Assessment of Energy Storage for Transmission-constrained Wind

Applied Energy 124 (2014) 377388Contents lists available at ScienceDirect

Applied Energy

journal homepage: www.elsevier .com/locate /apenergyAssessment of energy storage for transmission-constrained windhttp://dx.doi.org/10.1016/j.apenergy.2014.03.0060306-2619/ 2014 Elsevier Ltd. All rights reserved.

Corresponding author. Tel.: +1 (734) 763 3243.E-mail address: [email protected] (J.X. Johnson).Jeremiah X. Johnson , Robert De Kleine, Gregory A. KeoleianCenter for Sustainable Systems, School of Natural Resources & Environment, University of Michigan, 440 Church St., Ann Arbor, MI 48109, United States

h i g h l i g h t s

We assess the potential for energy storage to economically decrease wind curtailment or decrease system costs. We assume that the wind is under contract via a power purchase agreement. Maximum viable energy storage costs were $780/kW with ten hours of storage capacity. Sizing the energy storage to reduce a small portion of curtailment supports higher unit cost batteries. Significant curtailment persists even with high capacity energy storage.a r t i c l e i n f o

Article history:Received 17 June 2013Received in revised form 31 January 2014Accepted 2 March 2014Available online 11 April 2014

Keywords:WindCurtailmentEnergy storageTransmissionPower purchase agreementa b s t r a c t

Grid-scale energy storage is one option to reduce curtailment and increase deliverability of transmission-constrained wind. This study examines four hypothetical wind and transmission projects in the UnitedStates to quantify the reduction in curtailment under various energy storage configurations anddetermine the cost targets that energy storage must achieve to become a viable solution for use withremote wind. The delivered cost of wind is determined using a power purchase agreement approachand six AC transmission voltage classes are considered. The findings show that curtailment reductioncan be achieved with energy storage costs as high as $780/kW with ten hours of storage capacity, a valuethat is 5085% lower than current cost estimates for redox and sodium sulfur batteries. Batteries withhigher power ratings result in greater curtailment reduction, but also lower maximum viable costs. Sizingthe battery to reduce a small portion of curtailment allows for higher utilization of the storage andsupports higher cost batteries. Using energy storage to increase wind installed capacity can also beeconomically viable, but at costs lower than those for curtailment reduction. The results were mostsensitive to the elimination of wind subsidies, the installed cost of transmission, battery efficiencydegradation, and battery cycle life. The study did not show economic viability for the use of energystorage to reduce transmission voltage class.

2014 Elsevier Ltd. All rights reserved.1. Introduction

The highest quality onshore wind resources are often located farfrom load centers and a significant amount of new transmissionwill be needed to support high penetrations of wind energy [1].Minimizing the cost to deliver remote wind is essential for thistechnology to continue to compete with other renewables andwith traditional generation. Energy storage co-located with thewind resource can reduce curtailment, increase transmission lineutilization, allow for lower voltage lines to be used, and, poten-tially, decrease the delivered cost of energy. The cost of energystorage is currently too high to justify widespread deploymentfor this purpose. The goal of this paper is to quantify the reductionin curtailment under various energy storage configurations anddetermine target costs for grid-scale energy storage that improvesdeliverability or reduces costs of transmission-constrained wind.To do so, this study assumes that the delivered wind is under con-tract via a power purchase agreement, with contract prices basedon the delivered cost of energy (i.e., inclusive of wind and trans-mission). This analysis is useful to set cost targets for grid-scale en-ergy storage and illustrate the configuration and size of batteriesnecessary to reduce curtailment or increase the deliverability of re-mote wind. The analysis does not target specific types of energystorage, but intends to inform the discussion on the potential roleof energy storage for transmission-constrained wind.

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378 J.X. Johnson et al. / Applied Energy 124 (2014) 3773881.1. Delivering wind

Wind generation is a mature technology over 13 GW of newinstalled capacity was added in the U.S. in 2012, bringing the totalinstalled wind capacity to 60 GW [2]. Global installations now ex-ceed 280 GW [3]. The highest quality wind resources are often re-mote and lack access to transmission to bring it to market. Whenplanning for wind development, one must consider the economictradeoff between developing lower quality local resources or build-ing transmission to access distant, but higher quality, wind re-sources. Wind output is variable and the average project capacityfactors are 33% across the large sample of projects examined byLawrence Berkeley National Labs, with very few projects achievingcapacity factors greater than 50% [4]. Accessing remote wind withdedicated transmission forces a trade-off between building wind inexcess of the available transmission capacity (resulting in curtail-ment) and maintaining transmission with low utilization.

The two main drivers for wind curtailment are inadequatetransmission capacity and the ability of conventional generatorsto vary output, particularly during off-peak hours [5]. In recentyears, forced curtailment of wind has significantly reduced totaldelivered wind energy. In 2009, 17% of potential wind generationwas curtailed in ERCOT, the grid operator in Texas. This droppedto 8.5% in 2011, due in part to a new transmission line linkingthe West zone with the South [4]. While the ERCOT region hasencountered some of the most significant wind curtailment, otherregions face non-trivial levels; in 2011, 3% of potential wind gener-ation in the Midwest ISO (less Northern States Power) was cur-tailed in 2011 [4].

Options to reduce wind curtailment and increase wind deliver-ability include increasing transmission loadability, increasing loadat the wind site, increasing the diversity of the wind resource, andadding energy storage. Increasing transmission capacity beyondthe cost-optimal level will result in the rising delivered cost ofwind unless the excess transmission capacity is used to carry other,non-wind generation. Increasing the load at the wind site is notwithin the influence of wind developers; while low cost energyfrom wind may attract industry, this is not typically a planningobjective for developers. Increasing the diversity of wind resourcecan result in a flatter, less variable wind shape, which in turnwould lead to higher transmission line utilization. This is withinthe ability of transmission developers to influence, but one mustconsider the additional cost of spur transmission lines to reachprojects in multiple wind regimes. Energy storage offers the poten-tial to flatten the wind generation shape, reducing curtailment andincreasing transmission line utilization. This study examines thisoption using energy storage for transmission-constrained wind to assess the cost targets needed to achieve viability.

1.2. Grid-scale energy storage for wind

With the exception of several dozen pumped storage hydrofacilities, there are few grid-scale energy storage facilities in cur-rent operation. In 2010, the Electric Power Research Institute(EPRI) estimated that there is 127,000 MW of global pumped hydrocapacity, dwarfing 440 MW of compressed air energy storage(CAES), and approximately 400 MW of batteries [6]. Despite thelack of wide-spread adoption, there is recognition of the varietyof potential applications for large scale energy storage, includingproviding balancing services to accommodate variable renewables,energy arbitrage to reduce peak prices and manage congestion,load following, deferring transmission and distribution invest-ment, and improving power quality and reliability.

Major studies, including those by the Pacific NorthwestNational Laboratory [7], Sandia National Laboratory [8], and theEPRI [6], have evaluated the market potential and value of variousapplications for energy storage. Denholm and Sioshansi found thatco-location of energy storage and transmission-constrained windallows for more efficient use of the winds transmission capacity,but also subjects the energy storage to line losses and limits itsability to maximize revenues on the grid [9]. The findings showthat reducing transmission capacity by co-locating energy storagewith wind would be economically justified for a significant numberof projects based on recent costs for transmission.

In an examination of the ERCOT market, Denholm and Handfound that greatly increasing the flexibility of traditional genera-tion could allow penetration of wind and solar up to 50% with cur-tailment rates less than 10%. To achieve 80% penetration, loadshifting and storage equal to one day of average demand is needed[10]. Fertig and Apt also examined the ERCOT region to assess com-pressed air energy storage (CAES) integration at specific sites usinga multiparameter optimization of wind, CAES, transmission, anddispatch. They found that a baseload CAES/wind system is lessprofitable than a natural gas combined cycle under most scenarios[11]. Greenblatt et al. also examined the competition between nat-ural gas combined cycles and CAES to make baseload wind [12].Their findings suggested that high natural gas prices (>$9/GJ) orhigh carbon prices ($35/tCeq) would be necessary for CAES to bea competitive option. DeCarolis and Keith demonstrated thatincreasing wind diversity through spatial distribution of sites pro-vides benefits in excess of the costs of additional transmissioninfrastructure and there is a trade-off between wind site diversityand storage [13]. Succar et al. developed a model to jointly opti-mize the wind turbine specific rating and CAES configuration usinga levelized cost of energy approach, and found that such an optimi-zation would decrease the baseload plants storage capacity anddecrease greenhouse gas emissions [14]. Madlener and Latzexamined a wind and CAES system using a profit-maximizingalgorithm and found that centralized storage performed betterthan integrated storage [15].1.3. Objectives

This study examines the potential of grid-scale energy storageto reduce the delivered cost of remote, transmission-constrainedwind. This study is novel because it assumes that the wind is undera power purchase agreement (PPA), as opposed to receiving marketenergy prices. In 2011, 51% of new U.S. wind development wasunder a PPA and 25% was utility owned, while only 21% wasmerchant or quasi-merchant [4]. That implies that three-quartersof new wind (i.e., PPA and utility-owned) was likely priced on adelivered cost of energy basis, while a far smaller fraction receivedmarket energy rates. Another differentiator is that this studyexamines the AC transmission development considering multiplevoltage classes. Most comparable studies conducted to dateassume DC transmission despite the fact that the vast majority oftransmission is AC in the U.S.2. Methods

In this analysis, we develop a constrained optimization problemto minimize the delivered cost of energy of a wind and transmis-sion system which represents the cost of delivered energy for aPPA-based project. These optimizations are conducted in a VisualBasic model that maintains the chronological nature of the windgeneration data and the associated behavior of energy storageand deconstructs the delivered costs into three elements: therevenue requirement for the wind, the revenue requirement forthe transmission, and the amount of delivered wind after account-ing for curtailment and line losses. The approach taken for each ofthese elements is discussed in Sections 2.2.12.2.3, respectively.

J.X. Johnson et al. / Applied Energy 124 (2014) 377388 379After minimizing the cost of delivered wind, we then introducebatteries in varying configurations to determine the breakevenbattery cost (i.e., the battery cost below which would decreasethe delivered cost of energy) for three applications: reducing cur-tailment, reducing the transmission voltage class, and increasingthe wind installed capacity. With base case assumptions, the deliv-ered cost of energy is constant across all hours (i.e., the PPA isstructured to value all hours equally). A time of day contract whichvaries the cost for on-peak and off-peak hours is also examined, inaddition to a sensitivity analysis on several key assumptions.Fig. 2. Wind durations curves for four selected sites.2.1. Scenario description

Four hypothetical transmission lines are represented, selectedto provide a variety of wind resource quality and transmission dis-tance, as shown in Fig. 1. Line A represents a 500 mile transmissionline connecting west Iowa wind with the Chicago area market,while Line B is a 100 mile transmission line interconnecting theMinneapolis area with wind resources in southern Minnesota. LineC connects upstate New York to the metro New York City area (300miles) and Line D connects Maine with Boston area load (260miles). The transmission line length is 40% higher than thestraight-line distance between the points, to allow for the trans-mission path to avoid difficult terrain and populated areas. SitesA and B were developed with a range of 0 MW to 1000 MW ofwind, Site C has between 0 MW and 700 MW, and Site D has be-tween 0 MW and 600 MW. These ranges of potential developablewind were selected to provide illustrative examples of a varietyof wind-transmission scenarios. In each case, the theoretical windresource exceeds these limits.2.2. Determining the power purchase agreement price by cost-minimizing a wind-transmission system

2.2.1. Calculating the revenue requirements for windWind speed data for each site, at ten minute intervals and 80 m

hub height, are from National Renewable Energy Labs EasternWind Dataset [16]. A wind power curve representative of a con-temporary GE 2.5 MW wind turbine (IEC Class II) was employedto determine generation as a function of wind speed. An outagerate of 4% was applied randomly across all time intervals.

Fig. 2 shows the wind duration curves, representing one year ofhourly wind generation at each site, sorted in descending order.The capacity factor at Site A is 51%, Site B is 46%, Site C is 43%,and Site D is 35% (prior to including the impact of transmissionlosses and curtailment). The shape of these curves determine thelevel of curtailment at a given transmission capacity.

The annual revenue requirement needed to support wind ineach scenario is determined by levelizing the project costs overFig. 1. Map of four scenarios. Wind map adapted from the National RenewableEnergy Laboratory.the project life based on the assumption that the discountedproject costs would equal the discounted revenue requirement(and thus the PPA terms) over the project life, as shown inEq. (1) and following the approach described in CBO, 2008 [17].

XT

t01 rWACCt RRwind;t

XT

t01 rWACCt Cwind;t 1

where rWACC equals the weighted average cost of capital, RRwind;t isthe revenue requirement for the wind project in year t in $, andCwind;t is the cost of the wind project in year t in $.

The costs for each project are evaluated twice: once with theproduction tax credit (PTC) which is a subsidy for the first ten yearsof operation and is a function of generation (as shown in Eq. (2)),and once with the investment tax credit (ITC) which provides asubsidy as a function of installed cost (as shown in Eq. (3)). Thelower cost option is selected.

Cwind;t rdebt Bdebt;t requity Bequity;t PTCt CFt 8760 h=yr Incomet Intt Dept rincome tax Taxproperty;t Inst FOMt CAPwind 2

where

Bdebt;0 Covernight 1 AFUDC /debt

Bequity;0 Covernight 1 AFUDC /equity

Cwind;t rdebt Bdebt;t requity Bequity;t Incomet Intt Dept rincome tax Taxproperty;t Inst FOMt CAPwind 3

where

Bdebt;0 Covernight 1 AFUDC /debt 1 ITC bITC

Bequity;0 Covernight 1 AFUDC /equity 1 ITC bITC

where rdebt is the interest rate on debt, Bdebt,t is the balance of debt inyear t in $, requity is the nominal return on equity, Bequity,t is the bal-ance of equity in $/MW, PTCt is the value of the Production Tax Cred-it in $/MWh, CFt is the capacity factor of the wind project in %, Incometis the project income in $/MW, Intt is the interest paid in $/MW,Dept is the depreciation expense in $/MW (with both evaluationsincluding bonus and accelerated depreciation), rincome tax is the totalincome tax rate (with the federal rate not paid on the value of statetax collections), Taxproperty,t is the property tax in $/MW, Inst is thecost of insurance in $/MW, FOMt is fixed operations and mainte-nance costs in $/MW, CAPwind is the installed capacity of the windproject in MW, Covernight are the overnight costs of the wind projectin $/MW, AFUDC is the allowance for funds used during construc-tion in % of overnight costs, /debt and /equity are the share of projectcosts paid by debt and equity, ITC is value of the Investment Tax

380 J.X. Johnson et al. / Applied Energy 124 (2014) 377388Credit as a % of installed costs, and bITC is the share of installed costseligible to receive the ITC.

Table 1 provides a summary of the assumptions used to deter-mine the cost of wind.2.2.2. Calculating the revenue requirements for transmissionThis study includes six AC transmission line voltage classes:

115 kV, 230 kV, 345 kV, 345 kV double circuit, 500 kV, and765 kV. Table 2 provides a summary of the cost assumptions usedfor new AC transmission by voltage class. It is recognized thattransmission costs vary greatly from project to project. These costsare representative of line paths dominated by non-mountainous,lowly populated terrain. More challenging terrain would quicklyescalate project costs, as is tested in the sensitivity analysis.Assumptions for taxes, insurance, inflation, and the cost of capitalare consistent with the assumptions used for wind, provided inTable 1Wind Assumptions.

Site A Site B Site C Site D

Cost assumptionsa

Overnight capital cost ($/kW) 2099 2099 2300 2521Fixed O&M ($/kW-yr) 27.2 27.2 29.8 32.7Variable O&M ($/MW h) Allowance for funds during construction 3% 3% 3% 3%

Tax and insurance assumptionsb

State tax 5.0%Fed tax 35.0%Tax rate (exc. property tax) 38.3%Property tax 1.0%Insurance 1.0%

Cost of capital assumptionsc

Nominal return on equity 14.0%Percent equity 30.0%Interest rate on debt 6.0%Life of debt 20Weighted average cost of capital 6.8%

Inflation assumptiond

Inflation (%/yr) 2.0%

Depreciation assumptionse

5-Year MACRS (% of installed cost) 45.0%20-YrMACRS (% of installed cost) 2.5%No MACRS (% of installed cost) 2.5%Bonus deprecitation (% of installed cost) 50.0%

Tax credit assumptionsf

Production tax credit ($/kW h) 0.022Investment tax credit (% of installed cost) 30%Share of installed cost covered under ITC (%) 95%ITC Value that is depreciable (%) 50%

a Installed cost assumptions are based on Wind Technologies Market Report,selected for each region [4]. All O&M costs are treated as fixed costs (i.e., inde-pendent of generation levels) and escalate at the rate of inflation. O&M costs do notinclude property tax or insurance, which are included separately. Allowance forfunds used during construction is consistent with construction financing costs inTegan et al. [18].

b Tax and insurance rates are estimated. Property tax and insurance costs escalateat the rate of inflation.

c The debt to equity ratio was estimated based on the amount of secured debt for4000 MW of wind [4]. Debt rates under 6% are noted in the same reference.

d Estimate.e Bonus depreciation was extended in American Taxpayer Relief Act of 2012.

Accelerated (MACRS) depreciation is allowed under 26 USC 48(a)(3)(A). The shareof installed cost that is eligible for 5-year depreciation (after bonus depreciation) isbased on Bolinger et al. [19].

f Wind projects are eligible for either the federal production tax credit (PTC) orthe investment tax credit (ITC). The PTC and ITC were renewed in January 2013under the American Taxpayer Relief Act of 2012. The share of installed costs thatqualify for the ITC is from Bolinger et al. [19]. The Internal Revenue Service allowshalf of the value of the ITC to be depreciable.Table 1. Straight line depreciation was employed over a 30-yearhorizon and a 30-year life of debt was assumed. Based on the costassumptions employed, the annual revenue requirements fortransmission were determined following a formula analogous toEq. (1).

2.2.3. Calculating the quantity of delivered windWe assessed AC line power carrying capability using St. Clair

curves, a method developed to provide a universal approach toquantifying limits of the load carrying ability of a transmission line(loadability) for various line lengths and voltage classes [23].Dunlop et al. subsequently developed the analytical basis for theSt. Clair curve and expanded its use to higher voltages [24]. St. Claircurves represent the thermal, voltage, and stability limits for trans-mission lines based on their surge impedance loading (SIL) and arecommonly used for transmission planning. Thermal limits deter-mine loadability below approximately 50 miles, voltage limitsare binding between approximately 50 and 190 miles, and stabilitylimits are binding for lines longer than approximately 190 miles. Inthis study, only lines longer than 50 miles were examined. A 300mile line has a loadability of 1.0 SIL, regardless of the voltage class.Loadability is calculated as the product of the line loadability inper unit of SIL for a given distance and the SIL for the relevantvoltage class (Table 3).

Similar to Newcomer and Apt [22], line losses were modeled asresistive, varying by the electricity generated, conductor resis-tance, line length, and voltage class, as shown in Eq. (4):

Loss % Q r dV2

4

where Q is the wind production at a given time in MW, r is theresistance in ohm/mile, d is the distance in miles, and V is voltageclass of the line in kV. Assumptions for resistance are provided inTable 3.

2.2.4. Minimizing the cost of delivered energyBased on the assumptions and calculations for line loadability,

wind cost, wind shape, and transmission cost, the minimized costof delivered wind (Cdelivered) is calculated using Eq. (5).

Cdelivered RRwind RRTXP52;560

t1 Qt h Xt 1 Lt5

where RRwind and RRTX are the annual revenue requirements forwind and transmission in $, Q is wind production (MW), h is time(hours), X is the energy lost to curtailment (MWh), and L representsthe transmission loss rate (%), summed over all time intervals t forthe year (there is 52,560 ten-minute time intervals in a non-leapyear). The minimized delivered energy cost is bounded by the max-imum installed wind capacity and solved using the site-specific linedistance and wind shape, coupled with cost assumptions providedin Tables 1 and 2. Delivered costs are calculated for each of thesix voltage classes. The minimized cost determines the lowest costcombination of wind capacity and voltage class and represents thetarget value of a signed PPA with a load serving entity. The effectiveintroduction of energy storage to the wind-transmission systemshould result in lower delivered costs or more wind delivered atthe same cost.

2.3. Determining the breakeven cost for energy storage integrationinto wind-transmission system

For each scenario, we assessed the opportunity to introduce en-ergy storage into the wind-transmission system for three applica-tions: (1) mitigation of curtailment, (2) reduction of transmissionvoltage class, and (3) increasing the wind installed capacity. For

Table 2Transmission cost assumptions.

115 kV 230 kV 345 kV 345 kV 2 circuit 500 kV 765 kV

Cost assumptionsLine ($000/mile)a 483 927 1298 2077 1854 3060Station ($M)b

Less than 300 miles 2.7 12 32 61 65 148300480 miles 2.7 14 38 71 79 175More than 480 miles 2.7 15 42 79 90 200

Allowance for funds during construction and overheadc 17.5% 17.5% 17.5% 17.5% 17.5% 17.5%Fixed O&M (% of installed cost)d 3% 3% 3% 3% 3% 3%

a Costs for 115 kV project based on project proposal estimates. Transmission line costs for 230 kV, 345 kV, and 500 kV are based on Black & Veatch analysis [20]. Costs for765 kV are based on selected projects detailed in Mills et al. and escalated to current dollars [21].

b Station costs are based on the same references in footnote a, following the approach employed by Newcomer and Apt [22].c Based on NREL review [18].d Estimate.

Table 3Transmission loadability and loss assumptions voltage class.

115 kV 230 kV 345 kV 500 kV 765 kV

SILa MW per unit 35 140 420 1000 2280Resistanceb ohm/mi 0.24 0.07 0.048 0.024 0.012

a The surge impedance loading for each voltage class is representative of typicalassumptions for 60-Hz overhead lines [25].

b Line resistance can vary greatly within a voltage class. The assumed values areconsistent with the weighted averages for U.S. transmission lines by voltage class,as published in Kappenman (2010) [26].

J.X. Johnson et al. / Applied Energy 124 (2014) 377388 381each application in each scenario, the breakeven battery costs weredetermined for a series of battery power ratings and battery energyto power ratios.2.3.1. Batteries to mitigate curtailmentTo determine the amount of curtailment that can be mitigated

and the value provided by energy storage, the following approachis used:

Pcharge;t Qt CAPTX ;bounded by the requirements thatPcharge;t 6 Pbatt;t ; SOCt 6 1:00 6

where Pcharge,t is the charge rate for the battery at time t in MW, Qt isthe wind output in MW, CAPTX is the transmission line loadability inMW, Pbatt,t is the batterys rated power in MW at time t, SOCt is thebatterys state of charge as a percentage of the total storagecapacity.

Pdischarge;t CAPTX Qt ; bounded by the requirements thatPdischarge;t 6 Pbatt;t ; SOCi P 0; Pdischarge;t Qt 6 CAPTX 7

where Pdischarge is the discharge rate for the battery in MW.The initial state of charge, SOC0, is assumed to be 0.50 and the

roundtrip cycle efficiency, gt, is assumed to be 0.75 (but is testedin the sensitivity analysis). The state of charge at a given time isdetermined by:

SOCt1 SOCt Pcharge;t t gt Pdischarge;t t; such that0 6 SOCi1 6 1:00 8

The reduction in curtailment by the battery is assumed to be thedifference in curtailment with and without the battery plus anydifference between the initial and final state of charge. The addi-tional energy delivered by reducing curtailment is assumed to havethe same value as the cost-minimized delivered energy before theintroduction of the battery. These additional revenues are used todetermine the maximum cost of the battery, taking into accountthe cycle life.The base case assumption for battery life is the equivalent of2000 cycles and maintenance efforts eliminate battery roundtripefficiency, storage capacity, and rated power degradation over time,consistent with approaches employed in other studies (e.g., [6]).While the design of this model is intended to represent genericgrid-scale energy storage, these base case assumptions for batterylife and degradation are more representative of compressed air en-ergy storage or redox flow batteries with periodic cell stack replace-ment [27]. With redox flow batteries, design can minimizedegradation of electrode surface and the storage capacity degrada-tion can be mitigated by using electrolytes with different oxidationstates of the same element (e.g., vanadium) so that crossover wouldnot irreversibly consume the electrolytes [28]. Such assumptions ofmitigating storage capacity fade would not be appropriate for tech-nologies such as lithium ion batteries. To better understand the im-pacts of alternative battery technology options, these assumptions(cycle life, roundtrip efficiency degradation, and storage capacityfade) are tested in the sensitivity analysis.

For each battery configuration, the annual number of cycles isused to determine battery life, which is used to calculate theannual carrying cost as a percentage of installed battery cost. Amaximum lifetime of 20 years is assumed. Given that the modelrepresents generic grid-scale energy storage, the number ofcycles or maximum years in service determines the storage life.Thus, the effect of usage patterns such as the rates and durationsof charging and discharging are not directly included in the model,but the sensitivities on cycle life and degradation can inform howvarious usage patterns would impact the results of this study.

The maximum cost of the battery is determined for a range ofbattery designs, varying the battery power and energy storage asfollows:

Range of Pbatt 0 to CAPwind CAPTX

Range of Storage Capacity Pbatt t; with range of t from10 min to 10 h

We assume that the ramp rate is not binding constraint. Addi-tionally, the battery allows for full depth of discharge, which is arealistic assumption for some energy storage technologies (e.g.,vanadium redox flow batteries [6]). With technologies for whicha lower depth of discharge should or must be used (e.g., sodiumsulfur batteries, for which EPRI assumes a 90% depth of discharge[6]), the allowable cost targets for the energy storage woulddecrease accordingly.

2.3.2. Batteries to reduce transmission voltage classIn addition to reducing curtailment, batteries could be inte-

grated into a wind-transmission system to allow for the use of alower, less expensive voltage class for the transmission. To assess

Fig. 3. Wind curtailment and transmission loadability.

382 J.X. Johnson et al. / Applied Energy 124 (2014) 377388if energy storage could be used to reduce the transmission voltageclass, the cost minimized results determined in Section 2.2.4 areemployed. The installed wind capacity is applied to a transmissionsystem with a lower voltage class, coupled with energy storage.Only battery configurations that result in a lower delivered costare viable options to reduce transmission voltage class.

2.3.3. Batteries to increase wind installed transmission capacityThe introduction of energy storage to support increasing wind

capacity is also examined. Based on the results determined in Sec-tion 2.2.4, additional wind capacity in added in 20 MW increments.For each increment, battery configurations are tested to determineif the additional wind could be incorporated within increasing thedelivered energy costs.

2.4. Sensitivity analysis

A sensitivity analysis is conducted for Case A to determine theimpact of key assumptions. Case A was selected because it offeredthe most promising (i.e., highest) results to support grid-scaleenergy storage.

2.4.1. Sensitivity to time-of-day pricingBase case assumptions assume a flat PPA price for delivered

wind, irrespective of the time of day of generation. A time of dayPPA scenario is conducted to determine the impact of structuringa PPA with on-peak and off-peak pricing. As shown in Eqs. (9)and (10), the off-peak PPA price (Cdel;off ) and on-peak PPA price(Cdel;on) are calculated such that the average price received matchesthe minimized cost of delivered energy (Cdelivered), as described inSection 2.2.4, and the difference between the off-peak and on-peakPPA price is equal to the difference between the historical annualaverage off-peak and on-peak locational marginal price at the pointof delivery (LMPoff; LMPon).

Cdelivered X52;560

t1

Cdel;off Qt;off Cdel;on Qt;onQt;off Qt;on

9

Cdel;on Cdel;off LMPon LMPoff 10

On-peak hours are assumed to be between 8:00 am and 12:00am on weekdays. The difference between on-peak and off-peakrates is insufficient to support energy arbitrage with the assumedroundtrip charging cycle losses. The approach to battery dischargemaximizes revenues by optimally delaying discharge until on-peakhours, assuming a perfect wind forecast is available.

2.4.2. Sensitivity to key parametersFor the base case scenario, the sensitivity of the results to

curtailment reduction and maximum battery costs for sevenassumptions were tested:

1. Wind installed cost was tested at 20% above and 20% belowbase case assumptions. This yields a range of overnight capitalcosts from $1,679/kW to $2,519/kW for Site A, which coversmuch of the range of individual project costs detailed inWiser and Bolinger (2012) [4].

2. Transmission installed cost was also tested. A sensitivity at 20%below base case assumptions was conducted to illustratepotential economies of scale or lower commodity prices. A highsensitivity was created that illustrates the impact of transmis-sion development through more difficult terrain and more pop-ulated areas. Using the same Black & Veatch source for data[20], the transmission costs are assumed to increase by 28%over the base case based on the following assumed terrain:25% hills, 20% suburban development, and 10% forested land.3. Given their significant value, the impact of expiration of federalwind subsidies (i.e., the PTC and ITC) were tested.

4. Battery cycle life was tested at 1000 cycles and 5000 cycles,intended to represent the impact of different usage patternsand technology choices on the results.

5. Financing costs can vary considerably from year to year and,given the large capital investments required for these projects,can significantly influence the delivered costs of energy. Sensi-tivities were tested at 20% above and below base case financingcosts to provide context on the magnitude and direction of theimpacts.

6. Because this analysis does not assume a specific technology isproviding the energy storage, a base case assumption of 75%round trip efficiency is assumed. Actual energy storage applica-tions can achieve higher and lower results, so a sensitivityanalysis was conducted to test the impact of 60% and 90% roundtrip efficiencies.

7. Battery roundtrip efficiency degradation was tested with 2%and 5% roundtrip efficiency decreases per year.

8. Energy storage capacity fade was tested based on assumptionsappropriate for two lithium-based batteries. Lithium iron phos-phate batteries have been found to experience capacity fade at arate of approximately 0.3% per 100 accumulated dischargecycles under charging patterns typical for wind generation,while lithium cobalt oxide-nickel manganese composite batter-ies show capacity fade at a rate of 1.5% per 100 accumulateddischarge cycles [29]. A linear relationship between capacityfade and accumulated discharge cycles is assumed, which iswell reflected in the results of Krieger et al. (2013).

The sensitivity analysis was conducted by minimizing the deliv-ered cost of energy without storage (as described in Section 2.2)using the new assumptions and then determining the break-evencost of introducing energy storage (as described in Section 2.3).These new assumptions will yield different wind installed capaci-ties, transmission voltage classes, and break-even storage costs,when compared to the base case.3. Results

3.1. Determining the power purchase agreement price

The shape of the wind duration curves, as shown in Fig. 2, deter-mine the amount of wind curtailed for given transmission loadabil-ities. Fig. 3 shows the relationship between wind curtailment andthe ratio of wind installed capacity and transmission loadability.While the differences between the scenarios may appear modest,small differences in curtailment can greatly affect the viability ofwind projects. Case B (Minnesota wind) has a flatter generation

J.X. Johnson et al. / Applied Energy 124 (2014) 377388 383profile, resulting in lower curtailment rates than other sites withlower capacity factors.

Fig. 4 shows the cost-minimized results for each of the fourscenarios, with the left side charts showing all of the voltageclasses that were examined and the right side charts showing onlythe optimal voltage class for the transmission. Fig. 4a shows thatCase A (Iowa wind) is optimized with 809 MW of wind on a500 kV line, resulting in 6.5% curtailment, 46.4% effective capacityFig. 4. Minimized cost of delivered wind for (a and b) Site A Iowa wind; (c and d) Sitewind. Left side graphs = all voltage classes; right side graphs = only the optimal voltagefactor, and a PPA price for delivered energy of $118.12/MW h.This case demonstrates the value of allowing some curtailmentin order to achieve higher line utilization on long or costly trans-mission lines. Fig. 4b shows that increasing the wind capacityserves to increase the delivered cost of wind due to curtailmentand, to a lesser extent, increasing transmission loss rates, while itdecreases the unit cost of transmission by more fully utilizingthe line.B Minnesota wind; (e and f) Site C New York wind; and (g and h) Site D Maineclass for transmission.

384 J.X. Johnson et al. / Applied Energy 124 (2014) 377388Fig. 4c and d show that Case B (Minnesota wind) is optimizedwith 861 MW of wind on a 345 kV line, resulting in no curtailment,44.8% effective capacity factor, and a PPA price for delivered energyof $69.29/MW h. This case demonstrates the value of eliminatingcurtailment for short transmission distances, where transmissioncosts area a smaller share of total costs. As shown in Fig. 4e and4f, Case C (New York wind) is optimized with 700 MW of windon a 500 kV line, resulting in no curtailment, 41.9% effective capac-ity factor, and a PPA price for delivered energy of $118.45/MW h.This case demonstrates that building a higher voltage line evenwhen there is insufficient wind for maximum loadability can stillproduce the most cost effective outcome. Fig. 4g and h show CaseD (Maine wind) is optimized with 492 MW of wind on a 345 kVline, resulting in 1.7% curtailment, 33.4% effective capacity factor,and a PPA price for delivered energy of $146.77/MW h. This casedemonstrates that some curtailment may be optimal even withlower wind quality (as compared to Case A).

These results set the target prices for the delivered cost of en-ergy, representative of a PPA. The introduction of energy storageto each of these systems should either increase deliverability ofwind at the same cost or decrease delivered energy costs.

3.2. Assessing batteries to mitigate wind curtailment

Of the four sites examined, the optimized wind-transmissionsystems for only Sites A and D resulted in wind curtailment.Optimized Site A (Iowa wind) resulted in 235,000 MW h of windcurtailment per year before incorporating energy storage, whileSite D (Maine wind) resulted in 26,500 MWh of wind curtailmentbefore storage. Based on the PPA prices identified in Section 3.1,this represents lost revenues of $28 million and $3.9 million peryear, respectively. Fig. 5 shows the reduction in curtailment foreach of these sites upon introduction of energy storage as a func-tion of energy storage power rating and storage capacity.

The width of the charts in Fig. 5 show that battery power ratingswere examined up to the difference between wind capacity andtransmission loadability (129 MW for Case A, 30 MW for Case D).Energy storage capacities were examined from 10 min to 10 h.Generally, a relative increase in energy storage capacity resultedin greater mitigation of curtailment than a comparably scaledincrease in battery power. It is important to note that largestbatteries examined (i.e., ones with 100% of needed power outputand 10 h of storage) still did not eliminate all of the wind curtail-ment. For Case A, 55% of the curtailment was eliminated, whilefor Case D, 61% was eliminated using this battery configuration.

The results of the curtailment reduction were used to calculatethe maximum battery cost, based on the assumption that the addi-tional energy would receive the same PPA price and the batteryslifetime would be 2000 cycles (up to 20 years). Fig. 6 shows theseresults in both cost per rated power ($/kW) and cost per unit ofFig. 5. Annual reduction in wind curtailment with batteries of varying power and storagand 100% of curtailment equals 235,000 MW h) and (b) Site D Maine wind (where 10energy storage ($/MW h). The maximum cost can be determinedusing either convention; the results are not intended to be additive.

As shown in Fig. 6a, batteries for curtailment at Site A could beviable with installed costs as high as $603/kW if backed with tenhours of storage at maximum power, $366/kW with four hoursof storage, or $132/kW with one hour of storage. With a lowerpower rating, the maximum battery costs increase to values ashigh as $780/kW. Assessing the installed cost as a function of stor-age capacity (Fig. 6b) shows that with small amounts of storage,the installed cost can be as high as $180,000/MWh of storage. Withone hour of storage, costs are viable up to $149,000/MWh of stor-age, dropping to $77,000/MW h with ten hours of storage. (Notethat the axis for Fig. 6b and d are reversed to allow for easierviewing.)

For Site D, battery costs to support curtailment reduction can beup to $353/kW with ten hours of storage at maximum power rat-ing, $244/kW with four hours of storage, and $108/kW with onehour of storage (Fig. 6c). As a function of storage capacity, costsup to $172,000/MW h of storage can be supported for batterieswith ten-minutes of storage capacity, dropping to $43,000/MW hfor batteries with ten hours of storage capacity.3.3. Assessing batteries to reduce transmission voltage class

For three of the scenarios (A, B, and D), dropping to the nextlower voltage class while maintaining wind installed capacitywould represent a major increase in the delivered cost of wind,as much as 100% over the optimized cost. These large increasesin installed costs are driven primarily by reduced line loadability,resulting in significant increases curtailment and reductions inthe amount of delivered electricity. For Site C (NY), dropping from500 kV to 345 kV transmission, before introducing energy storage,increases the delivered cost of wind by 21%. This smaller increase isbecause the cost minimized system with the 500 kV line had sig-nificant excess transmission capacity and dropping to the lowervoltage line would cause a more modest amount of curtailment.Therefore, Site C was examined to test the viability of introducingenergy storage to reduce voltage class.

Even for very large batteries (289 MW with 2890 MW h of stor-age capacity), the ability of the battery to flatten the wind shapewas insufficient to decrease the delivered cost of wind on the345 kV system below the costs found using 500 kV line. This sug-gests that, for the scenarios examined, batteries at no cost wouldstill not be beneficial for use to decrease voltage class. These sce-narios do not paint a comprehensive picture given that more trans-mission design alternatives could be examined, but suggest thatusing batteries for this purpose may only be appropriate in veryspecific situations. In addition, building transmission with lowerloadability reduces the potential for greater use in the future.e capacity for (a) Site A Iowa wind (where 100% of battery power equals 129 MW0% of battery power equals 30 MW and 100% of curtailment equals 26,500 MW h).

Fig. 6. Maximum installed battery cost for Site A Iowa wind (a) per power rating and (b) per energy storage capacity (where 100% of battery power equals 129 MW); and forSite D Maine wind (c) per power rating and (d) per energy storage capacity (where 100% of battery power equals 30 MW).

J.X. Johnson et al. / Applied Energy 124 (2014) 377388 3853.4. Assessing batteries to increase wind installed capacity

Coupling additional wind (beyond the optimized level) with en-ergy storage can produce economically viable results. Fig. 7 showsthe maximum cost of energy storage to incorporate more windwith one hour of energy storage capacity for Sites A and D, andten hours of energy storage capacity for Sites A, B, and D. (Site Bdid not produce positive results with one hour of storage. Basedon the available developable wind resource assumptions provideddescribed in Section 2.1, Site C had developed all available wind.)When integrating additional wind, the maximum cost of energystorage is lower than the costs that can be supported for curtail-ment reduction.

3.5. Sensitivities

A sensitivity analysis was conducted to test the results of max-imum battery costs for curtailment reduction at Site A with tenhours of energy storage capacity on a 10 MW battery. Site A wasselected for the sensitivity analysis because the base case resultsfor this site proved to be the most promising for energy storage,allowing for more expensive energy storage options than the othersites that were examined. Base case assumptions yielded a maxi-mum battery cost of $778/kW, and as shown in Fig. 8, the sensitiv-ities selected result in a range of maximum battery costs from$403/kW to $915/kW.

The elimination of wind subsidies (i.e., the production taxcredit, investment tax credit, and accelerated depreciation) greatlyreduces the maximum acceptable battery cost. Without thesubsidies, the cost of wind increases and, in an optimizedwind-transmission system, less wind is built in order to reducecurtailment and achieve the lowest delivered energy cost. Thus,the potential for curtailment reduction via energy storage isreduced and the maximum battery cost decreases by 48%.

With subsidies in place, the sensitivity to the installed cost ofwind was tested. An increase in wind costs of 20% resulted in a2% increase in the maximum battery cost, while a 20% decreasein the installed cost of wind resulted in a 9% reduction in maxi-mum battery cost. The results were more sensitive to transmissioncosts, with a 28% increase in transmission costs increasing themaximum battery cost by 18%, while a 20% decrease in transmis-sion costs yielded a maximum battery cost 18% lower.

Increasing the financing costs for all investments (wind, trans-mission, and battery) by 20% increased the maximum battery costsby 9%. A decrease in financing costs of 20% reduced maximumbattery costs by 9%.

The base case assumed no battery efficiency degradation overtime. Assuming 2% degradation of roundtrip cycle efficiency peryear reduces the maximum battery cost by 10%, while a 5%degradation reduces maximum battery cost by 23%. The base caseround trip efficiency was 75%. Decreasing that to 60% dropped themaximum battery cost by 10%, while increasing the round tripefficiency increased the maximum battery cost by 7%. The impactof improving (or decreasing) the batterys efficiency is dampenedby the fact that the curtailed wind generation could not be, bydefinition, sold elsewhere and thus has no direct cost associatedwith its use. It is expected that energy storage which purchasesmarket energy to charge would be more sensitive to battery degra-dation and roundtrip cycle efficiency.

The effect of capacity fade was more modest. Using assump-tions appropriate for lithium iron phosphate batteries, which expe-rience only slight capacity fade, the maximum battery cost isreduced by only 2%. Under assumptions for lithium cobalt oxide-nickel manganese composite batteries, the maximum battery costis reduced by 5%.

Fig. 7. Maximum installed battery cost for increased wind capacity at Site A Iowa wind with one hour of storage (a and b); ten hours of storage (c and d); at Site B with tenhours of storage (e and f); at Site D with one hour of storage (g and h); ten hours of storage (i and j).

386 J.X. Johnson et al. / Applied Energy 124 (2014) 377388

Fig. 8. Results of sensitivity analysis for Site A (Iowa wind) with 10 MW battery and100 MW h of energy storage capacity. When low and high sensitivities are tested,the results of the first assumption listed are shown in blue (decrease in maximumcosts), while the results from the second assumption are shown in gray (increase inmaximum costs). (For interpretation of the references to colors in this figure legend,the reader is referred to the web version of this paper.)

J.X. Johnson et al. / Applied Energy 124 (2014) 377388 387A PPA with on-peak and off-peak pricing was examined for SiteA. Due to its point of delivery, the on-peak to off-peak energy pricedifference was based on the hourly locational marginal price forthe ComEd zone in PJM [30]. Based on 2012 data, average on-peakprices were $9.69/MW h higher than average off-peak prices. A PPAfor Site A that reflects this difference would offer $122.89/MW hfor delivered on-peak wind and $113.20/MW h for off-peak windin order to meet the revenue requirements for the wind andtransmission. Given a round trip battery efficiency of 75%, thisdifference is insufficient to justify time of day arbitrage (i.e., timeshifting to on-peak hours). Because the annual wind resource isnearly evenly divided between on-peak and off-peak generation,and the battery discharge is divided between on-peak and off-peakhours, the introduction of a time of day PPA has minimal impact onthe maximum battery price. A discharge strategy in which abattery maximizes revenues by optimally delaying the dischargeof some energy to on-peak hours, assuming perfect wind forecast,results in a trivial (0.1%) increase in revenues. This suggests thatthe need to incorporate wind forecasting errors is unnecessaryfor this analysis.4. Discussion

This analysis found that energy storage can be used to improvethe deliverability of transmission-constrained wind if ambitiouscost targets for energy storage are met. In instances where theoptimal wind-transmission system results in some wind curtail-ment, it was found that energy storage could be incorporated to re-duce curtailment at costs as high as $780/kW. Not surprisingly,higher delivered costs can support more expensive energy storage.Energy storage can also be introduced to facilitate the incorporationof additional wind, beyond the optimized installed capacity, but of-ten with lower energy storage cost targets. As the overbuild of windincreases, it becomes more difficult to cost effectively incorporateenergy storage. The results were most sensitive to the eliminationof wind subsidies, the installed cost of transmission, battery effi-ciency degradation, and battery cycle life. In the cases examined,energy storage was not a viable option to decrease transmissionvoltage class (and thus decrease transmission installed costs).

Researchers at Pacific Northwest National Labs summarizedcurrent capital costs for battery options [7]. Converting their re-sults to a system with ten hours of energy storage capacity, therange of costs in 2011 is $2600$4900/kW for sodium sulfurbatteries, $880$1170/kW for CAES, and $2700$3900/kW for re-dox flow batteries. The studys potential costs in 2020 would dropthese values to $1800$3300/kW, $530$1170/kW, and $1500$2700/kW, respectively. With the exception of CAES, none of thesevalues would be low enough for use with transmission-constrainedwind based on this studys results.

The PNNL findings are largely consistent with a 2010 EPRI studywhich evaluated electricity energy storage applications, costs, andbenefits, with current costs totaling $1,000/kW for CAES with 8 h ofstorage, $1,440$3700/kW for redox batteries (spanning severaltechnologies), and $31003300/kW for sodium sulfur batteries[6]. The study examined ten key applications, including Renew-ables Integration which provides time shifting, load, and ancillaryservices for grid integration. The present value target benefits fortransmission congestion relief were calculated as $368/kW, withhigh benefits reaching $1838/kW. The target and high benefitsfor renewable energy integration are $311/kW and $1555/kW,respectively.

Sandia National Laboratories identified eight potentially attrac-tive value propositions for grid-scale energy storage, which in-cluded renewables energy time-shift plus electric energy time-shift [8]. Based on a ten year battery life cycle, renewables energytime shift was demonstrated to have a benefit between $233/kWand $389/kW, with a potential across the U.S. of 37 GW. This valueis based on the time of day of energy prices and not due to trans-mission-constrained curtailment.

Based on current and near-term projections for the cost of en-ergy storage, current batteries are too costly to support curtailmentreduction or increased deliverability of transmission-constrainedwind. CAES may present the best opportunity to economicallyserve this role, but is constrained to geographically-appropriatesites. Viability for energy storage for these applications can beachieved through reductions in the installed costs, as well as otherhigh impact efforts such as increasing the cycle life, decreasing oreliminating degradation of performance, and improving roundtripcycle efficiency. This is generally consistent with Hittinger et al.findings that capital costs are consistently important, with effi-ciency and length of capital investment also be important for somestorage technologies [31].

Energy storage options must not only compete with these costtargets, but must also be more cost effective than other, non-stor-age options. Flexible, dispatchable generation at the wind site canbe used to better integrate wind and fully utilize transmissioncapacity. Increasing transmission loadability with new lines, sub-stations, or series capacitors are other potential alternatives to en-ergy storage. Increasing the diversity of the wind resource couldflatten the wind output and reduce costs, even in excess of thecost of any additional transmission.

This study relied on a PPA-based structure for the cost of deliv-ered energy, representative of roughly three-quarters of the windin the U.S., while other studies (e.g., [9]) have used wholesale elec-tricity prices. PPA prices for wind energy typically exceed marketenergy rates, but because of state-level renewable portfolio stan-dards which mandate the development of renewables, such ratesare paid by load serving entities to meet these obligations. Struc-turing the analysis in this way, as opposed to using market energyprices, captures the full cost of the wind and the value of therenewable attributes.

Future work that could augment the findings of this study in-clude expanding to other applications for energy storage, increasingthe number of transmission line designs considered, and testing theimpact of wind diversity on the need and value of energy storage.

Acknowledgements

This work was supported by the U.S. National Science Founda-tions Sustainable Energy Pathways program (Grant #1230236:Non-Aqueous Redox Flow Battery Chemistries for SustainableEnergy Storage).

388 J.X. Johnson et al. / Applied Energy 124 (2014) 377388Appendix A. Definition of variablesWeighted average cost of capital % rWACC

Wind revenue requirement $ RRwind

Annual cost of wind project $ Cwind

Interest rate on debt % rdebt

Balance of debt $/MW Bdebt

Return on equity % requity

Balance of equity $/MW Bequity

Value of Production Tax Credit $/MW h PTC

Capacity factor % CF

Project income $/MW-yr Income

Interest paid $/MW-yr Int

Depreciation expense $/MW-yr Dep

Total federal and state income

tax rate

% rincome taxProperty tax cost $/MW-yr Taxproperty

Insurance cost $/MW-yr Ins

Fixed operations and

maintenance costs

$/MW-yr FOMInstalled wind capacity MW CAPwind

Overnight costs of wind project $/MW Covernight

Allowance for funds used during

construction

% AFUDCShare of project costs debt % adebt

Share of project costs equity % aequity

Value of Investment Tax Credit % ITC

Share of installed costs eligible

for ITC

% bITCSIL MW perunitSILResistance Ohm/mile r

Loss % L

Wind production MW Q

Distance Miles d

Voltage class kV V

Delivered cost $/MW h Cdelivered

Delivered cost, off-peak hours $/MW h Cdel,off

Delivered cost, on-peak hours $/MW h Cdel,on

Locational marginal price at

delivery, off-peak hours

$/MW h LMPoffLocational marginal price atdelivery, on-peak hours$/MW h LMPonTransmission revenuerequirement$ RRTXCurtailment MWh X

Battery charge rate MW Pcharge

Transmission line loadability MW CAPTX

Battery rated power MW Pbatt

State of charge % SOC

Battery discharge rate MW Pdischarge

Roundtrip cycle efficiency % g

Battery installed cost $/kW Cbattery,power$/MW-h Cbattery,storageReferences

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Assessment of energy storage for transmission-constrained wind1 Introduction1.1 Delivering wind1.2 Grid-scale energy storage for wind1.3 Objectives

2 Methods2.1 Scenario description2.2 Determining the power purchase agreement price by cost-minimizing a wind-transmission system2.2.1 Calculating the revenue requirements for wind2.2.2 Calculating the revenue requirements for transmission2.2.3 Calculating the quantity of delivered wind2.2.4 Minimizing the cost of delivered energy

2.3 Determining the breakeven cost for energy storage integration into wind-transmission system2.3.1 Batteries to mitigate curtailment2.3.2 Batteries to reduce transmission voltage class2.3.3 Batteries to increase wind installed transmission capacity

2.4 Sensitivity analysis2.4.1 Sensitivity to time-of-day pricing2.4.2 Sensitivity to key parameters

3 Results3.1 Determining the power purchase agreement price3.2 Assessing batteries to mitigate wind curtailment3.3 Assessing batteries to reduce transmission voltage class3.4 Assessing batteries to increase wind installed capacity3.5 Sensitivities

4 DiscussionAcknowledgementsAppendix A Definition of variablesReferences