# Short Term Load Forecasting with Expert Fuzzy-Logic System - PowerPoint PPT Presentation

PPT – Short Term Load Forecasting with Expert Fuzzy-Logic System PowerPoint presentation | free to view - id: 4ec8ba-MGQ1O

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Short Term Load Forecasting with Expert Fuzzy-Logic System

Description:

### Short Term Load Forecasting with Expert Fuzzy-Logic System Load forecasting with Fuzzy- expert system Several paper propose the use of fuzzy system for short term ... – PowerPoint PPT presentation

Number of Views:200
Avg rating:3.0/5.0
Slides: 59
Provided by: GeorgeG99
Category:
Tags:
Transcript and Presenter's Notes

Title: Short Term Load Forecasting with Expert Fuzzy-Logic System

1
Short Term Load Forecasting with Expert
Fuzzy-Logic System
2
Load forecasting with Fuzzy- expert system
• Several paper propose the use of fuzzy system for
• Presently most application of the fuzzy method
• For the demonstration of the method a Fuzzy
Expert System is selected that forecasts the

3
Fuzzy- Expert System
• X is set contains data or objects.
• Example Forecast Temperature values
• A is a set contains data or objects
• x is an individual value within the X data set
• mA(x) the membership function that connects the
two sets together

4
Fuzzy- Expert System
• The membership function mA(x)
• Determines the degree that x belongs to A
• Its value varies between 0 and 1
• The high value of mA(x) means that it is very
likely that x is in A
• Membership function is selected by trial and error

5
Fuzzy- Expert System
• Typical membership functions are
• Triangular
• Trapezoid

Membership function
x variable
6
Fuzzy- Expert System
Membership function
DLmid
DLmin
DLmax
x variable
7
Fuzzy- Expert System
• A fuzzy set A in X is defined to be a set of
ordered pairs
• Example Figure before shows that x - 750
belongs a value of A 0.62

8
Fuzzy- Expert System
• Triangular membership function equation
• Triangular membership function is defined by
• DLmax or DLmin value when function value is 0
• DLmaid value when function value is 1
• Between DLmax and DLmin the triangle gives the
function value
• Outside this region the function value is 0

9
Fuzzy- Expert System
• The coordinates of the triangle are
• x1 DLmin and y1 0 or m(x1) 0
• x2 DLmid and y1 1 or m(x2) 1
• The slope of the membership function between x1
DLmin and x2 DLmid is

10
Fuzzy- Expert System
• The equation of the triangles rising edge is

11
Fuzzy- Expert System
• The complete triangle can be described by taking
the absolute value
• This equation is valid between DLmin and DLmid
• Outside this region the m(x) 0

12
Fuzzy- Expert System
• The outside region is described by
• The combination of the equations results in the
triangular membership function equation

13
Fuzzy- Expert System
• Combination of two fuzzy sets
• A and B are two fuzzy sets with membership
function of mA(x) and mB(x)
• The two fuzzy set is combined together
• Union
• Intersection
• sum
• The aim is to determine the combined membership
function

14
Fuzzy- Expert System
• Union of two fuzzy sets points included in both
set A and B
• The membership function is

15
Fuzzy- Expert System
• Union of two fuzzy sets points included in both
sets A or B

mB
mA
16
Fuzzy- Expert System
• Intersection of two fuzzy sets points which are
in A or B
• The membership function is

17
Fuzzy- Expert System
• Intersection of two fuzzy sets points which are
in A and B

mB
mA
18
Fuzzy- Expert System
• Sum of two fuzzy sets
• The membership function is

19
Fuzzy- Expert System
• Sum of two fuzzy sets

mA
ms mA mB
mB
20
Load forecasting with Fuzzy- expert system
• Steps of the proposed peak and through load
forecasting method
• Identification of the day (Monday, Tuesday,
etc.). Let say we select Tuesday.
• Forecast maximum and minimum temperature for the
upcoming Tuesday
• Listing the max. temperature and peak load for
the last 10-12 Tuesdays

21
Load forecasting with Fuzzy- expert system
• Plot the historical data of load and temperature
relation for selected 10 Tuesdays.

22
Load forecasting with Fuzzy- expert system
• The data is fitted by a linear regression curve
• The actual data points are spread over the
regression curve
• The regression curve is calculated using one of
the calculation software (MATLAB or MATCAD)
• As an example
• MATCAD using the slope and intercept function
• MATLAB use
• to determine regression curve equation

23
Load forecasting with Fuzzy- expert system
• The result of the linear regression analysis is
• Lp is the peak load,
• Tp is the forecast maximum daily temperature,
• g and h are constants calculated by the
least-square based regression analyses.
• For the data presented previously g 300.006 and
h 871.587

24
Load forecasting with Fuzzy- expert system
• This equation is used for peak load forecasting
• As an example if the forecast temperature is Tp
35C
• The expected or forecast peak load is

25
Load forecasting with Fuzzy- expert system
• The figure shows that the actual data points are
• The regression model forecast with a statistical
error.

26
Load forecasting with Fuzzy- expert system
• In addition to the statistical error, the
uncertainty of temperature forecast and
unexpected events can produce forecasting error.
• The regression model can be improved by adding an
error term to the equation
• The error coefficient is determined by Fuzzy
method.
• The modified equation is

27
Load forecasting with Fuzzy- expert system
• Determination of the error coefficient e by Fuzzy
method.
• DLp error coefficient has three components
• Statistical model error
• Temperature forecasting error
• Operators heuristic rules

28
Load forecasting with Fuzzy- expert system
• Statistical model error
• The data is fitted by a linear regression curve
• The actual data points are spread over the
regression curve
• The statistical error is defined as the
difference between the each sample point and the
regression line
• This statistical error will be described by the
fuzzy method

29
Load forecasting with Fuzzy- expert system
• Statistical model error
• Different membership function is used for each
day of the week (Monday, Tuesday etc.)
• The membership function for the statistical error
is determined by an expert using trial and
error.
• A triangular membership function is selected.
• The membership function is 1, when the load is 0
and decreases to 0 at a load of 2s.

30
Load forecasting with Fuzzy- expert system
• s is calculated from the historical data with
the following equation
• Lpi is the peak load
• Tpi is the maximum temperature
• n is the number of points for the selected day
• s 450 MW in our example shown before.

31
Load forecasting with Fuzzy- expert system
• The data of the triangular membership F1(DL1)
function is
• DL1_min - 450MW, DL1_mid 0 MW
• The substitution of these values in the general
equation gives

32
Load forecasting with Fuzzy- expert system
• The data of the triangular membership F1(DL1)
function is
• DL1_min - 450MW, DL1_mid 0 MW
• The substitution of these values in the general
equation gives

33
Load forecasting with Fuzzy- expert system
• The membership function is shown below if s
450MW and DL -1500MW..500MW

DL1_min - 450MW
DL1_mid 0 MW
DL1_max 450MW
34
Load forecasting with Fuzzy- expert system
• Temperature forecasting error
• The forecast temperature is compared with the
actual temperature using statistical data (e.g 2
years)
• The average error and its standard deviation is
calculated for this data.
• As an example the error is less than 4 degree in
our selected example.

35
Load forecasting with Fuzzy- expert system
• Temperature forecasting error produces error in
• The error for peak load is calculated by the

36
Load forecasting with Fuzzy- expert system
• Temperature forecasting error
• The error in peak load is proportional with the
error in temperature
• This suggests a triangular membership function.

37
Load forecasting with Fuzzy- expert system
• Temperature forecasting error
• A fuzzy expert system can be developed using the
method applied for the statistical model
• A more accurate fuzzy expert system can be
obtained by dividing the region into intervals
• A membership function will be developed for each
interval
• The intervals are defined by experts using the
following criterion's

38
Load forecasting with Fuzzy- expert system
• Temperature forecasting error
• The intervals for the temperature forecasting
error are defined as follows
• The temperature can be much lower than the
forecast value. (ML)
• The temperature can be lower than the forecast
value. (L)
• The temperature can be close to the forecast
value. (C)

39
Load forecasting with Fuzzy- expert system
• Temperature forecasting error
• The temperature can be higher than the forecast
value. (H)
• The temperature can be much higher than the
forecast value. (MH)
• A membership function is assigned to each
interval.
• d -4 for ML, d -2 for L, d0 for C, d 1
for H and d 2 for MH

40
Load forecasting with Fuzzy- expert system
• Temperature forecasting error
• The membership functions are determined by expert
using the trial and error technique
• A triangular membership function with the
following coordinates are selected
• DLmin 2 gp d g and DLmid d gp
• These values are substituted in the general
membership function

41
Load forecasting with Fuzzy- expert system
• Temperature forecasting error
• The membership function for change in peak load
due to the error in temperature forecasting is
• Where d and gp are a constants defined earlier

42
Load forecasting with Fuzzy- expert system
• Temperature forecasting error
• The membership function for change in peak load
due to the error in temperature forecasting is
• Where d and gp are a constants defined earlier

43
Load forecasting with Fuzzy- expert system
• Temperature forecasting error
• An expert select the appropriate membership
function for the study
• The membership functions are

ML
MH
H
L
C
Membership function
44
Load forecasting with Fuzzy- expert system
• Combination of Model uncertainty with Forecast
-temperature uncertainty.
• The peak load should be updated by an amount
• The membership function for DL3

45
Load forecasting with Fuzzy- expert system
• The analytical method to calculate the combined
membership function F3(DL3) is based on
• Every value of the membership function value has
to be updated using
• The method is illustrated in the figure below.

46
Load forecasting with Fuzzy- expert system
• The combined membership function will be a
triangle with the following coordinates
• DL3_min DL1_min DL2_min s (2gp d gp)
• DL3_mid DL1_mid DL2_mid 0 g d
• The substitution of this values in the general
equation gives the membership function

47
Load forecasting with Fuzzy- expert system
• Combined of Model uncertainty and Forecast
-temperature uncertainty membership function
(F3(DL3) .

48
Load forecasting with Fuzzy- expert system
• Operators Heuristic Rules
• The experienced operator can update the forecast
by considering the effect of unforeseeable events
or suggest modification based of intuition.
• The operator experience can be included in the
fuzzy expert system
• The operator recommended change has to be limited
to a reasonable value.
• The limit depend on the local circumstances and
determined by discussion with the staff

49
Load forecasting with Fuzzy- expert system
• Operators Heuristic Rules
• How much load change he/she recommends. (X MW)
• What is his confidence level
• Quite confident, use factor K 0.8
• Confident, use factor K 1
• Not confident, use factor K 1/0.8 1.25
• Triangular membership function is selected

50
Load forecasting with Fuzzy- expert system
• Operators Heuristic Rules
• Triangular membership function parameters
determined through discussion with operators.
• Historically the operator prediction error is in
the range of 200-300MW
• The selected data are
• L4_mid X selected value for the example is X
-250MW
• L4_min K XX selected value for the example
is K 0.8,

51
Load forecasting with Fuzzy- expert system
• Operators Heuristic Rules
• The substitution of this values in the general
equation gives the membership function
• The membership function for the operators
heuristic rule is shown the next slide

52
Load forecasting with Fuzzy- expert system
• Membership function for Operators Heuristic Rules

Not confident
Quite confident
Confident
53
Load forecasting with Fuzzy- expert system
• The prediction of the DLp error coefficient
requires the combination of the membership
function of
• Operators Heuristic Rules (F4(DL4) with the
• Combined of Model uncertainty and Forecast
-temperature uncertainty membership function
(F3(DL3)
• The next slide shows the two function

54
Load forecasting with Fuzzy- expert system
• Membership functions F3 and F4, (K 0.8) which
has to be combined together

55
Load forecasting with Fuzzy- expert system
• The error coefficient is determined by
combination of combined Model Temperature error
and Operators Heuristic Rule.
• The and relation suggests that the intersection
of two fuzzy sets, which are points in F3 and F4
• The membership function in case of the
intersection is

56
Load forecasting with Fuzzy- expert system
• The membership function can be calculated by the
following equation
• The combined membership function is presented on
the next slide.
• The maximum of the membership function gives the
error coefficient DLp

57
Load forecasting with Fuzzy- expert system
Dlcorrection - 273.25MW
58
Load forecasting with Fuzzy- expert system
• The error coefficient DLp is determined by the
presented fuzzy expert system method