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Methodological considerations on the need for electricity storage: power versus energy

Andreas Belderbos, Erik Delarue, William D‘haeseleer

TME WORKING PAPER - Energy and Environment Last update: March 2016

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Methodological considerations on the need forelectricity storage: power versus energy

Andreas Belderbosa,b*, Erik Delaruea,b and William D’haeseleera,baApplied Mechanics and Energy Conversion, University of Leuven, Leuven, BelgiumbEnergyVille, Genk, Belgium (Joint Venture of VITO NV and University of Leuven)

*Email: andreas.belderbos@kuleuven.be

Abstract—Different storage technologies can be used to enablean increasing share of variable renewable generation in theelectricity system by reducing the temporal mismatch betweengeneration and demand. To time-shift the delivery of electricityto loads, both electric power (instantaneous electricity flow [W])and electric energy (power integrated over time [Wh]) ratingsof storage are important. An optimal storage portfolio dependson the energy systems setting and is composed of differenttechnologies, each having specific characteristics. This paperanalyzes the optimal storage portfolio for different residualdemand profiles. The analysis is performed for different typesof storage technologies individually to analyze the need forpower and energy capacity and for different types of storagetechnologies simultaneously to analyze their mutual interaction.

Index Terms—Energy storage, optimal storage portfolio, mod-eling, renewable generation, temporal arbitrage.

I. INTRODUCTION

The amount of installed renewable capacity has grownsignificantly in recent years and is expected to grow furtherin the future [1], [2]. Some of these renewable energy sources(RES) such as wind and solar are highly variable and havea limited predictability. A growing amount of RES in theelectricity system therefore leads to an increasing need forflexibility. This flexibility can be provided by different means:dynamic operation of conventional generation, extension ofthe electricity grid, energy storage, demand response andcurtailment of the intermittent energy sources [3]–[5]. It isclear that not all means are equivalent in use.

Storage is an interesting option as it can both absorband generate electricity. Many different electricity storagetechnologies exist, which are divided in two categories inthis paper. A first type of storage technologies are thosewhere charging power, discharging power and energy ratingare coupled, e.g. most battery types. For this type of storagetechnologies, all power and energy ratings are fixed, i.e.,locked in, once one of them is determined. This storage typeis referred to as ’integrated storage’ in this paper. For a secondtype of storage technologies, charging power, dischargingpower and energy rating can be installed and operatedindependently from each other, e.g. power-to-gas (P2G),compressed air energy storage and redox flow batteries. Thisstorage type is referred to as ’disjoint storage’ in this paper.

In order to serve a given demand at lowest cost, a welfareoptimal generation and storage portfolio can be determined.The precise constellation of this portfolio depends onnumerous factors, such as investment and operational cost,technology characteristics, environmental targets, demand andvariable RES generation profiles. Many different studies areperformed to investigate the optimal generation and storageportfolio in different case studies or to determine the effectof a certain portfolio on the electricity system [6]–[11]. Thispaper presents an addition to the existing literature as itprovides a methodological explanation for the effect of thestorage profile on the optimal storage portfolio. The storageprofile is defined as the difference between the instantaneouselectric power demand and renewable power generation. Itcan thus contain both periods of shortage and surplus electricpower generation. The profile depends on the demand andRES generation profiles.

The objective of this paper is to explain the optimal storageportfolio for a given storage profile, taking into account thegeneral technical constraints of storage technologies. Thisis done first for each storage technology individually andsecond for both integrated and disjoint storage simultaneously,allowing interactions between both storage technologies.

The paper is organized as follows: first, the energy systemunder consideration is described, the calculation approachand numerical model is presented, characteristics of therepresentative storage technologies are given and generalstorage principles are discussed. The calculation of the optimalstorage portfolio is presented in the following sections. Section3 covers the determination of the necessary and optimalstorage capacity for methodological block profiles. In section4 the necessary and optimal storage capacity is determinedfor a sinusoidal RES profile. Conclusions finalize the paper.

II. INPUT DATA, ASSUMPTIONS AND GENERAL PRINCIPLES

The aim of this work is to provide a methodologicalexplanation for the effect of the storage profile on theoptimal storage portfolio. Therefore the optimal portfolio iscalculated and examined. In this section, the system scopeunder investigation is presented. The approach to calculatethe different portfolios and characteristics of generation and978-1-4673-8463-6/16/$31.00 c© 2016

storage technologies are given. Finally the general storageprinciples are elaborated.

A. System description

This paper focuses on the electricity system. An optimalgeneration and storage portfolio is calculated to serve agiven electricity demand. A renewable target is imposedequal to 100% of the electric energy demand, implying noelectricity is generated from fossil fuels. In a first instance, aflat methodological profile will be used for both demand andRES generation. Afterwards, sinusoidal profiles are used asRES profiles. Using a methodological profiles and imposinga RES target of 100% makes the obtained results not directlyapplicable to realistic scenarios but simplifies interpretationof the results to explain the mechanisms determining theoptimal storage portfolio. Insights obtained from thesemethodological exercises can be used to analyze real demandand RES generation profiles, this is discussed with the results.

B. Calculation approach

The generation and storage portfolios are optimized usinga linear program (LP). Starting from a green field, the totalsystem cost is minimized. The total cost equals the sum of theequivalent annual cost (EAC) of all installed RES capacity(cRES), integrated storage capacity (ci), disjoint chargingcapacity (ccd) and disjoint discharging capacity (cdd).

Cost = EACRES · cRES + EACi · ci+EACcd · ccd + EACdd · cdd (1)

The electric power demand (edem(t)) has to be servedat all times, either by RES generation or by dischargingstored energy but curtailment of RES generation (ecurt(t))is allowed. PRES denotes the RES generation profile, whichscales linearly with the installed RES capacity (cRES). eci (t)and edi (t) represents respectively the charging and dischargingpower of the integrated storage technology while ecd(t) andedd(t) represent the charging and discharging power of thedisjoint technology at time t.

∀t : edem(t) = PRES + edi (t) + edd(t)

− eci (t)− ecd(t)− ecurt(t) (2)

The optimization takes steady state operational constraintssuch as efficiency and energy-to-power ratio into account. ei(t)and ed(t) represent respectively the integrated and disjointenergy storage level. ηci and ηdi denote the charging anddischarging efficiency of the integrated storage technologywhile ηcd and ηdd denote the efficiencies of the disjointtechnology. EPi represents the energy-to-power ratio of theintegrated storage technology.

∀t : ei(t) = ei(t− 1) + eci (t)ηci −

edi (t)

ηdi(3)

∀t : ed(t) = ed(t− 1) + ecd(t)ηcd −

edd(t)

ηdd(4)

∀t : ei(t) ≤ ci · EPi (5)

Charging and discharging power is for each technologylimited to the installed capacity.

∀t : eci (t) + edi (t) ≤ ci (6)∀t : ecd(t) ≤ ccd (7)

∀t : edd(t) ≤ cdd (8)

Dynamic operational and grid constraints are outside thescope of this work. The time resolution of demand andgeneration profiles is one hour.

C. Available generation and storage technologies

For all numerical calculations, generation and storage tech-nologies are chosen to serve as an example. Further work willrequire careful sensitivity analyses. Onshore wind is chosenas RES generation technology although only methodologicalRES profiles are used. The cost characteristics are given intable I. The RES profiles are composed ad-hoc and will beexplained further on.

Table I: Cost and operational characteristics of onshore wind [12].

Unit Onshore

CAPEX [AC/kW] 1700OPEX [AC/kW/y] 25.5

Lifetime [y] 20Discount rate [%] 5

Combined Cycle Gas Turbines (CCGT) can be usedas discharge capacity for the disjoint storage technology.Technical and cost characteristics [11] are presented in tableII. In this paper CCS is always used in combination withCCGTs to have a closed carbon loop, the cost and efficiencylosses due to CCS are included in the costs listed in table II.The charging technology for disjoint storage is representedby P2G [11]. It is assumed that the synthetic methane can, ina first instance, be stored in existing natural gas infrastructureand gas storages. Therefore, no additional cost is takeninto account for the energy storage capacity of the disjointtechnology. The integrated storage is represented by NaSbatteries [13].

D. General storage principles

As mentioned in the introduction, storage technologies aredefined by three main operational characteristics: chargingpower, discharging power and energy storage capacity.Depending on the specific residual demand1, each of these

1The difference between electric power demand and RES generation. Theterm net demand is also used in the literature.

Table II: Cost and operational characteristics of different storage technologies.

Unit Integrated Disjoint

Charging Dischar. Energy

Efficiency [%] 90a 60 47b 100CAPEX [AC/kW] 1500 1500 1900 0OPEX [AC/kW/y] 15 30 66 0

Lifetime [y] 12 20 20 40Discount rate [%] 5 5 5 5

E/P ratio [Wh/W] 7.2 - - -

aSingle-trip efficiencyb55% if CCGT is used without CCS

characteristics can determine the minimum necessary storagecapacity.

The residual demand should be served entirely by storagewhen only RES generation and storage can be used to servethe electric power demand. A positive residual demandrepresents a demand for electricity which is not served byRES generation directly. Therefore, the highest positiveresidual demand determines the necessary discharge powercapacity of the storage technology. A negative residualdemand represents a surplus of RES generated electricpower, the accompanying energy of which can be stored.If curtailment of RES generation is not allowed, the mostnegative residual load determines the necessary chargingcapacity. However, if curtailment is allowed, the necessarycharging capacity can be less than the most negative residualdemand, as long as the charging capacity is high enough totake-up the necessary amount of electric power. The exactcharging capacity will be defined by the specific residualdemand curve, as shown in fig. 1. It can be seen that thenecessary charging capacity is independent of the temporalcharacteristics of the residual demand.

Figure 1: Residual load duration curve with discharged and charged electricity fromstorage. Surplus RES generation is given by a negative residual demand. Therefore Ps

depicts the necessary charging capacity.

The necessary energy storage capacity is determined by themaximum amount of electric energy that needs to be storedover a given time period, which depends on the temporalcharacteristics of the residual demand. After all, storing a totalamount of energy over a certain period requires less installedenergy storage capacity if the amount of charging/dischargingcycles increases.

For disjoint storage technologies, the installed capacitieswill be determined by the charging, discharging and energycapacity separately. For the integrated storage, the installedcapacity is determined by the highest necessary capacity ofthe three capacity types. The next section considers somesimplified profiles with the aim to show how each storagecharacteristic can determine the installed capacity.

III. METHODOLOGICAL CASE: BLOCK PROFILES

A methodological block profile will be used in this sectionfor which results are calculated analytically. The analyticalformulation yields the same results as the LP formulationpresented before, but allows to gain more insight in theobtained results. This way, a good understanding of themechanisms which determine the necessary and optimalstorage capacity can be obtained.

A. Necessary storage capacity

A block profile is created with a flat demand of Pd forthe entire time horizon, between t = 0 and t = tp. The RESgeneration profile is a block profile with a generation power ofPRES equal to the amount of installed RES capacity betweent = 0 and t = ts. For the remainder of the time horizon(ts < t < tp) the RES generation is assumed to be zero. Bothdemand and RES generation profiles are shown in fig. 2.

Figure 2: Methodological demand and RES generation block profiles with parameters tsand tp.

When the entire electric energy demand needs to be servedby renewable electricity and fixed values for PRES andPd are given, it is clear that ts = 0 is an impossible caseand no storage is needed if ts = tp. For 0 < ts < tp, theamount of storage capacity depends on both ts and tp. Forthe flat demand and generation profiles presented in fig.2, the necessary charging power, discharging power andenergy capacity are calculated analytically as presented in theequations below. The presented formulation is applicable toboth the integrated and the disjoint technology.

In these equations cc, cd and ce are the charging powercapacity, discharging power capacity and energy storagecapacity respectively. ηc and ηd are the charging anddischarging efficiencies. ∆t is the time step (1h). Pd, ts andtp are as shown on fig. 2.

cc =

tp∑t=ts

(Pd(t)·∆t)

ηc·ηdts∑t=0

∆t

(9)

cd = Pd (10)

ce =

tp∑t=ts

(Pd(t) ·∆t)

ηd(11)

1) The effect of the surplus and shortage duration:For disjoint storage technologies, charging, discharging andenergy capacity are chosen independently. The amount ofeach capacity type depends on tp and ts. Fig. 3 shows theinstalled capacity for a block profile of fig. 2 with a fixedtp = 48h and a varying ts. Note that the horizontal axisshows ts and thus expresses the number of hours where thedemand is directly served by RES.

(a) Disjoint capacity

(b) Integrated capacity

Figure 3: Installed power and energy capacity as a function of ts for a fixed tp of 48h.

The necessary installed integrated storage capacity isshown in fig. 3(b). For integrated storage technologies, it isassumed that both charging and discharging can occur at fullinstalled power capacity. The energy capacity is linked tothe power capacity by an energy-to-power ratio (EPi). Thisratio determines the amount of energy that can be stored perinstalled amount of power capacity. The resulting amount ofinstalled capacity is thus equal to the maximum of charging,discharging and energy capacity as given by the followingequation:

ci = max(cci , cdi ,

ce

EPi) (12)

Fig. 3(b) clearly shows three different zones, characterizedby a different capacity constraint that determines the installedcapacity. At the uttermost left side of the graph, more than 40hours of the demand need to be served by stored energy whileless than 8 hours of surplus RES are available (tp = 48h).Therefore, all necessary energy should be stored in a limitednumber of hours, leading to high charging capacity. Theinstalled storage capacity is thus determined by the necessarycharging capacity. At the uttermost right side, more than42 hours of the demand are served directly by RES andonly little storage is necessary. In this case the necessarydischarging power will determine the installed capacity. In themiddle zone of the graph, the amount of energy capacity isbigger than the amount of necessary charging and dischargecapacity. Therefore, the energy capacity will determine theinstalled storage capacity.

2) The effect of varying tp: Increasing tp leads to a relativeincrease of the interval where energy capacity determines theinstalled storage capacity in the integrated case, as shownin fig. 4. The three intervals are generally applicable forintegrated technologies, although the precise point at whicha different characteristic becomes constrained depends on thetechnical storage parameters.

(a) tp = 24h (b) tp = 168h

Figure 4: Installed integrated storage capacity as a function of ts for different fixed tp.

In fig. 5, tp is varied while keeping ts equal to tp2 . For the

disjoint storage technology, discharge power is constant asthe demand is flat. Charging power is independent of tp asthe relative charging time ( tstp ) is constant. Only the energystorage capacity increases linearly with an increasing tp. Forthe integrated storage technology, the installed capacity isdetermined by the necessary charging power for low valuesof tp. While for higher values of tp it is determined by thenecessary energy capacity.

3) A continued set of block profiles: Several single blockprofiles as used before (fig. 2) can be added sequentiallytogether to form a profile of identical block profiles. Fora profile consisting of identical block profiles, equations(9)-(11) are applicable to calculate the necessary capacities.It is thus possible to identify the same effects of a varyingts and tp as before. The findings for a single storage cyclecan therefore be generalized for a repetitive (continued) set

(a) Disjoined storage technology

(b) Integrated storage technology

Figure 5: Installed storage capacity as a function of tp with ts =tp2 , for both types

of storage technologies.

of storage cycles.

B. Optimal storage portfolioThe total storage cost for block profiles as a function

of a varying ts for tp = 168h is shown in fig. 6. Thiscost includes all installed storage related capacity (chargingcapacity, discharging capacity and energy storage capacity forthe disjoint technology) as well as the cost of RES generationcapacity necessary to compensate for storage losses. Variableoperational cost of RES generated electricity is assumed zero.

Figure 6: Total storage cost for integrated and disjoint technologies as a function of tsfor tp = 168h.

Figure 6 shows three distinct parts in the total cost ofintegrated storage, according to a part where charging capacity

determines the installed capacity, where energy capacity isdetermining and where discharge capacity is determining.This is in accordance with the results from fig. 4. When thenecessary energy capacity determines the installed integratedcapacity, the disjoint technology is often cheaper to install.Since a block profile is used where PRES is either equalto the installed RES capacity or zero, the optimal storageportfolio contains only one type of storage technologydepending on the surplus time ts. This is different comparedto other profiles where it can be optimal to install bothstorage technologies simultaneously as will be elaborated inthe next section.

IV. SINUSOIDAL PROFILE

The block profile from the previous section is now replacedby a single-frequency sinusoidal profile. Signals with a periodof a few hours up to months are used, not to be confusedwith the frequency of the instantaneous power (e.g.; 50 or60 Hz). The calculations are made with the Linear Program(LP) investment model, introduced in section II-B instead ofthe analytical formulation.

A. Necessary storage capacity

The single-frequency sinusoidal profile, representing theRES generation, has a period tp and a magnitude between 0and 1 (and thus an average of 0.5). This leads to a minimumRES generation of 0 and maximum RES generation PRESequal to the installed RES capacity. The demand profile is stilla flat demand with magnitude Pd. Note that for sinusoidalprofiles, the duration of surplus RES generation, previouslydenoted as ts, is fixed once Pd, PRES and tp are determined.

It is again interesting to see the effect of a varying periodtp. Fig. 7 shows the installed charging, discharging andenergy capacity of the disjoint storage technology and theinstalled capacity of the integrated storage technology as afunction of the period tp. Comparing fig. 7 to fig. 5 showsthe same trend for both types installed storage capacity. Forlow periods tp, necessary charging capacity is dominating theinstalled capacity for the integrated storage technology. Forhigher periods tp, the necessary energy capacity determinesthe installed capacity.

B. Interactions between storage technologies

In this section, the optimal storage portfolio is investigatedwhen both integrated and disjoint storage technologies canbe installed simultaneously. The exact interactions betweenthe different storage types will depend on their relative costand technical constraints presented in table II before butconclusions can be generalized.

Fig. 8 shows the installed storage capacity for a flatdemand profile and a sinusoidal RES generation profile with

(a) Disjoined storage technology

(b) Integrated storage technology

Figure 7: Installed storage capacity in function of period tp.

a single varying period tp. As can be expected based on theresults shown in fig. 6, all energy is stored using integratedstorage capacity for short periods. For long periods, almost allenergy is stored using disjoint storage technology. Howeverfor 60h < tp < 200h both integrated and disjoint storagetechnologies are used simultaneously. For profiles withsuch time period, the necessary energy storage requirementsdetermine the minimum amount of installed capacity anddisjoint storage is generally preferred. It is however moreeconomic to store the peak of the sinusoidal generationprofile using integrated storage technology.

Figure 8: Installed integrated capacity and disjoint charging and discharging capacitiesas a function of a single sinusoidal residual demand with a varying period tp.

Although these sinusoidal profiles are not directlyrepresentative for real demand and RES generation, resultsare applicable to real profiles as they give a clear indicationof the preferred storage technology type as a function of thesinusoidal period tp. In future work, frequency spectra ofreal demand and RES generation profiles will be analyzedto identify the dominant sinusoidal components and relate

these to the results obtained here for single sinusoidal profiles.

V. CONCLUSION

This paper provides a methodological explanation for theeffect of the residual demand on the optimal storage portfolio.It is shown that both charging, discharging and energy storagecapacity can be optimized for disjoint storage while themost stringent capacity type will determine the installedcapacity for integrated storage technologies. This meanseither the highest necessary charging or discharging poweror the necessary energy capacity determines the installedcapacity. The results are based on methodological profilesfor both demand and RES generation to gain clear insightin the underlying mechanisms driving the desirability of theinstalled storage capacity.

By optimizing the storage portfolio for different residualdemand profiles, it is shown that integrated storage capacityis predominantly used for storage cycles with shorter periods.The disjoint storage technology is predominantly used forstorage cycles with longer periods.

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