Determining and Forecasting Load Reductions from Demand Side Programs September 11-12, 2007...

Determining and Forecasting Load Reductions from Demand Side Programs

September 11-12, 2007

Presented by:Bill Bland, V.P. Consulting, GoodCents

Liza Thompson, Supervisor-Load Research, GoodCents

Introduction to Sample DesignSample Size

• Determining Sample Size• General formula• N=CV2/(D/Z)2 , where CV is coefficient of

variation, D is percent accuracy desired, and Z is the standard normal deviate for the confidence level desired, Z=1.65 for 90% confidence, 1.96 for 95% confidence


• Determining Sample Size• Example, 100,000 AC, estimate connected load

CV estimate is 0.5• What sample size is necessary to know average

connected load to within 10% at 90% confidence?

• N=CV2/(D/Z)2 , N=(0.5)2/(0.1/1.65)2

• N=68


Sample Size as a funcion of CV for +/- 10% accuracy

0

100

200

300

400

500

600

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

CV

SS 90% confidence

95% Confidence


• Determining Sample Size• Problems encountered in Research

– No estimate of Population CV available– Solution, Use a correlated readily available variable-

almost always billed kWh use– For AC load Management, recommend using July or

August kWh use


• Determining Sample Size• If we have population data available on a

correlated variable such as billed kWh or AC connected load, we can use an alternate formula for sample size


• Determining Sample Size• N=(1-R2)*CV2/(D/Z)2

• Where R is an estimate of the correlation of AC load and August billed kWh and CV is the coefficient of variation of August billed kWh


Sample Size as a Function of R and CV

0

20

40

60

80

100

120

140

160

180

0.4 0.5 0.6 0.71 0.8 0.9

R-Correlation

SS

CV=0.7085

CV=0.6

CV-0.8


Maximum Monthly AC Demand as a function of monthly kWh

0

2

4

6

8

10

12

0 1000 2000 3000 4000 5000 6000

August kWh

kW acmax


• AC Maximum Demand versus August kWh- R=0.5833 using actual End Use LR data, Assume CV of August kWh=0.75

N=(1-R2)*CV2/(D/Z)2

N=(1-.5833 2)*153

N=101


• Note on CV Estimates• CV for Residential Class varies widely

– CV Examples- 500,000 population- 0.82– 700,000 population – 0.6– Calculate CV from Actual Billing Records


• Note on Residential Sample Sizes, CV Estimates

• Typical sample size assuming CV of 0.75 is 150• Use of Regression Estimator typically reduces

sample size to about 115 points assuming R=0.5

Introduction to Sample DesignStratification

• Stratification- Dividing the population into smaller groups with like variance

• We recommend stratification to improve the overall load reduction estimates


• Stratification

• How to determine strata boundaries to minimize variance?

• Use method of Dalenius and Hodges (DH)


Frequency Analysis of AC Connected Load

0

200

400

600

800

1000

1200

0.5 1

1.5 2

2.5 3

3.5 4

4.5 5

5.5 6

6.5 7

7.5 8

8.5 10 11

11.5

24.5 52

kW

Cum

. C

ust

s.

Series1

Introduction to Sample DesignAllocation of Sample to Strata

• We now know our strata and we will assume a sample size of 150

• Do we assume 50 sample points per strata? • We use Neyman allocation to allocate to strata

based on σ of design variable and number of units in each strata

Introduction to Sample DesignAllocation of Sample to Strata

Sample Allocation to Strata based on AC sizing information

Stratum Sizes Neyman AllocationStrata DH Limits sd kW N wt*sd Sample Fraction n-sample size

1 0-3 kW 0.56486 528 0.287882317 41.88% 632 3-4.5 kW 0.36004 406 0.141096757 20.53% 313 >4.5 2.6249 102 0.2584361 37.60% 56

1036 0.687415174 100.00% 150

Introduction to Sample DesignTest and Control Groups

• Don’t we need a test and control group since this is basically an experiment to see the effects of load control on AC use?

• The problems with a test and control group involve cost to do the research and matching up customer demographics and usage patterns to get comparable groups

Introduction to Sample DesignTest and Control Groups

• We prefer to use the test group as its own control, therefore we do not have to match up demographics and we only need one sample

• Customers will be controlled on some days and not controlled on others

• Comparison will be of AC or premise loadshapes on control versus no-control days

• We will use regression analysis to develop the control estimates from our sample

Data Collection and AnalysisMetering Equipment

• Interval Load Data– Interval load data is necessary to develop load

impact estimates for load management programs

– We recommend the collection of at least hourly interval load data and if possible 15-minute data

– The 15 minute data is averaged to get the hourly data


• Premise Metering– Meter Premise with interval meter– Estimate AC load reduction using premise

data– Data must be collected monthly or can be

collected real time if an AMR system is deployed

– Costs $200.00- 300.00 per point


• Premise Metering– Utility may have interval meters for cost of service

load study- no extra cost for equipment– Customer may not need to be recruited, Utility can

gather data since utility owns meter– Load Reduction may be due to other equipment being

turned off– Recommend sample size of at least 150 points if

using premise meters only


• End Use Metering– Can Meter AC Compressor and other load managed

end uses directly, highly accurate (99%)– Load Reduction Estimates are very accurate, smaller

sample sizes (<100) can be used since CV of AC is less than CV of premise

– Customer has to be recruited. Unit must be located next to Home load center( panel box), Unit needs a telephone line, either dedicated line or use customer’s line for downloads. May need to pay customer incentive


• End Use Metering– Can also gather indoor temperature data and

premise data– Cost per site for installation, equipment and

12 months of data collection is $2,000-

$3,000 or more per point


• Run Time Data Collection• This involves a low cost device (<$100) that

senses the on and off time of the compressor• Data must be collected on site and downloaded

to a shuttle once a month• A large sample size is recommended due to high

failure rate (15-20%) of data collection


• Run Time Data Collection failure is usually due to improper placement of the equipment or other equipment interfering with the signal

• This data requires more analysis time since the on-off time must be converted to kW, Data is discontinuous

Data Collection and AnalysisCharacteristics Data

• Characteristics data should be collected at each home– Necessary Data

• AC/ WH Nameplate, Make, Model, Serial Number• Total Square Footage• Indoor Daytime Thermostat Setting

– Like to HaveNumber of Floors (square footage of each if available)

• Number of people in household• Outdoor Construction

Data Collection and AnalysisWeather Data

• We have found that NWS or CMS data for the nearest station is preferable to data collected at the site.

• This is because site data is not collected using NWS/CMS standards.

• Daily and Hourly data can be used in the modeling process.

• We typically use Daily maximum temperature data.• Indoor temperature Data is useful if end use

metered data is available.

Data Collection and AnalysisEnd Use Database

• The interval load, weather,control and characteristics data must be combined into one database for analysis.

• We recommend careful review of the database to ensure that the various files have been merged correctly before beginning modeling.

• Plots of data are helpful in identifying problems.• We recommend and use SAS® for data analysis,

graphics and modeling.

Data Collection and AnalysisRegression Modeling

• Our methodology is to develop a model from a sample of customers with interval data gathered on control and non-control days.

• The model is typically developed by strata and over a maximum outdoor temperature range for which AC load data is available.


The SAS System 14:17 Thursday, December 8, 2005 8 The FREQ Procedure Table of control by Maximum Temperature control Maximum TemperatureFrequency‚Percent ‚Row Pct ‚Col Pct ‚ 93‚ 94‚ 95‚ 96‚ 97‚ 98‚ 99‚ 100‚ Totalƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 0 ‚ 1228 ‚ 604 ‚ 664 ‚ 104 ‚ 184 ‚ 0 ‚ 52 ‚ 52 ‚ 22963 ‚ 4.37 ‚ 2.15 ‚ 2.36 ‚ 0.37 ‚ 0.65 ‚ 0.00 ‚ 0.19 ‚ 0.19 ‚ 81.73 ‚ 5.35 ‚ 2.63 ‚ 2.89 ‚ 0.45 ‚ 0.80 ‚ 0.00 ‚ 0.23 ‚ 0.23 ‚ ‚ 86.97 ‚ 47.34 ‚ 37.03 ‚ 50.00 ‚ 30.46 ‚ 0.00 ‚ 50.00 ‚ 100.00 ‚ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 1 ‚ 184 ‚ 672 ‚ 1129 ‚ 104 ‚ 420 ‚ 288 ‚ 52 ‚ 0 ‚ 5134 ‚ 0.65 ‚ 2.39 ‚ 4.02 ‚ 0.37 ‚ 1.49 ‚ 1.03 ‚ 0.19 ‚ 0.00 ‚ 18.27 ‚ 3.58 ‚ 13.09 ‚ 21.99 ‚ 2.03 ‚ 8.18 ‚ 5.61 ‚ 1.01 ‚ 0.00 ‚ ‚ 13.03 ‚ 52.66 ‚ 62.97 ‚ 50.00 ‚ 69.54 ‚ 100.00 ‚ 50.00 ‚ 0.00 ‚ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆTotal 1412 1276 1793 208 604 288 104 52 28097 5.03 4.54 6.38 0.74 2.15 1.03 0.37 0.19 100.00


• A model we typically use assumes AC use is determined by the temperature difference between the maximum daily temperature and the daytime thermostat setting squared multiplied by the size of the AC compressor in kW

• Models are developed by AC size strata used in the sample design process


• ACLOAD(Hour t, SiteJ) =A+B1*controlmaxmaxt2:(ACMaxkW(site J))*(0=no control in hour t, 1=control in hour t)*(max temperature-thermostat setting)**2+B2*maxacdb2:(ACMaxkW(site J))*(max temperature-thermostat setting)**2+B3*aclag:Hour 13 ACLoad(site(J))


• A is the regression intercept and B1, B2 and B3 are regression coefficients determined during the modeling process. The B1 coefficient is the load reduction estimate for a 1 kW AC at hour t and a given temperature and thermostat setting. A total of 12 regressions were estimated. These are cross-sectional models and are estimated with all data from all sites for each strata and hour of control.


Strata=1 (0-3 kW) HR=15 The REG ProcedureModel: MODEL1Dependent Variable: ac Number of Observations Read 1303Number of Observations Used 1302Number of Observations with Missing Values 1 Analysis of Variance Sum of MeanSource DF Squares Square F Value Pr > F Model 3 641.34869 213.78290 1611.81 <.0001Error 1298 172.16052 0.13264Corrected Total 1301 813.50920 Root MSE 0.36419 R-Square 0.7884Dependent Mean 0.95349 Adj R-Sq 0.7879Coeff Var 38.19574


Strata=1 (0-3 kW) HR=15 The REG ProcedureModel: MODEL1Dependent Variable: ac Parameter Estimates Parameter StandardVariable DF Estimate Error t Value Pr > |t| Intercept 1 0.12832 0.02378 5.40 <.0001controlmaxmaxt2 1 -0.00032607 0.00003430 -9.51 <.0001maxacdb2 1 0.00018540 0.00004344 4.27 <.0001aclag 1 0.99087 0.01595 62.11 <.0001


LG&E Hourly AC Load Model

CoefficientsDependent R Adjusted

Strata Hour Variable Intercept controlmaxmaxt2 maxacdb2 aclag Square _RSQ_1 15 ac 0.12832 -0.000326066 0.000185404 0.99087 0.78837 0.787881 16 ac 0.19995 -0.000376267 0.00020641 0.95812 0.68031 0.679571 17 ac 0.28118 -0.000384897 0.000190502 0.96479 0.66315 0.662371 18 ac 0.35877 -0.000333858 0.000157913 0.95987 0.61608 0.61522 15 ac 0.69212 -0.000481236 0.000485099 0.52252 0.31275 0.311492 16 ac 0.90309 -0.000518439 0.000454306 0.48436 0.29176 0.290452 17 ac 1.11754 -0.000470959 0.000379024 0.44483 0.24123 0.239832 18 ac 1.20034 -0.000415672 0.000337376 0.44722 0.23871 0.237313 15 ac 0.46358 -0.000364872 0.000372091 0.8088 0.62725 0.626973 16 ac 0.69294 -0.000439462 0.000484818 0.74195 0.53416 0.533823 17 ac 0.91922 -0.000490264 0.00060167 0.66098 0.44087 0.440463 18 ac 1.02006 -0.000452093 0.000666458 0.61136 0.38618 0.38573


Mean AC Size, Thermostat Settings By Strata

•Daytime•AC Size •AC Size •Thermostat

•Strata •kW •Tons •Setting

•1 •2.41198 •2.21634 •74.3256•2 •3.55388 •3.10004 •74.7773•3 •6.03214 •5.19299 •75.0606


A sample calculation for strata 3 for hour 17 for a temperature of 98 Degrees is shown below using data from Tables above.

Control Coefficient (controlmaxmaxt2) -0.000490264Temperature- 98 DegreesDaytime Thermostat Setting- 75.0606Average Connected AC kW- 6.03214Control Estimate= -0.000490264*(98-75.0606)*(98-75.0606)*6.03214= -1.5562 kW.


Strata 1 Weighted Control Estimate = -.5195 kW *.426521=-.22155 kWStrata 2 Weighted Control Estimate = -0.9037 kW *.366568= -.33129 kWStrata 3 Weighted Control Estimate = -1.5562 kW *.206911= -.32197 kWPopulation Weighted Average Control Estimate for Hour 17, Maximum Daily Temperature 98 Degrees= -.87481 kW at Customer’s meter.

Data Collection and AnalysisTesting the Model

• Statistical Validity– Do coefficients have the right sign?– Are coefficients significant, T>1.65?

• Do the results make sense?– Is the control too much >average connected

load times cycling percentage?– Is the control too small <<average connected

load times cycling percentage?

Data Collection and AnalysisModel Accuracy

• The stratified regression coefficients can be used to develop an estimate of the accuracy of the load reduction estimate by calculating the overall variance of the control estimate.

Forecasting Load Reductions Current Forecast

• The results of the regression model can be used to forecast current load reductions

• The output is typically a time-temperature matrix of load reductions

• The weighted load reduction mean estimate for each control hour is multiplied by the number of program participants


AC Load Control Estimate 87,236 Customers

(100,000.0)

(90,000.0)

(80,000.0)

(70,000.0)

(60,000.0)

(50,000.0)

(40,000.0)

(30,000.0)

(20,000.0)

(10,000.0)

-

Hour of Control

kW

100 Degrees

95 Degrees

90 Degrees

85 Degrees

100 Degrees (78,800.4) (89,509.1) (90,021.8) (80,420.7)

95 Degrees (50,673.9) (57,556.2) (57,876.2) (51,696.8)

90 Degrees (28,732.3) (32,630.7) (32,803.1) (29,294.4)

85 Degrees (12,975.4) (14,732.5) (14,802.5) (13,213.5)

1 2 3 4


• The forecast is only valid over the temperature range that the model was estimated over

• This may be an issue if you have only one year of history with maximum temperatures of say 93 degrees and you need estimates up to 100 degrees

Forecasting Load Reductions

• Thank You• Contact Information• [email protected]• 800-653-3445 X1067• Cell 678-409-2798

• [email protected]• 800-653-3445 X1059

Determining and Forecasting Load Reductions from Demand Side Programs September 11-12, 2007...

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