short-term load forecasting based on neural network and local regression

1

Short-term Load Forecasting based on Neural network and Local Regression

On Complex and Adaptive System SeminarOn Complex and Adaptive System SeminarCAS 502, Iowa State UniversityCAS 502, Iowa State University

3pm, Oct 25, 20023pm, Oct 25, 2002

Jie BaoJie BaoArtificial Intelligence Lab, Artificial Intelligence Lab, Dept of Computer ScienceDept of Computer Science

Iowa State University, Iowa State University, Ames, IA, 50010Ames, IA, 50010

[email protected]@cs.iastate.edu

2

Outline- A gradually improvement

1- Stereotyped General Introduction 1- Stereotyped General Introduction 2- Determining factors in STLF2- Determining factors in STLF 3- STLF by Neural Network (NN)3- STLF by Neural Network (NN) 4- STLF by Moving Average(MA)4- STLF by Moving Average(MA) 5- From MA to Local Regression(LR)5- From MA to Local Regression(LR) 6- Cooperation of NN and LR !6- Cooperation of NN and LR ! 7- Stereotyped Summary7- Stereotyped Summary

3

Outline


4

What’s Load Forecasting?

Tell the Future!Tell the Future! An central problem in the operation and planning An central problem in the operation and planning

of electrical power generation. of electrical power generation. To minimize the operating cost, electric supplier To minimize the operating cost, electric supplier

will use forecasted load to control the number of will use forecasted load to control the number of running generator unit. running generator unit.

Short-term load forecasting(STLF) is for hour to Short-term load forecasting(STLF) is for hour to hour forecasting and important to daily hour forecasting and important to daily maintaining of power plant maintaining of power plant

5

Taxonomy of Load Forecasting

Spatial forecastingSpatial forecasting : forecasting future : forecasting future load distribution in a special region, such as load distribution in a special region, such as a county, a state, or the whole country. a county, a state, or the whole country.

Temporal forecastingTemporal forecasting is dealing with is dealing with forecasting load for a specific supplier or forecasting load for a specific supplier or collection of consumers in future hours, collection of consumers in future hours, days, months, or even years. days, months, or even years.

6

Taxonomy of Load Forecasting(Cont)

Temporal forecastingTemporal forecasting Long-termLong-term load forecasting load forecasting (LTLF): mainly for (LTLF): mainly for

system planning, Typically covers a period of 10 to 20 system planning, Typically covers a period of 10 to 20 years years

Medium-termMedium-term load forecasting load forecasting (MTLF): mainly for (MTLF): mainly for the scheduling of fuel supplies and maintenance. the scheduling of fuel supplies and maintenance. usually covers a few weeks. usually covers a few weeks.

Short-termShort-term load forecastingload forecasting (STLF): for the day-to- (STLF): for the day-to-day operation and scheduling of the power system. day operation and scheduling of the power system.

7

Short-term load forecasting

A STLF forecaster calculates the estimated load A STLF forecaster calculates the estimated load for each hours of the day, the daily peak load, or for each hours of the day, the daily peak load, or the daily or weekly energy generation. the daily or weekly energy generation.

STLF is important to supplier because they can STLF is important to supplier because they can use the forecasted load to control the number of use the forecasted load to control the number of generators in operation, generators in operation, shut up some unit when forecasted load is low shut up some unit when forecasted load is low start up of new unit when forecasted load is high.start up of new unit when forecasted load is high.

8

Approaches Review

Time-series / Regression approachTime-series / Regression approach Group Method of Data HandlingGroup Method of Data Handling Feed-forward Network Approach MLP,BP,RBF)Feed-forward Network Approach MLP,BP,RBF) Recurrent Network ApproachRecurrent Network Approach Competitive Network ApproachCompetitive Network Approach Evolutionary Network ApproachEvolutionary Network Approach Modular / Hierarchical / Hybrid Network ApproachModular / Hierarchical / Hybrid Network Approach Fuzzy ApproachFuzzy Approach Bayesian Network ApproachBayesian Network Approach

9

Outline


10

Determining factors

CalendarCalendar Seasonal variation Seasonal variation Daily variation Daily variation Weekly Cyclic Weekly Cyclic Holidays Holidays

Economical or environmentalEconomical or environmental Weather Weather

Temperature Temperature Cloud cover or sunshine Cloud cover or sunshine Humidity Humidity

Unforeseeable random events Unforeseeable random events

11

Seasonal variation

Spring, Summer, Spring, Summer, Fall, Winter Fall, Winter ––Change of number Change of number

of daylight hoursof daylight hours ––Gradual change of Gradual change of

average temperature average temperature ––Start of school Start of school

year, vacation year, vacation whole year of 2001

12

Seasonal variation(Cont)

Three years (166 weeks, Jan 1,1999- Mar, 2002) Three years (166 weeks, Jan 1,1999- Mar, 2002)

0 20 40 60 80 100 120 140 160 180-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

13

Daily variation

NightNight MorningMorning NoonNoon AfternoonAfternoon

forecasted and actual forecasted and actual

load around Mar 3, 2002 =>load around Mar 3, 2002 =>

14

Weekly Cycle

Saturday and Saturday and Sunday significant Sunday significant load reductionload reduction

Monday and Friday Monday and Friday slight load slight load reduction reduction

Week circle in PSE data, 5 weeks, Week circle in PSE data, 5 weeks, 1/1/1999 – 2/4/1999 =>1/1/1999 – 2/4/1999 =>

05001000

1500200025003000

350040004500

1 64 127

190

253

316

379

442

505

568

631

694

757

820

15

Holidays

Apparent load Apparent load different between different between Christmas day (the Christmas day (the hour 121-145 in the hour 121-145 in the figure) and other days. figure) and other days.

Similar different can Similar different can be found in each year. be found in each year.

Christmas Eve and Christmas Eve and 12/26 also different to 12/26 also different to normal load curve. normal load curve.

Load around Christmas, from 12/20 to Load around Christmas, from 12/20 to 12/31, in 1999, 2000 and 2001.12/31, in 1999, 2000 and 2001.

16

Economical or Environmental Factors

Service area demographics (rural, residential)Service area demographics (rural, residential) Industrial growth.Industrial growth. Emergence of new industry, change of farmingEmergence of new industry, change of farming Penetration or saturation of appliance usagePenetration or saturation of appliance usage Economical trends (recession or expansion)Economical trends (recession or expansion) Change of the price of electricityChange of the price of electricity Demand side load management Demand side load management

17

Weather

Air TemperatureAir Temperature Dew TemperatureDew Temperature Wet Bulb TempWet Bulb Temp Relative HumidityRelative Humidity ThunderstormsThunderstorms Wind speedWind speed Rain, fog, snowRain, fog, snow Cloud cover or Cloud cover or

sunshine sunshine

0102030405060708090100

1 917 25 33 41 49 57 65 73 81 89 97

105

113

121

129

(1) Air Temp(2) Dew Temp(3) Wet Bulb Temp(4) Relative Humidity

(2)

(1)

(4)

(3)

18

Weather(Cont)

Not all weather factors are important. Not all weather factors are important. Some are typically random: wind speed and thundSome are typically random: wind speed and thund

erstorms. erstorms. Some factors are interrelated. Eg: temperature is pSome factors are interrelated. Eg: temperature is p

artly controlled by cloud cover, rain and snow. artly controlled by cloud cover, rain and snow. TemperatureTemperature is the most important because it has d is the most important because it has d

irect influence on many kind of electrical consumpirect influence on many kind of electrical consumptiontion

Leading weather influential factor for specific conLeading weather influential factor for specific consumer may be different. sumer may be different.

19

Temperature

Average temperature (CAverage temperature (City A, 1996), [ Postiveity A, 1996), [ Postively correlated with loaly correlated with load in summer ]d in summer ]

July: 73.99,July: 73.99, Aug: 70.84Aug: 70.84 Sept: 60.13 Sept: 60.13

0

100

200

300

400

500

600

J uly

Aug

Sept

20

Unforeseeable random events

Start or stop of large loads (steel mill, Start or stop of large loads (steel mill, factory, furnace)factory, furnace)

Widespread strikes Widespread strikes Sporting events (football games)Sporting events (football games) Popular television showsPopular television shows Shut-down of industrial facility Shut-down of industrial facility

21

Outline


22

Neural Network for STLP

…

……

……

…

Load History

CalendarInformation

WeatherInformation

Forecasted Load

23

Why can use Neural Network?

The Load is function of a lot of factorsThe Load is function of a lot of factors Can also be viewed as Time SeriesCan also be viewed as Time Series

L(n) = f( past(L), Calendar, Weather, Other)L(n) = f( past(L), Calendar, Weather, Other)

f is complex and unknown, but really f is complex and unknown, but really existent and existent and consistentconsistent

Use Neural network to approximate f !Use Neural network to approximate f !

24

Hour-ahead model Net Structure: 9 - 8 – 1 Net Structure: 9 - 8 – 1 INPUTINPUT

1-hour : 1-241-hour : 1-24 2-Temperature: real (not the forecasted temperature)2-Temperature: real (not the forecasted temperature) 3-load of last day, this hour3-load of last day, this hour 4-load of last hour4-load of last hour 5-load of this hour5-load of this hour 6-Weekend: 1,06-Weekend: 1,0 7,8,9 - Weekday: 001 - 1117,8,9 - Weekday: 001 - 111

OUPUTOUPUT load of next hourload of next hour

25

Hour-ahead model (Cont)

Training set: Jan 2- Training set: Jan 2- Jan 30 ,2002 ( 696 Jan 30 ,2002 ( 696 points)points)

Test set: Jan 31- Test set: Jan 31- Feb28, 2002 ( 696 Feb28, 2002 ( 696 points)points)

normalization : to normalization : to N(0,1)N(0,1)

Total Error: 1.53 % Total Error: 1.53 %

26

1- 24 hour ahead model Net Structure: 8 - 8 – 1 Net Structure: 8 - 8 – 1 INPUTINPUT

1-hour : 1-241-hour : 1-24 2-Temperature: real2-Temperature: real 3-load of two days ago, forecasting hour3-load of two days ago, forecasting hour 4-load of one day ago, forecasting hour4-load of one day ago, forecasting hour 5-load of 12 hours ago5-load of 12 hours ago 6-load of last hour6-load of last hour 7-load of this hour7-load of this hour 8-Weekday: 0 - 78-Weekday: 0 - 7 9-Weekend: 1,09-Weekend: 1,0

OUPUTOUPUT load of x hours later (x = 1..24)load of x hours later (x = 1..24)

27

Use Ensemble Neural Nets

Single net Average error

(%)

Single net Maximal error

(%)

Ensemble net Average error

(%)

Ensemble net Maximal error

(%)

Reduction on Average error

(%)

Reduction on Maximal error

(%)1.

1.66 9.35 2.

3.21 21.69 4.60 20.29 -43.30 6.45

3.

4.33 38.13 4.72 20.40 -9.01 46.504.

4.50 21.24 4.80 20.67 -6.67 2.68

5.

5.36 31.05 4.90 20.80 8.58 33.016.

5.71 30.25 4.93 20.99 13.66 30.61

7.

5.88 30.20 4.98 21.44 15.31 29.018.

6.73 35.57 5.00 21.21 25.71 40.37

9.

6.00 38.83 4.98 20.81 17.00 46.4110.

5.46 36.66 4.97 19.85 8.97 45.85

11.

5.60 29.74 5.00 18.65 10.71 37.2912.

5.26 21.06 5.02 17.97 4.56 14.67

13.

5.80 26.72 5.08 18.32 12.41 31.4414.

6.38 32.08 6.09 19.17 4.55 40.24

15.

5.90 24.57 5.06 18.86 14.24 23.2416.

6.31 26.85 5.07 18.94 19.65 29.46

17.

6.53 26.86 5.07 18.79 22.36 30.0418.

6.60 53.82 5.05 17.75 23.48 67.02

19.

6.68 58.55 4.96 19.64 25.75 66.4620.

7.85 41.83 5.01 21.93 36.18 47.57

21.

5.68 38.00 5.11 20.17 10.04 46.9222.

5.44 28.76 5.24 21.09 3.68 26.67

23.

6.15 32.59 5.49 23.24 10.73 28.6924.

5.45 22.52

28

Advantages of NN

Need little expertise knowledge for the probNeed little expertise knowledge for the problem, a good black-box mode tool to be begilem, a good black-box mode tool to be begining withning with

General algorithm is ready to be usedGeneral algorithm is ready to be used Can apply/hide inputs to guess importance Can apply/hide inputs to guess importance

of variablesof variables

29

Weakness of NN

Long training timeLong training time Not stableNot stable Hard to use known periodical informationHard to use known periodical information Can’t online updatingCan’t online updating Usually needs a bunch of nets for Usually needs a bunch of nets for

winter/summer, or weekday/weekendwinter/summer, or weekday/weekend Anyway, Not good enough: 1.53% / 5.45%Anyway, Not good enough: 1.53% / 5.45%

30

Outline


31

STLF by moving average Learn changing trend as time series!Learn changing trend as time series! Cycle at different levelCycle at different level

1-1- daily cycledaily cycle 2-2- weekly cycleweekly cycle 3-3- yearly cycleyearly cycle

so we can use some moving average model to foreso we can use some moving average model to forecast future load. cast future load.

LLii is load at past reference point, eg. a week ago , w is load at past reference point, eg. a week ago , w ii is its weight is its weight

i

iiLwL

32

Day-Ahead Forecast

Based on load of 6*24 hour Based on load of 6*24 hour before and adjust it with error before and adjust it with error between now and 7*24 hours between now and 7*24 hours ago.ago.

Jan 9 – Mar 10, 2002 Average Jan 9 – Mar 10, 2002 Average error = 5.74% , Maximal error = error = 5.74% , Maximal error = 30.74%,30.74%,

on whole year data of 2001, use on whole year data of 2001, use past weeks data 75% last week + past weeks data 75% last week + 25% last last week25% last last weekaverage error = 4.62%, max error average error = 4.62%, max error = 42.38% = 42.38%

33

Temperature shifting

Temperature as a shift factor for average loadTemperature as a shift factor for average load Eg: Basic pattern for user SIC5411,ID143 in July, Aug and Sept , Eg: Basic pattern for user SIC5411,ID143 in July, Aug and Sept ,

1996. Average temperature: July: 73.99, Aug: 70.84, Sept: 60.131996. Average temperature: July: 73.99, Aug: 70.84, Sept: 60.13 Average temperature is positively related during summer for this useAverage temperature is positively related during summer for this use

rr

0 5 10 15 20 25350

400

450

500

550

600

650

0 5 10 15 20 25350

400

450

500

550

600

0 5 10 15 20 25380

400

420

440

460

480

500

520

540

560

580

34

Temperature shifting(Cont)

Whole year for 2001(52 Whole year for 2001(52 weeks) weeks)

Normalized average load Normalized average load and temperature (dashed and temperature (dashed line) for every weekline) for every week

linear regressive -38.0 linear regressive -38.0 T + 4332.5 = L T + 4332.5 = L

Nearly linear Nearly linear relationship !relationship !

35


Three winter (1999- 2002) -49.2T + 4967.5 = LThree winter (1999- 2002) -49.2T + 4967.5 = L

Three summers (1999- 2002) -6.1T + 2595.3 = L - Three summers (1999- 2002) -6.1T + 2595.3 = L - hardly any linear relationshiphardly any linear relationship

0 20 40 60 80 100 120-3

-2

-1

0

1

2

3

30 35 40 45 50 55 602200

2400

2600

2800

3000

3200

3400

0 10 20 30 40 50 60 70-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

50 52 54 56 58 60 62 64 66 68 701900

2000

2100

2200

2300

2400

2500

36


apparent apparent linear relationshiplinear relationship during winters but no during winters but no strong linear relationship during summer. strong linear relationship during summer.

So we can modify original moving average with So we can modify original moving average with tetemperature shifting factormperature shifting factor: Modified 7-days-ago lo: Modified 7-days-ago load with (T1-T2)*38. ad with (T1-T2)*38.

where T1 is mean T(past 7 days) and T2 is mean T(from 7 daywhere T1 is mean T(past 7 days) and T2 is mean T(from 7 days to 14 days ago). 38 is temperature coefficients to 14 days ago). 38 is temperature coefficient

Whole year 2001: average error = 4.62%->4.39% Whole year 2001: average error = 4.62%->4.39% Jan – Mar 2002: average error = 5.74% ->5.08%Jan – Mar 2002: average error = 5.74% ->5.08%

37

1-48 hour forecasting by weekly moving

Forecasting span Average error Average error with no temperature adjusting Average error in NN model

1 0.0124 0.0124 1.66

2 0.0216 0.0216 3.21

3 0.0290 0.0291 4.33

4 0.0352 0.0353 4.50

5 0.0400 0.0402 5.36

12 0.0513 0.0516 5.26

13 0.0518 0.0521 5.80

14 0.0523 0.0527 6.38

15 0.0528 0.0534 5.90

16 0.0531 0.0538 6.31

17 0.0531 0.0540 6.53

18 0.0527 0.0537 6.60

24 0.0439 0.0453 5.45

48. 0.0547 0.0574

38

MA with forecasted temperature

We can buy forecasted temperature from weather We can buy forecasted temperature from weather company company

Forecasted load L is modified by forecasted Forecasted load L is modified by forecasted temperature: temperature:

LfLf =Average (L of ref dates) - ( Tf - meanT)*31; =Average (L of ref dates) - ( Tf - meanT)*31;Where Tf(k) is forecasted temperature and meanT is average Where Tf(k) is forecasted temperature and meanT is average

temperature over all reference dates. temperature over all reference dates.

Reference dates: -7*24; -14*24, -52*7*24; 104*7Reference dates: -7*24; -14*24, -52*7*24; 104*7*24, -156*7*24 days ago ……*24, -156*7*24 days ago ……

Usually needs a error feedbackUsually needs a error feedback

39

MA with forecasted temperature (Cont)

Day-ahead. test set: Day-ahead. test set: Jan 2,2002 – Feb 28, Jan 2,2002 – Feb 28, 2002, average error = 2002, average error = 3.54% 3.54%

0 200 400 600 800 1000 1200 14001500

2000

2500

3000

3500

4000

40

Advantages of MA

long-range influence from reference dates: long-range influence from reference dates: remains complex calendar information which is remains complex calendar information which is difficult to be encoded in NN: moving average difficult to be encoded in NN: moving average very wellvery well and very simple!and very simple!

short-range influence from Temperature factor: short-range influence from Temperature factor: linear adjust linear adjust

Simple, Stable, Quick and needn’t LearningSimple, Stable, Quick and needn’t Learning

41

Weakness of MA

Needs careful insight expertiseNeeds careful insight expertise Temperature coefficient may not be same Temperature coefficient may not be same

among different weeksamong different weeks Also, not good enough: 1.24% / 3.54% (NN Also, not good enough: 1.24% / 3.54% (NN

is 1.53% / 5.45%)is 1.53% / 5.45%)

42

Outline


43

Three key assumptions:

Week cycle is the most important cycle Week cycle is the most important cycle (includes both week and daily cycle)(includes both week and daily cycle)

If two weeks are adjacent, their pattern are If two weeks are adjacent, their pattern are similarsimilar

The different between calendar similar hour The different between calendar similar hour is basically due to linear influence of is basically due to linear influence of temperature. temperature.

44

From MA to Local Regression

MA : LfMA : Lf =Average (L of ref dates) - ( Tf - =Average (L of ref dates) - ( Tf - meanT)*31;meanT)*31;

Can we use local information other than global regCan we use local information other than global regression in MA? => Local Regressionression in MA? => Local Regression

LR: Lf = L0 + a*TfLR: Lf = L0 + a*Tfwhere Lf : Forecasted Loadwhere Lf : Forecasted Load Tf : Forecasted Temperature Tf : Forecasted Temperature L0: basic load, not temperature sensitive L0: basic load, not temperature sensitive a: a: coefficient coefficient How to get L0 and a locally?How to get L0 and a locally?

45

Local Regression

Do linear regression with (L,T) pairs of ref Do linear regression with (L,T) pairs of ref dates:dates:

L= L0 + a*T L= L0 + a*T => L0, a=> L0, a

Error feedbackError feedback Assumes similar error trends to occur among most Assumes similar error trends to occur among most

of adjacent days. Use last forecasting error to of adjacent days. Use last forecasting error to modify current estimation.modify current estimation.

Average error on Jan – Feb 2002:Average error on Jan – Feb 2002: Day-ahead: 3.22% (MA3.54%, NN5.45%)Day-ahead: 3.22% (MA3.54%, NN5.45%) 2-hour ahead: 2.14% 2-hour ahead: 2.14%

46

Advantages/Weakness of LR

AdvantagesAdvantages Simple but works wellSimple but works well Can online updatingCan online updating No learning requiredNo learning required Uniform model for all seasons: adaptiveUniform model for all seasons: adaptive

WeaknessWeakness Only use week ahead information! Waste too Only use week ahead information! Waste too

much recent temp/load value.much recent temp/load value.

47

Outline


48

Local regression with Neural Network

LR gives a roughly estimation and then NN LR gives a roughly estimation and then NN refines itrefines it

Input to NN:Input to NN: result of local regressionresult of local regression load and temperature of this hourload and temperature of this hour load and temperature of two hour beforeload and temperature of two hour before forecasted (actual) temperature of 24 hours laterforecasted (actual) temperature of 24 hours later

Output to NN: Output to NN: load of 24 hours laterload of 24 hours later

49

Local regression with Neural Network(Cont)

1) Test on 1) Test on WinterWinter days 2001-2002 days 2001-2002 Training set: 8282 point (345 days) Nov 2, Training set: 8282 point (345 days) Nov 2,

2000 – Oct 12, 20012000 – Oct 12, 2001 Test Set: 3550 points (148 days) Oct 13,2001 – Test Set: 3550 points (148 days) Oct 13,2001 –

Mar 9 ,20002Mar 9 ,20002 Average Error = 3.33 %Average Error = 3.33 %

50

Local regression with Neural Network(Cont)

2) Test on 2) Test on SummerSummer days 2001 days 2001 Test set : April 2 2001 - Oct 31, 2001, 5136 hour, 214 Test set : April 2 2001 - Oct 31, 2001, 5136 hour, 214

daysdays Training set: other daysTraining set: other days Average Error = 3.28% (compare with LR:3.43%)Average Error = 3.28% (compare with LR:3.43%)

3) Test on Jan-Feb 20023) Test on Jan-Feb 2002 Training set: 10200 point ( 425 days) Nov 2, 2000 – Training set: 10200 point ( 425 days) Nov 2, 2000 –

Dec 31, 2001Dec 31, 2001 Test Set: 1632Test Set: 1632 points (68 days) Jan 1,2002 – Mar points (68 days) Jan 1,2002 – Mar

9 ,200029 ,20002 2.97% (compare: NN5.45%, MA3.54%,LR 3.22% )2.97% (compare: NN5.45%, MA3.54%,LR 3.22% )

51

Error Feedback’s Fault

Note that in LR, we do error feed back after local Note that in LR, we do error feed back after local regression to improve accuracy.regression to improve accuracy.

However, it may break the possible relationship However, it may break the possible relationship between regression result and actual load. between regression result and actual load.

So now we don’t feed the final result form LR, but So now we don’t feed the final result form LR, but the interim result just after local regression and the interim result just after local regression and before error feedback, into NNbefore error feedback, into NN

52

Error Feedback’s Fault (Cont)

Test on winter 2000 - 2002Test on winter 2000 - 2002 Nov 2 2000 - Mar 31, 2001 & Nov1 2001- Mar 9 2002Nov 2 2000 - Mar 31, 2001 & Nov1 2001- Mar 9 2002 TestNum = 1632 points (68 days) Jan 1,2002 – Mar 9 ,TestNum = 1632 points (68 days) Jan 1,2002 – Mar 9 ,

2000220002 TrainNum = 5064 all other daysTrainNum = 5064 all other days av_err = 2.70%av_err = 2.70%

compares with compares with local regression : 3.22%local regression : 3.22% LR + NN: 2.97%LR + NN: 2.97%

53

Outline


54

Gradually Improvement

NN: 5.45%NN: 5.45% MA: 3.54%MA: 3.54% LR: 3.22%LR: 3.22% NN+LR: 2.97%NN+LR: 2.97% NN+LR+no ErrFeedBack: 2.70%NN+LR+no ErrFeedBack: 2.70%

55

Black box -> White box

At the beginning, we know nothing, so use At the beginning, we know nothing, so use NN to probe, to gropeNN to probe, to grope

Then we find some rule, so we gradually Then we find some rule, so we gradually transfer to white box methodstransfer to white box methods

But there always something we can’t But there always something we can’t understand, so the help of black box is still understand, so the help of black box is still importantimportant

56

Something more

This research:This research:http://www.cs.iastate.edu/~baojie/acad/current/http://www.cs.iastate.edu/~baojie/acad/current/

load/2002-03-22_load.htmload/2002-03-22_load.htm Organized literature :Organized literature :

http://www.cs.iastate.edu/~baojie/acad/http://www.cs.iastate.edu/~baojie/acad/reference/2002-03-13_load.htmreference/2002-03-13_load.htm

57

Thank you!

short-term load forecasting based on neural network and local regression

Technology

stereotyped

iowa state

unforeseeable

error feedbacks

term load

stereotyped

black box

reference