Investment in Intermittent Renewables under a Renewable Electricity Standard

Becky A. Lafrancois* (


A key challenge facing economies across the globe is satisfying an increasing demand for electricity while controlling greenhouse gas emissions and other forms of pollution, as well as addressing additional concerns including energy security and economic development.  Renewables can be an important part of the solution, but to date many renewable technologies have been significantly more expensive than fossil fuels.  Governments around the world have adopted policies to encourage a greater use of renewables.  In the United States, the main policies have been tax incentives at the federal level and renewable electricity standards (RES) at the state level.

As the most widely used policy in the U.S. promoting the generation of electricity from renewable sources, an RES requires electric utilities, or “load serving entities” (LSE), to supply a minimum amount of their retail portfolio with eligible sources of renewable electricity.  Although the RES is the dominant U.S. renewables policy, there has been relatively little economic analysis of the incentives it creates.  Fischer (2006) explores the potential impacts of an RPS on electricity prices, Huang et al. (2007) and Lyon and Yin (2007) examine the factors that influence the adoption of a state RES, and Carley (2009) analyzes the impact of RES policies on the deployment of renewable electricity.

This article considers how the characteristics of the RES and the LSE’s underlying electricity supply portfolio are likely to impact the success of an RES in generating investment in renewables.  The results discussed in this article are based on a decision model of an LSE that incorporates both the uncertainty associated with contracting for renewable electricity and the consequent risk of a noncompliance penalty.  Given costly renewable electricity, an LSE optimally complies with the RES by weighing the tradeoffs between acquiring high cost renewables and facing a noncompliance penalty, balancing the marginal cost of access to additional renewable capacity against the expected costs of failing to comply with the RES.

The results in this article show that the extent of development of renewable electricity under an RES hinges on two key points.  First, the structure and enforcement of penalties for noncompliance strongly influence the optimal capacity of renewables contracted for by the LSE.  A penalty that varies directly with the magnitude of noncompliance will drive more investment in renewables than will a fixed penalty.  Second, the cost premium of renewable electricity, which depends both on the relative costliness of renewables and the composition of the LSE’s existing supply portfolio, impact the effectiveness of the RES.

Overview of Electricity in the United States

Electricity generation in the United States stems from three primary sources, fossil fuels, nuclear fuel, and renewable resources.  About 90 percent of electricity generated in the U.S. in 2007 was generated using fossil (73 percent) and nuclear (19 percent) fueled power plants.  The remaining 8 percent was produced using renewable resources, including hydro (6 percent), geothermal, biomass, wind, and solar (2 percent).  In 2007, for every kWh of electricity generated using wind energy, over 57 were generated using coal and 20 using natural gas.

Not only do renewable sources of electricity lag far behind in electricity generation, they also lag in terms of installed capital stock.  Table 1 shows the installed capacity for various sources of electricity in 2007.  For each MW of wind capacity in the United States, there was 18 MW of coal and 21 MW of natural gas.  For each MW of solar capacity, 606 MW of coal capacity and 696 MW of natural gas capacity was installed.

Renewable Electricity Standards seek to increase both the capacity of plants fueled using renewables and the overall amount of electricity that is generated using renewables.  When thinking about increasing the use of renewables, it is important to consider the scalability of different renewable sources.  Hydro, biomass, and geothermal sources can all be used to generate baseload electricity; however the expansion of these sources is limited by geographic availability.  On the other hand, sun and wind (intermittent renewables) can be found no matter the location, although magnitude and frequencies vary.  As a result of their scalability, intermittent renewables will play a prevalent role in satisfying renewable standards. However, due to their stochastic nature, it is important to consider how a load server may integrate intermittent renewables into its electricity portfolio.


Integrating Intermittent Renewables

In the absence of intermittent renewables, an LSE follows the load curve in the traditional manner of using baseload and peaking plants. Base demand for electricity is satisfied by utilizing conventional baseload plants, which produce a relatively invariable amount of electricity, Qc. To cover loads higher than the base, the load server acquires electricity from dispatchable suppliers who have the ability to quickly modulate their output of electricity, Qg. Thus, equilibrium in an electricity market without intermittent renewables is

where Qd is the market demand for electricity.

After the passage of an RES mandating the acquisition of renewable electricity, the LSE will satisfy at least a portion of the requirement using intermittent renewables because of the scalability issues discussed above.  Thus, the LSE will purchase an uncertain amount of electricity from suppliers of intermittent renewables, Qr.  A stylized model of integrating these intermittent renewables will now be presented.

Suppose that each unit of renewable capacity is capable of generating b units of electricity when operating at maximum capacity.  Also suppose that the LSE engages in N contracts with a supplier of renewable electricity and that each contract represents the construction of one unit of capacity and the obligation of the LSE to purchase output from each unit. This model assumes that all N units are located on the same site, so that the maximum amount of renewables purchased by the LSE can be represented by

Because of the intermittency of renewable electricity generation, the actual amount of renewables purchased by the LSE is

where  is the actual realization of renewable electricity.  The model also assumes that were renewables operating at their maximum capacity, the LSE would satisfy the demand for electricity using only conventional and renewable sources.  However, due to the intermittency of renewables dispatchable electricity sources are required to provide back-up during the periods where renewables are not operating fully.  Thus, after integrating intermittent renewables into the LSE’s supply, the market equilibrium for electricity is

Analytical Framework[1]

In principle, a load server has some control over whether it will comply with the RES by acquiring a satisfactory amount of renewable electricity or will not comply and face a penalty.  In selecting the optimal amount of renewables to acquire, a risk neutral LSE will seek to maximize its expected profits or minimize its expected costs, thereby selecting an implicit degree of compliance.  The LSE generates revenue from the sale of electricity to end users and faces two classes of costs, the cost of purchasing electricity from the supplier and any costs paid to the regulator resulting from noncompliance.  The LSE’s costs of obtaining electricity can be represented by

where pc, pg, and pr are the prices paid by the LSE for conventional, dispatchable, and renewable electricity and F is the noncompliance penalty.

In minimizing its expected costs, the LSE selects the number of contracts, N, at which the reduction in the expected penalty from acquiring more renewables is just offset by the increased costs of purchasing those renewables.  The reduction in the expected penalty will depend on the type of penalty structure imposed by the regulator of the electricity market and the increased cost of acquiring renewables is simply the cost premium, k, where

Key Results and Policy Considerations

It is hardly a surprise that the optimal quantity of renewable contracts selected by the LSE is positively related to both the size of the RES and the noncompliance penalty and inversely related to the cost premium for renewables.  As the renewables target set in the RES increases, the probability of noncompliance by the LSE increases thereby increasing its expected penalty and inducing a greater utilization of renewables.  Similarly, as the size of the noncompliance penalty increases, the expected penalty faced by the LSE increases leading the LSE to increase its use of renewables.  On the other hand, an increase in the cost premium of renewables increases the cost of compliance to the LSE and reduces the optimal number of contracts as paying the noncompliance penalty becomes more appealing than bearing the burden of higher cost renewables.

The importance of the cost premium comes into play in a multitude of ways, including the importance of the type of conventional baseload fuel that is used by the producers of electricity and the interaction of an RES with a potential carbon tax or other policy that changes the relative price of renewables to conventional sources of electricity.  One component of the renewables cost premium is the difference in cost between the conventional and dispatchable electricity sources.  This value is higher in states that use coal as the primary baseload fuel than in states that use nuclear or gas as their primary baseload fuels.  Thus, all else equal, a state with lower cost baseload generation will invest in fewer contracts for renewables.  Additionally, any policy that reduces the relative cost of renewable electricity is likely to work in tandem with an RES.  These findings suggest that policymakers will reap greater rewards in term of renewables investment and generation through targeting the relative price of renewables.

The overall success of an RES in increasing the development of renewable electricity sources hinges strongly on the penalty for noncompliance.  The first key to driving the development of renewables is for regulators to actually enforce the noncompliance penalties.  If the LSE feels that the policies will not be enforced by the regulator, there is no incentive for it acquire renewables and to increase its operating costs.  In addition to enforcing its compliance rules, the regulator or policymaker must also take care in designing the structure of noncompliance penalties.  Currently, there are two primary penalty structures in use in the U.S.- lump sum penalties that do not depend on the degree of noncompliance[2] and variable penalties that vary directly with the degree of noncompliance.[3] Results of the model discussed above indicate that variable penalties will be much more effective at inducing the use of renewables than lump sum penalties, primarily because under realistic lump sum penalties, it is less costly for the LSE to pay the fine rather than integrate renewables into their portfolio.

Figure 1 provides a visual interpretation of the findings discussed above using results from a numerical simulation of the full model presented in Lafrancois (2010).  Each point in the figure represents a renewable electricity target, variable penalty, and lump sum penalty that all induce a given level of investment.  The top line depicts the policy combinations that yield 1,400 contracts when coal is used as baseload, and the bottom line depicts natural gas as the baseload fuel.

Renewable electricity standards are currently the United States’ leading state-level policy used to promote the use of renewables in electricity generation.  Despite their widespread use, there has not been any research evaluating the incentives that such policies place on regulated load servers.  This article finds that the ultimate success of renewable electricity standards depends heavily on the enforcement of noncompliance penalties, preferably those that vary with the magnitude of noncompliance, and on the overall cost premium for renewable electricity.



Carley, S., (2009). “State renewable energy electricity policies: An empirical evaluation of effectiveness.” Energy Policy 37(8): 3071-3081.

Fischer, C., (2010). “Renewable Portfolio Standards: When do they lower energy prices?” The Energy Journal 31(1): 101-120.

Huang, M., et al, (2007). “Is the choice of renewable portfolio standards random?” Energy Policy 35(11): 5571-5575.

Lyon, T.P., Yin, H., (2007). “Why Do States Adopt Renewable Portfolio Standards? An Empirical Investigation.” Available at SSRN:


* Ph.D. Candidate, Department of Economics, Syracuse University,


[1] Lafrancois (2010) provides a more complete derivation of the model used in this article, Available at

[2] e.g. New Hampshire, Oregon, Delaware

[3] e.g. California, Ohio, Missouri

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