CO2 Reduction from Energy Storage


For my first graduate school environmental analysis class project, I wanted to measure the emissions reduction that energy storage could provide. This class focused on Life Cycle Analysis (LCA). This measures the emissions and pollution of a product or energy source over its entire lifecycle. In the past I’ve looked at various aspects of energy storage. Measuring the effects of energy storage on greenhouse gas emissions seemed like the perfect combination of these two areas.

SB700 CA Energy Storage Mandate

I chose to focus on the SB700 bill in California that passed the Senate and is currently postponed for the Assembly until next year. It’s a fairly straightforward mechanism to offer $1.4 Billion in the form of rebates to energy storage devices. It would run from 2018-2027 and be funded by fees to customers as most energy programs are through an increased rate base. It will be carried out through the California Energy Storage Initiative program. The general premise as described is to –

“The distributed energy resource technology shifts onsite energy use to off-peak time periods or reduces demand from the grid by offsetting some or all of the customer’s onsite energy load, including, but not limited to, peak electric load.”


“Make energy storage mainstream”

There are a few biggest uncertainties with the biggest being how much will be offered for each device or MWh? I’ll leave this question alone since I’ll only be focusing on the overall effect of the bill. Looking at the text of the bill, there are a few important points to note:

  1. There is an additional 20% available for products manufactured in the state of California.
  2. Must use existing transmission and distribution systems.
  3. Must be made available to all ratepayers.
    -This point and the previous point are a big deal as they don’t allow for distributed energy that is not connected to the grid. This propogates the centralistic nature of the grid allowing less independence for individuals. It also doesn’t support storage in more disconnected sites.
  4. “Dispatch capable”
    -This is a concern becuase financial incentive may or may not be in-line between the owner and utility. There is a disconnect between who is paying for the storage (customers) and who is receiving the benefit (utility or CAISO).
  5. Success based on reduction in GHG emissions, and other emissions.
    -If this is the core goal of the $1.4 Billion, it’s worth investigating how much of an impact can be had. This is the core question of my research investigation.

Does Energy Storage Reduce Greenhouse Gas (GHG) Emissions?


This is an important question because although energy storage is hailed as the savior of solar and wind, it isn’t immediately apparent that adding storage will immmediately lead to a reduction in GHG Emissions. This is because:

  1. Storage is not a source of energy itself. It still requires generation from somewhere and that primary source may generate greenhouse gases.
  2. Storage results in a loss in efficiency. The amount of energy you get out of a storage device is never as much as you put in. This means that you are having to generate more energy from somewhere.

The way that it can lead to decreased emissions is by changing the electricity production bundle in a positive way. After a little research on CAISO operations, it becomes apparent that the first step in doing this is by reducing the curtailment of renewables. Curtailment is happening in CA when the grid is not able to properly use all the renewable energy being produced. The following two graphs show when this is happening by month –


and by hour –



The overview of my analysis is to define how much CO2 is produced in a day based on a typical energy mix profile and then compare that to an energy mix profile with a greater percentage of solar.

To start, $1.4 Billion can buy you 3.5GWh of storage at a price of $400/kWh. Since I’m taking a focus on taking advantage of solar and wind being curtailed, I measure the curtailment size per day in the maximum month of June to be: 85,000 MWh / 30 days = 2,833 MWh (2.83 GWh) per day. This is the limit of the size of energy that can be moved since it’s the smaller of 3.5GWh and 2.83GWh. I randomly pick a day when deciding the amount of energy California uses in a day to be 620 GWh. Dividing the 2.83 GWh stored curtailment by the 620 GWh daily use gives .456% storage size as percentage of daily use. This can be re-attributed from fossil-fuel to wind and solar. The renewable energy being curtailed and wasted during the day can be stored until the peak load hours of the afternoon. The .456% storage size percent of daily use and 620 GWh daily use will be used as the inputs in GREET.



GREET is a Life Cycle Analysis (LCA) analysis tool developed by Argonne National Labs. It By analyzing the inputs and production that goes into producing a product, generating energy, or operating a vehicle, it outputs numbers on emissions and pollution. In regards to energy, it’s a fairly straightforward process of setting the percentage source mix of generation, distribution pathways, and the amount of energy. GREET then outputs pollution quantities.

Plugging in the daily production of 620 GWh and using the base electricity generation mix that GREET assumes, I get a pollution level of 206,282 tons of CO2. In my increased storage case, I reduce coal and NG by .228% each (.456% / 2), and increase a solar plus storage source .456%. This source includes a 80% battery efficiency pathway. This results in 204,165 tons of CO2 produced. In a third case scenario, I assume that storage costs are reduced to $200/kWh making the total storage size 7GWh. I assume that this is able to be fuly used because there is also increased solar or wind made available. This best case scenario gives a result of 201,022 tons of CO2. The percentage generation mix in this scenario is shown in the following pie graph.

CA Generation Mix

The results of the analysis are summarized in the following table. The columns contain the carbon output in a day, how much carbon is saved over 15 years, and the cost of that carbon reduction based on the $1.4 Billion.

Scenario Storage Size tCO2 tCOReduced over 15 years Cost per tCO2
Base Case 0 206,282
Storage 2.83 GWh 204,165 11,590,575 $120
Storage Best Case 7 GWh 201,022 28,798,500 $49

As you can see the $49-$120 cost to reduce a ton of CO2 is in the low to middle range for the estimate of the social cost of carbon. Based on these assumptions, storage can be an effective mechanism for reducing GHG emissions when properly coupled with clean energy sources.


There are a few caveats about this analysis. The biggest is that it makes some gross simplifications. Storage is very complicated as to the effect that it can have, but I employ it in a simplified manner in order to keep things simple when studying its effects. There are many different ways to get value from storage that are more complicated than hourly energy shift. How the storage is employed can make a big differnet as to the carbon reduction effect it will have.

The other uncertainty comes from the input assumptions I used. I tried to make reasonable assumptions and research the numbers used; however, many of these numbers have a wide range or are difficult to estimate such as curtailment or daily energy use. Others numbers such as the cost of storage continue to fall and change quickly.

More important than the exact numbers is the understanding of the mechanism by which storage is able reduce carbon emissions. Storage is able to reduce carbon emissions in spite of the downfalls of reduced efficiency and the fact that it is not itself a source of generation. As more solar and wind come onto the grid with falling prices, storage will be able to ensure the reliability of the grid with reduced GHG emissions.

Gamma Hedging: Energy Storage vs. Financial Options


Abstract :

Gamma is a change in the price of a derivative with a change in underlying at a changing rate (2nd degree). In the electricity markets the phenomenon is seen that when electricity prices deviate from the expected price, the load to serve also deviates. This correlation creates a compounding effect on losses. Historically, in vertically-integrated regulated markets, the utility owns all the peaker plants necessary to cover these events. In de-regulated markets, these functions are broken up, but connected through options gamma hedging. A novel alternative I propose is to use energy storage to cover these events. This is a novel use for energy storage distinct from arbitrage, solar combination, or back-up applications. This paper compares the costs of hedging against gamma events using energy storage vs. financial options.


Gamma is the second degree price change of a derivative with the price change of an underlying (The Greeks). This creates exponential moves in the derivative as compared to the underlying. In the electric industry, this is seen in the set-up of a retailer having to buy electricity from the wholesale market and sell to consumers at a fixed rate. The retailer is able to hedge their predicted load with a future to match the fixed rate and predicted load. This is a fairly straight forward delta hedge which ensures a fixed profit as prices (and only prices) deviate. The problem is that this doesn’t take into account a deviation of volume of load from what was predicted. The econo-physical fact is that there is a correlation between volume and prices. When load is higher than expected, prices react by rising, and when load is lower than expected, prices drop. This is supply and demand economics. I refer to times when both price and load highly deviate from expected as “gamma events”.

The profitability is governed by the product of the volume of electricity and the difference in retail and wholesale rates. The volume (V) and wholesale price (p) can deviate from expected which creates financial risk (Equation 1- Profitability).


Profitability – Oum, Y., Oren, S., & Deng, S. (2010). Volumetric Hedging in Electricity Procurement. Retrieved from

We can see the effects of this risk in Figure 1- Gamma Risk which shows the company’s obligatory load to serve short position, the future hedge long position, and the deviation from the $0 P&L gamma position. The problem is that the retailer feels the negative effects on profit/loss in both directions. When prices drop, they are forced to sell back excessive electricity at depressed prices. They’re protected against price drops, but not for the decreased volume. On the price up side, they are forced to buy additional electricity at higher prices. Once again, they are hedged against price increases, but no longer at the proper volume. When both are combined in the profit equation, this creates a downward droop in their P&L.


Gamma Risk
Gamma Risk – Meerdink, E. (n.d). Hedging Retail Electricity. Hess Corporation. Retrieved from

In trying to compensate for this gamma risk, various solutions have been proposed. In vertically-integrated energy markets, the utilities own the peaker power plants necessary for these events. The principal alternative is to cover distinct deviations from expected by building an options portfolio at strike prices form at the money. This is best described by Oum, Oren, and Deng (Oum, Oren, & Deng, 2010). Other alternatives include using weather options, or volumetric option as proposed by Lloyd Spencer (Spencer, 2001).

One novel solution that has not been examined is to use energy storage for gamma events. I have not been able to find any instances of energy storage being used exclusively for lower probability events of high price & load or low price & load.  This would be distinct from more common storages uses of price arbitrage, solar panel combination, or black-out back-up (RMI). The question is whether energy storage is a cost-effective alternative to options gamma hedging.


I analyze the two alternatives from the viewpoint of a retail electricity provider. It must provide electricity to customers at a fixed rate and buy it on the wholesale market. It owns no generation sources itself.

Data comes from PJM-West wholesale market. Data for these wholesale prices can be found at PJM’s website (Wholesale Prices). Load to serve comes from PJM’s estimated load (Estimated Load). These are hourly data points for the whole year of 2016. Predicted load and price were created by taking random normal deviations at a 15% scale. The correlation between load and price is .5 for both predicted and actual. This is a bit low of a correlation for gamma risk to take place, but will suffice for this analysis.

The cost of gamma risk comes from a volume which deviates from expected. Price deviations at load volumes consistent with what was predicted are already covered in the theta (futures) hedge that was put on. This means that the gamma hedge to be concerned with is the price deviations multiplied by load deviations, Equation 2 – Gamma P&L.

Gamma P&L Equation
Gamma P&L Equation

In an effort to keep things consistent, I only consider deviations that create 95th percentile profit losses. These are when the load and price deviation have the same sign to create a loss. I measure deviations in terms of dollar moves (strikes) of actual prices from predicted prices (at-the-money). The energy deviations are then calculated at each strike point.

95th Percentile Load to Serve
95th Percentile Load to Serve

Financial Options Hedging

The cost of the financial options hedge can be constructed by finding the cost of calls and puts as strike deviations from the at-the-money strike. The at-the-money strike can be considered to be the price of the future since the option delivers into the future contract. The future contract can be considered to be expected or predicted price. A generalized schedule of this options cost can be prepared based on a day for options two months out. I use options on PJM Western Hub Real-Time Peak Fixed Price Future prices on March 23, 2017 for May 2017 contracts (ICE Options Report) – Figure 2 – Options Prices.

Options Prices
Options Prices – ICE Options Report. (n.d.). Retrieved from ICE:

The difference between expected and actual price is the same as an options strike deviation from the at-the-money price telling us historically which options strikes would have been needed. Finally, the load deviation tells us how many contracts would have been needed. As we pay for these whether they are used or not, this is the total cost of hedging 95th percentile gamma moves or greater with financial options.

Excluding 95% of the hours ensures we are not wasting our time on small profitability losses, and it ensures we are not studying a battery for a cyclical time-of-use arbitrage scenario. Everything can then be re-categorized by summation into the strike distance from at-the-money. The costs incurred are then split between the cost of the option itself and the cost of the underlying electricity at the price that the option affords us the right to buy it. This is taken as the predicted price for each strike multiplied by the summed absolute value of load deviations.It can be seen in that the cost of the option itself is minimal in comparison to the cost of electricity.

Options Hedging Cost
Options Hedging Cost

Energy Storage Hedging

It is proposed that energy storage can help serve unplanned, un-hedged load and lower the down-side risk. By charging at lower cost times in preparation to serve unplanned load, battery storage can mitigate having to buy extra electricity at high wholesale prices. This scenario would entail operating a battery with a different algorithm than typical time-of-use, back-up, or ancillary support models.

The cost of using a battery is comprised of two costs, the cost to charge the battery and capital costs. I calculate the cost to charge the battery as the 20th percentile price of all energy. This is combined with the energy across the whole year of 1,224,474 MWh. An estimated efficiency loss of 15% gives a yearly cost of electricity at $20,149,936.

The O&M cost includes the cost of the battery itself and maintenance costs. The longest 95th percentile gamma event only lasts 3 hours with 2,843 MWh needed across these 3 hours. This largest demand is the size of the battery needed. This power and energy scale would only be achievable with a distributed storage network. The capital cost of a flow battery is $372-$1,115 ($743 avg) per kWh (Lazard). Adding in a battery lifespan of 20 years, the Capital cost is calculated to be $105,607,809.41. For purposes of simplicity, this doesn’t included maintenance cost or inflation. The combined cost of the battery is $133,496,994 or $109 per MWh.

Battery Analysis
Battery Analysis


Comparing the costs of covering 95th percentile gamma events using financial options vs. batteries entails calculating the cost of electricity and options price or capital costs for each. The significant drivers are that the battery is able to use a much lower cost of electricity because it can charge when prices are lower compared to the options price of electricity being based on predictions. However, the capital costs for batteries are significantly higher than the options price cost. This makes energy storage the higher cost option. Even with cheaper hydro-electric capital costs of $300 per kWh, the total energy storage cost per MWh of $57 is higher than options.

Overall Analysis
Overall Analysis

Future Work

There have been quite a few factors that have been left out or oversimplified including costs of batteries, cost of electricity for the battery, and options prices. Another consideration is that a 2,843 MWh battery deserves a qualification. This would have to be distributed storage. It would also be more likely that anything past 99th percentile losses wouldn’t be planned for. A more detailed economic analysis taking into account the time value of money, maintenance costs, and tax considerations that use better qualified inputs would also be valuable.

Future work includes doing a back-test that would better model the actual cash flows in each hour.  In practice, this situation could also be done by owning the batteries and selling options. You could gain money by collecting on the price of options, and then when a gamma event happens, you could pay the option with the income generated from selling the battery reserves onto the market. This would be a similar analysis from a different agent’s perspective.

Works Cited

Estimated Load. (n.d.). Retrieved from PJM:

ICE Options Report. (n.d.). Retrieved from ICE:

Lazard. (n.d.). Lazard’s Levelized Cost of Storage Analysis. Lazard. Retrieved from

Meerdink, E. (n.d.). Hedging Retail Electricity. Hess Corporation. Retrieved from

Oum, Y., Oren, S., & Deng, S. (2010). Volumetric Hedging in Electricity Procurement. Retrieved from

RMI. (n.d.). The Economics of Battery Storage. Retrieved from

Spencer, L. (2001, Oct 1). The Risk That Wasn’t Hedged: So What’s you Gamma Position? Fortnightly Magazine. Retrieved from

The Greeks. (n.d.). Retrieved from

Wholesale Prices. (n.d.). Retrieved from PJM:

Home Battery Optimization: Power Arbitrage

Storage of energy is one of the major hurdles for the electric grid. Electricity is best managed by instantaneous generation and consumption. Economic storage of energy could allow for cleaner generation and decreased peak accommodation. In this post, I investigate the optimization of storage independent from renewable generation.

The first case is trading electricity using a battery and grid connection by buying or selling electricity at hourly prices. The second case incorporates a houses’ load. In each case, the goal will be to optimize when the battery should be charging or discharging.

It is important to note that the price and load data is deterministic, as if future price and load is already known from a prediction model. In actuality, the data comes from Comed’s load and price sites. The data is hourly for the first week of January 2016. Load data is measured in kWh and price data is in dollars per kWh.


The battery is a 7 kWh Tesla Powerwall. The optimization model ensures that the battery can’t be charged above 6.4 kWh max based on Tesla’s specifications, nor below the minimum of zero. Besides the battery size, another restriction is a maximum power flow of 3.3kW based on Tesla’s website.


2 Tesla Powerwalls


The optimization is done with scipy package’s optimize. Minimize is the function that was used. This means that the function being optimized needs to return a negative dollar value because we actually are trying to solve a maximize optimization problem.

The first scenario is optimizing when power is bought or sold from the grid and stored as needed in the battery. The goal is to maximize the revenue made from buying electricity when its cheap and selling electricity when the price is high. It’s a classic financial scenario of making money by buying low and selling high. The model states that we are able to make $1.62 over the course of the week. The results come in the form of an hour by series of how much power to buy or sell. Graphed, we can see the results of the state of the battery as compared to the price of electricity.


The second scenario incorporates the residential load in kWh for a house. The previous assumptions are the same, except that now, the system also needs to provide for the electricity needs of a house. This ultimately costs -$3.57 which makes sense because you’re now using the electricity you acquire, and not able to sell it.


There are certainly many considerations that were not taken into account such as the lost efficiency of the battery. The model was a bit oversimplified as you wouldn’t be able to perfectly predict the price and load for a residence’s electricity. All in all, the main goal of using python’s optimization function was accomplished. We also learned something about what money there is to be made using Tesla’s Powerwall to arbitrage power prices. If you can make $1.62 over the course of a week, and a Powerwall costs $3,000; you can turn a profit in 1,852 weeks or 36 years. No get rich quick scheme here.

Python code on Github.