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Authors: J.A. Hausman, M. Kinnucan, and D. McFadden Presented by: Jared Hayden

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Time-of-Day Electricity Pricing Time-of-day electricity pricing began to be seriously considered when electricity prices skyrocketed in the mid- 1970’s Generating capacity can be split into three main types: base load, intermediate, and peak The marginal cost of generation increases from base load to intermediate to peak Pricing accordingly gives price signals that can flatten demand peaks The result is a transfer of peak and intermediate demand to instead be demanded during times of base load generation

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Benefits of Time-of-Day Pricing Pricing different periods according to marginal cost can be used to attain a near welfare optimum Oil and natural gas usage can be cut down Oil and natural gas are typically used in intermediate and peak production The smoothing demand fluctuations The smoothing of demand fluctuations would allow a greater percentage of the generation to come from coal and nuclear, which are more economic over long load durations.

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Study Background Increased attention in time-of-day pricing led to 6 large scale time-of-day experiments in the mid-70’s This paper analyzes the results of the Connecticut Peak Load Pricing Test as conducted in the Connecticut Light and Power Service area Conducted from October 1975 to October 1976 in 199 households Recorded electricity uses every 15 minutes for one year Household in study were subject to a time-of-day pricing structure: Peak = $0.16/kWh Intermediate = $0.03/kWh Base Load = $0.01/kWh

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Time-of-Day Model Overview Employed a two-level budgeting model Reduces complication that price depends on quantity consumed (declining block rate structure) Requires a linear homogeneity assumption on the relative load Estimates own price effect, although a multi-variate approach could derive cross-price effects First level shows relative load demand. Once prices corresponding to the first level are derived, a second level looks at daily consumption.

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Two-level Budgeting Model Model considers electricity consumption in a representative day. Household appliance holdings assumed to be predetermined. Variation in daily usage ignored. Day divided into time periods t 1 + t 2 +…+ t n x= (x 1 + x 2 +…+ x n ) is the vector of corresponding electricity consumption p= (p 1 + p 2 +…+ p n ) is the corresponding vector of electricity rates. u = V(x 0, x) denotes the house hold utility function.

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Model Derivation (1) Budget Constraint (2) Indirect utility function giving maximum utility at p 0 …p n and expenditure I Uses price index for electricity consumption at different times of the day Separates electricity consumption from consumption of other commodities The share of expenditure allocated to electricity consumption in each time period depends on relative electricity prices only Can use to transform indirect utility function

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Derivation… U(x 0, x 1 … x n ) = W(x 0, f(x 0, x 1 … x n )) Where f is homogenous of degree one Can be written as: Where theta can be thought of as the inverse price index Homogeneity assumption means that if all electricity prices were to double, relative allocation among periods wouldn’t change, but total consumption would.

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Derivation…

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Derivation….

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Impact on Consumption Incorporates appliance holding, socioeconomic factors, weather, and a stochastic error term Shows effect on consumption relative to period n

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Total Daily Consumption (9) Estimates correct price index from estimated demand weighted average price of electricity (10) Estimates consumption for pre-experimental period

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Multivariate approach Addresses cross-equation restrictions and consumer theory maximization restrictions. Uses a more general approach, starting with the unrestricted indirect utility function By Roy’s Identity,

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Translog Form Must assume symmetry and linearity in parameters, assuming that income elasticities are unitary

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Consumption/Expenditure Shares After Restrictions Approach relies heavily on consumer theory and linear homogeneity assumptions Limits estimation of all desired price effects

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Estimation of the Two Level Demand System Estimated derived two level demand system using sample of 150 households with both pre-experimental and time-of- use experimental periods 20 households are used as a control for model validation First Level Demand Estimation Estimates relative load curve Relative demands for electricity is estimated on daily data on a hourly basis using equation 8 price index estimated using equation 9 Daily consumption function estimated using equation 10 Allows analysis and forecasts of household demand on household level with demand determined marginal price from pre-experimental period

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First Level Demand Estimation Estimates four periods: week days and weekends during winter and summer peak periods Hourly rates differ due to the time-of-day hourly pricing structure

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Parameter Estimates-Price Elasticity

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Construction of Appropriate Prices Pre-experimental rate structure The experimental prices increase 16% Consumption decrease: 1% from previous year %5 from control household of same year

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Second Level Demand Estimation Estimates daily consumption Uses four different daily demand equations using the equation 10 Week day and weekend summer and winter peak periods Table 2 presents weekday consumption estimates

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Parameter Estimates

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Estimation Conclusions Estimation of first level, estimating the relative load curve, is quite successful Captures the pattern of hourly demands for electricity From the first level demands, construct a price index that goes into seconds level daily consumptions demand equations The second level estimations are significantly less successful in capturing demand behavior Conclusion, estimation of relative load curve is superior to forecasting the absolute levels

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Relative Consumption Validation Peak period does well in forecasting relative load curve Intermediate period forecast have 3 of 9 periods with high forecast error Off-peak forecast do well at night but poor during the day

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Aggregate Into 3 Periods When averaged across the day… Extremely accurate!

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Population Strata Validation Over estimation of stratum 1 and underestimation of stratum 5, expected due to somewhat biased sample Corrected in model by weighted average Only a 5.3% forecast error

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Combining Relative Load and Daily Consumption Forecasts Used to predict absolute system load (fig 7) 16% forecast error overall 14% forecast error during peak periods Slightly overestimates increment to peak design by 8% Under-predicts usage by 5% Results are aggregated into peak, intermediate, and off- peak to show final results in figure 8 Forecasts capture the shift from peak periods to off peak periods

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Fig. 7 – Hourly Load Fig 8-Period aggregations

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Conclusion Flexible procedure to model time-of-day structured electricity demand with two-level budgeting framework Alternative approach to time series and single level models Forecast relative load curve well May be a superior method if daily consumption (second level) forecasts well in the aggregate Needs further testing with different data to know the full extent of it usefulness

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The End Questions?

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