This document discusses five models traditionally used for electrical load predictions: 1. The Scheer formula, a long-term forecasting model that predicts annual generation growth. 2. The Belgium formula, another long-term model that extrapolates energy consumption trends. 3. Chen's additive model, which separates load into normal, weather, event, and random components. 4. A multiplicative model that multiplies a base load by correction factors like weather and growth. 5. Feinberg's mid-term model, which uses regression to model load as daily-hourly patterns and weather impacts. The document also outlines short-term forecasting methods like similar-day, regression, time series, neural

1. FIVE MODELS TRADITIONALLY
USED FOR ELECTRICAL LOAD
PREDICTIONS
DR.MRINMOY MAJUMDER (ORCID ID : 0000-0001-6231-5989)
“RENEWABLE ENERGY” of MTECH(HYDROINFORMATICS ENGG
“ INNOVATE FOR SUSTAINABILITY”- www.baipatra.ws

2. IMPORTANCE
Load forecasting helps an electric utility to make
important decisions including decisions on
purchasing and generating electric power, load
switching, and infrastructure development.
Load forecasts are extremely important for
energy suppliers, ISOs, financial institutions, and
other participants in electric energy generation,
transmission, distribution, and markets.
Most forecasting methods use statistical
techniques or artificial intelligence algorithms
such as regression, neural networks, fuzzy logic,
and expert systems.

3. DEFINITION
Prediction of load or generation requirement can
be performed to assist in operation planning,
expansion strategy and policy formulations.
Hydropower plants has a gestation period of 10 to
15 years
Forecasting of load can be done for three
different duration based on accuracy required and
circumstances prevailing.
Models can be conceptual or statistical depending
on the requirement.

4. Type of Forecasting Models
LOAD PREDICTION MODEL
TYPES
SHORT TERM MEDIUM TERM LONG TERM
COVERING A PERIOD OF 20
YEARS OR MORE
COVERING A PERIOD OF 8
TO 10 YEARS
COVERING A PERIOD OF 4
TO 5 YEARS
PURRPOSE :
OPERATION PLANNING
PURRPOSE :
BASIS FOR EXPANSION
PURRPOSE :
POLICY FORMULATION

5. Model One : SCHEER FORMULA
G
=
10 𝐶
𝑈0⋅15
WHERE G = ANNUAL GROWTH IN GENERATION(PER CENT)
U = PER CAPITA GENERATION
C = CONSTANT
= 0.02(POPULATION GROWTH RATE)+1.330
THE CONSTANT IN THE SUPERSCRIPT OF U IS ASSUMED AS PER THE THUMB RULE THAT ‘A HUNDRED FOLD INCREASE IN U WILL REDUCE
THE RATE OF GROWTH BY HALF’
LONG TERM LOAD FORECASTING MODEL

6. POINTS TO REMEMBER
MAGNITUDE OF
FOLLOWING
PARAMETERS ARE
REQUIRED :
•GENERATION OF THE
STARTING YEAR IS
•POPULATION OF
STARTING YEAR
•POPULATION OF THE
CONSEQUENT YEARS
1
IF THE VALUE OF ABOVE
PARAMETERS IS KNOWN
THEN U AND C CAN BE
CALCULATED FROM
WHICH THE
GENERATION
REQUIREMENT OF THE
STARTING YEAR IS
DERIVED FROM THE
SCHEER FORMULA
2
THE RATE OF GROWTH IN
THE NEXT YEAR IS
CALCULATED BY
MULTIPLYING THE GROWTH
RATE OF STARTING YEAR
WITH (1+G)/100.
3
FROM THE GROWTH RATE
OF SECOND YEAR AND THE
POPULATION OF THE SAME
YEAR AS KNOWN FROM THE
FIRST POINT THE U AND C
OF SECOND YEAR CAN BE
PREDICTED FROM WHICH
RATE OF GROWTH CAN BE
ESTIMATED BY THE SAME
FORMULA.
4
IN THIS WAY YEAR BY YEAR
PREDICTION OF
GENERATION REQUIREMENT
IS DETERMINED.
5

7. Model two : BELGIUM FORMULA
E
= 𝐾 × 𝑀0⋅6
× 2 0.465𝑡
WHERE E = ELECTRICITY CONSUMPTION
M = INDEX OF MANUFACTURE OF PRODUCTION
t = TIME FOR WHICH CONSUMPTION TO BE PROJECTED
K = ADJUSTMENT FACTOR
LONG TERM LOAD FORECASTING MODEL

8. POINTS TO REMEMBER
THIS FORMULA IS AN EMPIRICAL FORMULA FOR EXTRAPOLATION OF TREND OF ENERGY
CONSUMPTION
DIFFERENT COUNTRIES HAVE SEPARATE FORMULA FOR THE ESTIMATION OF ENERGY
CONSUMPTION
THE ACCURACY OF THE FORMULA DEPENDS ON THE CALIBRATION AND MAY VARY WITH TYPE
OF DATA AVAILABLE AND OTHER RELATED APPROXIMATIONS.

9. Model Three : Additive Model by Chen et.al.
𝐿 = 𝐿 𝑛 + 𝐿 𝑤 + 𝐿 𝑠 + 𝐿 𝑟
where L is the total load,
Ln represents the “normal” part of the load, which is a set of standardized load
shapes for each “type” of day that has been identified as occurring throughout
the year,
Lw represents the weather sensitive part of the load,
Ls is a special event component that create a substantial deviation from the
usual load pattern, and
Lr is a completely random term, the noise.
LONG TERM LOAD FORECASTING MODEL

10. Model Four : Multiplicative Model
𝐿 = 𝐿 𝑛 × 𝐹𝑤 × 𝐹𝑆 × 𝐹𝑟
where
Ln = the normal(base) load
Fw, Fs, and Fr are positive numbers representing the corrections based on current weather (Fw),
special events (Fs), and random fluctuation (Fr).
Factors like electricity pricing (Fp) and load growth (Fg) can also be included.
LONG TERM LOAD FORECASTING MODEL

11. Model Five : Feinberg’s Load Forecasting Model
𝐿 𝑡 = 𝐹𝑎 + 𝑅𝑡
where Fa is 𝐹 ⅆ 𝑡 ⋅ ℎ 𝑡 ⋅ 𝑓 𝑤𝑡
L(t) is the actual load at time t,
d(t) is the day of the week,
h(t) is the hour of the day,
F(d,h) is the daily and hourly component,
w(t) is the weather data that include the temperature
and humidity,
f(w) is the weather factor,
R(t) is a random error.
And f(w) is estimated by :
𝑓 𝑤 = 𝛽0 + 𝛽𝑗 𝑋𝑗where Xj are explanatory variables which are nonlinear functions of current and past weather parameters
and βo, βj are the regression coefficients.
MID TERM LOAD FORECASTING MODEL

12. Types of Models used in Short Term load forecasting
Similar-day approach
Historical data for days within the last one to three years are searched for similar characteristics for
forecasting the data of a similar day or season.
Regression methods
Various regressive techniques are used to model the relationship between load consumption and
other factors such as weather, day type, and customer class.
Time series
Time series Models depends on the assumption that the data have an “internal structure”,
represented by the autocorrelation, trend, or seasonal variation. The different methods used in Time
Series Modelling is:
ARMA (autoregressive moving average), ARIMA (autoregressive integrated moving average), ARMAX
(autoregressive moving average with exogenous variables), and ARIMAX (autoregressive integrated
moving average with exogenous variables).

13. Contd.
Neural networks
The artificial neural networks (ANN) has been widely used for electric load forecasting since
1990.
Expert systems
“Rule based forecasting” uses mostly heuristic rules of nature for accurate forecasting.
Expert systems, incorporates the rules and procedures used by human experts into a software
framework for automatically making forecasts without human assistance.

14. Resources and References
1.E. A. Feinberg and D.Genethliou.Load Forecasting, Applied Mathematics for Power Systems.
2.E.A. Feinberg, J.T. Hajagos, and D. Genethliou. Load Pocket Modelling. Proceedings of the 2nd
IASTED International Conference: Power and Energy Systems, 50–54, Crete, 2002.
3.E.A. Feinberg, J.T. Hajagos, and D. Genethliou. Statistical Load Modelling. Proceedings of the
7th IASTED International Multiconference: Power and Energy Systems, 88–91, Palm Springs, CA,
2003.
4.H. Chen, C.A. Canizares, and A. Singh. ANN-Based Short-Term Load Forecasting in Electricity
Markets. Proceedings of the IEEE Power Engineering Society Transmission and Distribution
Conference, 2:411–415, 2001.
5.M.M. Dandekar and K.N.Sharma. Water Power Engineering, Vikas Publishing House Pvt
Ltd.,1979.