1. Load forecasting
Prepared by N.CHATHRU

2. 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

3. 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

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

5. 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

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

7. 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:

8. 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

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

10. 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

11. 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.

12. 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.

13. 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.

14. 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).

15. 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

16. 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

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

18. 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.

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

20. 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.

21. 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.

22. Thank you