SHORT TERM LOAD FORECASTING USING NEURAL NETWORKS AND FUZZY LOGIC

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SHORT TERM LOAD FORECASTING USING NEURAL
NETWORKS AND FUZZY LOGIC

• George G Karady
• Arizona State University

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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)

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Short Term Load ForecastingContent

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

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Overview of Short Term Load Forecasting (STLF)
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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.

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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

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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

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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.

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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)

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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

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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

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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)

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Definitions and Expected Results(Big picture)

• Typical short-term, daily load forecast from Salt
  River Project. Hourly Load in MW

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Definitions and Expected Results(Big picture)

• Typical short-term, daily load forecast from Salt
  River Project. Hourly Load in MW

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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

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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)

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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.

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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

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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

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Impute Data and System Parameters for Load
Forecasting

• The factors affecting the load are
• economical or environmental
• time
• weather
• Unforeseeable random events

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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

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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

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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

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Impute Data and System Parameters for Load
Forecasting

• Typical Seasonal Variation of Load
• Summer peaking utility

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Impute Data and System Parameters for Load
Forecasting

• Time Factors affecting the load
• Daily variation of load. ( night, morning,etc)

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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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

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Major Load Forecasting Techniques

• Statistical methods
• Artificial Neural Networks
• Fuzzy logic
• Evolutionary programming
• Simulated Annealing and expert system
• Combination of the above methods

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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

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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

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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)

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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

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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

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Artificial Neural Networksfor STLF
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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

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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.

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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)_

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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

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Artificial Neural Networksfor STLF
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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

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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

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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

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Building Blocks of a Feed Forward Network

• The output Hj of the jth hidden layer node is

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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

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Building Blocks of a Feed Forward Network

• The output Y is

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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.

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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

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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

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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.

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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.

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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

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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.

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Load Forecasting Engine
The construction of the engine shows the four
groups of neural networks.
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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 .

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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

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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

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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)

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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.)

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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

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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

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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

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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.

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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.

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Load Forecasting Results
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Load Forecasting Results
Comparison of forecasted and actual loads
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Load Forecasting Results

• Accuracy less than 3 for the next days
  forecast is considered good
• The longer term forecast accuracy is less (7-8)

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Appendix 1

• Derivation of Learning Algorithm

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Derivation of Learning Algorithm

• The output of the hidden and output layer and the
  error function are

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Derivation of Learning Algorithm

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

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Derivation of Learning Algorithm

• After substitutions the equations are

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Derivation of Learning Algorithm

• The derivation of the error function results in
• The derivative of the u function is

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Derivation of Learning Algorithm

• The derivative of the output function is

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Derivation of Learning Algorithm

• The derivation of the auxiliary function Y2
  gives
• The derivative of Y1 function is

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Derivation of Learning Algorithm

• Substituting the results in the equations

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Derivation of Learning Algorithm

• The rearrangement of the output equation results
  in
• The final equation for the update of dwj is

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Derivation of Learning Algorithm

• The derivative of the hidden layer function is

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Derivation of Learning Algorithm

• The derivation of the auxiliary function h2
  gives
• The derivative of h1 function is

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Derivation of Learning Algorithm

• Substituting the results in the equations

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Derivation of Learning Algorithm

• The rearrangement of the output equation results
  in
• The final equation for the update of dWij is

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Derivation of Learning Algorithm

• Substituting the results in the equations which
  is used to iterate the wj value

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Derivation of Learning Algorithm

• The two training algorithms are