Load forecasting Prepared by N.CHATHRU

Content Introduction Methodology & Techniques Extrapolation Estimation of periodic components Estimation of stochastic component Auto-regressive Models Long-term load prediction using econometric models Reactive load forecasting

Introduction Process to predict future demand based on past data Nature of load forecasts based on lead time Nature Lead time Application Very short term A few seconds to several minutes Generation, distribution schedules, contingency analysis Short term Half an hour to a few hours Allocation of spinning reserve, unit commitment, maintenance scheduling Medium term A few days to a few weeks Seasonal peak planning Long term A few months to a few years Generation growth, plant expansion

Methodology & Techniques Methodologies Extrapolation Correlation Both extrapolation and correlation Techniques Deterministic Stochastic or probabilistic

Extrapolation Fitting trend curves Historical data Straight line Parabola S curve Exponential Gempertz Historical data Coefficients and exponents (a to d) to be obtained by least square technique

Estimation of average and trend terms Total demand can be expressed in general by Now deterministic term can be given by Here to note:

Estimation of average and trend terms Average and trend term are determined using least square technique to solve performance index or objective function To have minimum J index with respect to average and trend terms, necessary conditions are:

Estimation of average and trend terms If total N data are assumed to be available for determining the time averages, these two relationships can be equivalently expresses as

Estimation of periodic components Deterministic part of load may contain some periodic components in addition to the average and polynomial terms.

Estimation of periodic components Once harmonic load model is identified, it is simple to make prediction of the future load Suppose 168 load data in one period are collected so that load pattern may be expressed in terms of Fourier series with fundamental frequency being equal to

Estimation of stochastic component If yd(k) is subtracted from y(k), the result would be a sequence of data for stochastic part of the load. We have to identify model for ys(k) and then use it to make prediction ys(k+j). Convenient way for this is based on the use of the stochastic time series models. The simples form of this is so-called auto-regressive model which has been widely used to represent the behaviour of a zero mean stationary stochastic sequence.

Auto-regressive model (An AR model) The sequence ys(k) is to satisfy an AR model of order n i.e. it is [AR(n)], if it can be expressed as: Where ai are the model parameters and w(k) is a zero mean white sequence.

Auto-regressive model (An AR model) In order that solution of this equation may represent a stationary process, it is required that the coefficients ai make the roots of the characteristics equation lie inside the unit circle in the z-plane. The problem in estimating n is referred to as the problem of structural identification, while the problem of estimation of the parameters ai is referred to as the problem of parameter identification.

Auto-regressive model (An AR model) An AR model has advantage that both these problems are solved relatively easily if the autocorrelation functions are first computed using given data. Once model order n and parameter vector a have been estimated, next problem is that of estimating the statistics of the noise process w(k).

Auto-regressive model (An AR model) The best that can be done, is based on the assumption that an estimate of w(k) is provided by residual The variance of w(k) is then estimated using relation

Long-term load prediction using econometric models If load forecasts are for planning purposes, it is necessary to select the lead time to lie in the range of few months to a few years. In such cases, load demand should be decomposed in a manner that reflects the dependence of the load on various segments of economy of concerned region. For example the total demand y(k) may be decomposed

Long-term load prediction using econometric models For example the total demand y(k) may be decomposed

Long-term load prediction using econometric models Relatively simple procedure is to retrieve the model equation in the vector notation: The regression coefficients may then be estimated using the convenient least square algorithm.

Long-term load prediction using econometric models Load forecasts are then possible through the simple relation

Reactive load forecasting Reactive loads are not easy to forecast as compared to active loads, since reactive loads are made up of not only reactive components of loads but also of transmission and distribution networks & compensation VAR devices such as FACTs devices. Therefore past data may not yield the correct forecasts as reactive load varies with variations in network configuration during varying operating conditions.

Reactive load forecasting Use of P with power factor would result into somewhat satisfactory results. Of course only very recent past data (few minutes/hours) may be used with steady state network configuration. Such forecasted reactive loads are adapted with current reactive requirements of the network including VAR compensation devices. Such forecasts are needed for security analysis, voltage/reactive power scheduling etc.

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