To assess the photovoltaic (PV) energy yield potential of a site, we run models using best available data and methods. The result of the modelling is the P50 estimate, or in other words, the “best estimate”. P50 is essentially a statistical level of confidence suggesting that we expect that the predicted solar resource/energy yield may be exceeded with 50% probability. This also means that with at same probability the expectation may not be achieved.
P50 level of confidence may represent too high risk for some investors. Therefore, other probabilities of exceedance such as P90 (estimate exceeded with 90% probability) or P75 (estimate exceeded 75% of the time) are considered. Lenders and investors typically use P90 estimates to be confident that sufficient energy is generated, allowing to safely repay the project debt.
In solar energy, distribution of uncertainty does not perfectly follow normal distribution. Yet for the sake of simplified calculations, and also because statistically representative data is not always available, a concept of normal (Gaussian) distribution of uncertainty is used (bell-shaped curve, see Figure 1). P50 value is the center/mean, and it represents the estimate that occurs with the highest probability.
Figure 1: P50 value represented in a normal distribution
The P90 value is a lower value, and it is expected to be exceeded in 90% of the cases (Figure 2). The P75 value is a value higher than P90 (and lower than P50), and it is expected to be exceeded in 75% of the cases. Similarly, any Pxx exceedance level can be defined (Figures 2 and 3).
Figure 2: P90 value represented in a normal distribution
Figure 3: P50, P75, P90 and P99 value represented in a normal distribution
P50 is the most probable value, also called best estimate, and it can be exceeded with 50% probability. P90 is to be exceeded with 90% probability, and it is considered as a conservative estimate.
All Pxx values are constructed by knowing (i) the best estimate or P50 (the value calculated by the models or measured by solar sensor) and (ii) the value of total uncertainty associated with this estimate. There is nothing what we could call P50 uncertainty: P50 is the best estimate and there is a level of uncertainty associated to it, which in turn can be used for calculation of exceedance values at different confidence levels, all of them based on the same probability distribution of values.
The calculation of Pxx scenarios from the P50 estimate takes into account the total uncertainty that summarizes all factors involved in the PV energy yield modelling. For valid characterization of long term climate patterns, solar resource and meteorological data representing at least 10 years is required.
In the following text we will consider evaluation of uncertainty of annual (yearly) values. The following sources of uncertainty are to be considered in evaluating a total uncertainty:
The final P90 (Pxx) is obtained by combining P50 with all factors of uncertainty expressed for the same exceedance level
It is quite common to see the uncertainty expressed in terms of standard deviation (STDEV), which represents a confidence interval equivalent to approximately 68.27% of occurrence (84% probability of exceedance). Simplified assumption of the normal distribution, the uncertainty at P90 can be calculated simply by multiplying standard deviation by 1.282, resulting in a slightly higher number calculated from the same cumulative probability curve (Figure 4).
Figure 4: Uncertainty intervals, expressed at standard deviation and 80% confidence levels (P90 exceedance)
To round the values up or down to the desired figure (P90, P75 or similar) we can convert STDEV into any Pxx value based on the Gaussian distribution formulas (Table 1).
Table 1: Calculation of different PXX from a normal distribution of probability.
Obtaining the Pxx value from P50 estimate is quite straightforward if the uncertainty has been correctly calculated, as shown in Table 2.
Table 2: Calculation of different Pxx exceedance values for a normal distribution of probability.
As mentioned before, uncertainty is composed of several factors, so one thing we should keep in mind is working at the same exceedance level when combining them. In Solargis, the standard uncertainty estimates are provided at P90 level of exceedance.
The uncertainty sources are independent of each other and all the contributing factors are combined in a total uncertainty Utotalin a quadratic sum:
For calculating TMY P90, we take as a reference P90 values of solar resource (GHI and DNI; the weighting depends on the type of TMY and geographical location).The yearly P90 value is calculated as shown in Table 2. P90 uncertainty for solar parameters represents the total uncertainty, it is calculated as shown in Equation 1, where two sources of uncertainty are considered: uncertainty of the solar model and interannual variability for any single year.
Solargis offers 3 type of hourly datasets that can be used for simulation of expected energy output for P50, P90, and other Pxx scenarios. Description and sample data files for each data type is given below:
From the description above it is clear that in the best case full historical time series data should be used so that all types of weather patterns are represented in the energy simulation. Yet a typical practice in solar energy industry is to use TMY P50 data, representing ‘standard’ year. This is partially due to the speed and efficiency of energy simulation. The other reason also is that current PV energy simulation software has very limited or no possibilities to use full time series. TMY P90 data type is also widely used as it offers a comfortable and, to a great extent, standardised solution to work with a year that represent ‘conservative’ (suboptimal) weather conditions. The important benefit of using TMY P90, as add-on to TMY P50, is that it includes some of the hourly data patterns that may indicate critical weather conditions.
Depending on the dataset chosen in PV energy simulation for P90 (Pxx) level of confidence, the uncertainty factors should be applied in slightly different order and hence the simulation results will differ. The differences are in the approach differences are described in Table 3.
Table 3: Uncertainties that should be considered when using different Solargis datasets when running a PV energy simulation.
Steps to be taken for estimate of P90 annual PV energy yield when using three different data steps are described below.
Calculating PVOUT P90 annual value from full historical time series
Calculating PVOUT P90 annual value from TMY P50 data set
Calculating PVOUT P90 annual value from TMY P90 data set
Simulation results for the sample of Almeria (Spain) are presented in Table 4: for full historical time series, TMY P50 and TMY P90. The selection of months calculated as the outcome of the TMY algorithm is shown in the column ‘Month:Year’.
Table 4: Summary of GHI and PVOUT values obtained for a sample site in Plataforma Solar de Almeria, Spain.
For the sample considered in this article, the results of applying the uncertainties for each dataset are presented in the Table 5. In comparison to using time series for the simulation (most accurate and complete approach), for this particular site using TMY P50 for the simulation resulted in 1% overestimation of P90 energy value, while using TMY P90 dataset resulted in 4% underestimation of P90 energy value. These deviations are related to the assumptions taken when calculating the interannual variability on the one hand, and the loss of information related to TMY generation on the other hand. This exercise was done as an example, and the obtained results may not show the same trend for other locations.
Table 5: How to calculate PV energy yield value for P90 using different data sets for the sample site considered.
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