Distributed Solar Generation

Transcription

1 Project Final Report for Distributed Solar Generation Laura Criste, John Hoffman, Josh Grant George Mason University May 12, 2017

2 1 TABLE OF CONTENTS 2 Acknowledgements Executive Summary Background Problem Scope Data Collection and Utilization Sensitivity Analysis Limitations Future Work Appendix A: Project Plan Appendix B: R Probability Distribution Code Appendix C: Monthly Probability Distributions Appendix D: Team Biographies and Roles ACKNOWLEDGEMENTS The team would like to express its appreciation to the sponsor, NOVEC, for dedicating the time and resources to support the SEOR graduate program. The team would like to thank Robert Bisson, NOVEC s Vice President Electric System Development, who provided the challenge, and offered key guidance throughout the project. Mr. Bisson was very gracious with his time, including a couple of Saturdays, always happy to discuss our progress, and available to help resolve issues the team encountered. The team would also like to recognize Angie Thomas, NOVEC Manager of Forecasting and NERC Compliance & Business Systems, and Kevin Whyte, NOVEC Manager of Distribution Engineering. Ms. Thomas was a key POC for the team, and was instrumental in facilitating interactions with NOVEC. Mr. Whyte was able to identify, extract, and provide the data required to complete the DSG project. Mr. Whyte s expertise, and knowledge of the system allowed for the transmission and receipt of these exceptionally large data sets. Finally, the team would like to acknowledge Dr. Kathryn Laskey, Systems Engineering and Operations Research Professor at George Mason University Volgenau School of Engineering. Dr. Laskey was the instructor for the Capstone Project, and provided key guidance and insight along the way, assuring the success of our team. 2

3 3 EXECUTIVE SUMMARY The Northern Virginia Electric Cooperative presented the George Mason University Systems Engineering and Operations Research graduate capstone class with a problem concerning distributed solar generation, and its ability to recover costs associated with electric distribution. NOVEC recovers its operational and infrastructure costs through a monthly flat fee and a per kilowatt hour charge to distribute electricity to the customer. The pricing structure is the same for solar and non-solar customers, so the charges are distributed based on the kilowatt hours of electricity the customer uses. Customers with solar panels reduce the amount of power sold by NOVEC but they do not reduce the distribution costs because NOVEC must be prepared to distribute power to them any time the solar panels are not producing energy. This requirement increase the cost to distribute each kilowatt hour and reduces NOVEC s revenue. If NOVEC increase the distribution charge, it would unfairly impact the customers without solar panels. The SEOR capstone team evaluated solar customers use of NOVEC s operations and infrastructure, projected the impact of an increasing solar penetration level, and proposed two methods to recover NOVEC s distribution costs without discouraging solar panel use or burdening the non-solar customers with all of the increased costs. Both methods recommend separating the pricing structure for solar and non-solar customers. The first method is to recover costs by increasing the distribution charge proportionally by kilowatt hour used for only solar customers. The second method is to recover costs by first charging solar customers NOVEC s current pricing structure rate to distribute excess solar energy back to NOVEC and then recover any costs not accounted for by the redistribution charge by increasing the distribution charge proportionally by kilowatt hour used for all customers. The final recommendation is a combination of the two methods and dependent on the solar penetration level. 3

4 4 BACKGROUND 4.1 NORTHERN VIRGINIA ELECTRICITY COOPERATIVE Northern Virginia Electricity Cooperative, or NOVEC, is an electricity distributer in Northern Virginia and the sponsor of this project. NOVEC serves approximately 165,000 customers in Northern Virginia with 62 electric substations and roughly 7,100 circuit miles of overhead and underground lines. 1 The company purchases and generates electricity at an annual average of cost of $80 per megawatt hour. NOVEC recovers its annual energy sales and delivery costs through a tariff, which breaks out the cost of energy used and cost of delivery on a per kilowatt basis. The cost of delivery is associated with the infrastructure (e.g., power lines and substations) acquisition, and maintenance. NOVEC s portion of the infrastructure is shown in Figure 1. As the country continues to move toward renewable energies, there is a greater demand by individual customers to supplement their power needs by installing solar panels. Solar panels are capable of reducing the overall load on the system, and at times providing power back to the system. Figure 1. NOVEC portion of infrastructure (Source: NOVEC s website) With the introduction of solar power to the grid, NOVEC s ability to recover operations costs becomes more complicated. NOVEC is responsible for meeting 100 percent of the required power 100 percent of the time. While the sun is shining, solar panels reduce the load requirements on NOVEC and potentially become an intermittent supplier of power. When the sun is not shining, even momentarily, the full load is transferred back to NOVEC. 4.2 DISTRIBUTED GENERATION 1 Northern Virginia Electric Cooperative, NOVEC Overview, accessed on May 6, 2017, 4

5 Distributed generation is the production of power where it is intended to be used for electricity. This power can be generated by solar photovoltaic (PV), small wind turbines, combined heat and power, fuel cells, and micro-turbines. The largest percentage of this is by solar PV, and the amount of solar PV has been steadily increasing for the last several years. This generated power is intended to be used at the source without storage capacity such as batteries. The excess supplies the local grid and reduces the energy that the utility company is required to supply. United Sates solar PV generation amounts to about 9 gigawatts annually and in the next few years, it is expected to exceed 20 gigawatts SOLAR IRRADIANCE Solar irradiance is the light energy available from the sun, as measured on earth, to be converted to electricity Figure 2. Annual mean insolation at the top of Earth's atmosphere and at the planet's surface (Source: William M. Connolley using HadCM3 data) by PV cells at the earth s surface. 3 This energy is uniform when measured in space, but the energy varies when measured at the earth s surface due to atmospheric effects. The atmosphere plays a large role in the amount of solar irradiation available to the PV cells. In Figure 2 the average solar irradiance is shown above the atmosphere on the top, and after passing through the atmosphere on the bottom. Part of the energy reaches the earth s surface is reflected and part is absorbed. The portion that is absorbed is the portion utilized by the PV cells. 4.4 PHOTOVOLTAIC PANELS AND SYSTEMS The ability to convert the sun s energy to electricity using the PV effect wasn t discovered until the early 19th century. 4 The basic photovoltaic system is comprised of PV modules (panels) and an inverter. A PV module is an assembly of PV solar cells, which is typically a package of connected six inch by 10 inch Figure 3. Basic PV system (Source: DeGunther) 2 American Public Power Association, Solar Distributed Generation, February 2016, Generation.pdf. 3 National Aeronautics and Space Administration, Solar Irradiance, January 2008, 4 Asowata, Osamede, James Swart, and Chriso Pienaar, Correlating the Power Conversion of a PV Panel to the Solar Irradiance Obtained from Meteonorm, February 2013, 5

6 solar cells. 5 The panels generate a direct current (DC), which the inverter converts to an alternating current (AC). The AC power is fed into the fuse box. The output of today s panels typically range from 100 to 365 watts under standard test conditions, which is the best the panels can produce under ideal conditions. 6 The modules create PV systems that supply solar energy to commercial and residential buildings. Adding these systems to a home or commercial building may lead to the utility meter being change to a net meter to measure when power is being fed back onto the grid. 4.5 COST OF BUYING AND OWNING SOLAR PANELS When considering the cost of any system, operating and maintaining the system should be factored into the equation. For solar panels, this cost is minimal. The main cost associated with solar panels is purchase and installation, which ranges from approximately $25,000 to $35, If the system is being installed on a roof, the age of the roof should be a consideration. If the roof needs to be replaced during the life of the solar panels, they will need to be removed, and reinstalled. Removing the panels costs between $300 and $500, and assuming the cost to reinstall is similar, the total could approach $1, This should be the main consideration related to the ongoing cost of owning solar panels. Repair and cleaning costs should be negligible. PV systems do not tend to break because there are no moving parts, and if something does break, the warranties usually cover many years since the life expectancy of the system is 25 years. Accumulation of dirt on the panels reduces their efficiency, but rain is very effective at keeping them clean due to them being tilted to optimize sun collection. Even without rain, the efficiency loss is small. During a 145 day drought in California, uncleaned solar panels lost 7.4 percent efficiency. 9 Since cleaning costs between $10 and $20 per panel, the solar customer is unlikely to see a return on the investment and should wait for the next rain instead. 4.6 INCENTIVES Historically, there have been tax incentives at the federal, state, and local government levels for the installation of residential solar panels. While most state incentives expired at the end of 2016, there are still federal and Prince William County incentives for installing residential solar panels. 5 DeGunther, Rik, The Basic Components of a Home Solar Power System, Accessed on May 6, 2017, 6 Sunrise Solar, Solar Panel, September 2016, 7 Solar Power Authority, How Much Does it Cost to Install Solar on an Average US House?, April 2016, 8 Ioana Patringenaru (2013). 9 Patringenaru, Ioana, Cleaning Solar Panels Often Not Worth the Cost, Engineers at UC San Diego Find, UC San Diego News Center, August 2013, uc_san_diego_fi. 6

7 At the Federal government level there is a 30 percent solar Investment Tax Credit (ITC) for residential installation of solar panels through This drops to 26 percent in 2020, 22 percent in 2021, and then to zero after The ITC is based on the amount of investment in solar property, which can include labor costs for preparing, installing and connecting the panels to the home. 10 Prince William County offers a tax exemption for installed certified solar energy equipment. This exemption pertains to property tax, and is good for five years as long as the equipment is operational during that year PROBLEM Network costs do not decrease as the proportion of solar panel users, also called the solar penetration level, increases. As the solar penetration level increases, network costs could go up due to a requirement for a more rigorous grid. Since the greater the penetration level, the less total power consumed, the cost per kilowatt hour must increase in order to recover network costs. The customers with solar generation capability are driving the increased costs and transferring a large portion of those costs to the customers without solar generation. This could drive the incentive to install more solar panels and force the cost of distribution higher, making the NOVEC s requirement of recovering its costs increasingly difficult. Approximately 0.1 percent, or 160, of NOVEC s residential customers own and operate solar panels. This proportion is only expected to increase with a national interest in renewable energy, expiring tax incentives, and the dropping cost of system acquisition and installation. NOVEC asked the team to develop a model that considers different proportions of distributed solar generation to determine a fair pricing structure, the goal being to recommend a method for charging customers based on a combination of kilowatt hours used and the proportion of the operations and infrastructure required from NOVEC. 12 The result must both allow NOVEC to meet the operational and financial requirements of a healthy utility provider and avoid discouraging its customers to supplement power requirements through the installation of solar panels. The recommendation must determine whether there is a penetration level where NOVEC should switch from charging customers by unit of energy to charging for the proportion of the system used. The team does this by exploring solar penetration levels at one, three, five, 10, 15, and 20 percent. Each of these levels may have a different recommendation that includes changing the cost per unit of energy consumed, creating a fee based on percent of system consumed, or a combination of the two. 10 Department of Energy, Residential Renewable Energy Tax Credit, Accessed on May 7, 2017, 11 Prince William County, Solar Exemption, Accessed on May 7, 2017, 12 Massachusetts Institute of Technology, The Future of Solar Energy, 2015, 7

8 6 SCOPE This project considers residential customers, who grow at a rate of between two and three percent each year, rather than residential and commercial customers because there is insufficient data available for commercial customers using solar generation. The project also focuses on the cost of NOVEC s operations and not on the cost of energy. There are three electric energy price predictor variables that make the price of energy volatile and difficult to predict: fuel, weather, and equipment outages. Predicting quantitative savings from reduced energy purchases under these uncertainties could be its own semester-long project, making it out of scope for this semester. Further, NOVEC has a solid methodology for energy purchasing that involves accounting for solar users and the threat of weather and outages through financial hedging and risk analysis. Therefore, the team focused on recovering costs through changing the distribution cost structure rather than how and when NOVEC purchases electricity. 6.1 PROJECT USE CASES NOVEC customers, solar and non-solar, have varying requirements of the electrical grid. Ultimately, both customer sets require an electrical grid that can meet 100 percent of their demand. The solar customer has an additional requirement of being able to pass excess energy back to the electrical grid Use Case 1: No Solar This use case describes a non-solar customer s use of the electrical grid. The customer is 100 percent dependent on the grid, 100 percent of the time. Figure 4. Use case Use Case 2: Solar Without Sun This use case describes a solar customer s use of the electrical grid when the sun is not shining (e.g. nights or cloudy days). The customer is 100% dependent on the grid. 8

9 Figure 5. Use case Use Case 3: Solar with Sun and High Load This use case describes a solar customer s use of the electrical grid when the sun is shining and the customer is in a time of high energy demand. The solar panel will meet a portion of the demand and the customer is dependent on the electrical grid for the remainder of the customer s power needs. Figure 6. Use case Use Case 4: Solar with Sun and Low Load This use case describes a solar customer s use of the electrical grid when the sun is shining and the customer is in a time of low energy demand. The solar panel will fully meet the customer s demand, and any excess power is provided back to the electrical grid. Figure 7. Use case PROJECT REQUIREMENTS The operational requirements include probability distributions based on current electricity consumption on a monthly basis. Solar penetration levels shall be considered at 1%, 3%, 5%, 10%, 15%, and 20% of NOVEC customers. This will allow NOVEC to predict solar generation 9

10 consumption and determine the impact to its infrastructure requirements. The data to develop these distributions was provided by NOVEC. The financial requires include a cost recovery methodology, which provides NOVEC a cost structure that gives a high probability of recovering all its operational cost on an annual basis. The cost recovery methodology shall provide recommendations that continue to provide a financial savings to the solar customer. For the purpose of this project, the team assumed that NOVEC is required to purchase excess solar power at the same rate that it sells electricity to the solar customer and that solar users won t increase the size of their solar panels. The team also assumed that NOVEC s operating costs and total customer size will remain steady. Finally, the team also assumed that the data provided by NOVEC is a good representation of all NOVEC customers. 7 DATA COLLECTION AND UTILIZATION NOVEC provided the data and documentation needed to complete the analysis. That information and the portions the team used is explained below. 7.1 DATA ON ENERGY DELIVERED TO AND FROM NOVEC NOVEC provided a sample of the kilowatt hours of electricity that NOVEC delivered to 471 nonsolar customers. The data was given in hourly kilowatt hours delivered from January 1, 2014 through February 17, NOVEC provided a sample of 38 solar customers hourly kilowatt hour use over the same time period. For solar, the data included the kilowatt hours NOVEC delivered, the kilowatt hours the solar customer provided back to NOVEC and the net kilowatt hours used by the solar customer. The team condensed the hourly non-solar customer electric use into monthly kilowatt hours used. The approximately three years of data was chosen as a result of the team studying whether three years of irradiance is similar. The team collected the most current 10 years of irradiance data they could find in the Northern Virginia area, 2001 through The team separated it into months and found the average irradiance over the 10 years by month. The team then calculated the average irradiance for each set of consecutive years for each month. Finally the team determined the percent difference between each month for each set of three consecutive years and that same month for the set of all 10 years. The largest difference in irradiance was in the average of all January irradiance and January irradiance for 2001 through 2003, and the difference was 0.16 percent. The team determined that irradiance stayed consistent in threeyear chunks over 10 years, so it would be unlikely for irradiance from 2014 through 2016 to vary drastically. The team used this reasoning to ask for three years of data, which would also provide a large sample without being too large to analyze in Excel. 7.2 DATA ON ENERGY DELIVERED TO NOVEC S TOTAL CUSTOMER BASE Data for hourly total residential energy use from January 1, 2014 through February 17, 2017 was also provided by NOVEC. The data included the sum of hourly kilowatt hours that NOVEC provided to its entire residential customer base. 10

11 NOVEC provided another breakdown of this data by residential class. This dataset is presented in monthly kilowatt hours used by five groups of residential customers for 2014 through It also provides the number of customers in each group. NOVEC had 152,478 residential customers in December NOVEC s customer base grows approximately 1 percent annually, so the team conducted the analysis assuming a 154,000 residential customers. 7.3 FINANCIALS FOR 2014 AND 2015 The finance documentation included NOVEC s revenues and expenses by month, divided by commercial and residential sales. It also included the company s net margins. The revenues include distribution, electricity supply and other revenues. The team considered all revenues other than those from the electricity supply since those are the operating and distribution revenues. The expenses include purchasing electricity, distribution, interest on debt, taxes, administrative, and other miscellaneous costs. The team considered all expenses other than the transmission and distribution costs. 7.4 RESIDENTIAL RATES NOVEC published its rates on its website. 13 The rates for residential services are Schedule R-1. These rates apply to residential customers, residential-farm customers, and churches located on or near the Cooperative s distribution lines. There is a monthly rate of $15 plus a distribution delivery charge and an electricity supply service charge. To deliver the energy, NOVEC charges $ per kilowatt hour for the first 300 kilowatt hours or less and $ per kilowatt hour for any additional kilowatt hours delivered. NOVEC charges $ per kilowatt hour for the energy itself. The team used this pricing structure in its analysis to compare NOVEC s current revenue to possible future revenues with more solar panel users. NOVEC also lists Time-of-Use Pricing on its website, where weekdays from June through September, between 1pm and 6pm the energy charge is higher and during the remaining hours, there is a discount. 14 The team did not consider this pricing because it doesn t apply to the distribution and because the team studied monthly rather than hourly customer energy use. 8 METHODOLOGY 8.1 FOUND PROBABILITY DISTRIBUTIONS OF HISTORIC ELECTRIC USE The team used NOVEC s data for kilowatt hours distributed to non-solar customers and converted it from hourly data to monthly electric use per customer. With this data, the team used R to find a probability distribution of historic non-solar customer electric use for each month. 15 The first step for determining what distribution best fit our data was to obtain the Cullen and Fray graph, seen in Figure 8, for each month. The Cullen and Fray graph plots the squared 13 Northern Virginia Electric Cooperative, Terms and Conditions for Providing Electric Service, August 2011, Pg. 45, 14 Northern Virginia Electric Cooperative, Time-of-Use Pricing, accessed on April 29, 2017, 15 See Appendix B for the code and a guide to using it. 11

12 kurtosis and the squared skewness against each other to see what distribution(s) are a likely fit. For example, in Figure 8, the blue dot representing the team s data falls between the lines that represent lognormal and gamma. This indicates that our data is likely to follow a gamma, lognormal, or Weibull distribution. The reason that the data may also fit a Weibull distribution is because the estimate for a Weibull distribution falls somewhere between lognormal and gamma on the Cullen Fray graph. Figure 8. Cullen and Fray Graph for the month of June Figure 9. June Weibull distribution fit check 12

13 Because the data most likely follows a Gamma, lognormal, or Weibull distribution, the next step was to find which of the three distributions provides the best fit. The Q-Q and P-P plots indicate that a Weibull distribution is a good fit for the data, which is shown in Figure 9. Although the best fit for each month was not always a Weibull distribution, the team chose a Weibull distribution for each month because it offered simplify without removing much accuracy. The resulting distributions are shown in Table Table 1. Shape and scale of Weibull distribution corresponding to kwh distributed to non-solar customers Month Shape Scale January February March April May June July August September October November December DETERMINED HOW MUCH LESS ELECTRICITY SOLAR CUSTOMERS PURCHASE FROM NOVEC THAN NON-SOLAR CUSTOMERS The solar customer sample size was too small to use the same probability distribution method as for non-solar customers. Instead, the team used the solar and non-solar data for the amount of kilowatt hours that NOVEC distributes to find the percent difference in electricity each customer type uses during peak hours. The team defined peak hours differently for each month by viewing the average kilowatt hours distributed to solar customers by NOVEC by the hour and determining which hours had a noticeable drop in purchased power. These were assumed to be the hours with sunlight and the hours that the solar panels were supplying electricity. Table 2 shows which hours were considered peak in each month. 16 To see a graphical representation of all distributions and the fit tests conducted, see Appendix C. 13

14 Table 2. Peak hours for each month Month Peak hours Number of peak hours Percent of peak hours January % February % March % April % May % June % July % August % September % October % November % December % To approximate how much less electricity solar customers use during the peak hours, the team compared the average monthly kilowatt hours that solar customers bought from NOVEC during peak and non-peak hours. This method is shown in Figure 10 for January. Figure 10. January example for finding decrease in electricity that solar customers buy from NOVEC during peak hours This method has a flaw, which the team addressed. The method assumes that in peak hours customers will not use more electricity. This is a bad assumption because peak hours are aligned with hours of sunlight, and in the summer, more electricity is used during the day. To 14

15 address the issue, the team completed the same calculation of removing peak hours and comparing the difference in kilowatt hours purchased from NOVEC for non-solar customers. This showed the difference in the amount of electricity the non-solar customers use during the peak hours or daylight hours. In the winter, they use less electricity during the day because the sun warms their homes and requires less heat. During the summer, they use more electricity during the day also because the sun warms their homes and requires more air conditioning. This step of the method is shown in Figure 11 for January. Figure 11. January example for finding difference in electricity that non-solar customers buy from NOVEC during peak hours To see the percent difference of solar-customer electric use from non-peak to peak and of the non-solar user electric use from non-peak to peak for all months, see Table 3. Table 3. Difference in electric bought between non-peak and peak hours for solar and non-solar customers Month Solar Non-solar Difference between solar and non-solar January -49% -10% -39% February -50% -16% -34% March -63% -6% -56% April -82% 5% -87% May -69% 25% -94% June -49% 39% -88% July -36% 42% -78% August -38% 43% -81% September -40% 30% -70% October -51% 7% -58% November -56% -6% -50% December -38% -4% -34% 15

16 The non-solar column now addresses the flaw by showing how much more or less electricity is used when the sun is out. The two percentages were combined to get the difference between solar and non-solar customer electric use by month. By combining them, the team included both factors of the sun: the irradiance and the heat to determine how much less electricity solar customers need to buy from NOVEC each month due to the energy generated by their panels. This combination, shown in the fourth column in Table 3, is how much less solar customers use during only the peak hours. The total kilowatt hour difference for a full should only be applied to the percent of the day that peak hours occur, which is shown in the last column of Table 2. The team multiplied that column by the final column in Table 3 to get the percent less energy that an average solar customer requires from NOVEC as compared to a non-solar customer. Those percentages are shown in Table 4. Table 4. How much less electricity solar customers require from NOVEC than non-solar customers, by month Jan Feb March April May June July Aug Sept Oct Nov Dec -13% -14% -24% -40% -39% -37% -33% -34% -29% -24% -19% -13% 8.3 CREATED CUSTOMER POPULATIONS WITH DIFFERENT SOLAR PENETRATION LEVELS For each month, the team generated 154,000 random numbers based on that month s distribution, as shown in Table 1. These represent the kilowatt hours used by each customer in each month for a 100 percent non-solar population. To increase the number of solar customers to the current penetration level of 160 customers, the team reduced 160 of the randomly generated monthly electric use by the appropriate monthly percentages shown in Table 4. For each penetration level, the team did the same but increased the number of customers with reduced electricity purchased to 1540 for 1 percent penetration, 4620 for 3 percent penetration, and so on. The months were then combined to determine the anticipated annual electric consumption of populations at each penetration level. 8.4 DETERMINED NOVEC DISTRIBUTION REVENUE AT EACH PENETRATION LEVEL Using NOVEC s current pricing structure for distributing electricity to customers, which is a $15 flat fee and a charge of $ per kwh for first 300 kwh and $ per kwh for over 300 kwh, the team determined the revenue that NOVEC would receive at each penetration level. To find it, the team calculated the amount NOVEC would charge each customer for each month of the randomly generated population at each penetration level. The results are shown in Table 5. The distribution revenue drops from $74.65 million with 160 solar customers to $72.37 million with 20% solar customers. 16

17 Table 5. NOVEC's expected revenue at each solar penetration level, as compared with current distribution revenue. Solar penetration level and number of customers Distribution revenue (in millions) Current (160 customers) $ percent (1,540 customers) $ percent (4,620 customers) $ percent (7,700 customers) $ percent (15,400 customers) $ percent (23,100 customers) $ percent (30,800 customers) $72.37 It s important to note that the distribution revenue isn t divided by commercial and residential in NOVEC s 2014 or 2015 financials, which makes it difficult to compare NOVEC s distribution revenue to the revenue determined by the randomly generated population with 160 solar customers. About 60 percent of NOVEC s 2015 electric sales came from residential customers, and 60 percent of NOVEC s 2015 distribution revenue was about million. Although this is not a precise number, the approximation shows that the $74.65 million that came from the randomly generated population is probably larger than NOVEC s actual distribution revenue. For this reason, the calculations for finding a new pricing structure are compared to $74.65 million, which is the revenue the team found for the randomly generated population with 160 solar customers. This is the revenue each pricing structure method will recover. 8.5 APPLIED NEW PRICING STRUCTURES All the pricing structure methods began with determining the difference in revenue with 160 solar customers and the revenue at each of the other solar penetration levels, shown in Table 5. This is the amount the new pricing structure would need to charge in order for NOVEC to continue recovering costs the way it currently is Flat fee increase One method for increasing NOVEC s revenue was to increase the flat fee to account for the reduction in revenue as solar customers increase. This method was rejected because it puts the bulk of the cost on non-solar customers Proportional increase for all customers Another method was to increase the per kilowatt hour distribution charge proportionally to account for the decrease in revenue. This method was also rejected because it also puts the bulk of the cost on non-solar customers Proportional increase for only solar customers The third method was increasing the per kilowatt hour distribution charge proportionally for only the solar customers to account for the decrease in revenue. The table below shows the different rates for each penetration level. The non-solar rate stayed consistently at $ per kilowatt 17

18 hour for the first 300 kilowatt hours or less and $ per kilowatt hour for any additional kilowatt hours delivered, which matches the 160 solar customer level. Table 6. Solar rates with proportional increase for only solar customers at each penetration level Solar penetration level Solar rate (first 300 kwh) Solar rate (beyond 300 kwh) 160 customers $ $ percent $ $ percent $ $ percent $ $ percent $ $ percent $ $ percent $ $ Charge solar customers to distribute excess solar energy back to NOVEC and increase all customers rate proportionally to balance revenue The last method the team explored was to charge solar customers to distribute solar energy back to NOVEC at the current pricing structure. Since the monthly distribution of energy from NOVEC to solar customers would never be negative, the team approximated the amount each customer would distribute back to NOVEC based on NOVEC s solar customer data, discussed in Section 7.1. Using that data, the team determined the amount of solar energy that NOVEC bought back from each customer by month for each penetration level. The team calculated the proportion of kilowatt hours up to 300 and over 300 for each month to match the structure used by NOVEC, and then using NOVEC s current pricing, the team calculated the average annual revenue that NOVEC would receive from a sample solar customer. This was then multiplied by the number of solar customers in each penetration level to find an estimate for the revenue NOVEC would receive from the total solar population to distribute their excess solar energy back to NOVEC. This is shown in Table 7. Table 7. Revenue from charging to distribute excess energy back to NOVEC and remaining revenue to offset with proportional charge Solar penetration level Revenue from distribution charge back to NOVEC Remaining revenue to offset with proportional charge 1 percent $73,473 $(21,961) 3 percent $220,418 $62,512 5 percent $367,363 $159, percent $734,726 $375, percent $1,102,089 $610, percent $1,469,452 $807,762 The team then determined the difference in that revenue with NOVEC s revenue with 160 solar customers, also shown in Table 7. This difference was proportionally applied across solar and non-solar customers. At a 1 percent penetration level, this returned a negative number, so nonsolar customers paid less than they currently do. The new solar pricing structure combined the proportional increase or decrease and the charge per kilowatt hour for distributing back excess solar energy. The non-solar pricing structure 18

19 increased or decreased only based on the proportional change. The different pricing structures are shown in Table 8. Solar penetration level Table 8. Rates for solar and non-solar customers for the fourth method Non-solar rate (first 300 kwh) Non-solar rate (beyond 300 kwh) Solar rate (first 300 kwh) Solar rate (beyond 300 kwh) 160 customers $ $ $ $ percent $ $ $ $ percent $ $ $ $ percent $ $ $ $ percent $ $ $ $ percent $ $ $ $ percent $ $ $ $ ANALYSIS The team analyzed the third and fourth pricing structure methods as described in sections and The other methods were rejected because they put the bulk of the cost on non-solar customers. Both of the remaining methods have a different pricing structure for solar and nonsolar customers with solar customers paying for either all or more of the cost. For both methods, the team analyzed the results to determine the difference in monthly distribution payment to NOVEC for both solar and non-solar customers and the additional time it would take for solar customers to see a return on their investment in solar panels. 9.1 AVERAGE DISTRIBUTION PAYMENT CHANGE To analyze the distribution payment change, the team calculated the average payment for solar and non-solar customers at the current pricing structure and the two methods that were determined to be fair. This is shown in Table 9. Table 9. Average monthly distribution payment to NOVEC under different pricing structures Current pricing structure Proportional increase for only solar Solar pays to distribute excess solar back and proportional increase to balance revenue Solar Nonsolasolar Solar Non- Solar Non-solar Solar penetration level 160 customers $40.40 $34.17 N/A N/A N/A N/A 1 percent $40.43 $33.84 $40.43 $36.62 $40.42 $ percent $40.43 $34.13 $40.43 $39.23 $40.46 $ percent $40.42 $34.13 $40.42 $39.84 $40.64 $ percent $40.42 $34.13 $40.42 $40.14 $40.76 $ percent $40.40 $34.16 $40.40 $40.34 $40.87 $ percent $40.41 $34.15 $40.41 $40.31 $41.00 $

20 As the solar penetration level increases the non-solar and solar average NOVEC payments stay approximately the same. They are slightly different due to the randomly generated kilowatt hours used by each customer. In the proportional increase for only solar customers option, the average non-solar charge stays the same, which confirms that the calculations are correct. The solar charge increases with each penetration level until 20 percent penetration, when it when decreases. The charge increase ranges from about $33 annually at the 1 percent solar penetration level to about $74 at the 15 percent solar penetration level. In the charge solar customers to distribute excess solar back to NOVEC option, the average non-solar customer saves 10 cents annually when the solar penetration is 1 percent. The charge increases as the solar penetration level increases, with the highest average difference at the 20 percent penetration level. At that level, the non-solar customer pays an average increase of about $7 annually. The solar customer pays a fairly consistent level extra at all solar penetration levels, ranging from about a $48 increase at 1 percent to about a $52 increase at 20 percent. The first option is cheaper for solar customers at the 1 percent penetration level and more expensive in all higher penetration levels. For non-solar customers, the cost increase in the second option is small, about 60 cents per month. 9.2 MAXIMUM PAYMENT INCREASE The team also determined the maximum payment of solar and non-solar customers for each pricing structure to understand the largest monthly increase that a customer would see, shown in Table 10. Solar penetration level Table 10. Maximum monthly distribution payment to NOVEC under different pricing structures Current pricing structure Solar Proportional increase for only solar Nonsolar Nonsolar Solar pays to distribute excess solar back and proportional increase to balance revenue Solar Non-solar Solar 160 customers $ $ N/A N/A N/A N/A 1 percent $ $ $ $ $ $ percent $ $ $ $ $ $ percent $ $ $ $ $ $ percent $ $ $ $ $ $ percent $ $ $ $ $ $ percent $ $ $ $ $ $ The maximum solar customer kilowatt hour use varies substantially between penetration levels because of the randomly generated populations. Typically, the larger the penetration level, the 20

21 larger the maximum because there are more opportunities to see a larger value as the randomly generated population is created. The values should be compared across rows for this reason. The customers who use the most electricity will see large increases in their monthly bills. For example, the non-solar customer who uses the most electricity would pay almost $700, or 32 percent, more per month in the second option at a 20 percent penetration level. The average customer would pay only 1.5 percent more. The solar customer using the most electricity would pay about $240, or 24 percent, more per month in the second option at a 20 percent penetration level. In the first option, the solar customer would pay 34 percent more at the 20 percent solar penetration level. The average customer would pay 18 percent more in the first option and 12 percent more in the second option at the 20 percent level, which is closer to the increase that requires the most electricity from NOVEC than it was for the non-solar customer. The biggest takeaway from this analysis is that even small changes in the pricing structure can have large impacts on customers who use a large amount of electricity. NOVEC could consider another pricing structure where the charge to distribute over 300 kilowatt hours remains unchanged or increases at a lower rate and the fee to distribute under 300 kilowatt hours is where all or the majority of the cost increases. 9.3 PRICING STRUCTURE IMPACT ON SOLAR PANEL RETURN ON INVESTMENT To analyze the increase in the number of years that each pricing structure would add for solar customers see a return on investment for their solar panels, the team started by calculating the number of years it would take under the current pricing structure. First the team determined how much solar customers save annually on electricity and distribution costs because of the energy the solar panels produce. The savings are shown in Table 11. Table 11. Amount solar saves annually due to solar panel energy production for each pricing structure Solar penetration level Current pricing structure Proportional solar increase Charge to distribute excess solar back to NOVEC 1 percent $ $ $ percent $ $ $ percent $ $ $ percent $ $ $ percent $ $ $ percent $ $ $ To determine the number of years it would take to see a return on investment, the team assumed that solar panels cost $30,000 to purchase and install and that maintenance costs are negligible. Since there is currently a federal tax credit of 30 percent, which will be available through 2019, the team assumed the penetration level could reach 1 percent by the end of 2019 and that for those penetration levels, the total cost to buy the solar panels would be $21,000 after the tax credit. The tax credit drops to 26 percent in The team assumed the penetration level could reach 3 percent by 2020, so the cost to purchase the panels in 2020 would be $22,200 after the credit. The team made a similar assumption for 2021, where the credit drops to 22 percent, expecting that the solar penetration could reach 5 percent. The 21

22 panels in 2020 would cost $23,400. After 2020, the credits are no longer offered. The team assumed the solar population will not reach the 10, 15, or 20 percent penetration levels before Therefore the solar panels would cost the buyer the full $30,000 after See section 4.5 for more information on the cost of owning solar panels. To calculate the number of years before the owners see a return on investment, the team calculated the amount solar customers currently save in distribution and energy costs. As a reminder, NOVEC charges $ per kilowatt hour for the energy itself. The same method was used to determine the years until return on investment with the two proposed pricing structure options. The results are shown in Table 12. Table 12. Years to see a return on solar panel investment and the increase in ROI for the proposed pricing structures Solar penetration level Current pricing structure (years) Proportional solar increase (percent more years) 1 percent % 9% 3 percent % 10% 5 percent % 10% 10 percent % 8% 15 percent % 11% 20 percent % 9% Charge to distribute excess solar back to NOVEC (percent more years) The number of years to ROI are high at the current pricing structure since solar panels typically last 25 years before needing to be replaced. This is probably the case for one of three reasons: solar users didn t purchase them to save money and instead purchased them for environmental reasons, the cost or tax incentive assumptions are incorrect, or the data provided by NOVEC didn t provide a good sample of the difference in solar and non-solar use. It s important to compare the percent difference in the number of years at each of the penetration levels rather than the exact number of years for this reason. 10 SENSITIVITY ANALYSIS 10.1 RESULTS WITH INCREASED EFFICIENCY One of the team s assumptions was that the average solar panel used by NOVEC s solar customers would have an efficiency of 17 percent, which is typical according to solar panel manufactures. 17 The efficiency of a solar panel refers to the percentage of sunlight that reaches a solar panel is converted into electricity. For a sensitivity analysis, the team studied the impact that changing the average efficiency of solar panels would have on the results. This provides NOVEC different pricing options if in the future it observes an increase in solar panel efficiency. As solar users gain access to more efficient solar panels, they will need less electricity from NOVEC and will sell back more electricity. Figure 12 shows that as solar users gain access to more efficient solar panels, the fee that they pay for distribution will also increase. 17 Suniva, Suniva Optimum Series Monocrystalline Solar Modules, August 2015, 22

23 Figure 12. Pricing options for increased solar panel efficiency One of NOVEC s goals is to not dissuade users from switching to solar panels. Although solar users will be subjected to a higher distribution fee as solar panel efficiency increases, Figure 11 shows that solar users will still increase their yearly saving through reducing the cost of the energy itself with more efficient solar panels. Figure 13. Yearly savings for solar users 11 RECOMMENDATIONS The team recommends either not changing the pricing structure or increasing the distribution rate only for solar until somewhere between 1 and 3 percent. The exact penetration is an option for future work. Before the 3 percent penetration level, the pricing increase for only solar is best for solar customers and non-solar customers would stay at the same rate rather than getting a discount. Solar customers would also have a shorter time until they get a return on their solar panel investment. At and above 3 percent solar penetration, the team recommends changing the pricing structure to the option where NOVEC charges the solar customer to distribute excess solar energy to NOVEC to make up for a portion of the lost revenue and the remaining revenue is recovered through a proportional increase to all customers. The solar customer will still see savings 23

24 through a decrease in the electricity charge per kilowatt hour. This method puts the majority of the increased cost on solar customers while choosing the option with the fewer years before they see a return on investment. Table 13 provides the recommended pricing structure at each penetration level. At all penetration levels, NOVEC would still charge a flat $15 each month and would still charge $ for each kilowatt of electricity consumed. Solar penetration level Table 13. Recommended pricing structure at each penetration level Non-solar rate (first 300 kwh) Non-solar rate (beyond 300 kwh) Solar rate (first 300 kwh) Solar rate (beyond 300 kwh) 160 customers $ $ $ $ percent $ $ $ $ percent $ $ $ $ percent $ $ $ $ percent $ $ $ $ percent $ $ $ $ percent $ $ $ $ LIMITATIONS There were a couple of limitations, and the team recommended ways to address them in the Future Work section. First, the sample data wasn t a good representation of total population. The team received about three years of data for 450 non-solar customers and 38 solar customers. The sample population led to a distribution that used 13 percent more kwh annually than residential totals. The difference ranged from 15 percent less and 41 percent more depending on the month. The second limitation is that the non-solar data consisted of almost 4 million entries, which made the data difficult to work with in Excel. The team moved the data to R in order to sort, filter and clean up the data. Since not all teammates had the technical expertise to use R or another programming language, the team then continued the work in Excel, and the spreadsheets were very slow and difficult to use. 13 FUTURE WORK The team conceived a number of ideas for follow-on work through research and discussions with the project sponsor. These ideas were either out of scope or there was not enough time remaining to explore them. The team recommends that either a future George Mason University team or NOVEC considers the following options. As a fifth pricing structure option, a future team could separate the solar population into different groups based on solar use to explore charging each group a different rate. This would allow NOVEC to charge a higher rate to solar customers with larger houses who would likely require more electricity from NOVEC during hours without much sunlight, therefore requiring more of NOVEC s infrastructure. This may be an even fairer way to distribute the cost. 24

25 As a sixth pricing structure option, NOVEC could consider another keeping the rate to distribute over 300 kilowatt hours the same or increase it at a lower rate and increasing the fee to distribute under 300 kilowatt hours only or more rapidly. To expand upon the current recommendation, another project could find the exact penetration at which it is best to switch from the option that increases only the solar costs and the one that charges solar customers to distribute the excess energy back to NOVEC. As another method for determining the amount of electricity the solar customers panels produce, NOVEC could convert the historical monthly irradiance to the electricity a typical residential solar panel would produce. The decrease in monthly solar use could be used to increase the solar penetration level. Three options arose as possibilities for the future even though they are not issues currently. It would be interesting to study customers who are able to store their excess solar energy, the difference in NOVEC s revenue if it was not required by law to buy back excess solar energy, and the impact is residential customers bought larger solar panels that produce more energy. Two options arose as ways to improve the results. First, because the sample data provided by NOVEC didn t align with the data for the full residential population, the team recommends using the methodology outlined in this paper with the data for all residential customers to find the results with more accurate data. Secondly, to speed up the analysis, NOVEC would benefit from moving the Excel files into a database or code. 25

26 14 APPENDIX A: PROJECT PLAN The project plan defines the work to be completed, assigns resources, coordinates the execution, and defines the method of tracking the progress. The team scoped the project to take approximately 15 weeks to complete on a part time basis by a team of three. The team was two operations research students and one systems engineering student. A combined work breakdown structure (WBS) and Gantt chart are shown in Figure 14. The team tracked the project was using earned value management (EVM). The team initially scheduled the project to conclude on May 16 after hours of effort. As the project progressed, some tasks were removed to make the May 8 deadline and hours were adjusted to hours. 26

27 14.1 WORK BREAKDOWN STRUCTURE AND SCHEDULE The work breakdown structure (WBS) is developed by identifying the components required to complete the effort and dividing those components into manageable work sets. The main components of this effort were project management, research, analysis, and reporting. The WBS for this effort is shown in Figure 14 with the associated schedule in the form of a Gantt chart. Figure 14. Work breakdown structure and Gantt chart

28 14.2 EARNED VALUE MANAGEMENT EVM is a method of tracking progress towards a project s completion. With the effort broken down into the WBS above, each work package is assigned a value. As a work package is completed, the project earns the value of that package. The work completed is continuously compared to the work scheduled and the cost of the work completed. Acronyms BCWS Budgeted Cost of Work Scheduled BCWP Budgeted Cost of Work Performed ACWP Actual Cost of Work Performed CV Cost Variance (BCWP ACWP) CPI Cost Performance Index (BCWP/ACWP) SV Schedule Variance (BCWP BCWS) SPI Schedule Performance Index (BCWP/BCWS) Figure 15. Weekly tracking of the DSG Team s performance against Cost and Schedule.

29 Figure 16. Cost Performance Index (CPI) and Schedule Performance Index (SPI) Figure 17. Earned Value Tracking 29

30 15 APPENDIX B: R PROBABILITY DISTRIBUTION CODE ## Following code can be copied and pasted straight into R ## ## Code used to determine which distributions to use ## #Required Packages install.packages("fitdistrplus") library(fitdistrplus) # Call in the excel files that will be used for each month Apr <- read.csv(file.choose(), header = TRUE) Aug <- read.csv(file.choose(), header = TRUE) Dec <- read.csv(file.choose(), header = TRUE) Feb <- read.csv(file.choose(), header = TRUE) Jan <- read.csv(file.choose(), header = TRUE) Jul <- read.csv(file.choose(), header = TRUE) Jun <- read.csv(file.choose(), header = TRUE) Mar <- read.csv(file.choose(), header = TRUE) May <- read.csv(file.choose(), header = TRUE) Nov <- read.csv(file.choose(), header = TRUE) Oct <- read.csv(file.choose(), header = TRUE) Sep <- read.csv(file.choose(), header = TRUE) # Set s=3 since we only care about data in the third column # Set X to a month and do the following for all 12 months s=3 X= Jun # Creates a Cullen Frey Graph. Compares the square Kurtosis and squared skewness to determine which distributions are most likely to fit the data descdist(x[,s], discrete = FALSE) 30

31 # All 12 months for our data seemed to be a close fit to either lognormal, gamma, or weibull fit.g <- fitdist(x[,s], "gamma",method = "mme") fit.ln <- fitdist(x[,s], "lnorm") fit.w <- fitdist(x[,s], "weibull") # Check the fit for the three possible distributions plot(fit.g) plot(fit.ln) plot(fit.w) # qqplot(x[,s], y=1:5,distribution = "weibull", scale=837, shape=1.3, las=1, pch=19) # Used to determine the scale and shape for each month assuming that they have a weibull distribution fitdistr(jan[,s], densfun="weibull", lower = 0) fitdistr(feb[,s], densfun="weibull", lower = 0) fitdistr(mar[,s], densfun="weibull", lower = 0) fitdistr(apr[,s], densfun="weibull", lower = 0) fitdistr(may[,s], densfun="weibull", lower = 0) fitdistr(jun[1:549,s], densfun="weibull", lower = 0) #the last data point in June was causing some issues fitdistr(jul[,s], densfun="weibull", lower = 0) fitdistr(aug[,s], densfun="weibull", lower = 0) fitdistr(sep[,s], densfun="weibull", lower = 0) fitdistr(oct[,s], densfun="weibull", lower = 0) fitdistr(nov[,s], densfun="weibull", lower = 0) fitdistr(dec[,s], densfun="weibull", lower = 0) 31

32 16 APPENDIX C: MONTHLY PROBABILITY DISTRIBUTIONS The following sections provide the January and September graphs created in R to determine the probability distributions for each month based on historical non-solar use. The remaining graphs were created by the team and can be replicated using the R code in Appendix B JANUARY DISTRIBUTION GRAPHS Figure 18. Cullen and Fray graph for January Figure 19. Gamma fit check for January 32