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
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:
( ) ( ) ( )
d s
y k y k y k
( ) ( )
d d
y k y bk e k
( )
( ) mod
d d
y Avereage or mean value of y k
bk Trend term growing with lead time k learnealy
e k Error of elling
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:
2
[ ( )]
(.) exp
J E e k
E is ectation operation
2
[ ( ) ] 0
[ ( ) ] 0
d d
d d
E y y k bk
E y k y k k bk
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
1 1
1 1 1
2
2
1 1
1
( )
( ) ( )
N N
d d
k k
N N N
d d
k k k
N N
k k
y y k b k
N
N y k k k y k
b
N k k
9. Estimation of periodic
components
Deterministic part of load may contain some
periodic components in addition to the average
and polynomial terms.
1
( ) [ sin cos ] ( )
: sin
: cos
L
i i
i
i
i
y k y a iwk b iwk e k
L Total harmonics
a Amplitudesof usoidal component
b Amplitudesof inusoidal component
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
( ) ( ) ( )
d
y k j h k j x k
2
168
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
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.
1
( ) ( ) ( )
n
s i s
i
y k a y k i w k
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
1 2
1 2
1 ...... 0
n
n
a z a z a z
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
1
( ) ( ),
( ) ( )
s s
n
i s
s
i
e k y y k where
y k a y k i
2 2
1
1
( )
n
k
e k
N
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
1
( ) ( ) ( )
: Re
( ) var
( )
M
i i
i
i
i
y k a y k e k
a ression Coefficients
y k Chosen economic iables
e k Modelling error
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.
1 2 3
1 2
( ) ( ) ( )
( ) [ ( ) ( ) ( )... ( )]
[ ...... ]
M
M
y k h k x e k
h k y k y k y k y k
and x a a a
19. Long-term load prediction using
econometric models
Load forecasts are then possible through the
simple relation
1
( 1) ( )
( )
int
1
( )
th
y k x k h k
k
x k estimateof coefficient vector based
on data availabe till the k sampling po
and h k is one step ahead prediction
k
of vector h k
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.
