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SHORT TERM LOAD FORECASTING USING NEURAL

NETWORKS AND FUZZY LOGIC

- George G Karady
- Arizona State University

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)

Short Term Load ForecastingContent

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

Overview of Short Term Load Forecasting (STLF)

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.

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

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

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.

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)

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

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

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)

Definitions and Expected Results(Big picture)

- Typical short-term, daily load forecast from Salt

River Project. Hourly Load in MW

Definitions and Expected Results(Big picture)

- Typical short-term, daily load forecast from Salt

River Project. Hourly Load in MW

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

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)

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.

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

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

Impute Data and System Parameters for Load

Forecasting

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

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

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

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

Impute Data and System Parameters for Load

Forecasting

- Typical Seasonal Variation of Load
- Summer peaking utility

Impute Data and System Parameters for Load

Forecasting

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

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

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

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

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

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

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

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

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

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.

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

Major Load Forecasting Techniques

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

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

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

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)

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

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

Artificial Neural Networksfor STLF

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

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.

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)_

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

Artificial Neural Networksfor STLF

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

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

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

Building Blocks of a Feed Forward Network

- The output Hj of the jth hidden layer node is

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

Building Blocks of a Feed Forward Network

- The output Y is

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.

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

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

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.

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.

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

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.

Load Forecasting Engine

The construction of the engine shows the four

groups of neural networks.

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 .

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

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

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)

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.)

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

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

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

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.

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.

Load Forecasting Results

Load Forecasting Results

Comparison of forecasted and actual loads

Load Forecasting Results

- Accuracy less than 3 for the next days

forecast is considered good - The longer term forecast accuracy is less (7-8)

Appendix 1

- Derivation of Learning Algorithm

Derivation of Learning Algorithm

- The output of the hidden and output layer and the

error function are

Derivation of Learning Algorithm

- The update of the weight factors require

iteration - For the calculation of the derivative the

following substitutions are used

Derivation of Learning Algorithm

- After substitutions the equations are

Derivation of Learning Algorithm

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

Derivation of Learning Algorithm

- The derivative of the output function is

Derivation of Learning Algorithm

- The derivation of the auxiliary function Y2

gives - The derivative of Y1 function is

Derivation of Learning Algorithm

- Substituting the results in the equations

Derivation of Learning Algorithm

- The rearrangement of the output equation results

in - The final equation for the update of dwj is

Derivation of Learning Algorithm

- The derivative of the hidden layer function is

Derivation of Learning Algorithm

- The derivation of the auxiliary function h2

gives - The derivative of h1 function is

Derivation of Learning Algorithm

- Substituting the results in the equations

Derivation of Learning Algorithm

- The rearrangement of the output equation results

in - The final equation for the update of dWij is

Derivation of Learning Algorithm

- Substituting the results in the equations which

is used to iterate the wj value

Derivation of Learning Algorithm

- The two training algorithms are