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SHORT TERM LOAD FORECASTING USING NEURAL NETWORKS AND FUZZY LOGIC

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Title: SHORT TERM LOAD FORECASTING USING NEURAL NETWORKS AND FUZZY LOGIC


1
SHORT TERM LOAD FORECASTING USING NEURAL
NETWORKS AND FUZZY LOGIC
  • George G Karady
  • Arizona State University

2
Short Term Load ForecastingContent
  • Overview of Short term load forecasting
  • Introduction
  • Definitions and expected results
  • Importance of Short-term load forecasting
  • Impute data and system parameters required for
    load forecasting
  • Concept
  • Major load forecasting techniques
  • Concept of STLF model Development
  • Statistical methods
  • (Multiply liner regression,
  • stochastic time series e.t.c)

3
Short Term Load ForecastingContent
  • Artificial Neural Networks
  • Building block a feed forward network
  • Load forecasting engine
  • Results
  • Numerical example
  • Fuzzy logic and evolutionary programming

4
Overview of Short Term Load Forecasting (STLF)
5
Introduction
  • The electrical load increases about 3-7 per year
    for many years.
  • The long term load increase depends on the
    population growth, local area development,
    industrial expansion e.t.c.
  • The short term load variation depends on weather,
    local events, type of day (Weekday or Holiday or
    Weekend) e.t.c.

6
Introduction
  • The building of a power plant requires
  • 10 years (Nuclear)
  • 6 years (Large coal-fired)
  • 3 years (combustion turbine)
  • The electric system planing needs the forecast of
    the load for several years.
  • Typically the long term forecast covers a period
    of 20 years

7
Introduction
  • The planning of maintenance, scheduling of the
    fuel supply etc. calls for medium term load
    forecast .
  • The medium term load forecast covers a period of
    a few weeks.
  • It provides the peak load and the daily energy
    requirement

8
Introduction
  • The number of generators in operation, the start
    up of a new unit depends on the load.
  • The day to day operation of the system requires
    accurate short term load forecasting.

9
Introduction
  • Typically the short term load forecast covers a
    period of one week
  • The forecast calculates the estimated load for
    each hours of the day (MW).
  • The daily peak load. (MW)
  • The daily or weekly energy generation. (MWh)

10
Introduction
  • The utilities use three types of load
    forecasting
  • Long term (e.g. 20 years)
  • Medium term. (e.g. 3-8 weeks)
  • Short term (e.g. one week)
  • This lecture presents the short term load
    forecasting techniques

11
Definitions and Expected Results(Big picture)
  • The short term load forecasting provides load
    data for each hour and cover a period of one
    week.
  • The load data are
  • hourly or half-hourly peak load in kW
  • hourly or half-hourly values of system energy in
    kWh
  • Daily and weekly system energy in kWh

12
Definitions and Expected Results(Big picture)
  • The short term load forecasting is performed
    daily or weekly.
  • The forecasted data are continuously updated.
  • Typical short-term, daily load forecast is
    presented in the Table in the next page. (Salt
    River Project, SRP)

13
Definitions and Expected Results(Big picture)
  • Typical short-term, daily load forecast from Salt
    River Project. Hourly Load in MW

14
Definitions and Expected Results(Big picture)
  • Typical short-term, daily load forecast from Salt
    River Project. Hourly Load in MW

15
Importance of Short-term Load Forecasting
  • Provide load data to the dispatchers for economic
    and reliable operation of the local power system.
  • The timeliness and accuracy of the data affects
    the cost of operation.
  • Example The increase of accuracy of the
    forecast by 1 reduced the operating cost by L
    10M in the British Power system in 1985

16
Importance of Short-term Load Forecasting
  • The forecasted data are used for
  • Unit commitment.
  • selection of generators in operation,
  • start up/shut down of generation to minimize
    operation cost
  • Hydro scheduling to optimize water release from
    reservoirs
  • Hydro-thermal coordination to determine the least
    cost operation mode (optimum mix)

17
Importance of Short-term Load Forecasting
  • The forecasted data are used for
  • Interchange scheduling and energy purchase.
  • Transmission line loading
  • Power system security assessment.
  • Load-flow
  • transient stability studies
  • using different contingencies and the predicted
    loads.

18
Importance of Short-term Load Forecasting
  • These off-line network studies
  • detect conditions under which the system is
    vulnerable
  • permit preparation of corrective actions
  • load shedding,
  • power purchase,
  • starting up of peak units,
  • switching off interconnections, forming islands,
  • increase spinning and stand by reserve

19
Impute Data and System Parameters for Load
Forecasting
  • The system load is the sum of individual load.
  • The usage of electricity by individuals is
    unpredictable and varies randomly.
  • The system load has two components
  • Base component
  • Randomly variable component

20
Impute Data and System Parameters for Load
Forecasting
  • The factors affecting the load are
  • economical or environmental
  • time
  • weather
  • Unforeseeable random events

21
Impute Data and System Parameters for Load
Forecasting
  • Economical or environmental factors
  • Service area demographics (rural, residential)
  • Industrial growth.
  • Emergence of new industry, change of farming
  • Penetration or saturation of appliance usage
  • Economical trends (recession or expansion)
  • Change of the price of electricity
  • Demand side load management

22
Impute Data and System Parameters for Load
Forecasting
  • The time constraints of economical or
    environmental factors are slow,
  • measured in years.
  • This factors explains the regional variation of
    the load model (New York vs. Kansas)
  • The load model depends on these slow changing
    factors and has to be updated periodically

23
Impute Data and System Parameters for Load
Forecasting
  • Time Factors affecting the load
  • Seasonal variation of load (summer, winter etc.).
    The load change is due to
  • Change of number of daylight hours
  • Gradual change of average temperature
  • Start of school year, vacation
  • Calls for a different model for each season

24
Impute Data and System Parameters for Load
Forecasting
  • Typical Seasonal Variation of Load
  • Summer peaking utility

25
Impute Data and System Parameters for Load
Forecasting
  • Time Factors affecting the load
  • Daily variation of load. ( night, morning,etc)

26
Impute Data and System Parameters for Load
Forecasting
  • Weekly Cyclic Variation
  • Saturday and Sunday significant load reduction
  • Monday and Friday slight load reduction
  • Typical weekly load pattern

27
Impute Data and System Parameters for Load
Forecasting
  • Time Factors affecting the load
  • Holidays (Christmas, New Years)
  • Significant reduction of load
  • Days proceeding or following the holidays also
    have a reduced load.
  • Pattern change due to the tendency of prolonging
    the vacation

28
Impute Data and System Parameters for Load
Forecasting
  • Weather factors affecting the load
  • The weather affects the load because of weather
    sensitive loads
  • air-conditioning
  • house heating
  • irrigation

29
Impute Data and System Parameters for Load
Forecasting
  • Weather factors affecting the load
  • The most important parameters are
  • Forecasted temperature
  • Forecasted maximum daily temperature
  • Past temperature
  • Regional temperature in regions with
  • diverse climate

30
Impute Data and System Parameters for Load
Forecasting
  • Weather Factors Affecting the Load
  • The most important parameters are
  • Humidity
  • Thunderstorms
  • Wind speed
  • Rain, fog, snow
  • Cloud cover or sunshine

31
Impute Data and System Parameters for Load
Forecasting
  • Random Disturbances Effects on Load
  • Start or stop of large loads (steel mill,
    factory, furnace)
  • Widespread strikes
  • Sporting events (football games)
  • Popular television shows
  • Shut-down of industrial facility

32
Impute Data and System Parameters for Load
Forecasting
  • The different load forecasting techniques use
    different sets of data listed before.
  • Two -three years of data is required for the
    validation and development of a new forecasting
    program.
  • The practical use of a forecasting program
    requires a moving time window of data

33
Impute Data and System Parameters for Load
Forecasting
  • The moving time window of data requires
  • Data covering the last 3-6 weeks
  • Data forecasted for the forecasting period,
    generally one week

34
Impute Data and System Parameters for Load
Forecasting
  • The selection of long periods of historical data
    eliminates the seasonal variation
  • The selection of short periods of historical data
    eliminates the processes that are no longer
    operative.

35
Impute Data and System Parameters for Load
Forecasting
  • The forecasting is a continuous process.
  • The utility forecasts the load of its service
    area.
  • The forecaster
  • prepares a new forecast for everyday and
  • updates the existing forecast daily
  • The data base is a moving window of data

36
Major Load Forecasting Techniques
  • Statistical methods
  • Artificial Neural Networks
  • Fuzzy logic
  • Evolutionary programming
  • Simulated Annealing and expert system
  • Combination of the above methods

37
Major Load Forecasting Techniques
  • The statistical methods will be discussed briefly
    to explain the basic concept of the load
    forecasting
  • This lecture concentrates on load forecasting
    methods using neural networks and fuzzy logic

38
Concept of STLF Model Development
  • Model selection
  • Calculation and update of model parameters
  • Testing the model performance
  • Update/modification of the model if the
    performance is not satisfactory

39
Concept of STLF Model Development
  • Model selection
  • Selection of mathematical techniques that match
    with the local requirements
  • Calculation and update of model parameters
  • This includes the determination of the constants
    and
  • selection of the method to update the constants
    values as the circumstance varies. (seasonal
    changes)

40
Concept of STLF Model Development
  • Testing the model performance
  • First the model performance has to be validated
    using 2-3 years of historical data
  • The final validation is the use of the model in
    real life conditions. The evaluation terms are
  • accuracy
  • ease of use
  • bad/anomalous data detection

41
Concept of STLF Model Development
  • Update/modification of the model if the
    performance is not satisfactory
  • Due to the changing circumstances (regional
    gross, decline of local industry etc.) the model
    becomes obsolete and inaccurate,
  • Model performance, accuracy has to be evaluated
    continuously
  • Periodic update of parameters or the change of
    model structure is needed

42
Artificial Neural Networksfor STLF
43
Artificial Neural Networksfor STLF
  • Several Artificial Neural Network (ANN) based
    load forecasting programs have been developed.
  • The following neural networks were tested for
    load forecasting
  • Feed-forward type ANN
  • Radial based ANN
  • Recurrent type ANN

44
Building Blocks of a Feed Forward Network
  • A Feed forward Three-Layered Perceptron Type ANN
    was selected to demonstrate the short term load
    forecasting technique.
  • The selected network forecasts
  • Hourly loads
  • Peak load of the day
  • Total load of the day.

45
Building Blocks of a Feed Forward Network
  • The forecasting with neural network will be
    demonstrated using a feed forward three-layered
    network to forecast the peak load of the day.
  • The network has
  • one output (load in kW)
  • three input (previous day max. load and
    temperature, forecasted max. temperature)_

46
Building Blocks of a Feed Forward Network
  • The structure of the Feed Forward Three-Layered
    Perceptron Type ANN is presented on the next
    page.
  • The network contains
  • i 1.. 3 input layer nodes
  • j 15 hidden layer nodes
  • k 1 output layer nodes

47
Artificial Neural Networksfor STLF
48
Building Blocks of a Feed Forward Network
  • The inputs are
  • X1 previous day max. load
  • X2 previous day max. temperature
  • X3 forecasted max. temperature
  • Wij weight factor between input and hidden
    layer
  • wj weight factor between hidden layer and
    output

49
Building Blocks of a Feed Forward Network
  • A sigmoid function is placed in the nodes
    (neurons) of the hidden layer and output node.
  • The sigmoid equation for an arbitrary Z function
    is
  • Y output maximum load

50
Building Blocks of a Feed Forward Network
  • Inputs Xi are multiplied by the connection
    weights (Wij) and passed on to the neurons in the
    hidden layer.
  • The weighted inputs (XiWij) to each neurons are
    added together and passed through a sigmoid
    function.
  • Input of hidden layer neuron 1 is

51
Building Blocks of a Feed Forward Network
  • The output Hj of the jth hidden layer node is

52
Building Blocks of a Feed Forward Network
  • Inputs Hj are multiplied by the connection
    weights (wk) and passed on to the neurons in the
    output layer.
  • The weighted inputs (Hjwk) to each output
    neurons are added together and passed through a
    sigmoid function.
  • Input of output neuron is

53
Building Blocks of a Feed Forward Network
  • The output Y is

54
Training of the Feed Forward Neural Network
  • The described neural network is trained using
    historical data.
  • Typical data set contains 2-3 years of load and
    weather data.
  • Error back propagation (BP) method is used for
    the training.
  • During the learning the weights are adjusted
    repeatedly.

55
Training of the Feed Forward Neural Network
  • The output produced by the ANN in response to
    inputs are repeatedly compared with the correct
    answers
  • Each time the weights are adjusted slightly by
    beck-propagating the error at the output layer
    through the ANN
  • Equations for the training are presented in the
    next page

56
Training of the Feed Forward Neural Network
  • The equations used for the training are
  • Weight is between input and hidden layer
  • Weight is between hidden layer and output

57
Training of the Feed Forward Neural Network
  • In the equations
  • Yactual is the true value of the output load
  • e is learning factor (0.3-0.8)
  • n is the number of learning cycles
  • Xj is the input value belongs to Yactual
  • A numerical example demonstrates the use of
    neural forecasting method.

58
Training of the Feed Forward Neural Network
  • The over training has to be avoided using the
    cross validation method
  • The training set is divided into two parts.
    (Part 1 two years data, Part 2 one year data)
  • Part 1 is used to train the network, by passing
    the data through the network.
  • Few hundred times pass represents a training
    period.

59
Training of the Feed Forward Neural Network
  • The over training of the network has to be
    avoided
  • Part 2 is used to check the effectiveness of the
    training.
  • After each training period the error is
    calculated when the network is supplied by the
    input data of Part 2.
  • The increase of error indicates over training,
    when the training has to be stopped

60
Load Forecasting Engine
  • The EPRI developed a Load Forecasting Engine
    using 24 Neural networks.
  • One network forecasts the load for each hour of
    the day.
  • The networks are grouped into four (4) categories
    depending on time of the day.
  • The categories have different inputs.

61
Load Forecasting Engine
The construction of the engine shows the four
groups of neural networks.
62
Load Forecasting Engine
  • The four categories are
  • Category 1. Nine neural networks. Forecasts the
    load between 1-9AM .
  • Category 2. Nine neural networks. Forecasts the
    load between 10AM -2PM and 7 -10PM .
  • Category 3. Four neural networks. Forecasts the
    load between 3-6 PM .
  • Category 4. Two neural networks. Forecasts the
    load between 11-12 PM .

63
Load Forecasting Engine
  • The inputs in four categories are
  • Category 1. Forecast for early morning
  • general input
  • load in the last three-four hours
  • temperature in the last three-four hours
  • Category 2. Forecast for off peak hours
  • general input
  • forecast temperature of previous hours
  • yesterdays load and temperature of hours close
    to this hours

64
Load Forecasting Engine
  • The inputs in four categories are
  • Category 3. Forecast for afternoon peak hours
  • general input
  • forecast temperatures of previous and feature
    hours close to this hours.
  • yesterdays load and temperature of hours close
    to this hours
  • Category 4. Forecast for late night hours
  • general input
  • forecast temperatures for the four proceeding
    hours

65
Load Forecasting Engine
  • The general input variables are
  • same hour load, temperature and humidity of one
    day ago. (3)
  • same hour load, temperature and humidity of two
    days ago. (3)
  • same hour load and temperature seven (7) days ago
    (2)

66
Load Forecasting Engine
  • The general input variables are (continuation)
  • same hour forecast temperature and relative
    humidity of the next day (2)
  • day of the week index (Sunday 01, Monday 02 etc.)

67
Load Forecasting Engine
  • The load forecasting engine has one output for
    the hourly load
  • The extended forecast uses the forecasted values.
    E.g. The two-day ahead forecast uses values
    obtained by the one-day ahead forecast.
  • The forecast can be updated each hour using the
    recent load and weather data

68
Load Forecasting Engine
  • The weights in the neural network are adjusted
    daily.
  • The retraining uses the actual load and weather
    data of the past few days.
  • The retraining helps to follow the trends,
    changes of weather patter e.t.c

69
Load Forecasting For Holidays
  • The load during the holidays has different
    patterns and is significantly reduced.
  • The forecast is inaccurate because of the small
    number of historical data.
  • The holiday is treated as
  • Saturday if the shopping centers are open
  • Sunday if the shopping centers are not open

70
Hourly Weather Forecast
  • The weather service provides forecasts for
  • daily maximum and minimum temperature
  • daily maximum and minimum relative humidity
  • rain and fog
  • maximum wind speed
  • No hourly data are provided.

71
Hourly Weather Forecast
  • EPRI developed an hourly temperature and humidity
    forecasting engine.
  • Single neural network with
  • 28 inputs
  • hourly temperature of the previous day)
  • high and low temperature of the two previous day
  • 24 outputs expected hourly temperatures.

72
Load Forecasting Results
73
Load Forecasting Results
Comparison of forecasted and actual loads
74
Load Forecasting Results
  • Accuracy less than 3 for the next days
    forecast is considered good
  • The longer term forecast accuracy is less (7-8)

75
Appendix 1
  • Derivation of Learning Algorithm

76
Derivation of Learning Algorithm
  • The output of the hidden and output layer and the
    error function are

77
Derivation of Learning Algorithm
  • The update of the weight factors require
    iteration
  • For the calculation of the derivative the
    following substitutions are used

78
Derivation of Learning Algorithm
  • After substitutions the equations are

79
Derivation of Learning Algorithm
  • The derivation of the error function results in
  • The derivative of the u function is

80
Derivation of Learning Algorithm
  • The derivative of the output function is

81
Derivation of Learning Algorithm
  • The derivation of the auxiliary function Y2
    gives
  • The derivative of Y1 function is

82
Derivation of Learning Algorithm
  • Substituting the results in the equations

83
Derivation of Learning Algorithm
  • The rearrangement of the output equation results
    in
  • The final equation for the update of dwj is

84
Derivation of Learning Algorithm
  • The derivative of the hidden layer function is

85
Derivation of Learning Algorithm
  • The derivation of the auxiliary function h2
    gives
  • The derivative of h1 function is

86
Derivation of Learning Algorithm
  • Substituting the results in the equations

87
Derivation of Learning Algorithm
  • The rearrangement of the output equation results
    in
  • The final equation for the update of dWij is

88
Derivation of Learning Algorithm
  • Substituting the results in the equations which
    is used to iterate the wj value

89
Derivation of Learning Algorithm
  • The two training algorithms are
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