There’s more than one way to deal with a duck (curve)

The good news is: solar. The bad news is: uncontrollable rooftop solar. How do we utilize the production of rooftop solar in the middle of the day?

This is an especially significant problem for California. The California ISO coined the term “duck curve” to describe that state’s net load – that is, load minus renewable production from solar photovoltaic (PV), wind, and run-of-river hydro production. On a mild sunny day, the problem that the duck curve illustrates is that net load falls so low that other generation cannot follow it.

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The same challenge is emerging in other places, as well. In Australia, for example, Paul Simshauser of Griffith University, South East Queensland, describes the same situation there in his warm, northern state. (Click here to download his paper.)

BTW, I would suggest we might replace “duck curve” with “magpie goose curve” in honor of an Australian native bird. (Photo credit: Fir0002/Flagstaffotos)

Interestingly, Simshauser’s data shows that air-conditioning (AC) is a significant contribution to the rising neck of the magpie goose during critical summer days (that is, a significant contribution to the increase in net load during the evening of such days after the sun goes down). Although I do not have the specific data on hour-to-hour consumption for inland California, I believe that a similar pattern would apply there and in many regions with high AC consumption. In Texas, for example, residential consumption in summer greatly exceeds that in spring and fall. It is well understood that summer peak consumption is driven by AC load during times of high temperatures that persist into evenings.
Figure 1: Average net load (kW) of homes with AC and solar and net load with pre-cooling. (Ross Baldick)

To illustrate, Figure 1 shows net load for Central Texas during August 2018 (data courtesy of Grant Fisher and Esha Choudhary of Pecan Street Inc.). The blue line shows net load (consumption, including AC, minus rooftop PV production) for a sample of Austin homes. The data points are 15-minute average power consumption, averaged over the sample of homes with both AC and rooftop PV that Pecan Street monitors. Each day, net load falls (becoming negative, implying net export to the electric distribution system) during the day, but then rises again and experiences a peak in the late afternoon and evening, with solar production decreasing just as AC consumption increases: the upward sloping “neck” of the duck or magpie goose.

This combination of AC needs that persist after the sun goes down and PV production that falls precipitously at sundown suggests a way forward: to pre-cool houses in the hours before sundown. Researchers working under the U.S. Department of Energy’s Building America program have modeled two example homes for several regions using EnergyPlus. (Click here to download the report.) They found that pre-cooling is an effective way to reduce peak residential load.

However, pre-cooling will result in higher energy consumption by 2% to 8% overall. This increase in energy consumption can be thought of as analogous to “round-trip losses” in a battery storage system, implying that storing energy involves overall more energy consumption than using the energy when it is produced. Results depend on both weather patterns and the thermal insulation and thermal mass of the housing stock.

How does pre-cooling interact with the duck curve?  Pre-cooling can increase consumption when the sun is shining and decrease it after the sun goes down. This has two advantages.  First, with significant rooftop solar, there is significant export during the day to the electric distribution system. There are limits to the amount of such exports, and California is heading toward a situation where PV production may otherwise have to be curtailed during the day. Therefore, pre-cooling could offer significant benefits by increasing utilization of renewables during the day, while also reducing non-renewable production in the evening. Second, pre-cooling will reduce the “ramp rate” of net load; that is, the rate of increase in net load over time, which is represented by the upward sloping neck of the duck. Because net load must be matched by other generation, and because generation has limited ability to ramp, reducing the slope of the “neck” can ease the need for ramping capacity.

Sometimes chemical battery storage is advocated as a solution to the mismatch between PV production and electrical demand. Interestingly, the higher energy consumption with pre-cooling found by the DOE Building America program is similar in magnitude to the round trip losses of a Tesla battery. In contrast to a chemical battery, pre-cooling does not require (much) capital investment, at least for a well-insulated home. While pre-cooling might not work for typical current Queensland housing stock, it might be effective in regions where there is already significant investment in insulation. Much housing stock in Texas, for example, has double-glazing as well as ceiling and wall insulation, and further investments in building efficiency would not only help with improving prospects for energy storage but also pay dividends in overall energy savings. I understand from Scott Jarman of Austin Energy that this Austin utility already practices pre-cooling in some of its controlled residential thermostats in preparation for critical peaks.

So, could we pre-cool all residences all the time? Pre-cooling homes could effectively be practiced more widely and not just on critical peak days. The idea would be to significantly pre-cool well-insulated homes while PVs were still producing significant power, and then to allow indoor temperatures to drift upward as the sun goes down. This would facilitate better utilization of PV production and reduce the slope of net load in the evening.

I have not performed the detailed modeling to evaluate the potential explicitly, but figure 1 suggests what might be possible for Austin. I considered shifting the AC consumption represented in the Pecan Street data to occur three hours earlier. I accounted for the round-trip losses by assuming that 10% more electricity for AC would be required when shifting consumption by three hours. The result is shown in the orange line, which has less variation than the blue line: peak consumption is significantly lowered, there is lower net export of solar to the grid, and the ramp rate of the net load is significantly reduced. To be clear: the blue line simply shows the effect on net load of bringing forward AC consumption by three hours and increasing it by 10%, whereas a more careful simulation is required to obtain actual results with a real home.
Figure 2: Average net load 9 (kW) of homes with AC and net load with pre-cooling, on August 1, 2018. (Ross Baldick)

What does data for a single day tell us? Figure 2 depicts net load for the specific day of August 1, 2018. We can see that the general duck-like shape of the net load as shown by the blue line has been flattened by bringing AC consumption forward in time: as shown by the orange line, peak of net load is lower, net electricity exports from homes have been eliminated for this day, and the “neck” of the duck rising to the peak has a lower slope. Simulation of a pre-cooling strategy would undoubtedly show a different detailed pattern of net load, but a similar general effect could be expected.

Won’t consumers balk at spending more money on higher electricity usage to pre-cool their homes? California is addressing this problem by introducing new lower time-of-use (TOU) rates for electricity during sunny hours.

Traditional TOU rates were designed to shift consumption to nighttime, say after 10pm or 11pm, when load is typically lowest. Some argue, however, that these traditional TOU rates are ineffective, and recent evidence from Bruce Mountain, Victoria University, Melbourne, (click here to download the presentation) supports that claim, by suggesting that such traditional rates, with low prices overnight, have not convinced homeowners to shift their consumption to nighttime in the state of Victoria. No one wants to do their laundry in the middle of the night to save a few pennies.

But with the new TOU rates they would be willing to do their laundry, dishes, and electric-vehicle charging – and pre-cool their homes — in the afternoon. The new, improved version of TOU with lower prices during middle hours of the day was mentioned in the DOE Building America study, and that’s exactly what California is doing.

Renewables challenge us to rethink our basic assumptions. To mix metaphors, there is more than one way to skin a duck — or a magpie goose. With high PV penetration, we cannot always control supply to meet demand. We need to change demand to follow supply. And that’s what pre-cooling will achieve.

Next time: more ways to change demand to follow supply.

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Applied Optimization book: new and improved!

Cambridge University Press bookstore

Last summer, when I was visiting the University of Cambridge to present a seminar, I happened upon the university press bookstore.

And what did I find inside? A hardback copy of my 2006 book, Applied Optimization.

Applied Optimization

Even if you are in Cambridge, I do not advise you to buy the hardback copy. Instead, there is now an updated paperback copy available that includes corrections and additions. Click here to purchase.

There are a number of other optimization books out there, but if you want a careful introduction to optimization, convexity, and optimization, with multiple power systems case studies, please consider this book and the slides for my associated graduate course, “Optimization of Engineering Systems.”

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Renewable chic and the expense of small-scale solar

RossBaldick.comThis is what I came across recently: a luxury brand store window display of “renewable chic,” where a solar panel, as part of the vignette, is being used to partially illuminate the mannequin. Putting aside the irony that the solar panel itself was apparently being illuminated by grid-powered lights, there are broader implications we need to anticipate with the increasing popularization of small-scale solar. Let’s think twice about increasing small-scale rooftop solar, because right now the economics just don’t make sense.


First of all, there is the compromise in quality of service. Small-scale—up to a few kW—rooftop solar systems are set up primarily to inject as much power as can be generated from available sunlight. In small numbers on individual distribution feeders, this is not a problem. But in large numbers, technical challenges such as voltage control and fault protection on distribution feeders become problematic. Until recently, interconnection standards did not allow rooftop solar systems to participate in voltage control. (This may be remedied for new installations with updates to the IEEE 1547 Interconnection Standard.)


RossBaldick.comThis leaves us with at least two salient and interacting concerns.


First, the expense. Small-scale rooftop solar remains much more expensive to install than large-scale solar, because existing household rooftop sites are unlikely to have the best exposure and orientations toward the sun and because the small-scale is almost always going to involve higher costs per unit capacity than large-scale installations. The store display shows this latter issue in microcosm: there was presumably several hours of labor and significant installation cost for this panel of just a few hundred watts! Rooftops of several kW are less expensive per unit capacity than this small panel, but even larger installations are less expensive per unit capacity. In the United States, it is reported that small-scale solar is double or more the cost of large-scale solar.


(An added concern: if large-scale solar is located far from urban centers, the solar may be cheap, but it may also require expensive transmission upgrades. A good compromise will often be medium-scale developments using large commercial and industrial rooftops and community installations. This way, the solar is nearly as cheap and there is no significant extra cost for transmission. Click here to read more about locating distributed generation in urban areas.)


Second, solar production is variable, depending on the available sunlight, which means that the power injection into the grid is variable. But, as I said earlier, small-scale installations are mostly set up to inject as much power as possible from the sunlight. So, as sunlight levels change, the power will vary. Sometimes large amounts of solar power production will coincide with times when the power is not needed.  


In contrast, large-scale installations are easier to set up as being dispatchable. That is, large-scale solar can be controllable to produce less power when that power is not needed. Such circumstances are bound to become more common, as the so-called California duck curve shows. To date, essentially no residential rooftop solar has been dispatchable, so when it is sunny in California but demand is low, there is a need to dispatch down the remaining thermal generation. This might be acceptable by itself, but when the sun goes down in the evening, the demand typically increases in California, and this is threatening to result in situations where the thermal generation has insufficient ramping capacity to cope with the net variation–that is, to cope with the difference between load and solar generation that must be supplied by the rest of the system.


Storage is sometimes put forward as a solution to the duck curve. Moreover, additional power electronics associated with battery storage can help both with the fluctuations in solar production and with the regulation of voltage levels in the distribution system.  Storage can be a cost-effective solution when there are issues such as distribution feeder capacity limits that can be alleviated through storage. So while there are specific situations when investment in battery storage can make sense, it is generally still a relatively expensive solution. There is no doubt in my mind that battery storage will eventually be cost-effective when costs decline significantly from today’s levels. In the meantime, until battery prices become much lower, existing pumped-storage and reservoir hydro facilities are important storage resources to be utilized now. Moreover, dispatchability of solar would mitigate some of the immediate need for storage. In an analogous situation in Texas, dispatchability of large-scale wind has been helpful in ERCOT being able to integrate so much wind power.  


RossBaldick.comThis brings the discussion back to small- versus large-scale. Large-scale installations are likely to be more cost-effective ways to provide large amounts of solar. They also are easier to set up, so that they can be dispatched down when required. However, having gone down the path to installing a lot of expensive, non-dispatchable small-scale rooftop solar installations, jurisdictions such as California, Australia, and Germany have consigned themselves to spending even more money to buy battery storage to balance the solar. It is hard to reconcile this policy with the imperative to decarbonize the electricity system cost-effectively. Other states and countries should take note: until storage becomes cheaper, larger-scale solar installations will reliably bring more cost-effective decarbonization results.

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