California’s rooftop solar mandate is an opportune moment to revisit a pair of prescient studies by Michael Cohen and coauthors.
A couple of months ago I wrote a blog post called “Why Am I Paying $65/year for Your Solar Panels?” Readers offered many interesting and, er, colorful responses. One of the objections was that my calculation failed to incorporate the benefits of rooftop solar to the distribution system.
“Utility scale solar does not provide the distribution system and line loss benefits that distributed solar provides.” – Jim Lazar, Regulatory Assistance Project
“For example, expensive utility transformers can get overloaded on hot summer days when people are using more energy to cool their homes. Rooftop solar can reduce strain on the system on these days, which extends the life of utility equipment and creates savings for everyone.” – Sean Gallagher, Solar Energy Industries Association
Today I want to dig into this argument. I review the evidence of distribution system impacts, focusing on a pair of peer-reviewed studies by Michael Cohen and coauthors. The studies find that rooftop solar does help the distribution system, but that the magnitude of the benefit is very small. When you actually quantify these benefits, they are way too small to be used as an argument to prefer rooftop solar over grid-scale renewables.
Peer into the Peer-Reviewed Literature
The pair of studies (here and here) are appropriately titled, “Effects of Distributed PV Generation on California’s Distribution System” Parts 1 and 2, covering engineering and economics. The first paper is by Michael Cohen and Duncan Callaway; the second paper is by Michal Cohen, P.A. Kauzmann, and Duncan Callaway. The papers were published in 2016, but are more relevant today than ever.
Note: Michael Cohen is a recent PhD graduate of UC Berkeley’s Energy & Resources Group, and is Lead Developer at New Sun Road. Duncan Callaway is Associate Professor at UC Berkeley’s Energy and Resources Group and often discusses these topics at dinner with his wife (and fellow Energy Institute blogger) Meredith Fowlie.
Both studies are peer-reviewed. This matters. The peer-review process is not perfect, but it imposes a discipline on researchers. Both papers carefully describe all data sources, methods, and assumptions. Refreshingly, the papers are also upfront about potential limitations of the analyses, and don’t try to oversell their results.
What I like most about these two studies is that they are based on real data. Solar City provided the authors with 15-minute data on 7,000 California rooftop solar systems, and PG&E provided the authors with historical financial data on distribution system costs. The authors build a numerical power flow model, and the analyses are grounded by these data from actual solar customers and an actual utility.
Deferring Capacity Investments
Probably most importantly, rooftop solar potentially allows the utility to defer capacity investments like transformer banks and conductors. Cohen and coauthors quantify this benefit by simulating increased rooftop solar penetration for a representative set of California feeder locations. Then they “levelize” these savings as benefits per kWh of rooftop solar generation.
Source: Cohen, Kauzmann, and Callaway (2016).
The main finding, summarized in the figure above, is that capacity benefits are small. For most cases, capacity benefits are less than 0.2 cents per kWh. To put this in some perspective, typical California wholesale electricity prices are about 4.0 cents per kWh, and average retail prices are 19.0 cents per kWh. Thus the deferred capacity benefits are small compared to the energy value of rooftop solar, and tiny compared to what California solar customers receive with net metering.
Not only are the capacity benefits small, but Cohen and coauthors’ results imply that capacity benefits will shrink over time. As the figure above shows, capacity benefits decrease sharply with rooftop solar penetration. Why? Because as more and more solar is deployed, the net peak load gets pushed later into the afternoon and evening, making subsequent installations less and less effective for reducing peak load.
Reducing Energy Losses
Another distribution system benefit you hear about is reduced energy losses. When electric current travels through the distribution system, part of the energy is lost in the form of heat. Rooftop solar tends to reduce energy losses because electricity doesn’t need to travel as far.
Source: Cohen and Callaway (2016).
As the figure above illustrates, Cohen and Callaway find that rooftop solar indeed reduces energy losses. With more and more rooftop solar, energy losses decrease by 10%, 20%, even 30% at very high penetration levels. The 24 different lines represent eight different types of feeders in three different cities. While in many cases the losses drop by just 10%, there are some cases where energy losses decrease by as much as 30%.
But let’s put this in perspective. While these are significant percentage reductions, they imply benefits that are small in absolute terms. Total energy losses in the distribution system are less than 5%, so even a 30% decrease means that total energy losses go from 5% to, say, 3.5%. Reducing waste is great, but this ends up being a small dollar value, worth less than 0.2 cents per kWh of rooftop solar generation.
An Elixir of Youth for Transformers?
Another category of possible benefits is reduced transformer aging. Rooftop solar could reduce the strain on transformers, potentially extending their effective lifetimes.
This is a tough category to evaluate because there is not a lot of data on existing transformers. In practice, many transformers fail for idiosyncratic reasons (car accidents, lightning, etc.), so utilities historically have not done detailed data collection or monitoring. Most transformers are probably over-sized to begin with, which would limit the gain from reducing load, but this is not something for which there is good direct evidence.
Cohen and coauthors use their model to simulate impacts for a large set of representative locations. In general, they find very limited reductions in transformer aging. There are also a small number of locations where rooftop solar significantly increases transformer aging, driven by a surge of power back to the grid in places with large amounts of rooftop solar. Data constraints limit their ability to make definitive statements but, overall, this appears to be another category where the benefits are likely quite small. Cohen and coauthors also examine voltage regulation, and several other smaller categories of potentially benefits, in all cases finding the benefits to be very small or even negative.
Larger Benefits in Certain Locations
But wait a minute, aren’t there large (or at least larger) benefits in certain specific locations? Yes. Cohen and company find capacity benefits exceeding $60 kilowatt-year in the top 1% of all locations. This is about 10 times what they find for average capacity benefits. It makes sense that, for example, certain circuits are very close to needing a capacity upgrade, and that benefits would be large in these places.
This is very interesting. But it is also largely irrelevant from a policy perspective. We don’t have policies that can target certain locations. Net metering benefits all rooftop solar adopters – including those in the 1% of highest-value locations, as well as the other 99%. Federal tax credits benefit all rooftop solar adopters – including both the 1% and the 99%. There is no policy currently in place that allows for this kind of highly-granular pricing of rooftop solar benefits, so it is the average that is what matters for evaluating policy.
Too Little of Good Thing
Thus, overall, the Cohen studies find that the distribution system benefits of rooftop solar are small. The positive impacts probably exceed the negative impacts, but the overall magnitude is likely less than 0.4 cents per kWh.
What does this mean for California’s rooftop solar mandate? Like most energy economists including my colleagues Severin Borenstein and Jim Bushnell, I’m disappointed and perplexed by the policy. We know that residential rooftop solar is much more expensive than grid-scale renewables. At least 4 times more expensive, according to Lazard estimates.
Distribution system impacts don’t begin to close the gap. The Lazard estimate for the levelized cost of residential rooftop solar (midpoint) is 25.3 cents per kWh. If the distribution system benefits are 0.4 cents, this still leaves 24.9 cents per kWh. Compare this to 5.0 cents per kWh (or less) for grid-scale solar, and 3.0 to 6.0 cents for wind. It is not even close. The distribution system benefits are way too small to be used as an argument to prefer rooftop solar over grid-scale renewables.
Note: Image licensed under creative commons.
Lucas Davis is the Jeffrey A. Jacobs Distinguished Professor in Business and Technology at the Haas School of Business at the University of California, Berkeley. He is Faculty Director of the Energy Institute at Haas, a coeditor at the American Economic Journal: Economic Policy, and a Faculty Research Fellow at the National Bureau of Economic Research. He received a BA from Amherst College and a PhD in Economics from the University of Wisconsin. Prior to joining Haas in 2009, he was an assistant professor of Economics at the University of Michigan. His research focuses on energy and environmental markets, and in particular, on electricity and natural gas regulation, pricing in competitive and non-competitive markets, and the economic and business impacts of environmental policy.