ANN and Statistical Theory Based Forecasting and Analysis of Power System Variables

ANN and Statistical Theory Based Forecasting and Analysis of Power System Variables Sruthi V. Nair 1, Poonam Kothari 2, Kushal Lodha 3 1,2,3 Lecturer, G. H. Raisoni Institute of Engineering & Technology, Pune Abstract Careful planning of the electrical power sector is of great importance since the decisions to be taken involves the commitment of large resources, with potentially serious economic risks for the electrical utility and the economy as a whole. There are different types of techniques available for analysis and prediction of randomly varying parameters. They are classified as statistical, intelligent systems, time series, fuzzy logic, neural networks. In this paper the Weibull density function, Beta Density function and arithmetic mean method has been used to estimate the load demand. The results are compared to determine the most efficient method. Another issue of great importance is that day by day fossil fuels are getting depleted. Another option for conventional sources of energy is increase in generation of renewable sources of energy. Wind generation forecasting is necessary as large intermittent generations have influence on the grid security, system operation, and market economics. Although wind energy may not be dispatched, the cost impacts of wind can be substantially reduced if the wind energy can be scheduled using accurate wind speed forecasting. In this paper Statistical Method is used for analysis of load demand of power system and Artificial Neural Network (ANN) is used for wind speed forecasting. Keywords Artificial Neural Network, Backpropagation Algorithm, Wind speed forecasting, Statistical Method. I. INTRODUCTION This document is template. Load forecasting has always been the essential part of an efficient power system planning and operation. Several Electric Power companies have adopted several methods for forecasting the future demands. But these methods are not accurate and in today s competitive market accuracy in forecasting is vital to the business. In this paper statistical methodology of finding Weibull mean, Beta mean and arithmetic mean for analyzing and planning the load demands is are used. These methods are then compared with each other to determine the best possible planning technique. The required historical data is obtained from state Load Dispatch Centre, Kalwa. Along with it ANN based technique for wind speed prediction is used to increase the wind power penetration in Power sector. Wind speed prediction has applications not only in Electric sector but also in Military and Civilian fields for air traffic control, rocket launch, ship navigation, target tracking, missile guidance, and satellite launch. The wind speed in near future depends on the values of meteorological variables, such as atmospheric pressure, moisture content, humidity, temperature, and wind direction which are obtained from Meteorological Department, Shivajinagar. Several factors could improve the attractiveness of wind power to a utility: i. Improvements in the model accuracy of wind power forecasting. ii. iii. iv. Shorter start-up and ramping times for thermal plants. Changes in conventional plant mix such as a larger amount of fast response plants or energy storage. Load management to better accommodate fluctuations in available wind power. II. EVALUATION OF AVERAGE LOAD USING PROBABILITY THEORY There are two types of Probability Distributions: A. Continuous Probability Distribution B. Discrete Probability Distribution The load change in power system varies on daily, weekly, monthly and seasonal basis. So the probability distribution of load changes is continuous. Various weather variables could be considered for load forecasting. Temperature and humidity are the parameters which affect the most. The electric usage pattern is different for customers that belong to different classes. Hence, most utilities distinguish load behavior on a class-by-class basis. The algorithm for evaluation of load demand is as follows: Collection of Data Calculation of Arithmetic Average Arrange the Data in a proper Range and find out the occurrences Normalization of the data Calculation of Standard Deviation & Mean 753

Calculate Shape Parameters Calculation of Beta PDF Values Draw Beta PDF graph & Weibull density function graph. Hourly values of Load demand for January month of 2009, 2010 and 2011 is collected for analysis. A. Calculation of Arithmetic mean The above collected data is arranged in ascending order. Then the maximum, minimum values are found out. The arithmetic average is found out by adding all the values and dividing it by the total number of values. Arithmetic Average = (1) B. Arrange the Data in a Range and Find out the Total Occurrences of Data The collected data is bifurcated in a proper range. The total no. of occurrences in a particular range is found out. Accordingly, a graph is plotted between Total no of Occurrences v/s Range of Data. The nature of the graph decides the type of distribution normal or skewed. Then the individual probability and cumulative probability of the occurrences is calculated. The cumulative probability values are used to plot another graph between cumulative probability v/s load values.for Example Table 1 shows the data for the month of January from 2009 to 2011 year. TABLE 1 CUMUATIVE PROBABILITY FOR THE MONTH OF JANUARY Data Range 9500-10000 10001-10500 A. Normalization of data No. Of Cumulative Probability Occurrences Probability 12 0.0057 0.0057 49 0.0234 0.0292145 The data collected is converted in normalized form. The normalization of data is done using the following formula: Value= Where V 1 = Value to be normalized V min = Minimum value of the total data V max = Maximum value of the total data (2) The Normalization of data is done because the Beta Distribution requires the data to be in the range of 0 to 1. B. Calculation of Standard Deviation & Mean The normalized data is used to find out the standard deviation & mean. Standard Deviation is given by, C. Calculation of shape parameter S.D = (3) A shape parameter affects the shape of a distribution rather than simply shifting it (as a location parameter does) or stretching/shrinking it (as a scale parameter does). The shape parameters are: i. alpha (α) ii. Beta (β) C. Calculation of Beta PDF Values Mean= (4) = (5) The beta distribution is a family of continuous probability distributions defined on the interval (0, 1) parameterized by two positive shape parameters, typically denoted by α and β. From the above calculated alpha & beta values we can find out Beta Probability Distribution Function Values. The Beta Distribution is given by, D. Draw Beta PDF graph & Weibull density function graph The estimates of the parameters of the Weibull distribution can be found graphically on probability plotting paper or analytically using either least squares or maximum likelihood. One method of calculating the parameters of the Weibull distribution is by using probability plotting. This paper illustrates calculation of Weibull PDF using cumulative probability graph shown in Fig. 1 and beta distribution graph is Fig.2. (6) 754

Table 2 AVERAGE LOAD FOR THE MONTH OF JANUARY Arithmetic Mean Load Demand Beta dist. Mean Load Demand Cumulative(Weibull) Mean Load Demand 14836 MW 15010 MW 15510 MW Figure 1 Cumulative Distribution cumulative for load in January Figure 3 Comparison graph Comparison graph of all the three methods is shown in Fig.3.So we can infer that Beta PDF function is a better technique than other two methodologies discussed above. Figure 2 Beta Distribution cumulative for load in January Cumulative (Weibull) mean = 15510 MW. (This Weibull mean is calculated from the cumulative probability graph. It is 63.2% (i.e. 0.632) of the cumulative probability. D. Comparison Of Arithmetic Mean, Beta Mean & Weibull Mean The Mean calculated by different methods as mentioned above are compared with each other in Table II. III. PREDICTION OF WIND SPEED USING ANN A neural network is a computational structure which resembles a biological neuron. It can be defined as a massively parallel distributed processor made up of simple processing units, which has a natural propensity for storing experimental knowledge and making it available for use. It resembles the human brain in two respects: a) Knowledge is acquired by the network from its environment through a learning process. b) Interneuron connection strengths, also known as synaptic weights, are used to store the acquired knowledge. 755

A. Design of neural Network The design of the neural network involves designing the three field neurons: one for input layer, one for hidden processing elements and one for the output layer. The connections are for the feedforward activity. There are connections from every neuron in the field 1 to every neuron in the field 2 to every neuron in the field 3. Thus there are two sets of weights, those figuring in the activation of hidden layer neurons, and those that help determine the output neuron activatons. Using back propagation algorithm, in each training set, the weights are modified so as to reduce the mean squared error [MSE] between the network s prediction and the actual value. These modification are made in the reverse direction, from output layer, through each hidden layer down to the first hidden layer, till the terminating condition is reached. PARAMETERS Temperature Humidity Wind Gust Wind Direction Barometric Pressure Wind Speed of (d-1) Wind Speed of (d-2) Table 3 List of input parameters UNITS Deg.C %RH m/s Deg.M Mb m/s Training & validation data: Samples of Oct 2006, 2007, 2008 are used. For training of network 70% sample and for testing 30% sample are used. A code is written in Matlab for training of neural network and performance graph obtained shown in Fig.5 is evaluated. By using the model generated in MATLAB wind speed can be forecasted. m/s B. Algorithm Figure 4 ANN model obtained after training The algorithm of this forecasting technique is as follows Collection of data: For prediction of wind speed, historical data (i.e., wind speed, wind gust, temperature, humidity, wind direction and barometric pressure) of October month for year 2006, 2007 and 2008 is collected. Selection of input & output: For wind speed prediction, historical data (i.e., wind speed, wind gust, temperature, humidity, wind direction and barometric pressure) of October month for year 2006, 2007 and 2008 is used. Figure 5 Performance graph C. Evaluation of performance of ANN model for forecasting: Once the ANN model is trained then samples which were neither used during training and testing are used for the evaluating the performance of the back propagated ANN model. 756

Hourly wind speed values are predicted for seven days of October 2008 and then compared with actual wind speed values of these samples. The performance of back propagation model is evaluated in terms of Absolute percentage error (APE) and Mean Absolute Percentage Error (MAPE). Figure 6 shows comparison between predicted and actual values of the wind speed for 24 th October 2008. It is observed that minimum absolute percentage error (APE) is found as 2.17% and maximum APE is 16.87%. The mean APE found is 9.72% (7) (8) Fig.8 shows comparison of actual and predicted values of wind speed for 26 th October 2008. It is observed that the minimum absolute percentage error is 0.87% and maximum APE is 33.29%. The mean absolute percentage error is found as 13.90%. Figure 8 Actual and estimated wind speed for 26 th October 2008 Figure 6 Actual and estimated wind speed for 24 th October 2008 Comparison between actual and predicted wind speed of 25 th October 2008 is shown in Fig.7. Here minimum APE is found as 2.17% and maximum APE found 29.17%. The mean APE found is 9.49% IV. CONCLUSION In this paper, load data for Kalwa region of Maharashtra State has been analyzed. The statistical methods such as Beta Probability Distribution Function & Cumulative (Weibull) Distribution have been used for calculating average load demand on monthly as well as daily basis. From the results we can conclude that Beta Density Function is a better technique than Arithmetic Mean and Weibull Density Function. This analysis will be helpful for future generation planning. The result Back propagation Neural Network used for short term wind speed forecasting for Pune region shows that the network has a good performance and reasonable prediction accuracy. Its forecasting reliabilities were evaluated by computing the minimum APE which was obtained to be 0.133.5% which represents a high degree of accuracy. The result suggests that ANN model with the developed structure can perform good prediction with least error and finally this neural network could be an important tool for short term wind speed forecasting. Further studies on this work can incorporate additional information (such as wind power prediction, unit commitment and so on) into the network so as to obtain a more user friendly forecasting tool. Figure 7 Actual and estimated wind speed for 25 th October 2008 757

REFERENCES [1] Yuan-Kang Wu, Member, A literature review of wind forecasting technology in the world, presented in the Proc. IEEE, Jing-Shan Hong [2] K. Sreelakshmi, P. Ramakanthkumar, Performance Evaluation of Short Term Wind Speed Prediction Techniques, IJCSNS International Journal of Computer science and Network Security, Volume 8 No.8, pp-162-169, August 2008. [3] K. Sreelakshmi, P. Ramakanthkumar, Short Term Wind Speed prediction Using Support Vector Machine Model, WSEAS Transactions on Computer Science, Issue 11, Volume 7, pp-1828-1837, November 2008. [4] K.N.Toosi, University of Technology, Tehran, Iran, One-Hour- Ahead Forecasting Of Wind Turbine Power Generation Using Artificial Neural Networks [5] M. G. De Giorgi, A. Ficarella & M. G. Russo, Department of Engineering Innovation,Centro Ricerche Energia e Ambiente, University of Salento, Italy, presented Short-term wind forecasting using artificial neural networks (ANNs) 758