V . RESULTS AND DISCUSSION
The proposed PV yield forecasting method can predict with an overall error of less than 7 % on an average day for a 10-kW peak installation . Fig . 2 shows the predicted PV yield forecast in green and the measured PV yield in red . The overall shape of the AC power output is forecasted accurately . However , the deviation , between the forecasted and measured results , is attributed to local clouds which cannot be forecasted using this method . The error distribution , Fig . 3 , illustrates the overall accuracy of the proposed PV yield forecasting strategy . A difference , between the predicted and measured PV yield , of less than 5 kWh per day is obtained for 68 % of the observations . It should be noted that the PV size utilized for forecasting PV yield is derived from an actual 10-kW PV panel installed in a Belgian household . For safety considerations , the inverter ’ s peak power is restricted to 6.6 kW . In our simulations , we employ a PV size of 3.5 kW ; consequently , we scale down the initial 6.6 kW to align with the 3.5 kW capacity .
Load prediction results are heavily dependent on the chosen metric . Based on extensive simulation studies we suggest a modified version of MSE : Peak-Weighted MSE to give more weight to accurately predicted peak values . The best-performing models are presented in Table 1 . Overall , Elastic Net ( ridge regression ), N-BEATS , XGBoost ( two variants ) and ARIMA provided the best results . For each prediction step , Elastic Net , XGBoost and ARIMA use the last 60 days prior to the target day as input . N-BEATS initially trains a model on the training data and uses only the prior three days for prediction . Different combinations of the number of stacks , blocks and layers were tested , with best performance given by a N-BEATS model with three stacks , 8 blocks , and two layers .
TABLE I .
TOP FIVE PERFORMING MODELS VS . NAIVE BASELINE ON OPEN FLUVIUS DATASET , SORTED BY MSE
Model MSE MAE ACDE PWMSE Elastic Net 0.0298 0.0647 2.792 0.308
XGBoost ( gblinear )
0.0304 0.0656 2.788 0.312
N-BEATS 0.0318 0.0698 2.880 0.308
XGBoost ( gbtree )
0.0330 0.0685 2.954 0.328 ARIMA 0.0364 0.0740 3.125 0.363
as Elastic Net ) achieves the smallest ACDE and N-BEATS yields the best results for the PWMSE metric ( tied ).
Fig . 4 shows the load forecast for a single day using the different prediction methods . The results are shown for a randomly selected day ( Tuesday , November 8 ) for the first household in the dataset . Although many methods claim to provide accurate forecasts for electric load , most methods fail to offer better accuracy than the naive approach of using the previous day as a prediction for the next day . As can be seen from this figure , Elastic Net is the most accurate in predicting the largest peak , while also giving an accurate prediction for the overall course of the curve .
In the first phase , the actual load and PV production data are provided to both optimization and maximizing self-consumption approaches in order to examine the impact of the PV system and battery on the consumer ’ s electricity bill . Initial findings unmistakably demonstrate that adding batteries to the system by using a suitable control system can lower the cost of monthly electricity by 44 % and is advantageous , particularly with hourly electricity tariffs . Without a PV system and integrated battery , the consumer ’ s monthly electricity bill is € 17 , based on the dynamic tariff . However , by utilizing both the PV system and battery in conjunction with maximizing self-consumption strategies , the consumer can receive a € 47 cashback from the power distributor ( saving of € 64 ). When the electricity rate is flat , optimization does not lower the cost of electricity when compared to the maximum self-consumption approach , and it is not profitable to use this optimization method ( it can only save € 5 / month ). However , when the hourly electricity rate is considered , optimization lowers the monthly electricity cost and saves € 22 more than maximizing self-consumption ( 43 % extra saving ), proving to be advantageous in this case .
In the first phase , the actual load and PV production data are provided to both optimization and maximizing self-consumption approaches in order to examine the impact of the PV system and battery on the consumer ’ s electricity bill . Initial findings unmistakably demonstrate that adding batteries to the system by using a suitable control system can lower the cost of monthly electricity by 44 % and is advantageous , particularly with hourly electricity tariffs .
Prev . Day 0.0477 0.0732 3.004 0.328
Because of daily periodicity , the seasonality of a seasonal ARIMA model is high ( s = 96 ) and results in slow convergence speed due to s-1 terms in the regression equation . Therefore we use a Fourier series of order K = 11 as covariates ( Dynamic Harmonic Regression ).
Elastic Net with a recursive prediction strategy ( whereby the time series prediction problem is translated into an autoregressive problem ), parameters α = 0.1 and an L1 ratio of 0 ( resulting in a closed-form Ridge regression ) performs best on MSE , MAE and PWMSE ( tied ). The gblinear variant of XGBoost ( combined with the same recursive prediction strategy
Fig . 2 PV yield , predicted in green compared to measure in red for a single day , the 17th of July 2022 .