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Short Term Load Forecasting with Expert Fuzzy-Logic System

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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

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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
    short term load forecasting
  • Presently most application of the fuzzy method
    for load forecasting is experimental
  • For the demonstration of the method a Fuzzy
    Expert System is selected that forecasts the
    daily peak load

3
Fuzzy- Expert System
  • X is set contains data or objects.
  • Example Forecast Temperature values
  • A is a set contains data or objects
  • Example Maximum Load data
  • 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
    spread over the regression curve.
  • 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 peak load forecast
  • The error for peak load is calculated by the
    derivation of the load-temperature equation

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
Load ( MW)
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
  • The operator asked
  • 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
  • This coefficient has to be added to the load
    forecast obtained by the liner regression method
  • The corrected load forecast is
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