Statistically adjusted engineering (SAE) modeling of metered roof-top photovoltaic (PV) output: California evidence

Energy 35 (2010) 4178e4183

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Statistically adjusted engineering (SAE) modeling of metered roof-top photovoltaic (PV) output: California evidence A. DeBenedictis a, *, T.E. Hoff b, S. Price a, C.K. Woo a, c a

Energy and Environmental Economics, Inc., 101 Montgomery Street, Suite 1600, San Francisco, CA 94104, USA Clean Power Research, 10 Glen Court, Napa, CA 94558, USA c Hong Kong Energy Studies Centre, Baptist University of Hong Kong, Hong Kong b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 February 2010 Accepted 27 June 2010 Available online 13 August 2010

Accurate hourly photovoltaic (PV) output data are useful for engineering design, cost-effectiveness evaluation, rate design, system operation, transmission planning, risk management, and policy analysis. However, a large sample of hourly metered PV data is seldom available, and engineering simulation is often the only practical means to obtain hourly PV output. Based on an analysis of net energy metering (NEM) funded by the California Public Utilities Commission (CPUC), this paper presents statistically adjusted engineering (SAE) modeling of metered output of 327 roof-top PV installations in California for the 12-month period of JanuaryeDecember 2008. The key findings are: (a) the metered PV output is on an average 80e90% of simulated performance; and (b) the simulated data have useful information for accurately predicting metered PV performance. Plausible causes for (a) include incomplete input data for PV simulation, occasional failures in metered data recording, and less than ideal conditions for PV performance in the real world. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaic SAE modeling PV Simulation

1. Introduction Mitigation of global warming caused by greenhouse gas (GHG)1 emissions requires accelerated development of zero-emissions renewable energy such as hydro, wind and solar. One example is the recent projection of solar energy potentially meeting nearly all of the US energy needs by 2100, while reducing GHG emissions to 90% of their 2005 levels [1]. Realizing this projection, however, will require research on many fronts, including energy management [2], engineering design [3e8], cost-effectiveness evaluation [9e14], rate design [15e17], transmission planning [18,19], system operation [20,21], risk management [22,23], and policy analysis [1,24e26]. The aforementioned research benefits from accurate hourly photovoltaic (PV) output data. An example is a PV cost-effectiveness analysis that utilizes hourly avoided cost data, whose components are time-varying transmission and distribution costs and hourly wholesale generation prices [27e30]. Unfortunately, a large sample of hourly metered PV output data is seldom available, and

* Corresponding author. Tel.: þ1 415 391 5100; fax: þ1 415 391 6500. E-mail address: [email protected] (A. DeBenedictis). 1 Note that a list of all acronyms and symbols used in this paper appears in Table 1. 0360-5442/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2010.06.041

engineering simulation is often the only practical means to obtain hourly PV output data [31e33]. Extant literature suggests that the metered data closely match the simulated data; however, the reported comparisons typically entail fewer than 10 installations [34e41]. If this close matching extends to a larger sample, engineering simulation is more likely a reliable and useful method to obtain accurate PV output information for a wide range of applications. This paper applies statistically adjusted engineering (SAE) modeling to analyze metered PV output of 327 roof-top PV installations in California for the 12-month period of JanuaryeDecember 2008. This research is based on a study funded by the California Public Utilities Commission (CPUC), which is required to report how net energy metering (NEM) may impact the electricity rates of utilities across the state [42]. The cost-effectiveness of NEM can be determined by comparing three components: (a) the sum of bill savings for customers with NEM; (b) additional billing cost to the utilities; and (c) the avoided cost of exported PV generation to the utilities. Since avoided costs, and time of use (TOU) rates (on which many PV owners are) vary on an hourly basis, the analysis requires hourly energy consumption and hourly PV output data [42]. However, Table 2 shows that missing metered PV data abound, chiefly due to the short operation history of many PV units and occasional failure in meter data recording. This raises a substantive question to be addressed in this

A. DeBenedictis et al. / Energy 35 (2010) 4178e4183

Acronym or Symbol

Definition

GHG PV SAE CPUC NEM TOU OLS CSI PMRS PG&E SCE SDG&E DST PTC j h Yjh Xjh

Green House Gas Photovoltaic Statistically Adjusted Engineering California Public Utilities Commission Net Energy Metering Time of Use Ordinary Least Squares California Solar Initiative Performance Monitoring and Reporting Service Pacific Gas and Electric Southern California Edison San Diego Gas and Electric Daylight Savings Time PVUSA Test Conditions Dummy index for installation Dummy index for hour of year Metered kWh for installation j in hour h Simulated kWh for installation j in hour h Intercept coefficient for installation j Slope coefficient for installation j OLS estimate of aj OLS estimate of bj Additive random error with zero mean and finite variance Number of hourly reads for installation j Coefficient of determination for installation j Sum of Squared Errors of installation j Total Sum of Squares of installation j

aj bj

aj bj

ejh

Nj R2j SSEj TSSj

paper: how may one solve the missing metered data problem shown in Table 2?2 One option is interpolation, such that a small data gap, for example between 11:00 and 12:00 on a given day, can be filled by the simple average of the two metered kWh values in the adjacent hours from 10:00 to 11:00 and 12:00 to 13:00. This alternative, however, cannot meaningfully fill large data gaps that may span several days or even months. A second alternative is to retain only those installations with at least 80% non-missing metered data. This alternative is unattractive because it would reduce the sample size of 327 installations to 45 installations. A third alternative is to use engineering simulation to generate the necessary data to directly fill the metered data gaps. However, the simulated data may differ significantly from the metered data, thus raising concern about the empirical validity of the NEM analysis. A fourth alternative is to statistically fill the metered data gaps with simulated data because the extant literature indicates that the simulated data have useful information content that enables an unbiased prediction of metered PV performance. We use SAE modeling to implement the fourth alternative via linear regressions that relate the hourly simulated PV data to the hourly metered output [43,44].3 We find: (a) the metered PV output is on average 80e90% of simulated performance; and (b) the simulated data have useful information for accurately predicting metered PV performance for all 327 systems. Close examination of the data reveals plausible causes for the difference between metered and simulated performance, including: (a) inaccurate simulation results caused by inaccurate system specifications used as simulation inputs; (b) occasional meter failures, leading to approximated readings, false zero reads, or incorrect timestamps; and (c) less than ideal conditions for PV

Table 2 Hourly metered kWh data availability for a sample of 327 roof-top PV installations in California for the 12-month period of JanuaryeDecember 2008. Utility service area

Number of Number of Number of Total installations installations with installations with number of with 100% data at least 80% data at least 50% data installations

Pacific Gas 10 and Electric Company (PG&E) Southern 0 California Edison (SCE) San Diego 4 Gas and Electric (SDG&E) Total 14

38

83

183

1

8

84

6

14

60

45

105

327

Source: California Solar Initiative (CSI) Performance Monitoring and Reporting Service (PMRS) providers.

performance in the real world (e.g., roof-top shading by trees and buildings [47] and poor system maintenance). These causes suggest a future analysis using improved data, which would entail more accurate system specifications, better metered data collection, and more information on shading. Such an analysis would help further determine the SAE method’s usefulness in real world applications. 2. Statistically adjusted engineering (SAE) model of hourly metered PV output Originally developed for estimating end-use consumption and loads, SAE modeling entails a linear regression that relates the metered kWh to the simulated kWh [43,44]. The SAE approach suits our purpose here because it enables unbiased kWh predictions for hours without metered kWh data. Our SAE model is the following ordinary least squares (OLS) regression:

Yjh ¼ aj þ bj Xjh þ 3jh ;

(1)

where Yjh ¼ metered kWh for PV installation j in hour h; Xjh ¼ simulated kWh for PV installation j in hour h; and ejh ¼ additive random error with zero mean and finite variance. This regression assumes that the simulated kWh are a good summary of the installation’s physical attributes and weather conditions that Max 95th percentile

Q3 Mean

Median Q1

5th percentile Min

40 35 N ameplate C apacity (kW_D C )

Table 1 List of acronyms used in this paper.

4179

30 25 20 15 10 5

2

As such, this paper is not a comparative study of how the results of metered vs. simulated data may vary by sample size. 3 Our SAE modeling does not analyze PV output changes due to variations in weather and a PV unit’s physical attributes as done in [44e46]. Section 2 describes our approach, which assumes that the simulated data is a good summary of weather and PV attributes for explaining the metered performance.

0 Flat - 0 to 10° Tilt Flat - 10 to 20° Tilt Flat - 20 to 30° Tilt Flat - Over 30° Tilt Dual-Axis Tracker n = 25 n = 116 n = 141 n = 44 n=3

Fig. 1. Box plot of nameplate DC capacities of 327 roof-top installations by PV configuration.

4180

A. DeBenedictis et al. / Energy 35 (2010) 4178e4183

6

Simluated Metered

5

kWh

Table 3 PVUSA test conditions (PTC) derate factors by kW size category.

PG&E

7

4

Maximum Average Minimum Number

3 2 1 0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

kWh

Hour Ending SCE

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Simluated Metered

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour Ending SDG&E

5

Simluated Metered

kWh

4 3

0 to 5 kW DC

5 to 10 kW DC

> 10 kW DC

All Sizes

90.28% 84.76% 81.14% 148

90.57% 84.88% 79.99% 129

90.14% 85.86% 82.37% 50

90.57% 84.98% 79.99% 327

Source: California Solar Initiative (CSI) Performance Monitoring and Reporting Service (PMRS) providers

The installation-specific coefficients to be estimated are the intercept aj and slope bj. The assumption of the metered data matching the simulated data implies the testable hypothesis of aj ¼ 0 and bj ¼ 1. If the hypothesis is not rejected, the unbiased expectation of Yjh is Xjh, so that the simulated kWh can directly fill the metered data gaps shown in Table 2. The metered vs. simulated data sample may reject the hypothesis of aj ¼ 0 and bj ¼ 1. Nonetheless, we can use (aj, bj), the OLS estimates of (aj, bj), to compute (aj þ bj Xjh), an unbiased prediction for an hour with missing metered kWh. While (aj þ bj Xjh) is an unbiased prediction, its precision depends on the fit of the installation-specific SAE regression. To assess the regression’s goodness-of-fit, we compute the percent of metered kWh’s variance explained by the simulated kWh [48, p.242]:

2

R2j ¼ 1  SSEj =TSSj

1 0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour Ending

Fig. 2. Metered vs. simulated kWh comparison: average hourly profiles for a summer day (July 16, 2008) by utility service area.

determine the installation’s hourly metered kWh. This assumption is reasonable because a PV installation’s actual output, after the PV unit is already in place, is largely independent of the owner’s characteristics (e.g., income, household size, and applicable electricity rates). However, simulated performance seldom perfectly matches metered performance due to unobserved factors (e.g., unknown roof-top shading and random equipment failure) that influence a PV installation’s metered performance. Moreover, the regression’s specification is only a linear approximation of the true, but unobservable, relationship between metered and simulated data. These reasons lead to the random error in our SAE regression.

(2)

where SSEj ¼ intallation j’s sum of squared errors ¼  ðaj þ bj Xjh Þ2 and TSSj ¼ installation j’s total sum of squares P ¼ h ðYjh  Yj Þ2 with Yj ¼ h Yjh =Nj average of Nj hourly metered kWh values for installation j. When SSEj ¼ 0, R2j ¼ 1 and the regression has a perfect fit. If SSEj ¼ TSSj so that R2j ¼ 0, the simulated data do not have useful information for fitting the SAE regression. Since hourly metered kWh data exhibit intra-day and inter-day volatility by month, our SAE regression may be seen to have achieved a relatively good fit when its R2j is around 0.8. P

½Y h P jh

3. Data 3.1. PV installations Supplied by California Solar Initiative (CSI) Performance Monitoring and Reporting Service (PMRS) providers, our sample has 327

Max 95th Percentile

Q3 Mean

Median Q1

5th Percentile Min

1.2

1

R

2

0.8

0.6

0.4

0.2

0

PGE

Fig. 3. Scatter plot of metered vs. simulated kWh for all data points.

SCE

SDGE

Total

Fig. 4. Box plot of R2 values of the SAE regression model by utility service area.

A. DeBenedictis et al. / Energy 35 (2010) 4178e4183

Max 95th Percentile

Q3

Median

Mean

Q1

Max 95th Percentile

5th Percentile Min

0.6

3

0.4

2.5

Slope Estimate

0.2 Intercept Estimate

4181

0 -0.2

Q3

Median

Mean

Q1

5th Percentile Min

2

1.5

1 -0.4 0.5

-0.6

0

-0.8 PGE

SCE

SDGE

Total

Fig. 5. Box plot of intercept estimates of the SAE regression model by utility service area.

PV installations in Northern California served by Pacific Gas and Electric Company (PG&E) and Southern California served by Southern California Edison (SCE) and San Diego Gas and Electric Company (SDG&E). Fig. 1 portrays the wide size distribution of each type of roof-top PV installation, broken down by tracking and tilt. This figure shows that while the average sizes for the flat systems in the sample are between 5 and 10 kW, the individual sizes may range from a minimum of 1.2 kW to a maximum of 35 kW. The sample contains only three dual-axis tracker installations, with an average size of about 16.3 kW. Also, a wide variety of different module types is present in the sample. 3.2. Metered PV output An initial examination of the metered data reveals occasional errors, including false zero reads, approximated reads (in whole kWh), and incorrect timestamps. While most metering errors cannot be corrected due to insufficient information, incorrect timestamps attributable to Daylight Savings Time (DST) can be remedied. Specifically, systems whose metered data exhibit a 1 h forward shift from March 9 to November 1, while matching well during the rest of the year, are adjusted to account for the DST shift. To illustrate metered PV output, Fig. 2 shows the average (over PV installations) of hourly output by utility service area of a sub-sample of PV installations for a summer day (Wednesday, July 16, 2008), a date chosen because of hourly data completeness, the tendency of the middle of the week to have higher loads, and California being summer-peaking.4 This figure shows that PV production begins around 06:00, peaks around 13:00 or 14:00, and declines to zero around 21:00. This output profile corroborates the commonly held view that PV helps meet California’s high summer afternoon hourly demands. Though the hourly average of simulatedkWh in Fig. 2 is higher, it tracks the hourly average of metered kWh. To presage the SAE regression’s goodness-of-fit results, Fig. 3 is a scatter plot of simulated and metered kWh for every hour in the entire data set. A perfect match of simulated and metered kWh would place all observations on the 45-degree line; and a poor match would show no correlation of data along the 45-degree line. The fact that the bulk of the hourly observations surround the

4 California’s summer load pattern is based on the hourly MW data available at: http://oasishis.caiso.com/.

PGE

SCE

SDGE

Total

Fig. 6. Box plot of slope estimates of the SAE regression model by utility service area.

45-degree line suggests that, when a system is specified correctly and the measured data are recorded correctly, the simulated and metered kWh match closely, despite changing weather patterns that significantly affect system output. Worth noting are the horizontal lines that span the plot, marking approximated metered data that is reported to the nearest integer. 3.3. Simulated PV output The simulated hourly output of the 327 PV installations for the 12-month period of JanuaryeDecember 2008 is the result of running PVSimulator developed by Clean Power Research [49].5 PVSimulator requires the following inputs to specify system configurations and weather data:  An electrical model for PV arrays and inverters. Of the models supported by PVSimulator, this analysis uses Clean Power Estimator, which requires a minimal amount of information about a PV system.  An optional shading and obstruction analysis. However, this option cannot be used in this analysis, as the details about the obstructions surrounding the 327 PV installations are not known.  A system description for each PV installation. This includes the location (zip code), orientation (azimuth, tracking, and tilt), and system rating (PVUSA Test Conditions (PTC) rating) for each installation. Table 3 shows the PTC derate factor distributions by kW size category, reflecting the diversity of the 327 installations. The description also has system configuration information on the number of inverters and the number of PV arrays.  Weather data. This analysis uses SolarAnywhereÒ [49], a weather data source that utilizes satellite photometry to calculate geographically gridded insolation estimates. SolarAnywhere provides these location-specific insolation estimates, as well as actual ambient temperature and wind speed

5 PVSimulator is a software service that produces a time series of PV output. Unlike most PV simulation software products [49], it is implemented as a web service, enabling software products designed with different purposes to access the same simulation code. Moreover, it has a modular architecture, providing users with the ability to mix and match from an assortment of models and weather data sets. Finally, it can produce results in one simulation for thousands of PV installations spread across a wide geographic area.

4182

A. DeBenedictis et al. / Energy 35 (2010) 4178e4183 Simulated

Metered

Adjusted Simulation

5.5 5 4.5 4

kWh

3.5 3 2.5 2 1.5 1 0.5 0 1 1 /2 7 / 2 0 0 8

1 1 /2 6 / 2 0 0 8

1 1 /2 5 / 2 0 0 8

1 1 /2 4 / 2 0 0 8

1 1 /2 3 / 2 0 0 8

1 1 /2 2 / 2 0 0 8

1 1 /2 1 / 2 0 0 8

1 1 /2 0 / 2 0 0 8

1 1 /1 9 / 2 0 0 8

1 1 /1 8 / 2 0 0 8

1 1 /1 7 / 2 0 0 8

1 1 /1 6 / 2 0 0 8

1 1 /1 4 / 2 0 0 8

1 1 /1 5 / 2 0 0 8

-0.5

Date Fig. 7. Simulated, metered, and SAE PV output profiles of a PV installation in zip code 94062 for the two-week period of November 14 e November 27, 2008.

data, for the 12-month period of JanuaryeDecember 2008 needed to simulate the 327 PV systems.

0.21 kWh and þ0.08 kWh. Thus, we find that metered kWh are proportional to simulated kWh.

4. Results

4.3. Slope estimate

4.1. Goodness of fit

Fig. 6 is a box plot of installation-specific slope estimates by ua. This figure shows that the SAE regression has area-specific average slope estimates between 0.80 and 0.95 and an overall average of 0.85 for all areas. The 5th- and 95th-percentiles of the distributions are 0.45 and 1.15, indicating the slope estimates’ relatively wide dispersion. However, the 25th- and 75th-percentiles (i.e., Q1 and Q3) tightly bound the average estimates, suggesting that metered kWh are on average 80e90% of simulated kWh.

Fig. 4 is a box plot of installation-specific R2 by utility service area. This figure shows that the SAE regression has a relatively good fit, with an average area-specific R2 between 0.88 and 0.93 and an overall R2 of 0.90 for all areas. This finding is further supported by the 5th-percentiles of the R2 distributions, which are around 0.7. Thus, the simulated data have useful information for predicting the metered PV output.

5. Conclusion 4.2. Intercept estimate Fig. 5 is a box plot of installation-specific intercept estimates by utility service area. This figure shows that the SAE regression has area-specific average intercept estimates between 0.04 and 0.01 kWh and an overall intercept average of 0.03 kWh for all areas. This finding of small intercept estimates is supported by the 5th- and 95th-percentiles of the distributions, which are between

Final

Metered

Motivated by the need for hourly roof-top PV output as a component of the NEM analysis, SAE modeling of metered PV data supports the claim, purported by extant literature, that simulated data contain useful information for predicting metered PV performance. To close, we illustrate how SAE modeling helps fill the metered data gaps shown in Table 2. Consider Fig. 7, which shows, for a PV installation with many hours of missing data, the hourly metered data, simulated

Adjusted Simulation

5 4.5 4 3.5

kWh

3 2.5 2 1.5 1 0.5 0 -0.5 11/14/2008

11/15/2008

11/16/2008

11/20/2008

11/23/2008

11/27/2008

Date Fig. 8. Six selected days of the two-week period in Fig. 6 to show the final PV output profile obtained by filling the missing data with SAE prediction.

A. DeBenedictis et al. / Energy 35 (2010) 4178e4183

data and SAE prediction. This figure demonstrates that the SAE prediction closely tracks the metered data. Now consider Fig. 8, which shows, for several selected days, the final output curve, composed of metered kWh readings filled with the SAE kWh values where necessary. This figure demonstrates that the SAE prediction can reasonably fill the data gaps on these days, suggesting that SAE modeling is useful to address the metered data availability problem encountered in PV research, as exemplified by the NEM study. References [1] Fthenakis V, Mason JE, Zweibel K. The technical, geographical, and economic feasibility for solar energy to supply the energy needs of the US. Energy Policy 2007;37(2):387e99. [2] Clastres C, Ha Pham TT, Wurtz F, Bacha S. Ancillary services and optimal household energy management with photovoltaic production. Energy 2010;35:55e64. [3] Chang TP. Performance evaluation for solar collectors in Taiwan. Energy 2009;34:32e40. [4] Ai B, Yang H, Shen H, Liao X. Computer-aided design of PV/wind hybrid system. Renewable Energy 2003;28:1491e512. [5] Manolakos D, Papadakis G, Papantonis D, Kyritsis S. A simulation-optimisation programme for designing hybrid energy sytems for supplying electricity and fresh water through desalination to remote areas e case study: the Merssini village, Donoussa Island, Aegean Sea, Greece. Energy 2001;26:679e704. [6] Mahderekal I, Halford CK, Boehm RF. Simulation and optimization of a concentrated photovoltaic system. Journal of Solar Energy Engineering 2006;128:139e45. [7] Quaschning V. Technical and economic system comparison of photovoltaic and concentrating solar thermal power systems depending on annual global irradiation. Solar Energy 2004;77:171e8. [8] Walker A, Balcomb D, Kiss G, Weaver N, Becker-Humphry M. Analyzing two federal building-integrated photovoltaic projects using ENERGY-10 simulations. Journal of Solar Energy Engineering 2003;125(1):28e33. [9] Su WF, Huang SJ, Lin CE. Economic analysis of demand-side hybrid photovoltaic and battery energy storage system. IEEE Transactions on Industry Applications 2001;37(1):171e7. [10] Byrne J, Letendre S, Govindarajalu C, Wang YD, Nigro R. Evaluating the economics of photovoltaics in a demand-side management role. Energy Policy 1996;24(2):177e85. [11] Rahman S, Kroposki BD. Photovoltaics and demand side management performance analysis at a university building. IEEE Transactions on Energy Conversion 1993;8(3):491e8. [12] Bakker M, Zondag HA, Elswijk MJ, Strootman KJ, Jong MJM. Performance and costs of a roof-sized PV/thermal array combined with a ground coupled heat pump. Solar Energy 2005;78(2):331e9. [13] Shabani B, Andrews J, Watkins S. Energy and cost analysis of a solar-hydrogen combined heat and power system for remote power supply using a computer simulation. Solar Energy 2010;84(1):144e55. [14] Hoff T, Wenger HJ, Keane DM. Evaluating the revenue impacts of customersited renewable generation using load research data. San Francisco, California: Western load research association meeting, http://www.clean-power.com/ research/customerPV/CustSitedGeneration.pdf; 1992. [15] Mills A, Wiser R, Barbose G, Golove. The impact of retail rate structures on the economics of commercial photovoltaic systems in California. Energy Policy 2008;36(9):3266e77. [16] Scheuermann K, Hanna D. Tariff selection support for net-metered PV system owners. See also. In: Proceedings of the Solar Conference, http://www. apricusanalytics.com/ASES2002%20Tariff.PDF; 2002. [17] Woo CK, Kollman E, Orans R, Price S, Horii B. Now that California has AMI, what can the state do with it? Energy Policy 2008;36:1366e74. [18] Olson A, Orans R, Allen D, Moore J, Woo CK. Renewable portfolio standards, greenhouse gas reduction, and long-line transmission investments in the WECC. Electricity Journal 2009;22(9):38e46. [19] Orans R, Price S, Williams J, Woo CK, Moore J. A Northern California -British Columbia partnership for renewable energy. Energy Policy 2007;35(8):3979e83. [20] Denholm P, Margolis RM. Evaluating the limits of solar photovoltaics (PV) in traditional electric power systems. Energy Policy 2007;35(5):2852e61. [21] Denholm P, Margolis RM, Milford. Production cost modeling for high levels of photovoltaics penetration. Golden, Colorado: National Renewable Energy Laboratory, http://www.nrel.gov/docs/fy08osti/42305.pdf; 2008. See also. [22] Woo CK, Horowitz I, Olson A, Horii B, Baskette C. Efficient frontiers for electricity procurement by an LDC with multiple purchase options. OMEGA 2006;34 (1):70e80.

4183

[23] Deng SJ, Xu L. Mean-risk efficient portfolio analysis of demand response and supply resources. Energy 2009;34:1523e9. [24] Mahone A, Woo CK, Williams J, Horowitz I. Renewable portfolio standards and cost-effective energy efficiency investment. Energy Policy 2009;37 (3):774e7. [25] Pearce JM. Expanding photovoltaic penetration with residential distributed generation from hybrid solar photovoltaic and combined heat and power systems. Energy 2009;34:1947e54. [26] Galbraith K. California and Texas: renewable energy’s odd couple. New York Times 2009;October 17. [27] Baskette C, Horii B, Kollman E, Price S. Avoided cost estimation and postreform funding allocation for California’s energy efficiency programs. Energy 2006;31:1084e99. [28] Longstaff FA, Wang AW. Electricity forward prices: a high-frequency empirical analysis. Journal of Finance 2004;59:1877e900. [29] Mount TD, Ning Y, Cai X. Predicting price spikes in electricity markets using a regime-switching model with time-varying parameters. Energy Economics 2006;28:62e80. [30] Park H, Mjelde JW, Bessler DA. Price dynamics among U.S. electricity spot markets. Energy Economics 2006;28:81e101. [31] Gilman P. A comparison of three free computer models for evaluating PV and hybrid system designs: HOMER, HYBRID2, and RETSCREEN. In: Proceedings of ASES Annual Conference. American Solar Energy Society, http://swera.unep. net/uploads/media/Gilman_Solar2007.pdf; 2007. See also. [32] Perez R, Reed R, Hoff T. Validation of a simplified PV simulation engine. In: Proceedings of ASES Annual Conference. American Solar Energy Society, http://www.cleanpower.com/research/customerPV/PVModelValidation.pdf; 2003. See also. [33] Celik AN. Long-term energy output estimation for photovoltaic energy systems using synthetic solar irradiation data. Energy 2003;28:479e93. [34] Carr AJ. A detailed performance comparison of PV modules of different technologies and the implications for PV system design methods. Perth, Western Australia: Murdoch University, http://wwwlib.murdoch.edu.au/adt/ pubfiles/adt-MU20050830.94641/02Whole.pdf; 2004. See also. [35] Carr AJ, Pryor TL. A comparison of the performance of different PV module types in temperate climates. Solar Energy 2004;76(1e3):285e94. [36] Cameron CP, Boyson WE, Riley DM. Comparison of PV system performancemodel prediction with measured PV system performance, https://www.nrel. gov/analysis/sam/pdfs/2008_sandia_ieee_pvsc.pdf; 2008. San Diego, California: 33rd IEEE PVSCSee also. [37] Rahman S, Chowdhury BH. Simulation of photovoltaic power systems and their performance prediction. IEEE Transactions on Energy Conversion 1988;3 (3):440e6. [38] Bialasiewicz JT, Muljadi E, Nix G, Drouilhet S. RPM-Sim: A comparison of simulated versus recorded data. Golden, Colorado: National Renewable Energy Laboratory, http://md1.csa.com/partners/viewrecord.php?requester¼ gs&collection¼TRD&recid¼A0116971AH&q¼&uid¼788850422&setcookie¼yes; 2001. See also. [39] Ross MMD, Turcotte D, Fry MA. PVTOOLBOX simulation output compared with monitored data from PV hybrid test bench. Burnaby, British Columbia: SESCI Conference, http://www.rerinfo.ca/documents/artSESCI2005validation. pdf; 2005. See also. [40] Perez R, Doty J, Bailey B, Stewart R. Experimental evaluation of a photovoltaic simulation program. Solar Energy 1994;52(4):359e65. [41] Mondola JD, Yohanisa YG, Smytha M, Nortonb B. Long-term validated simulation of a building integrated photovoltaic system. Solar Energy 2005;78 (2):163e76. [42] Constantine S, Tirpak Sterkel M. Introduction to the net energy metering cost effectiveness evaluation. See also. Sacramento California: California Public Utilities Commission, http://www.cpuc.ca.gov/NR/rdonlyres/0F42385A-FDBE4B76-9AB3-E6AD522DB862/0/nem_combined.pdf; 2010. [43] Train K. An assessment of the accuracy of statistically adjusted engineering (SAE) models of end-use load curves. Energy 1992;17(7):713e23. [44] Train K, Herriges J, Windle R. Statistically adjusted engineering (SAE) models of end-use load curves. Energy 1985;10(10):1103e11. [45] Liu Q, Ryu Y, Gao W, Ruan Y. Field study and sensitivity of PV system by multiple regression method. Journal of Asian Architecture and Building Engineering 2004;3(2):247e52. [46] Perpinan O. Statistical analysis of the performance and simulation of a twoaxis tracking PV system. Solar Energy 2009;83(11):2074e85. [47] Levinson R, Akbari H, Pomerantz M, Gupta S. Solar access of residential rooftops in four California cities. Solar Energy 2009;83(12):2120e35. [48] Kmenta J. Elements of econometrics. , NY: Macmillan; 1986. [49] Ressler J. PV output validation with solar anywhere and PV simulator. See also. Napa, California Clean Power Research, http://www.californiasolarcenter.org/ pdfs/forum/2008.2.8_SolarForum_JRessler-CPR_PVSimulatorOverview.pdf; 2008.