[ ] POWER SYSTEM OPERATION AND CONTROL TITLE : LOAD FORECASTING : INTRODUCTION, METHODOLOGY & ESTIMATION OF AVERAGE AND TREND TERMS. UNIVERSITY : GUJARAT TECHNOLOGICAL UNIVERSITY COLLEGE : VADODARA INSTITUTE OF ENGINEERING DEPARTMENT : ELECTRICAL ENGINEERING [E.E.– I] SEMESTER : VIII COMPILED BY : [ MEET JANI ] [ JESTY JOSE ] [ JOBIN ABRAHAM ] [ SAGAR KALAL ] GUIDED BY : PROF. PIYUSH PARMAR [ELECTRICAL DEPARTMENT] [ELECTRICAL DEPARTMENT] 1

 Outline  Introduction Introduction  Load forecasting Load forecasting  Load curves Load curves  Forecasting methodology Forecasting methodology  Forecasting techniques Forecasting techniques  Extrapolation Extrapolation  Correlation Correlation  Estimation of Average and Trend Terms Estimation of Average and Trend Terms  References References2

 Introduction  Definition  A process in which the aim is to decide on new as well as upgrading existing system elements, to adequately satisfy the loads for a foreseen future  Elements can be:  Generation facilities  Substations  Transmission lines and/or cables  Capacitors/Reactors  Etc. 3

 Introduction{contd.}  Decision should be  Where to allocate the element (for instance, the sending and receiving end of a line),  When to install the element (for instance, 2020),  What to select, in terms of the element specifications (for instance, number of bundles and conductor type).  The loads should be adequately satisfied. 4

 Load forecasting  The first crucial step for any planning study  Forecasting refers to the prediction of the load behavior for the future  Words such as, demand and consumption are also used instead of electric load  Energy (MWh, kWh) and power (MW,kW) are the two basic parameters of a load.  By load, we mean the power.  Demand forecast  To determine capacity of generation, transmission and distribution required  Energy forecast  To determine the type of generation facilities required 5

 Load curves  Variations in load on a power station from time to time  Daily load curves  Monthly load curves  Annual load curves  Load curve gives:  Variation of load during different time  Total no. of units generated  Maximum demand  Average load on a power station  Load factor 6

Daily load curve - example7

 Forecasting methodology  Forecasting: systematic procedure for quantitatively defining future loads.  Classification depending on the time period:  Short term  Intermediate  Long term  Forecast will imply an intermediate-range forecast  Planning for the addition of new generation, transmission and distribution facilities must begin 4-10 years in advance of the actual in-service date. 8

 Forecasting techniques  Three broad categories based on: Extrapolation – Time series method – Use historical data as the basis of estimating future outcomes. Correlation – Econometric forecasting method – identify the underlying factors that might influence the variable that is being forecast. Combination of both 9

 Extrapolation  Based on curve fitting to previous data available.  With the trend curve obtained from curve fitted load can be forecasted at any future point.  Simple method and reliable in some cases.  Deterministic extrapolation:  Errors in data available and errors in curve fitting are not accounted.  Probabilistic extrapolation  Accuracy of the forecast available is tested using statistical measures such as mean and variance. 10

{contd.}  Extrapolation{contd.}  Standard analytical functions used in trend curve fitting are:  Straight line:  Parabola:  s curve:  Exponential:  Gompertz:  Best trend curve is obtained using regression analysis.  Best estimate may be obtained using equation of the best trend curve. 11

 Correlation  Relates system loads to various demographic and economic factors.  Knowledge about the interrelationship between nature of load growth and other measurable factors.  Forecasting demographic and economic factors is a difficult task.  No forecasting method is effective in all situations.  Designer must have good judgment and experience to make a forecasting method effective. 12

 Estimation of Average and Trend Terms:  Estimation of Average and Trend Terms – The simplest possible form of the deterministic part of y(k) is given by  where y d represents the average or the mean value of y d (k), bk represents the `trend’ term that grows linearly with k and e(k) represents the error of modeling the complete load using the average and the trend terms only.  The question is one of estimating the values of the two unknown model parameters y d and b to ensure a good model.  As seen earlier, when little or no statistical information is available regarding the error term, the method of LSE is helpful.  If this method is to be used for estimating y d and b, the estimation index J is defined using the relation 13

{contd.}  Estimation of Average and Trend Terms{contd.}  where E() represents the expectation operation. Substituting for e(k) from Eq. (16.2) and making use of the first order necessary conditions for the index J to have its minimum value with respect to y d and b, it is found that the following conditions must be satisfied.  Since the expectation operation does not affect the constant quantities, it is easy to solve these two equations in order to get the desired relations. 14

{contd.}  Estimation of Average and Trend Terms{contd.}  If y(k) is assumed to be stationary (statistics are not time dependent) one may involve the ergodic hypothesis and replace the expectation operation by the time averaging formula.  Thus, if a total of N data are assumed to be available for determining the time averages, the two relations may be equivalently expressed as follows. 15

{contd.}  Estimation of Average and Trend Terms{contd.}  These two relations may be fruitfully employed in order to estimate the average and the trend coefficient for any given load data.  Note that Eqs. (16.6a) and (16.6b) are not very accurate in case the load data behaves as a non-stationary process since the ergodic hypothesis does not hold for such cases.  It may still be possible to assume that the data over a finite window is stationary and the entire set of data may then be considered as the juxtaposition of a number of stationary blocks, each having slightly different statistics.  Equations (16.6a) and (16.6b) may then be repeated over the different blocks in order to compute the average and the trend coefficient for each window of data. 16

 References 1. D.P. Kothari, I.J. Nagrath “Modern Power System Analysis”, McGraw-Hill Education (INDIA) Pvt. Ltd., Fourth Edition, Eighth Reprint : 2013, ISBN : Hadi Saadat “Power System Analysis”, WCB/McGraw-Hill Companies Inc., Library of Congress Cataloging-in-Publication Data : 1999, ISBN : Allen J. Wood, Bruce F. Wallenberg “POWER GENERATION OPERATION AND CONTROL“, JOHN WILEY & SONS, INC., SECOND EDITION (USA) 1996, ISBN JOHN J. GRAINGER, WILLIAM D. STEVENSON,JR. “POWER SYSTEM ANALYSIS“, McGRAW-HILL, INC., INTERNATIONAL EDITION (SINGAPORE) 1994, ISBN phpapp02_1_ phpapp02_1_ phpapp02_1_17

ANY QUESTIONS? SUGGESTIONS ARE WELCOME! 18