Reducing Electricity System Variability with Solar Power

Solar power is often thought to increase the variability of electricity systems. In a recent paper (open access), Ken Caldeira and I show that adding solar to electricity systems, where solar power correlates with electricity demand, can actually reduce the variability in peak residual electricity load.

Residual Load

Residual load is electricity load (demand) minus generation from variable resources, such as wind and solar. Residual load represents the load that must be supplied by more controllable resources: firm generation (gas, nuclear, etc.), energy storage, and demand response.

Depiction of residual load (dashed line) and the peak residual load value

For a system operator, peak residual load indicates a lower bound on the quantity of firm generation, stored energy, and demand response that must be available in their system to supply all electricity loads.

As wind and solar are added to our electricity systems, system planners will likely rely on estimates of future peak residual load and how the peak values vary from year to year as crucial planning metrics.


We estimate the peak residual load and how much it varies from year to year as wind and solar generation are added to four example electricity systems. From this, we find that the variability in the peak values changes as more wind and solar are added.

The variability (spread) in the peak residual load values from year to year is depicted for systems as wind and solar generation increase. In PJM, for example, progressing vertically in the figure indicates adding solar generation. As solar generation is added, the variability decreases as indicated by the darker colors.

Interestingly, for the three modeled systems that experience their peak electricity usage in the summer months (ERCOT in Texas, PJM in the mid-Atlantic, and NYISO in New York state), adding solar statistically reduces the spread in the peak values from year to year.

These three summer peaking systems show a strong correlation between peak electricity usage and the hottest days. The hottest days are indicated by the largest “daily degree day” values in the below figure.

Thus, by adding generation that correlates with the most extreme peak load hours, electricity systems can become more predictable even if that generation is from a variable renewable resource like solar.

Reducing the spread in the peak values from year to year could possibly make system planning simpler by having more predictable peak residual load values.


We used historical electricity load data from the four studied systems: ERCOT, PJM, NYISO, and France.

Ten years of historical electricity load (demand) for the studied regions.

We used historical weather data to derive plausible wind and solar generation profiles concurrent with the load data.

We incrementally increased the contributions of wind and solar generation from zero to generation equivalent in quantity to providing 100% of annual load. For each residual load profile, we assessed the spread in the peak values from year to year.

To calculate the spread in the peak values, called the inter-annual variability (IAV), we take the mean of the 10 peak residual load values from each year of data and calculated the standard deviation of these 10 mean values.

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Comparing FERC and EIA electricity demand data

The United States government coordinates the collection of hourly electricity demand data from regional entities for use in planning and decision making processes.  The Federal Energy Regulatory Commission (FERC) provides easily accessible data records spanning 2006-2018 for a mix of Balancing Authorities (BAs) and Planning Areas with Form 714.

While the Energy Information Administration (EIA) began their collection of hourly electricity demand data in July of 2015 for all BAs with Form 930. The EIA data are updated in near real-time and bring other benefits such as including hourly generation by resource type: coal, hydropower, natural gas, nuclear, wind, solar, petroleum, and other.

An interesting question for the energy modeling community is, does the 2017 data gathered by FERC align with the 2017 data gathered by EIA?  Can these records be used almost interchangeably?  Additionally, benefits will be realized by stitching together the longer historical FERC data records with the EIA records that contain more details of the current system.

One of our collaborators, Zane Selvans (@ZaneSelvans) of the Catalyst Cooperative (@CatalystCoop), mapped the ~200 FERC respondents to the ~70 EIA BAs and arranged the FERC data into a more usable format.  With this, we compared the hourly demand values for the successfully mapped BAs for 2017.  Details of the comparison methods are at the end of this post.


We compare the ratio of FERC hourly values to EIA hourly values and calculate the ratio of mean, minimum, and maximum values for each region.

California Independent System Operator (CISO)

Midwest Independent System Operator

The two examples here show hourly comparisons for CISO, with most values nearly identical and nearly all within 10%, and MISO, with most values agreeing within 10% and overall agreement based on the ratio of mean values of 1.01.

ISO New England (ISNE)

PJM Interconnection (PJM)

Some regions show a mean value close to 1 yet have non-uniform features in their distributions, such as ISNE (ratio of mean values = 0.99) and PJM (ratio of mean values = 0.98).

Furthermore, other regions have substantial discrepancies in the ratio of their mean values.  A histogram of the ratios of the mean values for each compared BA shows agreement within a few percent for over 30 BAs (a csv file is attached at the bottom showing the ratio of their mean, minimum, and maximum values). Additionally, we compare the minimum and maximum values and see a distribution similar to the mean value comparison.

Ratio of the mean of demand values for each mapped BA (FERC mean value/EIA mean value)

Ratio of the minimum and maximum demand values for each mapped BA


There are a considerable number of Balancing Authorities that have reasonably similar FERC and EIA hourly demand records based on agreement within a few percent of the ratios of mean, minimum, and maximum values.  This indicates that the FERC and EIA records may be approximately interchangeable for these BAs if the exact hourly profile is not a concern (see excel file for list).  The fact that many histograms contain a spread about 1.0 is worth exploring for anyone considering using these profiles as replacements for each other while modeling. Are there biases in which hours are misaligned?

In the future, this could also allow analysts to stitch together the longer FERC records with the more current and detailed EIA records.  The Catalyst Cooperative and Zane are pursuing work along these lines.  We wish them the best of luck!


The FERC data contains records from both Balancing Authorities and Planning Areas, while the EIA records are only for Balancing Authorities.  Therefore, many of the FERC records do not have EIA equivalents.  We only compare records that we think should align.

Both the FERC and EIA data records are imperfect, containing zero values, missing values, and the occasional outlier value.  For the EIA data, we use the EIA records after removing outlier values based on the details in this paper.  For the FERC data, we use the FERC records arranged by Zane with all zero values removed.  Hours are only included in the comparison if the corresponding hourly value in each record was present and was not removed by these two cleaning methods.

  • Summary csv file: comparing the mean, minimum, and maximum values in the FERC 714 and EIA 930 hourly demand data for year 2017 for the matched BAs.
  • FERC to EIA mapping: the mapping of FERC respondents to their EIA codes and acronyms provided by Zane.

More realistic data leads to more realistic models

There are many quirks of being an ex-high energy particle physicist who completed their PhD with the CMS experiment. For one, waking up in the middle of the night for an upset child doesn’t seem too bad compared to the many nights when I was “on-call” and woken up at 3am to help debug data collection issues with our experiment. I would much rather be “on-call” for my son than for a 14,000 tonne inanimate object.

Another quirk is that I am a year into my Postdoc at Carnegie Science and only now am I publishing my first ever first author paper. It is hard, in fact nearly impossible, to get to the front of the 3,000 person author list for the papers published by the CMS experiment. Needless to say, I did not make it to the front while I was part of the CMS team.

Now, I have the pleasure of being the first of only four authors on a paper discussing data cleaning and preparation for use in our energy models. While not the most glorious of papers, we hope this paper and the data we cleaned can be used by the energy modeling community. After all, more realistic data leads to more realistic models.

See this friendly blog post about the paper.

The Renewables Cliché

Part III of an energy and research discussion for my parents (part I & part II)

Who hasn’t heard the cliché renewable energy complaint, “the sun doesn’t always shine and the wind doesn’t always blow”? Solar and wind energy operate in stark contrast to the mechanical predictability of a natural gas power plant. Grid operators can not request a solar power plant to produce more electricity, only the sun can do that.

The biggest challenge for carbon-free, renewable energy technologies, like solar and wind, are their variability and intermittency. What does this actually look like and why does it matter?

Variability refers to the predictable changes in renewable energy output throughout the day and seasons. For example, solar power very predictably drops to zero every night. Solar output is also higher during the summer months because we have more hours of daylight.

Intermittency refers to the less predictable changes in renewable energy output. These can result from clouds passing over solar panels or from storm fronts rolling through and increasing the power output of wind turbines. In general, intermittency is caused by weather events. With improved forecasting, we can more easily predict and plan for intermittency.

Renewable Electricity Output

An installations of solar panels or wind turbines will provide a changing amount of power to the grid throughout the day.

This chart shows the availability of solar and wind energy over three October days in 2017.

To estimate the power output of a solar installation at any moment, multiply the output rating of the system by the availability (a.k.a. capacity factor). For example, a 10 Megawatt (MW) solar installation would produce 7.5 MW of power at 10:00am, which is indicated by the arrow above. Predictably, the solar capacity factor plummets to zero overnight.

The wind energy availability fluctuates up and down. It lacks a simple pattern like solar and is a great example of intermittency.

Renewables on the Grid

Wind and solar power never perfectly align with electricity demand. Because of this, they add complexity to operating the grid. Let’s take an example from one of the demand curves in the previous post for a small utility in Florida. I will use a few fictitious scenarios to illustrate some interesting points without getting bogged down in the details.

  1. their only power source is a natural gas plant
  2. they have a solar installation rated at 20 MW and natural gas provides the rest of their power
  3. same as 2) except 40 MW of solar
  4. same as 2) except 100 MW of solar

How large must a natural gas power plant be to satisfy all of the demand?

In scenario 1, the natural gas plant must provide power to meet the demand peak of 80 MW. So, the utility needs to build at least an 80 MW natural gas plant.

How much demand is satisfied by solar power in scenario 2? The yellow shaded region answers this question. It is the product of the 20 MW solar rating times the solar capacity factor. The solar output is slightly less than 20 MW at its peak and zero at night.

The remaining demand in scenario 2 must be covered by the natural gas plant. To calculate this, subtract the generated solar power from the demand curve as is shown by the orange dashed line. Therefore, a smaller, 65 MW natural gas facility will suffice.

In scenario 3, one of the challenges of solar power is apparent. Despite adding more solar, the required natural gas plant is still approximately 65 MW. There is a new “peak” in the remaining demand. And, it can not be addressed by simply building more solar.

If we continue to build even more solar as in 4, then we arrive at a situation where the generated solar power is greater than demanded. In a real-life situation, overproduction could either be: sent to an adjacent region if the transmission lines are capable of this, stored in batteries for use later, or “curtailed” which essentially means it is wasted.

I’ll have more discussions on curtailment, energy storage, and ways researchers and utilities are approaching these issues soon.

What does your electricity use look like?

Part II of an energy and research discussion for my parents (part I)

We all expect that when we flip the light switch at night, the lights will turn on. We won’t have to stumble around in the dark feeling around for a glass of water or to let the dog out. There are people and algorithms working around the clock to make sure when you and I request power, it is available.

This is exactly what our electric utilities do. They focus on delivering reliable and safe power to meet our “demand”. Because most utilities do such a good job of delivering electricity, we never think about the details.

The chart below gives a good idea of my family’s electricity demand last Thursday, October 24th. You can see there are many spikes as we made coffee and ran the dishwasher in the morning and other larger spikes later when we returned from work. Your energy use probably looks just as spiky though the details will certainly differ.

Cartoon of my family’s energy demand on Thursday, October 24th.

Our household daily usage is fairly similar day-to-day, even if the exact timing of making Henry and myself breakfast can differ quite a bit.

Sharp spikes to smooth curves

If every household has spiky electricity demand, how can our utilities anticipate the amount of power they need to produce at any one moment? Utilities rely on my demand, the demand of all my neighbors, and your demand being similar day after day. This helps them figure out a daily quantity which will likely be requested.

What about the precise timing of our morning coffee, how do they get that right? Utilities rely on having many customers and the law of large numbers. Not everyone makes coffee at 6:00am. Some make coffee earlier, some make it later, some not at all. When the actions of thousands of electricity customers are added together, their small differences smooth out the jagged spikes you see from my household when viewed in isolation. This leads to a very predictable energy demand throughout the day for a utility territory.

The below charts show electricity demand over three October days in 2017. The first is for a small utility with only 26,000 customers. This demand curve is already much smoother than my single household’s usage. And, the total demand across the contiguous United States is even smoother. In both of these cases, the demand has a cyclic peak-and-trough pattern with the lowest demand late at night.

The left figure shows the electricity demand for a small utility with 26,000 customers while the right figure is the total demand for the contiguous U.S. 1 Megawatt = 1,000,000 Watts

Utilities can make accurate forecasts of their territory’s electricity usage 24 hours in advance. Most can predict 24 hours ahead within 3% of the real value. This makes the cyclic peak-and-trough structure of demand very approachable for utilities.

Providing Electricity the Traditional Way

Over the past century, utilities have traditionally built enough coal, gas, nuclear, and hydro plants to match the peak electricity demand for their territory.

When a utility forecasts demand will reach 5,000 Megawatts tomorrow at 5:00pm in their territory, they make sure 5,000 Megawatts of their power plants will be ready to produce at that time. Human errors and mechanical failures can happen, and when they do, they are addressed. But, overall, the traditional system is very predictable.

The large scale introduction of intermittent renewable energy is changing this and will be the topic of the next post. Let me know if you have any questions or would love more detail. Check out the current energy use in your region with this amazing map.

Electricity Demand

Creating electricity to power our industries, schools, hospitals, and modern lifestyles consumes 40% of all primary energy in the U.S. At Carnegie Science, we are studying what paths the electricity system could take to become net zero in carbon emissions in the future.

It would be incredible to have a clean 100% renewable wind and solar based electricity system. However, there are real challenges in meeting energy demand at all hours because the sun does not always shine and the wind does not always blow. These hurdles can be overcome with smart choices in energy storage and by wise planning based on studying the variability of wind and solar resources.

At Carnegie Science, we have built a computer model of a simplified energy system to study net zero emissions systems. Any energy system our model designs must be able to supply electricity to meet the desired consumption of the U.S. for every hour of every day in the future. To begin to understand what is required, we use historical hourly electricity demand as one of the model inputs.

One of my colleagues, David Farnham (@farnham_h2o), and I are working on preparing these historical electricity demand data for our model. The U.S. Energy Information Administration (EIA) graciously collects hourly information from the utilities across the U.S. and publishes that data for analysis and use by the public.

However, we are all at the mercy of the reporting practices of each utility. If utilities report outrageous numbers, the EIA publishes outrageous numbers. And, when these numbers are used in an energy model, they can lead to wild results.

David and I have been developing algorithms to identify these anomalous values. After identifying anomalies, we replace them with a best estimate of what the true value probably was. A great example of some strange values can be seen in the below graphic, which shows the hourly electricity demand for the PacifiCorp West service territory over 10 December days in 2016.

Electricity demand during 10 December days in 2016 in the PacifiCorp West service territory of the U.S. Data pulled from EIA database Sept. 3, 2019.

Even without any background knowledge of what electricity demand should look like, the problem region jumps out immediately. The demand increases by a factor of 7 for 24 hours compared to the surrounding data. There is also a sudden one hour drop in demand which we also flag as anomalous. Our brain is phenomenal at pattern recognition and at identifying regions which do not conform with their surroundings.

Imagine designing an energy system which had to provide electricity for those 24 anomalous hours. You would build a system 7 time larger than what is needed for the rest of the year. Utility rate payers would be up in arms.

We could visually check all 56 reporting regions in the U.S. for all four years of hourly data: 56 regions * 4 years * 8760 hours per year = 1,962,240 data points! Instead, we devise algorithms to scan the data for us.

A good algorithm is reusable. We are putting in extra effort now to design the best algorithms possible for the task with an aim of reusability. In 6 months, when there is a new 6 month chunk of data, we will simply run our code to clean it up and share the results with colleagues. David and I plan to publish our techniques and make the clean data available for everyone.

In two weeks, I am going to be sharing our techniques at an upcoming Open Energy Modeling workshop at the National Renewable Energy Laboratory. I hope that the intense effort we put into this work leads to a data product that other research teams can also use for their modeling.