P50

Quick Facts

What is P50?

Formal definition

The P50 annual energy yield is the value Q where the cumulative probability function P(annual energy ≥ Q) = 0.50. In plain English: there’s a 50% chance the plant produces at least P50 in any given year.

Engineering definition

Calculated by combining hourly time-series simulation (PVsyst, SAM) with statistical analysis of:

1. Inter-annual weather variability (multi-year TMY).
2. Modeling uncertainty (PVsyst ±3%, IAM, soiling, thermal).
3. Long-term degradation (typically modeled separately for year-N P50).

Industry definition

P50 is the headline “expected” yield reported in every Energy Yield Assessment (EYA).

Permitting definition

Not a permit term, but P50 appears in interconnection cost-benefit analyses and PPA prices indexed to expected production.

How P50 is Used

Equity investors

Equity returns (IRR, NPV) are projected against P50 — the central expectation.

Lenders

Debt service coverage ratio (DSCR) is calculated against P90 or P95, not P50. Lenders want assurance that worst-case revenue still covers debt.

Developers

Use P50 for project pricing, PPA negotiation, and revenue forecasting.

EPCs

EPC performance guarantees are typically set to P90 or P95 of year-1 production.

P50 Calculation Method

Step 1: Hourly simulation

PVsyst or SAM produces 8,760 hourly energy values for a typical year using TMY weather.

Step 2: Inter-annual variability

Multi-year weather records (typically 20+ years from Meteonorm or Solargis) provide the standard deviation of annual GHI/POA.

Step 3: Modeling uncertainty

PVsyst published uncertainty is ±3% for well-instrumented inputs. IAM, soiling, and thermal models add another 2–4%.

Step 4: Combined uncertainty

Combine inter-annual variability + modeling uncertainty as root-sum-square (RSS):

σ_total = √(σ_weather² + σ_modeling²)

Typically σ_total = 4–8% of mean.

Step 5: Confidence interval

Assuming approximately normal distribution:

• P50 = μ (mean)
• P75 = μ − 0.67 × σ
• P90 = μ − 1.28 × σ
• P99 = μ − 2.33 × σ

Worked example

Mean simulated yield μ = 250 GWh/yr. Combined uncertainty σ = 6% of mean = 15 GWh.

• P50 = 250 GWh
• P75 = 250 − 0.67 × 15 = 240 GWh
• P90 = 250 − 1.28 × 15 = 231 GWh
• P99 = 250 − 2.33 × 15 = 215 GWh

Sources of Uncertainty

Year-1 vs. Lifetime P50

Year-1 P50 reflects fresh modules. Year-25 P50 applies cumulative degradation:

Energy_yr25 = Energy_yr1 × (1 − annual_degradation)^24
            ≈ Energy_yr1 × 0.88 (at 0.5%/yr degradation)

Lifetime average P50 ≈ 0.94 × Year-1 P50 (with linear degradation).

Common Mistakes

1. Reporting P50 without specifying year-1 vs. lifetime average.
2. Ignoring inter-annual variability — P90 = P50 is wrong.
3. Combining uncertainties additively instead of in RSS.
4. Using assumed σ instead of measured weather variability.
5. Not differentiating P50 from energy guarantee in contracts.

Best Practices

• Always report P50, P90, and P99 together.
• Specify year-1 and 25-year average for both metrics.
• Document the uncertainty sources used.
• Use 20+ years of weather data for inter-annual variability.
• Apply Monte Carlo simulation for complex/storage projects.

Comparison Tables

Confidence Levels in Use

Key Takeaways

• P50 is the median expected annual energy yield — equal probability of beating or missing.
• Calculated from hourly simulation + inter-annual variability + modeling uncertainty.
• Equity investors use P50; lenders use P90; EPC guarantees often P95.
• Year-1 P50 vs. 25-year average P50 differ by ~6% due to degradation.
• Always report P50, P90, and P99 together with uncertainty breakdown for full transparency.