Capacity Value of Solar Power and Other Variable Generation
S. Awara, M. Lynch, S. Pfenninger, K. Schell, R. Sioshansi, I. Staffell, N. Samaan, S.H. Tindemans, A.L. Wilson, S. Zachary, H. Zareipour, C.J. Dent
11 Capacity Value of Solar Power and Other VariableGeneration
S. Awara, M. Lynch, S. Pfenninger, K. Schell, R. Sioshansi, I. Staffell, N. Samaan, S.H. Tindemans, A.L. Wilson,S. Zachary, H. Zareipour, C.J. Dent
Report of the IEEE PES Task Force on Capacity Value of Solar Power
Abstract —This paper reviews methods that are used for ade-quacy risk assessment considering solar power and for assessmentof the capacity value of solar power. The properties of solarpower are described as seen from the perspective of the power-system operator, comparing differences in energy availability andcapacity factors with those of wind power. Methodologies forrisk calculations considering variable generation are surveyed,including the probability background, statistical-estimation ap-proaches, and capacity-value metrics. Issues in incorporatingvariable generation in capacity markets are described, followedby a review of applied studies considering solar power. Finally,recommendations for further research are presented.
Index Terms —Solar power, capacity value, capacity credit, re-source adequacy, loss of load expectation, effective load-carryingcapability, capacity market, probability
I. I
NTRODUCTION A key issue for power-system planning is the contributionof renewable and other emerging energy resources tomeeting demand reliably. Mechanical failures, planned main-tenance, or lack of generating resource in real-time may leavea system with insufficient capacity to meet load—requiringload curtailment. The contribution of a resource to servingdemand reliably is measured typically by estimating capacity-value metrics, defined through the effect that its addition to thesystem has on the calculated risk of load-curtailment events.The issue of real-time resource availability is particularlysalient with renewable resources, as their output is governedby uncontrollable weather conditions.An IEEE Task Force focused on techniques for estimatingthe capacity value of wind power published a survey on thattechnology [1]. This new paper has a similar purpose ofsurveying methods for estimating the capacity value of solarpower and recent activity applicable to both wind and solar.We place strong emphasis on critical review of modellingmethodology, particularly with respect to capacity marketsand statistical modelling, which distinguishes our review workfrom related publications [1]–[3]. The paper builds on earlierTask Force papers which concentrate more specifically onsolar power [4], [5]—while the high-level topics covered inthis new paper are broadly similar to those in a previousconference paper [5], the material is revised entirely for thisas the Task Force’s final report apart from Sections III-A–III-C (these cover the essentials of the relevant probabilisticand statistical modelling, where the Task Force’s thinkinghas evolved less rapidly.) Throughout the Task Force’s activ-ity, there is particular emphasis on matters of solar-resource assessment (with which the power-system community maybe less familiar as compared to wind). In the solar-specificsections, we focus on photovoltaic (PV) solar rather thanconcentrating solar power (CSP). CSP has intrinsic energy-storage capability [6], [7], providing some control of co-incidence of output with high demands. This characteristicof CSP makes relevant modelling approaches fundamentallydifferent from PV. A brief discussion regarding the interactionbetween solar power and co-located energy storage, which isapplicable to CSP, is given in Section III-F.This paper addresses four major issues that are related tosolar power. First, Section II discusses key properties andassessment of solar resource. Solar availability features uniquespatial and temporal correlations, which are modified by de-sign considerations such as panel orientation and the inclusionof sun-tracking systems or energy storage. Section III providesa detailed discussion of the statistical methods that are usedfor adequacy-index and capacity-value estimation—much ofwhich applies equally to other variable generation (VG) tech-nologies, as well as solar. We highlight the importance of cap-turing statistical relationships between renewable resource anddemand, and consequences of limited data. It discusses alsorelevant theory associated with capacity markets. Section IVsurveys recent capacity value studies and practice in theindustrial and research literature, emphasising consequences ofdifferent methodology choices. Finally, Section V concludesand discusses key research needs in this area.II. PV-R ESOURCE A SSESSMENT
Surface solar irradiance follows predictable diurnal andseasonal cycles. However, solar irradiance can be difficult tomodel and forecast, due to cloud cover and other meteorologi-cal effects. The recent emergence of PV and its distributed na-ture make reliable long-term output data rare, forcing relianceon modeled PV-generation data [8]. Weather variability occursat different temporal and spatial scales, from clouds movingacross individual panels (seconds to minutes [9]) to weatherfronts moving over a region (hours to days [10]) to multi-day regimes that dictate continental-scale weather patterns[11]. Fig. 1 demonstrates the variability in PV output at asingle location over short timescales and that this variability isreduced if many PV systems over a wide area are aggregated.Modelling PV power output accurately is hampered bythe difficulty of estimating solar irradiance [12], especiallydue to cloud cover. Aerosols and other atmospheric particles a r X i v : . [ s t a t . A P ] J u l Fig. 1. Daily-average capacity factor for a single PV system near Milan andfor PV deployed across Italy during . Single-site and Italy-wide data arefrom PVOutput and Terna, respectively.Fig. 2. Simulated power generation for a -kW system installed in Jaen,Spain, averaged hourly over all days of (left) and summed over theentire year (right). The tilted systems are installed at scatter incoming light even with clear skies [13], affecting theproductivity of concentrating technologies (CSP and concen-trating PV) and, to a lesser degree, PV. Moreover, depositionof aerosols and particles on panels affects productivity [14].Output depends also on many secondary parameters: the PVtechnology that is used, tilt and azimuth angles, whetherpanels are fixed or have tracking systems, module temperature[15], and panel shading as a function of sun angle [16].Fig. 2 illustrates the impact of orientation on PV output,using data for Jaen, Spain. Other weather variables play arole as well: the severity of soiling is mediated by rainfall[17] and snow can cover panels (reducing output) and reflectsunlight off the ground (increasing output) [18]. Finally, aPV system’s inverter determines AC power output, with anefficiency that depends on utilization (power level and inputvoltage) and operating temperature [19]. It is common forinverters to be undersized relative to peak DC output of apanel, giving flattened power-output peaks. While this affectssummer peak output in particular, snow affects winter peaks.PV output during both summer and winter peaks contribute tothe capacity value of a PV system. A. Calculating Power Output
A key challenge in modeling overall system performance isobtaining accurate irradiance data. Several methods exists toconvert irradiance to DC power output from PV panels. Com-mon approaches are empirical models, which are parameter-ized from manufacturer datasheets, and experimental data [15],[20]. The two primary weather inputs—module irradiance and temperature—are modified by the secondary parameters thatare described above, requiring assumptions ( e . g ., on panelorientation) or additional data ( e . g ., aerosol optical depth orsnowfall volume). These secondary parameters are of criticalimportance for the diurnal profile of PV generation, which, inturn, is relevant for its capacity contribution. The impacts ofthese secondary parameters are illustrated in Fig. 2.The sun’s average power output (the solar constant) andinclination are fundamental values. Thus, libraries such asPVLIB [21] can estimate overall power output over a typicalmeteorological year (TMY) easily. TMY data provide syn-thetic hourly power outputs, which are sufficient for manytypes of analyses [22], [23]. The sufficiency of TMY datastem, in part, from national-scale solar capacity factors havingless internannual variability compared to those for wind ( e . g ., ± . % in Europe versus ± . % for wind [8], [24]). However,the use of TMY data requires correct depiction of the temporaland spatial dependency of PV generation under real weatherconditions and preserving correlations with temperature, de-mand, and wind [25]. B. Sources of Irradiance and Weather Data
There are three primary sources of data: ground-based mea-surements, satellite imagery, and meteorological reanalyses.Ground-station data are best for accuracy and high temporalresolution. However, freely available data are limited andof mixed quality, suffering from missing data, measurementerrors, and time aggregation. Data are available from Base-line Surface Radiation Network (BSRN) [26], Global EnergyBalance Archive (GEBA) [27], Surface Radiation Budget(SURFRAD) [28], Southern African Universities RadiometricNetwork (SAURAN) [29], and some national weather services.Geostationary weather satellites cover specific regions andprovide half-hourly images which can be processed to derivedirect and diffuse surface irradiance [30]. Meteosat coversEurope, northern Africa, and parts of Asia, with free dataavailable through Satellite Application Facility on ClimateMonitoring (CM-SAF) [31] and Copernicus Atmosphere Mon-itoring Service (CAMS) [32]. Geostationary Operational En-vironmental Satellite (GOES) covers the Americas [33], butno equivalent data provider exists. Prospective users of GOESmust process imagery themselves or use derived products, suchas National Solar Radiation Data Base (NSRDB) [34]. Whilesatellite data are considered state-of-the-art (due to high spatialresolution), they suffer from extensive periods of missing dataand do not provide global coverage yet [8].Reanalyses are more consistent across space and time andprovide global coverage, created by assimilating historical me-teorological measurements into a numerical weather-predictionmodel [35]. As such, reanalyses generate internally-consistentpictures of the state of the global atmosphere. Thus, reanalysesare gaining traction in simulating wind resources [24], [36],[37]. However, spatial resolution is coarse, typically via a -km to -km square grid [35]. Moreover, reanalyses’focus on three-dimensional atmospheric flow means that so-lar irradiance so far has not been a primary consideration.Nevertheless, with appropriate bias correction, reanalyses can provide accurate PV-output simulations [8]. Recently, severalturnkey services have launched which provide freely availablePV (and wind) simulations based on reanalysis data, includingfrom National Renewable Energy Laboratory [34], EuropeanClimatic Energy Mixes Demonstrator [38], Photovoltaic Ge-ographical Information System [39], Joint Research Centre’sEuropean Meteorological derived HIgh resolution RES gener-ation dataset (covering Europe) [37], and the Renewables.ninjaweb platform (which offers simulations that are based on CM-SAF) [8], [24]. C. Measured Power-Output Data
Metered data from individual PV systems are an alternativeto simulation. These are more challenging to obtain than forother generation technologies, due to the small and distributednature of PV. For example, there are . million PV systems inAustralia [40], compared to less than generators registeredin National Electricity Market [41]. The lack of metered dataposes a challenge to system operators, for which PV output isvisible only as a reduction of demand [42].Early government-funded field trials produced metered out-put data from small numbers of PV panels ( e . g ., systemsin United Kingdom from between and [43]).Such datasets are becoming increasingly common, with someproviding comprehensive real-time updates, for example fromAustralian Photovoltaic Institute ( systems in Australia[40]) and Sheffield Solar ( systems in United Kingdom[44]). These rely on the proliferation of web-enabled inverters,which can upload data with high temporal resolution ( e . g .,five-minute) data to online aggregator services.System operators in many regions include PV output as partof their public data now. These data must be estimated, oftenby combining bottom-up approaches that are listed above withtop-down statistical estimation [44], as operators cannot meterevery PV system in a country. D. Future Improvements
Many methodologies, including cloud imagery, physical cli-mate models, and machine learning, are employed to improvesolar-power modeling [12], [45], [46]. No single techniqueappears to be dominant for all applications. However, hybridor ensemble machine-learning models appear to offer betteraccuracy than other techniques [47]. With improved models,important data issues remain: averaging data to hourly or lowerresolutions, PV generation modeled inaccurately, and errors inelectricity-demand data contribute uncertainty in PV capacityvalues [9]. Even seemingly small systematic errors ( e . g ., a -minute shift in some modelled data) can have a large impacton capacity-value estimates if they affect the relative timingof peak PV generation and demand [9].From a decision-analytic perspective, there is also a needto build statistical error models for the relationship betweenresource datasets and real-world analogues, i . e ., going beyondimproved central estimates of historic resource.Improvements in the data and modeling for solar-powerprediction brings real benefits for system planning and opera-tions, e . g ., the California system must handle extensive over- generation of solar power, with system-wide curtailment ofsolar power in exceeding GWh [48].III. M
ETHODOLOGY
This section outlines the general framework that is usedfor risk-based adequacy and capacity-value assessments insystems with substantial VG penetrations. Most of the materialis applicable equally to all VG. Thus, this material seldommakes specific reference to solar power. Specific considerationof energy storage is beyond the scope of this paper. Thus,energy storage is not discussed except in Section III-F.
A. Probability Background
In adequacy assessment, we are interested in the values ofavailable conventional capacity, X t , available VG capacity, Y t ,and demand, D t , during multiple points in time, which areindexed by t . Let the (random) vector, S t = ( X t , Y t , D t ) ,denote the system state at t = 1 , . . . , n within the periodthat is under study. The system margin, Z t = X t + Y t − D t ,is a function of S t . A full probability model for the systemwould be sequential, describing S t as a stochastic process overthe entire time period. Such a stochastic process is neededto calculate some risk metrics, e . g ., frequency and durationindices, or the distribution of total energy unserved across theperiod under study.However, some quantities, such as loss-of-load expectation(LOLE), which is defined as: [ LOLE ] = n (cid:88) t =1 Prob { Z t < } , (1)may be defined in terms of the marginal distributions of S t integrated over time. LOLE may be specified equivalently interms of a simpler time-collapsed or snapshot model with atime-independent state vector, S = ( X, Y, D ) , the distributionof which is specified by:Prob { S ∈ A } = 1 n n (cid:88) t =1 Prob { S t ∈ A } , (2)for any event, A . In (2) the distribution of the state vector, S ,is the same as that of state vector, S t , sampled at a uniformlyrandomly chosen point in time. The specification in (2) is help-ful for some computational or theoretical analyses. Using (2),LOLE is given as (∆ t ) Prob { Z < } , and expected energyunserved as (∆ t ) E [max {− Z, } ] , where Z = X + Y − D and ∆ t is the length of the period under study. The distributionof S typically is estimated from the empirical distributionof observations of S t . Thus, the time-collapsed model isused almost always in adequacy studies that measure riskusing quantities, such as LOLE, which do not require a fullsequential model. B. Statistical Estimation
In the use of probabilistic and statistical concepts such asindependence or correlation, it is essential to be clear as towhich of the sequential and time-collapsed models these refer.For example, suppose Y t is available solar power at time t and that at any given time, t , the random variables, Y t and D t , areindependent (neither being informative about the other giventhe knowledge at time t ). Because daily minimum demandusually occurs overnight when it is dark, within the time-collapsed model the lowest values of D are associated withzero values of Y , introducing substantial probabilistic depen-dence between these two time-collapsed random variables.In reality, even conditional on information at time t , there istypically still some dependence between variable generation, Y t , and demand, D t , due to the existence of unmodelledweather effects, which influence both Y t and D t . This modifiesthe dependence between the corresponding time-collapsedrandom variables, Y and D .If dependence between VG output and demand is consideredin a time-collapsed model, often this is done using a ‘hindcast’approach, in which the empirical historical distribution of VG-output/demand pairs, ( y τ , d τ ) , is used as the predictive jointdistribution of ( Y, D ) . The random variable, X , usually isassumed independent of the pair, ( Y, D ) , with a distributionestimated from an appropriate model. Then: [ LOLE ] = ∆ N (cid:88) τ Prob { X + y τ < d τ } , (3)where ∆ is the length of a time step, N is the number ofhistoric years of data, and the sum is over historic times, τ .Inevitably, there are limited relevant data in the hindcastapproach for estimation of the empirical distribution at timesof high demand and low VG output, which dominate theestimates of risk measures. This can be dealt with by us-ing statistical extreme-value theory to smooth the extremesof a dataset [49]. To the best of our knowledge, the onlyworks using more sophisticated direct joint modelling ofthe relationship between VG output and demand in a time-collapsed model are the work of Wilson et al . [50] (whichuses temperature as an explanatory variable for both windand demand, and invokes independence of wind and demandconditional on temperature and on time of day, week, andyear); and the work of Gao and Gorinevsky [51] (which usesquantile regression to model explicitly the distribution of windconditional on demand).Studies that consider estimation of the uncertainty that arisesfrom the use of limited numbers of years of data typicallyassume that a result derived from the longest available datasetis ‘the truth’ [52], [53]. However, this is not fully satisfactory,as the result may be driven by a small number of historicweather systems, and there may be a tendency for extremepeaks to cluster in neighbouring years, reducing further thenumber of fully independent datapoints. Some discussion ofthis is provided in the literature [49], [50], although more workin this area and on the consequences for decision support isrequired.Most studies using a sequential model assume that VGoutput and demand may be modelled as independent processeswithin the season under study [54], [55]. In reality, as dis-cussed above, some dependence between these processes maybe introduced by the variability of the weather. There is littleresearch on multivariate-stochastic-process modelling of VGoutput and demand for adequacy assessment [56], [57]. C. Capacity-Value Metrics
Capacity-value metrics are used commonly to visualise thecontribution of VG (or other resources) in adequacy studies[1]. For instance, in the time-collapsed model and with respectto the loss of load probability (LOLP) risk index, the effectiveload-carrying capability (ELCC) of a resource, Y , when addedto a background, M , is given by the solution of:Prob { M < } = Prob { M + Y < [ ELCC ] Y,M } , (4)and the equivalent firm capacity (EFC) is given by solving:Prob { M + Y < } = Prob { M + [ EFC ] Y,M < } . (5)These capacity-value metrics are functions of the chosen riskmetric and the background, M , to which it is added, as wellas of the additional capacity. Thus, it is incorrect to refer tothe capacity value of Y without that caveat , or to use a singlecapacity-value figure across multiple circumstances [58]. Thisnuance is particularly important in capacity-market applica-tions. Such capacity-value metrics are also non-additive, i . e .,the ELCC (or EFC) of an addition, Y + Y , typically will notequal the sum of the ELCCs (of EFCs) of Y and Y addedto the same background.As is clear from (4) and (5), when adding a single relativelysmall resource to the background of a much larger system,ELCC and EFC take very similar values. This similarityapplies when calculating the marginal capacity value of asingle unit in a capacity market. In other applications, it mightbe of interest to calculate the capacity value of an entire fleetof wind or solar generation when added to the backgroundof the other resource and demand. In such cases, ELCC andEFC may take different values and it is necessary to considerwhich capacity value metric is appropriate. ELCC is used mostcommonly, however it is not always clear whether this choiceis considered carefully with respect to the specific application.Various special cases ( e . g ., small Y and exponentiallydistributed X ) are surveyed by Dent and Zachary [59], build-ing on earlier work [60]–[63]. These cases are helpful inunderstanding what is driving the results of capacity-value cal-culations. Computation is usually sufficiently straightforwardthat these special cases are not needed typically for modeltractability. D. Including VG in Capacity-Remuneration Mechanisms
Capacity-remuneration mechanisms (CRMs) incentivise thepresence of an appropriate level of generation and equivalentcapacity for resource-adequacy purposes. They take a rangeof forms, with a useful taxonomy that is provided by Agencyfor Cooperation of Energy Regulators (ACER) [64] and sum-marized in Fig. 3. Further detailed surveys of CRMs may befound in other works [3], [65], [66], with Table . in the latterproviding a more granular taxonomy than that of ACER. Forcrediting VG in CRMs, appropriate modelling of the adequacycontribution of the resource is needed. This applies similarlyto all volume-based mechanisms, and in a different mannerto price-based mechanisms. Thus, this section describes thetheory behind volume- and price-based CRMs, particularly therole of capacity-value metrics in including offers from VG. Volume based Price basedTargetedMarket-wide Strategic reserveCapacity obligationsCapacity auctionReliability option Capacity payment
Fig. 3. Taxonomy of capacity-remuneration mechanisms [64].
1) Volume-Based CRMs:
Here a central authority definesa volume of capacity to procure, e . g ., based on a target risklevel or a cost-benefit analysis. Then, typically an auction isheld to determine the units that are selected and the capacityprice.There is a standard theory for capacity procurement involume-based markets, in which all offers are from resourcesequivalent to conventional generation [58]. Suppose that (to agood approximation) adding or subtracting a limited capacityof conventional resource shifts the distribution of the margin, Z , with changes in the shape or width of that distributionbeing a lower-order effect. Then, it is possible to define thevolume of capacity in terms of expected available capacity,with the product offered by an individual unit being itsexpected available capacity. Units are added in ascending orderof their ratio of offer price to expected capacity, until thesum of their expected available capacities equals the target.This is referred to then as an auction with expected availablecapacity (sometimes referred to as ‘de-rated capacity’) as a‘simple additive commodity’. Without significant additionalcomplication, the fixed capacity target could be replaced bya demand curve, implying that at a higher auction price theamount procured will be lower.The assumptions that are required to run an auction withan additive commodity do not hold when non-conventionalresources, such as VG or energy storage, participate in themarket. Instead, the above mechanism may be generalised byadding units in ascending order of the ratio of offer price to themarginal EFC against the background of the finally acceptedset of resources, until a specified risk target is reached.Crucially, however, the final accepted set of resources cannotbe known ex ante . Thus, it is necessary to perform an iterativeprocess of running the auction and recalculating EFCs withthe latest auction outcome, until convergence is obtained [58].This is in contrast to how quantity-based capacity marketsoperate currently, wherein all bidders submit price/quantityoffers that are based on their (possibly de-rated) capacity,which is determined ex ante . Therefore, quantity-based CRMs (as structured currently) cannot consider contributions of alltypes of resource on an equal basis.Volume-based CRMs typically require specification of apenalty if a contracted resource cannot deliver when required.One specific form of penalty is a reliability option (RO)[67], which is a one-way contract for differences against theenergy-market price. Whenever the market price rises above aspecified level, any firms that hold a RO are required to pay thedifference between the strike price and the market price to thesystem operator. VG can face significant risk in taking on suchcontracts, due to its uncertain and variable output. However,this is not discussed in detail here as penalty regimes are aseparate matter from capacity value and procurement.
2) Price-Based CRMs:
Under price-based CRMs, the reg-ulator or system operator determines the total remunerationfor capacity, and how this is assigned ex post to resourcesaccording to their performance. The total capacity investmentis a market outcome, based on incentives provided by the CRMand other sources of income.Total remuneration typically is calculated as the product of avolume element (the total generation capacity that is requiredto ensure system adequacy) and price element. The volumeelement is calculated similarly to the capacity target for avolume-based mechanism, and is multiplied by a specifiedper-MW cost of new entry to give the total remuneration.Variants include pre-
England and Wales, wherein therewas no fixed capacity payment. Instead, for each time the totalpayment was the product of day-ahead LOLP and a specifiedvalue of lost load [68].Price-based mechanisms do not require the use of a de-rating factor or capacity value in a capacity auction, as theoutcome of the generator availability is used to distributethe revenues. Thus, the complications surrounding ex ante assignment of capacity values do not arise. However, thismeans that resources are rewarded implicitly on the basis ofsome form of mean output, which may not reflect well aresource’s contribution within an ex ante risk calculation. Thisis particularly problematic for VG, the contribution of whichwithin probabilistic risk calculations can be much less thanthat of firm capacity equal to its mean output.
E. Generation-Expansion Models
Several works embed adequacy risk calculations ingeneration-expansion optimization models [69]–[71]. Theseworks minimise the cost of capital investment, unservedenergy, and (possibly) operations. Typically, unserved-energycosts are included through a hindcast risk calculation usingmultiple years of demand and VG-output data. To give a linearoptimization model, it is necessary to simplify representationof conventional generators, e . g ., assuming that conventional-plant availability is deterministic and equal to its mean.Bothwell and Hobbs [71] assess social-welfare losses if VGcapacity is credited inappropriately and express the value ofadditional VG in terms of its marginal EFC at an economicoptimum. They do not provide, however, a practical scheme foroperating a CRM with both VG and conventional generation.In energy-system models with wider scope, e . g ., The Inte-grated MARKAL-EFOM System (TIMES), security of elec- tricity supply is represented typically via a target de-rated mar-gin of installed capacity over peak demand [72], as embeddingany kind of risk calculation would be too computationallyexpensive. F. Hybrid VG and Energy Storage
At a system level, energy storage can enhance the capacityvalue of VG [73]. Here we consider integration of energystorage with VG at a single site ( i . e ., with a single gridconnection). Such energy storage can be inherent in the VG,as for CSP plants [6], [7], or dedicated energy storage thatis co-located with VG, as in grid-connected microgrids [74].Typically, integrated energy storage can recharge only from theassociated VG resource ( e . g ., heat from irradiance in the caseof CSP), and not directly from the grid [75]. Thus, capacityvalue can be computed only for the integrated system.Examples of such capacity-value estimations for CSP in-clude the work of Madaeni et al . [7], which uses a capacity-value approximation that is based on the highest-LOLPhours of each year. They conclude that increased energy-storage capacity increases capacity value and reduces its inter-annual variation. Usaola [76] study a CSP plant with determin-istic dispatch using a time-sequential Monte Carlo calculationand obtain qualitatively similar results, with differences arisingfrom sizing of the CSP plant and different generation anddemand statistics. Mills and Rodriguez [77] consider a looserform of coupling, wherein PV that is co-located with batteriesshare inverters, necessitating an integrated assessment.On the other hand, if VG and energy storage can be operatedindependently ( e . g ., a battery with a separate inverter), thecapacity value of the integrated system may be calculatedas the sum of capacity values of its constituent components, if two conditions are satisfied. First, the contribution of theVG and energy storage must be small with respect to thetotal system size, so that their capacity values are marginal[58]. Second, each constituent capacity-value calculation mustaccount for the ability to re-dispatch existing generation andenergy storage. The difference of this integrated capacity value and a simple dispatch adjustment can be very substantial—up to an order of magnitude for a combination of pumpedhydroelectric energy storage and solar [78], [79].IV. S URVEY OF C URRENT P RACTICE
This section reviews the literature to illustrate points madeearlier. It does not attempt an exhaustive literature survey ofpractice, as in Doorman et al . [3] and S¨oder et al . [2], whichare referenced as relevant. The number of individual works thatare cited in this section is relatively small, as many studiesuse similar methodologies. One limitation of many broadersurveys is that they do not provide our critical discussion oftechnical modeling approaches.
A. Recent Methodology-Related Research
As described in Section III, if a statistical relationshipbetween VG output and demand is taken into account, thisis done typically through the ‘hindcast’ approach. We note examples of formative works taking such an approach withwind [1], [2] and solar generation [9], [80] generation. Severalstudies review the variants of methodology that are used indifferent studies or the consequences of different approachesfor numerical results. Mills and Wiser [81] provide a list of thecapacity-value approaches that are used in different utilities forplanning purposes. Madaeni et al . [82] use the western UnitedStates as a case study, Zhou et al . [83] emphasise the impactsof mis-estimating capacity value, and Awara et al . [84] surveythe impact on calculation results of making different modellingdecisions.Other recent research considers associated data issues. Gami et al . [9] examine consequences for calculation results ofinput data resolutions such as temporal resolution and am-biguity over definitions of data fields in recording PV output.Madaeni et al . [7] use hindcast to compare how differentapproximations to the full risk calculation affect LOLE-basedELCC results. Abdel-Karim et al . [80] demonstrate carefullyhow issues in data rounding affect comparison of results fromdifferent codes, in the context of using the hindcast approachon the IEEE Reliability Test System.
B. Capacity Markets
Capacity-value metrics for VG are of most relevance involume-based CRMs: renewables often do not participate instrategic reserve/targeted mechanisms. Price-based CRMs donot require assigning a capacity value ex ante ( cf . Section III-Cand examples such as the Nordic system [2]).In volume-based CRMs, the most common method ofaccounting for the adequacy contribution of different tech-nologies is application of a de-rating factor. Thus, a unit iscompensated for only a portion of its nameplate capacity inauction processes and in consequent payments, to account forits estimated statistical availability properties. Mean availabil-ity is used typically for conventional generation.Applying an appropriate de-rating factor to VG is challeng-ing, however, as we discuss previously. A range of modellingapproaches for resource-adequacy assessments, partly basedon the characteristics of the relevant power system, can beused. Bothwell and Hobbs [71] and S¨oder et al . [2] includesurveys of current practice in North America and Europe,with the latter examining the case of wind generation onlybut providing a survey of a much larger number of systems.Table in the work of S¨oder et al . [2] summarises themethods that are used to determine capacity value of windin the systems that are surveyed. Where wind is eligiblefor capacity payments, a risk-based capacity-value metric isused typically, e . g ., marginal EFC in Great Britain, averageEFC in Italy, and marginal ELCC in Ireland. Some systems,particularly those that rely on strategic reserves, such as theNordics, preclude renewables from receiving payments at all.Great Britain permits wind generators to receive a capacitypayment if they are not in receipt of low-carbon support, whichin practice means that most wind farms do not participate.The Irish and Italian systems allow all renewable projects toparticipate in capacity auctions. However, to date, renewableprojects represent only a tiny proportion of successful offersin Ireland and Italy. From a risk-modelling perspective, there are different con-texts in which it may be necessary to consider VG withincapacity auctions. Clearly, in systems in which VG receivesa capacity payment on the basis of a risk-based capacity-value metric, it must be included in the risk calculations.There are other examples in which VG does not receivecapacity payments, but is included in the risk modelling whichunderpins the capacity market, e . g ., in Finland, where windcan reduce the need for strategic reserves. In other markets( e . g ., Sweden), wind is excluded explicitly, which potentiallycould lead to over-procurement of other capacity.Other systems use a summary statistic of an estimatedprobability distribution of available resource to representthe contribution of VG in capacity markets or policy-facingresource-adequacy studies. For instance, PJM uses the meanconditional on summer-peak hours, Texas uses mean fromhighest-load hours during the previous years, Spain uses thelower fifth quantile of the distribution, and a system that wasproposed (but never implemented) in Alberta uses hoursof lowest historic margin during the last five years, whichaccounts for significant risk contribution in the maintenanceseason. All of these approaches credit VG on the basis of itsown properties, i . e ., in contrast with a risk-based approach,not on how its properties affect the risk level in the system asa whole. This property of these approach has potential seriousconsequences when VG penetration is very high, as it is inTexas. However, these approaches may be more appropriateat very low penetrations of VG, which can be checked ona case-by-case basis. Bothwell and Hobbs [71] examine theeconomic consequences of using alternatives to an appropriaterisk-based capacity credit ( e . g ., techniques that are employedin ERCOT, IESO, ISO New England, PJM, and California).It is not clear in all cases whether historic metered outputis used, or whether historic meteorological data are used incombination with a future scenario of installed VG capacity.The former has the advantage of being based on actualhistorical performance, whereas the latter often is preferableas it permits consideration of newer or future sites where thereis little or no metered historic record.V. C ONCLUSIONS
This paper reviews methods that are used for adequacy riskassessment considering solar power and other VG technolo-gies, and for assessing the capacity value of VG installations.This includes the spatial and temporal properties of solar out-put, solar-design considerations, methods for capacity-valueassessment,and including VG in CRMs. Our survey of currentpractice reveals broad heterogeneity, confirming that a reviewpaper of this type is warranted.Although there is a growing literature on reliability as-sessment and capacity value considering solar and other VG,several outstanding issues call for additional research. Whileconsiderable advances have been made in resource assessmentof solar and wind power, there is little work on buildingerror models quantifying the consequences of uncertainty inreconstruction of historic resources. Further statistical workon resource-adequacy assessment is needed. This includes work on non-sequential approaches beyond hindcast and jointVG/demand modelling for sequential models and on use ofthese more advanced approaches in practical circumstances.The overall emphasis should be on how these various de-velopments could improve decision analysis. Finally, thereis limited understanding of how to operate capacity marketson a technology-neutral basis with a full range of resources,including conventional plant, VG, energy storage, and otheremerging resources. R
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