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Forecasting Power Output of Photovoltaic System Using A BP Network Method
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9th International Conference on Applied Energy, ICAE2017, 21-24 August 2017, Cardiff, UK
Forecasting Power Output of Photovoltaic System Using A BP The 15th International Symposium on District Heating and Cooling Network Method aa a a*of usingb a Assessing feasibility the heat demand-outdoor Luyao Liuthe ,, Diran Diran Liu Liua, Qie Qie Sun Suna*, Hailong Hailong Li Lib,, Ronald Ronald Wennersten Wennerstena Institute Science University, Road and temperature function for aShandong long-term district heatJinan demand forecast Institute of of Thermal Thermal Science and and Technology, Technology, Shandong University, Jingshi Jingshi Road No.17923, No.17923, Jinan and 250061, 250061, China China aa
b bSchool
School of of Business, Business, Society Society and and Technology, Technology, Mälardalen Mälardalen University, University, Sweden Sweden
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc a
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract Abstract b c
Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
The The characteristics characteristics of of intermittent intermittent and and stochastic stochastic of of solar solar energy energy has has brought brought great great challenges challenges to to power power grid grid system system in in terms terms of of operation operation and and regulation. regulation. Power Power forecasting forecasting is is an an important important factor factor for for optimal optimal schedule schedule of of power power grid grid system system and and assessing assessing the the working working performance performance of of PV PV systems. systems. In In order order to to forecast forecast the the power power output output of of aa PV PV system system located located in in Ashland Ashland at at 24-hour-ahead 24-hour-ahead for for higher efficiency, higher efficiency, aa back back propagation propagation (BP) (BP) neural neural network network model model is is proposed. proposed. Before Before designing designing the the model, model, correlation correlation analysis analysis is is Abstract done done to to investigate investigate the the relationship relationship between between power power output output and and solar solar irradiance irradiance and and ambient ambient temperature, temperature, which which are are key key parameters parameters affecting power output systems. on analysis, the admitted the parameters: affecting the power output of of PV systems. Based Based on aaincorrelation correlation analysis, theofmodel model admitted the following following input parameters: District the heating networks arePV commonly addressed the literature as one the most effective solutions input for decreasing the hourly solar intensity, highest, the lowest daily the and power of hourly solar radiation radiation intensity, thethe highest, thesector. lowestThese daily and and the average average daily temperature, and hourly hourly power output output of the the PV PV greenhouse gas emissions fromthe building systems requiredaily high temperature, investments which are returned through heat system. The the is forecasted PV output 24 ahead. on the network is system. The output output ofchanged the model model is the theconditions forecasted and PV power power output 24 hours hourspolicies, ahead. Based Based on the the datasets, datasets, the neural neural network is sales. Due to the of climate building renovation heat demand in the future could decrease, trained to improve its accuracy. The best performance is obtained with the BP neural network structure of 28-20-11. The analysis trained to improve its accuracy. The best performance is obtained with the BP neural network structure of 28-20-11. The analysis prolonging the investment return period. of the error indicator MAPE shows the proposed model has accuracy and for the output of ofThe the main error scope indicator MAPE shows that thethe proposed model has great great accuracy and–efficiency efficiency for forecasting forecasting the power power output of of this paper is to that assess feasibility of using the heat demand outdoor temperature function for heat demand photovoltaic systems. photovoltaic systems. forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 © 2017 Published by Ltd. ©buildings 2017 The The Authors. Authors. Published by Elsevier Elsevierperiod Ltd. and typology. Three weather scenarios (low, medium, high) and three district vary in both construction © 2017 Thethat Authors. Published by Elsevier Ltd. committee of the 9th International Conference on Applied Energy. Peer-review under responsibility of the scientific Peer-review under responsibility of the scientific of 9th on renovation scenarios were developed (shallow, intermediate, deep). To estimate Conference the error, obtained heatEnergy. demand values were Peer-review under responsibility of the scientific committee committee of the the 9th International International Conference on Applied Applied Energy. compared with results from a dynamic heat demand model, previously developed and validated by the authors. Keywords: PV power BP variables; correlation analysis Keywords: PV showed power forecast; forecast; BP neural neural network; input variables; correlationthe analysis The results that when only network; weather input change is considered, margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1. Introduction 1.The Introduction value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and The of and stochastic of energy brought challenges to systems renovation scenarios considered). On the hand, function increased for great 7.8-12.7% per decade (depending on in the The characteristics characteristics of intermittent intermittent andother stochastic of solar solarintercept energy has has brought great challenges to power power systems in terms of due potentially unpredictable fluctuations [1]. At the same PV coupled scenarios). and Theregulation values suggested be used to modify thegrid function parameters considered, and terms of operation operation and regulation due to to could potentially unpredictable grid fluctuations [1].for At the thescenarios same time, time, PV power power improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * * Qie Sun. Tel.: +86-0531-88399000-2306. Qie Sun. Tel.: +86-0531-88399000-2306. Cooling. E-mail E-mail address: address: [email protected] [email protected]
Keywords: Heat demand; Forecast; Climate change 1876-6102 © 1876-6102 © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. Peer-review Peer-review under under responsibility responsibility of of the the scientific scientific committee committee of of the the 9th 9th International International Conference Conference on on Applied Applied Energy. Energy. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy. 10.1016/j.egypro.2017.12.126
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generation technology is the focus of renewable energy and the scale of PV technology including many kinds of application has kept growing in the world [2]. Therefore, prediction of PV power output is an important issue for planning and managing of grid systems. The traditional physical prediction method for forecasting PV outputs consists of the solar radiation model, PV conversion model and the circuit and inverter model. However, the uncertainty in solar radiation, blocking by the cloud, rainy weather, battery temperature and other factors will reduce the accuracy of short-term predictions [3]. The prediction method of power output based on statistics and artificial neural network (ANN) technology can largely compensate the influence of the above factors [4]. The accuracy of the methods is dependent on the volume of data. Generally speaking, continuous and complete datasets for several months are necessary for training an ANN model to obtain satisfying results [5]. In addition, the quality and characteristics of the data, e.g. sampling interval, accuracy, collection, pretreatment and standardization will also affect the accuracy [6]. Another important issue for forecasting PV outputs is the determination of key factors, which can affect the selection and application of specific ANN technology. Various methods such as radial basis function network (RBFN) model, support vector machine (SVM) and other hybrid models that considered different factors have been developed [7][8][9]. However, the RBFN method needs more neurons and the fitting results are sensitive; while the SVM algorithms have limitations in solving nonlinear regression problems; the implementation of hybrid models adds to more complexity. In general, the above studies have recognized key factors and obtained relatively good results. However, these models don’t have a wide applicability and have some shortcomings in training process. To summarize, a good ANN model should consider the characteristics of the systems and the environmental information in order to generate high-quality results. The training algorithm should also be easy to adjust for good prediction effect. Among ANN-related methods, back propagation (BP) neural network has been more widely used and can effectively realize the forecasting. A prominent feature of BP-based forecasting method is its strong generality, large fault data tolerance and excellent nonlinear mapping ability, especially suitable for solving complex regression problems [10]. Recently, based on the shortcomings such as slow convergence rate and easy to fall into local minimum value, some improved algorithms have been developed on BP network to enhance better convergence [11] Therefore, the contribution of this paper is aimed at looking into the data processing and disposing meticulously and estimating power output of a PV system. To this aim, a BP neural network based on adaptive learning rate and weight is proposed. The data is collected from a PV system in Ashland, Oregon, with an installed capacity of 15kW, which is recorded every one hour. The hourly solar radiation is collected from NASA [12], the daily air temperature comes from a meteorological website [13]. First, the paper conducted a correlation analysis to choose proper input variables and classified the data type before selecting the similar day. Then, BP neural network was trained by historical meteorological data and hourly power output of PV system, after which weather datasets of the objective day were used as input variables of the model to predict hourly PV power output. Finally, an error analysis was performed to validate and test the model in order to ensure the forecast accuracy and achieve the optimal performance. 2. Data processing Many factors, such as solar irradiation, air temperature and wind speed can influence the output of PV systems. The output characteristics can largely be influenced by weather variables and the accuracy of network forecasting relies heavily on the chosen input variables [14]. The accuracy of the forecasting model may be enhanced using large number of inputs, while the computational complexity will be also increased. Hence, it is important to determine the optimal number of model inputs to deal with complexity issue [15]. Therefore, this paper performed a correlation analysis of the historical data to identify the variables that are closely correlated with the power output. 2.1 Correlation analysis of main factors A correlation analysis of PV power output with solar intensity and air temperature has been conducted, by using Pearson product-moment correlation coefficient (PPMCC) (1), based on continuous hourly historical data in several typical days.
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𝑟𝑟𝑥𝑥,𝑦𝑦 =
cov(x, y) = 𝜎𝜎𝑥𝑥 𝜎𝜎𝑦𝑦
3
1 𝑛𝑛 ∑ (𝑥𝑥 − 𝑥𝑥̅ )(𝑦𝑦𝑖𝑖 − 𝑦𝑦̅) 𝑛𝑛 𝑖𝑖=1 𝑖𝑖 √1 ∑𝑛𝑛𝑖𝑖=1(𝑥𝑥𝑖𝑖 − 𝑥𝑥̅ )2 √1 ∑𝑛𝑛𝑖𝑖=1(𝑦𝑦𝑖𝑖 − 𝑦𝑦̅)2 𝑛𝑛 𝑛𝑛
(1)
where cov (x, y) is the covariance of the variables x and y, 𝜎𝜎𝑥𝑥 and 𝜎𝜎𝑦𝑦 are the standard deviations of s x and y. The relationship between PV power and solar radiation intensity and air temperature are shown in Table1. Table 1 Correlation analysis of PV power with solar intensity and ambient temperature Date
Season type
Weather type
G-P
T-P
2013.01.13
Winter
Sunny
0.9741
0.1243
2013.03.04
Spring
Sunny
0.9515
0.6321
2013.05.30
Summer
Sunny
0.9801
-0.0844
2013.10.18
Autumn
Sunny
0.9795
-0.0906
2013.03.05
Spring
Overcast
0.8507
0.3424
2013.03.06
Spring
Drizzle to cloudy
0.6656
0.8106
2013.03.19
Spring
Cloudy to overcast
0.9218
-0.2367
2013.03.26
Spring
Sunny to cloudy
0.8559
-0.1492
2013.03.31
Spring
Moderate rainy
0.8538
-0.3151
2013.04.20
Spring
Sunny
0.9762
0.0579
As is shown, the PV power output shows a strong linear correlation with the hourly solar radiation intensity. The correlation coefficients in different seasons and weather conditions are all close to 1, and the minimum value under a rainy day is greater than 0.6. For air temperature, it is found that the relationship between power output and air temperature is a little complicated, which is neither positive nor negative linear. That is, the PV power output shows a non-linear correlation with air temperature, which cannot be described simply. Therefore, air temperature is an important parameter that will influence the power output. Considering the calculation complexity, we choose the historical power output sequence P1(i), P2(i)…P11(i) (i.e. at the time i) from 8am to 6am, the hourly solar intensity G1(i), G2(i)…G11(i) (i.e. at the day i), the highest, the lowest and the average temperature of the previous day and the objective day 𝑇𝑇ℎ(𝑖𝑖) , 𝑇𝑇𝑙𝑙(𝑖𝑖) , 𝑇𝑇𝑎𝑎(𝑖𝑖) , 𝑇𝑇ℎ(𝑖𝑖+1) , 𝑇𝑇𝑙𝑙(𝑖𝑖+1) , 𝑇𝑇𝑎𝑎(𝑖𝑖+1) as input variables. 2.2 Similar day selection
2013.03.05 2013.03.06 2013.03.19 2013.03.26 2013.04.20 2013.03.31
15000 12000 9000 6000 3000
15000
Power output(W)
Power output (W)
The historical PV output data may contain different spikes and non-stationary components due to uncertain and variable meteorological conditions [16]. In fact, different weather and season types can largely influence the power output characteristics of PV systems, as can be seen from Fig. 1 and Fig. 2. The corresponding season and weather information is shown in Table1. 2013.01.13 2013.03.04 2013.05.30 2013.10.18
12000 9000 6000 3000 0
0
Time (h) Fig. 1 Power output curves in different weather types.
Time (h)
Fig. 2 Power output curves in different seasons.
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The influence of weather types on the PV power output is obvious, which is due to the great difference in solar radiation intensity. Fig. 1 shows the power output curves of Ashland 15 kW PV system under the same season type and different weather conditions. As can be seen, the power output curves change greatly with different weather types. This difference is not only reflected in power output changing trend, but also in the magnitude. The seasonal variation of solar intensity also results in the seasonal difference of the power output. Fig. 2 represents the PV power output curves under the same weather type and different seasons. As can be seen, the power output curves show the similar changing trend under the same weather conditions. However, there are some differences in the power size in different seasons, which is mainly caused by the difference of solar intensity in different seasons. From the above analysis, it is found that the values of power output of PV system vary largely with different weather and season types. As a result, these non-stationary and spikes in data of power output will leads to higher forecast error due to improper data preprocessing. In this paper, we use historical data in sunny days to make the power output prediction. In order to select the closest date which has similar weather conditions to the objective forecasting day, here we conducted a similar day algorithm. The daily feature vectors in the similar day algorithm can be set as follows (2): 𝑋𝑋𝑖𝑖 = [𝐺𝐺1(𝑖𝑖) , 𝐺𝐺2(𝑖𝑖) … 𝐺𝐺11(𝑖𝑖) , 𝑇𝑇ℎ(𝑖𝑖) , 𝑇𝑇𝑎𝑎(𝑖𝑖) , 𝑇𝑇𝑙𝑙(𝑖𝑖), 𝑇𝑇ℎ(𝑖𝑖+1) , 𝑇𝑇𝑎𝑎(𝑖𝑖+1) , 𝑇𝑇𝑙𝑙(𝑖𝑖+1) ]
(2)
Where 𝑋𝑋𝑖𝑖 represents the daily feature vector sets at day i. We use Euclidean distance (3) to describe the overall difference of meteorological factors between the two days. 2 𝑑𝑑𝑖𝑖𝑖𝑖 = √∑𝑚𝑚 𝑘𝑘=1(𝑥𝑥𝑖𝑖𝑖𝑖 − 𝑥𝑥𝑗𝑗𝑗𝑗 )
(3)
Where 𝑑𝑑𝑖𝑖𝑖𝑖 represents Euclidean distance between feature vectors of 𝑥𝑥𝑖𝑖𝑖𝑖 and 𝑥𝑥𝑗𝑗𝑗𝑗 in days i and j; k is the serial number of the feature vector; m indicates the number of feature vectors. If the correlation value is greater than a certain value, the data of the selected day can be used. 3. Model description 3.1 Nodes selection for the model The relationship between PV power output and the multiple factors are nonlinear and complex, which can be estimated based on the weights and the bias of the optimal BP network structure by using a non-linear approximation function [17]. Hence, it is important to select the proper parameters. In general, a BP model consists of one input layer, one hidden layer and one output layer. Therefore, the prediction model can be constructed when the network parameters are determined [18]. The input layer nodes correspond to the input variables and the number of input layer nodes cannot be too much nor insufficient. As is analyzed above, the input layer nodes number in this paper is set as 28. In this paper, the number of hidden layer nodes is initially set according to the below empirical formula (4): 𝑁𝑁ℎ = √𝑁𝑁𝑖𝑖 + 𝑁𝑁𝑜𝑜 + 𝑎𝑎
(4)
Where 𝑁𝑁ℎ is the number of the hidden layer nodes; 𝑁𝑁𝑖𝑖 is the number of input layer nodes; 𝑁𝑁𝑜𝑜 represents the number of output nodes. Usually 𝑎𝑎 is a constant number between 1 to 5. Here we set the hidden nodes as 12 preliminarily. For the output layer, the output layer gives as parameters the hourly PV power output from 8am to 6pm at the next day (i.e. at the day i+ 1). Thus, the number of the output layer of the model is 11. 3.2 Model training and forecasting After the first step of setting the structure of the model, the selection of the number and quality of the datasets are
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5
also crucial [19]. Before applying the training algorithm, individual singular observations should be removed, and the input data should be normalized to [0, 1] using Eq. (5) to avoid the saturation of neurons at the same time. 𝑥𝑥𝑖𝑖𝑖𝑖 ∗ =
𝑥𝑥𝑖𝑖𝑖𝑖 −𝑥𝑥𝑚𝑚𝑚𝑚𝑚𝑚
𝑥𝑥𝑚𝑚𝑚𝑚𝑚𝑚 −𝑥𝑥𝑚𝑚𝑚𝑚𝑚𝑚
(5)
where 𝑥𝑥𝑖𝑖𝑖𝑖 is the original data value; 𝑥𝑥𝑖𝑖𝑖𝑖 ∗ is the corresponding normalized variable; 𝑦𝑦𝑚𝑚𝑚𝑚𝑚𝑚 and 𝑦𝑦𝑚𝑚𝑚𝑚𝑚𝑚 is the minimum value and the maximum value in original data sets, respectively. When 𝑥𝑥𝑖𝑖𝑖𝑖 is the minimum value in the datasets, 𝑥𝑥𝑖𝑖𝑖𝑖 ∗ correspond to 0; when 𝑥𝑥𝑖𝑖𝑖𝑖 is the maximum value in the datasets, 𝑥𝑥𝑖𝑖𝑖𝑖 ∗ correspond to 1. All the historical datasets are divided into three groups, of which the datasets of the three months from March to May are used to train the model repeatedly and find the optimal weights and the bias of the BP neural network. The data of one month of June is used for validating, while the final part of datasets is used for testing. After training the model, we use the well trained model to forecast the power output of the forecasting day. According to similar day principle, we choose the historical data of the similar day as input variables to make the prediction of July 2nd 2013. Similarly, the data of the closest previous days can be selected as the inputs of the prediction model for the different forecasting days July 3 rd, July 4th and July 5th. The forecast scheme was simulated on MATLAB R2015a. The model was optimized by varying the following internal network parameters: activation functions, dataset division ratios, data pre-processing functions, number of hidden neurons, performance functions and training algorithms. The optimal network structure was identified on the base of the performance plot, training state plot, and scatter plot. 3.3 Error evaluation In order to evaluate the obtained results, the mean absolute percentage error (MAPE) is used, which is given in the below formula (6). The error index provides information on the short-term performance and represents a measure of the variation of predicted values around the measured data. MAPE =
1
𝑁𝑁
∑𝑁𝑁 𝑖𝑖=1 |
𝑃𝑃𝑖𝑖 −𝑃𝑃𝑖𝑖 ∗ 𝑃𝑃𝑖𝑖
| × 100%
(6)
Where 𝑃𝑃𝑖𝑖 is the measured value of power out of the system; 𝑃𝑃𝑖𝑖 ∗ is the forecasting value of the power output. N represents the number of model forecasting samples. Different simulations have been performed in order to compare errors. And the error analysis is used to select the optimal number of hidden nodes.
4. Results and discusssion The number of the neurons within the hidden layers is optimized during the learning step of the network, according with a specified criterion of MAPE in this paper. Finally, the number of the hidden layer nodes is selected to be 20. Fig.3 presents the optimum network configuration for BP network model in MATLAB platform. The optimal network structure was identified on the basis of the performance plot, training state plot, and scatter plot in Fig.4.
Fig.3 Optimum network configuration for BP neural network model in MATLAB R2015a.
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Fig.4 The performance plot, training state plot and scatter plot of optimum network.
Fig.5 indicate the changing curves of the forecasted values of power output and measured data by BP neural network model for July 2nd, 2013. Fig.6 shows the absolute errors between the two kinds of data. As can be seen, the predicted values of power output have a good agreement with the measured values for this day. Similarly, the results for the other three different forecasting days can be compared.
Fig. 5 Comparison curves between forecasting and measured power output
Fig.6 Absolute errors between forecasting and measures values
In addition, the calculated error indexes of MAPE are summarized in Table 2 for different forecasting days (July 2nd–5th 2013). According to the results obtained in Table 2, it can be noticed that the corresponding error of MAPE is 6.78%, 6.93%, 7.67%, and 7.27% for four different forecasting days on July 2nd, 3rd, 4th and 5th, 2013. Table 2 Error comparison for four forecasting days Forecasting date
MAPE(%)
July 2nd
6.78
July 3rd
6.93
July 4th
7.67
July 5th
7.27
As can be seen from the comparison, the errors are within a reasonable range and the developed BP neural network model is very suitable for the prediction of power output of the PV system used in this paper. 5. Conclusions This paper designed an improved adaptive neural network forecasting model by using BP algorithm. The model accepts as input parameters the hourly solar radiation intensity, the highest daily temperature, the lowest daily temperature, the average daily temperature, and the hourly power output of the PV system. For the output layer, in
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this paper, the output layer gives as parameters the hourly power output of the PV system from 8am to 6pm at the next day. After several simulations, the best performance is obtained with the following settings: the number of neurons in the input layer is 28, the number of neurons in the output layer is 11, and the numbers of hidden nodes is 20. Results from the application of the proposed method to an actual PV power system show that it can be employed to forecast the daily power output of PV power system precisely. This method can play a very important role in an efficient planning of the operation of PV power systems. Acknowledgements This work was supported in part by Project ZR2014EEM025 supported by Natural Science Foundation of Shandong Province, China; and the 973 Program 2013CB228305, China.
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9th International Conference on Applied Energy, ICAE2017, 21-24 August 2017, Cardiff, UK
Forecasting Power Output of Photovoltaic System Using A BP The 15th International Symposium on District Heating and Cooling Network Method aa a a*of usingb a Assessing feasibility the heat demand-outdoor Luyao Liuthe ,, Diran Diran Liu Liua, Qie Qie Sun Suna*, Hailong Hailong Li Lib,, Ronald Ronald Wennersten Wennerstena Institute Science University, Road and temperature function for aShandong long-term district heatJinan demand forecast Institute of of Thermal Thermal Science and and Technology, Technology, Shandong University, Jingshi Jingshi Road No.17923, No.17923, Jinan and 250061, 250061, China China aa
b bSchool
School of of Business, Business, Society Society and and Technology, Technology, Mälardalen Mälardalen University, University, Sweden Sweden
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc a
IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract Abstract b c
Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
The The characteristics characteristics of of intermittent intermittent and and stochastic stochastic of of solar solar energy energy has has brought brought great great challenges challenges to to power power grid grid system system in in terms terms of of operation operation and and regulation. regulation. Power Power forecasting forecasting is is an an important important factor factor for for optimal optimal schedule schedule of of power power grid grid system system and and assessing assessing the the working working performance performance of of PV PV systems. systems. In In order order to to forecast forecast the the power power output output of of aa PV PV system system located located in in Ashland Ashland at at 24-hour-ahead 24-hour-ahead for for higher efficiency, higher efficiency, aa back back propagation propagation (BP) (BP) neural neural network network model model is is proposed. proposed. Before Before designing designing the the model, model, correlation correlation analysis analysis is is Abstract done done to to investigate investigate the the relationship relationship between between power power output output and and solar solar irradiance irradiance and and ambient ambient temperature, temperature, which which are are key key parameters parameters affecting power output systems. on analysis, the admitted the parameters: affecting the power output of of PV systems. Based Based on aaincorrelation correlation analysis, theofmodel model admitted the following following input parameters: District the heating networks arePV commonly addressed the literature as one the most effective solutions input for decreasing the hourly solar intensity, highest, the lowest daily the and power of hourly solar radiation radiation intensity, thethe highest, thesector. lowestThese daily and and the average average daily temperature, and hourly hourly power output output of the the PV PV greenhouse gas emissions fromthe building systems requiredaily high temperature, investments which are returned through heat system. The the is forecasted PV output 24 ahead. on the network is system. The output output ofchanged the model model is the theconditions forecasted and PV power power output 24 hours hourspolicies, ahead. Based Based on the the datasets, datasets, the neural neural network is sales. Due to the of climate building renovation heat demand in the future could decrease, trained to improve its accuracy. The best performance is obtained with the BP neural network structure of 28-20-11. The analysis trained to improve its accuracy. The best performance is obtained with the BP neural network structure of 28-20-11. The analysis prolonging the investment return period. of the error indicator MAPE shows the proposed model has accuracy and for the output of ofThe the main error scope indicator MAPE shows that thethe proposed model has great great accuracy and–efficiency efficiency for forecasting forecasting the power power output of of this paper is to that assess feasibility of using the heat demand outdoor temperature function for heat demand photovoltaic systems. photovoltaic systems. forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 © 2017 Published by Ltd. ©buildings 2017 The The Authors. Authors. Published by Elsevier Elsevierperiod Ltd. and typology. Three weather scenarios (low, medium, high) and three district vary in both construction © 2017 Thethat Authors. Published by Elsevier Ltd. committee of the 9th International Conference on Applied Energy. Peer-review under responsibility of the scientific Peer-review under responsibility of the scientific of 9th on renovation scenarios were developed (shallow, intermediate, deep). To estimate Conference the error, obtained heatEnergy. demand values were Peer-review under responsibility of the scientific committee committee of the the 9th International International Conference on Applied Applied Energy. compared with results from a dynamic heat demand model, previously developed and validated by the authors. Keywords: PV power BP variables; correlation analysis Keywords: PV showed power forecast; forecast; BP neural neural network; input variables; correlationthe analysis The results that when only network; weather input change is considered, margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1. Introduction 1.The Introduction value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and The of and stochastic of energy brought challenges to systems renovation scenarios considered). On the hand, function increased for great 7.8-12.7% per decade (depending on in the The characteristics characteristics of intermittent intermittent andother stochastic of solar solarintercept energy has has brought great challenges to power power systems in terms of due potentially unpredictable fluctuations [1]. At the same PV coupled scenarios). and Theregulation values suggested be used to modify thegrid function parameters considered, and terms of operation operation and regulation due to to could potentially unpredictable grid fluctuations [1].for At the thescenarios same time, time, PV power power improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * * Qie Sun. Tel.: +86-0531-88399000-2306. Qie Sun. Tel.: +86-0531-88399000-2306. Cooling. E-mail E-mail address: address: [email protected] [email protected]
Keywords: Heat demand; Forecast; Climate change 1876-6102 © 1876-6102 © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. Peer-review Peer-review under under responsibility responsibility of of the the scientific scientific committee committee of of the the 9th 9th International International Conference Conference on on Applied Applied Energy. Energy. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy. 10.1016/j.egypro.2017.12.126
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generation technology is the focus of renewable energy and the scale of PV technology including many kinds of application has kept growing in the world [2]. Therefore, prediction of PV power output is an important issue for planning and managing of grid systems. The traditional physical prediction method for forecasting PV outputs consists of the solar radiation model, PV conversion model and the circuit and inverter model. However, the uncertainty in solar radiation, blocking by the cloud, rainy weather, battery temperature and other factors will reduce the accuracy of short-term predictions [3]. The prediction method of power output based on statistics and artificial neural network (ANN) technology can largely compensate the influence of the above factors [4]. The accuracy of the methods is dependent on the volume of data. Generally speaking, continuous and complete datasets for several months are necessary for training an ANN model to obtain satisfying results [5]. In addition, the quality and characteristics of the data, e.g. sampling interval, accuracy, collection, pretreatment and standardization will also affect the accuracy [6]. Another important issue for forecasting PV outputs is the determination of key factors, which can affect the selection and application of specific ANN technology. Various methods such as radial basis function network (RBFN) model, support vector machine (SVM) and other hybrid models that considered different factors have been developed [7][8][9]. However, the RBFN method needs more neurons and the fitting results are sensitive; while the SVM algorithms have limitations in solving nonlinear regression problems; the implementation of hybrid models adds to more complexity. In general, the above studies have recognized key factors and obtained relatively good results. However, these models don’t have a wide applicability and have some shortcomings in training process. To summarize, a good ANN model should consider the characteristics of the systems and the environmental information in order to generate high-quality results. The training algorithm should also be easy to adjust for good prediction effect. Among ANN-related methods, back propagation (BP) neural network has been more widely used and can effectively realize the forecasting. A prominent feature of BP-based forecasting method is its strong generality, large fault data tolerance and excellent nonlinear mapping ability, especially suitable for solving complex regression problems [10]. Recently, based on the shortcomings such as slow convergence rate and easy to fall into local minimum value, some improved algorithms have been developed on BP network to enhance better convergence [11] Therefore, the contribution of this paper is aimed at looking into the data processing and disposing meticulously and estimating power output of a PV system. To this aim, a BP neural network based on adaptive learning rate and weight is proposed. The data is collected from a PV system in Ashland, Oregon, with an installed capacity of 15kW, which is recorded every one hour. The hourly solar radiation is collected from NASA [12], the daily air temperature comes from a meteorological website [13]. First, the paper conducted a correlation analysis to choose proper input variables and classified the data type before selecting the similar day. Then, BP neural network was trained by historical meteorological data and hourly power output of PV system, after which weather datasets of the objective day were used as input variables of the model to predict hourly PV power output. Finally, an error analysis was performed to validate and test the model in order to ensure the forecast accuracy and achieve the optimal performance. 2. Data processing Many factors, such as solar irradiation, air temperature and wind speed can influence the output of PV systems. The output characteristics can largely be influenced by weather variables and the accuracy of network forecasting relies heavily on the chosen input variables [14]. The accuracy of the forecasting model may be enhanced using large number of inputs, while the computational complexity will be also increased. Hence, it is important to determine the optimal number of model inputs to deal with complexity issue [15]. Therefore, this paper performed a correlation analysis of the historical data to identify the variables that are closely correlated with the power output. 2.1 Correlation analysis of main factors A correlation analysis of PV power output with solar intensity and air temperature has been conducted, by using Pearson product-moment correlation coefficient (PPMCC) (1), based on continuous hourly historical data in several typical days.
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𝑟𝑟𝑥𝑥,𝑦𝑦 =
cov(x, y) = 𝜎𝜎𝑥𝑥 𝜎𝜎𝑦𝑦
3
1 𝑛𝑛 ∑ (𝑥𝑥 − 𝑥𝑥̅ )(𝑦𝑦𝑖𝑖 − 𝑦𝑦̅) 𝑛𝑛 𝑖𝑖=1 𝑖𝑖 √1 ∑𝑛𝑛𝑖𝑖=1(𝑥𝑥𝑖𝑖 − 𝑥𝑥̅ )2 √1 ∑𝑛𝑛𝑖𝑖=1(𝑦𝑦𝑖𝑖 − 𝑦𝑦̅)2 𝑛𝑛 𝑛𝑛
(1)
where cov (x, y) is the covariance of the variables x and y, 𝜎𝜎𝑥𝑥 and 𝜎𝜎𝑦𝑦 are the standard deviations of s x and y. The relationship between PV power and solar radiation intensity and air temperature are shown in Table1. Table 1 Correlation analysis of PV power with solar intensity and ambient temperature Date
Season type
Weather type
G-P
T-P
2013.01.13
Winter
Sunny
0.9741
0.1243
2013.03.04
Spring
Sunny
0.9515
0.6321
2013.05.30
Summer
Sunny
0.9801
-0.0844
2013.10.18
Autumn
Sunny
0.9795
-0.0906
2013.03.05
Spring
Overcast
0.8507
0.3424
2013.03.06
Spring
Drizzle to cloudy
0.6656
0.8106
2013.03.19
Spring
Cloudy to overcast
0.9218
-0.2367
2013.03.26
Spring
Sunny to cloudy
0.8559
-0.1492
2013.03.31
Spring
Moderate rainy
0.8538
-0.3151
2013.04.20
Spring
Sunny
0.9762
0.0579
As is shown, the PV power output shows a strong linear correlation with the hourly solar radiation intensity. The correlation coefficients in different seasons and weather conditions are all close to 1, and the minimum value under a rainy day is greater than 0.6. For air temperature, it is found that the relationship between power output and air temperature is a little complicated, which is neither positive nor negative linear. That is, the PV power output shows a non-linear correlation with air temperature, which cannot be described simply. Therefore, air temperature is an important parameter that will influence the power output. Considering the calculation complexity, we choose the historical power output sequence P1(i), P2(i)…P11(i) (i.e. at the time i) from 8am to 6am, the hourly solar intensity G1(i), G2(i)…G11(i) (i.e. at the day i), the highest, the lowest and the average temperature of the previous day and the objective day 𝑇𝑇ℎ(𝑖𝑖) , 𝑇𝑇𝑙𝑙(𝑖𝑖) , 𝑇𝑇𝑎𝑎(𝑖𝑖) , 𝑇𝑇ℎ(𝑖𝑖+1) , 𝑇𝑇𝑙𝑙(𝑖𝑖+1) , 𝑇𝑇𝑎𝑎(𝑖𝑖+1) as input variables. 2.2 Similar day selection
2013.03.05 2013.03.06 2013.03.19 2013.03.26 2013.04.20 2013.03.31
15000 12000 9000 6000 3000
15000
Power output(W)
Power output (W)
The historical PV output data may contain different spikes and non-stationary components due to uncertain and variable meteorological conditions [16]. In fact, different weather and season types can largely influence the power output characteristics of PV systems, as can be seen from Fig. 1 and Fig. 2. The corresponding season and weather information is shown in Table1. 2013.01.13 2013.03.04 2013.05.30 2013.10.18
12000 9000 6000 3000 0
0
Time (h) Fig. 1 Power output curves in different weather types.
Time (h)
Fig. 2 Power output curves in different seasons.
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The influence of weather types on the PV power output is obvious, which is due to the great difference in solar radiation intensity. Fig. 1 shows the power output curves of Ashland 15 kW PV system under the same season type and different weather conditions. As can be seen, the power output curves change greatly with different weather types. This difference is not only reflected in power output changing trend, but also in the magnitude. The seasonal variation of solar intensity also results in the seasonal difference of the power output. Fig. 2 represents the PV power output curves under the same weather type and different seasons. As can be seen, the power output curves show the similar changing trend under the same weather conditions. However, there are some differences in the power size in different seasons, which is mainly caused by the difference of solar intensity in different seasons. From the above analysis, it is found that the values of power output of PV system vary largely with different weather and season types. As a result, these non-stationary and spikes in data of power output will leads to higher forecast error due to improper data preprocessing. In this paper, we use historical data in sunny days to make the power output prediction. In order to select the closest date which has similar weather conditions to the objective forecasting day, here we conducted a similar day algorithm. The daily feature vectors in the similar day algorithm can be set as follows (2): 𝑋𝑋𝑖𝑖 = [𝐺𝐺1(𝑖𝑖) , 𝐺𝐺2(𝑖𝑖) … 𝐺𝐺11(𝑖𝑖) , 𝑇𝑇ℎ(𝑖𝑖) , 𝑇𝑇𝑎𝑎(𝑖𝑖) , 𝑇𝑇𝑙𝑙(𝑖𝑖), 𝑇𝑇ℎ(𝑖𝑖+1) , 𝑇𝑇𝑎𝑎(𝑖𝑖+1) , 𝑇𝑇𝑙𝑙(𝑖𝑖+1) ]
(2)
Where 𝑋𝑋𝑖𝑖 represents the daily feature vector sets at day i. We use Euclidean distance (3) to describe the overall difference of meteorological factors between the two days. 2 𝑑𝑑𝑖𝑖𝑖𝑖 = √∑𝑚𝑚 𝑘𝑘=1(𝑥𝑥𝑖𝑖𝑖𝑖 − 𝑥𝑥𝑗𝑗𝑗𝑗 )
(3)
Where 𝑑𝑑𝑖𝑖𝑖𝑖 represents Euclidean distance between feature vectors of 𝑥𝑥𝑖𝑖𝑖𝑖 and 𝑥𝑥𝑗𝑗𝑗𝑗 in days i and j; k is the serial number of the feature vector; m indicates the number of feature vectors. If the correlation value is greater than a certain value, the data of the selected day can be used. 3. Model description 3.1 Nodes selection for the model The relationship between PV power output and the multiple factors are nonlinear and complex, which can be estimated based on the weights and the bias of the optimal BP network structure by using a non-linear approximation function [17]. Hence, it is important to select the proper parameters. In general, a BP model consists of one input layer, one hidden layer and one output layer. Therefore, the prediction model can be constructed when the network parameters are determined [18]. The input layer nodes correspond to the input variables and the number of input layer nodes cannot be too much nor insufficient. As is analyzed above, the input layer nodes number in this paper is set as 28. In this paper, the number of hidden layer nodes is initially set according to the below empirical formula (4): 𝑁𝑁ℎ = √𝑁𝑁𝑖𝑖 + 𝑁𝑁𝑜𝑜 + 𝑎𝑎
(4)
Where 𝑁𝑁ℎ is the number of the hidden layer nodes; 𝑁𝑁𝑖𝑖 is the number of input layer nodes; 𝑁𝑁𝑜𝑜 represents the number of output nodes. Usually 𝑎𝑎 is a constant number between 1 to 5. Here we set the hidden nodes as 12 preliminarily. For the output layer, the output layer gives as parameters the hourly PV power output from 8am to 6pm at the next day (i.e. at the day i+ 1). Thus, the number of the output layer of the model is 11. 3.2 Model training and forecasting After the first step of setting the structure of the model, the selection of the number and quality of the datasets are
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5
also crucial [19]. Before applying the training algorithm, individual singular observations should be removed, and the input data should be normalized to [0, 1] using Eq. (5) to avoid the saturation of neurons at the same time. 𝑥𝑥𝑖𝑖𝑖𝑖 ∗ =
𝑥𝑥𝑖𝑖𝑖𝑖 −𝑥𝑥𝑚𝑚𝑚𝑚𝑚𝑚
𝑥𝑥𝑚𝑚𝑚𝑚𝑚𝑚 −𝑥𝑥𝑚𝑚𝑚𝑚𝑚𝑚
(5)
where 𝑥𝑥𝑖𝑖𝑖𝑖 is the original data value; 𝑥𝑥𝑖𝑖𝑖𝑖 ∗ is the corresponding normalized variable; 𝑦𝑦𝑚𝑚𝑚𝑚𝑚𝑚 and 𝑦𝑦𝑚𝑚𝑚𝑚𝑚𝑚 is the minimum value and the maximum value in original data sets, respectively. When 𝑥𝑥𝑖𝑖𝑖𝑖 is the minimum value in the datasets, 𝑥𝑥𝑖𝑖𝑖𝑖 ∗ correspond to 0; when 𝑥𝑥𝑖𝑖𝑖𝑖 is the maximum value in the datasets, 𝑥𝑥𝑖𝑖𝑖𝑖 ∗ correspond to 1. All the historical datasets are divided into three groups, of which the datasets of the three months from March to May are used to train the model repeatedly and find the optimal weights and the bias of the BP neural network. The data of one month of June is used for validating, while the final part of datasets is used for testing. After training the model, we use the well trained model to forecast the power output of the forecasting day. According to similar day principle, we choose the historical data of the similar day as input variables to make the prediction of July 2nd 2013. Similarly, the data of the closest previous days can be selected as the inputs of the prediction model for the different forecasting days July 3 rd, July 4th and July 5th. The forecast scheme was simulated on MATLAB R2015a. The model was optimized by varying the following internal network parameters: activation functions, dataset division ratios, data pre-processing functions, number of hidden neurons, performance functions and training algorithms. The optimal network structure was identified on the base of the performance plot, training state plot, and scatter plot. 3.3 Error evaluation In order to evaluate the obtained results, the mean absolute percentage error (MAPE) is used, which is given in the below formula (6). The error index provides information on the short-term performance and represents a measure of the variation of predicted values around the measured data. MAPE =
1
𝑁𝑁
∑𝑁𝑁 𝑖𝑖=1 |
𝑃𝑃𝑖𝑖 −𝑃𝑃𝑖𝑖 ∗ 𝑃𝑃𝑖𝑖
| × 100%
(6)
Where 𝑃𝑃𝑖𝑖 is the measured value of power out of the system; 𝑃𝑃𝑖𝑖 ∗ is the forecasting value of the power output. N represents the number of model forecasting samples. Different simulations have been performed in order to compare errors. And the error analysis is used to select the optimal number of hidden nodes.
4. Results and discusssion The number of the neurons within the hidden layers is optimized during the learning step of the network, according with a specified criterion of MAPE in this paper. Finally, the number of the hidden layer nodes is selected to be 20. Fig.3 presents the optimum network configuration for BP network model in MATLAB platform. The optimal network structure was identified on the basis of the performance plot, training state plot, and scatter plot in Fig.4.
Fig.3 Optimum network configuration for BP neural network model in MATLAB R2015a.
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Fig.4 The performance plot, training state plot and scatter plot of optimum network.
Fig.5 indicate the changing curves of the forecasted values of power output and measured data by BP neural network model for July 2nd, 2013. Fig.6 shows the absolute errors between the two kinds of data. As can be seen, the predicted values of power output have a good agreement with the measured values for this day. Similarly, the results for the other three different forecasting days can be compared.
Fig. 5 Comparison curves between forecasting and measured power output
Fig.6 Absolute errors between forecasting and measures values
In addition, the calculated error indexes of MAPE are summarized in Table 2 for different forecasting days (July 2nd–5th 2013). According to the results obtained in Table 2, it can be noticed that the corresponding error of MAPE is 6.78%, 6.93%, 7.67%, and 7.27% for four different forecasting days on July 2nd, 3rd, 4th and 5th, 2013. Table 2 Error comparison for four forecasting days Forecasting date
MAPE(%)
July 2nd
6.78
July 3rd
6.93
July 4th
7.67
July 5th
7.27
As can be seen from the comparison, the errors are within a reasonable range and the developed BP neural network model is very suitable for the prediction of power output of the PV system used in this paper. 5. Conclusions This paper designed an improved adaptive neural network forecasting model by using BP algorithm. The model accepts as input parameters the hourly solar radiation intensity, the highest daily temperature, the lowest daily temperature, the average daily temperature, and the hourly power output of the PV system. For the output layer, in
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this paper, the output layer gives as parameters the hourly power output of the PV system from 8am to 6pm at the next day. After several simulations, the best performance is obtained with the following settings: the number of neurons in the input layer is 28, the number of neurons in the output layer is 11, and the numbers of hidden nodes is 20. Results from the application of the proposed method to an actual PV power system show that it can be employed to forecast the daily power output of PV power system precisely. This method can play a very important role in an efficient planning of the operation of PV power systems. Acknowledgements This work was supported in part by Project ZR2014EEM025 supported by Natural Science Foundation of Shandong Province, China; and the 973 Program 2013CB228305, China.
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