| $$\theta$$ | $$\mu$$ | $$\sigma$$ |
|---|---|---|
| 0.5375716 | 0.6930431 | 0.6299931 |
Badosa
Notations
- \(H_t^{0}\): extraterrestrial radiation, it is the theoretical radiation outside the atmosphere.
- \(GHI_t^{max}\) clearsky-max radiation, in theory it is an upper bound of the solar radiation. The clearsky-max radiation is less than the extraterrestrial one due to the reduction given by the atmosphere.
- \(GHI_t\) is the radiation that is able to reach the ground. In a completely sunny day it is equal to the clearsky-max radiation, while it drops as the days became more cloudy.
- \(X_t\) transmittance coefficient defined as \(\frac{GHI_t}{GHI_t^{max}}\).
Badosa’s model
The SDE proposed by Badosa is the following:
\[dX_t = -\theta(X_t - \mu)dt + (X_t)^{\alpha}(1-X_t)^{\beta} \sigma dW_t \tag{1}\] \[X_t= \theta \mu + (1-\theta) X_{t-1}\] \[X_t= \alpha + \beta X_{t-1}\]
\[ \begin{align} \begin{aligned} \beta = (1-\theta) \Rightarrow \theta = 1- \beta \\ \alpha = \theta \mu \Rightarrow \mu = \frac{\alpha}{1-\beta} \end{aligned} \end{align} \] - \(\beta = (1-\theta) \Rightarrow \theta = 1- \beta\)
- \(\alpha = \theta \mu \Rightarrow \mu = \frac{\alpha}{1-\beta}\)
