Development of Short Term Solar Forecasts

power systems eehlaboratory Seraina Buchmeier Development of Short Term Solar Forecasts Semester Project EEH Power Systems Laboratory Swiss Federal Institute of Technology (ETH) Zurich Supervisors: Olivier Mégel Prof. Dr. Göran Andersson January 7, 2014

Abstract In the following work we contribute a new short term solar forecasting method based on meteorological forecasts and on the photovoltaic (PV) power production of the last hours. We used a PV model and weather forecasts to predict the expected power output of several meteorological stations at different locations. In order to improve the accuracy of the short term solar forecasts obtained with the PV model we developed different neural network models. In the end the predicted PV power and the PV power forecast errors of the different models were evaluated and compared. The average value of the PV power forecast error obtained with the neural network models varies from 9.91 % to 9.08 % whereas the forecast error of the PV power obtained with weather predictions and the PV model is 11.35 % on average. The short term solar forecast accuracy improves most when the global horizontal irradiance, temperature and wind speed predictions as well as the measured PV power of the last hours are considered for power prediction. i

Acknowledgements I would like to thank my supervisor Olivier Mégel for enabling this interesting and challenging Semester Project. His encouragement and advice were invaluable. Further I wish to thank Prof. Dr. Göran Andersson of the Power Systems Laboratory for approving this Semester Project. I also want to thank everyone who has supported me. ii

Contents Abstract Acknowledgements i ii 1 Introduction 1 1.1 Related Work........................... 1 1.2 Contribution........................... 2 2 Weather Data and Load Data 3 2.1 Meteorological Stations..................... 3 2.2 Meteorological Data....................... 3 2.3 Meteorological Forecast Errors................. 5 2.4 Load Data............................. 7 3 Photovoltaic Model 9 3.1 Modelling Steps.......................... 9 3.2 PV Power Prediction....................... 10 3.3 PV Power Forecast Error.................... 13 3.4 PV Model with Load....................... 14 4 Neural Network Models 16 4.1 Modelling Steps.......................... 16 4.2 Applied Models.......................... 17 4.3 PV Power Prediction....................... 18 5 Evaluation of the Short Term Solar Forecasts 22 6 Conclusion and Outlook 24 Bibliography 26 iii

Chapter 1 Introduction The amount of photovoltaic (PV) power production in Europe is constantly increasing. Together with line export constraints this might lead to PV curtailment during hours with high insolation [1]. Combined with a storage device the grid-connected PV systems could deliver hourly constant power profiles and thus PV curtailment could be prevented. Meteorological predictions as well as short term solar forecasts are therefore highly valuable for the efficient use of PV power and the optimal operation of storage devices. Accurate forecast information is also required for the management of the grid, for trading on the power market and for the improvement of the grid integration of renewable energy technologies such as wind power [2]. Thus the main target of this work is to develop short term (up to one day ahead) solar forecasts and to evaluate the PV power forecast errors. 1.1 Related Work On the one hand, there has been done a lot of work on irradiance forecasting and PV power prediction. Since most of the regional PV power prediction methods are based on meteorological forecasts they depend on the forecast accuracy of the weather predictions. An approach to predict the regional PV power output based on irradiance forecasts up to three days ahead has been presented by E. Lorenz et al. [3]. They evaluated the forecast uncertainty for different meteorological situations and derived weather specific prediction intervals in order to improve the accuracy of the PV power prediction. E. Lorenz et al. also developed a regional PV power prediction system based on irradiance forecasts for improved grid integration which provides forecasts up to two days ahead with hourly resolution [4]. The regional power forecasts are derived by up-scaling from a predetermined set of small PV sites. Another short term PV power forecast approach up to one and a half days ahead has been proposed by P. Bacher et al [5]. Both the 1

CHAPTER 1. INTRODUCTION 2 past PV power values and the meteorological forecasts are used to predict the hourly PV power of different sites with this method. On the other hand, a lot of work has been done on short term wind power forecasts and the evaluation of different prediction models. Since the wind power and the solar power production are both weather dependent and therefore strongly fluctuating, the forecast methods are similar. P. Pinson et al. proposed a method which generates statistical scenarios of short term wind power production from probabilistic forecasts of wind generation [6]. Due to the predictive distributions and the interdependence structure of the prediction errors, the wind power forecasts provide highly valuable information about the development of the forecast uncertainty in the coming time period. H. Madsen et al. compared a number of advanced approaches for short term wind power prediction and proposed a standardized protocol for their performance evaluation [7]. The most important error measures, factors influencing the error measures such as the time and reference models are summarized in their work. 1.2 Contribution This work is partly based on a previous Semester Project done at ETH Zurich by L. Theodoulou which concludes, that the short term irradiance forecasts alone are not especially accurate for PV power prediction[8]. Hence in this work we contribute a new short term solar forecasting method based on meteorological forecasts and on the PV power production of the last hours. We used a PV model and weather forecasts to predict the expected power output of several meteorological stations at different locations. In order to improve the accuracy of the short term solar forecasts obtained with the PV model we developed different neural network models. In the end the predicted PV power and the PV power forecast errors of the different models were evaluated and compared. The contents of this work are structured as follows. In Chapter 2 the meteorological stations as well as the weather data and the load data are described. An overview of the PV model, the resulting PV power output and the forecast error is given in Chapter 3. The different neural networks modelled in this work in order to improve the forecasts of the PV model are illustrated in Chapter 4. The predicted PV power and the PV power forecast errors of the different models are evaluated and compared in Chapter 5. In Chapter 6 we conclude our findings and refer to future work.

Chapter 2 Weather Data and Load Data The following chapter describes the weather data and load data used in this work. An overview of the meteorological stations and the predicted and real weather parameters is given. The prediction and measurement period as well as the forecast horizon are defined. Furthermore the evaluation of the meteorological forecast errors is described in detail. In the last part the characteristics of the load data are illustrated. 2.1 Meteorological Stations The predicted and real weather data as well as the information about the meteorological stations in this work are from the Federal Office of Meteorology and Climatology MeteoSwiss. We used the data of 10 geographically distributed weather stations in order to compute and evaluate our short term solar forecasts and models. The stations differ in the site longitude, site latitude and site elevation and cover a wide range of the country. The meteorological station information including the geographical positions are summarized in Table 2.1. 2.2 Meteorological Data Numerous different parameters are measured at the meteorological stations and predicted for different time horizons. In this work we only used the global horizontal irradiance, the temperature (2 m above ground) and the wind speed (10 m above ground) data. The time is given in UTC values and all measured parameters are given as hourly mean values. The predicted global horizontal irradiance is an hourly mean value as well, while the predicted temperature and wind speed are instantaneous values. The predicted meteorological data are from the local scale numerical weather prediction 3

CHAPTER 2. WEATHER DATA AND LOAD DATA 4 Table 2.1: Weather station information. The information is from the Federal Office of Meteorology and Climatology MeteoSwiss. No. Weather Station Longitude Latitude Elevation [m] 1 Stabio 8 56 45 51 353 2 Aadorf/Tänikon 8 54 47 29 539 3 Davos 9 51 46 49 1594 4 Basel/Binningen 7 35 47 32 316 5 Interlaken 7 52 46 40 577 6 Möhlin 7 53 47 34 344 7 Sion 7 20 46 13 482 8 Pully 6 40 46 31 455 9 Zürich/Fluntern 8 34 47 23 555 10 Bullet/La Frétaz 6 35 46 50 1205 system COSMO-2 [9]. The measured weather data are from the meteorological data archive [10]. The meteorological parameters used in this work are summarized in Table 2.2. The prediction and measurement period of the weather data is exactly one year and ranges from the 1st August 2011 to the 31st July 2012. Since the year 2012 is a leap year the observed period has 366 days respectively 8784 hours. Table 2.2: Meteorological parameters used in this work. All three measured parameters and the predicted global horizontal irradiance are hourly mean values. The predicted temperature and wind speed are instantaneous values. Parameter Unit Global Horizontal Irradiance W/m 2 Temperature C Wind Speed m/s Since the forecast horizon of the global horizontal irradiance does not have a significant impact on the prediction accuracy of short term solar forecasts, we chose to use a forecast horizon of 24 hours starting at 00:00 for all parameters [8]. In case the measurement data were incomplete the corresponding data of the day ahead were taken to replace the missing values. The predicted and measured meteorological parameters at station No. 1 (Stabio) are illustrated for the time period of one week from the 1st to the 7th July 2012 in the following. The global horizontal irradiance forecast and measurement data are illustrated in Figure 2.1. On a cloudless day the global horizontal irradiance reaches values up to 1000 W/m 2. The difference between the predicted and the measured data is larger on days with unsettled weather. Figure 2.2 illustrates the curves of the predicted

CHAPTER 2. WEATHER DATA AND LOAD DATA 5 1000 900 Forecast Measurement 800 Global horizontal irradiance [W/m²] 700 600 500 400 300 200 100 0 1st July 2nd July 3rd July 4th July 5th July 6th July 7th July Date Figure 2.1: Predicted and measured global horizontal irradiance at station No. 1 (Stabio) from the 1st to the 7th July 2012. The predictions are worse on days with unsettled weather. and the real temperature. The temperature ranges from 14 C at night to over 30 C at day. The predictions generally get slightly worse in the course of the day since the forecast horizon starts at 00:00 and lasts 24 hours. The predicted and measured wind speed are illustrated in Figure 2.3. The wind speed ranges from 0 m/s to 6 m/s and varies rapidly. Even though some hours can be predicted quite well, accurate forecasts with a long forecast horizon are very difficult to obtain [6]. 2.3 Meteorological Forecast Errors The normalized root mean square error (RMSE) was used to evaluate the forecast errors of the predicted and measured global horizontal irradiance, temperature and wind speed. Lower values indicate a smaller difference between the predicted values and the measured ones [7]. The RMSE was evaluated for every meteorological station and as average value over all stations. The formula is the following: RMSE = 1 N ( ) predicted(i) real(i) 2. (2.1) N P norm i=1

CHAPTER 2. WEATHER DATA AND LOAD DATA 6 32 30 Forecast Measurement 28 26 Temperature [ C] 24 22 20 18 16 14 1st July 2nd July 3rd July 4th July 5th July 6th July 7th July Date Figure 2.2: Predicted and measured temperature at station No. 1 (Stabio) from the 1st to the 7th July 2012. The predictions get slightly worse in the course of the day. 6 Forecast Measurement 5 4 Wind speed [m/s] 3 2 1 0 1st July 2nd July 3rd July 4th July 5th July 6th July 7th July Date Figure 2.3: Predicted and measured wind speed at station No. 1 (Stabio) from the 1st to the 7th July 2012. Accurate forecasts are difficult to obtain since the wind speed varies rapidly.

CHAPTER 2. WEATHER DATA AND LOAD DATA 7 In the formula above the variable i denotes the hourly values of the meteorological parameter while N equals the 8784 hours in the observed year 2011/2012. The formula for the global horizontal irradiance, the temperature and the wind speed is the same. The normalization constant P norm equals the maximum value of the respective meteorological parameter at every station [7]. The forecast errors of the global horizontal irradiance, temperature and wind speed are summarized in Table 2.3. The forecast error of the predicted and the real global horizontal irradiance only has small deviations from station to station and is 9.42 % on average. The average value of the temperature forecast error is 5.72 % and has slightly more deviations from station to station while the wind speed forecast error is the most varying one with 15.30 % on average. Table 2.3: Forecast errors of the global horizontal irradiance, temperature and wind speed for every meteorological station and as average value over all stations. No. Weather Station RMSE (%) Irradiance Temperature Wind Speed 1 Stabio 9.46 8.08 20.21 2 Aadorf/Tänikon 9.62 5.99 15.71 3 Davos 9.48 7.53 17.25 4 Basel/Binningen 9.18 4.35 7.50 5 Interlaken 9.17 6.06 11.76 6 Möhlin 9.50 5.52 11.13 7 Sion 9.12 5.64 12.52 8 Pully 9.57 4.38 19.20 9 Zürich/Fluntern 9.47 4.55 8.59 10 Bullet/La Frétaz 9.64 5.13 29.16 Average Value 9.42 5.72 15.30 2.4 Load Data The load data in this work are from the European Network of Transmission System Operators for Electricity ENTSO-E. The time period matches the one of the weather data and ranges from the 1st August 2011 to the 31st July 2012. The load data correspond to the total German consumption and are given as hourly mean values [11]. Figure 2.4 illustrates the load data for the time period of one week from the 1st to the 7th July 2012.

CHAPTER 2. WEATHER DATA AND LOAD DATA 8 The consumption reaches from 30 GW to 80 GW depending on the time of the day and the weather. The load is much larger during the week than on weekends. In this work we assumed to supply 40 % of the total German load with PV stations. 75 Measurement 70 65 60 Load [GW] 55 50 45 40 35 30 1st July 2nd July 3rd July 4th July 5th July 6th July 7th July Date Figure 2.4: Measured load from the 1st to the 7th July 2012. The load is given as hourly mean values and depends on the time of the day and the weather.

Chapter 3 Photovoltaic Model The following chapter describes the simplified PV model used in this work. In the first part the general model and its parameters are defined. Furthermore the resulting predicted and real PV power output, the PV power difference and the forecast error of the PV power are described in detail. In the last part the influence of the load on the PV power difference and the forecast error are illustrated. 3.1 Modelling Steps In order to predict the expected PV power output of the meteorological stations at different locations the PV-LIB Toolbox for Matlab developed by the PV Performance Modelling Collaborative of the Sandia National Laboratories was used [12]. The model requires numerous specification variables such as the system design and the environment including the weather data. While some of the PV system parameters are constant, such as the geographical position and the size of the site, most of them are weather dependent and vary over the year. The same PV site was modelled at each meteorological station in order to ease the evaluation of the PV power forecast error. The PV module and the inverter specifications were obtained from the Sandia National Laboratories database [13]. Each PV site comprises 2 x 8 modules in series, which are tilted by a fixed angle of 45 degrees and are oriented southwards. The date and time as well as the hourly mean values of the predicted and the measured global horizontal irradiance, temperature and wind speed are PV model inputs. Furthermore the site latitude, site longitude and site elevation must be known. The PV model parameters are summarized in Table 3.1. Details on the predicted and real weather data as well as the meteorological station information can be found in Chapter 2. The direct 9

CHAPTER 3. PHOTOVOLTAIC MODEL 10 normal irradiance and the diffuse horizontal irradiance are both derived from the global horizontal irradiance. The sun position as well as the incident radiation result from the above parameters [12]. Possible shading, soiling and reflection losses are treated with a constant derate factor. The PV cell temperature is influenced by a number of variables including the module material, the incident irradiance, the wind speed and the ambient temperature. Further the IV performance of the array at each time step is derived. Finally the power conversion of the inverter results in the PV power output of the PV model. The maximum PV power is 3000 W due to the number of modules and the chosen inverter. Since the inverter is slightly undersized it clips the PV power during hours with very high irradiance values [13]. Table 3.1: PV model parameters. The PV site parameters are constant whereas the meteorological parameters change over time. PV Model Parameter Station Name Station Number Site Latitude Site Longitude Site Elevation Date and Time Global Horizontal Irradiance Temperature Wind Speed 3.2 PV Power Prediction In a first step we used the above PV model and weather forecasts in order to predict the expected PV power output of the meteorological stations at different locations and to evaluate the forecast error of the PV power. On the one hand we predicted the power output with the forecasts of the global horizontal irradiance, temperature and wind speed. On the other hand we evaluated the expected PV power output with the real weather measurements. The PV power obtained from the meteorological measurements is further referred to as the measured or real PV power. Figure 3.1 illustrates the predicted and measured PV power at station No. 1 (Stabio) for the time period of one week from the 1st to the 7th July 2012. The power production reaches values up to 2400 W on a cloudless day. In some hours the obtained PV power forecast is far too low and in other hours the PV power prediction is much to high. The difference between the predicted and the measured PV power depends on the weather forecast errors and is thus larger on days with

CHAPTER 3. PHOTOVOLTAIC MODEL 11 2500 Forecast Measurement 2000 PV power [W] 1500 1000 500 0 1st July 2nd July 3rd July 4th July 5th July 6th July 7th July Date Figure 3.1: Predicted and real PV power at station No. 1 (Stabio) from the 1st to the 7th July 2012. The difference between the predicted and the real PV power depends on the weather forecast errors. 3000 2500 PV power difference [W] 2000 1500 1000 500 0 20 15 Hour of day 10 5 0 0 50 100 150 200 Day of year 250 300 350 Figure 3.2: PV power difference at station No. 1 (Stabio) over a whole year. The PV power difference varies with the hour of the day, the day of the year and the weather forecast uncertainties.

CHAPTER 3. PHOTOVOLTAIC MODEL 12 unsettled weather. The PV power difference equals the absolute value of the predicted PV power minus the real PV power and is computed as follows: PV power difference = real PV Power - predicted PV Power. (3.1) The PV power difference at station No. 1 (Stabio) over a whole year is illustrated in Figure 3.2. The period observed begins on the 1st August 2011 and lasts till the 31st July 2012. The PV power difference depends on the hour of the day and the day of the year. In the winter months the days are muchshorter than in the summer monthsand therefore the time with no PV power production is longer. Moreover, the PV power difference gets larger in summer due to higher irradiance values and thus more uncertainties in the weather forecast. 3000 2500 2000 PV power difference [W] 1500 1000 500 0 20 15 Hour of day 10 5 0 Figure 3.3: PV power difference at station No. 1 (Stabio) over a whole year depending on the hour of the day. The PV power difference is larger on days with unsettled weather. The PV power difference at station No. 1 (Stabio) is illustrated from other points of view in the following. Figure 3.3 illustrates the PV power difference depending only on the hour of the day. The PV power difference can get quite large during days with high irradiance values or wrong meteorological forecasts. The PV power difference depending only on the day of the year is illustrated in Figure 3.4. The PV power difference is smaller

CHAPTER 3. PHOTOVOLTAIC MODEL 13 3000 2500 2000 PV power difference [W] 1500 1000 500 0 0 50 100 150 200 250 300 350 Day of year Figure 3.4: PV power difference at station No. 1 (Stabio) over a whole year depending on the day of the year. The PV power difference gets larger in summer due to higher irradiance values. in winter due to lower irradiance values and hence less uncertainties in the weather forecast. Even though the PV power difference is quite constant over the whole year, large PV power differences appear from time to time. 3.3 PV Power Forecast Error The RMSE was used to evaluate the forecast error of the PV power. The formula is the same as the one given for the meteorological parameters in Chapter 2. The normalization constant P norm equals the maximum PV power value of 3000 W. The RMSE was evaluated for every meteorological station and as average value over all stations. The forecast errors of the PV power are summarized in Table 3.2. The forecast error of the PV power obtained with weather predictions and the PV model is 11.35 % on average and is therefore slightly higher than the forecast error of the global horizontal irradiance. The average value of the PV power forecast error in this work is smaller than in the work done by L. Theodoulou [8]. In the previous work there was a data point missing in the meteorological forecasts and thus part of the weather predictions were shifted by three hours. In the further work we present a new forecasting method in order to improve the PV power forecast error obtained with the PV model.

CHAPTER 3. PHOTOVOLTAIC MODEL 14 Table 3.2: Forecast error of the PV power for every meteorological station and as average value over all stations. No. Weather Station RMSE AC Power (%) 1 Stabio 10.36 2 Aadorf/Tänikon 11.47 3 Davos 12.29 4 Basel/Binningen 10.79 5 Interlaken 11.14 6 Möhlin 11.17 7 Sion 11.72 8 Pully 10.62 9 Zürich/Fluntern 11.29 10 Bullet/La Frétaz 12.63 Average Value 11.35 3.4 PV Model with Load InalaststepwenormalizedthePVpowerdifferencewiththeloadinorderto evaluate the impact of the load on the PV power difference and the forecast error. We scaled the load by a factor of 8.3 10 9 in order to supply 40 % of the total load with PV stations. Details on the load data can be found in Chapter 2. The normalized PV power difference equals the relative value of the real PV power minus the predicted PV power divided by the load and is computed as follows: normalized PV power difference = real PV Power - predicted PV Power. (3.2) Load Figure 3.5 illustrates the normalized PV power difference at station No. 1 (Stabio) over a whole year. The period observed begins on the 1st August 2011 and lasts till the 31st July 2012. On the one hand there are hours where the predicted PV power is too low, while on the other hand there are hours where the PV power forecast is much to high. The PV sites could be combined with storage devices in order to balance the power fluctuations and deliver hourly constant power profiles. In hours with high insolation and low load the power could be stored and then used in hours with overcast sky or more consumption. The size of the storage and the accuracy of the delivered profile depend mainly on the forecast error of the predicted PV power [14].

CHAPTER 3. PHOTOVOLTAIC MODEL 15 The normalized PV power difference ranges from -500 % to 500 %. It is often positive in the first hours of the day and gets negative in the course of the day. However the normalized PV power difference is nearly zero on average over the whole year. Same as in Figure 3.2 the days are much shorter in the winter months than in the summer months and therefore the time with no PV power production is longer. Moreover, the normalized PV power difference gets larger in summer due to higher irradiance values and thus more uncertainties in the weather forecast. In order to compensate the large PV power difference with other power plants or storages, the forecast accuracy of the PV power should be improved particularly in summer. The change of the normalized PV power difference from positive to negative in the course of the day could also be relevant for storage dimensioning. 500 400 Normalized PV power difference with load (%) 300 200 100 0 100 200 300 400 500 20 15 10 5 0 0 50 100 150 200 250 300 350 Hour of day Day of year Figure 3.5: Normalized PV power difference at station No. 1 (Stabio) over a whole year. The normalized PV power difference changes considerably in the course of the day.

Chapter 4 Neural Network Models The following chapter describes the different neural networks modelled in this work in order to improve the short term solar forecasts obtained with the PV model. In the first part neural networks and their parameters are described. Later on the structure of the models and the corresponding meteorological data are illustrated. In the last part the resulting PV power predictions of the different models are evaluated. 4.1 Modelling Steps In order to improve the accuracy of the short term solar forecasts obtained with the PV model we developed two different neural network models. The general models and parameters are from the Matlab Neural Network Toolbox [15]. While the PV model described in Chapter 3 requires a lot of specification variables such as the number of modules or the tilt angle in order to predict the PV power output, the neural network models are only based on the measured PV power of the last hours and the meteorological forecasts. They try to find a relation between the weather predictions and the expected PV power output without modelling the PV stations. Neural networks hence act like their counterpart in the biological nervous system and predict future values and events by learning from the past [15]. In this work we developed a simple autoregressive (AR) model and an autoregressive model with external input (ARX). Both models predict the PV power output of the PV sites based on the measured PV power of the last hours. Moreover the ARX model includes weather forecasts of the global horizontal irradiance, temperature and wind speed for PV power prediction. Most of the model parameters such as the ideal input delay, number of network layers and number of neurons per layer are unknown and are difficult to identify with a standard approach. Hence we evaluated the effect 16

CHAPTER 4. NEURAL NETWORK MODELS 17 of different model parameters on the PV power forecast error and chose the most consistent values. In both models the Levenberg-Marquardt backpropagation algorithm is used as training function [15]. Furthermore all initial input weights and layer weights are set to zero. The weather forecast data as well as the real PV power are divided into a larger period for training and validation of the model and a smaller period for testing. The initial training data is used to adjust the weights and biases of the neural network according to the errors during training. The subsequent validation data belongs to the training period and is used to evaluate the network generalization and to halt the training when the network starts overfitting the data and the prediction of the PV power stops improving. The last period comprises the testing data and is independent of the training and validation period[15]. We divided the weather forecast data as well as the real PV power production over the whole year from the 1st August 2011 to the 31st July 2012 into three data sets which correspond to different time periods of the year. In our model the initial training data comprises eight successive months and the subsequent validation period lasts three months. Thus the testing period corresponds to one month. The PV power forecast error of the neural network is only evaluated during the testing period and is therefore out-ofsample. Since the forecast error is only evaluated in one month the neural network is modelled 12 times for each meteorological station in order to obtain the forecast error over the whole year. 4.2 Applied Models In this work we developed two different neural network models which include the measured PV power output of the last hours and meteorological forecasts for power prediction. The AR model has a simple structure and predicts the PV power based on the measured power production of the last hours. The structure of the two layer AR model is illustrated in Figure 4.1. The neural network performs best with ten neurons on the first layer and one neuron on the second layer. Thefeedback delay is 1 to 4 hours, therefore the current PV power prediction is always based on the last four measured PV power values. Modifications of the above model parameters lead to better results at some single stations or during some months, but lead to worse results regarding the average value of the PV power forecast error. The ARX model predicts the PV power based on the measured power production of the last hours and the weather forecast data. In order to identify the importance of the temperature and wind speed forecasts, we created two different neural networks using weather predictions. The first

CHAPTER 4. NEURAL NETWORK MODELS 18 Figure 4.1: Structure of the two layer AR model. The model predicts the PV power output based on the measured PV power of the last hours. ARX model predicts the PV power based on the forecast of the global horizontal irradiance and the measured PV power of the last hours. The second ARX model predicts the PV power based on the hourly mean values of the predicted global horizontal irradiance, temperature and wind speed and the measured PV power of the last hours. Details on the meteorological forecasts can be found in Chapter 2. Both ARX models perform best with twelve neurons on the first layer and one neuron on the second layer. Figure 4.2 illustrates the structure of the two layer ARX models. The input delay is 1 to 4 hours, therefore the current PV power forecast is based on the last four values of the meteorological predictions. The feedback delay of the PV power is only 1 to 2 hours, hence the current PV power prediction is always based on the last two measured PV power values. The above model parameters are chosen based on the average value of the PV power forecast error. We also modelled the neural networks with the season and the hour as further inputs, the PV power forecast error increased though. 4.3 PV Power Prediction Later on the neural network models described above were trained and tested in order to improve the PV power forecasts of the meteorological stations obtained with the PV model. The PV power forecasts of the different models at station No. 1 (Stabio) are illustrated for the time period of one week from the 1st to the 7th July 2012 in the following. The predicted PV power

CHAPTER 4. NEURAL NETWORK MODELS 19 Figure 4.2: Structure of the two layer ARX model. The model predicts the PV power output based on meteorological forecasts and the measured PV power of the last hours. obtained with the AR model is illustrated in Figure 4.3. As already described above, the PV power prediction is based on the measured PV power of the last hours. The model predicts a quite constant PV power of around 46 W in most of the hours at night even though the real PV power is zero. On days with unsettled weather and therefore varying PV power production the model performs well though. The measured PV power is obtained with the PV model from Chapter 3 and is based on the real weather data. Figure 4.4 and Figure 4.5 illustrate the predicted PV power obtained with the ARX models in the same week in July 2012. The first model predicts the PV power based on the forecast of the global horizontal irradiance and the measured PV power of the last hours. The PV power forecast improves on days with high global horizontal irradiance values but worsens on days with unsettled weather and therefore varying PV power production. Moreover the model predicts a quite constant PV power of around 68 W in most of the hours at night even though the real PV power is zero. The second model predicts the PV power based on the predicted global horizontal irradiance, temperature and wind speed and the measured PV power of the last hours. The PV power forecast and the real PV power are similar independent of the weather situation. Furthermore the model predicts several hours with zero PV power at night.

CHAPTER 4. NEURAL NETWORK MODELS 20 2500 Forecast Measurement 2000 PV power [W] 1500 1000 500 0 1st July 2nd July 3rd July 4th July 5th July 6th July 7th July Date Figure 4.3: Predicted and real PV power at station No. 1 (Stabio) from the 1st to the 7th July 2012. The AR model predicts the PV power fairly well on days with unsettled weather. 2500 Forecast Measurement 2000 PV power [W] 1500 1000 500 0 1st July 2nd July 3rd July 4th July 5th July 6th July 7th July Date Figure 4.4: Predicted and real PV power at station No. 1 (Stabio) from the 1st to the 7th July 2012. The first ARX model predicts the PV power best on days with high irradiance values.

CHAPTER 4. NEURAL NETWORK MODELS 21 2500 Forecast Measurement 2000 PV power [W] 1500 1000 500 0 1st July 2nd July 3rd July 4th July 5th July 6th July 7th July Date Figure 4.5: Predicted and real PV power at station No. 1 (Stabio) from the 1st to the 7th July 2012. The second ARX model improves the PV power prediction independent of the weather conditions.

Chapter 5 Evaluation of the Short Term Solar Forecasts In this work we modelled two different neural networks which include the measured PV power of the last hours and meteorological forecasts in order to improve the accuracy of the PV power prediction obtained with the PV model. The RMSE was used to evaluate the forecast error of the PV power. The formula is the same as the one given for the meteorological parameters in Chapter 2. The normalization constant P norm equals the maximum PV power value of the respective station and month. The RMSE was evaluated for every meteorological station and as average value over all stations. The forecast error of the PV power was also evaluated for every month and as average value over the whole year. The forecast errors of the PV power are summarized in Table 5.1 and Table 5.2. The average value of the PV power forecast error is 9.91 % with the AR model and 9.46 % respectively 9.08 % with the two ARX models. The forecast error of the PV power obtained with weather predictions and the PV model is 11.35 % on average. Thus the PV power forecast error decreases considerably with the use of neural networks. The short term solar forecast accuracy improves most when the past global horizontal irradiance, temperature and wind speed predictions as well as the measured PV power of the last hours are considered in the model. Duringthesummermonthstheforecast error of thear model seems to be higher than during the winter months, yet the deviations depending on the time of the year are small. Both ARX models manage to improve the PV power forecast errors in summer. The average value of the PV power forecast error remains largest in the months February, July and August. 22

CHAPTER 5. EVALUATION OF THE SHORT TERM SOLAR FORECASTS23 Table 5.1: Forecast error of the PV power for every meteorological station and as average value over all stations. No. Weather Station RMSE AC Power (%) AR Model ARX Model I ARX Model II 1 Stabio 9.23 8.23 7.79 2 Aadorf/Tänikon 10.86 9.71 9.05 3 Davos 9.83 10.78 9.52 4 Basel/Binningen 10.76 9.97 9.61 5 Interlaken 10.40 9.61 9.74 6 Möhlin 9.51 9.43 8.86 7 Sion 9.36 9.34 8.77 8 Pully 9.11 8.41 8.92 9 Zürich/Fluntern 9.84 9.68 9.22 10 Bullet/La Frétaz 10.18 9.47 9.28 Average Value 9.91 9.46 9.08 Table 5.2: Forecast error of the PV power for every month and as average value over the whole year. No. Month RMSE AC Power (%) AR Model ARX Model I ARX Model II 1 January 9.70 9.07 8.65 2 February 10.65 10.91 10.07 3 March 8.68 8.49 8.00 4 April 10.37 8.95 8.68 5 May 10.80 9.50 9.33 6 June 10.20 9.54 8.92 7 July 10.82 11.87 10.54 8 August 11.47 10.99 11.26 9 September 9.32 9.20 9.12 10 October 9.09 8.59 8.52 11 November 8.83 8.12 7.93 12 December 8.96 8.31 7.91 Average Value 9.91 9.46 9.08

Chapter 6 Conclusion and Outlook In this work we contribute a new short term solar forecasting method based on meteorological forecasts and on the PV power production of the last hours. We used a PV model based on weather forecasts to predict the expected power output of several meteorological stations at different locations. In order to improve the accuracy of the short term solar forecasts obtained with the PV model we developed different neural network models. In the endthepredictedpv powerandthepvpowerforecast errorsofthedifferent models were evaluated and compared. This work allowed us to find out that there was a missing data point in the meteorological forecasts. The average value of the PV power forecast error obtained with the neural network models varies from 9.91 % to 9.08 % whereas the forecast error of the predicted and real PV power obtained with the PV model is 11.35 % on average. The short term solar forecast accuracy improves most when the global horizontal irradiance, temperature and wind speed predictions as well as the measured PV power of the last hours are considered for power prediction. The PV model used in this work to predict the expected power output of several meteorological stations at different locations performs well in general. The accuracy of the PV power prediction depends on the forecast errors of the global horizontal irradiance, temperature and wind speed though. Moreover the meteorological forecasts have to be purchased from a weather institute. The PV model also requires detailed information about the PV site which is perhaps not always available. One advantage of the neural networks modelled in this work in order to improve the accuracy of theshorttermsolar forecasts obtained withthepv model is that nodetailed information about the PV sites is required. The AR model predicts the PV power output based only on the measured PV power of the last hours while the ARX models include weather forecasts for PV power prediction. The accuracy of the PV power prediction thus depends on the forecast errors of the weather prediction. Furthermore the short term PV power forecasts are 24

CHAPTER 6. CONCLUSION AND OUTLOOK 25 only available one hour ahead since the predicted PV power is based on the measured PV power output of the last hours. As future work we propose the evaluation of the PV power forecast error over a longer time period than one year. A larger number of PV stations as well as other model parameters could possibly improve the PV power prediction accuracy. Furthermore the snow cover of PV modules in winter has not been considered for PV power prediction in this work. One could also replace the measured PV power of the last hours with the measured PV power of the previous day and evaluate the consequences on the PV power forecast error.

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