DAY AHEAD FORECAST OF SOLAR POWER FOR OPTIMAL GRID OPERATION Jeenu Jose 1, Vijaya Margaret 2 1 PG Scholar, Department of Electrical & Electronics Engineering, Christ Uinversity, India. 2 Assistant Professor, Department of Electrical & Electronics Engineering, Christ Uinversity, India. Abstract: The demand for power is ever increasing in the wake of energy crisis faced by the world. With the decreasing conventional energy resources, green and environmental-friendly renewable energy (solar energy, wind energy, biomass energy) have already raised a focus of attention. However, the solar resource at ground level is highly dependent on local meteorological conditions, rendering it inherently variable. This poses a major threat to the reliability of power dispatch. As a result, high accuracy forecasts are required on multiple time horizons. This paper has targeted to investigate statistical models like Moving Average, Regression s, Single Exponential Smoothing and Holt Winter s models and also hybrid models These models are used for a day ahead Solar Power prediction. Keywords Forecast, Hybrid s,statistical s, Solar Irradiance, Solar Power. 1. INTRODUCTION The world now uses energy at a rate of approximately 13TW [1].One of the major challenges faced by scientists today is the inability to meet the ever increasing energy demands. With the rise in human population and increasing energy needs the conventional energy resources like fossil fuels are being insufficient. Hence the demand for renewable energy resources is increasing day by day. Of the various renewable resources solar energy is the most popular as it is clean and it can be easily harnessed than any other form of renewable resources. The major drawback of solar energy lies in its non-continuous generation: PV power drops as the Solar Irradiance drops. A significant decrease in the grid's PV power delivery due to reduced irradiance can pose problems for grid operators who must compensate for the shortfall. For effective integration of PV power generator s to the existing grid it is essential to forecast the accurate solar power generation [2]. The solar power generation mainly depends on Solar Irradiance and Air Temperature. Hence accurate forecasting of solar irradiance is very essential for prediction of solar power. Forecasting is the process of making statements about events whose actual outcomes have not yet been observed. Forecasting is designed to help decision making and planning in the present. Frequently there is a time lag between awareness of an impending event or need and occurrence of that event. This lead time is the main reason for planning and forecasting. If the lead time is zero or very small there is no need for planning. If the lead time is long and the outcome of the final event is conditional on identifiable factors, planning can perform an important role. In such situations forecasting is needed to determine when an event will occur or a need arises, so that appropriate actions could be taken [2]. www.jrret.com 82
In this paper we develop various models to predict the day ahead solar irradiance and hence solar power which is very essential for the optimal operation of the grid. The various statistical models discussed here are Regression s, Time Series s like Moving Average, Exponential Smoothing s and Holt Winter s s. Here we also discuss the hybrid model of Artificial Neural Network built for forecasting the solar power. The errors of each models and its drawbacks are also discussed in the subsequent sections. The data used for this paper is collected from Bagalkot Weather station for the months of February through May 2013. The data samples are available for every minute in the given period. Here since the amount of data is huge, the data was normalized by averaging it to ten minutes. For the models proposed in this paper a portion of the available data was used as training set and a portion of it used as test set. II. REGRESSION MODELS Linear Regression analysis is of two types single variate and multivariate analysis. In single variate analysis, the dependent variable is modeled as a linear function of a single independent variable. In this case, the solar irradiance is the dependent variable or forecast variable and the air temperature and relative humidity each are the independent variables [3-4]. In both single variate and multivariate regression, only the data points corresponding to non-zero solar irradiance values are considered. In this model, the solar irradiance for the dark period of each day, that is, the 14 hour period 18:09 pm to 7:08 am IST is considered to be zero. A. Solar Irradiance as a function of Air Temperature Here the input variable is Air Temperature while the output is Solar Irradiance. ANOVA table obtained from above procedure provides the coefficients and intercepts. The following equation (1) is formed after extracting the data: SI = - (846.724) + 35.3621*AT (1) Fig 1 Line fit plot for Solar Irradiance as a Function of Air Temperature B. Solar Irradiance as a function of Relative Humidity The input variable is Relative Humidity while the output is Solar Irradiance, which is same as previous model. The equation for this single variate model is defined in equation (2) SI = 761.7121-7.75085*RH (2) Fig 2 Line fit plot for Solar Irradiance as a function of Relative humidity www.jrret.com 83
Solar Irrad (Watts/m^2) Journal of Recent Research in Engineering and Technology As it can be seen from the above Fig 1 and 2, the single variate analysis does not effectively model the output. The goodness of fit with Air Temperature and relative humidity are just 12.70% and 15.54% respectively. Hence it is evident that multivariate regression model is to be done to get a better fitting model. C. Multi Variate Linear Regression Multi Variate Regression model with Air Temperature and relative humidity as input variables and Solar Irradiance as the output variable is modeled. The linear equation of solar irradiance from the model is given in equation (3). SI = 868.7226 2.81035*AT 8.60128*RH (3) III. TIME SERIES MODELS A time series is a sequence of observations on a variable measured at successive points in time or over successive periods of time. The measurements may be taken every hour, day, week, month, or year, or at any other regular interval. The pattern of the data is an important factor in understanding how the time series has behaved in the past. If such behaviour can be expected to continue in the future, we can use the past pattern to guide us in selecting an appropriate forecasting method [5]. The various time series models that are used in this paper are discussed in the subsequent sections. A. Moving Average This model specifies on modifying the influence of all past data to specify how many past values will be included in the mean. The idea behind this is that the future is affected only by the recent past. Moving Averages are a fundamental building block in all the decomposition methods [3].Moving average describes the procedure of trend cycle. Each average is computed by dropping the oldest observation and including the next observation. The formula for moving average is as given by the equation (4). (4) Here we consider the non-zero points only for analysis from 7:09am to 18:08pm. Since the data is normalized for 10 minutes we obtain 66 samples per day for analysis. However a major drawback for Moving Average is that a too large value of interval can result in an erroneous forecasting model. Hence this model is not suitable for day ahead forecasting of solar irradiance. The plot of moving average model with an interval of 66 for a day ahead prediction is shown in Fig 3. 800 600 400 200 0 1 8 1522293643505764 Time (in 10 min) Fig 3 Plot of moving average Solar Irradiance prediction B. Single Exponential Smoothing actual forecast Extension of moving average is forecast by weighted moving average (the weighting scheme stresses that the most recent past will provide best indication of future). Single Exponential smoothing is one such weighted method [3]. This gives better result than the moving averages when there are abrupt jumps in the data. In exponential smoothing there are one or more smoothing parameters to be determined explicitly and these choices determine the weights assigned to the observations. The equation for single exponential smoothing forecasting model is given below F t+1 = F t + α (Y t F t ) (5) www.jrret.com 84
Solar irrad (watts/m^2) Solar irrad (watts/m^2) Journal of Recent Research in Engineering and Technology Different values of damping factors were tried for the solar irradiance data 29 days and the forecast was validated using the values of solar irradiance of the next day of the month of April 2013. By determining the mean square and optimizing it to least value the optimal value of α was determined to be 0.6825. The curve showing day ahead solar irradiance with optimal value of α is shown in Fig 4. 800 600 400 200 0 1 7 131925313743495561 Time (in 10 min) Fig 4 Day ahead prediction of Solar Irradiance using Single Exponential Smoothing C. Holt Winter s Single exponential smoothing method is mostly used for simple data with no trend or seasonal component. But when the data has any of these components, the double and triple exponential smoothing is considered for better modeling of the data. This method is also called as the Holt-Winter s method [6]. This method is popular because it is simple, has low data-storage requirements, and is easily automated. It also has the advantage of being able to adapt to changes in trends and seasonal patterns when they occur. This means that slowdowns or speed-ups in demand, or changing solar irradiance [7]. It achieves this by updating its estimates of these patterns as soon as each new data arrives. Double Exponential Smoothing actual forecast α=0.6825 If data contains not only level but also trend component like solar irradiance we go for double exponential smoothing where level component is given by smoothing factor α and trend is given by β [3]. The specific formula for simple double exponential smoothing is given by equations (6) and (7). Level: L t = α (Y t ) + (1 α) (L t-1 + b t-1 ) (6) Trend: b t = β (L t L t-1 ) + (1 β) b t-1 (7) The forecast is obtained from both the level and trend components, Forecast: F t+m = L t + b t m (8) The following double exponential smoothing analysis is carried out in Microsoft Excel in a feature called Double Exponential Smoothing available under Num Excel which is an add on in Microsoft Excel. The Fig 5 below shows the double exponential smoothing curve during the month February 2013 for optimal value of α and β. 800 600 400 200 0-200 1 7 131925313743495561 Time (in 10 min) Fig 5 Plot of day ahead double exponential smoothing Solar Irradiance Triple Exponential Smoothing Triple exponential smoothing method is used when the data shows trend and seasonality. To handle seasonality, we have to add a third parameter γ [3]. The formula for triple exponential smoothing is given below. Level:Lt = α (Yt St-s) + (1 α) (Lt-1 + bt-1) Trend: bt = β (Lt Lt-1) + (1 β) bt-1 Seasonal: St = γ (Yt Lt) + (1 γ) St-s actual forecast α=0.6825 β=0.5679 (9) (10) (11) www.jrret.com 85
The forecast is obtained from the level, trend and seasonal components as in equation (12) Forecast: F t+m = L t + b t m + S t-s+m (12) The triple exponential smoothing analysis is carried out in Microsoft Excel feature called Triple Exponential Smoothing available under Num Excel which is an add on in Microsoft Excel. The Fig 6 below show the triple exponential smoothing curves for optimal value of α, β and γ. or more hidden layers, whose nodes are called hidden neurons [9]. The function of hidden neuron is to interpose between the external input and the network output in some useful manner[10]. In this model the input is taken as solar irradiance and air temperature. The output is solar power. Here we consider only non-zero points so we have 66 samples of solar irradiance and air temperature respectively. The output also contains 66 samples. By using an iterative method we determine the number of neurons in the hidden layer. We get the best results with four number of neurons. The Fig 7 shows the prediction of day ahead solar power using ANN. Here we using one month data for training and predict the next month s solar power. Fig 6 Plot of day ahead solar irradiance forecast using triple exponential smoothing Once the solar irradiance is predicted using the above mentioned models the day ahead solar power can be determined from the equation (13) P PV = η PV S I (1 0.005 (t 0 + 25)) Watts (13) Where, η PV is the conversion efficiency of PV array, S is the area of PV array, I is the solar irradiance, t 0 is air temperature.here the conversion efficiency is taken to be 35% [8]. IV. HYBRID MODELS The hybrid model discussed in this paper is Artificial Neural Network (ANN). For short term forecasting of solar power using ANN we use Multilayer Feed forward Networks. A Feed forward neural network consists of one Fig 7 Plot of day ahead solar power using ANN V. ERROR COMPARISON OF DIFFERENT MODELS The mean average percentage error (MAPE) of different models for day ahead prediction of solar irradiance is shown in the table below. www.jrret.com 86
One day ahead prediction MAPE Moving Average Regression Single Exponential Double Exponential Triple Exponential Hybrid (ANN) Journal of Recent Research in Engineering and Technology Table 1: Error comparison for day ahead forecast of solar power for different models Holt Winter s REFERENCES [1] Renée M. Nault, Basic Research Needs for Solar Energy Utilization Report on the Basic Energy Sciences Workshop on Solar Energy Utilization, A survey published by Argonne National Laboratory, Apr. 18-21, 2005. 102.7 4 97.8 1 37.3 2 27.8 3 24.8 3 15.07 [2] Prema V. and Uma Rao K, Predictive s For Power Management Of A Hybrid Microgrid-A Review, 2nd International Conference on Advances in Energy Conversion Technologies (ICAECT 2014), Manipal, India,pp. 7-12, 23-25 Jan. 2014. VI. CONCLUSION The data was analyzed extensively before the models were fitted. Multivariate and single variate linear regression models were fitted for the data to forecast solar irradiance from air temperature and relative humidity. However we see that the error of regression models is high compared to time series models. In time series models we see Holt Winter s models are best suited for forecasting solar power than any other models. However the data manipulation in time series models is difficult hence we go for hybrid models such as ANN. Here once we train the data we can use the model to predict the solar power for any day. Moreover the MAPE is very less for ANN than any other models developed. The detailed investigations and research into different models have proved that Solar Power generation could be predicted for a day ahead with great accuracy. These results will help to plan the spinning reserves and scheduling of conventional generators in our power system which helps in the optimal operation of the grid. [3] J. W. Taylor, L. M. de Menezes, and P. E. McSharry, "A comparison of univariate methods for forecasting electricity demand up to a day ahead," International Journal of Forecasting, vol. 22, pp. 1-16, June 2006. [4] Sypros Makridakis, Steven C Wheelwright and Rob J Hyndman, Forecasting Methods and Applications, Wiley Student Edition, 3rd edition, 2013. [5] Henrik Madsen, Henrik Aalborg Nielsen, Tryggvi Jonsson, Pierre Pinson, Peder Bacher, "Forecasting of Wind and Solar Power Production", Research Thesis, Technical University of Denmark, Nov. 2011. [6] Zibo Dong, Dazhi Yang, Wilfred M.Walsh, Thomas Reindl, Armin Abrle, "Short-term Solar Irradiance Forecasting Using Exponential Smoothing State Space " International Journal of Energy, vol. 55, pp. 1104 1113, Jun. 2013. [7] P.J.Brockwell and R.A.Davis, "Time Series: Theory and Methods", Springer, 2nd edition, 2013. [8] Cheng Hang, Ge Peng-jiang, Cao Wushun, "Forecasting Research of Longterm Solar Irradiance and Output Power for Photovoltaic generation system", IEEE Fourth International Conference on www.jrret.com 87
Computational and Information Sciences, Chongqing, China, pp. 1224-1227, Aug. 2012. [9] Slobodan A. Ilic, Srdjan M. Vukmirovic, Aleksandar M. Erdeljan, and Filip J. Kulic, Hybrid Artificial Neural Network System For Short-Term Load Forecasting, International Journal of Hybrid Artificial Neural Network System for Short-Term Thermal Science, vol. 16, pp. S215-S224, 2012. [10] Rabindra Behera, Bibhu Prasad Panigrahi, Bibhuti Bhusan Pati, A Hybrid Short Term Load Forecasting of an Indian Grid, International Journal of Energy and Power Engineering, vol. 3, no. 2, pp. 190-193, May 2011. www.jrret.com 88