- Email: [email protected]
KWh effects of residential optional dynamic pricing: Winter evidence from British Columbia, Canada
The Electricity Journal 29 (2016) 44–47
Contents lists available at ScienceDirect
The Electricity Journal journal homepage: www.elsevier.com/locate/electr
KWh effects of residential optional dynamic pricing: Winter evidence from British Columbia, Canada Chi-Keung Wooa , Jay Zarnikaub , Raymond Lic, Alice Shiuc,* a b c
Department of Asian and Policy Studies, Education University of Hong Kong, Hong Kong Frontier Associates LLC, 1515 S. Capital of Texas Highway, Suite 110, Austin, TX 78746, USA School of Accounting and Finance, Hong Kong Polytechnic University, Hong Kong
A R T I C L E I N F O
Article history: Available online xxx
Keywords: Residential electricity demand Dynamic pricing Automatic load control British columbia
A B S T A R C T
Using a large sample of customer-day observations from BC Hydro’s residential optional dynamic pricing pilot for the winter-peaking city of Campbell River in British Columbia, Canada, we estimate a system of two electricity demand regressions for daily peak and off-peak periods during November 2007 to February 2008. Our findings support using automatic load control-enhanced dynamic pricing to shave a smart electric grid’s system peak demand and improve the grid’s capacity utilization. ã 2016 Elsevier Inc. All rights reserved.
1. Introduction Using time-of-use (TOU) and critical peak pricing (CPP) tariffs, residential optional dynamic pricing (RODP) of electricity improves an electric grid’s operation and investment through time-varying price signals that discourage a household’s kWh consumption during the peak hours of high marginal costs (Joskow and Wolfram, 2012). These tariffs also encourage the household’s kWh consumption during the off-peak hours of low marginal costs. Implementing RODP does not incur additional metering costs when an electric utility has installed smart meters capable of measuring and storing electricity consumption readings at hourly intervals (Woo et al., 2008). With the smart meters already in place, an electric utility can implement an optional TOU tariff with prices based on a moderate peak-to-off-peak price ratio (e.g., 2–4) that applies to a participating household’s daily consumption by TOU in a billing month (e.g., January) of a season (e.g., winter). The utility can also implement an optional CPP tariff with a very high peak price that only applies to a limited number of CPP days (e.g., not more than 10) in the season. With 24-h advanced notice to the household, the CPP price is typically triggered by a critical event like an expected system demand spike caused by severe weather or a capacity shortfall due to an outage of a major generation plant or transmission line. The CPP tariff’s non-CPP days may have TOU prices, like those used in BC Hydro’s RODP pilot described in Table 1.
* Corresponding author. E-mail address: [email protected] (A. Shiu). http://dx.doi.org/10.1016/j.tej.2016.10.012 1040-6190/ã 2016 Elsevier Inc. All rights reserved.
When aided by an automatic load control (ALC) device, the household likely has larger kWh responses to dynamic pricing (DOE, 2006; Faruqui and Palmer, 2012; Faruqui and Sergici, 2010; Newsham and Bowker, 2010). Relative to non-TOU pricing with a nonlinear tariff (Ito, 2014), ALC-enhanced dynamic pricing improves how an electric utility may price its service for and transmit its price signals to its residential customers who may prioritize some of their end-use loads (e.g., space and water heating) to be curtailable during the CPP hours (Woo et al., 2014). This article aims to address two related questions: Did a participating household’s kWh consumption respond to BC Hydro’s RODP? Did the ALC device magnify the household’s kWh responses on a CPP day? Our affirmative answers enrich the limited evidence based on winter dynamic pricing, which is dwarfed by the extensive evidence based on summer dynamic pricing (DOE, 2006; Faruqui and Palmer, 2012; Faruqui and Sergici, 2010; Newsham and Bowker, 2010). By reinforcing the extant evidence, we recommend that ALC-enhanced dynamic pricing be used to improve an electric grid’s operational and economic efficiency. To empirically develop our answers, we use a large sample of 29,884 customer-day observations derived from BC Hydro’s RODP pilot for the winter-peaking city of Campbell River (CR) on Vancouver Island in the Canadian province of British Columbia (BC). Based on Table 1, these observations come from 376 opt-in households living in single-family homes for the 83 working weekdays in November 2007–February 2008.
C.-K. Woo et al. / The Electricity Journal 29 (2016) 44–47
45
Table 1 BC Hydro’s Residential Optional Dynamic Pricing Pilot’s Design for the City of Campbell River on Vancouver Island of the Canadian Province of British Columbia; Peak Period = 8–11 a.m. and 4–8 p.m., Working Weekdays; Off-period = Remaining Hours. Rate schedule number: Description
Number of participants
1101: Non-TOU flat price = 6.33¢/kWh 1144: TOU; peak price = 15¢/kWh, off-peak price = 4.5¢/kWh 1144A: CPP/TOU; CPP price = 50¢/kWh on CPP days, peak price = 15¢/kWh on non-CPP days, off-peak price = 4.5¢/kWh 1145: TOU; peak price = 20¢/kWh, off-peak price = 4.5¢/kWh Total
Using this sample, we estimate a Generalized Leontief (GL) system of electricity demand regressions (Diewert, 1971) for CR’s daily peak period (8–11 am and 4–8 pm, working weekdays, November–February) and daily off-peak period (remaining hours). We find that BC Hydro’s RODP reduced a participating household’s peak kWh, corroborating the experimental results for the winterpeaking countries of New Zealand and Ireland (Carroll et al., 2014; Di Cosmo et al., 2014; Thorsnes et al., 2012). Further, BC Hydro’s RODP increased the household’s off-peak kWh, thereby improving the BC grid’s capacity utilization. Finally, BC Hydro’s remote activation of the ALC device almost tripled the household’s kWh responses on a CPP day, adding to the extant empirical evidence on ALC’s kWh effects (DOE, 2006; Faruqui and Palmer, 2012; Faruqui and Sergici, 2010; Newsham and Bowker, 2010). These findings suggest that ALC-enhanced dynamic pricing can help achieve a clean and sustainable electricity future, like the one envisioned in BC’s Clean Energy Act. 2. Methodology Our methodology entails estimating a GL system of peak and off-peak demand regressions detailed in the Appendix A. Each regression’s dependent variable is a RODP customer’s daily kWh consumption for a given TOU period. Besides the intercept, the independent variables are: (a) the square root of a suitably defined peak-to-off-peak price ratio; (b) the binary indicators for the ALC’s successful activation and failed activation; (c) the customer’s historic kWh size, use of electric space heating and local weather; and (d) the binary indicators that capture the kWh effects of dayof-week and month-of-year. After estimating the peak and off-peak demand regressions, we estimate the kWh responses sans ALC by TOU period to a change in
Without ALC
With ALC
Total
79 70 114 69 332
0 0 44 0 44
79 70 158 69 376
the peak-to-off-peak price ratio from 1 for a flat rate to what is commonly used in a TOU tariff (e.g., 2, 3 or 4). We also estimate the kWh responses with and without ALC for a CPP ratio that ranges from 8 to 16. Finally, we construct the 95% confidence intervals of these estimated responses. 3. Results Our regression results in Table 2 are empirically plausible. To wit, the adjusted R2 is 0.57 for the peak kWh regression and 0.65 for the off-peak kWh regression, indicating a reasonable fit for a large sample of noisy daily kWh data. We now turn our attention to the regressions’ coefficient estimates. The two-tailed t-test results show all of the reported coefficient estimates are significant at the 5% level. In particular, the b12 estimate is 1.4561 (p-value < 0.0001) and the b12A estimate is 2.5894 (p-value < 0.0001), suggesting that the peak and off-peak kWh are substitutes and have downward sloping demand curves. As the estimated b12A > 0, the ALC device’s successful activation magnifies a CPP day’s kWh response estimates. Using the estimated b12 and its variance, we construct Fig. 1 that portrays the kWh response estimates sans ALC for a price ratio change from 1 to (P1/P2) shown on the horizontal axis. This figure shows that the peak response estimates are 0.43 to 1.09 kWh, smaller in size than the off-peak response estimates of 0.60– 4.37 kWh. The total response estimates are therefore between 0.18 and 3.28 kWh. Using the estimated value for (b12 + b12A) and its variance, we construct Fig. 2 that portrays the ALC-enhanced kWh response estimates for a price ratio change from 1 to (P1/P2) shown on the horizontal axis. The peak response estimates are 2.62 to 3.03 kWh, the off-peak response estimates 7.40–12.14 kWh, and the
Table 2 GL System of Electricity Demand (kWh) Regressions by Time of Use for the Sample Period of November 2007–February 2008. Variable definition; key coefficients are in [] for their easy cross-correspondence to the main text and Peak (8–11 a.m. and 4–8 p.m., the regression specification in the Appendix A working weekdays)
Adjusted R2 Dependent variable’s mean Dependent variable’s standard deviation Root mean squared error (kWh) Intercept [b12, b22] (off-peak price/peak price)1/2 [b12] (peak price/off-peak price)1/2 [b12] (off-peak price/peak price)1/2 Binary indicator for the ALC device’s activation on a CPP day [b12A] (peak price/off-peak price)1/2 Binary indicator for the ALC device’s activation on a CPP day [b12A] (off-peak price/peak price)1/2 Binary indicator for the ALC device’s failed activation [b12F] (peak price/off-peak price)1/2 Binary indicator for the ALC device’s failed activation [b12F]
Off-peak (remaining hours)
Estimate Standard error
p-value
Estimate
Standard error
0.567 18.72 12.10 8.0157 3.7949 1.4561
0.4231 0.1316
2.5894
0.3687
1.8991
0.7923
0.648 38.00 24.89 14.8402 <0.0001 10.7771 0.9060 <0.0001 1.4561 0.1316 <0.0001 2.5894 0.3687 0.0165 1.8991 0.7923
p-value
<0.0001 <0.0001 <0.0001 0.0165
Notes: (1) The sample has 29,884 non-missing customer-day observations from BC Hydro’s winter dynamic pricing pilot’s 376 participating single-family customers in the city of Campbell River for the 83 working weekdays in November 2007–February 2008. (2) The GL demand system is estimated using the ITSUR technique in PROC MODEL of SAS/ETS. Each p-value is based on a two-tail t-test of the null hypothesis of coefficient = 0. (3) For brevity, this table omits the estimates for the other kWh effects, most of which are found to be significant with p-values < 0.05.
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C.-K. Woo et al. / The Electricity Journal 29 (2016) 44–47
Peak kWh Response
0
Off-peak kWh Response
-0.2
5
5
-0.4
4
4 3
-0.8
3
kWh
kWh
-0.6 kWh
Total kWh Response
6
2
2
-1 1
1
-1.2 0
-1.4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 P1/P2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 P1/P2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 P1/P2
Fig. 1. Estimated kWh Responses by Peak-to-Off-Peak Price Ratio (P1/P2) and Their 95% Confidence Intervals Sans the Automatic Load Control (ALC) Device for A Price Ratio Change from 1 to 2, 3, . . . , 15, or 16.
Fig. 2. Estimated kWh Responses by Peak-to-Off-Peak Price Ratio (P1/P2) and Their 95% Confidence Intervals with the Automatic Load Control (ALC) Device in Place for A Price Ratio Change from 1 to 8, 9, . . . , 15, or 16.
total response estimates 4.78–9.10 kWh. These kWh response estimates are almost thrice those in Fig. 1, highlighting the ALC device’s role in magnifying the kWh responses on a CPP day. All kWh response estimates in Figs. 1 and 2 are statistically significant. They are non-trivial when compared to the sample’s mean peak consumption of about 18.7 kWh and off-peak consumption of about 38.0 kWh. For example, the estimated peak kWh reduction at CR’s (P1/P2) = 11 in Fig. 2 is 15% (=2.83/18.72) of our sample’s mean peak kWh consumption. 4. Conclusion By estimating a GL electricity demand system for a large sample of 29,884 customer-day observations derived from BC Hydro’s RODP pilot, we document the pilot’s statistically significant and non-trivial effects of reducing a participating household’s peak kWh consumption, while increasing the household’s off-peak kWh consumption. BC Hydro’s activation of the ALC device almost tripled the estimated kWh response on a CPP day. Since ALC’s costs of installation and operation will likely decline with the technological advances in electronics, an ALC-enhanced dynamic pricing has a promising future role in improving an electric grid’s operational and economic performance, thereby furthering a clean and sustainable electricity future. Acknowledgments The authors thank B.C. Hydro for providing the data used in this article and Education University of Hong Kong for funding the first author’s research on energy demand estimation. The views expressed herein do not reflect the position of B.C. Hydro on
dynamic pricing and automatic load control. Without implication, all errors are those of the authors. Appendix A. Regression specification Let Y1j = daily peak kWh and Y2j = daily off-peak kWh observed on customer-day j, which are billed at the applicable prices of P1j and P2j. Further let Aj = 1 if customer-day j sees an ALC activation, 0 otherwise; and Fj = 1 if the ALC activation fails, 0 otherwise. Our postulated GL system comprises the following peak and off-peak demand regressions: Y1j = b11 + b12 (P2j/P1j)1/2 + b12A (P2j/P1j)1/2 Aj + b12F (P2j/P1j)1/ 2 Fj + other kWh effects; Y2j = b22 + b12 (P1j/P2j)1/2 + b12A (P1j/P2j)1/2 Aj + b12F (P1j/P2j)1/ 2 Fj + other kWh effects. The other kWh effects in the above regressions are attributable to a customer’s kWh size based on a customer’s pre-pilot monthly consumption, a customer’s use of electric space heating, the local weather, and the kWh impacts of the day-of-week and month-ofyear. Suppose b12 > 0 and b12A > 0 are the estimates for b12 and b12A. We use b12 and b12A to estimate the kWh responses to a proposed system-wide implementation of RODP, which alters the peak-tooff-peak price ratio of 1.0 under non-TOU pricing to (P1/P2) 2 R = {2, 3, . . . , 15, 16}, the set of price ratios used in dynamic pricing (Faruqui and Palmer, 2012). Thus, the (P1/P2) ratio is a nonstochastic tariff design parameter of the proposed RODP program. When the (P1/P2) ratio is relatively low (e.g., 3), it corresponds to a TOU tariff that daily applies to a household’s consumption. When the (P1/P2) ratio is relatively high (e.g., 10), it corresponds to a CPP tariff with a very high peak price triggered only on a CPP day. For
C.-K. Woo et al. / The Electricity Journal 29 (2016) 44–47
example, the BC Hydro RODP pilot’s CPP price is 50 ¢/kWh, about 11 times the off-peak price of 4.5 ¢/kWh. Suppose the implementation is not ALC-enhanced. For a price ratio change from 1 to (P1/P2) 2 R, the estimated daily responses per participating household are: Peak kWh response = Q1 = b12 [(P2/P1)1/2–1] < 0; Off-peak kWh response = Q2 = b12 [(P1/P2)1/2–1] > 0; Total kWh response = Q = Q1 + Q2 = b12 [(P2/P1)1/2 + (P1/P2)1/2– 2] > 0. When aided by ALC, the estimated responses are: Peak kWh response = Q10 = (b12 + b12A) [(P2/P1)1/2–1] < 0; Off-peak kWh response = Q20 = (b12 + b12A) [(P1/P2)1/2–1] > 0; Total kWh response = Q0 = (b12 + b12A) [(P2/P1)1/2 + (P1/P2)1/2– 2] > 0. Using the formula in (Diewert, 1971), we find the variance of each response estimate for constructing its 95% confidence interval, like those portrayed in Figs. 1 and 2. References Carroll, J., Lyons, S., Denny, E., 2014. Reducing household electricity demand through smart metering: the role of improved information about energy saving. Energ. Econ. 45, 234–243. DOE, 2006. Benefits of Demand Response in Electricity Markets and Recommendations for Achieving Them: A Report to the United States Congress Pursuant to Section 1253 of the Energy Policy Act of 2005. . Available at: http:// energy.gov/oe/downloads/benefits-demand-response-electricity-marketsand-recommendations-achieving-them-report. Di Cosmo, V., Lyons, S., Nolan, A., 2014. Estimating the impact of time-of-use pricing on Irish electricity demand. The Energy J. 35 (2), 117–136. Diewert, W.E., 1971. An application of the Shephard duality theorem: a Generalized Leontief production function. J. Polit. Econ. 79 (3), 481–507. Faruqui, A., Palmer, J., 2012. The Discovery of Price Responsiveness – a Survey of Experiments Involving Dynamic Pricing of Electricity. . (Available at:) http:// papers.ssrn.com/sol3/papers.cfm?abstract_id=2020587. Faruqui, A., Sergici, S., 2010. Household response to dynamic pricing of electricity: a survey of 15 experiments. J. Regul. Econ. 38 (2), 193–225. Ito, K., 2014. Do consumers respond to marginal or average price? Evidence from nonlinear electricity pricing. Am. Econ. Rev. 104, 537–563.
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Joskow, P.L., Wolfram, C.D., 2012. Dynamic pricing of electricity. Am. Econ. Rev. 102 (3), 381–385. Newsham, G.R., Bowker, B.G., 2010. The effect of utility time-varying pricing and load control strategies on residential summer peak electricity use: a review. Energy Policy 38 (7), 3289–3296. Thorsnes, P., Williams, J., Lawson, R., 2012. Consumer responses to time varying prices for electricity. Energy Policy 49, 552–561. Woo, C.K., Kollman, E., Orans, R., Price, S., Horii, B., 2008. Now that California has AMI, what can the state do with it? Energy Policy 36, 1366–1374. Woo, C.K., Sreedharan, P., Hargreaves, J., Kahrl, F., Wang, J.H., Horowitz, I., 2014. A review of electricity product differentiation. Appl. Energy 114, 262–272. C.K. Woo is a professor of Asian and Policy Studies at Education University of Hong Kong, a senior partner (now on leave) of Energy and Environmental Economics, Inc. (www.ethree.com), and a senior fellow of the United States Association for Energy Economics. With over 130 refereed publications in electricity economics and applied microeconomics, he is a member of the editorial boards of Energy, Energy Policy and The Energy Journal. He hold a Ph.D. in Economics from the University of California, Davis.
Jay Zarnikau is President of Frontier Associates (www.froniterassoc.com), providing consulting assistance in the design and evaluation of energy efficiency programs, retail market strategies, electricity pricing, demand forecasting, and energy policy. As an adjunct professor at the University of Texas in Austin, he teaches applied statistics and energy economics. He formerly served as Director of Electric Utility Regulation at the Public Utility Commission of Texas. He holds a Ph.D. in Economics from UT Austin.
Raymond Li is a teaching fellow at the School of Accounting and Finance at Hong Kong Polytechnic University. His research focuses on applied econometrics and fossil fuel markets. He teaches microeconomics, engineering economics and energy economics. He holds a Ph.D. in Economics from Macquarie University.
Alice Shiu is an Assistant Professor of Economics at the School of Accounting and Finance at Hong Kong Polytechnic University. She teaches engineering economics and econometrics. She is currently working with the research team led by C.K. Woo on different energy research projects. She holds a Ph.D. in Economics from the University of New South Wales.
Contents lists available at ScienceDirect
The Electricity Journal journal homepage: www.elsevier.com/locate/electr
KWh effects of residential optional dynamic pricing: Winter evidence from British Columbia, Canada Chi-Keung Wooa , Jay Zarnikaub , Raymond Lic, Alice Shiuc,* a b c
Department of Asian and Policy Studies, Education University of Hong Kong, Hong Kong Frontier Associates LLC, 1515 S. Capital of Texas Highway, Suite 110, Austin, TX 78746, USA School of Accounting and Finance, Hong Kong Polytechnic University, Hong Kong
A R T I C L E I N F O
Article history: Available online xxx
Keywords: Residential electricity demand Dynamic pricing Automatic load control British columbia
A B S T A R C T
Using a large sample of customer-day observations from BC Hydro’s residential optional dynamic pricing pilot for the winter-peaking city of Campbell River in British Columbia, Canada, we estimate a system of two electricity demand regressions for daily peak and off-peak periods during November 2007 to February 2008. Our findings support using automatic load control-enhanced dynamic pricing to shave a smart electric grid’s system peak demand and improve the grid’s capacity utilization. ã 2016 Elsevier Inc. All rights reserved.
1. Introduction Using time-of-use (TOU) and critical peak pricing (CPP) tariffs, residential optional dynamic pricing (RODP) of electricity improves an electric grid’s operation and investment through time-varying price signals that discourage a household’s kWh consumption during the peak hours of high marginal costs (Joskow and Wolfram, 2012). These tariffs also encourage the household’s kWh consumption during the off-peak hours of low marginal costs. Implementing RODP does not incur additional metering costs when an electric utility has installed smart meters capable of measuring and storing electricity consumption readings at hourly intervals (Woo et al., 2008). With the smart meters already in place, an electric utility can implement an optional TOU tariff with prices based on a moderate peak-to-off-peak price ratio (e.g., 2–4) that applies to a participating household’s daily consumption by TOU in a billing month (e.g., January) of a season (e.g., winter). The utility can also implement an optional CPP tariff with a very high peak price that only applies to a limited number of CPP days (e.g., not more than 10) in the season. With 24-h advanced notice to the household, the CPP price is typically triggered by a critical event like an expected system demand spike caused by severe weather or a capacity shortfall due to an outage of a major generation plant or transmission line. The CPP tariff’s non-CPP days may have TOU prices, like those used in BC Hydro’s RODP pilot described in Table 1.
* Corresponding author. E-mail address: [email protected] (A. Shiu). http://dx.doi.org/10.1016/j.tej.2016.10.012 1040-6190/ã 2016 Elsevier Inc. All rights reserved.
When aided by an automatic load control (ALC) device, the household likely has larger kWh responses to dynamic pricing (DOE, 2006; Faruqui and Palmer, 2012; Faruqui and Sergici, 2010; Newsham and Bowker, 2010). Relative to non-TOU pricing with a nonlinear tariff (Ito, 2014), ALC-enhanced dynamic pricing improves how an electric utility may price its service for and transmit its price signals to its residential customers who may prioritize some of their end-use loads (e.g., space and water heating) to be curtailable during the CPP hours (Woo et al., 2014). This article aims to address two related questions: Did a participating household’s kWh consumption respond to BC Hydro’s RODP? Did the ALC device magnify the household’s kWh responses on a CPP day? Our affirmative answers enrich the limited evidence based on winter dynamic pricing, which is dwarfed by the extensive evidence based on summer dynamic pricing (DOE, 2006; Faruqui and Palmer, 2012; Faruqui and Sergici, 2010; Newsham and Bowker, 2010). By reinforcing the extant evidence, we recommend that ALC-enhanced dynamic pricing be used to improve an electric grid’s operational and economic efficiency. To empirically develop our answers, we use a large sample of 29,884 customer-day observations derived from BC Hydro’s RODP pilot for the winter-peaking city of Campbell River (CR) on Vancouver Island in the Canadian province of British Columbia (BC). Based on Table 1, these observations come from 376 opt-in households living in single-family homes for the 83 working weekdays in November 2007–February 2008.
C.-K. Woo et al. / The Electricity Journal 29 (2016) 44–47
45
Table 1 BC Hydro’s Residential Optional Dynamic Pricing Pilot’s Design for the City of Campbell River on Vancouver Island of the Canadian Province of British Columbia; Peak Period = 8–11 a.m. and 4–8 p.m., Working Weekdays; Off-period = Remaining Hours. Rate schedule number: Description
Number of participants
1101: Non-TOU flat price = 6.33¢/kWh 1144: TOU; peak price = 15¢/kWh, off-peak price = 4.5¢/kWh 1144A: CPP/TOU; CPP price = 50¢/kWh on CPP days, peak price = 15¢/kWh on non-CPP days, off-peak price = 4.5¢/kWh 1145: TOU; peak price = 20¢/kWh, off-peak price = 4.5¢/kWh Total
Using this sample, we estimate a Generalized Leontief (GL) system of electricity demand regressions (Diewert, 1971) for CR’s daily peak period (8–11 am and 4–8 pm, working weekdays, November–February) and daily off-peak period (remaining hours). We find that BC Hydro’s RODP reduced a participating household’s peak kWh, corroborating the experimental results for the winterpeaking countries of New Zealand and Ireland (Carroll et al., 2014; Di Cosmo et al., 2014; Thorsnes et al., 2012). Further, BC Hydro’s RODP increased the household’s off-peak kWh, thereby improving the BC grid’s capacity utilization. Finally, BC Hydro’s remote activation of the ALC device almost tripled the household’s kWh responses on a CPP day, adding to the extant empirical evidence on ALC’s kWh effects (DOE, 2006; Faruqui and Palmer, 2012; Faruqui and Sergici, 2010; Newsham and Bowker, 2010). These findings suggest that ALC-enhanced dynamic pricing can help achieve a clean and sustainable electricity future, like the one envisioned in BC’s Clean Energy Act. 2. Methodology Our methodology entails estimating a GL system of peak and off-peak demand regressions detailed in the Appendix A. Each regression’s dependent variable is a RODP customer’s daily kWh consumption for a given TOU period. Besides the intercept, the independent variables are: (a) the square root of a suitably defined peak-to-off-peak price ratio; (b) the binary indicators for the ALC’s successful activation and failed activation; (c) the customer’s historic kWh size, use of electric space heating and local weather; and (d) the binary indicators that capture the kWh effects of dayof-week and month-of-year. After estimating the peak and off-peak demand regressions, we estimate the kWh responses sans ALC by TOU period to a change in
Without ALC
With ALC
Total
79 70 114 69 332
0 0 44 0 44
79 70 158 69 376
the peak-to-off-peak price ratio from 1 for a flat rate to what is commonly used in a TOU tariff (e.g., 2, 3 or 4). We also estimate the kWh responses with and without ALC for a CPP ratio that ranges from 8 to 16. Finally, we construct the 95% confidence intervals of these estimated responses. 3. Results Our regression results in Table 2 are empirically plausible. To wit, the adjusted R2 is 0.57 for the peak kWh regression and 0.65 for the off-peak kWh regression, indicating a reasonable fit for a large sample of noisy daily kWh data. We now turn our attention to the regressions’ coefficient estimates. The two-tailed t-test results show all of the reported coefficient estimates are significant at the 5% level. In particular, the b12 estimate is 1.4561 (p-value < 0.0001) and the b12A estimate is 2.5894 (p-value < 0.0001), suggesting that the peak and off-peak kWh are substitutes and have downward sloping demand curves. As the estimated b12A > 0, the ALC device’s successful activation magnifies a CPP day’s kWh response estimates. Using the estimated b12 and its variance, we construct Fig. 1 that portrays the kWh response estimates sans ALC for a price ratio change from 1 to (P1/P2) shown on the horizontal axis. This figure shows that the peak response estimates are 0.43 to 1.09 kWh, smaller in size than the off-peak response estimates of 0.60– 4.37 kWh. The total response estimates are therefore between 0.18 and 3.28 kWh. Using the estimated value for (b12 + b12A) and its variance, we construct Fig. 2 that portrays the ALC-enhanced kWh response estimates for a price ratio change from 1 to (P1/P2) shown on the horizontal axis. The peak response estimates are 2.62 to 3.03 kWh, the off-peak response estimates 7.40–12.14 kWh, and the
Table 2 GL System of Electricity Demand (kWh) Regressions by Time of Use for the Sample Period of November 2007–February 2008. Variable definition; key coefficients are in [] for their easy cross-correspondence to the main text and Peak (8–11 a.m. and 4–8 p.m., the regression specification in the Appendix A working weekdays)
Adjusted R2 Dependent variable’s mean Dependent variable’s standard deviation Root mean squared error (kWh) Intercept [b12, b22] (off-peak price/peak price)1/2 [b12] (peak price/off-peak price)1/2 [b12] (off-peak price/peak price)1/2 Binary indicator for the ALC device’s activation on a CPP day [b12A] (peak price/off-peak price)1/2 Binary indicator for the ALC device’s activation on a CPP day [b12A] (off-peak price/peak price)1/2 Binary indicator for the ALC device’s failed activation [b12F] (peak price/off-peak price)1/2 Binary indicator for the ALC device’s failed activation [b12F]
Off-peak (remaining hours)
Estimate Standard error
p-value
Estimate
Standard error
0.567 18.72 12.10 8.0157 3.7949 1.4561
0.4231 0.1316
2.5894
0.3687
1.8991
0.7923
0.648 38.00 24.89 14.8402 <0.0001 10.7771 0.9060 <0.0001 1.4561 0.1316 <0.0001 2.5894 0.3687 0.0165 1.8991 0.7923
p-value
<0.0001 <0.0001 <0.0001 0.0165
Notes: (1) The sample has 29,884 non-missing customer-day observations from BC Hydro’s winter dynamic pricing pilot’s 376 participating single-family customers in the city of Campbell River for the 83 working weekdays in November 2007–February 2008. (2) The GL demand system is estimated using the ITSUR technique in PROC MODEL of SAS/ETS. Each p-value is based on a two-tail t-test of the null hypothesis of coefficient = 0. (3) For brevity, this table omits the estimates for the other kWh effects, most of which are found to be significant with p-values < 0.05.
46
C.-K. Woo et al. / The Electricity Journal 29 (2016) 44–47
Peak kWh Response
0
Off-peak kWh Response
-0.2
5
5
-0.4
4
4 3
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3
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6
2
2
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-1.4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 P1/P2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 P1/P2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 P1/P2
Fig. 1. Estimated kWh Responses by Peak-to-Off-Peak Price Ratio (P1/P2) and Their 95% Confidence Intervals Sans the Automatic Load Control (ALC) Device for A Price Ratio Change from 1 to 2, 3, . . . , 15, or 16.
Fig. 2. Estimated kWh Responses by Peak-to-Off-Peak Price Ratio (P1/P2) and Their 95% Confidence Intervals with the Automatic Load Control (ALC) Device in Place for A Price Ratio Change from 1 to 8, 9, . . . , 15, or 16.
total response estimates 4.78–9.10 kWh. These kWh response estimates are almost thrice those in Fig. 1, highlighting the ALC device’s role in magnifying the kWh responses on a CPP day. All kWh response estimates in Figs. 1 and 2 are statistically significant. They are non-trivial when compared to the sample’s mean peak consumption of about 18.7 kWh and off-peak consumption of about 38.0 kWh. For example, the estimated peak kWh reduction at CR’s (P1/P2) = 11 in Fig. 2 is 15% (=2.83/18.72) of our sample’s mean peak kWh consumption. 4. Conclusion By estimating a GL electricity demand system for a large sample of 29,884 customer-day observations derived from BC Hydro’s RODP pilot, we document the pilot’s statistically significant and non-trivial effects of reducing a participating household’s peak kWh consumption, while increasing the household’s off-peak kWh consumption. BC Hydro’s activation of the ALC device almost tripled the estimated kWh response on a CPP day. Since ALC’s costs of installation and operation will likely decline with the technological advances in electronics, an ALC-enhanced dynamic pricing has a promising future role in improving an electric grid’s operational and economic performance, thereby furthering a clean and sustainable electricity future. Acknowledgments The authors thank B.C. Hydro for providing the data used in this article and Education University of Hong Kong for funding the first author’s research on energy demand estimation. The views expressed herein do not reflect the position of B.C. Hydro on
dynamic pricing and automatic load control. Without implication, all errors are those of the authors. Appendix A. Regression specification Let Y1j = daily peak kWh and Y2j = daily off-peak kWh observed on customer-day j, which are billed at the applicable prices of P1j and P2j. Further let Aj = 1 if customer-day j sees an ALC activation, 0 otherwise; and Fj = 1 if the ALC activation fails, 0 otherwise. Our postulated GL system comprises the following peak and off-peak demand regressions: Y1j = b11 + b12 (P2j/P1j)1/2 + b12A (P2j/P1j)1/2 Aj + b12F (P2j/P1j)1/ 2 Fj + other kWh effects; Y2j = b22 + b12 (P1j/P2j)1/2 + b12A (P1j/P2j)1/2 Aj + b12F (P1j/P2j)1/ 2 Fj + other kWh effects. The other kWh effects in the above regressions are attributable to a customer’s kWh size based on a customer’s pre-pilot monthly consumption, a customer’s use of electric space heating, the local weather, and the kWh impacts of the day-of-week and month-ofyear. Suppose b12 > 0 and b12A > 0 are the estimates for b12 and b12A. We use b12 and b12A to estimate the kWh responses to a proposed system-wide implementation of RODP, which alters the peak-tooff-peak price ratio of 1.0 under non-TOU pricing to (P1/P2) 2 R = {2, 3, . . . , 15, 16}, the set of price ratios used in dynamic pricing (Faruqui and Palmer, 2012). Thus, the (P1/P2) ratio is a nonstochastic tariff design parameter of the proposed RODP program. When the (P1/P2) ratio is relatively low (e.g., 3), it corresponds to a TOU tariff that daily applies to a household’s consumption. When the (P1/P2) ratio is relatively high (e.g., 10), it corresponds to a CPP tariff with a very high peak price triggered only on a CPP day. For
C.-K. Woo et al. / The Electricity Journal 29 (2016) 44–47
example, the BC Hydro RODP pilot’s CPP price is 50 ¢/kWh, about 11 times the off-peak price of 4.5 ¢/kWh. Suppose the implementation is not ALC-enhanced. For a price ratio change from 1 to (P1/P2) 2 R, the estimated daily responses per participating household are: Peak kWh response = Q1 = b12 [(P2/P1)1/2–1] < 0; Off-peak kWh response = Q2 = b12 [(P1/P2)1/2–1] > 0; Total kWh response = Q = Q1 + Q2 = b12 [(P2/P1)1/2 + (P1/P2)1/2– 2] > 0. When aided by ALC, the estimated responses are: Peak kWh response = Q10 = (b12 + b12A) [(P2/P1)1/2–1] < 0; Off-peak kWh response = Q20 = (b12 + b12A) [(P1/P2)1/2–1] > 0; Total kWh response = Q0 = (b12 + b12A) [(P2/P1)1/2 + (P1/P2)1/2– 2] > 0. Using the formula in (Diewert, 1971), we find the variance of each response estimate for constructing its 95% confidence interval, like those portrayed in Figs. 1 and 2. References Carroll, J., Lyons, S., Denny, E., 2014. Reducing household electricity demand through smart metering: the role of improved information about energy saving. Energ. Econ. 45, 234–243. DOE, 2006. Benefits of Demand Response in Electricity Markets and Recommendations for Achieving Them: A Report to the United States Congress Pursuant to Section 1253 of the Energy Policy Act of 2005. . Available at: http:// energy.gov/oe/downloads/benefits-demand-response-electricity-marketsand-recommendations-achieving-them-report. Di Cosmo, V., Lyons, S., Nolan, A., 2014. Estimating the impact of time-of-use pricing on Irish electricity demand. The Energy J. 35 (2), 117–136. Diewert, W.E., 1971. An application of the Shephard duality theorem: a Generalized Leontief production function. J. Polit. Econ. 79 (3), 481–507. Faruqui, A., Palmer, J., 2012. The Discovery of Price Responsiveness – a Survey of Experiments Involving Dynamic Pricing of Electricity. . (Available at:) http:// papers.ssrn.com/sol3/papers.cfm?abstract_id=2020587. Faruqui, A., Sergici, S., 2010. Household response to dynamic pricing of electricity: a survey of 15 experiments. J. Regul. Econ. 38 (2), 193–225. Ito, K., 2014. Do consumers respond to marginal or average price? Evidence from nonlinear electricity pricing. Am. Econ. Rev. 104, 537–563.
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Joskow, P.L., Wolfram, C.D., 2012. Dynamic pricing of electricity. Am. Econ. Rev. 102 (3), 381–385. Newsham, G.R., Bowker, B.G., 2010. The effect of utility time-varying pricing and load control strategies on residential summer peak electricity use: a review. Energy Policy 38 (7), 3289–3296. Thorsnes, P., Williams, J., Lawson, R., 2012. Consumer responses to time varying prices for electricity. Energy Policy 49, 552–561. Woo, C.K., Kollman, E., Orans, R., Price, S., Horii, B., 2008. Now that California has AMI, what can the state do with it? Energy Policy 36, 1366–1374. Woo, C.K., Sreedharan, P., Hargreaves, J., Kahrl, F., Wang, J.H., Horowitz, I., 2014. A review of electricity product differentiation. Appl. Energy 114, 262–272. C.K. Woo is a professor of Asian and Policy Studies at Education University of Hong Kong, a senior partner (now on leave) of Energy and Environmental Economics, Inc. (www.ethree.com), and a senior fellow of the United States Association for Energy Economics. With over 130 refereed publications in electricity economics and applied microeconomics, he is a member of the editorial boards of Energy, Energy Policy and The Energy Journal. He hold a Ph.D. in Economics from the University of California, Davis.
Jay Zarnikau is President of Frontier Associates (www.froniterassoc.com), providing consulting assistance in the design and evaluation of energy efficiency programs, retail market strategies, electricity pricing, demand forecasting, and energy policy. As an adjunct professor at the University of Texas in Austin, he teaches applied statistics and energy economics. He formerly served as Director of Electric Utility Regulation at the Public Utility Commission of Texas. He holds a Ph.D. in Economics from UT Austin.
Raymond Li is a teaching fellow at the School of Accounting and Finance at Hong Kong Polytechnic University. His research focuses on applied econometrics and fossil fuel markets. He teaches microeconomics, engineering economics and energy economics. He holds a Ph.D. in Economics from Macquarie University.
Alice Shiu is an Assistant Professor of Economics at the School of Accounting and Finance at Hong Kong Polytechnic University. She teaches engineering economics and econometrics. She is currently working with the research team led by C.K. Woo on different energy research projects. She holds a Ph.D. in Economics from the University of New South Wales.