1. Battery Storage Systems: A Backward Induction Approach with Multiple Daily Discharging Opportunities Joohyun Cho Andrew Kleit The Pennsylvania State University 1

2. Storage and Electricity Markets A crucial problem in electricity markets is that electricity is very difficult to store. Technological advances in Energy Storage Systems (ESS) has made energy storage at least conceptually possible. Recent FERC Orders have made it easier for storage systems to hook up with the grid. Here we present a methodology for evaluating the revenues available to ESS. 2

3. ESS Literature Review Arbitrage opportunities in PJM (Sioshansi et. al. 2009). Not profitable based on operating simulations using 2000-2007 PJM price data. ESSs in NYISO for energy and ancillary service (Walawalkar et. el. 2007). Only profitable in New York City, not in the rest of NYISO Storage from using batteries of electric vehicles in NYISO (Peterson et. al. 2010). Profitable only with no degradation cost. 3

4. Additional Literature Returns from renewables with battery ESS in Kansas (Jones & Powell 2015) The authors assume the storage are charged by wind and solar power, and the stored energy is sold to the grid. The battery costs are far greater than the estimates of revenue. Storage batteries from electricity vehicles in Ontario, Canada, avoided fuel and transmission cost (Heymans et al. 2014) Not profitable with only revenues from the battery operations. Integration with wind farms in Greece, avoided fuel cost and emission reduction (Zafirakis et. el. 2013). Storage is only profitable with the feed-in-tariffs.

5. Methodology 1) We use backwards induction, day by day, to determine available profits; 2) We give the battery operator the opportunity to supply power to either the energy or an ancillary market; 3) Following Hotelling (1931) we allow for a shadow cost to be assigned to battery usage, rising over time; 4) Here we allow for multiple discharges per day.

6. Methodology Daily operation simulations for a year Find annual revenues and used cycles by with different shadow values, λ ($/Mwh). Building functions Build functions R(λ) (annual revenue) CY(λ) (annual used cycles) Finding the maximum total revenues Initial shadow value,, which maximizes NPV of revenues with T years or till using up M cycles. 6 Three stages approach (Shcherbakova et.el. 2013)

7. Model Parameters Battery specifications (Raslter, 2010) 3.2MWh/1MW Li-ion battery 4,500 cycles 90% Depth of Discharge(DoD), 85% round trip efficiency 20 years of operations Price ERCOT Houston Hub (Jan.-Dec. 2012) Energy prices and RRS prices Probability that the reserve service call is place: 1% Interest rate : 2%/year 7

8. Battery operation assumptions At installation, the battery is fully charged.. The battery operator has perfect information on that day’s prices. Bids occur at the market clearing price. The device is charged on hours between hour 1 to 6 the next day; thus no discharging can occur during these hours. Discharging schedule can be assigned for multiple hours between 7 and 24, either to energy service or ancillary service. As the battery is charged, the i-th discharged energy is charged at i-th least expensive cost on the next day. For example, the 1 st discharged energy is charged at the least expensive cost hour among the first six hours of the next day. 8

9. Methodology-first stage Battery’s multiple states of charge 9 3.2MWh / 1MW battery 90% DoD = 3.2MWh x90%=2.88MWh is available for storage

10. Methodology-first stage Backward induction Finding the optimal decision schedule from the last state Find the optimal discharging schedule for the day Enables us to capture all potential profits from the following hours in calculating revenues at present hour in case energy is not discharged at hour t 10

11. Some examples: optimal bidding decisions for April 28 th, 2012 at the last state of charge when the price of replacement energy is $11.65/MWh Hour (t) Expected payments for each bidding strategy Revenue maximizing bidding decision 243.517.253.532.880.003.53Reserve Service 234.2119.257.754.503.537.75Reserve Service 228.1723.6315.928.057.7515.92Reserve Service

12. Optimal bidding decision for April 28 th, 2012 at the second state of charge when the price of replacement energy is $11.30/MWh Hour (t) Expected payments for each bidding strategy Revenue maximizing bidding decision 243.517.253.533.543.650.003.65Energy Service 234.2119.257.757.919.023.659.02Energy Service 228.1723.6315.9217.2717.289.0217.28Energy Service

13. Bidding decisions at each hour given state of charge when the shadow value is $0/MW - Most bids were made to reserve service for all state of charges In early hours (9~14) under the third state of charge Rate for energy service is higher after hour 14 13

14. Second Stage:-Building yearly revenue and used cycle functions From the first stage, we can generate expected revenues and cycles for a year given a shadow value. At the second stage, we built functions to estimate expected annual revenues and expected annual use cycles as a function of the shadow value. This information is needed to find the shadow value which maximizes total revenues, in the third stage. Expected annual revenues had a maximum value of $80,200 when the shadow value was $0/MWh, and decreases in a linear fashion as the shadow value increased, to about $49,000 when the shadow value was $500/MWh.

15. Cycles Used Per year Expected use cycles decreased from 173 to 22 cycles/year for shadow values between $0 and $12/MWh. Expected use cycles then decreased gradually from22 to 14 cycles/year when the shadow value increases from $12 to $500/MWh.

16. Third Stage—NPV of expected revenues under given cycles Given annual revenue and used cycle models in the second stage, we next found the NPV under limited life cycles and operating years, and the corresponding shadow value in the first year., we found that the NPV of revenue had a maximum value of $1.30 million when the initial shadow value was $0/MWh, The battery is expected to use less than 3,500 of the available 4,500 cycles in that circumstance, and uses fewer cycles with larger shadow values. So, for these parameters, the battery has too much capacity. With battery specifications in Table 3.3.1, expected revenues for 20 years were The $1.30 million in revenues was smaller than the investment cost of $2.6 million..

17. Is the round trip efficiency the problem? One of the challenges for a battery operator is the round trip efficiency. In this model we have an 85% round trip efficiency, which implies 15% of the power is wasted. So we increased the round trip efficiency to see how it affected our results. 17

18. Sensitivity analysis on the round trip efficiency Applied linear combination method Revenues are increasing as the efficiency is improved. The device uses all given cycles with 91% + efficiencies, resulting in optimal shadow values to be positives. Very little impact 18 Round trip efficiency NPV of revenuesCycles usedOptimal ($, with 2%/year discount) during operations Initial shadow value ($/MWh) 85%1,339,6043,435.540 86%1,341,9963,589.960 87%1,344,4773,780.000 88%1,347,0413,930.520 89%1,349,7044,139.580 90%1,352,4794,352.380 91%1,355,1764,500.000.0217 92%1,356,4504,500.000.2140 93%1,357,8174,500.000.3942 94%1,359,1694,500.000.5744 95%1,360,5834,500.000.7470 96%1,361,9594,500.000.9226 97%1,363,3684,500.001.0938

19. Conclusion Using the battery ESS in ERCOT is not profitable $1.34 mile rev. vs. $2.6 mil investment cost 3,435 cycles are expected to be used (vs. 4,500 cycles) Compared to the single discharge opportunity $150,000 more or 13.56% additional revenues in total Sensitivity analysis on the round trip efficiency 91% + efficiencies use all cycles, implying a positive shadow value. NPV of revenues are still short for the investment cost Our results suggest either the battery has too much capacity, or two slow an input/output rate. 19