# Improved Probability Prediction Method Research for Photovoltaic Power Output
## 4 Experiment
### Evaluation Criteria  
This paper introduces the evaluation criteria of point prediction value and confidence interval prediction value, which can evaluate the prediction probability distribution performance.  
1) The root mean square error is defined as follows:  
\[RMSE=\sqrt{\frac{\sum\limits_{i=1}^{N}{(y_{i}-y_{i}^{\prime})^{2}}}{N}} \tag{18}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Unit** & **Score** \\ \hline Total column liquid water (TCLW) & kg\(\cdot\)m\({}^{-2}\) & 13.2 \\ Total column ice water (TCIW) & kg\(\cdot\)m\({}^{-2}\) & 19.4 \\ Surface pressure (SP) & Pa & 15.1 \\ Relative humidity at 1000 mbar (RH) & \% & 62.6 \\ Total cloud cover (TCC) & 0–1 & 16.8 \\
10 meter U wind component (10 U) & m\(\cdot\)s\({}^{-1}\) & 21.7 \\
10 meter V wind component (10 V) & m\(\cdot\)s\({}^{-1}\) & 13.3 \\
2 meter temperature (2T) & K & 39.7 \\ Surface solar rad down (SSRD) & J\(\cdot\)m\({}^{-2}\) & 370.3 \\ Surface thermal rad down (STRD) & J\(\cdot\)m\({}^{-2}\) & 50.7 \\ Top net solar rad (TSR) & J\(\cdot\)m\({}^{-2}\) & 208.0 \\ Total precipitation (TP) & M & 11.4 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Variable description.  
where \(N\) indicates the number of test set data, and \(y_{i}\) and \(y_{i}^{\prime}\) represent the \(i\)-th predicted value and the actual value, respectively. The smaller the root mean square error value is, the higher the prediction accuracy of the model.  
2) The continuous ranking probability score is a comprehensive criterion for evaluating probability prediction performance. It can simultaneously evaluate the calibration degree and sharpness of the probability distribution. The smaller the value is, the better the prediction effect of the model will get. CRPS is defined as follows:  
\[CRPS(F,x)=\left\{\begin{array}{l}\int\limits_{-\infty}^{\infty}{{{{\left[{F (y)-1}\right]}^{2}}dy},\ y\geq x}\\ \int\limits_{-\infty}^{\infty}{{{{\left({F(y)}\right)}^{2}}dy}}\,\ y<x\end{array}\right. \tag{19}\]  
where \(x\) is the actual observed value and \(F\) is the predicted cumulative distribution function.  
3) The confidence interval average width (PINAW) represents the average of the confidence interval widths. The smaller the width value gets, the higher the accuracy. PINAW is defined as follows:  
\[PINAW=\frac{\sum\limits_{i=1}^{N}{{{\left({up-down}\right)}}}}{N} \tag{20}\]  
where \(up\) is the upper bound of the confidence interval, \(down\) is the lower bound of the confidence interval, and \(N\) is the number of data in the test set.  
4) The prediction interval coverage (PICP) is the ratio of the number of target values falling within the confidence interval to the total number of predicted samples. The value ranges from 0 to 1. The closer the value is to 1, the better the prediction performance of the model is. PICP is defined as follows:  
\[PICP=\frac{\gamma^{1-\alpha}}{N}\times 100\% \tag{21}\]  
where \(\gamma^{1-\alpha}\) is the number of target values that fall within the confidence interval.  
When the PINAW becomes smaller, the PICP becomes larger, and the prediction performance is better. CRPS is the evaluation criterion that includes coverage and interval width, which can comprehensively reflect the performance of models.