Pointing out the Convolution Problem of Stochastic Aggregation Methods for the Determination of Flexibility Potentials at Vertical System Interconnections
Johannes Gerster, Marcel Sarstedt, Eric MSP Veith, Sebastian Lehnhoff, Lutz Hofmann
PPointing out the Convolution Problem of Stochastic Aggregation Methods for theDetermination of Flexibility Potentials at Vertical System Interconnections
Johannes Gersterand Sebastian Lehnhoff
Dept. of Computing ScienceCvO Universität Oldenburg [email protected]
Marcel Sarstedtand Lutz Hofmann
Inst. for Electric Power SystemsLeibniz Universität Hannover [email protected]
Eric MSP Veith
OFFIS e.V.R&D Division EnergyOldenburg, Germany [email protected]
Abstract —The increase of generation capacity in the areaof responsibility of the distribution system operator (DSO)requires strengthening of coordination between transmissionsystem operator (TSO) and DSO in order to prevent conflictingor counteracting use of flexibility options. For this purpose,methods for the standardized description and identification ofthe aggregated flexibility potential of distribution grids (DGs)are developed. Approaches for identifying the feasible operationregion (FOR) of DGs can be categorized into two main classes:Data-driven/stochastic approaches and optimization based ap-proaches. While the latter have the advantage of working inreal-world scenarios where no full grid models exist, whenrelying on nai¨ve sampling strategies, they suffer from poorcoverage of the edges of the FOR. To underpin the need forimproved sampling strategies for data-driven approaches, inthis paper we point out and analyse the shortcomings of nai¨vesampling strategies with focus on the problem of leptocurticdistribution of resulting interconnection power flows (IPFs). Werefer to this problem as convolution problem , as it can be tracedback to the fact that the probability density function (PDF)of the sum of two or more independent random variables isthe convolution of their respective PDFs. To demonstrate the convolution problem , we construct a series of synthetic 0.4 kVfeeders, which are characterized by an increasing number ofnodes and apply a sampling strategy to them that draws set-values for the controllable distributed energy resources (DERs)from independent uniform distributions. By calculating the powerflow for each sample in each feeder, we end up with a collapsingIPF point cloud clearly indicating the convolution problem . Keywords — TSO/DSO-coordination; convolution of probabilitydistributions; random sampling; aggregation of flexibilities; feasibleoperation region; active distribution grid; hierarchical grid control
I. I
NTRODUCTION
The increasing share of DERs in the electrical energy systemleads to new challenges for both, TSO and DSO. Flexibilityservices for congestion management and balancing, so farmostly provided by large scale thermal power plants directlyconnected to the transmission grid (TG), increasingly have tobe provided by DERs connected to the DG. Thus, DGs evolvefrom formerly mostly passive systems to active distributiongrids (ADGs) that contain a variety of controllable componentsinterconnected via communication infrastructure and whosedynamic behaviour is characterized by higher variability ofpower flows and greater simultaneity factors.TSO-DSO coordination is an important topic which hasbeen pushed by ENTSO-E during the last years [1, 2, 3, 4]. Coordination between grid operators has to be strengthened toprevent conflicting or counteracting use of flexibility options [5].To reduce complexity for TSOs at the TSO/DSO interface andto enable TSOs to consider the flexibility potential of DGs in itsoperational management and optimization processes, methodsare needed which allow for the determination and standardizedrepresentation of the aggregated flexibility potential of DGs.The aggregated flexibility potential of a DG can be describedas region in the PQ-plane that is made up from the set offeasible IPFs [6]. Thereby, feasible IPFs are IPFs which canbe realized by using the flexibilities of controllable DERsand controllable grid components such as on-load tap changer(OLTC) transformers in compliance with grid constraints i.e.,voltage limits and maximum line currents.In the literature, there are various concepts to determinethe FOR of DGs. They can be categorized into two mainclasses: Data-driven/stochastic approaches and optimization-based approaches.For data-driven approaches, the general procedure is suchthat a set of random control scenarios is generated by assigningset-values from a uniform distribution to each controllableunit. By means of load flow calculations the resulting IPFsare determined for each control scenario and classified intofeasible IPFs (no grid constraints are violated) and non-feasibleIPFs (at least one grid constraint is violated). The resultingpoint cloud of feasible IPFs in the PQ-plane serves as stencilfor the FOR [6]. A problem that comes with this approach isthat drawing set-values from independent uniform distributionsleads to an unfavourable distribution of the resulting IPFs inthe PQ-plane and extreme points on the margins of the FORare not captured well [7].This is where optimization-based methods come into play.The basic idea behind these methods is not to randomlysample IPFs but systematically identify marginal IPFs bysolving a series of optimal power flow (OPF) problems [8].In addition to better coverage of the FOR, optimization-based approaches have the advantage of higher computationalefficiency. An important drawback is however that, exceptfor approaches which solve the OPF heuristically, solving theunderlying OPF requires an explicit grid model [9]. On theother hand, the only heuristic approach published so far, suffersfrom poor automatability as it relies on manual tweaking ofhyperparameters [10]. a r X i v : . [ ee ss . S Y ] F e b n practice, considering the huge size of DGs, complete datarelated to grid topology (data related to operating equipmentincl. its characteristics and topological connections) is notcommonly stored [11], which complicates parametrization ofexplicit grid models. In such circumstances, black-box machinelearning (ML) models trained on measurement data providedby current smart meters can be an alternative to physics-based,explicit grid models [12]. Due to their compatibility with black-box grid models, we argue that it is worthwhile to researchand improve data-driven approaches to determine the FORof DGs. This paper is intended to point out and analyse theproblem of leptocurtic distribution of IPFs with naïve samplingstrategies and thus to underpin the need for more effective andmore efficient data-driven sampling strategies, such as thosepublished by Contreras et al. [13], when this paper was alreadyadvanced.The remainder of the paper is structured as follows: A surveyon existing approaches (data-driven and optimization-based)and the contribution of this paper are given in section II. Next,in section III the construction of a series of synthetic feederswith increasing number of nodes is explained. On the basisof these feeders we performed our sampling experiments, theresults and evaluation of which are presented in section IV.Finally, in section V the paper is summarized, the conclusionis given and an idea for a distributed sampling strategy ispresented which does not suffer from unfavourable distributionof resulting IPFs.II. S URVEY ON GRID FLEXIBILITY AGGREGATION METHODSAND CONTRIBUTION OF THIS PAPER
As outlined in the introduction, relevant literature can begrouped into two main categories: Data-driven/stochastic andoptimization-based approaches for exploring the FOR of DGs.
A. Data-driven approaches
Heleno et al. [7] are the first to come up with the idea ofestimating the flexibility range in each primary substation nodeto inform the TSO about the technically feasible aggregatedflexibility of DGs. In order to enable the TSO to perform acost/benefit evaluation, they also include the costs associatedwith adjusting the originally planned operating point of flexibleresources in their algorithm. In the paper two variants ofa Monte Carlo simulation approach are presented, whichdiffer in the assignment of set-values to the flexible resources.While in the first approach independent random set-values forchanging active and reactive power injection are associatedto each flexible resource, in the second approach a negativecorrelation of one between generation and load at the same buswas considered. In a direct comparison of the two presentedapproaches, the approach with negative correlation betweengeneration and load at the same bus performs better and resultsin a wider flexibility range and lower flexibility costs with asmaller sample size. Nevertheless, even with this approach,the capability to find marginal points in the FOR is limited.Therefore, in the outlook the authors suggest the formulation ofan optimization problem in order to overcome the limitations of the Monte Carlo simulation approach, increasing thecapability to find extreme points of the FOR and reducingthe computational effort. In Silva et al. [8], which is discussedin the next subsection, the authors take up this idea again.Mayorga Gonzalez et al. [6] extend in their paper themethodology presented by Heleno et al. [7]. First, they describean approach to approximate the FOR of an ADG for aparticular point in time assuming that all influencing factorsare known. For this, they use the first approach of Heleno et al. [7] for sampling IPFs (the one that does not considercorrelations). That is, random control scenarios are generatedby assigning set-values from independent uniform distributionsto all controllable units. In contrast to [7], no cost valuesare calculated for the resulting IPFs. Instead, for describingthe numerically computed FOR with sparse data, the region isapproximated with a polygon in the complex plane. In addition,a probabilistic approach to assess in advance the flexibilityassociated to an ADG that will be available in a future timeinterval under consideration of forecasts which are subject touncertainty is proposed. The authors mention that for practicalusage the computation time for both approaches has to besignificantly reduced. However, the problem of unfavourabledistribution of the resulting IPF point cloud, when drawingcontrol scenarios from independent uniform distributions, whichis a mayor factor for the low computational efficiency, is notdiscussed.When this paper was already advanced, Contreras et al. [13]came up with new sampling methods for data-driven approaches.They show that, when focusing the vertices of the flexibilitychart of flexibility providing units during sampling, the qualityof the data-driven approach can be dramatically improvedin comparison to the nai¨ve sampling. On top of that, theypresent a comparison of OPF-based and data-driven approaches,whose results show that with their improved sampling strategiesboth approaches are capable of assessing the FOR of radialdistribution grids but for grids with large number of busesOPF-based methods are still better suited.
B. Optimization-based approaches
Silva et al. [8] address the main limitation of their sampling-based approach in Heleno et al. [7], namely estimating extremepoints in the FOR. To this end, they propose a methodologywhich is based on formulating an optimization problem withbelow-mentioned objective function, whose minimization fordifferent ratios of α and β allows to capture the perimeter ofthe flexibility area. α P DSO → TSO + β Q DSO → TSO (1)where P DSO → TSO and Q DSO → TSO are the active and reactivepower injections at the TSO-DSO boundary nodes. Silva etal. [8] work out that the underlying optimization problemrepresents an OPF problem. Due to its robust characteristicsthey use the primal-dual, a variant of the interior point methodsto solve it. The methodology was evaluated in simulation andvalidated in real field-tests on MV distribution networks inrance. The comparison of simulation results with the randomsampling algorithm in Heleno et al. [7] shows the superiorityof the optimization-based approach by illustrating its capabilityto identify a larger flexibility area and to do it within a shortercomputing time.Capitanescu [14] propose the concept of active-reactivepower (PQ) chart, which characterizes the short-term flexibilitycapability of active distribution networks to provide ancillaryservices to TSO. To support this concept, an AC optimal powerflow-based methodology to generate PQ capability charts ofdesired granularity is proposed and illustrated in a modified34-bus distribution grid.Contreras et al. [9] present a linear optimization model forthe aggregation of active and reactive power flexibility of dis-tribution grids at a TSO-DSO interconnection point. The powerflow equations are linearized by using the Jacobian matrix ofthe Newton-Raphson algorithm. The model is complementedwith non-rectangular linear representations of typical flexibilityproviding units, increasing the accuracy of the distribution gridaggregation. The obtained linear programming system allowsa considerable reduction of the required computing time forthe process. At the same time, it maintains the accuracy ofthe power flow calculations and increases the stability of thesearch algorithm while considering large grid models.Fortenbacher et al. [15] present a method to compute reducedand aggregated distribution grid representations that providean interface in the form of active and reactive power (PQ)capability areas to improve TSO-DSO interactions. Based on alossless linear power flow approximation they derive polyhedralsets to determine a reduced PQ operating region capturing allvoltage magnitude and branch power flow constraints of theDG. While approximation errors are reasonable, especially forlow voltage grids, computational complexity is significantlyreduced with this method.Sarstedt et al. [10] provide a detailed survey on stochasticand optimization based methods for the determination of theFOR. They come up with a comparison of different FORdetermination methods with regard to quality of results andcomputation time. For their comparison they use the Cigrémedium voltage test system. On top of that, they present aparticle swarm optimization (PSO) based method for FORdetermination.
Contributions of this paper
In summary, it can be stated that optimization-basedapproaches show high computational efficiency with goodcoverage of the FOR. However, methods used for solving theunderlying OPF problem rely—except for heuristic approaches,which have other drawbacks—on explicit grid models of theDG, which must be parametrized with grid topology data oftennot available in practice. Data-driven approaches, on the otherhand, do not require explicit grid modeling and are compatiblewith black-box grid models, but suffer from low computationalefficiency and poor coverage of peripheral regions of the FOR,when using conventional sampling strategies. This is where our approach comes in. We are heading to-wards improved sampling strategies for data-driven approaches,which mitigate the weak points of data-driven methods (lowcomputational efficiency and poor coverage of FOR) whileretaining their advantage of being compatible with black-boxgrid models. As a basis for this, in this paper we are the firstto come up with an experiment setup by means of which theproblem of resulting convoluted distribution of IPFs with naïvesampling strategies can be analyzed and pointed out in aneasily reproducible manner.III. E
XPERIMENT SETUP
To show the shortcomings of naïve sampling strategies,we apply a sampling strategy that draws set-values for thecontrollable DERs from independent uniform distributions toa series of synthetic . feeders as shown in Fig. 1. Thefeeders are characterized by an increasing number of nodes.To be able to consider the effect of the number of nodes onthe IPF-sample as isolated as possible, both, the total installedpower and the average transformer-node distance are chosenequal for all feeders. The installed power is distributed equallyamong all connected DERs: P i inst , DER j = P i inst , DERs N i , (2)where P iinst,DER j is the installed power of the DER connectedto the j th node n ij of feeder i , P iinst,DERs is the total installedpower of feeder i and N i is the number of nodes of feeder i .Nodes are equally distributed along feeders as shown in Fig. 1and the line length between adjacent nodes l il of feeder i withlength l if is: l il = l if N i . (3)The transformer-node distance of node n ij is: d it,n j = l il · j. (4)With (4) the average transformer-node distance d it,n of feeder i can be written as: d it,n = 1 N i N i (cid:88) j =1 d it,n j = 1 N i N i (cid:88) j =1 l il · j = l il N i N i (cid:88) j =1 j = l il N i · N ij · ( N ij + 1)2 . (5)Resolved after the line length l il , the result is: l il = d it,n · N i + 1 . (6)With (3) and (6) the length of feeder i results in:
27 DERs)feeder n n n n l l d node n ij n ... n DER j n ... n IPF IPF IPF (1 DER)feeder (3 DERs)feeder (9 DERs)feeder Figure 1. Synthetic . feeders l if = d it,n · N i N i + 1 . (7)For our experiments we have constructed four synthetic . feeders. The feeders differ in the number of nodes N i ,which has been set to , , or respectively. Line length l il and feeder length l if have then been calculated according to(6) and (7). There is one DER connected to each node and theinstalled power P iinst,DERs is distributed evenly among theDERs according to (2). To be able to cover the entire flexibilityarea of the feeders including its border areas where voltageband violations and/or line overloadings can be observed, allDERs are inverter-connected battery storages because they offermaximum flexibility with regard to both, active and reactivepower provision. The dimensioning of the inverters has beenchosen in such a way that a power factor cos φ of 0.9 can bekept, when the maximum active power is delivered: | S | imax,DER j = P iinst,DER j cos φ = P iinst,DER j . . (8)Active and reactive power ranges of the battery storages arethus: (cid:104) P imin,DER j ,P imax,DER j (cid:105) = (cid:104) − P iinst,DER j ,P iinst,DER j (cid:105)(cid:104) Q imin,DER j ,Q imax,DER j (cid:105) = (cid:104) −| S | imax,DER j , | S | imax,DER j (cid:105) . (9)Values for the technical parameters of the four feeders includingconnected DERs are listed in Table I.For all feeders we conduct the sampling in such a way thatfor each DER and each sample element we independently drawreal and reactive power values from uniform distributions: X iP,DER j ∼ U (cid:104) P imin,DER j , P imax,DER j (cid:105) X iQ,DER j ∼ U (cid:104) Q imin,DER j , Q imax,DER j (cid:105) . (10) Q I P F ( k v a r )
300 200 100 0 100 200 P IPF ( kW ) Q I P F ( k v a r )
300 200 100 0 100 200 P IPF ( kW )
27 DERs feasiblevoltage band violation line overloadingvoltage band viol. & line overloading
Figure 2. Results of naïve sampling strategy classified by feasibilitywith regard to grid constraints (voltage band limits and max. lineloading); inverter constraints are neglected
After assigning active and reactive power values to each DER,the pandapower library [16] calculates the power flow. Thisway we generate a sample of size for each feeder.Following this, the sample elements are first classified withregard to their adherence to grid constraints and in case of non-adherence with regard to the type of grid constraint violation(i.e., voltage band violation, line overload, or both). Second,inverter constraints are taken into account and the sampleelements are classified with regard to adherence to both, gridand inverter constraints. In this case, sample elements are onlyclassified as feasible, if neither grid constraints nor deviceconstraints for any of the connected inverters occur. In caseof non-feasibility we distinguish depending on the type ofconstraint violation (i.e., grid constraint violation, inverterconstraint violation, or both).Finally we plot the classification results in the domain ofactive and reactive IPFs P IP F and Q IP F .IV. E
XPERIMENT RESULTS
The resulting plots are shown in Fig. 2 and 3. The samplinghas been performed once for each feeder from Fig. 1. Thismeans that Fig. 2 and 3 only differ in how the sample elementsare classified. While for Fig. 2 only grid constraints have beenconsidered, Fig. 3 also incorporates inverter constraints. Bothfigures consist of four subplots—one for each of the fourfeeders from Fig. 1. Each dot of the point clouds representsone sample element—so every subplot contains dots. The
ABLE
I. C
ONFIGURATION OF THE SYNTHETIC FEEDERS P inst , DER j (kW) | S | max , DER j (kVA) Feeder Length(m) Line Length(m) Line Type Voltage Band(pu) Trafo Type1 200.0 222.2 400 400 NAYY 4x150SE 0.9–1.1 0.4 MVA20/0.4 kV3 66.7 74.1 600 200 NAYY 4x150SE 0.9–1.1 0.4 MVA20/0.4 kV9 22.2 24.7 720 80 NAYY 4x150SE 0.9–1.1 0.4 MVA20/0.4 kV27 7.4 8.2 771 29 NAYY 4x150SE 0.9–1.1 0.4 MVA20/0.4 kV Q I P F ( k v a r )
300 200 100 0 100 200 P IPF ( kW ) Q I P F ( k v a r )
300 200 100 0 100 200 P IPF ( kW )
27 DERs feasiblegrid constraint violation inverter constr. viol.grid and inverter constr. viol.
Figure 3. Results of naïve sampling strategy classified by feasibilitywith regard to both, grid and inverter constraints; please note: greendots are plotted above orange dots, i.e. no green dots are covered byorange dots shaded grey area marks the theoretically known aggregatedpower limit for the DERs: (cid:2) P imin,DERs , P imax,DERs (cid:3) = (cid:2) − P iinst,DERs , P iinst,DERs (cid:3)(cid:2) Q imin,DERs , Q imax,DERs (cid:3) = (cid:2) −| S | imax,DERs , | S | imax,DERs (cid:3) . (11)For the 1 DER case, shape and structure of the point cloudlook as one would expect from the configuration. It largelycovers the grey area—only slightly skewed and shifted towardslower active and reactive power values, which results fromactive and reactive power consumption of grid elements (linesand transformer). However, when increasing the number ofDERs, the convolution problem becomes obvious. With 3 DERs,the feasible area is still covered to some extent, but the pointdensity already decreases strongly towards the edges. In caseof 9 DERs the point density in the edges has decreased tosuch an extent that hardly any sample elements are detected which show grid constraint violations. Finally, with 27 DERsthe point cloud has collapsed to a fraction of the grey area andonly a small part of the theoretical FOR is covered.From the 3 DERs subplot in Fig. 2 it can be seen that withincreasing number of DERs not only the region covered bythe sample collapses, but at the same time the border betweenfeasible and infeasible elements (with regard to grid constraints)becomes less distinct: The absence of a sharp border betweenfeasible and non-feasible IPFs complicates the use of multi-class classification for identifying the FOR from the sampleand indicates the use of a one-class classifier for that purpose.Fig. 3, which additionally considers inverter constraints,shows an other problem of the nai¨ve sampling approach: In thisconsideration, not only the total area covered by the sampledecreases, but also the share of feasible examples shrinkssharply, such that with 27 DERs only very few sample elementsare identified which violate neither grid nor inverter constraints.This is because with the nai¨ve sampling approach powervalues are assigned to each DER at once. After that, the powerflow calculation is performed and only at the very end thefeasiblity with regard to grid and inverter constraints is checked.Even if the constraints of only a single inverter are violated,the example is classified as non-feasible with regard to inverterconstraints. If, for example, for a single converter one third ofthe possible power setpoints violate constraints, the likelihoodto observe no constraint violations with N inverters amountsto (cid:18) − (cid:19) N . For N = 27 inverters this would amount to approximately . × − .One way to address this would be to perform a successivesampling as proposed by Bremer et al. [17] for the use case ofactive power planning. With successive sampling the evaluationof inverter constraints is done immediately after the assignmentof setpoints to single DERs and in case of non-feasibilitydrawing of setpoints is repeated until a valid configuration isfound. The power flow calculation would then be carried outonly after setpoints compatible with inverter constraints havebeen found for each DER.To illustrate the convolution problem , in Fig. 4 we plotthe frequency density of active IPFs resulting from oursampling against the PDF of the Bates distribution. The Batesdistribution is the continuous probability distribution of themean of n independent uniformly distributed random variables
00 200 100 0 100 200 P IPF ( kW ) D e n s i t y Figure 4. Frequency density of active IPFs resulting from ourexperiments (solid lines) compared with probability density function ofBates distribution on the interval [ − P iinst,DERs , P iinst,DERs ] (dashedlines) on the unit interval and thus closely related to the Irwin-Hall distribution, which describes the sum of n independentuniformly distributed random variables. More general, instatistics the probability distribution of the sum of two ormore independent random variables is the convolution of theirindividual distributions. For the variant of the Bates distributiongeneralized to arbitrary intervals [ a, b ] : X ( a,b ) = 1 n n (cid:88) k =1 U k ( a, b ) (12)this results in the following equation defining the PDF: f ( x ) = n (cid:88) k =0 (cid:34) ( − k (cid:18) nk (cid:19) (cid:18) x − ab − a − kn (cid:19) n − sgn (cid:18) x − ab − a − kn (cid:19) (cid:35) if x ∈ [ a, b ]0 otherwise . (13)Comparison with the Bates distribution is motivated by thefact that with equations (2), (9) and (10) the active power rangefrom which we draw values during the sampling can be writtenas follows: X iP,DER j ∼ U ij (cid:34) − P iinst,DERs N i , P iinst,DERs N i (cid:35) = 1 N i U ij (cid:2) − P iinst,DERs , P iinst,DERs (cid:3) . (14)For a single sample element the active IPF P iIP F is made up ofthe sum of active power injections of connected DERs P iDER j and the grid losses P iloss : P iIP F = N i (cid:88) j =1 P iDER j + P iloss (15) We are interested in the distribution X iP,IP F of active IPFs.Ignoring grid losses P iloss in (15), with equations (14) and (15)we can write: X iP,IP F ∼ N i (cid:88) j =1 N i U ij (cid:2) − P iinst,DERs , P iinst,DERs (cid:3) = 1 N i N i (cid:88) j =1 U ij (cid:2) − P iinst,DERs , P iinst,DERs (cid:3) , (16)which is exactly the Bates distribution on the interval (cid:2) − P iinst,DERs , P iinst,DERs (cid:3) .V. C ONCLUSION AND F UTURE W ORK
Aggregating the flexibility potential of DGs is an importantprerequisite for effective TSO-DSO coordination in electricpower systems with high share of generation located in theDG level. In this paper we first gave an overview of existingflexibility aggregation methods and categorized them in terms ofwhether they are data-driven/stochastic or optimization-based.Following this, we discussed the strengths and weaknessesof both approaches (stochastic and optimization-based) andmotivated the investigation of improved sampling strategies fordata-driven approaches. As a basis for this, we presented anexperimental setup by means of which we demonstrated andanalyzed the shortcomings of nai¨ve sampling strategies withfocus on the problem of resulting leptokurtic distribution ofIPFs.In future work we will investigate approaches for mitigatingthe convolution problem . One idea is to formulate the samplingas a distributed optimization problem whose objective functiontakes into account the uniformity of the resulting set of IPFs.First experiments in this direction with the Combinatorial Op-timization Heuristic for Distributed Agents (COHDA) protocolby Hinrichs et al. [18] and with Ripleys-K as metric for theevaluation of the distribution show promising results.Additionally, we are working on making OPF-based methodscompatible with black-box grid models by solving the under-lying OPF with the help of evolutionary algorithms such asthe covariance matrix adaptation evolution strategy (CMA-ES)[19] or REvol, an algorithm which was originally developedfor training artificial neural networks [20]. Furthermore, wewant to investigate if the total number of required objectivefunction evaluations can be reduced when sampling the borderof the FOR in one run by dynamically adapting the underlyingobjective function. A
CKNOWLEDGEMENTS
This work was funded by the Deutsche Forschungsgemein-schaft (DFG, German Research Foundation) – 359921210.R
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