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Power Production Forecasting

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Renato De Leone
Renato De Leone

44th Annual Conference of the Italian Operational Research Society (AIRO 2014) Como September 2, 2014 – September 5, 2014

Science
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1 Power Production and Storage in Microgrids R. De Leone, A. Giovannelli, M. Pietrini† AIRO 2014, September 2014 Research@Energy, Loccioni Group, Angeli di Rosora, AN, Italy † Mathematics Division, School of Science and Technologies, University of Camerino, MC, Italy
Contents Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 2 Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids
Introduction Introduction Forecasting PV model Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 3
Forecasting PV model Introduction Forecasting PV model Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 4 Model Forecasting model for photovoltaic energy production
Forecasting PV model Introduction Forecasting PV model Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 4 Model Forecasting model for photovoltaic energy production Aim To obtain an accurately daily forecast for a PV energy production plant located in Italy with a quarter-hour frequency
Forecasting PV model Introduction Forecasting PV model Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 4 Model Forecasting model for photovoltaic energy production Aim To obtain an accurately daily forecast for a PV energy production plant located in Italy with a quarter-hour frequency Technique Support Vector Machines, in particular -SVR
Forecasting PV model Introduction Forecasting PV model Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 4 Model Forecasting model for photovoltaic energy production Aim To obtain an accurately daily forecast for a PV energy production plant located in Italy with a quarter-hour frequency Technique Support Vector Machines, in particular -SVR Scenario * scientific challenge: photovoltaic production depends on weather conditions * increasing development of electrical smartgrids
Support Vector Machines Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 5
-SVR (1) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 6 Support Vector Machines (SVM) nonparametric technique for data classification (SVC) and regression (SVR)
-SVR (1) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 6 Support Vector Machines (SVM) nonparametric technique for data classification (SVC) and regression (SVR) -SVR Given training data {(x1, y1), . . . , (xl, yl)}, where xi are input vectors and yi are the associated output values for xi, the support vector regression model requires the solution of the following optimization problem:
-SVR (1) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 6 Support Vector Machines (SVM) nonparametric technique for data classification (SVC) and regression (SVR) -SVR Given training data {(x1, y1), . . . , (xl, yl)}, where xi are input vectors and yi are the associated output values for xi, the support vector regression model requires the solution of the following optimization problem: min w,b,, 1 2 wTw + C l Xi=1 i + − (+ i ) subject to yi − (wT (xi) + b) + + i , (wT (xi) + b) − yi + − i , + i , − i 0, i = 1, . . . , l.
-SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are
-SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are the cost of error C
-SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are the cost of error C the width of the tube
-SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are the cost of error C the width of the tube the mapping function
-SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are the cost of error C the width of the tube the mapping function In dual formulation of the problem, the kernel function is introduced k(xi, x) = (xi)T (x)
-SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are the cost of error C the width of the tube the mapping function In dual formulation of the problem, the kernel function is introduced k(xi, x) = (xi)T (x) Kernel function Formulation Linear k(x, y) = xTAy Polynomial k(x, y) = (xT x + c)d Radial Basis Function (RBF) k(x, y) = e− kx−yk2 Principal kernel functions.
-SVR Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 8 -SVR The -Support Vector Machine problem is defined as follows:
-SVR Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 8 -SVR The -Support Vector Machine problem is defined as follows: min w,b,, 1 2 wTw + C( + 1 l l Xi=1 i + − (+ i )) subject to yi − (wT (xi) + b) + + i , (wT (xi) + b) − yi + − i , + i , − i 0, i = 1, . . . , l. where the parameter allows to control the number of support vectors and training errors.
Photovoltaic Energy Production Model Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 9
Model data (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 10 Collected measurements: historical data of an existing solar photovoltaic plant located in Angeli di Rosora (AN, Italy), provided by the Loccioni Group. Solyndra panels positioned on the roof of an industrial facility of Loccioni Group.
Model data (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 11 energy and power produced by the plant solar irradiance external environmental temperature
Model data (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 11 energy and power produced by the plant solar irradiance external environmental temperature Scatterplot of correlation between solar irradiance and energy production from the PV plant.
Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features:
Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features: solar irradiance
Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features: solar irradiance external environmental temperature
Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features: solar irradiance external environmental temperature -SVR training output features:
Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features: solar irradiance external environmental temperature -SVR training output features: energy production
Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features: solar irradiance external environmental temperature -SVR training output features: energy production Parameters choice 1. kernel type: Radial Basis Function (RBF) 2. constant appearing in kernel formula: = 1/features 3. number of support vectors: = 0.5 4. cost of error: C = 1.8 5. training data: 14 days
Prediction accuracy measures Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 13 Root Mean Square Error (RMSE) RMSE = rPn i=1(yi − ˆyi)2 n
Prediction accuracy measures Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 13 Root Mean Square Error (RMSE) RMSE = rPn i=1(yi − ˆyi)2 n Mean Absolute Percentage Error (MAPE) MAPE = 100% n n Xi=1 | yi − ˆyi yi |
Prediction accuracy measures Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 13 Root Mean Square Error (RMSE) RMSE = rPn i=1(yi − ˆyi)2 n Mean Absolute Percentage Error (MAPE) MAPE = 100% n n Xi=1 | yi − ˆyi yi | Coefficient of Determination (R2) R2 = Pn 2 i=1(ˆyi − ¯y)n 2 i=1(yi − ¯y)P
Prediction accuracy measures Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 13 Root Mean Square Error (RMSE) RMSE = rPn i=1(yi − ˆyi)2 n Mean Absolute Percentage Error (MAPE) MAPE = 100% n n Xi=1 | yi − ˆyi yi | Coefficient of Determination (R2) R2 = Pn 2 i=1(ˆyi − ¯y)n 2 i=1(yi − ¯y)Pwhere yi = actual data, ˆyi = estimated data, ¯y = mean of the actual data.
Computational results Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 14
Results (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 15 Comparison between real and forecasted PV energy production on 15th of June 2012.
Results (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 15 Comparison between real and forecasted PV energy production on 15th of June 2012. RMSE = 0.5275; MAPE = 0.0785; R2 = 0.9944.
Results (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 16 Scatterplot of correlation between real and forecasted energy production.
Results (3) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 17 Comparison between real and forecasted PV energy production on 16th of April 2012.
Results (3) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 17 Comparison between real and forecasted PV energy production on 16th of April 2012. RMSE = 0.2810; MAPE = 0.1143; R2 = 0.9926.
Results (4) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids What does it happen when the input values of solar irradiance for the next day are not fully accurate? 18
Results (4) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids What does it happen when the input values of solar irradiance for the next day are not fully accurate? 18 Comparison between real and forecasted solar irradiance on 11th of October 2013.
Results (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 19 Comparison between real energy production on 11th of October 2013 and forecasted one using actual data of irradiance and temperature and estimated weather data.
Results (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 19 Comparison between real energy production on 11th of October 2013 and forecasted one using actual data of irradiance and temperature and estimated weather data. RMSE = 3.5876; MAPE = 3.5718; R2 = 0.3616.
Observations about the model Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids accurate results compared with the three different evaluation statistics 20 (RMSE, MAPE, R2);
Observations about the model Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids accurate results compared with the three different evaluation statistics 20 (RMSE, MAPE, R2); predictive model risk concerning with forecasted errors on input weather data provided by internet weather site;
Observations about the model Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids accurate results compared with the three different evaluation statistics 20 (RMSE, MAPE, R2); predictive model risk concerning with forecasted errors on input weather data provided by internet weather site; good application of -SVR model with the possibility of choosing the number of support vectors.
Energy production, use and storage in smartgrids Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 21
Leaf Community (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 22 The study on photovoltaic energy production forecast is part of a greater project realized by Loccioni Group: the Leaf Community smartgrid. Leaf Community smartgrid by Loccioni Group.
Leaf Community (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 22 The study on photovoltaic energy production forecast is part of a greater project realized by Loccioni Group: the Leaf Community smartgrid.
Leaf Community (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 23 Leaf Community smartgrid consists of
Leaf Community (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 23 Leaf Community smartgrid consists of energy production systems from renewable sources: photovoltaic plant micro-hydroelectric power station
Leaf Community (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 23 Leaf Community smartgrid consists of energy production systems from renewable sources: photovoltaic plant micro-hydroelectric power station consumption buildings: industrial facility office building
Leaf Community (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 23 Leaf Community smartgrid consists of energy production systems from renewable sources: photovoltaic plant micro-hydroelectric power station consumption buildings: industrial facility office building energy storage device.
Leaf Community (3) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 24 The smartgrid architecture scheme.
Leaf Community System Model Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 25 The smartgrid optimization model will manage the energy flows within the network in order to ensure the maximum economic benefit achieve the goal of energy autonomy for the most of time.
Leaf Community System Model Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 25 The smartgrid optimization model will manage the energy flows within the network in order to ensure the maximum economic benefit achieve the goal of energy autonomy for the most of time. Flow chart of the smartgrid optimization problem.
Optimization Problem Formulation (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 26 The optimization problem is formulated as a mixed-integer linear programming problem.
Optimization Problem Formulation (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 26 The optimization problem is formulated as a mixed-integer linear programming problem. Each component of the smartgrid is modeled separately, based on its characteristics and constraints.
Optimization Problem Formulation (2a) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 27 Input data
Optimization Problem Formulation (2a) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 27 Input data • photovoltaic energy production forecast Photovoltaic energy production forecast using -SVR.
Optimization Problem Formulation (2b) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 28 Input data
Optimization Problem Formulation (2b) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 28 Input data • energy consumption forecast Energy consumption forecast using linear regression.
Optimization Problem Formulation (2c) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 29 Input data
Optimization Problem Formulation (2c) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 29 Input data • electricity tariffs Selling and purchased electricity tariffs.
Optimization Problem Formulation (3a) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 30 Problem data (t) energy purchased price at time t (e/kWh) cIND(t) energy consumption of the industrial facility at time t (kWh) cOF(t) energy consumption of the office building at time t (kWh) e(0) energy present in the battery storage at time 0 (kWh) pPV (t) photovoltaic energy production at time t (kWh) pHD(t) hydropower production at time t (kWh) (t) energy selling price at time t (e/kWh)
Optimization Problem Formulation (3b) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 31 Problem parameters cINV energy consumption of the inverter (kWh) m minimum energy to charge/discharge the battery storage (kWh) M maximum energy to charge/discharge the battery storage (kWh) mESS minimum energy capacity of the battery storage (kWh) MESS maximum energy capacity of the battery storage (kWh) C charging efficiency of the battery storage D discharging efficiency of the battery storage T1 efficiency of the transformer T1 T2 efficiency of the transformer T2
Optimization Problem Formulation (3c) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 32 Problem variables b1(t) energy to buy for Block 1 at time t (kWh) b2(t) energy to buy for Block 2 at time t (kWh) e(t) amount of energy present in the battery storage at time t (kWh) b(t) buying/not buying energy at time t (kWh) s(t) selling/not selling energy at time t (kWh) r12(t) residual energy from Block 1 to Block 2 at time t (kWh) s(t) energy to sell at time t (kWh) x1(t) energy sent to the battery storage from Block 1 at time t (kWh) x(t) energy sent to the battery storage from the main grid at time t (kWh) y1(t) energy to discharge from the battery storage to Block 1 at time t (kWh) y2(t) energy to discharge from the battery storage to Block 2 at time t (kWh) C(t) charging state of the battery storage at time t D(t) discharging state of the battery storage at time t
Optimization Problem Formulation (4) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 33 Objective function 192 Xt=1 h(t)s(t)T1 − (t)b1(t) + b2(t)i Maximize the difference between the income deriving from the sold energy to the main distribution grid and the cost paid for the purchased energy, whenever the generated output power from the renewable energy sources is insufficient to cover the load demand.
Optimization Problem Formulation (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 34 Constraints
Optimization Problem Formulation (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 34 Constraints Energy balance constraints: energy purchased from utility grid + energy generated by the different sources = the local demand + the energy loss in the transmission lines + the energy stored in the battery.
Optimization Problem Formulation (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 34 Constraints Energy balance constraints: energy purchased from utility grid + energy generated by the different sources = the local demand + the energy loss in the transmission lines + the energy stored in the battery. Battery storage constraints: capacity of the battery; battery charging/discharging range; energy level present in the battery; impossibility to simultaneously charge/discharge the storage.
Optimization Problem Formulation (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 34 Constraints Energy balance constraints: energy purchased from utility grid + energy generated by the different sources = the local demand + the energy loss in the transmission lines + the energy stored in the battery. Battery storage constraints: capacity of the battery; battery charging/discharging range; energy level present in the battery; impossibility to simultaneously charge/discharge the storage. Main grid constraints: only energy produced from the renewable sources can be sold; impossibility to simultaneously purchase/sell energy.
Leaf Community Optimization Problem: Results (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 35 The energy curves for two winter days with the storage fully charged.
Leaf Community Optimization Problem: Results (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 36 The energy curves for two summer days with the storage fully discharged.
Conclusions Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 37 The study on photovoltaic energy production forecast becomes an important tool in order to manage the energy flows in the smartgrid. The correctness of the forecasts is determinant for a good result of the optimization algorithm. Due to the time-varying nature of the consumptions and the variation of the battery state of charge, the optimization problem needs to respond to continuously changing operation conditions. Good results of the optimization problem are obtained.

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Power Production Forecasting

  • 1. 1 Power Production and Storage in Microgrids R. De Leone, A. Giovannelli, M. Pietrini† AIRO 2014, September 2014 Research@Energy, Loccioni Group, Angeli di Rosora, AN, Italy † Mathematics Division, School of Science and Technologies, University of Camerino, MC, Italy
  • 2. Contents Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 2 Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids
  • 3. Introduction Introduction Forecasting PV model Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 3
  • 4. Forecasting PV model Introduction Forecasting PV model Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 4 Model Forecasting model for photovoltaic energy production
  • 5. Forecasting PV model Introduction Forecasting PV model Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 4 Model Forecasting model for photovoltaic energy production Aim To obtain an accurately daily forecast for a PV energy production plant located in Italy with a quarter-hour frequency
  • 6. Forecasting PV model Introduction Forecasting PV model Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 4 Model Forecasting model for photovoltaic energy production Aim To obtain an accurately daily forecast for a PV energy production plant located in Italy with a quarter-hour frequency Technique Support Vector Machines, in particular -SVR
  • 7. Forecasting PV model Introduction Forecasting PV model Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 4 Model Forecasting model for photovoltaic energy production Aim To obtain an accurately daily forecast for a PV energy production plant located in Italy with a quarter-hour frequency Technique Support Vector Machines, in particular -SVR Scenario * scientific challenge: photovoltaic production depends on weather conditions * increasing development of electrical smartgrids
  • 8. Support Vector Machines Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 5
  • 9. -SVR (1) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 6 Support Vector Machines (SVM) nonparametric technique for data classification (SVC) and regression (SVR)
  • 10. -SVR (1) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 6 Support Vector Machines (SVM) nonparametric technique for data classification (SVC) and regression (SVR) -SVR Given training data {(x1, y1), . . . , (xl, yl)}, where xi are input vectors and yi are the associated output values for xi, the support vector regression model requires the solution of the following optimization problem:
  • 11. -SVR (1) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 6 Support Vector Machines (SVM) nonparametric technique for data classification (SVC) and regression (SVR) -SVR Given training data {(x1, y1), . . . , (xl, yl)}, where xi are input vectors and yi are the associated output values for xi, the support vector regression model requires the solution of the following optimization problem: min w,b,, 1 2 wTw + C l Xi=1 i + − (+ i ) subject to yi − (wT (xi) + b) + + i , (wT (xi) + b) − yi + − i , + i , − i 0, i = 1, . . . , l.
  • 12. -SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are
  • 13. -SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are the cost of error C
  • 14. -SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are the cost of error C the width of the tube
  • 15. -SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are the cost of error C the width of the tube the mapping function
  • 16. -SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are the cost of error C the width of the tube the mapping function In dual formulation of the problem, the kernel function is introduced k(xi, x) = (xi)T (x)
  • 17. -SVR (2) Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 7 The parameters which control the regression quality are the cost of error C the width of the tube the mapping function In dual formulation of the problem, the kernel function is introduced k(xi, x) = (xi)T (x) Kernel function Formulation Linear k(x, y) = xTAy Polynomial k(x, y) = (xT x + c)d Radial Basis Function (RBF) k(x, y) = e− kx−yk2 Principal kernel functions.
  • 18. -SVR Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 8 -SVR The -Support Vector Machine problem is defined as follows:
  • 19. -SVR Introduction Support Vector Machines -SVR (1) -SVR (2) -SVR Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids 8 -SVR The -Support Vector Machine problem is defined as follows: min w,b,, 1 2 wTw + C( + 1 l l Xi=1 i + − (+ i )) subject to yi − (wT (xi) + b) + + i , (wT (xi) + b) − yi + − i , + i , − i 0, i = 1, . . . , l. where the parameter allows to control the number of support vectors and training errors.
  • 20. Photovoltaic Energy Production Model Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 9
  • 21. Model data (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 10 Collected measurements: historical data of an existing solar photovoltaic plant located in Angeli di Rosora (AN, Italy), provided by the Loccioni Group. Solyndra panels positioned on the roof of an industrial facility of Loccioni Group.
  • 22. Model data (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 11 energy and power produced by the plant solar irradiance external environmental temperature
  • 23. Model data (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 11 energy and power produced by the plant solar irradiance external environmental temperature Scatterplot of correlation between solar irradiance and energy production from the PV plant.
  • 24. Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features:
  • 25. Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features: solar irradiance
  • 26. Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features: solar irradiance external environmental temperature
  • 27. Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features: solar irradiance external environmental temperature -SVR training output features:
  • 28. Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features: solar irradiance external environmental temperature -SVR training output features: energy production
  • 29. Model construction Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 12 -SVR training input features: solar irradiance external environmental temperature -SVR training output features: energy production Parameters choice 1. kernel type: Radial Basis Function (RBF) 2. constant appearing in kernel formula: = 1/features 3. number of support vectors: = 0.5 4. cost of error: C = 1.8 5. training data: 14 days
  • 30. Prediction accuracy measures Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 13 Root Mean Square Error (RMSE) RMSE = rPn i=1(yi − ˆyi)2 n
  • 31. Prediction accuracy measures Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 13 Root Mean Square Error (RMSE) RMSE = rPn i=1(yi − ˆyi)2 n Mean Absolute Percentage Error (MAPE) MAPE = 100% n n Xi=1 | yi − ˆyi yi |
  • 32. Prediction accuracy measures Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 13 Root Mean Square Error (RMSE) RMSE = rPn i=1(yi − ˆyi)2 n Mean Absolute Percentage Error (MAPE) MAPE = 100% n n Xi=1 | yi − ˆyi yi | Coefficient of Determination (R2) R2 = Pn 2 i=1(ˆyi − ¯y)n 2 i=1(yi − ¯y)P
  • 33. Prediction accuracy measures Introduction Support Vector Machines Photovoltaic Energy Production Model Model data (1) Model data (2) Model construction Prediction accuracy measures Computational results Energy production, use and storage in smartgrids 13 Root Mean Square Error (RMSE) RMSE = rPn i=1(yi − ˆyi)2 n Mean Absolute Percentage Error (MAPE) MAPE = 100% n n Xi=1 | yi − ˆyi yi | Coefficient of Determination (R2) R2 = Pn 2 i=1(ˆyi − ¯y)n 2 i=1(yi − ¯y)Pwhere yi = actual data, ˆyi = estimated data, ¯y = mean of the actual data.
  • 34. Computational results Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 14
  • 35. Results (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 15 Comparison between real and forecasted PV energy production on 15th of June 2012.
  • 36. Results (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 15 Comparison between real and forecasted PV energy production on 15th of June 2012. RMSE = 0.5275; MAPE = 0.0785; R2 = 0.9944.
  • 37. Results (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 16 Scatterplot of correlation between real and forecasted energy production.
  • 38. Results (3) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 17 Comparison between real and forecasted PV energy production on 16th of April 2012.
  • 39. Results (3) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 17 Comparison between real and forecasted PV energy production on 16th of April 2012. RMSE = 0.2810; MAPE = 0.1143; R2 = 0.9926.
  • 40. Results (4) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids What does it happen when the input values of solar irradiance for the next day are not fully accurate? 18
  • 41. Results (4) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids What does it happen when the input values of solar irradiance for the next day are not fully accurate? 18 Comparison between real and forecasted solar irradiance on 11th of October 2013.
  • 42. Results (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 19 Comparison between real energy production on 11th of October 2013 and forecasted one using actual data of irradiance and temperature and estimated weather data.
  • 43. Results (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids 19 Comparison between real energy production on 11th of October 2013 and forecasted one using actual data of irradiance and temperature and estimated weather data. RMSE = 3.5876; MAPE = 3.5718; R2 = 0.3616.
  • 44. Observations about the model Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids accurate results compared with the three different evaluation statistics 20 (RMSE, MAPE, R2);
  • 45. Observations about the model Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids accurate results compared with the three different evaluation statistics 20 (RMSE, MAPE, R2); predictive model risk concerning with forecasted errors on input weather data provided by internet weather site;
  • 46. Observations about the model Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Results (1) Results (2) Results (3) Results (4) Results (5) Observations about the model Energy production, use and storage in smartgrids accurate results compared with the three different evaluation statistics 20 (RMSE, MAPE, R2); predictive model risk concerning with forecasted errors on input weather data provided by internet weather site; good application of -SVR model with the possibility of choosing the number of support vectors.
  • 47. Energy production, use and storage in smartgrids Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 21
  • 48. Leaf Community (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 22 The study on photovoltaic energy production forecast is part of a greater project realized by Loccioni Group: the Leaf Community smartgrid. Leaf Community smartgrid by Loccioni Group.
  • 49. Leaf Community (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 22 The study on photovoltaic energy production forecast is part of a greater project realized by Loccioni Group: the Leaf Community smartgrid.
  • 50. Leaf Community (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 23 Leaf Community smartgrid consists of
  • 51. Leaf Community (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 23 Leaf Community smartgrid consists of energy production systems from renewable sources: photovoltaic plant micro-hydroelectric power station
  • 52. Leaf Community (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 23 Leaf Community smartgrid consists of energy production systems from renewable sources: photovoltaic plant micro-hydroelectric power station consumption buildings: industrial facility office building
  • 53. Leaf Community (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 23 Leaf Community smartgrid consists of energy production systems from renewable sources: photovoltaic plant micro-hydroelectric power station consumption buildings: industrial facility office building energy storage device.
  • 54. Leaf Community (3) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 24 The smartgrid architecture scheme.
  • 55. Leaf Community System Model Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 25 The smartgrid optimization model will manage the energy flows within the network in order to ensure the maximum economic benefit achieve the goal of energy autonomy for the most of time.
  • 56. Leaf Community System Model Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 25 The smartgrid optimization model will manage the energy flows within the network in order to ensure the maximum economic benefit achieve the goal of energy autonomy for the most of time. Flow chart of the smartgrid optimization problem.
  • 57. Optimization Problem Formulation (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 26 The optimization problem is formulated as a mixed-integer linear programming problem.
  • 58. Optimization Problem Formulation (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 26 The optimization problem is formulated as a mixed-integer linear programming problem. Each component of the smartgrid is modeled separately, based on its characteristics and constraints.
  • 59. Optimization Problem Formulation (2a) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 27 Input data
  • 60. Optimization Problem Formulation (2a) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 27 Input data • photovoltaic energy production forecast Photovoltaic energy production forecast using -SVR.
  • 61. Optimization Problem Formulation (2b) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 28 Input data
  • 62. Optimization Problem Formulation (2b) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 28 Input data • energy consumption forecast Energy consumption forecast using linear regression.
  • 63. Optimization Problem Formulation (2c) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 29 Input data
  • 64. Optimization Problem Formulation (2c) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 29 Input data • electricity tariffs Selling and purchased electricity tariffs.
  • 65. Optimization Problem Formulation (3a) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 30 Problem data (t) energy purchased price at time t (e/kWh) cIND(t) energy consumption of the industrial facility at time t (kWh) cOF(t) energy consumption of the office building at time t (kWh) e(0) energy present in the battery storage at time 0 (kWh) pPV (t) photovoltaic energy production at time t (kWh) pHD(t) hydropower production at time t (kWh) (t) energy selling price at time t (e/kWh)
  • 66. Optimization Problem Formulation (3b) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 31 Problem parameters cINV energy consumption of the inverter (kWh) m minimum energy to charge/discharge the battery storage (kWh) M maximum energy to charge/discharge the battery storage (kWh) mESS minimum energy capacity of the battery storage (kWh) MESS maximum energy capacity of the battery storage (kWh) C charging efficiency of the battery storage D discharging efficiency of the battery storage T1 efficiency of the transformer T1 T2 efficiency of the transformer T2
  • 67. Optimization Problem Formulation (3c) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 32 Problem variables b1(t) energy to buy for Block 1 at time t (kWh) b2(t) energy to buy for Block 2 at time t (kWh) e(t) amount of energy present in the battery storage at time t (kWh) b(t) buying/not buying energy at time t (kWh) s(t) selling/not selling energy at time t (kWh) r12(t) residual energy from Block 1 to Block 2 at time t (kWh) s(t) energy to sell at time t (kWh) x1(t) energy sent to the battery storage from Block 1 at time t (kWh) x(t) energy sent to the battery storage from the main grid at time t (kWh) y1(t) energy to discharge from the battery storage to Block 1 at time t (kWh) y2(t) energy to discharge from the battery storage to Block 2 at time t (kWh) C(t) charging state of the battery storage at time t D(t) discharging state of the battery storage at time t
  • 68. Optimization Problem Formulation (4) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 33 Objective function 192 Xt=1 h(t)s(t)T1 − (t)b1(t) + b2(t)i Maximize the difference between the income deriving from the sold energy to the main distribution grid and the cost paid for the purchased energy, whenever the generated output power from the renewable energy sources is insufficient to cover the load demand.
  • 69. Optimization Problem Formulation (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 34 Constraints
  • 70. Optimization Problem Formulation (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 34 Constraints Energy balance constraints: energy purchased from utility grid + energy generated by the different sources = the local demand + the energy loss in the transmission lines + the energy stored in the battery.
  • 71. Optimization Problem Formulation (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 34 Constraints Energy balance constraints: energy purchased from utility grid + energy generated by the different sources = the local demand + the energy loss in the transmission lines + the energy stored in the battery. Battery storage constraints: capacity of the battery; battery charging/discharging range; energy level present in the battery; impossibility to simultaneously charge/discharge the storage.
  • 72. Optimization Problem Formulation (5) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 34 Constraints Energy balance constraints: energy purchased from utility grid + energy generated by the different sources = the local demand + the energy loss in the transmission lines + the energy stored in the battery. Battery storage constraints: capacity of the battery; battery charging/discharging range; energy level present in the battery; impossibility to simultaneously charge/discharge the storage. Main grid constraints: only energy produced from the renewable sources can be sold; impossibility to simultaneously purchase/sell energy.
  • 73. Leaf Community Optimization Problem: Results (1) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 35 The energy curves for two winter days with the storage fully charged.
  • 74. Leaf Community Optimization Problem: Results (2) Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 36 The energy curves for two summer days with the storage fully discharged.
  • 75. Conclusions Introduction Support Vector Machines Photovoltaic Energy Production Model Computational results Energy production, use and storage in smartgrids Leaf Community (1) Leaf Community (2) Leaf Community (3) Leaf Community System Model Optimization Problem Formulation (1) Optimization Problem Formulation (2a) Optimization Problem Formulation (2b) Optimization Problem Formulation (2c) Optimization Problem Formulation (3a) Optimization Problem Formulation (3b) Optimization Problem Formulation (3c) 37 The study on photovoltaic energy production forecast becomes an important tool in order to manage the energy flows in the smartgrid. The correctness of the forecasts is determinant for a good result of the optimization algorithm. Due to the time-varying nature of the consumptions and the variation of the battery state of charge, the optimization problem needs to respond to continuously changing operation conditions. Good results of the optimization problem are obtained.