From ef7751f585245d538d5f2af4a48392be6a918a4a Mon Sep 17 00:00:00 2001 From: Megawattz Date: Wed, 20 Sep 2023 14:38:30 +0000 Subject: [PATCH] PVNet comparison report draft and images --- reports/imgs/pvlin_all_heatmap_MAE_Month.png | Bin 0 -> 30183 bytes reports/imgs/pvlin_all_heatmap_MAE_Week.png | Bin 0 -> 43265 bytes reports/imgs/pvnet_all_MAE_monthly.png | Bin 0 -> 87903 bytes reports/imgs/pvnet_all_MBE_monthly.png | Bin 0 -> 99013 bytes reports/imgs/pvnet_all_RMSE_monthly.png | Bin 0 -> 91287 bytes reports/imgs/pvnet_all_heatmap_MAE_Month.png | Bin 0 -> 28834 bytes reports/imgs/pvnet_all_heatmap_MAE_Week.png | Bin 0 -> 41581 bytes reports/imgs/pvnet_all_heatmap_MAE_month.png | Bin 0 -> 33796 bytes reports/imgs/pvnet_all_heatmap_MAE_week.png | Bin 0 -> 58279 bytes reports/imgs/pvnet_all_heatmap_MBE_month.png | Bin 0 -> 33960 bytes reports/imgs/pvnet_all_heatmap_MBE_week.png | Bin 0 -> 58540 bytes reports/imgs/pvnet_all_horizon_MAE.png | Bin 0 -> 59909 bytes reports/imgs/pvnet_all_horizon_MBE.png | Bin 0 -> 66138 bytes reports/imgs/pvnet_all_horizon_RMSE.png | Bin 0 -> 60503 bytes ...pvnet_pvlin_Error_nights_excluded_hist.png | Bin 0 -> 34865 bytes .../pvnet_pvlin_Error_nights_excluded_kde.png | Bin 0 -> 62674 bytes reports/imgs/pvnet_vs_pvlin_MAE_monthly.png | Bin 0 -> 97152 bytes reports/imgs/pvnet_vs_pvlin_MBE_monthly.png | Bin 0 -> 82030 bytes reports/imgs/pvnet_vs_pvlin_RMSE_monthly.png | Bin 0 -> 98480 bytes reports/pvnet_comp.md | 304 ++++++++++++++++++ 20 files changed, 304 insertions(+) create mode 100644 reports/imgs/pvlin_all_heatmap_MAE_Month.png create mode 100644 reports/imgs/pvlin_all_heatmap_MAE_Week.png create mode 100644 reports/imgs/pvnet_all_MAE_monthly.png create mode 100644 reports/imgs/pvnet_all_MBE_monthly.png create mode 100644 reports/imgs/pvnet_all_RMSE_monthly.png create mode 100644 reports/imgs/pvnet_all_heatmap_MAE_Month.png create mode 100644 reports/imgs/pvnet_all_heatmap_MAE_Week.png create mode 100644 reports/imgs/pvnet_all_heatmap_MAE_month.png create mode 100644 reports/imgs/pvnet_all_heatmap_MAE_week.png create mode 100644 reports/imgs/pvnet_all_heatmap_MBE_month.png create mode 100644 reports/imgs/pvnet_all_heatmap_MBE_week.png create mode 100644 reports/imgs/pvnet_all_horizon_MAE.png create mode 100644 reports/imgs/pvnet_all_horizon_MBE.png create mode 100644 reports/imgs/pvnet_all_horizon_RMSE.png create mode 100644 reports/imgs/pvnet_pvlin_Error_nights_excluded_hist.png create mode 100644 reports/imgs/pvnet_pvlin_Error_nights_excluded_kde.png create mode 100644 reports/imgs/pvnet_vs_pvlin_MAE_monthly.png create mode 100644 reports/imgs/pvnet_vs_pvlin_MBE_monthly.png create mode 100644 reports/imgs/pvnet_vs_pvlin_RMSE_monthly.png create mode 100644 reports/pvnet_comp.md diff --git a/reports/imgs/pvlin_all_heatmap_MAE_Month.png b/reports/imgs/pvlin_all_heatmap_MAE_Month.png new file mode 100644 index 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Fig 4: PVNet MAE heatmap for Hour vs Month.Fig 5: PVNet MAE heatmap for Hour vs Week.
+ + + + + + + + + + + + +
Fig 6: PVNet MBE heatmap for Hour vs Month.Fig 7: PVNet MBE heatmap for Hour vs Week.
+ + + + + + + + + +### Evaluation Across Horizons + + +![PVNet Horizon MAE](./imgs/pvnet_all_horizon_MAE.png) +*Fig 8: PVNet horizon vs MAE averaged across 2022.* + +![PVNet Horizon RMSE](./imgs/pvnet_all_horizon_RMSE.png) +*Fig 10: PVNet horizon vs RMSE averaged across 2022.* + +![PVNet Horizon MBE](./imgs/pvnet_all_horizon_MBE.png) +*Fig 11: PVNet horizon vs MBE averaged across 2022.* + + + +### Probabalistic Forecasts Evaluation + +Pinball Scores + +% of predicitons over certain value + + + +## PVlin and PVNet vs PVlup + +### Results Table + +| Forecast | MAE | RMSE | R2 | MBE |RTRR +|----------|-------------------------|------------------------|--------|-------------------------|---- +| PVLin | 197.37 ± 4.19 | 357.56 ± 7.33 | 0.978 | 187.91 ± 4.28 |64.96 ± 1.47 +| PVNet | 129.75 ± 2.73 | 233.49 ± 5.21 | 0.99 | 6.30 ± 3.28 |100.69 ± 2.17 + +The ± represents the standard error in the metric. + +### Standard Deviations of Metrics + +| Forecast | Std MAE | StdRMSE | Std MBE |Std RTRR +|----------|----------------|---------------|-------------|--------- +| PVLin | 298.17 | 521.04 | 304.23 |104.73 +| PVNet | 194.14 | 370.62 | 233.43 |152.01 + + + +### Plots + +![Model Forecast vs. Actuals](./imgs/pvnet_vs_pvlin_MAE_monthly.png) +*Fig : Average monthly MAE for PVNet and PVLive Intraday* + +![Error Distribution of Model A](./imgs/pvnet_vs_pvlin_RMSE_monthly.png) +*Fig : Average monthly RMSE for PVNet and PVLive Intraday* + +![Error Distribution of Model A](./imgs/pvnet_vs_pvlin_MBE_monthly.png) +*Fig : Average monthly MBE for PVNet and PVLive Intraday* + +### Heatmap + + +MAE + + + + + + + + + + +
Fig : PVLive Intraday MAE heatmap for Hour vs Month.Fig : PVNet MAE heatmap for Hour vs Month.
+ + + + + + + + + + +
Fig : PVLive Intraday MAE heatmap for Hour vs Week.Fig : PVNet MAE heatmap for Hour vs Week.
+ + + +MBE + + + + + + + + + + + +
Fig : PVLive Intraday MBE heatmap for Hour vs Month.Fig : PVNet MBE heatmap for Hour vs Month.
+ + + + + + + + + + + +
Fig : PVLive Intraday MBE heatmap for Hour vs Week.Fig : PVNet MBE heatmap for Hour vs Week.
+ +### Error Distribution + +![Model Forecast vs. Actuals](./imgs/pvnet_pvlin_Error_nights_excluded_kde.png) +*Fig : Kernel density estimation of error distribution of PVNet and PVLive Inraday, with nights removed.* + +![Model Forecast vs. Actuals](./imgs/pvnet_pvlin_Error_nights_excluded_hist.png) +*Fig : Histrogram of error distribution of PVNet and PVLive Inraday, with nights removed.* + + + +## Relative Performance of PVNet vs PVLive + + + + + +--- + +## Conclusion + +From this analysis + +--- + + + +## Appendix + +### Error Metrics +To compute the error metrics, we utilised the following mathematical formulas: + +1. **MAE (Mean Absolute Error)**: +$$\text{MAE} = \frac{1}{n} \sum_{i=1}^{n} \left| y_{\text{true},i} - y_{\text{pred},i} \right|$$ + +- **Mean Absolute Error (MAE)**: Represents the average of the absolute differences between the forecasted and actual values. It provides an idea of the magnitude of errors. + +2. **RMSE (Root Mean Squared Error)**: +$$\text{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} \left( y_{\text{true},i} - y_{\text{pred},i} \right)^2}$$ + +3. **R^2 (Coefficient of Determination)**: +$$R^2 = 1 - \frac{\sum_{i=1}^{n} \left( y_{\text{true},i} - y_{\text{pred},i} \right)^2}{\sum_{i=1}^{n} \left( y_{\text{true},i} - \bar{y_{\text{true}}} \right)^2}$$ + +Where $\bar{y_{\text{true}}}$ is the mean of the true values. + +4. **MBE (Mean Bias Error)**: +$$\text{MBE} = \frac{1}{n} \sum_{i=1}^{n} \left( y_{\text{pred},i} - y_{\text{true},i} \right)$$ + +5. **RealTimeRampRateDiff**: +$$\text{RampRateDiff} = \frac{1}{n} \sum_{i=1}^{n} \left| \Delta y_{\text{true},i} - \Delta y_{\text{pred},i} \right|$$ +Where $\Delta y$ represents the difference between consecutive values. + + + +### Variability of Error Metrics + +The **Standard Deviations** of these metrics are calculated as follows: +$$\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} \left( \text{Metric}_i - \bar{\text{Metric}} \right)^2}$$ +Where $\bar{\text{Metric}}$ is the mean of the metric across all data points. + +The **Standard Error of The Mean** of these metrics are calcuated as follows: +$$ SE = \frac{\sigma}{\sqrt{n}}$$ + + +

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