The Future of Solar Energy in the us: a technological, Political and Financial Enquiry



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  • Edison Electric Institute (EEI)

EEI is an association of all the shareholder owned electric companies in the US. EEI’s mission is to ensure members’ success by advocating public policy, expanding market opportunities, and providing strategic business information. The EEI, like ALEC is not officially against the adoption of solar energy - rather, it takes particular strong views against rooftop solar energy and policies that promote it. Rooftop solar is a long term competitive good for utility companies because it creates the threat of them losing their customers. Thus, most EEI efforts related to solar are concentrated on trying to remove government programs that support solar energy (such as RFS or net metering), as well as trying to lobby the government into implementing policies that actively inhibit rooftop solar from expanding (such as allowing them to charge customers with rooftop solar panels higher rates for power from the grid)52. EEI argues this is fair practice because utility providers must continue to pay the fixed costs of running their power station and that rooftop solar prohibits utilities from regaining their cost of business.

  • Americans for Prosperity (AFP)

AFP is “America's largest center-right grassroots organization” (Americans for Prosperity website). AFP is known for its vocal opposition to most things government. AFP argues against RPS, believing they drive up the price consumers pay for power, as well as arguing that government intervention distorts the energy market by circumventing individual liberties and placing an undue financial burden on taxpayers.53

It is worth noting that, like in the case of pro-solar lobbies, these lobbies tend to interact with each other. Thus, the EEI often sponsors ALEC54, which in turn is able to use its relationship with state legislators to lobby for policy the EEI may want enacted. the EEI may also lend its research to AFP to support AFP’s grassroots campaigns that are meant to mobilize its members into pressurizing their representatives into enacting the kind of legislation they want to see.

3.2.4 Political grassroots lobbies (left vs. right)

Curiously, while climate change is heavily contested by the left and right in America, solar energy receives support from grassroots political lobbies on both the left and right of the political spectrum in the US55. Left-leaning political lobbies tend to support solar energy because of its positive effect on the environment, while right-leaning political lobbies tend to support rooftop solar energy because they see it as a lowering of the role of the state. This bipartisan support for solar energy at the grassroots level holds immense potential for the future of pro-solar policy in the US, as these pressures have a strong tendency to diffuse up the political hierarchy.

3.4. Future of Solar Policy in US:

We now assume certain aspects of the behaviour of the actors in the solar energy arena in order to aid our analysis of what the future of solar policy in the US might look like.

To perhaps state a truism, solar energy companies have very strong interests in promoting pro-solar policies in most forms. RPS by definition increases the minimum market size these companies have, net metering reduces the real price of their product for the consumer without affecting the price they set, and government financing initiatives allow them to scale at affordable rates.

Consumers, which basically includes the entire US household market, have incentives to use solar energy if price relative to conventional energy is lower. It is impossible to say when solar energy will be able as affordable as conventional energy without government intervention (given that the technology is prone to rapid advancements that cannot be forecasted). However, we can say that non-price factors could play a significant role in increased demand for solar energy in the US. Political leanings can play a big role for consumers in supporting solar energy. Left-leaning environmentally concerned citizens are likely to support solar because of its positive effects on the environment, while right-leaning citizens concerned with the role of government are likely to support solar because it means independence from state-owned utilities monopolies.

Conventional energy companies do not have systemic interests against solar energy as a whole, as not all solar energy is a direct competitor to their business. For example, assuming that technology wasn’t a barrier for a moment, a utility company could set up a huge field of solar panels and then distribute the energy generated from that field to its customers. Here, solar energy would simply represent a change in the technology used by these companies. Utility companies do however have strong interests against their consumers setting up rooftop solar energy, as this directly eats into their market size and makes an industry that is premised on scalability less competitive.

3.4.1 Future of U.S. Solar Policy

With so many moving parts in the solar energy case, it is impossible to come up with a single case that describes the future. Rather, we list three cases here that show what the future might be assuming certain things happen.

Case 1: Bull Case

In this case, we assume that grassroots political organizations on both sides of the political spectrum are able to effectively organize, outvoice organizations with a narrower member base such as ALEC and EEI, and lobby the government into supporting solar energy. We assume that SEIA and SEPA are able to make use of this grassroot level political support and use their own network of political networks to promote pro-solar policy. As a result, the ITC is extended for another 5 years (a stated goal of the SEIA56), and current efforts to gut metering and increase the power rates rooftop solar consumers pay fail - leading demand to rise at an increasing rate. We assume that RPS carve-outs for solar expand as they have been doing for the past 3 years57, leading to increased mandates for solar energy, stimulating further supply and allowing increasing returns to be realized. We also assume that increased investment into solar technology research leads to increased improvements in efficiencies and decreases in cost of energy production for the existing technologies, and even leads to the commercialization of solar technologies that are currently in the early stages of development. Thus, the overall market size of the solar industry greatly increases by 2020, making the industry more profitable. This in turn attracts more financing, which places solar on a solid foundation to grow even faster in the future.

Case 2: Base Case

In this case, we assume that both pro-solar and anti-solar voices are able to influence in the government. This leads to tax credits being extended but weakened (currently an outcome that seems extremely likely58), which diminishes the profitability of solar projects, which attracts less private financing in the future than does Case 1. We assume that RPS and carve-outs stay constant, and while net metering is allowed, power companies are able to charge solar consumers high power rates59, causing demand to rise at a decreasing rate as there is now an added cost to using solar energy. This case involves more limited funding for solar technology research, meaning efficiencies rise only slightly, and costs decrease minimally. In this business-as-usual case, the solar industry grows at a similar rate to what it’s been growing at over the past 5 years.

Case 3: Bear Case

In this case we assume that anti-solar voices are able to dominate future policy discussions. This leads to tax credits not being extended, and a steady decrease in RPS. We assume that the EEI’s argument that the costs of net metering are greater than its benefits, and net metering is not allowed. Funding for solar technology research decreases tremendously, and few to no improvements in efficiency and cost are made. In this case, given that the costs of production and consumption of solar rise extremely high, the demand for solar (at least in rooftop form), begins to fall. The lack of tax credits as well as decreasing RPS lead to a smaller and less profitable market for solar, which in turn attracts less financing. This leads to a contraction of the solar energy industry.

Of the three cases, we argue that the 2nd case is the most likely, with the caveat that the extension of the 30% ITC is still possible. Power companies have legitimate arguments in saying that net metering forces poorer people to pay higher power rates (to offset the price they must pay solar installers power companies charge higher overall rates) and that it allows solar users to get away with paying for the fixed costs required to keep power plants operational. This, combined with the EEI’s political clout make it likely that net metering is unlikely to exist in the future as it does today.

It is important to note that these cases are not accounting for further developments in alternative sources of renewable energy, which might affect the market for solar in huge ways. A good avenue for further research would be attempting to forecast the future of solar energy in relation to developments in alternative renewable energy methods.

Given that the ultimate goal of solar policy is to make it profitable enough to attract private financing, we now turn to the financing section of the paper and will then begin to show how each of these seemingly disparate disciplines merge together with regards to solar energy policy and the United States.

4.0 Financing Utility-Scale Solar Power Projects

There are two important investment components for financing large-scale solar projects—debt and equity. Equity capital is provided by the project developers as well as by equity partners (institutional investors, hedge funds, private investors, individual firms, etc.) and this contribution serves as the initial “seed capital” that allows the project to start. This equity capital is usually between 15-20% of the total capital investment, however, the contribution is not made until debt financing is secured (without lender/creditor commitment to finance the rest of the project, providing the initial equity capital can be highly risky).60 Equity contributions are used to cover initial due-diligence expenses, which can broadly be categorized as legal, technical, and financial in nature; undertaking these due-diligence efforts is essential for project development. The cost of the preliminary legal assessment of necessary permits and contract terms (for engineering, construction, operations, and management) and technical due-diligence (ensuring the feasibility of the solar project and that permits and contracts accommodate the technical requirements of the project) will almost entirely be borne by the equity sponsors.61 Lender financing will only come into play once the equity stage due diligence is complete; debt capital will be used to support the more comprehensive legal, financial, and technical due-diligence required to begin project development. Given that loans are the most crucial component in solar project finance, it is important to understand how this capital will be deployed by private sector participants and under what conditions. The following sections will outline the current salient government incentive programs, partnerships, and financing structures that will allow solar infrastructure projects to progress from the equity stage to commercial viability.


4.1.0 Department of Energy Loan Programs
The Department of Energy Loan Programs Office has currently committed $30 billion across a diversified portfolio of loans, loan guarantees and commitments.62 Currently, the DoE LPO has over $40 billion remaining in loan and loan guarantees that can be deployed through two programs.63 The first program is the Innovative Clean Energy Projects (Title XVII) which provides loan guarantees for energy technology, ranging from advanced fossil fuel to nuclear and renewable energy.64 The terms of Title XVII loan guarantees (which are not direct loans by the LPO) strictly require that projects must use a novel technology or provide a high value-add to existing energy technology.. Additionally, the projects must “avoid, reduce, or sequester” greenhouse gases, which need to be quantified to be eligible. Given that the LPO is providing loan guarantees, it requires that all eligible projects are based in the United States (to directly capture the benefits of reducing greenhouse emissions and realize the economic benefit of investment in jobs and infrastructure) and that the projects have a reasonable prospect of repayment—after all the government guaranty transfers the risk of default to the LOP portfolio from participating non-government lenders. The other program under the DoE LPO—Advanced Technology Vehicle Manufacturing (ATVM)—is not directly applicable for energy investment, given that it is geared towards improving vehicle manufacturing facilities in the US.65

Source:Department of Energy Loan Programs Office

Of the $41.5 billion remaining in direct loans and loan guarantees under the Loan Program Office, $16 billion is destined towards the Advanced Technology Vehicles Manufacturing program.66 This leaves $25.5 billion for the innovative energy technologies, of which $21 billion is committed towards existing non-renewable energy sources—fossil and nuclear energy.67 At the moment, only about 11% ($4.5B) of the $41.5 billion availability for government funding is destined towards renewable energy.

Source:Department of Energy Loan Programs Office

These loan guarantees can best be described as incentives for solar infrastructure projects, however, these are distinct from public-private partnerships which hold promise for future solar infrastructure development (given that the current level of loan guarantees and incentives is low relative to what is required to hit federal and state mandates for solar electricity generation).

Source:Department of Energy Loan Programs Office


The effectiveness of the Department of Energy’s Loan Guarantee program has been questioned since the bankruptcy of Solyndra, a solar panel manufacturer who received a $535 million loan guaranteed by the Department of Energy.68 The controversy surrounding the default was not focused simply on the bankruptcy event itself, but rather, the failure of the government to conduct the proper due-diligence to review the claims made by Solyndra developers. In a report released by the Energy Department inspector general, Solyndra was found to have misled lenders (and the government) regarding the prices it was able to charge for its solar panels and the condition of its financials. While the company was responsible for fraud in this regard, the report also claims that the loan guarantee was approved due to “political pressure” and the resulting due-diligence process was unable to uncover the irregularities of the Solyndra financial statements and projections.

Source:Department of Energy Loan Programs Office

The Energy Department report also suggested that another failure (due to poor government due diligence) on the scale of Solyndra “could seriously undermine the [Department of Energy Loan Guarantee program] and its goals, perhaps even leading to its termination.” 69 Although the program appears to have stabilized and currently has a low default rate across its loan portfolio (2.28% in losses as a percentage of total commitments as of September 2014), future defaults could further reduce the limited availability of loan guarantees for solar photovoltaic infrastructure projects.70 While the risk of future solar photovoltaic project defaults cannot be dismissed, it is also worth evaluating some of the current solar projects that have been successful within the Department of Energy’s Loan Guarantee portfolio—Desert Sunlight, Mojave, and Ivanpah. The following sections are case studies of these successful projects and detail the costs, benefits, and financing mechanisms used to bring the utility-scale projects online.

4.1.1. Desert Sunlight Photovoltaic Case Study

Desert Sunlight is the second largest solar PV project in the LPO portfolio with nearly $1.5 billion guaranteed by the DoE.71 The loan was guaranteed for issuance September 2011 for construction of a 550-MW PV solar generation plant in Riverside County, California.72 One of the remarkable aspects of this project is the amount of financial institutions involved—fourteen in total. The DoE notes in Desert Sunlight’s project summary that “the loan guarantees helped attract new lenders into the utility-scale photovoltaic market and provided them with experience financing utility-scale photovoltaic projects.”73 Given that the project was financed as a syndicated loan with NextEra Energy, General Electric & Sumitomo of America as project owners, it provided substantial underwriting experience for all the lenders involved and set the stage for future syndicated loans of solar PV projects. The DoE also noted that an additional 17 PV projects with capacity greater than 100MW had been financed “without loan guarantees and many of them by banks that LPO had worked with through [Financial Institution Partnership Program].”74



Source:Department of Energy Loan Programs Office

The Desert Sunlight can be deemed a success due to the fact that the project reached full commercial viability in January 2015 and is currently generating electricity. Given that the Department of Energy’s Loan Guarantee program is judged based on the economic impact of the projects in its portfolio, it is also worth noting that 550 temporary construction jobs were created for the DS project along with 15 permanent jobs. In terms of environmental impact, 614,000 metric tons of annual carbon dioxide emissions are projected to be reduced due to the electricity generated by Desert Sunlight (annually 1,060,000 MWh).

4.1.2. Mojave Concentrating Solar Power Plant (CSP) Case Study

Mojave is another successful solar project in the LPO portfolio. With 250-MW capacity, the parabolic trough concentrating solar power plant (CSP) in San Bernardino County, California reached commercial viability in December 2014, barely three years after the $1.2 billion loan guarantee necessary to begin construction was secured by the DoE ($1.2 billion was guaranteed of a total investment of $1.6 billion).75 The project owner was spanish multinational Abengoa S.A. and its solar construction subsidiary, Abengoa Solar, LLC.76 77 The plant assets are currently owned by Abengoa’s YieldCo (a term to be defined later in the financing section of this paper); Mojave is expected to generate 617,000 megawatt-hours of clean energy annually and reduce 329,000 metric tons of carbon dioxide emissions per year. It is also important to note that the loan guarantee decision was aided by the fact that Abengoa had agreed to a 25 year power purchase agreement (PPA) with Pacific Gas & Electric (for the sale of energy produced by Mojave).78 Despite the PPA and estimated economic impact (830 temporary construction jobs, 70 permanent jobs, local tax revenues from electricity sales), the project was received with much opposition from politically conservative groups and environmentalists in the wake of the Solyndra debacle.79 80 Unsubstantiated accusations of waste, corruption, and illegal activities were attributed to Abengoa, however, none of these accusations have been addressed by politicians or government officials. By all accounts, the project is currently a success, as it is at full operational capacity and generating electricity. 81


4.1.3. Ivanpah Concentrating Solar Plant (CSP) Case Study

Our final case study of solar projects is Ivanpah, a 392 megawatt concentrating solar power (CSP) plant located in Ivanpah Dry Lake, California. The Department of Energy issued three loan guarantees in April 2011 covering a notional amount of $1.6 billion in loans; January 2014 marked the beginning of Ivanpah’s commercial operations.82 When completed, Ivanpah was the largest CSP plant in the world and according to the DOE, “Ivanpah nearly doubled the amount of solar thermal energy produced in the United States in previous years.”83 The economic and environmental impact of Ivanpah in the region is staggering, with annual electricity production of 940,000 megawatt-hours, 500,000 metric tons of carbon dioxide emissions prevented annually, 1,000 temporary construction jobs created with 61 permanent jobs. In recognition for its technological innovation and economic impact, Ivanpah was named “Plant of the Year” by POWER Magazine (a publication that has covered the power generation industry for over 130 years), given its status as largest solar thermal plant in the world and being the first commercial-scale solar project to use power tower technology.84 85 As is the case with Desert Sunlight and Mojave, Ivanpah is currently a successful project within the Department of Energy’s loan guarantee portfolio. As aforementioned, the Department of Energy currently has around $4.5 billion of available loan guarantees earmarked for renewable energy (not specifically solar) under Section 1703 of Title XVII Innovative Clean Energy projects. As we have seen with the case studies discussed in this section, even partial loan guarantees of solar mega projects (>250MW capacity) can result in highly successful economic and environmental impacts to the community, exceeding the risk of default in guaranteeing loans (which for large-scale commercial power projects is much lower early stage unproven technology companies). Additionally, loan guarantees result in further financing transactions without loan guarantees, as investment banks and financial institutions gain experience and familiarity underwriting and syndicating solar power infrastructure projects.



4.2.0 Public-Private Partnerships

Public-private partnerships are generally collaborative agreements between the government (usually federal and/or state) and private sector participants (investment banks and institutional investors) to develop long-term infrastructure projects. These projects are usually extremely costly to build and development takes several years to bring the project to full completion.86 Given the high initial capital costs and delayed payback period (toll roads/utilities that only begin earning revenues upon completion—after multi-year construction period), the entire project poses significant risk for any one party to bear.87 Through public-private partnerships, the private investor still bears a significant amount of risk (along with substantially all managerial responsibilities/costs), however, the participation by a government entity decreases the size of the burden.88 The government entity can choose to either finance part of the project directly (assuming it has the funds available to do so) or it can provide the private party with an agreement to allow the private investors to receive the operating profits of the infrastructure project.89 90This agreement can contain royalties to be received by the government or revenue-sharing models, both of which are increasing in proportion to the government entity with initial government capital contribution.


4.2.1. Power Purchase Agreements & Public-Private Partnerships

Specifically, when it comes to solar infrastructure projects that are expected to generate significant electricity, power purchase agreements can serve as the government contribution towards the partnership (while providing little to no direct capital upfront and the private investor(s) bearing the entirety of the initial capital cost).91 The importance of power purchase agreements for electricity-generating infrastructure is easy to see—investors undertake the task of financing a project with heavy initial capital costs and sustained cash outflows with a delayed payback period. The uncertainty of future revenues dissuades investors from committing their capital; the risk of realizing inadequate (low or negative) returns is high when there is no agreement in place for securing future demand. The power purchase agreement eliminates the uncertainty as project financiers can guarantee baseline future demand to cover their fixed costs (including costs of entry) as well as their variable costs of production.92 PPAs benefit both parties, as the government utility (party directly purchasing electrical output) secures future supply of electricity that conforms with government mandates while the private sector investors realize a return on their investment via the guaranteed purchases.



4.3.0. YieldCo Structure and Financing Capabilities

Yield Companies are financing vehicles that are very different from government loan guarantees, tax credits, and public-private partnerships. While Yield Cos. are often the beneficiaries of the aforementioned financing mechanisms and incentives, their structure and purpose is different from project finance. All the previous financing opportunities described in the previous sections have mainly dealt with project finance, which occurs in the development stage of solar power infrastructure projects. This concerns all the early stage equity and debt capital necessary to begin development due diligence and eventually construction. However, Yield Co’s take advantage of the public capital markets once projects have been fully developed and are fully operational. Investors seeking dependable dividend income turn toward these investments (Yield Co’s) with the expectation that the cash distributions increase over time.93 94 Typically, a solar power company (e.g. Abengoa, SunEdison, etc.) will bundle its solar power operating assets (PV, CSP facilities, etc.) into a non-subsidiary entity.95 These operating assets will be expected to generate consistent income from selling electricity to utility companies, usually under long-term contracts (>15 years) or long-term power purchase agreements.96 Yield Co.’s are structured similarly to Master Limited Partnerships (an investment vehicle used extensively in the oil & gas industry for midstream assets) and Real Estate Investment Trusts (commonly used to bundle commercial real estate assets) in order to be tax-efficient and to maximize the cash flows from the operating assets. The parent companies that create Yield Co.’s are typically large players, whether unregulated arms of utility companies, independent power producers, or specialist (pure-play/independent) solar project developers. In creating a Yield Co., the parent company is able to immediately monetize long-term operating assets (which normally would take several years to pay back the initial capital invested in the project before providing the company with a return), which allows it to redeploy that capital into new project developments. The Yield Co. is then spun off and publically traded as an independent entity, with an agreement in place for the parent company (which maintains an ownership interest in the Yield Co) to continue to pass through (sell, lease, etc.) operating assets to the Yield Co—investors require this agreement in order for their cash distributions (dividends) to increase over time. The Yield Co. finances the purchase of operating assets from the parent through a combination of debt and equity. The tax advantages of Yield Co’s are very important to the parent company and public shareholders of Yield Co. shares; due to the special organizational structure of Yield Co.’s, there is only taxation at one level (individual shareholder) rather than at two levels (company and then individual shareholder) as is the case with corporations.97 This allows Yield Co.’s to reinvest more cash by saving on taxes and allows shareholders to re-invest in the Yield Co. to generate more dividend income. Within the broader umbrella of financing mechanisms available for solar power projects, Yield Co.’s allow large project developers to monetize invested capital from existing operating assets (while realizing a return) and to redeploy that capital into new projects (which will be financed through project finance as described in the previous sections).

Although companies developing utility-scale solar projects have several financing alternatives to choose from, it is important to identify those that will be the most prominent for future projects. Given that the Department of Energy Loan Guarantees are nearly at their guarantee limit for renewable projects (and by extension, utility-scale solar) it is unlikely that this program will serve as a meaningful financing source for more than 2-3 utility-scale projects (>250 MW). With this in mind, Public-Private Partnerships and late-stage YieldCos. serve as more pragmatic sources of funds for companies developing utility-scale solar projects. Public-Private Partnerships can help finance projects early (assuming DOE Loan Guarantee limits are not increased) and the YieldCo. structure can provide early-stage investors with an exit for their investment. One indirect benefit of the Department of Energy’s Loan Guarantee program was the direct underwriting experience it provided to financial institutions (incentivized by the government’s loan guarantees) that would persist beyond the life of the loan guarantees. As the DOE program is phased out (assuming no extension of the loan guarantee limits—currently an uncertain prospect), the experienced financial institutions have continued participating in the financing of solar projects, which can be expected to continue in the future. The larger solar companies that are developing utility-scale solar projects can negotiate their purchase-power agreements and bundle the renewable assets attractively for sale to its YieldCo., distributing the funds received to early-stage equity investors and using the remaining balance towards new capital investments (utility-scale solar or otherwise).


5.0. Electricity Distributor Model98

We now use a basic electricity distributor model to illustrate a utility firm’s profit maximization decision. Our analysis is done in two stages. First, we aim to illustrate this representative firm’s choice of solar capacity up to 2040 under assumptions of projected electricity price and capital cost of increasing capacity. Then, we analyze the comparative statics of this choice of solar capacity under different ranges of assumptions on government subsidy, technological capability, and returns to scale of added capacity. By modeling these comparative statics, we examine the effects of the different possible outcomes of the technological, political, and financial situations detailed in this paper.



5.1.0 Assumptions

Our representative firm wants to maximize profits over a 25 year horizon, or in other words is making its decision based on information up to the year 2040. To model this consideration, we use a dynamic profit function:



c:\users\brian\downloads\codecogseqn (1).png

Note that the profit each year is given by the revenue, electricity price (pi) multiplied by electricity generation (yi), minus the cost, a function of total solar capacity (si), plus government subsidy. The firm considers the net-present value of future profits, given by discounting by the risk-free rate (r).

We make the assumption that the electricity price will not remain constant. Looking at the historical prices over the past 10 years, prices grew 25% and exceeded the natural inflation rate of 21%.99 Thus, we use the U.S. Energy Information Administration’s (EIA) projected electricity prices to capture this non-inflation price increase. We use the EIA’s reference case for oil price, economic growth, and oil and gas resources up to 2040; these assumptions formulate the EIA’s electricity price projection.100

We also model the firm’s costs as a function of its total solar capacity. As described previously, the predominant cost is the capital cost of solar installations. We want to capture the relationship between these capital costs plus operations costs and the number of utility-solar installations. However, the privatized nature of these installations make it difficult to get data on the number of installations each year; instead, we use total solar capacity as a proxy for measuring the number of installations. Furthermore, it is not standard to measure costs per total capacity. Cost more commonly given by levelized cost of electricity (LCOE), which is measured per electricity generation (yi) rather than total electricity capacity (si). Thus, it is necessary to define the relationship between capacity and generation:



c:\users\brian\downloads\codecogseqn (10).png

This serves as our production function. Ai is a measure of technological efficiency, or in other words the capacity factor of the solar installations. According to literature, the current maximum capacity factor for solar is about 25%.101 Note also that in order to solve our maximization problem, the production function cannot have increasing returns to scale. We make the assumption that doubling total capacity will increase generation by less than double; intuitively, simply increasing the available capacity does not mean that all of that will be utilized in the presence of other sources of electricity. Thus, we have the following constraints:



c:\users\brian\downloads\codecogseqn (27).png

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Now that we can express generation in terms of total capacity, we can define our cost as a function of generation:



c:\users\brian\downloads\codecogseqn (6).png

Note that since LCOE is measured as the cost per unit of generation, we can express the cost as LCOE multiplied by generation. LCOE represents the per-megawatthour cost (in real dollars) of building and operating a generating plant over an assumed financial life and duty cycle. Key inputs to calculating LCOE include capacity factor (Ai), capital costs of total capacity (Ki), and variable maintenance and operations costs (Ni).102 As we did for electricity prices, we use the EIA’s projections for LCOE up to 2040 for our model.103

Next, we define the rate at which total solar capacity grows. Since our representative firm makes its choice of total capacity based on information up to 2040, we assume that the firm will plan its capacity expansion at present (i=0). Further, we assume that the firm will execute its expansion plan at a rate such that the growth rate is constant. Intuitively, we do not expect total capacity to increase by a constant lump-sum each year. We expect that as more solar installations are made, the lump-sum additions from year to year will rise. From literature, certain projections suggest that capacity growth will be exponential.104 For the sake of accuracy, we make the more conservative assumption that the growth will be linear:

c:\users\brian\downloads\codecogseqn (7).png

Finally, we define government subsidy as a function of generation. As detailed previously, the government has a number of policies supporting solar. For our model of the representative firm’s decision, we define government support as a per unit subsidy on generation:



c:\users\brian\downloads\codecogseqn (8).png

This formulation is preferable to a lump-sum subsidy, which would not be distortionary on the firm’s decision. Further, we prefer using generation rather than total capacity since key government policies, such as RPS and net metering, focus on generation.

We rewrite our maximization problem as:

c:\users\brian\downloads\codecogseqn (18).png

5.2.0 Profit Maximization

To solve the general form of our profit maximization, we first factor and substitute in the production function:



c:\users\brian\downloads\codecogseqn (24).png

We also iteratively solve our capacity growth relationship to get:



c:\users\brian\downloads\codecogseqn (14).png

c:\users\brian\downloads\codecogseqn (25).png

We define the following for simplicity’s sake:



c:\users\brian\downloads\codecogseqn (23).png

We now differentiate with respect to n to find the optimality condition:



c:\users\brian\downloads\codecogseqn (22).png

Having found our optimality condition, we can now examine the firm’s choice of n under assumptions on Ai, gi, r, and α, along with given pi and LCOEi. As a base case, we make the following assumptions:



c:\users\brian\downloads\codecogseqn (28).png

Solving for optimal n, we get:



c:\users\brian\downloads\codecogseqn (29).png

Intuitively, we can understand why the optimal growth rate is negative by comparing the projected prices and costs. As shown in the chart below, the projected price does not exceed the projected cost until 2040. Since the firm is considering the net present value its profits up to 2040, there is no growth rate that allows the firm to achieve a positive profit. Under these assumptions of no government subsidy, the firm will not choose to increase its solar capacity under optimality.


5.3.0. Comparative Statics

Having made this observation that the firm cannot profit without government subsidy, we proceed by analyzing the relationship between optimal n and different values of g. From our optimality condition, we know that:



c:\users\brian\downloads\codecogseqn (30).png

This is easy to see intuitively: the more government subsidy, the more the firm will want to grow its solar capacity.

Next, we want to understand what level of government subsidy will incentivize the firm to choose a positive growth rate. We hold the same assumptions as before, except we vary g. We define that government subsidy is constant in all periods:

c:\users\brian\downloads\codecogseqn (31).png

We vary our x, beginning at 0 and incrementing by .001, to build a piece-wise curve illustrating the relationship between n and g. We introduce the following constraint on n to eliminate negative and infinite growth:



c:\users\brian\downloads\codecogseqn (32).png

Intuitively, this limits the firm’s growth rate such that it can at most double its capacity in one year. As shown below, the firm will choose not to grow for all values of g up to .951, after which it will always choose the maximum growth rate of 1. This is the smallest g at which the firm will be able to profit; in our further analysis, we will call this point the optimal g.


The above result indicates that perhaps our assumption of α = 1 is unrealistic; this defines a production function with constant returns to scale. Instead, we want to understand the relationship between n and g under a production function with decreasing returns to scale. Thus, we take the perspective of the government and search for the optimal g for each level of α. The graph below describes the relationship between optimal g and α; the dotted exponential trend line has an R2 of almost exactly 1, indicating a nearly perfect fit. Intuitively, higher levels of α have higher returns to scale of the production function. In our model, our constraints define that the production function must have decreasing returns to scale. This means that as α approaches 1, doubling capacity will nearly, but not quite, double generation. As α decreases, the production function has lower returns to scale. From the government’s perspective, it is optimal to provide subsidy at the optimal g; in other words, the government wants to stimulate solar capacity growth while spending the least that it can. We have shown that the government’s consideration of optimal g depends on the properties of the production function, which may change depending on the state of the solar industry.

6.0. Conclusion
Solar energy is perhaps the highest potential energy source in the US. However, its development is fraught with technological, political, economic and financial challenges. In this paper we sought to understand these challenges, as well as make tentative recommendations to future researchers. Technologically, we have learned that more funding must be granted to the development of more efficient and sustainable solar panels. Politically, we have learned that any policy recommendation must take into account the dramatic effect lobbies have on the policy process – we have highlighted which specific lobbies seem to have the loudest voice with respect to these issues. Finally, financially we have learned that future financing of solar projects must balance risk among public and private actors, as it is not yet feasible, nor sustainable, for any one sector to bear the all the risk. The future of solar energy in the U.S. is hard to predict, but if the challenges highlighted here can be overcome, it is sure to be bright.

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