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Methodologies for CVR Impact Measurement
A. Thomas Bozzo Christensen Associates Energy
Consulting April 16, 2014
1
Overview
• Challenges
• Test design
• Estimation approach
• Load model
• Data issues
• Estimation implementation
2
Challenges
• CVR impacts small vs. load variation
• CVRf may vary with end-use load mix
– CVR load impacts may vary by date, time, season
• Routine data issues can swamp CVR effects
– Large customers
– Data dropouts, outages
• Assess different operational models
– “Always on” vs. specific hours
3
Example: Substation Hourly Load
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Small CVR Load Differences
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Small CVR Load Differences
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Test Design
• Testing can try to do too much
– Variable voltage reductions (“notch tests”)
– Variable CVR-on test hours
– Testing multiple factors
– Reduced sample sizes, possible confounding
• Also can do too little
– Partial-day testing
– Can’t measure what you don’t test
7
Test Design
• Ideally—keep it simple
• Test CVR on/off only
• Single-level treatment (@ max voltage drop)
• Randomize where possible:
– Feeder/substation selection, N >> 2
– Prescreen for large customers, “episodic” loads
– CVR-on test day selection
• Test all hours of potential interest consistently
8
Estimation Approach
• Ordinary least squares vs. “robust” regression
• OLS computationally simple, but susceptible to outliers
• Robust regression computationally complex, algorithms can fail to reach estimates
• Results should be similar with clean data
– Robust w/r/t data outliers
– Robust estimates still have sampling variability
9
Estimating Equation
• Single hourly time series linear regression model for each tested substation
– Hourly frequency driven by weather data
– Sub load(MW)=f(weather variables, time-of-day, day-of-week, weather-time interaction terms, solar index, CVR on/off state)
• CVR impacts allowed to vary by hour and between weekdays/weekends
– Similar to running regressions for each hour
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Estimating Equation
• Evaluated several weather specifications
– Current weather and moving averages (MA)
– Different thresholds for cooling degree-hours (CDH; summer model)
• Evaluated for prediction error and fit
– The final weather specification (using current, 3-hour MA, and 24-hour MA of cooling degree hours) generally performed well with either 65- or 70-degree CDH thresholds
11
Data Issues
• Test schedule validation
– Generally can visually ID CVR on/off transitions
– Unreported exceptions to test schedule
– Periods w/ ambiguous CVR on/off states
• Reviewed loads for outages, data dropouts, other unusual data patterns
• Corrected CVR on/off state by hour as needed
• Dropped periods with gross anomalies
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Example: Voltage Transitions
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Estimation
• We used OLS on screened substation data
– Screen before estimation as much as possible
– Ran corresponding median regression to check adequacy of data screening
• Models explain most variation in sub load
• Average CVRf ~0.5, 90% margin of error 0.3
– Outliers often cases with worse model fit (R-squared <90%; >97% in best cases)
– Results by hour much more variable
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Example 1: CVRf By Hour
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-0.50
0.00
0.50
1.00
1.50
2.00
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
CV
Rf
(% lo
ad im
pac
t/%
vo
ltag
e c
han
ge)
OLS vs Median Regression CVRf by Hour, Test Substation A
Median OLS
Example 2: CVRf By Hour
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Summary
• Weather-sensitive model explains most cooling-season substation load
• Most tested substations have statistically significant impacts, average CVRf is around 0.5
• Similar impacts from median regression
• No clear relationship between substation characteristics and CVRf based on limited classification data
17
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