How to model P50, P75, and P90 energy yield?

How to model P50, P75, and P90 energy yield?

Lukas Duldinger, CFA Lukas Duldinger, CFA
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How to model P50, P75, and P90 energy yield? When estimating future cash flows for wind or solar investments, forecasting the energy yield is one of the most critical steps in building a reliable business plan, i.e., a financial model. As the production values of renewable energy assets vary from year to year, investors consider different probability figures within their analysis.

Probability figures P50, P75, and P90

In the renewable energy industry, energy yield refers to the amount of electricity generated by a power plant over a certain period, typically one year. Energy yield is an important metric for evaluating the financial performance of a renewable energy project. P50, P75, and P90 energy yield are three common measures of energy yield that are used to evaluate the expected performance and risk associated with a project.

P50 energy yield is the median expected energy yield, which means there is a 50% chance that the actual energy yield will be higher and a 50% chance it will be lower. P75 energy yield means that there is a 75% chance that the actual energy yield will be equal to or higher than the P75 value, and a 25% chance that it will be lower. P90 energy yield means that there is a 90% chance that the actual energy yield will be equal to or higher than the P90 value, and a 10% chance that it will be lower.

Gaussian distribution function – renewable energy yield is normally distributed

The Gaussian distribution function, also known as the normal distribution function, is often used to model energy yield data. This function assumes that the energy yield data follows a bell-shaped curve where the majority of the data falls near the mean value, and there is less data at the tails of the distribution. The median value is a measure of central tendency that represents the value in the middle of the distribution. The uncertainty associated with energy yield data is often expressed as a standard deviation, which represents the spread of the data around the mean value.

Equity vs. Debt Investors

Debt investors generally view projects from a more conservative P90 or P75 basis because they prioritize the stability of cash flows to ensure debt service payments can be met. If energy yield falls below the P90 or P75 values, the project may not generate enough revenue to cover the debt service payments, leading to financial difficulties for the project. Especially when debt sculpting according to a DSCR target is used, debt investors typically consider the P90 production figure.

On the other hand, equity investors are typically more willing to take risks and accept uncertainty, so they tend to focus on the median P50 value as it represents a more optimistic view of the project's potential performance. Equity investors are also typically interested in the upside potential of the project, while debt investors are more concerned with downside risks.

Energy Yield Assessment for the determination of P50, P75, P90, and uncertainty

The process of creating an energy yield assessment for potential wind farm projects or solar plant projects involves several steps, and a technical advisor typically performs this assessment. The following is a brief overview of the process:

1.     Resource assessment: The first step is to assess the wind or solar resource at the proposed site. This is typically done by installing meteorological equipment such as anemometers and solar radiation sensors at the site to measure wind speed, direction, and solar irradiance. The data collected from these sensors is used to create a site-specific resource profile.

2.     Energy production modeling: Once the resource profile has been developed, the technical advisor uses computer modeling software to predict the energy production potential of the wind farm or solar plant. The modeling software takes into account the characteristics of the wind turbines or solar panels, the topography of the site, and the expected weather patterns to estimate the amount of energy that the project can generate.

3.     Validation and calibration: The energy production estimates from the computer model are then compared to actual production data from similar projects in the same region to validate and calibrate the model. The validation process helps to ensure that the energy production estimates are accurate and reliable.

4.     Calculation of P50, P75, and P90 energy yields: The technical advisor then uses statistical analysis to calculate the P50, P75, and P90 energy yields.

5.     Calculation of uncertainty / standard deviation: The technical advisor also calculates the uncertainty associated with the energy production estimates. This is typically expressed as a standard deviation, which represents the spread of the data around the mean value.

6.     Calculation of net energy yield: Once the gross energy yield has been estimated, the technical advisor calculates the net energy yield. This is the amount of energy that the project can actually deliver to the grid after accounting for various factors that can reduce energy production.

The technical advisor uses a set of adjustment factors to calculate the net energy yield. These adjustment factors include:

·        Plant availability: This factor accounts for the amount of time that the project is available to generate energy. It takes into account downtime due to maintenance, repairs, and other factors.

·        Electrical losses: This factor accounts for losses that occur during the process of converting the energy from the wind or sun into usable electricity. These losses can occur in transformers, inverters, and other components of the electrical system.

·        Wake losses: This factor accounts for losses that occur when wind turbines are placed too close to each other. The turbulence created by one turbine can reduce the amount of wind that reaches the neighbouring turbines, reducing their energy production.

·        Maintenance losses: This factor accounts for losses that occur due to maintenance activities, such as the need to shut down turbines or solar panels for repairs or upgrades.

·        Curtailment losses: This factor accounts for losses that occur when the project is forced to curtail energy production due to grid constraints or other factors.

·        Degradation: This factor accounts for the gradual loss of energy production capacity over time due to wear and tear, aging, or other factors.

By applying these adjustment factors to the gross energy yield estimate, the technical advisor arrives at the net energy yield estimate. This net energy yield estimate is used to calculate  and analyze the financial performance of the project.

How to model P50, P75, and P90 production figures using uncertainty?

To reliably forecast a normal distribution of estimated energy yield, all that is needed is the median of the distribution, i.e., the P50 value and the distribution's uncertainty. Knowing the distribution's uncertainty, which essentially is a statistical term for the variability of estimated production figures, allows us to calculate any other P-value, may it be the P75, P90, or even P99.

Microsoft Excel can model any normal distribution with the NORM.INV function using two inputs only. All you need is a median (P50 value) and the uncertainty of the distribution.

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