicatively, not additively.
When to use it
Use this when estimating the long-term output of a solar panel, comparing warranties, or forecasting energy production over many years. It is especially useful in renewable-energy planning, cost analysis, and problems involving gradual efficiency loss.
Worked example, step by step
Given: P_0 = 300 W, d = 0.008, n = 20 Step 1: Substitute into the formula: P_n = P_0(1 - d)^n Step 2: P_20 = 300(1 - 0.008)^20 Step 3: P_20 = 300(0.992)^20 Step 4: (0.992)^20 ≈ 0.851 Step 5: P_20 ≈ 300 × 0.851 Step 6: P_20 ≈ 255 W Final answer: The panel’s output after 20 years is about 255 W.
Common mistakes to avoid
- Subtracting d × n from the initial power instead of compounding the loss each year
- Using d as a percentage without converting it to a decimal
- Forgetting that n is measured in years and must match the degradation rate’s time scale
Did You Know?
Quality panels degrade only ~0.5% a year, still delivering over 85% of rated power after 25 years.
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