A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS)

This paper discusses the financial and technical principles underlying the levelized cost (LC) method of computing the cost of storing photovoltaic (PV) electricity (LCOS). The paper presents a CL algorithm. The algorithm equations are presented. The algorithm uses nine recognized energy storage system (ESS) specifications (specs) to compute the levelized cost of the stored PV electricity. Published specs for the Eos Aurora® and Cabin Creek Pumped Storage ESS are used to demonstrate the algorithm. For rapid computation, an Excel worksheet is provided. The goal of this paper is to present a standard computational algorithm for financial analysts to use. A financial analyst can do a LC computation based on the paper’s LCOS algorithm and on the algorithm’s nine ESS specs. The paper’s LCOS algorithm gives the analyst who has the nine ESS spec values, a quick “back of the envelope” verification of a developer’s (utility-scale), manufacturer’s (C & I; residential), or researcher’s (prototype) value for the levelized cost ($/MWh; €/MWh) of the stored electricity (LCOS). A second paper will compute the LC of using an ESS to provide ancillary services to the grid. Keywords—levelized cost; algorithm; energy storage system, ESS; ancillary services, energy storage finance; bulk storage; grid scale energy storage; PV; solar thermal; ESS specifications; ESS CapEx; Cabin Creek I. A UNIFORM METHOD FOR COMPUTING THE LEVELIZED COST OF STORING PV ENERGY For this paper1, both “back of the envelope” simplicity and an accurate2,3 first approximation of the cost (US$/MWh; €/MWh) of storing PV4 energy in an energy storage system (ESS) are the two criteria for choosing a computational method. This paper’s levelized cost (LC) algorithm meets both criteria. The goal of this paper is to present a LCOS algorithm based on generally accepted financial and engineering principles with a recognized uniform set of ESS specifications (specs). Using this paper’s LCOS algorithm, financial analysts with the same ESS specs and spec values5 will always compute the 1 an Addendum with the 11/01/17-Version 2.00 Corrections and Updates is on page 12 2 from the technical, mathematical, and financial perspective 3 read Section X, Concluding Analytics 4 In Version 2.00, “solar (PV)” is replaced with just PV. “Solar (PV)” is technically redundant A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 2 of 20 same value for the levelized cost of storage (LCOS)6. For computational speed, the LCOS algorithm is presented below on Table I, Excel LCOS Algorithm Worksheet7 (page 14). Table II below presents the Table I algorithm equations (page 15). Readers who purchased this paper from the author also received a working copy of the paper’s Table I, Excel LCOS Algorithm Worksheet8. These readers can follow the paper by entering the nine ESS spec values on their Table I Worksheet and seeing the results. Readers who did not buy this paper9 will first have to reproduce10 the Table I Worksheet, from the equations on Table II. Readers should refer to Table I (page 14) while reading this paper because this paper discusses the ESS LCOS algorithm equations and the nine ESS specs in Table I order. On Table I are the nine ESS specs used in the algorithm. The values presented in this paper are the publically reported specs of utility-scale11, commercial & industrial (C & I), residential, or research prototype ESS. The author has provided any missing12 spec values. The paper’s LCOS algorithm gives the financial analyst who has a developer’s or manufacturer’s ESS specs, a tool to make a 5 hereafter spec value is referred to as spec unless it would be unclear whether the reference is to a specific spec or to its value 6 there is also the LCOE (the levelized cost of energy) 7 hereafter, Table I 8 hereafter, Table I Worksheet 9 So how did you get a copy of this paper if you did not buy it from me? 10 or buy this paper, the Table I Worksheet and the SPI-17 Poster from the author. Go to his website www.michaelstavy.com 11 bulk storage 12 in some cases actually undisclosed quick “back of the envelope” confirmation of a developer’s or manufacturer’s announced energy storage cost (LCOS--US$/MWh; €/MWh). Solar installers can use this algorithm to estimate the LCOS of adding an ESS to a residential project. Financial analysts can also use the LCOS algorithm with a researcher’s specs for their prototype ESS to quickly compute a prototype ESS LCOS. The presentation of a data base of ESS specs for developers’, manufacturers’, solar installers’ or researchers’ ESS with different technologies, functions and a technical maturity is not the primary goal of this paper [1]13. This author has the more modest goal of only presenting a recognized standard methodology, an accurate “back of the envelope” LCOS algorithm. Whichever ESS technology that is used, the ESS cycle is the same (charging, storage, discharging). This paper’s LCOS algorithm is, except for CAES14, ESS technology agnostic (e.g. pumped storage, flywheel, capacitor, hydrogen, “solar batteries of various chemistries” [e.g. Pb-a, NaS, NiMH, Zn, Zn-air, Li-ion]). Residential, small commercial and C & I ESS are used to store energy. Larger C & I and utility-scale ESS can be engineered to provide energy storage and/or ancillary grid services (voltage and frequency control and reactive power [var]). This paper’s algorithm only computes the cost of energy storage. It does not compute the LC of an ESS that is designed to primarily provide ancillary services to the 13 if reference [1] lists this paper’s nine ESS specs for each ESS, it would be one such data base. At US$2,500 (€2,191) the EPRI document is two magnitudes greater than the cost of this paper. This author has, therefore, not accessed this data base to find out. 14 This LCOS algorithm must be modified for the NG used in a CAES. Contact the author concerning this modification. A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 3 of 20 grid15. To use this paper’s financial algorithm the Table I Worksheet, the analyst must obtain and/or develop quantitative values for the algorithm’s nine required ESS specs. The Eos Aurora® is the first ESS case presented in this paper. Eos Energy Storage, a manufacturer of utility-scale ESS plants reported [2] that its Eos Aurora® is “a low-cost DC battery system specifically designed to meet the requirements of the grid scale energy storage market”. Eos Aurora® ESS spec values are used on Table I to demonstrate the paper’s LCOS algorithm. Cabin Creek Pumped Hydro Storage Plant [3] in Clear Creek County, Colorado is a utility-scale 300 MW [2] ESS owned by Xcel16 Energy (formally Public Service of Colorado [PSOC]). Section IX is a case study17 of how the reader (financial analyst) obtains (develops) the nine required Cabin Creek ESS specs from different data sources for entry on Table I. II. FOREIGN EXCHANGE Certain US$ worksheet values are converted [4] into € for readers who work in €. Line FX, US$17/€1718 exchange rate, is US$1.14103/€. This was the July 8, 2017 foreign exchange (FX) rate reported at Oanda [5]. On Line FX, 15 This LCOS algorithm must be modified to compute the cost of providing ancillary grid services with or without significant energy storage. Contact the author concerning this modification. 16 readers should not confuse Xcel, the Colorado Power Company, with Excel, the worksheet app. 17 the author earned his Northwestern Day Program MBA at Kellogg (1969) where the case approach was used 18 all monetary units (US$, €) in Sections I-VIII are in 2017 values. Section IX has monetary units in both 1967 and 2017 monetary values the reader can enter their own values for the US$/€ exchange rate. Worksheet Lines 1→9 have the nine ESS specs that are the independent variables that the LCOS algorithm requires. An analyst can enter their values for the nine specs. Lines A→O are the dependent variables that the LCOS algorithm then computes using the equations in Table II. III. ESS PLANT CAPEX ESS electric storage capacity is measured in MWh (kWh) while discharge power is measured in MW (kW)19. The ESS storage capacity to power ratio is computed. The capacity to power ratio is a derivative spec. A small MWh/MW ratio is a characteristic of an ESS that is designed to primarily supply ancillary services to the grid. ESS CapEx is priced in terms of energy storage capacity; US¢/kWh (€¢/kWh) US$/MWh (€/MWh). By comparison, a PV, wind or thermal power plant CapEx is priced in terms the cost of power output; US$/MW (€/MW); US$/kW (€/kW). An ESS CapEx is the result of the cost of manufacturing (constructing; installing) a particular ESS with its specific technology, power (MW) and energy storage (MWh) specs. The Eos Aurora® ESS specs are used on Table I to demonstrate the paper’s LCOS algorithm. The Eos Aurora® ESS [1] has 1 MW of power and 4 MWh of energy storage. The Eos Aurora® ESS 4:1 storage to power ratio is good. For certain ESS, once an ESS has its charging/discharging powertrain capacity (MW) and control system installed, adding extra energy storage (MWh) increases the ESS 19 Certain utility-sized ESS provide their public specs in terms of power (MW) and duration (hours). A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 4 of 20 storage to power ratio while reducing the powertrain’s fixed cost on a US$/MWh (€/MWh) basis and, therefore, the ESS CapEx. Worksheet Line 1, ESS Power Output, is 1 MW. Line 2, ESS-Daily Energy Storage Capacity, is 4 MWh. Line A, ESS-Yearly Energy Storage Capacity, is 1,450 MWh/year. Line A is Line 2 multiplied by 365. Line 3, ESS CapEx-US$/kWh, is US$160 ($160,000/MWh) (€140,224/MWh). For large orders (> 40 MWh), the Eos Aurora® ESS is priced at US$160/kWh (€148) [2]. ESS CapEx is currently priced in US$/MWh; US$/kWh (€/MWh; €/kWh). This Eos Aurora® ESS US$160/kWh price is not all-inclusive but is useful here for demonstrating the LCOS algorithm. Refer to Section IX (page 8 below) for how an all-inclusive price of US$17400/kWh (€351) for a utility-scale (> 40 MWh) Eos Aurora® l Northern Power ESS is obtained (developed). US$/kWh (US$/MWh) is a key specification for both the ESS and the electric vehicle (EV) battery. Reference [6] reported that EV batteries were in the US$270-US$300/kWh range (€238-263/kWh). Reference [7] reported that the new Tesla Gigafactory will be able to manufacture EV batteries for US$100/kWh (€88). Line B, Total ESS CapEx-US$/ESS Plant20, is US$640,000/ESS Plant (€560,897) for one complete Eos Aurora® ESS plant. Line B is Line 2 multiplied by Line 3. For comparison, the author, (also a financial analyst) estimates that the CapEx of a new US utility-scale PV power plant is in the range of US$1,000,00020 When the ESS Plant CapEx is the published spec; dividing this value by the energy storage capacity kWh (MWh) computes the US$/kWh US$/MWh spec. This is an “off-the-worksheet, back-of-theenvelope” computation. US$1,250,000/MW (€876,401-€1,095,501) (US$1,000-US$1,250/kW) (US$1.00/WUS$1.25/W). IV. THE COST OF THE STORED PV ELECTRICITY (COSE) Line 4, ESS Round Trip Efficiency [η], is 75%. The Eos Aurora® ESS [2] round trip η is reported to be 75%. ESS η is the % of the PV electric energy (MWh) put into the ESS that is later taken out of the ESS and put back on to the grid as stored PV electricity. The higher the ESS η, the lower the energy loss from storing PV electric energy. Increasing ESS η does not increase the MWh/yr put back on to the grid. It reduces the MWh/yr that has to be put into storage and then taken from storage, to get the specified MWh/yr put back on to the grid. If we assume the impossible, that the ESS η = 100%, the ESS will have no energy loss. Line 5, Cost of the PV Electricity (COE)US$/MWh to be stored, is US$50.16 (€43.96) (US¢5.02/kWh). This represents the cost of PV electricity (COE) sold to load serving entities (utilities) under a long-term contract (PPA) from a utility-scale PV power plant. Using the worksheet in [8], US$50.16/MWh is the computed levelized cost of electricity (LCOE) generated, without subsidies21, at a hypothetical new Nevada 100 MW PV plant with the following specs [source]; PV plant CapEx: US$1,000/kW (US$1,000,000/MW) (€876,401) [author’s estimate]; Annual Fixed O & M Cost: 1⁄2% of CapEx [same as the Table I ESS plant]; Variable O & M Cost: US$1.00/MWh [same as Table I ESS plant]; Physical life: 25 years [PV panels are warranted for 25 years; author]; Interest/ROE Rate: 8% [same as the Table I ESS plant]; PV plant Capacity factor: 5.6 sun 21 The updated unpublished version of the author’s 2002 JSEE LCOE algorithm and worksheet includes the US Solar ITC (30%). A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 5 of 20 hours/day (23%) [solar insolation; Las Vegas, NV [9]. If fossil electric power22 is stored in an ESS and if the fossil electricity COE is put on Line 5, the LCOS worksheet will then compute the LCOS for the fossil electric power. Line C, Cost of the Stored PV Electricity (COSE)-US$/MWh, is US$66.87 (€58.61) (US¢6.69/kWh). This is Line 5 divided by Line 4. Because of the ESS η loss, the cost of the stored electricity (Line C) discharged from the ESS is always greater than the cost of the electricity that charges the ESS (Line 5). Line D, Extra Cost of the Stored PV Electricity-(COSE-COE)-US$/MWh, is US$16.72 (€14.65) (US¢1.67/kWh). Line D is Line C minus Line 5. This is the extra cost of the stored PV electricity because of the ESS η loss. The higher the ESS η, the lower the energy loss from storing PV electricity and, therefore, the less is the extra cost of the stored electricity. If we again assume the impossible, that the ESS η = 100%, the ESS will have no energy loss and the COSE will equal COE and Line D will be zero. Even if hypothetically, the ESS η = 100%, the LCOS will always be greater than the COE because of the ESS capital amortization, interest expense and O & M costs. Line E, % Increase in the Cost of the Stored PV Electricity, is 33%. Line E is Line D divided by Line 5. Line E is the extra cost of the stored the PV electricity as a % of the original COE. V. ESS OPEX AND CAPITAL COSTS There are many physical, mechanical, electrical, IT and electronic components in an 22 Cabin Creek Pumped Storage Plant originally stored PSOC fossil electricity generated at night and then discharged it during the day when the load was greater. This was a cost effective for PSOC. ESS that must be operated and maintained (O & M). For utility-scale and C & I ESS, there are also the fixed costs for insurance and real estate taxes. Therefore, an ESS has fixed [Lines 6, F & J] and variable [Lines 7 & K] nonelectric energy O & M costs. These costs are included in the computation of the LCOS. The ESS Fixed O & M cost is computed to be a % of Line B. Line 6, Annual Fixed O & M Cost-% of Total ESS CapEx, is 1⁄2%. This is the author’s estimated value. Line F, Annual Fixed O & M Cost-US$/yr, is US$3,200. Line F is Line B multiplied by Line 6. Line 7, ESS Variable O & M Cost-US$/MWh, is US$1.00. This is the author’s estimated value. Line 8, Physical Life of the ESS, is 20 years. In one Eos Aurora® ESS [2] sales brochure, the physical life was reported to be 20 years while in another it was reported to have a 15 year life and in another a 30 year life. A 20 (30) year life requires the purchase of an optional 20 (30) year warranty. PV panels are warranted without any $ (€) add-ons for 25 years. Line 9, Interest/ROE Rate, is 8%. This is the author’s estimated value. This is the cost (as a %) of the invested capital (Line B) that the ESS plant owner either provides (equity) or borrows (debt) in order to own the ESS plant. This is also known as the return on assets. An ESS has a physical life (Line 8). During its physical life, as the ESS operates by first storing and then by releasing the stored electricity, Line B, Total ESS Plant CapEx, must be recovered (depreciation) and the cost of capital (Line 9) for using the invested capital must be paid. If borrowed money is used to construct the ESS, the cost of borrowing the money is called the lender’s interest. If the ESS owner uses their own money to construct the ESS, the cost of using the owner’s money is called the return on owner’s equity (ROE). The cost of capital (Line 9) is a weighted average A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 6 of 20 percent for both the lender’s interest and the owner’s ROE. Let us hypothesize that the ESS debt/owner’s equity ratio is 1:1; the interest on the debt is 6% and the required ROE is 10%; then the weighted average Interest/ROE Rate is 8%23. Line G, the Capital Amortization Factor-CAF, is 0.1019. This is the annual payment computed for a financial annuity having US$1.00 as the principal borrowed, a loan period of 20 years (Line 8) and an interest rate of 8% (Line 8). The annual payment is made at the end of each year. The worksheet uses the same formula [10] used to compute the monthly (here yearly) payment for a standard 20 year, 8%, US home mortgage. Line H, Annual Capital Amortization (ACA)US$/year, is US$65,185 (€57,129). Line H is Line B multiplied by Line G. The levelized cost method uses a financial annuity to compute Line H. The ACA-US$/yr is one constant yearly payment for both the depreciation of Line B and for the payment of Interest/ROE (Line 9) over the physical life of the ESS. This level (constant) capital amortization payment gives the method its name. The first year’s payment is almost all Interest/ROE, while the last year’s payment is almost all depreciation. VI. COMPUTING THE LEVILIZED COST OF THE STORED PV ELECTRICITY-US$/MWH (LCOS) Line M is the worksheet’s “bottom line”. Line M, Levelized Cost of the Stored PV ElectricityLCOS-US$/MWh, is US$114.71 (€100.53) (US¢11.47/kWh). The LCOS is the sum of Lines I + J + K + L. Line I, Annual Capital Amortization (ACA)US$/MWh, is US$44.65 (38.9% of the LCOS). Line I is Line H divided by Line A. 23 If the debt/ROE ratio is 2:1, then the weighted average Interest/ROE is 7.33% Line J, Fixed O & M Cost-US$/MWh is US$2.19 (1.9% of the LCOS). Line J is Line F divided by Line A. Line K, Variable O & M Cost-US$/MWh, is US$1.00 (0.9% of the LCOS). Line K is the value transferred from Line 7 above. Line L, Cost of the Stored PV ElectricityCOSE-US$/MWh, is US$66.87 [US¢6.69/kWh] (58.3% of the LCOS). Line L is the value transferred from Line C. The algorithm computes the Eos Aurora® ESS LCOS to be US¢11.47/kWh. This is a good price for peak power in many US wholesale energy markets. Reference [2] stated that the Eos Aurora® ESS with a 30 year life24 can provide peak electricity at a levelized cost of US¢1217/kWh (US$120-170/MWh). The LCOS algorithm computed25 the LCOS to be just below the manufacturer’s published range for the Eos Aurora® ESS Plant26 LCOS. VII. COMPUTING THE LEVELIZED EXTRA COST (MC) OF STORING PV ELECTRICITY (LECOS) Line N, Levelized Extra Cost (LECOS) of the Stored PV Electricity-US$/MWh, is US$64.56 (€56.58) (US¢6.46/kWh). Line N (LECOS) is Line M (LCOS) minus Line 5 (COE). Line N is the line “after the bottom line”. Line N is the difference (the Δ), the marginal cost (MC), between Line M and Line 5. The marginal revenue (MR) from storing electricity must be equal to or greater than the MC, Line N. Line O, % Increase in the Cost of the Stored PV Electricity, is 129%. Line O is Line N divided by 24 not the 15 or 20 years as previously reported 25 Using the a la carte (a not all inclusive US$ 160/kWh) for the Eos Aurora® ESS Plant CapEx and a 20 year life. 26 The industry convention is to refer to a smaller ESS as just ESS while grid-sized ESS are referred to as an ESS plant or even just as an ES plant A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 7 of 20 Line 5. Using the Eos Aurora® ESS to store solar (PV) electricity adds 129% to its cost. If, however, the Eos Aurora® ESS is put “behind the fence” by the owners of a utilityscale PV plant, then, to avoid double counting, only the extra cost (MC) of the energy storage should be considered, that is the LECOS. If this utility-scale PV plant operates as a merchant plant instead of as a PV plant under a long term PPA, then an Eos Aurora® ESS can store the solar PV energy until the wholesale price of electricity is equal to or greater than Line N, LECOS. Any time that the wholesale price is above its COE, the utility-scale PV plant should sell its power to the grid. It can also delay sales until the wholesale price is above the COE plus the LECOS. Because of the intermittence of PV electricity, a “behind the fence” Eos Aurora® ESS gives some firm capacity to a utility-scale PV plant. Line N, Levelized Extra Cost of the Stored PV Electricity, can also be computed as the sum of Lines I + J + K + D. The equation for Line N is below 27 Line I, Annual Capital Amortization (ACA)US$/MWh Line J, Fixed O & M Cost-US$/MWh Line K, Variable O & M CostUS$/MWh Line D, the Extra Cost (COSE-COE) of the Stored PV Electricity-US$/MWh Readers who purchased the Table I Worksheet will find this second computation of the LECOS on the worksheet itself. 27 LECOS-US$ = ACAMWh + FOM-US$MWh + VOMUS$MWh + ECOSE VIII. THE EFFECT ON THE LCOS FROM CHANGING ONE OR TWO ESS SPEC VALUES WHILE KEEPING THE OTHER ESS SPEC VALUES THE SAME If the new Tesla Gigafactory [7] is able to manufacture Powerpack® (utility-scale Li-ion batteries ESS) for US$100/kWh (€88/kWh) (US$1000/MWh) and if all the other Tesla Powerpack® specs are the same as the Eos Aurora® ESS specs are on Table I, then Line B, Total ESS CapEx, is reduced from US$640,000 to US$400,000 (€560,870 to €350,560) [37.5% reduction] and, Line M, the LCOS, is reduced from US$114.71 to US$97.15/MWh (US¢9.71/kWh) (€100.53 to €85.14/MWh) [15.3% reduction]. Readers should understand that the Tesla US$100/kWh Powerpack® battery cost is a la carte not an all-inclusive price for a completely constructed and installed utility-scale Powerpack®. If a hypothetical US ESS tax incentive allows Line 9, Interest/ROE, to be reduced from 8% to 6% [25% reduction], and if all the other Eos Aurora® ESS specs stay as they originally were on Table I, then Line H, Annual Capital Amortization –ACA-US$/yr, is reduced from US$65,185 to US$55,798 [14.4% reduction] and Line M, LCOS of the Aurora ESS is reduced from US$114.71 to US$108.90/MWh (€94.90) [5.6% reduction]. If the Eos Aurora® ESS batteries are now also manufactured at US$100/kWh, if the Interest/ROE is now also 6%, and if all the other Aurora ESS specs stay as they originally were on Table I, then the Aurora ESS Line M, LCOS, is reduced from US$114.71 to US$93.13/MWh (€81.62) [18.8% reduction]. Readers, who have the Table I Worksheet can enter the alternative specs presented in this section (VIII) to confirm the author’s results. A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 8 of 20 Readers, who also have the Case Study Comparison Excel LCOS Algorithm Worksheet28,29 can at the same time enter the specs for two different ESS. The worksheet will then compute the LCOS for both ESS. The Comparison Worksheet will also compute the differences (and % differences) between the specs of the two ESS and the worksheet computed values for the two ESS.30 Having the Table I Worksheet (and the Comparison Worksheet) will greatly help the reader to understand Section IX below. IX. A CASE STUDY—OBTAINING (DEVELOPING) THE VALUES FOR THE NINE ESS SPECS FROM ESS SPECS FOUND IN DIFFERENT DATA SOURCES IN ORDER TO COMPUTE THE LCOS AT CABIN CREEK To use this paper’s LCOS algorithm to compute the LCOS at Cabin Creek, the financial analyst must obtain quantitative values for the nine required Cabin Creek EES specs. This is a case study of how to obtain (or develop) Cabin Creek’s nine required ESS spec values. Getting good numbers31 is a challenge in all of renewable energy technology and finance. Financial analysts following the digital movie industry have the same problem that we, the reader and author, have in this case study. The Wall Street Journal [15] reported that there are “no third parties tracking the digital movie business making exact figures impossible to obtain”. Readers should enter the nine Cabin Creek 28 hereafter, Comparison Worksheet 29 the Table I Worksheet was included with your purchase of this paper. The Comparison Worksheet is sold separately 30 As a bonus, the Comparison Worksheet also has a check value for each ESS’ Total Annual O & M 31 getting accurate facts (not alternative facts) can also be a challenge spec values obtained (developed) in this section on their Comparison Worksheet32 and check the results. After finishing this paper, the reader should be able to start obtaining (developing) their own ESS specs, entering them on their worksheet and checking the results. Below on Table III, Sources for the Values of the Nine Cabin Creek Specs, (page 18) and in Table I order, the paper presents the nine required Cabin Creek spec values with an explanation how the author used different data sources and his analysis to obtain (develop) each spec value. Line 1, Cabin Creek Power Output, is 300 MW. Using a conservative approach the Compendium [11] value was entered. This is not the same value as reported by either B Cotie [13] or by US DOE [14]. Line 2, Cabin Creek-Daily Energy Storage Capacity, is 1,450 MWh. Using a conservative approach, the Compendium [11] value was entered. This is not the same value computed by B Cotie [13] or reported by US DOE [14]. Line A, Cabin Creek-Yearly Energy Storage Capacity, is 529,250 MWh/year. The LCOS algorithm computed this value. This is a check number for the reader’s computation. Line 3, Cabin Creek CapEx-2017 US$17/kWh, is US$17 283/kWh33 (US$17 $283,000/MWh). This is an all-inclusive cost. (ne pas a la carte34 pricing here). The Compendium [10] 1967 value of US$67105/kWh [11] was adjusted for 50 years of inflation (PPI) at 5% a year and with another adjustment for 50 years of increases in the productivity35 (MPP) of pumped storage 32 or on their Table I Worksheet 33 reference [12] page 13 lists $1,500/kWh (US$1,500,000/MWh). This value will be discussed later 34 is the author’s French getting better? A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 9 of 20 plant EPC {engineering, procurement, and construction} at 3% a year. Neither B Cotie [13] nor US DOE [14] had a CapEx-US$/MWh 1967 value (US$67kWh), 2013 value (US$13kWh) [13] or 2017 value (US$17kWh) [14]. Now case study will have a sidebar on the Eos Aurora® ESS CapEx. Everybody knows36 that pumped hydro is the least cost utility-scale ESS. The a la carte Line 3, ESS Plant CapEx, US$17160/kWh used on Table I for an Eos Aurora® ESS only includes [2] “the full DC system including the batteries mounted and wired, the energy stack outdoorrated enclosure and battery management system (BMS)”. This author has concluded that the price does not include the energy stack skins, base plates, warranties > 1 year, [a 20-30 year life requires an add-on 20-30 year warranty], 80% capacity guarantee [also a US$ (€) add-on], power control systems, engineering, procurement of all ESS components, CapEx of all other ESS components, construction [another major cost] of the ESS and shipping charges. EOS and Northern Power Systems announced [16] an all-in (all-inclusive; ne pas a la carte) price of less than US$17 400/kWh for a fully integrated utility-scale ESS using the Eos Aurora® DC battery system and Northern Power’s Wind Turbines. Computing the Eos Aurora® l Northern Power ESS LCOS by replacing the ESS CapEx of US$160/kWh (Line 3) with US$17 400/kWh [150% increase] and by replacing the 20 year Physical Life (Line 8) with 30 year Life [50% increase] and while leaving the seven other specs the same as they originally were on Table I, Line M, LCOS, now computes to be US$170.70/MWh (€149.60) (US¢17.07/kWh) [48.8% increase] compared to the original 35 the productivity of the operating Cabin Creek Pumped Storage ESS is its round trip η 36 Attributed to Leonard Cohen (Table I) LCOS values of US$114.71 (€100.53) (US¢11.47/kWh). Now this case study will return from this sidebar to the Cabin Creek Plant CapEx. Line B, Total Cabin Creek ESS Plant CapEx is computed by the algorithm to be US$17 410,350,000/ESS (€359,631,210) This US$17 value for a 300MW; 1,450 MWh utility-scale pumped storage ESS is an “in the ball park”37 number38 for proposed [17]39 new US utilityscale pumped storage plants and based on this paper’s “back of the envelope” LCOS approach. Line 4, Cabin Creek Round Trip Efficiency [η], is 80%. The Compendium [10] gives the average GWh/yr pumped to be 116 and the average GWh/yr generated to be 75. On Table III, η was computed to be 65%, which is also in the high range of Figure 3, Pumped Storage Plants vs Time (yrs), in [10]. However, the author used a Bayesian estimate of 80%40 because an η of 65% does not reconcile with the Line A value. A 1,450 MWh ESS will discharge 529 GWh/yr; not 75 GWh/yr. Cotie [13] states that the water turbine efficiency (η) will be increased from 86% to 91%. US DOE [14] did not report an η value. Line 5, Cost of the PV Electricity (COE) to be stored, is US$50.16 (€43.96) (US¢5.02/kWh). This is same value that was originally used for the Eos Aurora® ESS on this paper’s Table I. 37 CapEx (US$/MWh; €/MWh) is not a frequently published spec 38 Subject to verification by the author and the reader 39 There are many proposed US utility-scale pumped storage plants but none have been constructed in the last 10 years. 40 reference [12] page 5 also has 80% A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 10 of 20 Line 6, Annual Fixed O & M Cost-% of Total Cabin Creek CapEx, is 1⁄2%. This is the same value that was originally used for the Eos Aurora® ESS on this paper’s Table I. Line 7, Cabin Creek Variable O & M CostUS$/MWh, is US$1.00. This is the same value that was originally used for the Eos Aurora® ESS on this paper’s Table I. Line 8, Physical Life of Cabin Creek, is 100 years. The Eos Aurora® ESS [1] physical life was originally 20 years but is now 30 years based on [16]. PV panels are warranted for 25 years. The Compendium [11], Cotie [13] and US DOE [14] all reported that as of 2017, Cabin Creek has operated for 50 years. The author added 50 more years. Line 9, Interest/ROE Rate, is 6%. An 8% return on assets was used for the Eos Aurora® ESS (Table I). Xcel Energy (PSOC) is a vertically integrated legacy utility in Colorado, a regulated state with no retail competition. In today’s financial market, Xcel should earn41 6% on the Cabin Creek ESS assets which are a regulated “power generating” asset. For Cabin Creek, Line M, Levelized Cost of the Stored PV Electricity-LCOS, is US$114.23/MWh (€100.11) (US¢11.42/kWh). By coincidence, this value is almost the same as the Table I Aurora® ESS LCOS value of $114.71/MWh. The Eos Aurora® l Northern Power ESS LCOS was computed to be US$170.70/MWh (€149.60). The Cabin Creek LCOS is 49.4% less. Xcel is storing its own renewable electricity generation42 at Cabin Creek. To avoid double counting the cost of the electricity (COE) to be 41 until Cabin Creek is completely amortized 42 mostly wind, but also PV stored, only the levelized extra cost of storing the electricity (LECOS) should be considered when deciding whether to store wind (PV) energy at Cabin Creek or to directly dispatch it43. When the market price of PV generation is below zero44 the decision is easy. Avoiding double counting is done by using Table I, Line N, Levelized Extra Cost (LECOS) of the Stored PV Electricity-US$/MWh. The algorithm computes the LCOS and then subtracts the COE to compute the LECOS for solar (PV) power. With the nine spec values listed above, the algorithm computes the Cabin Creek Line N, Levelized Extra Cost (LECOS) of the Stored PV Electricity to be US$64.07 (€56.15) (US¢6.41/kWh). For readers who have the Table I Worksheet45 here are the Line N check numbers. Line N is the sum of Line I, Annual Capital Amortization (ACA)US$/MWh, US$46.66 (72.8% of the LECOS). Line J, Fixed O & M Cost-US$/MWh is US$3.88 (6.1% of the LECOS). Line K, Variable O & M Cost-US$/MWh, US$1.00 (1.6% of the LECOS). Line D, the Extra Cost (COSE-COE) of the Stored PV Electricity-US$/MWh, US$12.54 [US¢1.25/kWh] (19.6% of the LECOS). 43 Utility-scale solar dispatch depends on the time of day, the solar plant’s instant capacity factor, the current grid load and the wholesale price. Solar needs storage because of its intermittency and because it cannot follow the grid load. 44 or when PV is being curtailed by the grid 45 or the Comparison Worksheet A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 11 of 20 X. CONCLUDING ANALYTICS In the case study, this paper discussed obtaining (developing) Cabin Creek’s nine ESS specs, including its US$17 283/kWh CapEx spec (€248) (US$283,000/MWh) from public sources that are thought to be reliable. With a US$ 283/kWh CapEx, Cabin Creek’s LCOS was computed to be US$114.23 (€100.12). If the reference [12] ESS CapEx spec value46 US$ 1,500/kWh (€1,315/kWh) (US$1,500,000/MWh) is now substituted for the US$283/kWh CapEx and if the eight other Cabin Creek specs remain unchanged, the Cabin Creek LCOS is now computed to be US$331.55 (€290.57) (US¢33.16/kWh). The Cabin Creek LCOS is now 65.5% greater. In the case study, the sidebar LCOS computation for the Eos Aurora® l Northern Power ESS with a US$ 400/kWh CapEx, a 30 year life and with the seven other Table I specs remaining unchanged, was US$170.70 (€149.60) (US¢17.07/kWh). Cabin Creek’s LCOS with the US$ 1,500/kWh CapEx is now 48.5% greater. Compared to the original Table I Eos Aurora® LCOS of US$114.71 (€100.53) (US¢11.47/kWh), Cabin Creek’s LCOS with the US$ 1,500/kWh CapEx is now 65.4% greater. Since everybody knows47 that pumped storage is the least expensive ESS, it makes no sense that the Cabin Creek LCOS based on a US$ 1,500/kWh CapEx is greater than both the Table I Eos Aurora® LCOS and the Eos Aurora® l Northern ESS LCOS. This paper’s LCOS algorithm does not determine which ESS specs or which computed LCOS makes technical 46 undated white paper 47 Lenard Cohen again and financial sense and which are nonsense48. This is determined by the reader (yes, you! this paper’s LCOS algorithm user) based on your knowledge of current ESS specs and on your knowledge of which computed ESS LCOS make sense. Will a US non-carbon restrained wholesale market pay the LECOS of stored solar PV energy? Does the US¢6.46/kWh, Table I Eos Aurora® LECOS, make sense in today’s energy market? How about the US¢6.41/kWh Cabin Creek LECOS with the original US$17 283/kWh CapEx? Before you say NO, you should realize that Cabin Creek without a non-carbon restrained wholesale market, has now been in actual operation for more than 50 years. An explanation is beyond the scope of this paper. A nonsensical48 output can be caused by a nonsensical48 input or, heaven forbid dear reader, by this paper’s LCOS algorithm having technical, financial, algebraic or worksheet computational flaws in it. Let us address this possibility. First, this paper’s narrative described how the LCOS algorithm was constructed49. If you agree with this paper’s narrative explanation of how the LCOS algorithm was constructed, agreed with the Table II equations and if you tested, to your satisfaction, your copy of the Table I Worksheet50, then there are no flaws in the paper’s LCOS algorithm. Second, the reader should know that the paper’s LCOS algorithm will accurately51 compute the LCOS with ESS specs that makes no sense52. Logically, therefore, since the paper’s LCOS algorithm is correctly constructed, any nonsensical48 output must be caused by nonsensical48 input. 48 garbage 49 using a recognized standard methodology 50 or your copy of the Comparison Worksheet 51 mathematically; algebraically; financially; technically 52 garbage in; garbage out A Financial Algorithm for Computing the Levelized Cost of Storing PV Electricity (LCOS) ©Michael STAVY Printed on 11/11/2017 10:22 AM 11/01/17-Version: 2.00 Solar Power International 2017 (SPI-17), 10-13 September, Las Vegas Page 12 of 20 The current ESS industry pricing convention, which is nonsensical53, is to only publically quote ESS CapEx in terms of energy storage capacity 54 (US$/MWh; US$/kWh) and not in terms of both energy storage capacity and power output (MWh:MW). This paper’s LCOS algorithm has had to use this industry pricing convention because that is how ESS specs are presented in publically available data bases. This paper did not present a public data base of accurate55 ESS specs values. This author had the much more modest goal of only presenting, with a recognized standard methodology, an accurate “back of the envelope” LCOS algorithm. Not discussed56 in this paper is the reason for energy storage, the extra market value of PV power on a carbon constrained electric grid and how the extra cost of the energy storage is paid for. XI. ADDENDUM-11/01/17-Version 2.00 Corrections and Updates 1. Prior versions of this paper have used the term “solar (PV)” in both the title, in the narrative and in the worksheets. “Solar (PV)” has been replaced with PV because solar (PV) is technically redundant and because this paper only discusses storing PV electricity. Solar electricity can be generated with either solar PV technology or with solar thermal technology. The LCOS of thermal electricity requires a separate paper, although readers can put their “adjusted thermal specs” on their Table I 53 especially for utility-scale 54 or in duration but duration does not yet have a price dimension 55 which would include the CapEx for both power output and energy storage capacity 56 the author is available to clients to discuss these topics Worksheet (Comparison Worksheet) and compute the LCOS solar thermal energy. 2. LCOSE has been replaced with LCOS and LECOSE has been replaced with LECOS. 3. At SPI-17, the author had a conversation with a representative of the EOS Energy Storage Company that lead to him to the conclusion that he had the wrong value for Eos Aurora® spec # 2, Daily Energy Storage Capacity (MWh/day). The Eos Aurora® ESS [1] has 4 MWh of power and not the 6 MWh that he incorrectly reported in Version 1.0 of this paper. Opps, furthermore, the author could not find his original reference that he used to get the 6 MWh/day value. 4. Because the current industry custom is to quote ESS Plant CapEx only in terms of daily energy storage capacity (US$/MWh; €/MWh) and not in terms of both power (MW) and capacity (MWh), the algorithm’s LCOS (US$/MWh; €/MWh) is the same whether 4 MWh or 6 MWh is the Line 2, Daily Energy Storage Capacity, spec entered. Check the algorithm equations to confirm this. Enter both 4 and 6 MWh on your Table I Worksheet. The author is working on a revised algorithm that uses both ESS power and ESS capacity to compute the Line B, Total ESS Plant CapEx. 5. Page 4 had the value for Line A as 2,190 (6 x 365) instead of the correct 1,460 (4 x365). See this Addendum, Point 2. 6. The current industry convention is to only quote ESS CapEx in US$/kWh (€/kWh) and not in US$/MW (€/MW) even for large C & I and utility-scale57 ESS. The cost of the power output (kW; MW) is not publically used to price ESS CapEx. This paper, the Table I Worksheet