Modeling Electricity Prices in Rhode IslandJeremey AndersonRoss PelletierJuan HernandezChristopher Riely

Table of Contents

•Topic Overview•Research History•Data•Methodology and Model•Results and Elasticity Estimates•Conclusions and Policy Implications

Topic Overview• Attempt to explain variability in RI spot market

electricity prices by a variety of independent variables• Electricity – demand drives price (upward sloping

demand curve) as opposed to most goods where price drives demand

• De-regulation of electricity markets in 1999• ISO-NE (Independent Systems Operator)

▫ Independent entity that ensures reliable operation of New England’s power generation and transmission system

▫Oversees fair administration of regions wholesale electricity markets

Research History

• Econometric analysis of real-time pricing for residential customers - Aubin et al. (1995)

▫ Experiment by French state-owned electric utility

▫ Six different rates instead of two: three types of days, two periods per day (peak and off-peak)

▫ Direct similarities to our model (regression) but more complex

▫ Set of flexible rate periods is more practical than true real-time pricing

▫ Conclusion: real-time pricing improved welfare of majority of customers (measured by discounted present value of daily electricity expense)

Research History•Long-Run Effects and Efficiency of RTEP

and Wealth Transfer - Borenstein (2004, 2005)

▫ Cites confusion between economic efficiency gains and wealth transfers

▫ RTP removes subsidies to customers who consume disproportionately more electricity when prices are highest

▫ Significant efficiency gains even if demand is not very elastic

▫ Benefits of RTP are likely to far outweigh costs for largest customers

▫ “Time of use” rates a poor substitute for RTP (only 20% as efficient)

▫ Implementing RTP may be difficult without sister program compensating customers made worse off by the change

▫ Suggests two-part programs: baseline quantity at set rates + RTP

Research History

• Important variables explaining real-time price peak in independent power market of Ontario - Rueda and Marathe (2005)

▫ Conventional statistical analysis ruled out due to lack of validity

▫ Used alternative technique to select important variables a “support vector machines” based learning algorithm

▫ Sensitivity analysis to determine most important variables: Pre-dispatch average price peak Actual import peak volume Peak load of market Net available supply after accounting for load (i.e. excess energy)

Research History

•RTP and Electricity Markets – Allcott (2009)

▫ Applied results of residential RTP experiment to simulations using model of Pennsylvania-New Jersey-Maryland electricity market

▫ Another highly complex model with four central results Customer Behavior:

Energy conservation during peak hours, not a switch from peak to off-peak

Under certain conditions, RTP could actually increase wholesale electricity prices during peak hours

Increased demand elasticity from RTP reduces producers’ market power, but no spectacular efficiency gains

Welfare gains from residential RTP likely to outweigh costs of hourly meters

Data▫Hourly time series data ▫RI Zone▫Originally looked at full year period 2008-

2010▫Due to size of dataset we focused on one

year (December 2009- November 2010) and split data into 4 quarters to compare similarities/differences Winter (December – February) Spring (March – May) Summer (June – August) Fall (September – November)

Data•Plot below demonstrates unique demand

vs. price relationship

Methodology and Model• Demand theoretic model• Preliminary Investigation

▫Can’t make any final conclusions from results• Used Ordinary Least Squares

▫May not be most efficient model for high frequency time series data due to high presence of autocorrelation and heteroskedasticity

▫Non parametric model may be preferable𝑃𝐸 = 𝛼+ 𝛽𝑋1 + 𝛽𝑋2 + 𝛽𝑋𝑛 + 𝜀

Methodology and Model• Dependent Variable: Price (PE)• Potential Independent Variables:

▫Real Time Demand▫Day Ahead Price▫Day Ahead Demand▫System Congestion▫Temperature▫90F+ dummy (hot days)▫Time of day dummy (11am – 4pm)▫Seasonal dummy (winter/summer)▫Price in neighboring zones (CT and SE MASS)

Created interaction variable; multiplied two values together to form one and used that in regression

Hypotheses

•H0: The price of electricity is explained by the demand for electricity

•H1: The price of electricity is explained by the dry bulb temperature

•H2: The price of electricity is explained by the time of day

•H3: The price of electricity is explained by the congestion on the system

Results• Winter

• Spring

Results• Summer

• Fall

Results

•F-Test (Overall Model Fit)▫All 4 quarters <0.05 (significant); model

overall is good•Adjusted R2: represents variability in

dependent variable explained by the variability in the independent variables▫Winter: 93.9%▫Spring: 90.4%▫Summer: 94.4%▫Fall: 88.8%

Multi-Collinearity

•Two or more independent variables are correlated

•VIF (<10, ideally <=5)•Average VIF

▫All 4 quarters <5•Individual variable VIFs

▫Demand in summer and fall slightly over 5 but still <10

▫All others <5

Autocorrelation

•Correlation between error terms in time series data

•Two tailed Durbin Watson Test•All 4 models rejected null hypothesis

▫Presence of serial/autocorrelation▫More advanced model would attempt to

correct for this

Constant Variance

• Whites Test – Tests for constant variance in the error/residual term

• H0: Error terms are homoscedastic• Want p-value>0.05 to accept null hypothesis

• All four models produce p-value <0.05• No constant variance in error terms

Normality•Displays if error terms are normally

distributed• Winter • Spring

Normality• Summer • Fall

Elasticity Estimates

• Demand: Positive, 0<x<1▫ Highest during summer, slowly falls to lowest point of 0.08 in

spring• Day Ahead Price: Positive, 0<x<1

▫ No clear pattern between quarters• Congestion: Negative, -1<x<0

▫ Very small elasticity (inelastic)• Temperature: Negative, -1<x<0

▫ Negative and small• Dew Point: Positive, 0<x<1

▫ Positive and small• Time of Day Dummy: Positive, 0<x<1

▫ Positive and small• Neighboring Price: Positive, 0<x<1

▫ Positive around 0.2-0.25

Conclusions and Policy Implications• Modeling electricity prices and demand is difficult• More advanced analysis would include ability to look over

multiple years of data▫ Non OLS method▫ Better correct for autocorrelation and heteroskedasticity

• Demand and Capacity Planning▫ If/when to build new generation▫ Most efficient time to take units offline for maintenance

• Demand Response▫ Ability to model what price would have been absent demand

response and measure value gained by the system vs. payments made

• Real Time Pricing▫ Customers can shift or reduce usage according to their price

sensitivity (elasticity)▫ Incentive to move to off-peak hours

Research CitationsAllcott, Hunt (2009). Real-Time Pricing and Electricity Markets. (unpublished).

Aubin, Christophe, Denis Fougere, Emmanuel Husson, and Mrac Ivaldi (1995). Real-Time Pricing of Electricity for Residential Customers: Econometric Analysis of an Experiment. Journal of Applied Econometrics, 10, S171-S191.

Borenstein, Severin (2004). The Long-Run Effects of Real-Time Electricity Pricing. University of California Energy Institute, Center for the Study of Energy Markets, Working Paper 133.

Borenstein, Severin (2005). The Long-Run Efficiency of Real-Time Electricity Pricing. The Energy Journal, 26(3), 93-116.

Borenstein, Severin (2005). Wealth Transfers from Implementing Real-Time Retail Electricity Pricing. University of California Energy Institute, Center for the Study of Energy Markets, Working Paper 147.

Rueda, Ismael E. Arcinieagas and Achla Marathe (2005). Important variables in explaining real-time peak price in the independent power market of Ontario. Utilities Policy, 13, 27-39.