Short Term Load Forecasting by Using Time Series Analysis through Smoothing Techniques

Short Term Load Forecasting by Using Time Series Analysis through Smoothing Techniques

Mr. Dileshwar Prasad Patel 1, Assit.Prof.Amit Vajpayee 2 Assit.Prof. Jitendra Dangra 3

1 LNCT, Indore (M.P), 2 LNCT, Indore (M.P), 3 LNCT, Indore (M.P)

Abstract as the accuracy of the electricity load forecast is crucial in providing better cost effective risk management plans; this paper proposes a Short Term Electricity Load Forecast (STLF) model with high forecasting accuracy.A lot of researchers and academicians are engaged in the activity of developing tools and algorithms for load and price forecasting. This paper provides a highly accurate yet efficient load forecasting tools based on time series analysis: smoothing techniques model. Results and discussions from real-world case studies based on the electricity markets of Maharashtra Electricity Board are presented.

Index TermsShort-Term Load Forecasting, Maharashtra Data, Time Series Analysis.

1. INTRODUCTION

   Load forecasting is a vital and fundamental factor for a successful operation of energy system. In order to operate the electrical system effectively and efficiently, the system load should be correctly predicted. If the system load forecast is overstated, the system may over- commit the generation and leads to costly operation. On the other hand, if the system load forecast is understated, the reliability and security of the system may be compromised which may result in power interruptions. While load forecasting in a longer lead time is applied for long-term maintenance scheduling, power-sharing coordination or capacity expansion, short-term load forecasting is needed for economic scheduling of the generating units, security analysis and short-term maintenance.

   Several different methods and techniques have been developed to forecast load demands, with the focus on improving the prediction accuracy. The approach using time series analysis is among the main areas with rich research effort, with specially formulated methods for data in various contexts.

   In Maharashtras context, research efforts in load forecasting have been devoted primarily to hybrid fuzzy-neural approach. A one-day ahead load forecasting technique using hybrid fuzzy-neural networks is explained in details in. Due to the vastly different behaviour of loads in weekends and public holidays from weekdays, special attention is paid to such daysfor performance improvement. Reference proposed the implementation and evaluation of the parallel neural network-fuzzy expert system for local load demand forecasting.

   Two time series models, namely, the multiplicative decomposition model and the smoothing techniques model employed. The multiplicative decomposition technique has been profoundly used for forecasting tasks in the business sector, such as sales projection or financial forecasting.

   However, it has not been commonly employed for electricity demand forecasting. This may due to the fact that load demands usually vary to a large extent across seasons with changing temperatures and it is challenging to fit a trend line. In Maharashtra, on the other hand, the weather varies within a small degree and trend lines are more easily predicted. Thus, this technique is proposed in this paper. The proposed models are implemented to predict one week demand data. The accuracy of the two models are calculated and compared. The paper utilizes the mean absolute percentage error (MAPE) as a measure of forecast accuracy.

   The paper is organized as follows. Section II introduces the two abovementioned models and explains how they would be used in analysing and forecasting the load consumption with a brief note on forecasting error measurement. Section III is the case study whereby Maharashtra load demands are first plotted

   For visual comparison of weekday and weekend data. Then models would be applied with forecasts generated and compared with the amounts actually consumed.

2. TIME SERIES MODELS

   A time series is defined as a set of data generated sequentially in time. The time series models assume that in the absence of major disruptions to critical factors of a recurring event, the data of this event in the future will be related to that of the past events and can be expressed via models developed from the past events. In this analysis, time series model: smoothing techniques Model, are employed and presented in the followings.

3. SMOOTHINGTECHNIQUE

   This chapter we are going to cover the Different smoothing techniques and procedure to use those techniques.

   INTRODUCTION TO SMOOTHING TECHNIQUES

   Smoothing techniques are used to reduce irregularities

   (random fluctuations) in time series data. They provide a clearer view of the true underlying behaviour of the series. Moving averages rank among the most popular techniques for the pre-processing of time series. They are used to filter random "white noise" from the data, to make the time series smoother or even to emphasize certain informational components contained in the time series.

   the previous period's EMA in the first calculation. Second, calculate the weighting multiplier. Third, calculate the exponential moving average. The formula of EMA is shown below:

   Multiplier: (2 / (Time periods + 1))

   EMA: {Close SMA (previous day)} x multiplier + EMA (previous day).

   DIFFERENT SMOOTHING TECHNIQUES

   Many Smoothing Techniques are there but Moving Averages is the popular technique to smooth the data. So we are explaining the Moving Average Techniques below,

   Moving Averages: A moving average (MA) is an average of data for a certain number of time periods. It "moves" because for each calculation, we use the latest x number of time periods' data. Using an average of prices, moving averages smooth a data series and make it easier to spot trends. This can be especially helpful in volatile markets.

   Types of Moving Average: There are three major types of Moving Averages: Simple Moving average, Expontional Moving average and weighted moving average.

   Simple Moving Average (SMA)

   SMA is the most basic of the moving averages used for trading. A simple moving average (SMA) is formed by finding the average price of a currency or commodity over a set number of periods. Most often, the closing price is used to compute the moving average. A 5-day simple moving average is the five day sum of closing prices divided by five. As its name implies, a moving average is an average that moves. Old data is dropped as new data comes available.

   Exponential Moving Averages (EMA)

   Exponential moving averages reduce the lag by applying more weight to recent prices. The weighting applied to the most recent price depends on the number of periods in the moving average. An exponential moving average is similar to a simple moving average, but whereas a simple moving average removes the oldest prices as new prices become available, an exponential moving average calculates the average of all historical ranges, starting at the point you specify.

   There are three steps to calculating an exponential moving average. First, calculate the simple moving average. An exponential moving average (EMA) has to start somewhere so a simple moving average is used as

   Or

   We can also write this formula like: (SMA +multiplier (Last value SMA)

   Weighted Moving Average (WMA)

   This average is calculated by multiplying each of the previous days data by weight. Therefore it is designed to put more weight on recent data and less weight on past data. In other words, it is simply amoving average that is weighted so that more recent values are more heavily weighted than values further in the past. Evidence also indicates that the use of this type of moving average gives better volatility estimates than the simple moving average.

   The formula of the WMA average is:

   ((n * Pn) + ((n – 1) * Pn-1) + ((n – 2) * Pn-2) + … ((n – (n

   1)) * pn-(n-1)) /n + (n-1) + (n- (n-1)).

   Here n is the number of terms present; p is the values given there.

   Data Set: I have the data of Maharashtra state electricity distribution co. ltd. we took the data from the site www.mahadiscom.in. The monthly data is available in that site. The data is available from December 2007 to April 2010

   We selected the data from April 2008 to April 2010. Every months data is divided like Zone wise, Circle wise and Hour wise. There are 4-5 weeks are available in every month and every week has an hourly data.

   We had chosen pune zone, ganeshkhind (u) circle. From this zone, i had selected 5 areas of different feeders, but the division is same. The selected feeder names are: kasturba, sangam bridge, gk i, proof range and may fair tower. here is some brief explanation of all the areas:

   HR DATE 01-APR-08 02-APR-08 03-APR-08 04-APR- 08 05-APR-08 06-APR-08 07-APR08

   Fig. (1) Raw data

   This is the weekly data with 24 hours each, Like that I have a data of 2 years that is from April 2008 to April 2010 of 5 areas. The three variables of the data are:

   HR hour Date

   Day Monday to Sunday

   I used this data for the predictive analysis. Using the different smoothing techniques on the data, I had predicted the future values, their load and I also calculate their accuracy as well.

4. SIMPLE MOVING AVERAGE

   This Chapter explains how we can calculate the SMA and steeps to perform the SMA on our data set. How Pre-process the raw data, also learn to use MS- Excel for Time Series Analysis.

   INTRODUCTION TO SIMPLE MOVINGAVERAGE

   The moving average which serves as an estimate of the next period value of a variable given a period of length n. For example, a 10-day simple moving average of closing price is the mean of the previous 10 days' closing prices. If those prices are then the formula is

   STEPS USE TO CALCULATE THE SMA

   Step 1: We down load the raw data from the web site www.mahadiscom.in. Which is an official web site of the Maharashtra Electric Board after that we extract the Zip file in the folder and we select our area and after getting that area we copy that data into the Note pad to convert it in to CSV file? Once the data is converted into the CSV file we use the MS-EXCEL for our work

   Fig. (2) Sangam nagars data on Excel sheet

   Step 2: After converting the data into the CSV format we use the MS-EXCEL for the calculating the SMA for that we have to arrange the same day data together for that we are using the FILTER option in the EXCEL with the help of the filter we are able to separate the specific data from the hole data. I had selected all the Tuesdayof 2 month is from December 2007 to January 2008.

   Fig.(3) Sangam Nagars data after using the Filter.

   Step 3: SMA is Average value so we are using the simple formula to calculate the SMA the formula is SMA= sum of number of values / N, where N is the total numbers of values present in the sample. We are using the same formula to calculate the SMA in our data set.

   Fig. (4) Sangam Nagars data after applying the SMA.

   Here we are showing SMA techniques used in the all the Tuesdays of the Sangam Nagar.

   Step 4:

   Fig (5)Matlab GUI represents the calculated SMA and Predicted value.

   This is our MATLAB GUI which is used in our data set for calculating the 2PSMA, 3PSMA, 4PSMA, 5PSMA, 6PSMA, 7PSMA to predict the load of upcoming Tuesday. We are taking the data from our data set to solve these calculations.

   3PSMA = (N1+N2+N3)/N

   For 4PSMA =(N1+N2+N3+N4)/N

   Like this I apply this formula up to 7PSMA in our data set.

   Fig. (6) Calculated values of SMA.

   This is the calculated 3PSMA.

   7.4 Calculated values of SMA.

   SUM= It is the additions of the total numbers of values present on the data set.

   MEAN =Sum of vales / Total number

   MAPE=Mean absolute percentage error is measure of accuracy in a fitted time series.

   Where At is the actual value and Ft is the forecast value.

   ACTUAL VALUE= It the original value PREDICATED VALUE = It is the calculated value. ACCURACY= It is a measurement of a correctness; the accuracy of the model is near about 98%.

   ACCURACY = MAPE*100

   Fig (7) Graph between actual load and predicted load.

   This is the graph which shows the comparison between

   Actual Value and Predicted value. Where, Red line denotes the Actual data and Light Green line denotes the Predicted value.

   In this way, we can calculate Simple Moving Average for all 24 hours.

   HOW TO CALCULATE THE PREDICTED VALUES:

   We need to calculate the simple moving average of the data. Then we need to calculate the accuracy of all the models 3PSMA gives us the Accuracy up to 98%.

   For calculating the predicted values, we can select the last three values of 3PSMA of the 16th hour. We can calculate the 3PSMA of last three values

   Fig (8) Graphical representation of Predicted load.

   This is the graph, which shows the load of the predicted values of all the 24 hours of 12-feb-2008, after using the SMA technique.

   Fig (9) Comparison graph b/w 2PSMA, 3PSMA, and 4PSMA

5. CONCLUSION

Smoothing techniques used in this approach is very effective, efficient and helpful in any organization (Companies) for load forecasting and also the method Simple Moving Average used in this approach has better accuracy.The results also concluded that when we increase the no of periods the efficiency of load forecasting gets decreases as shown in result for comparison between 2PSMA, 3PSMA and 4PSMA technique.

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