THEME [ENERGY.2012.7.1.1] Integration of Variable Distributed Resources in Distribution Networks

(Deliverable–5.2)

Evaluation of forecasting techniques in the Greek Site Lead Beneficiary: ICCS September 2015

December

Deliverable – D 5.2: Evaluation of forecasting techniques in the Greek Site

Table of Contents LIST OF FIGURES ........................................................................................................... 3 LIST OF ACRONYMS AND ABBREVIATIONS .................................................................... 5 EXECUTIVE SUMMARY .................................................................................................. 6 1.

INTRODUCTION ..................................................................................................... 7

2.

DATA COLLECTION AND TRAINING ......................................................................... 8 2.1 The data collected from Rhodes power system ........................................................ 8 2.2 Wind power data ....................................................................................................... 8 2.3 Solar power data...................................................................................................... 10 2.4 Load data ................................................................................................................. 11

3.

ADVANCED LOAD FORECASTING TOOLS ............................................................... 15 3.1 Tools from ICCS ........................................................................................................ 15 3.2 Results from the timeseries obtained by the feeder P10........................................ 17 3.3 Results from the timeseries obtained by the feeder P20........................................ 20

4.

ADVANCED RES FORECASTING TOOLS .................................................................. 23 4.1 Tools from ICCS ........................................................................................................ 23 4.1.1 Solar power forecasting evaluation ............................................................. 24 4.1.2 Results from Rhodes case study ................................................................... 24 4.1.3 Results from Évora case study...................................................................... 28 4.1.4 Wind power forecasting evaluation on Rhodes case study ......................... 31 4.2 Tools from INESC ..................................................................................................... 36 4.2.1 Results for Évora Test Case .......................................................................... 36 4.2.2 Test Case Description ................................................................................... 36 4.2.3 Architecture of the PV Forecasting System .................................................. 37 4.2.4 Results – Very Short-term Horizon ............................................................... 38 4.2.5 Results – Complete Time Horizon ................................................................ 46

5.

CONCLUSION ....................................................................................................... 53

REFERENCES ............................................................................................................... 54 APPENDIX – MODEL OUTPUT STATISTICS .................................................................... 56

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List of Figures Figure 1 - The wind power timeseries of wind farms a) wf1, b) wf2, c) wf3 and d) wf4 .... 10 Figure 2 - The total wind power production of the Rhodes power system ........................ 10 Figure 3 - The total wind power production of the Rhodes power system ........................ 11 Figure 4 - The load timeseries obtained by the P10 feeder ................................................ 12 Figure 5 - The load timeseries obtained by the P20 feeder ................................................ 12 Figure 6 - The auto-correlation coefficients of the load timeseries recorded at the feeder P20 at the periods a) from 15/05/2013 to 24/06/2013, b) from 25/06/2013 to 21/01/2014 and c) from 22/01/2014 to 31/12/2014 .............................................................................. 14 Figure 7 - The mutual information between the original timeseries and the timeseries shifted with various lags at case of the feeder a) P10 and b) P20 ...................................... 14 Figure 8 - The NMAE of the load forecasting system in entire evaluation period at the case of the feeder P10 ................................................................................................................. 17 Figure 9 - The NRMSE of the load forecasting system in entire evaluation period at the case of the feeder P10 ......................................................................................................... 18 Figure 10 - The load predictions of the P10 feeder made at 09:00am of a) 21/12/2013 b) 29/01/2014 c) 05/05/2014 d) 07/07/2014 f) 07/09/2014 .................................................. 20 Figure 11 - The NMAE of the load forecasting system in entire evaluation period at the case of the feeder P20 ......................................................................................................... 21 Figure 12 - The NRMSE of the load forecasting system in entire evaluation period at the case of the feeder P20 ......................................................................................................... 21 Figure 13 - The load predictions of the P20 feeder made at 09:00am of a) 21/12/2013 b) 29/01/2014 c) 05/05/2014 d) 07/07/2014 f) 07/09/2014 .................................................. 23 Figure 14 - The NMAE of the proposed PV forecasting system at the Rhodes case study . 25 Figure 15 - The NRMSE of the proposed PV forecasting system at the Rhodes case study 25 Figure 16 - The NMAE of the solar power predictions made at 00:00am of each day in the evaluation period................................................................................................................. 26 Figure 17 - The NRMSE of the solar power predictions made at 00:00am of each day in the evaluation period................................................................................................................. 26 Figure 18 - The NMAE of the solar power predictions obtained by the ML-RBFNN at the Rhodes case study ............................................................................................................... 27 Figure 19 - The NMAE of the solar power predictions obtained by the GA-RBFNN from a single PV plant at the Rhodes case study ............................................................................ 27 Figure 20 - The NMAE of the proposed PV forecasting system at the Évora case study .... 28 Figure 21 - The NRMSE of the proposed PV forecasting system at the Évora case study .. 29 Figure 22 - The NMAE of the predictions made at 00:00am of each day in the evaluation period................................................................................................................................... 29 Figure 23 - The NRMSE of the predictions made at 00:00am of each day in the evaluation period................................................................................................................................... 30 Figure 24 - The NMAE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF1 case study ........................................................................... 31 Figure 25 - The NRMSE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF1 case study ........................................................................... 32

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Figure 26 - The NMAE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF2 case study ........................................................................... 32 Figure 27 - The NRMSE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF2 case study ........................................................................... 33 Figure 28 - The NMAE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF3 case study ........................................................................... 33 Figure 29 - The NRMSE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF3 case study ........................................................................... 34 Figure 30 - The NMAE of the proposed wind power forecasting system applied at the Rhodes power system ......................................................................................................... 34 Figure 31 - The NRMSE of the proposed wind power forecasting system applied at the Rhodes power system ......................................................................................................... 35 Figure 32 - The improvement of the wind power forecasting system w.r.t. persistence method for NMAE and NRMSE criteria ............................................................................... 35 Figure 33 - Architecture of the PV forecasting system........................................................ 38 Figure 34 - One step-ahead solar power forecast obtained with the AR and VAR models trained with RLS for one EB ................................................................................................. 39 Figure 35 - Impk of the VAR model fitted with OLS and GB for two EB and for the RMSE k calculated using the entire set of forecast errors [hourly resolution] ................................ 40 Figure 36 - Average RMSEk for each lead-time calculated with the individual RMSEk obtained for each EB [hourly resolution] ............................................................................ 41 Figure 37 - Impk of the VAR model fitted with GB for two EB and for the RMSE k calculated using the entire set of forecast errors [15 minutes resolution] .......................................... 42 Figure 38 - Impk of the VAR model for two EB and for the CRPS calculated using the entire dataset of forecast errors [hourly resolution] ..................................................................... 43 Figure 39 - Quantile loss of the AR and VAR models for lead-times 1 and 5 [hourly resolution] ........................................................................................................................... 44 Figure 40 - Improvement of the VAR model for two EB and averaged over the entire dataset [15 minutes resolution] .......................................................................................... 45 Figure 41 - Quantile loss of the VAR and AR models for each 5% quantile [15 minutes resolution] ........................................................................................................................... 46 Figure 42 - Average RMSEk for each lead-time of three datasets: (i) worst performance EB; (ii) best performance EB; iii) average of all EB .................................................................... 47 Figure 43 - Power curve comparison between fixed PV and one with solar tracker .......... 48 Figure 44 - Linear Combination - Average RMSEk for each lead-time of three datasets: (i) worst performance EB; (ii) best performance EB; (iii) average of all EB ............................. 49 Figure 45 - Average CRPSk for each lead-time of three datasets: (i) worst performance EB; (ii) best performance EB; (iii) average of all EB ................................................................... 50 Figure 46 - RMSE improvement of the VAR model over the AR model for three datasets: (i) worst performance EB; (ii) best performance EB; (iii) average of all EB......................... 51 Figure 47 - CRPS improvement of the VAR model over the AR model for three datasets: (i) worst performance EB; (ii) best performance EB; (iii) average of all EB ............................. 52

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List of Acronyms and Abbreviations Authors Authors

Organization

E-mail

George Sideratos

ICCS/NTUA

[email protected]

Aris Dimeas

ICCS/NTUA

[email protected]

Nikos Hatziargyriou

ICCS/NTUA

[email protected]

Ricardo Bessa

INESC Porto

[email protected]

Jorge Filipe

INESC Porto

[email protected]

Access:

Project Consortium European Commission Public

X

Status: Draft version Submission for Approval Final Version

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Deliverable – D 5.2: Evaluation of forecasting techniques in the Greek Site

Executive Summary

The aim of this document is to validate the forecasting models developed during the SUSTAINABLE project. In specific, forecasting models for wind and solar power prediction, as well as for load demand estimation were created in order to operate in real-time mode facilitating the functionalities of a DSO. The developed models are validated mainly to the isolated Rhodes power system according to the evaluation protocol [1]. DSO should manage the RES production flowing from the LV or the MV grid with the production connected in the HV grid in order to balance the consumption with the total production. In this case study, the RES forecasting models are applied to nine PV plants and to four wind farms while the load forecasting model is validated to a HV/MV power station. Due to the high RES penetration to the above substation, the load is recorded negative making its prediction especially challenging. In addition, the complex terrain of the Rhodes island together with the land-sea breezes reduces the predictability of wind power. Results also of PV forecasting from the Évora case study are presented validating the proposed models to different climate conditions. The results from both case studies show that the models have satisfactory performance and are robust to challenging conditions appeared to the energy management in MV/LV level [2].

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1. Introduction Integration of distributed generation, primarily from rooftop PV installations, impose requirements for novel monitoring and control functionalities at the MV level of the distribution system [3]. The RES forecasting and the load forecasting at the distribution level becomes extremely important in operating the system in a secure way providing high quality of energy supply at the lowest cost [4]. At lower voltage levels, accurate load forecasting becomes more difficult, because of smoothing effect of the diverse number of consumers is naturally reduced and the high RES penetration makes the power to flow backwards to the transmission system. Furthermore, more accurate RES forecasting models should be designed to permit load forecasting models to be accurate as well [5]. At the frame of SUSTAINABLE project, a load forecasting system and a RES forecasting systems were developed by ICCS/NTUA such as a PV forecasting model was proposed by INESC Porto. This report presents the performance of these forecasting systems obtained by the Rhodes case study and the Évora case study. Specifically, the load forecasting system is applied to estimate the load of an HV/MV substation located at the Rhodes power system. The substation is connected with two wind farms and with an unknown number of small PV installations. In order to estimate the load that flows through the substation feeders, the load forecasting system uses the solar power and the wind power predictions providing by the RES forecasting system created by ICCS/NTUA. The load forecasting system consists of multiple Random Forests (RF) designed in a structure to perform well in both short-term and long-term horizons. It runs every hour providing predictions in a 24 hour forecasting window. The RES forecasting system developed by ICCS has two main components. It uses two neural networks called here as GA-RBFNN [6-7] and ML-RBFNN [8-9]. The GA-RBFNN is used to predict the production of a single RES installation while the ML-RBFNN is applied to a single RES unit as well as to an entire region. In more specific, the GA-RBFNN is applied to the nine PV plants of the Rhodes power system and the ML-RBFNN is implemented for the prediction of the total solar production at Rhodes case study as well as at the Évora case study. For the wind power forecasting of the Rhodes power system, both neural networks are applied for each wind farm while the total production is estimated using the recursive least square algorithm (RLS). The report is structured as follows. Firstly, the available data is presented describing the difficulties appeared in each case. In following, the results of the load forecasting system are illustrated. At the next chapter, the performance of the RES forecasting system is analyzed from their evaluation in both wind power and solar power forecasting at the Rhodes case study. Finally, the results of both RES forecasting systems applied to the Évora case study are presented.

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2. Data Collection and Training 2.1 The data collected from Rhodes power system The forecasting models developed at the frame of the European project SUSTAINABLE are applied to the case study of the Rhodes power system. The Rhodes power system is autonomous with maximum annual load demand 233.1 MW. The total rated power capacity of the five wind farms connected to the system is 48.8 MW, while the total nominal power of its PV plants is 18.17 MWp. The available data used for the evaluation of the proposed forecasting models come from four wind farms and nine PV plants connected to the MV level of the power system. In addition, the data used for the load forecasting is obtained by two feeders located at HV side of the HV/MV Genadi substation. The substation is connected at the MV side with two wind farms and one PV plant while the number of household PV installations connected to the substation is unknown.

2.2 Wind power data The available wind power timeseries are corresponded to four wind farms (called here as wf1, wf2, wf3 and wf4) and are illustrated at the figures 1. Also, the total wind power production of the Rhodes power system is presented at the figure 2. The rated power of the above wind farms are 4MW, 11.5MW, 11.75 and 5.25MW respectively. All the available data starts at 01/01/2013 and ends at 15/05/2015. The wind power timeseries of the fifth wind farm of the Rhodes power system starts at 30/01/2014 and is not used for the evaluation of the proposed forecasting model. However, it is added to the data of the total production changing the rated power on the middle of timeseries (figure 2). Summing the production of the fifth wind farm which is the largest farm of the power system, the application of the forecasting models to the total wind power production turns to be challenging. The results presented in the next paragraph show that the proposed forecasting model is tolerant to the above disturbance due to its structure and its online training.

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Figure 2 - The total wind power production of the Rhodes power system

2.3 Solar power data Data from nine PV plants of the Rhodes power system are collected for the proposed RES forecasting system validation. The timeseries covers the period from 15/05/2013 to 15/05/2015 and has hourly time resolution. In addition, for the same period, the total solar production is available and is presented at the figure 3. The timeseries were cleared from missing values using two rules. The periods with non-zero constant measurements which are longer than two hours are considered to contain wrong values. In addition, the zero measurements that cover a period longer than one day are signed as missing values.

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2.4 Load data The load timeseries recorded on the two feeders (P10 and P20) of the Genadi substation are presented at the figures 1 and 2. Both timeseries cover the period from 15/05/2013 to 31/12/2014. The figures obviously show that the RES production overreaches the load demand, especially at the feeder P20. There are two critical dates where new RES installations seem to be connected to the feeders. These dates are 24/06/2013 and 21/01/2014. Beyond these dates, the load dynamics are changed dramatically. In addition, at the case of P10 feeder, new loads have been added at the summer of 2014. From the figures 4 and 5, it is also obvious that there are periods in the timeseries with false measurements. That explains the consecutive constant values appeared at the figures. In order to locate these periods and remove the ‘poor’ measurements from the timeseries, the gradient of the timeseries is computed. The measurements are characterized as wrong, when the gradient in a period longer than 12 hours is always zero. Knowing that production from RES is enhanced to the power system through the Genadi substation, the relations of the load timeseries with the wind power and solar power timeseries are investigated. Comparing linearly using the correlation coefficient, both load timeseries have meaningless relation with the wind and the solar timeseries. However, the mutual information between the load timeseries of the feeder P10 with the wind and the solar timeseries is 9.5 and 7.95 respectively. These values are very high considering the low mutual information is less than 4.5. In addition, at the case of the load timeseries of the feeder P20, the mutual information with the wind power timeseries is 8.6 and with solar power timeseries is 7.13. Consequently, information about the amount of the RES production is needed to make forecasts for the load at both feeders. So, the forecasting procedure is scheduled such as the wind power and solar power forecasts must be produced firstly in order to be used as input at the load forecasting model.

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The auto-correlation analysis is performed on both timeseries searching the autoregressive behavior on several lags and in different time periods. Considering the critical dates 24/06/2013 and 21/01/2014 mentioned above, the auto-correlation coefficients are computed to the lags reached three weeks before the initial date. The auto-correlation coefficients are illustrated to the figures 6a-c for the P10 load timeseries and to the figures 7a-c for the P20 load timeseries. The figures show the similar autoregressive behavior comparing the timeseries at the periods with RES penetration, namely after the day of 24/06/2013. The most valuable lags of the timeseries that should be used to the input of the load forecasting models are the last six hours before the prediction hour. However, at the period between 25/06/2013 and 21/01/2014, there is

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also important information to the lags corresponded to one day before the prediction hour. Sample Autocorrelation Function

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However, the mutual information of the timeseries is computed in order to figure out which training set is adequate for the load prediction and how long the load prediction model can be considered updated. The mutual information between the original load timeseries and the timeseries shifted with various lags is illustrated at the following figures. The figures show that the timeseries characteristics are changed after six months (about 4000 hourly lags). The load forecasting models should be retrained every six months in order to provide accurate predictions. For better performance, the load forecasting models are automatically retrained every two months on this evaluation.

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3. Advanced Load Forecasting tools 3.1 Tools from ICCS The load forecasting tool that was implemented to the two timeseries obtained by the feeders P10 and P20 of the Genadi substation of Rhodes power system, consists of two independent prediction units (PU I and PU II) and a combination unit (CU) to combine the initial forecasts in a 24 hour forecasting horizon [9]. PUs I and II consist of 24 predictors for normal days and 2 predictors for special days. For normal days each predictor is trained to predict the load demand for each separate hour of the day. PU I has been designed for short forecasting horizons, while PU II are customized for horizons longer than six hour-ahead. PU I utilizes the most recent data and produces iteratively the load predictions using as input the predictions of previous steps. Contrary, PU II uses as input load data with lags larger than 24 hours and employs only historical data for each prediction made in the 24 hour horizon. The features used for each PU predictor are selected from the Table I through a stepwise regression analysis applied to the dataset used for its training. TABLE Ι LIST OF THE PU INPUT DATA PU Ι

PU ΙΙ

The load values in lagged hours {from 1 to 12, from 24 to 32, from 48 to 50, from 72 to 74, 96, 120, 144 και from 168 to 172, 192}

The load values in lagged hours {from 24 to 36, from 48 to 50, from 72 to 74, 96, 120, 144 και from 168 to 176, 192, 336, 504}

The total daily consumption at the The total daily consumption at the lagged lagged days {1, 2, 3 και 7} days {1, 2, 3 και 7} The maximum temperature of the The maximum prediction day prediction day

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Week day indicator

Week day indicator

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The combining unit CU consists of 24 multi-layers perceptons (MLPs). The applied MLPs have 24 linear hidden layer neurons and are trained with the PU predictions obtained during the training period. The final version of the proposed load forecasting model employs random forests as the prediction method for the PU predictors construction. In random forests proposed by Breiman [11] each tree is constructed using a different bootstrap data sample and each node is split using the best among a subset of predictors randomly chosen at that node. The random forests (RF) algorithm for regression lists [12]:    

From the original data draw NT bootstrap samples For every bootstrap sample grow a tree without pruning and at each node randomly choose a number of the predictors and select the best split among them Combine the predictions of the NT trees by taking their average

If more trees are added to a random forest this will not overfit and its generalization error will achieve a limiting value [11]. As far as it concerns the RF computational time this is cNT√MNlog(N) where c is a constant, NT is the number of trees, M is the number of variables and N is the number of instances [13]. The RFs are applied in the proposed model without considering any special handling of their parameterization. As mentioned before, the proposed model requires training the 104 predictors utilized by the four PUs, as well as the 24 MLPs of the CU. The RF parameters that need to be defined are the number of trees forming the forest and the number of variables used to build a tree. Following some experimentation, the former parameter was set to 1000, while the latter – in accordance to Breiman’s proposal – [11] was equal to one third of the number of input variables variables and the randomForest package [12] was employed for this implementation. Due to the timeseries characteristics of the Genadi case study, during the evaluation, the load forecasting model was training periodically using the data of the last two months. The training was implemented automatically and its computational time was less than an hour. In specific, each RF training time is about 15 sec and the MLPs forming the CU needed 30 minutes for their training.

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3.2 Results from the timeseries obtained by the feeder P10 Firstly, the proposed load forecasting model was evaluated to the timeseries obtained by the feeder P10 of Genadi substation. The evaluation started at 08:00am of 09/12/2013. At the beginning, the data needed for the model training that corresponds to the period from 10/10/2013 to 08/12/2013, was gathered forming the datasets for each predictor of PU I and PU II. After the PU predictor training, the PU initial predictions for the above period were calculated and were employed to train the CU. This procedure was implemented every two months. For the evaluation of the model, the criteria mean absolute error (NMAE) and root squared error (NRMSE) are applied. NMAE measures the prediction accuracy while NRMSE gives a score for the model performance to capture the variations. Due to the zero measurements of the feeder load, the criteria are normalized with the installed power of the substation where it is considered here as the maximum absolute value of the timeseries (21MW). NMAE and NRMSE for each forecasting horizon are presented to the figures 9 and 10. The NMAE is ranged between 8% and 10.7% in entire forecasting horizon and it does not outreach 10% namely 2.1MW at the first twelve hourly forecasting steps. In addition, the NRMSE is always below 14% and is quite constant in horizons longer than twenty hours ahead. The average performance of the proposed model in entire forecasting horizon is 9.92% and 12.86% for NMAE and for NRMSE respectively. 11 10.5 10

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Figure 9 - The NRMSE of the load forecasting system in entire evaluation period at the case of the feeder P10

The following figures show 24 hour predictions made at several times by the proposed system during the evaluation together with the corresponding observations. The figures prove the difficulty of this case study since every day illustrated does not follow any typical known load profile. Due to the large scale RES penetration comparing the installed power of Genadi substation, large variations appeared during a day. However, the proposed load forecasting system is very accurate in many cases. In specific, at the figure 11a, the 24 hour prediction produced at 9:00am of 21/12/2013 is illustrated. The 21/12/2013 was a day with high wind power penetration and low solar penetration. Due to wind power prediction errors, the load forecasting system fails to estimate accurately the feeder load at some forecasting steps; however the average error is 4.37%. The 24 hour prediction made in a day after the critical day of the timeseries described at the previous section is illustrated at the figure 11b. Specifically, the day selected is the 29/01/2013 when the solar and the wind power penetration was high. Because of the new RES installation connected to substation, the forecasting system overestimates the feeder load (average error 14.43%). In contrary, the predictions made on 05/05/2014 at 09:00am are close enough with the corresponding observations with average error 13.24% (figure 11c). In a day during the summer the performance is better with average error 5.35% (figure 11d) while the prediction error obtained on 07/09/2014 at 09:00am is 6.53% (figure 11f).

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3.3 Results from the timeseries obtained by the feeder P20 The load forecasting system was also evaluated to the timeseries obtained by the second feeder of Genadi substation P20. The evaluation and the training procedure is similar with the case of the P10. Beginning at 08:00am of 09/12/2013 the system was trained with the data of the period from 10/10/2013 to 08/12/2013. Then the next training was implemented after two months. At this case, the evaluation criteria are normalized with 15MW which is approximately the recorded maximum absolute load. The criteria NMAE and NRMSE for each forecasting horizon are presented to the figures 11 and 12. The performance at this case is worse than the case of the P10 feeder since the wind farm connected to the P10 feeder has rated power 4MW and the wind power installed capacity of the P20 feeder is 11.7MW. The NMAE is ranged between 10% and 11.5%. In addition, the NRMSE is always below 15%. The average performance of the proposed model in entire forecasting horizon is 10.92% and 13.87% for NMAE and for NRMSE respectively.

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The figures 13 show the 24 hour predictions made by the proposed system at the same hours used for the error analysis at the case of the P10 feeder. During the days 21/12/2013 and 29/01/2014 there are long periods where the load was constant and the average prediction error is 2.05% and 3.25%. Largest errors appeared after the integration of the wind farm to the power system which reach 35%. The error at 05/05/2014 is 12.13% while for the case of 07/07/2014 it is 15.71%. Finally, the average error of the load prediction made at 09:00am of 07/09/2014 is 14.67%. The forecasting system performance is little worse at the case of the P20 feeder due to the larger variations and the smaller installed power. However, for both cases it was

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proven that the proposed system is very robust to high non-linearity timeseries and applicable to load forecasting at the MV level. 0 -0.2 -0.4

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4. Advanced RES Forecasting tools 4.1 Tools from ICCS The proposed RES forecasting system is built with two different radial basis function neural networks, called as GA-RBFNN [6-7] and ML-RBFNN [8-9]. The GA-RBFNN consists of two layers, the hidden and the output layer. The hidden layer contains radial basis functions (RBF) with kernels selected from the training set by the orthogonal least square algorithm and with variable widths estimated by a genetic algorithm. The variable width implementation facilitates the neural network to analyse each input variable with an adequate number of RBFs. The other component of the forecasting system - the ML-RBFNN - which was developed at the frame of the Sustainable project consists of four layers. The first layer has the same

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structure with the GA-RBFNN hidden layer. Namely, it uses RBF with different width for each input variable in order to analyse them adequately. The second layer is built with RBF groups that work independently. Each group is connected with a RBF of the first layer and learns those input patterns which have activated this RBF. The RBF groups of the second layer provide a different forecast. The final prediction is obtained by the average of independent forecasts of the RBF groups weighted with corresponding activations of the first layer. The ML-RBFNN is self-constructed and it is trained sequentially in real-time by adjusting its parameters each time new data become available.

4.1.1 Solar power forecasting evaluation The proposed PV forecasting system was applied to the Rhodes power system and to the Évora case study. The Rhodes case study consists of nine PV plants. Seven PV plants have rated power 100kWp and two have installed capacity 70kWp and 110kWp respectively. The total installed capacity of the power system is 18.17 MWp. At the Rhodes case study, a GA-RBFNN was applied for each PV plant and a ML-RBFNN was implemented to predict the total solar power production of each case study. Due to its architecture, the MLRBFNN is able to perform well with high dimension input space. For the prediction of the total solar power production, the recursive least square algorithm was applied for upscaling the GA-RBFNN predictions together with the ML-RBFNN predictions. The forecasting system was executed every hour providing 48 hour-ahead forecasts. Every neural network use the following inputs:    

values from the time series; NWP of short wave flux, cloud coverage, temperature and humidity corresponding to various points of the NWP grid that surrounds the RES installations; the hour and the month indicators; the forecasting time horizon

4.1.2 Results from Rhodes case study The forecasting system was evaluated at the period from 01/01/2014 to 31/12/2014. The figures 14 and 15 show the mean absolute error and the root mean square error of the proposed forecasting system normalized with the total rated power of the power system. The NMAE is approximately 4% for every forecasting horizon while the NRMSE is ranged between 7.5% and 8.5%.

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In order to illustrate the prediction errors during the day, the following figures show the performance of the proposed forecasting system considering only the predictions made at 00:00am. As expected, the largest errors were occurred during the midday. The NMAE does not overreach 10% at the day-ahead predictions while for two days ahead horizon it reaches 10.6%. On the other hand, the NRMSE criterion is always less than 15%.

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Finally, the performances of the ML-RBFNN and one of the GA-RBFNNs of the proposed system are illustrated at the figures 19 and 20 respectively. The NMAE of the ML-RBFNN is ranged between 4.5% and 4.8% of total installed capacity of Rhodes island while the 26/56

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NMAE of the GA-RBFNN is approximately 6.3% of the PV plant rated power which is 100kWp. 5 4.9

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4.1.3 Results from Évora case study At the Évora case study, the data covers the period from 01/02/2011 to 06/03/2013. The evaluation period started at 01/02/2012, but it finished at 30/06/2012, since there were not NWP available. Here, the aim was to predict the total solar power production of the Évora area where 44 PV plants are located. The novel neural network ML-RBFNN was implemented to estimate the solar production at once. It receives as input previous solar power values, NWPs of eight points surrounding the Évora area and calendar data. It is trained online using only the input patterns that corresponds to one hour ahead predictions. The NMAE from the evaluation of the ML-RBFNN at evaluation period is ranged between 5% and 6% in the entire forecasting horizon (figure 20). In addition, the NRMSE is always less than 10% (figure 21). Considering only the predictions made at midnight, the maximum error is about 12% for the NMAE criterion and 16% for the NRMSE criterion (figures 22-23).

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4.1.4 Wind power forecasting evaluation on Rhodes case study As mentioned in a previous section, the Rhodes power system is connected with five wind farms with total installed capacity 48MW. At this case study, the forecasting system contains models for four wind farms since the fifth wind farm begun to operate at 30/01/2014. The timeseries of the four wind farms were modeled with the application of the ML-RBFNN. In addition, the wind power forecasting model (WPF) described at [6] was applied to these wind farms and was operated in parallel with the ML-RBFNN. Here, the WPF uses the GA-RBFNNs for the wind power prediction. The prediction of each wind farm is obtained using the recursive least square algorithm (RLS) which combines the two predictions produced by the neural networks. The RLS is applied also for the upscaling of the wind farm predictions to the total wind power production of the Rhodes power system. Firstly, the errors obtained by three wind farms are illustrated comparing the performance of the two neural networks. The figures 24 and 25 show the NMAE and the NRMSE of both neural networks from their application to the wind farm (WF1). The RLS performance is also presented. As shown at the figures, the ML-RBFNN performs always better than GA-RBFNN except the first forecasting step. Using the RLS, the error reduced around 9% for the NMAE criterion and at least 6% for the NRMSE criterion.

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Figure 25 - The NRMSE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF1 case study

The performance of both networks and of the entire model at the case study of the second wind farm (WF2) is illustrated to the figures 26 and 27. Similarly with the case study of WF1, the ML-RBFNN is always better than the GA-RBFNN except the first forecasting step. Their combination using the RLS algorithm does not overreach 12% at the NMAE criterion. In addition, the NRMSE of the final prediction is less than 16% at the forecasting horizons until 37 hours ahead. The improvement [1] achieved by the RLS w.r.t the ML-RBFNN for NMAE criterion is reached 19% while the ML-RBFNN is better than GARBFNN at least 11% for the same criterion. 16

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Figure 26 - The NMAE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF2 case study

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Figure 27 - The NRMSE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF2 case study

The results of the largest of the four wind farms (WF3) are illustrated at the figure 28 and 29. At this case the performance of the proposed model is better at the first twelve hours ahead comparing it with the above cases, but slightly worse at the longer horizons. The NMAE of the GA-RBFNN is always less than 15% while the RMSE overreaches 20%. Contrary at the case of ML-RBFNN, the maximum of NMAE is 13.28%. The best performance achieved by their combination is at least 10% better than the ML-RBFNN performance. 16

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Figure 28 - The NMAE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF3 case study

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Figure 29 - The NRMSE of the GA-RBFNN predictions, of the ML-RBFNN predictions and of their combination at the WF3 case study

Finally, the performance of the whole forecasting system to the total wind power prediction of the Rhodes power system is presented at the figures 30 and 31 The forecasting system is compared with the persistence method. The proposed forecasting system is better than persistence method to every look-ahead time considering both NMAE and NRMSE criteria. The improvement achieved outreaches 60% to the forecasting horizons longer than 36 hours ahead. In addition, the improvement is greater than 50% to the horizons beyond 8 hours ahead (figure 32). For the one hour ahead predictions, the NMAE is 3.11% while at the rest forecasting window it is ranged between 5.5% and 8.5%. On the other hand, the RMSE is ranged between 7.5% and 11.5% for the forecasting horizon greater than one hour ahead. 25

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4.2 Tools from INESC 4.2.1 Results for Évora Test Case This section describes off-line results obtained using real data from the Évora demosite, Portugal. The method described in [1]-[16] is tested for data from the Évora demonstrator. Based on this proof of concept results, some changes in the solar power forecasting methodology developed in WP3 were made (final architecture described in section 4.2.3) and the outcome is a solar power forecasting system that was deployed for operational demonstration in Évora. This section describes off-line results obtained using real data from the different demo sites of the SuSTAINABLE project. In the case of Évora demo-site, Portugal, the results are presented separately for both time horizons.

4.2.2 Test Case Description In order to conduct a proof of concept test for the developed solar power forecasting algorithms, time-series from 44 EDP Energy Box (named EB dataset) in Évora were used. These were the time-series with better quality, or in other words, the ones with the lowest number of missing values and hours with zero generation due to maintenance operation or communication problems. The EB data comprise domestic PV, with installed capacity ranging between 1.1 kW and 3.7 kW. The “optimal” parameters of the clear-sky model are σh=0.01, σdoy=0.01, τ=85%. From trial-error tests, the forgetting factor λ for both AR and VAR was found to be 0.999. The original data was sampled in 15 minutes, but it was also resampled to hourly values. The period between 1 February 2011 and 31 January 2012 was used to fit the models, and the period between 1 February 2012 and 6 March 2013 was used to calculate the forecast errors. The point forecast results are evaluated with the root mean square error (RMSE) calculated for the k-th lead-time: (1) The RMSE is normalized with the solar peak power. The RMSE is calculated separately for each EB or DTC, but it is also calculated using the full dataset of errors as a summary performance metric for all DTC or EB. The probabilistic forecast results are evaluated with Continuous Ranking Probability Score (CRPS) modified to evaluate quantile forecasts [17]: (2)

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where ρ is the average of the quantile loss function (see Eq. 12) calculated on the test period dataset and is the quantile forecast. The integral is calculated through numerical integration with the Simpson’s rule. The performance of two models (VAR and VARX) is compared by computing the improvement over AR in terms of RMSE and CRPS: (3)

4.2.3 Architecture of the PV Forecasting System The final architecture of the PV forecasting system is presented in Figure 33 and a detailed explanation of the forecasting algorithms can be found in Deliverable D3.2 [1]. The modules that compose the forecasting system are: 

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VAR [GB]: The Vector Autogression (VAR) model combines solar power time series distributed in space to produce solar power forecasts for the next six lead-times. The model’s coefficients can be estimated with component-wise gradient boosting (GB) technique; VAR [OLS]: An alternative to the GB method is the use of recursive least squares (or Ordinary Least Squares – OLS). The framework is the same of VAR [GB], the difference is only the method used to estimate the coefficients; Local Median Regression: The local quantile regression (LQR) with the 50% quantile (or median) is used to produce point forecasts for the next 60 hours, based on Numerical Weather Predictions (NWP); Linear Combination: Since the forecasts from the VAR and Local Median Regression (LMR) models overlap for the first six lead-times, a linear model fitted with recursive least squares is used to combine both forecasts; Model Output Statistics (MOS): The NWP, due to a spatial resolution of kilometres, do not account for local effects, such as shadows or topography. This contributes to systematic forecast errors that can be corrected by a statistical method that compares the observations and forecasts for a fitting period and extrapolates this relation into the forecasting (or testing) period. Basically it consists in correcting the bias of the NWP. Here a non-parametric approach based on linear varying coefficient models (described in the appendix section) is used; Upscaling to substation level: The forecast that results from the MOS model is upscaled to the DTC (or secondary substation) level using a linear regression if historical offline observations are available from the other smart meters or data loggers. If these measurements are not available, the information about the rated power is used due to the spatial proximity between solar installations.

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

Local quantile regression: Local quantile regression is used to produce probabilistic forecasts represented by a set of quantiles ranging between 5% and 95%.

The inputs are observations collected by a subset of reference smart meters or data loggers with real-time communication and NWP. The output is a probabilistic forecast of solar power up to a 60 lead-times for each secondary substation.

Figure 33 - Architecture of the PV forecasting system

4.2.4 Results – Very Short-term Horizon The results for the very short-term horizon, i.e., up to six lead-times ahead, are presented in this section for 15 minutes and hourly time resolutions. Point Forecast – Hourly Time Resolution For this dataset, and by 5-fold cross-validation on the fitting period, it was determined that a second-order AR model (i.e., without the diurnal term) achieves the lowest square error for lead-time 1. The VAR model includes the diurnal term in all leadtimes. A one step-ahead solar power forecast obtained with the AR and VAR models is depicted in Figure 34. for one EB (with 3.5 kW) and six different days. For the three days in January, the forecast produced by the VAR model fits better the actual observation under cloudy and overcast conditions. In this case, the AR fails because it does not include information from neighbour sites. In the VAR framework, since all the other EB show a low solar generation level in the past observations, the solar power level for this specific EB is forecasted to be lower than one provided by the AR model (which only includes observations from the same EB). For the three days in April, the difference between the

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AR and VAR forecast is not very substantial, however 16th April was a clear-sky day and the AR, compared to VAR, also shows worst forecast accuracy.

Figure 34 - One step-ahead solar power forecast obtained with the AR and VAR models trained with RLS for one EB

Figure 35 shows the improvement obtained with the VAR model fitted with OLS and GB for two EB and for the RMSEk calculated with the full dataset of EB forecast errors. For lead-times 1-4, the VAR [OLS] model attained the highest improvement for EB number 16, with a value around 27% for lead-time 1 and around 18% for lead-time 4. The VAR [GB] attains the same improvement as VAR [OLS] for lead-time 5 and a higher one for lead-time 6 (i.e., around 14%). The lowest improvement was attained for EB number 39, with 3.5% obtained with VAR [OLS] for lead-time 1 and a negative value of around -1% for lead-time 5. The improvement obtained with VAR [GB] is around 1% for all lead-times. The global improvement for the EB dataset varies between 10% and 0.4% for VAR [OLS] and between 8% and 5% for VAR [GB]. The benefit from using the GB is to get a sparse matrix of coefficients. For the EB dataset, 78% of the coefficients have a null value for lead-time 1 and 80% for lead-time 6.

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The GB fitting, compared to OLS, also attains a higher and statistically significant improvement for lead-times 4-6. An interesting conclusion is that, in most cases, the improvement decays with the lead-time, meaning that the spatial-temporal information is more relevant for the first three hours. This makes sense since the forecasting model in this test case only includes information from a small municipality. If solar power data from neighbouring municipalities and regions is included in the model, a higher improvement for lead-times between 4 and 6 is expected.

Figure 35 - Impk of the VAR model fitted with OLS and GB for two EB and for the RMSEk calculated using the entire set of forecast errors [hourly resolution]

Figure 36 depicts the average values of the normalized RMSEk, calculated from the individual normalized RMSEk values (i.e., divided by the rated power of each PV site) of 40/56

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each EB and DTC. The forecast errors are from the AR (the benchmark model), VAR [OLS] and VAR [GB] model. This plot shows a RMSE, for the best model, ranging between 8.5% and 14.1%. The AR model exhibits an error between 9.5% and 14.1%. The RMSEk magnitude is consistent with the state of the art results for different locations [18][19].

Figure 36 - Average RMSEk for each lead-time calculated with the individual RMSEk obtained for each EB [hourly resolution]

Point Forecast– 15 Min Time Resolution Figure 37 shows the improvement obtained with the VAR model fitted with GB for two EB and for the RMSEk calculated with the full dataset of EB forecast errors. In EB number 10, the VAR model attained an improvement over AR between 15% and 20% for all lead-times, while for EB number 3 the improvement is negative for the first three lead-times and increases up to 10% for lead-time 6. The lowest improvement was attained in lead-time 3, which was around -6%. The average improvement ranges between 7% and 15%, which, considering the results for an hourly time resolution, indicates that the VAR framework can lead to superior in shorter time resolutions (i.e., 15 minutes). The same conclusion will be derived for probabilistic forecasts.

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Figure 37 - Impk of the VAR model fitted with GB for two EB and for the RMSEk calculated using the entire set of forecast errors [15 minutes resolution]

Probabilistic Forecast – Hourly Time Resolution The CRPS improvement obtained with the VAR model is depicted in Figure 38 In EB number 14 the improvement ranges between 7.3% and 21.4%, while in EB number 29 is negative between lead-times 2 and 6. The overall improvement (i.e., average of the individual improvements of the 44 EB) ranges between 4.6% and -2.8%. In contrast to the DTC dataset, the improvement is negative for lead-times between 4 and 6. These results are very different from the point forecast improvement results and also the improvement obtained with the median, which ranges between 6.5% (lead-time 1) and 3.3% (lead-time 6). This negative improvement is mainly explained by a poor performance of VAR models in some quantiles. This is illustrated in Figure 39 by the quantile loss calculated for each nominal probability and lead-times 1 and 5. For lead-

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time 1, the quantile loss of the VAR is lower than the one obtained with AR for quantiles, while in lead time 5 the performance of the VAR model is worse than the AR model for some quantiles (e.g., 5-20% quantiles). In this case, the information from distributed sensors decreases the forecast quality of some quantiles, which impacts the overall quantile loss. A potential future development to improve this probabilistic forecast would be to apply a method that combines different quantile forecasts (from the AR and VAR models in this case) to improve the individual quantile loss in each quantile. For instance, the VAR model performs better in quantile 40%, while the AR has a lower loss in the 10% quantile.

Figure 38 - Impk of the VAR model for two EB and for the CRPS calculated using the entire dataset of forecast errors [hourly resolution]

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The absolute values of CRPS are between 4.4% (normalize by the peak power) and 6.5% for the AR model, between 4.2% and 6.65% for the VAR model.

Figure 39 - Quantile loss of the AR and VAR models for lead-times 1 and 5 [hourly resolution]

Probabilistic Forecast – 15 Min Time Resolution The CRPS improvement obtained with the VAR model is depicted in Figure 40In EB number 23 the improvement ranges between 7% and 18.6%, while in EB number 6 there is negative improvement for lead-times 2 and 3. The overall improvement, which is the average of the individual improvements of the 44 EB, ranges between 4.6% and 9%. The QS results for the EB dataset depicted in Figure 40 show that the VAR model improves almost all the quantiles, only showing a similar performance for the upper tail quantiles. The QS results for lead-time 2 of EB number 6 show that the VAR model only outperforms the AR for the low tail, while the upper tail the QS is much higher. This explains the negative improvement in Figure 41.

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Figure 40 - Improvement of the VAR model for two EB and averaged over the entire dataset [15 minutes resolution]

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Figure 41 - Quantile loss of the VAR and AR models for each 5% quantile [15 minutes resolution]

4.2.5 Results – Complete Time Horizon This section presents results for the complete time horizon, i.e., up to 60 leadtimes ahead, considering hourly time resolution. Point Forecast – Local Median Regression In this section, results regarding the local quantile median model are presented. This model uses numerical weather predictions (NWP) as input, namely global horizontal irradiation and temperature, to forecast the electric power of the PV installation. The time horizon (and availability) of the NWP limits the forecast horizon, in this case the maximum lead-time possible is 60 hours with hourly resolution. Figure 42 depicts the RMSE for the EB with (i) worst performance; (ii) best performance, with maximum value of 15.82% and (iii) the global performance, which results from the average of all 44 EB, which achieved a maximum value of 17.95%. This simulation assumes a daily run at 00h UTC (when new NWP are made available), hence the match between the error curve and the solar cycle, i.e. 0% error at night and more significant errors at noon.

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The atypical shape illustrated in Figure 42 (i) occurs due to the technical characteristics of the PV installation (i.e., solar tracking PV).Figure 43 provides a visual comparison of the power curve between a fixed PV and another with a solar tracker for a typical clear sky day. The abrupt shift between night and day periods prevents the local model to perform accurately during those transitions, resulting in RMSE values as high as 30.14% for EB 35. This result, suggested the use of the Model Output Statistic (MOS) during the real-life demonstration in WP6 in order to mitigate these systematic forecasting errors.

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Point Forecast after the Linear Combination of Models Forecasts obtained with the local median regression model are combined with the very short-term model, VAR, through a linear combination. Since the VAR generates a new forecast every hour when a new observation is available, the linear combination is performed also every hour a new forecast is generated. This removes the match between error curve and solar cycle. Note that all night-time hours were removed by using a filter based on the solar zenith angle. Figure 44 illustrates the RMSE for the EB with (i) worst performance, ranging between 20.15% and 30.87%; (ii) best performance, with minimum error of 6.76% and maximum of 10.06%; and (iii) the overall RMSE of the 44 EB, with a range of values between 9.25% and 13.63%. The positive influence of the VAR in the linear combination is evident by the low forecast errors during the first lead-times, more evidently up to three hours ahead. Considering that after the tenth lead-time (forecast horizon defined for the VAR) the linear combination is equal to the local median regression forecasts, which slight increase in the RMSE values are due to the decrease in NWP’s quality (as the time horizon progresses).

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Figure 44 - Linear Combination - Average RMSEk for each lead-time of three datasets: (i) worst performance EB; (ii) best performance EB; (iii) average of all EB

Probabilistic Forecast Predictions resulting from the linear combination are used as input in the probabilistic model. This forecasting method is evaluated by the CRPS metric depicted in Figure 45. The EB number 35 registers the worst performance of all EB evaluated, with a CRPS ranging from 9.34% to 11.72%. On the contrary, EB 44 has the lowest CRPS with values ranging between 2.81% and 4.13%. The average CRPS of all PV installations has a minimum of 3.96% and maximum of 5.80%. From the analysis of the CRPS value it was possible to infer the reduced performance of the VAR for lead-times 7 to 10. In order to overcome this issue, in the real-life demonstration of WP6 from the seventh lead-time onwards only the local median regression model is considered.

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Improvement of the VAR model over the AR model In this section, the improvement of the VAR model over the benchmark model (i.e., AR model) is assessed for their combination with the NWP based forecast (i.e., generated by the local median regression). Figure 46 illustrates the improvement, regarding RMSE, for the EB with (i) worst improvement, ranging between -0.77% and 1.05%; (ii) best improvement, with a minimum of 0.02% and maximum of 19.62%; (iii) the overall RMSE improvement of the 44 EBs, which resulted in a range of values between 0.01% and 7.91%. Regarding the CRPS improvement, indicated in Figure 47, the lowest improvement occurs in EB 44 with values ranging between -1.08% and 1.11%. EB 12 registers the best

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results with a maximum improvement of 13.59%. The global CRPS improvement, which results from the average of all EB, attained a maximum value of 7.73%.

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5. Conclusion Load Forecasting – Rhodes case study In this report, the special characteristics of load timeseries obtained at the MV level of a power system with large-scale RES penetration are presented. Due to high wind and solar power production, the load was measured negative and the daily load profile was random. Instead of these difficulties, the proposed forecasting architecture performed well presenting an error around 2-3MW. To achieve these results, the forecasting system was trained automatically every two months. RES Forecasting – Rhodes Test Case The neural network ML-RBFNN developed at the frame of SUSTAINABLE project was evaluated to a single wind farm such as to the regional PV forecasting. Applied to a single wind farm, its performance was proved superior against the performance of the GARBFNN which is a RBFNN trained by a sophisticate method. It produced also very accurate predictions when it was implemented to predict the solar production of a wide area. It was proven that the proposed network is able to handle large information with uncertainties. For the Évora case study, the ML-RBFNN developed by NTUA was applied to estimate the total solar power production using the NWPs that correspond to several points around this area. The tool from INESC Porto was used to forecast the generation of each PV site, by exploring information from distributed time series. Nevertheless, although tested in different aggregation levels, both tools showed consistent and comparable performance. Large improvement was also achieved by using the RLS algorithm to upscale the individual predictions in both the wind power and the solar power forecasting. Generally, the results obtained at the Rhodes case study can be considered very satisfactory. Solar Power Forecasting – Évora Test Case The results for the set of 44 EB show that the information from smart grid equipment, such as smart meters and remote terminal units, can improve the solar power forecast accuracy in the very short-term horizon. This means that using information collected from sensors readily available in a smart grid is cheap option to capture the spatial effect of clouds as long as the communication infrastructure allows 15 to 60 minutes data transfer. Combining the very-short term forecasts with numerical weather predictions proved to be not only viable but also advantageous. The linear combination performed with a global RMSE ranging between 9.25% and 13.63%, excluding night-time period. This use-case provided valuable information for the real-life demonstration in WP6, specifically showed the necessity of using a MOS to improve the forecasting of PV installations with solar tracking capabilities and the importance of reducing the forecast horizon for the very short-term to six lead-times ahead.

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References [1] H. Madsen, P. Pinson, H. Aa. Nielsen, T. S. Nielsen, and G. Kariniotakis, ‘Standardizing the performance evaluation of short-term wind power prediction models’, Wind Engineering, vol. 29, issue 6, 475–489, 2005 [2] G. Kariniotakis, I. Martí, D. Casas, P. Pinson, T. S. Nielsen, H. Madsen, J. Giebel, G. and Usaola, I. Sanchez, A. M. Palomares, R. Brownsword, J. Tambke, U. Focken, P. Lange, M. and Louka, G. Kallos, C. Lac, G. Sideratos, and G. Descombes, ‘What performance can be expected by shortterm wind power prediction models depending on site characteristics?’. in Proc. of EWEC’04, London, UK., Nov. 2004 [3] EU Commission Task Force for Smart Grids, “Expert Group 1: Functionalities of smart grids and smart meters”, Final Deliverable, 2010 (available at http://www.gtengineering.it/uploads/allegati/25expert_group1.pdf) [4] Fang, X., Misra, S., Xue, G., Yang, D., “Smart Grid – The new and improved power grid: A survey”, IEEE Communications Surveys & Tutorials, vol 14, no. 4, pp. 944 – 980, 2012 [5] ANEMOS Deliverable 1.1 ‘The State-Of-The-Art in Short-Term Prediction of Wind Power: A Literature Overview’, 2003 [6] G. Sideratos, N. Hatziargyriou, ‘An Advanced Statistical Method for Wind Power Forecasting’, IEEE Transaction on Power System, Vol. 22, Issue 1, pp. 258-265, February 2007. [7] G. Sideratos, Nikos Hatziargyriou, ‘Probabilistic wind power forecasting using radial basis function neural networks’, IEEE Trans. on Power Systems, Vol 27 , Issue 4, pp 1788 - 1796, Nov. 2012 [8] G. Sideratos, N. Hatziargyriou, ‘Wind power forecasting focused on extreme power system events’. IEEE Transactions on Sustainable Energy, Vol. 3, Issue. 3 pp. 445 – 454, 2012 [9] G. Sideratos, N. Hatziargyriou, ‘A Multi-Layer, Multi-Width RBF Neural Network trained by an Hybrid Forward Algorithm’, IEEE Transactions on Neural Networks and Learning Systems, (pending review) [10]Sideratos, G., Vitellas, I., Hatziargyriou, N. D., ”A load forecasting hybrid method for an isolated power system”, in Proc. 16th International Conference on Intelligent System Application to Power Systems (ISAP), Crete, pp. 1 – 5, 2011 [11]Breiman, L., ”Random forests”, Machine Learning, 45, pp. 5 – 32, 2001

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[12]Liaw, A., Wiener, M., ”Classification and regression by randomForest”, R News 2(3), pp. 18 – 22, 2002 [13]Breiman, L., “RF/tools a class of two-eyed algorithms”, SIAM Workshop May 2003, (available at http://www.stat.berkeley.edu/~breiman/siamtalk2003.pdf) [14]R.J. Bessa, D. Fayzur, J. Leite, V. Miranda, G. Sideratos, N. Hatziargyriou, “Description of Preprototype for local RES prediction,” SuSTAINABLE Deliverable D3.2, December 2013. [15]R.J. Bessa, A. Trindade, V. Miranda, “Spatial–temporal solar power forecasting for Smart Grids,” IEEE Transactions on Industrial Informatics, vol. 11, no. 1, pp. 232-241, Feb. 2015. [16]R.J. Bessa, A. Trindade, C.S. Silva and V. Miranda, “Probabilistic solar power forecasting in smart grids using distributed information,” International Journal of Electrical Power & Energy Systems, vol. 72, pp. 16-23, Nov. 2015. [17]G. Anastasiades and P. McSharry, “Quantile forecasting of wind power using variability indices,” Energies, vol. 6, no. 2, pp. 662-695, 2013. [18]P. Bacher, H. Madsen, and H.A. Nielsen, “Online short-term solar power forecasting”, Sol. Energ., vol. 83, no. 10, pp. 1772-1783, 2009. [19]L.A. Fernandez-Jimenez, A. Muñoz-Jimenez, A. Falces, M. Mendoza-Villena, E. Garcia-Garrido, P.M. Lara-Santillan, E. Zorzano-Alba, and P.J. Zorzano-Santamaria, “Short-term power forecasting system for photovoltaic plants,” Renew. Energ., vol. 44, pp. 311-317, Aug. 2012. [20]J. Sumaili, R.J. Bessa, F. Rahman, R. Tomé, J.N. Sousa, “Electrical model parameter characterization for short-term solar power forecasting,” in Proc. of the 4th International Workshop on Integration of Solar Power into Power Systems, Berlin, Germany, Nov. 2014. [21]R.J. Bessa, “Solar power forecasting for smart grids considering ICT constraints,” in Proc. of the 4th International Workshop on Integration of Solar Power into Power Systems, Berlin, Germany, Nov. 2014

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Appendix – Model Output Statistics In this appendix section, a non-parametric Model Output Statistics (MOS) approach, based on linear varying coefficient model, is described [20]. The covariates used to correct the bias are the cosine of the solar zenith angle (related with the position of the sun), cos(θz), and the clearness index (related with sky condition), k*. The MOS for the Global Horizontal Irradiance (Gg) becomes:

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* NWP Ggobs ,t   U  cos  z ,t , V  kt  Gg ,t

(1)

where ω(.) is a vector of coefficient functions to be estimated, Gg,tobs and Gg,tNWP are the observed and forecasted global irradiance. The ω(.) functions are estimated at a number of distinct reference points by approximating the functions using the kernel-local polynomial smoothing method, which means fitting a linear model locally to each reference point (u,v). This allows the coefficients to vary smoothly according to the external variables (i.e., considering U=cos(θz) and V=k*) and therefore modelling nonlinear relations between (cos(θz), k*) and GgNWP. A first order polynomial is considered for both external variables. The local estimator

ˆu, v  of θ(u,v) is the part corresponding to a (if U and V are centred in u and v) of the

following weighted least squares function: NWP Ggobs   U ,V  b  U i  u   GgNWP ,i  a  Gg ,i ,i  min    K  NWP    c  V  v  G i 1    h i g ,i  2

N

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where u and v are the reference local points, K the tri-cube kernel, ||U,V|| the Euclidian norm, and h the kernel bandwidth. The nearest neighbour approach is used to find the bandwidth, meaning that The R function “lm” is used to solve the weighted least squares problem and linear interpolation is used for the coefficients between two equally-spaced reference points. A corrected GHI forecast for the fitting period is estimated through 10-fold cross validation and used to fit the model described in the next section. The MOS is fitted with all the fitting period and used to correct the GHI forecast for the forecasting (or testing) period.

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