RME EKSTERN RAPPORTpublikasjoner.nve.no/rme_eksternrapport/2019/rme_ekstern...Nr 01/2019 RME EKSTERN...

Nr 01/2019

RME EKSTERN RAPPORT

Power distance as an output parameter for grid companies

Formulation, application and comparison of minimal, power-flow based and grid-free power distance parametersTHEMA Consulting Group

Reguleringsmyndighetenfor energi – RME

Sammendrag:

Emneord:

Norges vassdrags- og energidirektorat Middelthunsgate 29

Postboks 5091 Majorstua 0301 OSLO

Telefon: 22 95 95 95 Epost: [email protected]: www.nve.no

RME Ekstern rapport nr 1-2019


Denne rapporten utforsker metoder for å beregne nye oppgavevariablersom kan brukes for å sammenligne nettselskapene. THEMA ConsultingGroup har utviklet tilnærminger for å beregne variablene effekt- ogenergiavstand. Metodene er testet ut på små datasett fra enkeltenettselskaper.

Effektdistanse, energidistanse, power-flow, sammenlignende analyser,inntektsregulering.

Utgitt av: Norges vassdrags- og energidirektorat

Redaktør: Tore Langset

Forfatter: THEMA Consulting Group

Trykk: NVEs hustrykkeri

Forsidefoto: Ole-Petter Kordahl

ISBN: 978-82-410-1962-3

ISSN: 2535-8243 (online)

Power distance as an outputparameter for grid companiesFormulation, application and comparison of minimal, power-flowbased and grid-free power distance parameters

Project infoClientRME

Project numberNVE-19-01

Project titlePower distance as an outputparameter for grid companies

Report infoReport availabilitypublic

THEMA report number2019-18

ISBN number978-82-8368-059-1

Date of publication25th November 2019

About the projectThis report investigates alternative output parameters for the DEA model in Norwegian DSO incomeregulation. The power distance parameter is introduced as a variable that reflects the task of gridcompanies by capturing the geographical distribution of demand in the high voltage distribution grid.Four methodologies to calculate a power distance, with different requirements on data quality andcomputational complexity, are introduced and applied to a selection of test cases. The results for hourlypower distances and annually aggregated energy distance parameters are discussed in the context ofapplicability and regulatory implications.

Project teamProject managerTheodor Borsche, Åsmund Jenssen

Contributors (alphabetically)Kristin ArnesenKristine FiksenLisa Zafoschnig

Executive Summary

Reguleringsmyndigheten for Energi (RME) is theNorwegian regulatory authority for energy. Amongits responsibilities is the regulation of income forDistribution System Operators (DSOs) and the res-ulting grid tariffs. In this context, Norway wasamong the pioneers of introducing a performancebenchmarking model to compare the efficiency ofgrid companies. The so-called Data EnvelopmentAnalysis (DEA) benchmarking model evaluates theperformance of each grid company based on anumber of indicators and determines the allowedincome based on the resulting relative efficiencyand the company’s actual annual cost. Currentlythe output parameters of the benchmarking modelare the number of customers, the total lengthof lines and the number of substations in thehigh-voltage distribution grid. As more data ismade available from smart-meters and centralisedinfrastructure databases, new output parametersfor the benchmarking process can be considered.Ideally, such parameters should represent the taskof the DSO (not its effort) and provide incentivesfor efficient grid reinforcement while being highlyexogenous, comparable and easy to compute fromavailable data.

The power distance as an outputparameter

THEMA Consulting Gorup has been commissionedby RME to investigate different methods to defineand compute new output parameters for the DEAmodel that take the distribution of demand into ac-count and thereby provide a more objective repres-entation of the task of a grid company. A parameterthat effectively captures the distribution of demandin a grid system is the power distance. The powerdistance parameter is the product of the distance

to each substation and transferred power, scaledby a factor that reflects how the investment costof power lines increases with higher capacity. Thedistance to each substation can be defined throughthe real lines in the grid, a synthetically created gridor a geographical length.

We investigate fourmethodologies for comput-ing a power distance parameter:

minimal power distance: The power distance inthe minimal radial grid configuration based onthe existing grid.

power-flow based power distance: The powerdistance based on physically optimal flows inthe existing grid where all line segments havethe same specifications.

artificial grid based power distance: A powerdistance computed for an artificially construc-ted grid that connects all substations based onthe minimal increase in power distance.

demand distribution based power distance: Apower distance obtained from the statisticaldistribution of demand around each trans-former station without considering a grid.

Analysis of the power distance basedon real grid areas

To analyse the computation methods on real distri-bution grid systems, six Norwegian DSOs providedpower demand and generation data for selectedgrid areas. The metering data, aggregated persubstation, were combined with data from RME’sextensive database on grid infrastructure to obtaina complete picture of each test case.

The provided data was generally of high qualitythough somemanual adjustments were required tocompile the grid data and match demand data to

©THEMA Consulting Group (2019) 3


the substations. For this project most challengesrelated to data availability could be overcome, how-ever, in a regulatory setting data quality is a crucialfactor as any manual handling will affect compar-ability and may increase administrative costs forthe regulator.

Minimal power distance

Due to the high computational complexity themin-imal power distance could not be computed for theprovided test cases. A real grid system is typicallycharacterised by a large number of meshes, allow-ing power to flow to one substation over differentpaths. The optimisation problem to compute theminimal power distance would have to iterate overall possible combinations of removing line seg-ments until a radial grid remains - a task that wasshown to be infeasible for real grid systems.

Power-flow based power distance

To compute the power-flow based power distanceit was necessary to compile the infrastructure dataper element into a complete grid system beforematching the demand data to each substation.This process, which was implemented with the useof standardised algorithms, could be performed forall grid companies in the reference group except forone, for which the line segments where stored in adifferent format.

The resulting hourly power distance showed alinear relation to the demand in each node scaledby the cost-parameter. Differences in the ratiobetween the demand and the power flow basedpower distance are a result of the line lengths in thesystem. More urban areas result in a larger ratioof power flow based power distance to demand,whereas rural areas are characterised by longeraverage line length to each substation which leadsto a lower ratio. This finding underlines that thepower distance accounts for challenges in supply-ing demand in different grid topologies.

Artificial grid based power distances

The lower data requirements for the grid-free para-meters – the artificial grid based power distanceand the demand distribution based power distance– that only use the location and demand per sub-station as input, made it possible to compute theoutput for all test cases. For the artificial gridbased power distance a synthetic radial grid iscreated based on an algorithm that connects sub-stations according to theminimum increase in totalpower distance. The resulting power distance foreach hour is computed from the power flow in theresulting radial grid.

Demand distribution based power distances

The demand distribution based power distancedoes not use a real or synthetic grid at all.Consequently, the requirements for data and com-putation time are low, which makes it comparablyeasy to compute the power distance for all testcases. Both grid-free power distance resultsshowed a linear correlation to the power-flowbased power distance, indicating that they canbe used as suitable proxies. The ratios betweenthe power distances obtained from different com-putation methods varied between test cases dueto differences in topography in each area. Whilethe power flow based power distance accountsfor obstacles in the grid and other area specificlimitations, such factors are not considered in thegrid-free methods. In further work we suggest toconsider potential geographical and topographicalcorrections that can be applied to the grid-freeparameters to improve comparability.

Concluding from the results of the differ-ent computation methods, the power-flow basedpower distance is identified as the most suitablemethod to represent the task of a DSO, with im-proved exogeneity compared to the current outputand high comparability between grid areas. At themoment, the use of grid data poses challengesthat can impede its use in a regulatory setting.

4 ©THEMA Consulting Group (2019)

Therefore, we suggest that the improvement ofdata quality and consistency should be a focusarea for further work. Should it not be possible toachieve a sufficiently high data quality, we proposeto apply the artificial grid based power distancewith an ex-post geographical adjustment.

Any computation of a power distance in thehigh-voltage distribution grid needs to be coupledwith a way of accounting for the demand in the low-voltage distribution grid. The location of custom-ers around a substation could be accounted for byusing a method similar to the demand distributionbased power distance or initially through the num-ber of substations.

Aggregation to an annual benchmark-ing parameter

To move from hourly power distance values to acomparable annual benchmarking output we in-vestigate how cost drivers can be represented bydifferent yearly aggregation methods. We refer toany annual parameter as an energy distance andapply the following methods:

1-norm: The sum or average over the full year –can be applied to the demand prior to comput-ing a power distance or to the hourly power dis-tance results. The 1-norm reflects the standardoperation of a system and is therefore a proxyfor the operational cost of a grid company.

2-norm: The sum of the squares of the differencebetween hourly values and mean – can be ap-plied with hourly and mean demand or hourlyand mean power distance. The 2-norm reflectsvariations in the system by emphasising hoursof large peaks, thereby potentially reflecting thecost of losses.

∞-norm The maximum value in a system – canbe applied to the total system demand, themaximum demand per substation/maximumflow per line or the respective power distances.The ∞-norm reflects the maximum load situ-ation for which the grid needs to be equipped.

It is a measure for the investment cost.

For the1-normweconclude that using the aver-age demand or the average power distance will notimpact comparability between DSOs. Either of themeasures will be a suitable parameter to reflect theoperational costs of a grid company. For reasonsof computational effort, we recommend to use theaverage system demand and compute the energydistance from it.

In the case of the 2-norm, we investigate differ-ent approaches to correctly account for variationsin the system. We conclude that the 2-norm shouldnot be used in the DEA model as the cost of lossesis already reflected by the computation of a powerdistance as transferred power and line length areaccounted for.

For the situation ofmaximum load, we proposeto use the maximum demand per substation or, ingrid-based computations, the maximum flow perline, to compute a ∞-norm energy distance. Inlarge grid areas the probability of all customersexperiencing their maximum load at the same timeis lower than in a smaller areawith less consumers.Due to these simultaneity effects, using the hourof maximum total demand or power distance willnot affect grid areas of different sizes to the sameextent and may underestimate the required invest-ment.

In addition, we propose to keep the numberof customers in the DEA benchmark to reflect theadministrative costs that a grid company is facing.

Implications of the power distance inDSO income regulation

By using a power distance computation and per-forming different yearly aggregations, we can rep-resent the main cost drivers in the distribution gridmore effectively than the currently usedDEA outputparameters. Through the choice of the power dis-tance parameter a compromise between the com-parability of grid areas, the data requirements, thecomputational complexity and the exogeneity can



be found according to the main regulatory require-ments. Future work on this topic should focus oninvestigating the applicability of the power distancemethods in larger grid systems and ultimately theentire Norwegian high-voltage distribution grid toconclude which output parameters are best suitedfor the purpose.


Contents

Contents

1. Introduction 91.1. The DEA benchmark model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2. Other relevant models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3. The power distance for DSO benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2. Formulation and computation of power distance parameters 142.1. General concept of power distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2. Minimal power distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3. Power-flow based power distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4. Artificial grid based power distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5. Demand-distribution based power distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.6. Power distance in the low-voltage distribution system . . . . . . . . . . . . . . . . . . . . . 232.7. Alpha parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3. From power distance to energy distance 273.1. Cost drivers in the distribution grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2. From hourly values to a yearly parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3. Input from the reference group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4. Test cases 374.1. Description of test cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2. Data quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5. Results per test case and per parameter 445.1. Minimal power distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.2. Power-flow based power distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.3. Artificial grid power distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.4. Demand distribution based power distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.5. Comparison of yearly output parameters - energy distance . . . . . . . . . . . . . . . . . . 485.6. Comparison of different alpha parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6. Evaluation 546.1. Discussion of key factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.2. Feedback from the reference group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

7. Recommendations and conclusions 617.1. Discussion of applicability and incentives per parameter . . . . . . . . . . . . . . . . . . . 617.2. Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.3. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66



A. Acronyms 72

B. References 73


1. Introduction

1. IntroductionReguleringsmyndigheten for Energi (RME) is re-sponsible for regulating Norwegian electricity net-work companies (Distribution System Operator(DSO)1). A key element of the regulation of distri-bution grids is RME’s Data Envelopment Analysis(DEA) model. RME’s DEA models are designed tobenchmark the costs of a network company givena set of outputs that describe the tasks of thegiven company. In the distribution grid, the outputsare the number of customers, kilometres of linesand the number of substations2 in the high-voltagedistribution grid 3as proxies for customer demandfor each DSO.

RME is now exploring the possibility to replacethe existing output measures by exogenous meas-ures that better reflects the distribution of demand.A parameter that considers the transferred powerand the distance to each demand node is theelectric power distance as an hourly value, or theenergy distance as an annual aggregation. In thisreport, THEMA provides a method for estimatingmeasures of electric power distance and energydistance, aswell as a discussion of the applicabilityof the proposed method. The main part of the re-port concerns the calculation of the power distanceusing differentmethodologies, andwealso discusshow to move from the electric power distance toan annual measure of the energy distance as abenchmarking parameter.

1The Norwegian term nettselskap is translated to grid com-pany or DSO in this report.

2In this report we use substation to refer to the Norwegiannettstasjon, i.e. a transformer station from the high-voltage (10 to 22 kV) distribution grid to the low-voltage(220 to 400V) distribution grid.

3high-voltage refers to a voltage level of 1 to 22 kV in theNorwegian distribution grid. In this report we will usehigh-voltage and low-voltage (220 to 400V) according toNorwegian grid standards.

1.1. The DEA benchmark model

The DEA model determines how much incomeeach grid company can collect from their custom-ers grid tariffs. The idea behind the design of theregulation is that each grid company incurs costs insolving their tasks. Costs are related to operationalcosts, capital costs, cost of losses, andCENS costs(Cost of Energy not Supplied, KILE in Norwegian).The task of the grid company is currently repres-ented by number of customers, number of substa-tions, and kilometres of lines, often referred to asthe outputs.

As a sum, the costs incurred by all grid compan-ies in the distributional level are covered (with theRME reference interest rate representing an expec-ted rate of return), but the regulation aims to rewardthe most efficient companies with higher income,and thus create incentives for operational improve-ment and socioeconomic investments. The DEAmodel is applied to benchmark the companiesagainst one another and determine which ones arethe most efficient. The most efficient companiesare called ”front” companies.

In short, the average company is classified as100% efficient, while the most efficient companiesare above 100% and less efficient companies havean efficiency below 100%. We will not describe theincome regulation of Norwegian companies in de-tail in this report, but simply state how a companycan collect its costs given its allowed income. Agrid company’s allowed income is given as

𝐼𝑅𝑡 = (1 − 𝜌) ⋅ 𝐾𝑡 + 𝜌 ⋅ 𝐾∗𝑡

Where 𝐾𝑡 is the company’s actual costs, 𝐾∗𝑡 is

the cost norm, and 𝜌 is a factor defining to whatextent the income of a grid company is bench-marked. If a company is an average company



(100% efficient), 𝐾𝑡 = 𝐾∗𝑡 . If the company has an

efficiency above 100%, then 𝐾𝑡 ≥ 𝐾∗𝑡 , and has a

rate of return higher than the RME interest rate. Aless efficient companywill have a rate of return thatis less than the RME interest rate – providing anincentive to become more efficient. Currently, 𝜌 isset to 60%, meaning that 40% of the cost base canbe directly passed on to consumers, while 60% arebased on the benchmarked cost norm.

As a grid company is evaluated on how costefficiently it covers its tasks, it is important thatthe output parameters are describing the task –or the cost drivers – of the grid company in arelevant way. The task is to cover demand of allcustomers at all times, and the main costs driversare investment costs (CAPEX), OPEX such as costof delivering power and cost of losses, O&M costsand administrative costs.

1.2. Other relevant models

There is no standardised framework for incomeregulation of grid companies and, in general, eachcountry has developed its own approach to de-termine the allowed income. Despite the largedisparities between the existing frameworks somecommon methods and tools can be identified.

Centralised planning An approval for each newproject is required before it can be added to theasset base, based on which the grid company isremunerated at a specified rate of return. Similarapproaches are more common in the transmissiongrid where investments are typically larger and lessfrequent.

Cost plus In this traditional model for regulatingmonopoly revenues the network company is al-lowed to recover its actual costs including a returnon invested capital. In a distribution grid the rev-enues would typically not depend on approval forindividual investments but rather be based on thecompanies’ reporting of their own costs, subject toregulatory approval of total spending and admiss-ible costs.

Revenue caps A cap on revenues is set basedon allowed costs per DSO plus additional factors.A common approach is the so-called RPI-X modelwhere the annual regulated revenue may not beincreased by more than the retail price index (RPI)minus a fixed adjustment factor (X). Another ex-ample is the RIIO (Incentives + Innovation + Output)approach used in the UK which includes allow-ances for innovation funding and incentive rewardsfor reliability, customer service and reduced losses.

Performance benchmarking The performanceof each company relative to its task is bench-marked against other grid companies or against asynthetic grid to define a revenue cap. The allowedincome is determined by a grid company’s relativeefficiency. The current DEA benchmarking modelin Norway is an example of a performance basedregulation.

In the context of the Norwegian DEA bench-marking and potential adjustments to its output, weconsider it relevant to comment on performancebenchmarking models from other countries. Twonoteworthy approaches are the Reference NetworkModel (RNM) in Spain and the Network Perform-ance Assessment Model (NPAM) in Sweden.

1.2.1. Spain

In Spain amethodology was developed to comparethe real grid of DSOs against an idealised radial gridthat is created by the so-called RNM. The frame-work, which is applied to all voltage levels in thedistribution grid, determines the efficiency of eachDSO individually relative to an ideal grid insteadof comparing the performance of grid companiesagainst one another.

The RNM is described as a large-scale planningtool which plans the electrical distribution networkusing the GPS coordinates and power of everysingle customer and distributed energy resource.In the process of creating an idealised grid themodel considers both technical constraints – suchas voltage limits and capacity constraints – andgeographical limitations – such as topography or


1. Introduction

water bodies. The cost of individual componentsin the idealised grid are based on a standardisedequipment library.

There are two set-ups of the RNM which areused in the benchmarking process. A greenfieldmodel that builds the entire grid system, includingtransformer stations, from scratch based on thedistribution of demand points, and a brownfieldmodel that considers extensions to the existinggrid based on new demand or production points.The greenfield model is used to determine the effi-ciency of the existing grid relative to an idealisedgrid. While the grid from the greenfield modelserves as an indicator as to which grid configur-ation would be best suited if all demand pointswere to be connected at the same time, it does notaccount for the historic development of the grid.The brownfieldmodel is applied to determinewhichnew investments in grid extensions and reinforce-ments aremost efficient based on the existing grid.[1]

Both efficiency measures are considered in theannual benchmarking that is performed before thetariffs of the next year are determined. [2]

Beyond its use as a regulatory tool, the RNMis also used by DSOs for planning purposes and toevaluate the impact of the integration of distributedgeneration.

1.2.2. Sweden

In Sweden a benchmarking model based on theso-called NPAM was introduced in 2004 and latersuspended. The NPAM was a newly developedmodel that compares existing grids to a standardasset. The aim was to evaluate the benefits to theconsumer from an artificial radial network withoutexcess capacity. In parallel to the development ofthe model a new legislative act was introduced toaccommodate for the changes in regulation.

The NPAM creates a radial network that con-nects all nodes in a system on four voltage levels.Additionally spare capacity is considered to reflectthe need for grid enforcements beyond a pure radialtopology to ensure security of supply. The capital

cost of the fictive network is referred to as thecost of connection which is based on standardcost functions per asset that take into accountthe physical properties of cables and transformers.The radial grid is also used to determine the cost ofdelivery, which describes the losses in the systemand the cost of reliability, which is linked to thespare capacity. Other cost components in themodel are the cost of administration, which scaleswith number of customers, and the cost of services,which are reported costs for connections to thetransmission grid. The total cost from the NPAMis then compared to the revenues per DSO. Overalla DSO would be allowed to collect revenues thatcorrespond to the customer value as calculated bythe model. [3]

Despite the innovative approach with a focuson the DSOs task and the resulting customer bene-fit, the NPAM faced large challenges and was latersuspended from the Swedish regulation. Generally,the complexmodel setupwas notwell documentedand therefore hard to understand for anyone out-side of the regulatory authority. Tests on the NPAMafter its release also raised concerns on the ro-bustness and fairness of the model. Geographicaldifferences of few meters, within the uncertaintyof data quality, resulted in entirely different syn-thetic networks and therefore different benchmark-ing premises for the same company.

It was also viewed critically that the model didnot account for the historic development of the gridor geographical constraints. Inherited assets canseem inefficient compared to a synthetic grid, eventhough they were an efficient solution at the time ofconstruction.

The main concern, however, was that theframework was designed as an ex-post model,meaning that the benchmarking was applied thefollowing year after tariffs had been determinedand paid. Results of the NPAM indicated that ”theSwedish network companies are overcharging theirsubscribers with approximately 20%” [4]. This couldlead to DSOs being obliged to pay back part of itsrevenue to the customers.

In 2008 the major criticism on the benchmark-



ing approach followed by the appeal of severalDSOs and a lawsuit led to its suspension from theSwedish regulation.

1.3. The power distance for DSObenchmarking

The aim of this report is to definemethodologies tocalculate an alternative benchmarking parameterfor DSO income regulation. The current bench-marking based on number of customers, substa-tions and length of lines has two main draw-backs:it does not necessarily reflect the challenges ofsupplying power over long distances and the outputis partly under control of the DSO through theirinvestment decisions. As the consumer patternsin the distribution grid change through technolo-gical advancements such as distributed genera-tion, local storage and EV charging infrastructure, abenchmarking parameter should be able to capturethe resulting changes in the task of a DSO. Addi-tionally, a higher quality of available data makesit possible to account for information that wasnot previously available. In [5] a so-called powerdistance parameter was suggested, that takes intoaccount the demand and the distance over whichpower has to be transferred to each customer. Inthis report we will focus on defining and comparingdifferent approaches to calculate such a powerdistance parameter. We further discuss how hourlypower distance parameters can be aggregated to ayearly value - an energy distance.

The suitability of different power distancemethodologies as benchmarking parameters de-pends on several factors. For a parameter to bean objective benchmark we deem the followingfactors to be most important:

Representation of the DSO’s task The power dis-tance should represent the task of the DSOrather than its effort. A DSO has the obligationto cover the demand of customers in the gridat all times. To fulfil this task a DSO needs to

equip the grid accordingly to ensure security ofsupply and cost effectiveness.

Data Requirements In terms of needed input datafor each methodology two factors are crucial:availability and ease of handling. The requireddata for a computation should be availableand easily accessible for each DSO from cent-ralised sources. Additionally, handling largeamounts of data can be challenging both forthose supplying it and those handling it in thefinal computation. With an increased needfor data, the consistency and quality can be afurther constraint.

Computational Effort The complexity of the cal-culation method can be a major limitation.Ideally, it should be possible to calculate thebenchmarking parameter with low computa-tional effort.

Exogeneity The chosen benchmarking parametershould be as neutral as possible. It should notbe possible for the DSO to influence the outputof the power distance calculation through theirdecisions on investments or operation. In thecurrent regulation the length of lines is underdirect control of the DSOwhichmay incentivisebuilding longer lines than necessary.

Incentives The choice of benchmarking para-meter may create different incentives. An idealparameter should not disincentivise any of thefollowing: building the shortest/most efficientconnections, investment in assets that improvesecurity of supply, providing input data of highquality, among others.

Intuitiveness The method to compute a powerdistance should be fairly intuitive and easyto communicate to stakeholders. Any entityaffected by the regulation should ideally beable to comprehend the computation steps andtheir implications.

While onemethodologymay give themost real-istic representation of the task of a DSO, compu-tation time may be a limitation and higher data


1. Introduction

requirements may pose challenges towards exo-geneity. On the other hand, a simple approach withminimal need for data and computational effortmay incentivise unnecessary investments. Thechoice of benchmarking parameter will be basedon a compromise between the criteria definedabove. The individual implications for each of theproposed methods will be discussed in more detaillater.

In this report we will introduce four method-ologies to compute a power distance parameter.Each approach for computing hourly power dis-tance values is described in detail in Section 2before possible aggregations to an hourly bench-marking parameter are described in Section 3. Themethodologies are tested on real grid data from sixNorwegian DSOs and compared in Section 5. As aresult, we can evaluate and compare the differentmethodologies and their implications in Section 6before we conclude with final recommendations inSection 7.



2. Formulation and computation of power dis-tance parameters

The power distance is identified as a parameterthat captures the distribution of demand in a gridarea, by including both the length over which powerneeds to be transported and the demand per node.In this chapter we describe the general concept andmathematical formulation of the power distancebefore providing a detailed overview of the differentapproaches to compute such a parameter. Forsimplicity, each computation method is introducedbased on an exemplary test case.

2.1. General concept of powerdistance

The general idea behind the power distance is tohave a more meaningful parameter describing thetask of a grid company. Currently, the length oflines is one of the parameters used. Previously,the demand served over a year was an indicatoras well, benefiting grid companies with large con-sumers close to transformer stations. The powerdistance improves on these two metrics by com-bining demand served and distance per consumerinto the product of the two indicators. Transportingmore power over a certain distance gives a higherpower distance than transporting less power overthe same line. In turn, serving a large load close byis considered much easier than serving the sameload if it is further away. The power distance shouldconstitute a more informative output parameterand thus lead to a fairer benchmarking of gridcompanies.

Mathematically, the power distance is definedas the sum of the products of the transportedpower and line length over all line elements. The

general equation for the power distance 𝑃d is

𝑃d = ∑∀𝑒𝐿𝑒 𝑃𝛼𝑒 , (2.1)

with 𝐿𝑒 the length of line element 𝑒, 𝑃𝑒 the (absolute)flowalong that line element, and 𝑒 ∈ ℰ1 the set of alllines ownedby the grid company. The externally setparameter 𝛼 describes the scaling effect of costs,i.e., a line able to carry twice the power is typicallyless than twice as expensive.

The main question related to the power dis-tance parameter is how the flows, i.e. the trans-ferred power, over each line 𝑃𝑖 are determined andhow the distance is defined. There are two mainchallenges: how to handle complex grid topolo-gies? And how to compute the power distance ifgrid data is not available?

In a purely radial or tree-shaped grid, the flowsare determined by the demand. While comput-ing the power distance requires care, the result isuniquely determined. If, however, there are meshesin the topology, the power may be distributed to theconsumer along different paths. In turn, the powerdistance is no longer uniquely determined. If griddata is altogether missing, one needs to pursue analternative approach based on the location of thedemand and possibly on local geographical limita-tions to define the distance. To address these chal-lenges, we are proposing different algorithms tocompute the power flow on grid lines, and hence ar-rive at different power distance parameters. Theseare the minimal power distance (Section 2.2), thepower-flowbased power distance (Section 2.3), theartificial grid power distance (Section 2.4), and thedemand distribution based power distance (Sec-1𝑒 as in edge in a graph


2. Formulation and computation of power distance parameters

tion 2.5). All of these parameters have different re-quirements on data availability, computation timeand exogeneity – meaning the extent to which theparameter can or cannot be influenced by the gridcompany.

For simplicity, all our algorithms aggregate thedemand per substation (nettstasjon). Section 2.6discusses how this could distort incentives againstusing 3-phase systems on the low voltage level.Section 2.7 discusses different approaches andresults for estimating the 𝛼 parameter needed inthe power distance calculation.

Exemplary Test Case

In the following sections each of the proposedmethodologies is described based on a simplifiedtest case. The following points are critical in defin-ing a representative test case for this purpose:

The test case should be simple enough to ex-plain each methodology but complex enoughto highlight challenges with each method.

The grid lines should not always be a dir-ect connection between two points, to reflectobstacles that occur in a real grid such asbuildings, water bodies or steep terrain.

x

12

3

45

67

0(0)

(1)

(2)

(3)

(4)

(5)(6)

(7)

(8)

Figure 2.1.: Test Case for the power distance calcula-tions

The grid should have meshes to reflect thatthere are different lines over which power canbe distributed to the same node.

The demand per node should be chosen in away that makes the effect of the cost scalingparameter alpha visible when constructing anartificial grid.

The demand point should be distributed geo-graphically to better visualise the demand dis-tribution based power distance.

Based on the above-mentioned criteria we haveselected a grid topology that reflects the propertiesof each parameter, shown in Figure 2.1.

Nodes 2 are numbered in bold where node 0is the transformer station that connects the dis-tribution grid to the regional grid. For simplicitythe test case only contains one transformer station3. In a case with multiple transformer stations,each algorithm assigns nodes to one transformereither through the closest distance or the existinggrid connections. In the test case, there are ninestraight line segments, numbered with an index inbrackets e.g. (1), that connect the nodes and createone mesh (between lines (3),(4) and (5)) and onecorner (lines (2) and (7)) in the grid. The demandat each node is summarised in Table 2.1

Node 1 2 3 4 5 6 7Demand 200 20 50 100 40 60 50

Table 2.1.: Demand per node in the test case in kW

The test case was created based on real geo-graphical coordinates at a selected location in Nor-way. The resulting line lengths per segment aresummarised in Table 2.2. Additionally the start andend point of each line is given in accordance withFigure 2.1.

Note that demand is given in kW and linelengths in m for the test case while the power2Node refers to each point in the graph. In the case of thisreport a node is equivalent to a substation

3transformer (station) refers to the transformer between theregional grid (R-nett) and the high voltage distribution grid



Line from node to node length [m](0) 0 1 456(1) 0 2 357(2) 0 x 496(3) 2 3 237(4) 2 4 238(5) 3 4 258(6) 4 5 137(7) x 6 254(8) 6 7 86

Table 2.2.: Details on lines in the test case, x refers to theconnection point between lines (6) and (7)

distance uses the unit MW𝛼 km. Due to the scalingof the alpha parameter the unit conversion is:

𝑃d [MW𝛼 km] = 1000(𝛼+1) ⋅ 𝑃d [kW𝛼 m] (2.2)

𝑃d [MW𝛼 km] = 1000𝛼 ⋅ 𝑃d [kW𝛼 km] (2.3)

𝑃d [MW𝛼 km] = 1000 ⋅ 𝑃d [MW𝛼 m] (2.4)

2.2. Minimal power distance

The minimal power distance 𝑃mind refers to the

minimal power distance that can be achieved givena certain demand distribution and the existing gridtopology. Mathematically, this can be written as

𝑃mind = min

𝑝𝑒∑𝑒∈𝐸

𝐿𝑒 |𝑝𝑒|𝛼 . (2.5)

As was shown in [5], finding the minimal powerdistance will always result in a radial system, butiteratively scanning for the minimal grid configur-ation is computationally expensive if the topologyhas meshes. We were able to describe a globallyoptimal4 algorithm for finding the minimal powerdistance, but it scales exponentially with the num-ber of meshes.

In this approach the upper bound on the com-

4”Global optimality” means in simplified terms that the al-gorithm always finds the best solution to a problem

plexity is

𝒪(𝐸𝐶) , (2.6)

with 𝐸 the number of lines in the graph and 𝐶 thenumber of meshes.5

The algorithm uses the finding that an optimalcost minimising topology is always tree-shaped.The approach is to effectively test all possible com-binations between removing lines, and searchingfor the one tree within the given grid topologythat minimises the power distance. If there isone mesh, the algorithm iterates over all lines thatconstitute the mesh. If there are two meshes,the algorithm has to iterate over all combinationsof removing two lines, one from each mesh. Ifthere are 𝐶 meshes, the algorithm needs to iterateover all combinations of removing 𝐶 lines from thegrid. This is why the computational complexitygrows exponentially with the number of meshes.For more details and alternative, sub-optimal al-gorithms, see [5].

On the test case the algorithm iterates overeach line segment ((3),(4),(5)) that constitutesthe mesh in the system. At each combina-tion of removing a line a radial grid remains forwhich the power distance can be calculated. Theresulting grid systems are shown in Figure 2.2where the mesh elements are marked in red.Removing line (4) gives the highest power dis-tance (16.54MW𝛼 km) for the system, while re-moving lines (3) gives a lower power distance of15.93MW𝛼 km). The minimal power distance forthe system is 15.60MW𝛼 km for a radial systemwhen line (5) is removed.

For the test case, computing the minimalpower distance is a simple task with few iterationsthrough a single mesh. However, each additionalmesh in a systemwill greatly increase the complex-ity. In the case of real grid systems this reaches anextent where the minimal power flow calculation is

5As shown in [5], this bound can be formulated somewhatmore tightly as 𝒪(∏𝑐∈𝐶 𝐸𝑐), with 𝐸𝑐 the number of linesconstituting eachmesh. However, this does not affect theexponential scaling property.



12

3

45

67

0(0)

(1)

(2)

(3)

(4)

(5)(6)

(7)

(8)

(a) Total grid with one mesh

12

3

45

67

0(0)

(1)

(2)

(4)

(5)(6)

(7)

(8)

(b) Radial grid by removing line (3)

12

3

45

67

0(0)

(1)

(2)

(3)(5)

(6)

(7)

(8)

(c) Radial grid by removing line (4)

12

3

45

67

0(0)

(1)

(2)

(3)

(4)

(6)

(7)

(8)

(d) Radial grid by removing line (5)

Figure 2.2.: Illustration of the iteration for finding the minimal power distance based on the test case

too complex to be performed.

2.3. Power-flow based powerdistance

In [5], we also proposed an alternative to theminimal power distance. Instead of finding thetree which minimises the power distance, the full,meshed topology is used. The flows are determ-ined by a power flow computation, with equal im-pedance per km for each line.

This power-flow based power distance 𝑃flowdhas two main strengths: the 𝑝𝑒 are easily com-puted using existing tools for power flows, and

the approach is far more intuitive and more easilycommunicated to stakeholders affected by the reg-ulation.

The power distance is computed as in (2.8),

𝑃flowd = ∑∀𝑒𝐿𝑒 𝑃𝛼𝑒 (2.7)

where 𝑃𝑒 is computed by an optimal power flowalgorithm.

An optimal power flowmodel is a common toolfor the analysis of electrical system operation andcomponent sizing for system expansions. A powerflow analysis determines the optimal steady-stateoperation of a grid system based on generation,



12

3

45

67

0(0)

(1)

(2)

(3)

(4)

(5)(6)

(7)

(8)

Figure 2.3.: Power flow based power distance, thick-ness of lines defines flow on line, arrow defines direc-tion of flow

demand, and line specifications. In the case ofconstant line specifications and known demandper node, the power flow computation determinesthe flow per line that minimises the real and re-active losses in the system within component con-straints.

For the power-flow based power distance thefull meshed grid is used. In the test case all nodesand lines are considered in the algorithm whichallows power to be distributed to one node overmultiple lines. For the radial part of the grid thepower flow is defined by the demand (and gener-ation) at each node. In the meshed part of the grid(lines (3),(4),(5)) power can flow towards node 4 vialine (4) and via the lines (3) and (5). Alternativelypower could flow to node 3 via the line (3) or via line(4) and (5). The power flow algorithm calculatesthe flow on each line segment based on the idealphysical flow. The resulting flows for the test caseare visualised in Figure 2.3, where the arrows definethe flow direction and the thickness indicates theintensity of flow on each line. From the results ofpower flow per segment and the length of eachline a power distance can be calculated. For thetest case the power-flow based power distance is16.68MW𝛼 km .

2.4. Artificial grid based powerdistance

Using the existing grid has two drawbacks: 1) itrequires an extensive amount of high-quality data,and 2) it affects the exogeneity of the parameter, asthe grid companies, theoretically, have the possibil-ity to affect the power distance benchmarking para-meter with their investment decisions. The latterissue may lead to undesired investment incentivesor disincentives, as was shown in [5].

Alternatively, one may attempt to construct anideal grid given the demand and the location ofthe closest transformer station. The benchmarkingmodels used in Sweden and still in use in Spain doexactly this. However, constructing a realistic gridas a direct benchmark is by no means a trivial task.Many restrictions would need to be accounted for(streets, buildings, bodies of water, steepness ofterrain, other zonal restrictions), and an extensivecost and infrastructure data base would need to beused.

We do not attempt to construct a realistic gridlayout, but rather aim for an idealised grid. Thisgrid should take into account the demand distri-bution and the alpha parameter, but it should notbe seen as the best achievable topology. Rather,it should be used as a relative benchmark in thesense ”how close does each grid company cometowards the idealised grid?” and then benchmark-ing the grid companies against each other. Com-plicating factors such as the terrain, building dens-ity or coastal obstacles can be taken into account inadditional correction factors in the benchmarking.

To compute the idealised grid, we follow thisalgorithm:

1. We identify the closest substation to any trans-former station, and connect it to its transformerstation.

2. The closest unconnected substation - the freesubstation - is identified.

3. All demand except the demand from the freesubstation is allocated to the closest node



(transformer station or connected substation).The power distance is computed.

4. The free substation is connected to the nodewhere it increases the power distance by theleast amount.

5. The algorithm repeats Step 2 to 4 until all sub-stations are connected.

Step 3 is essential to incorporate the 𝛼-Parameterinto the algorithm. The algorithm itself is a de-terministic heuristic to find a good approximationfor the ideal grid connecting all substations to thetransformer station(s), given an 𝛼. Since it is de-terministic, it will always yield the same result fora given set of data. Being a heuristic, it is oneapproach to obtaining a result for which there is noguarantee on optimality.

Based on the artificial grid a power distance iscomputed using a power flowmethod. Themethoddetermines the flowon each line element of the gridand calculates the power distance as follows:

𝑃𝑎𝑟𝑡d = ∑∀𝑒𝐿𝑒 𝑃𝛼𝑒 , (2.8)

with 𝐿𝑒 the length of line element 𝑒, 𝑃𝑒 the (absolute)flow along that line element, and 𝑒 ∈ ℰ the set of alllines in the artificial radial grid.

Note, that there are two possibilities to usethe artificial grid methodology. One can eithercompute a new grid for each hour and demanddistribution or build an artificial grid once and popu-late the nodes with hourly demand values for eachcalculation. We consider it the most objective tocreate one artificial grid per DSO based on a rep-resentative hour, e.g. the hour of highest demand,and use the same grid for each hourly calculation.Creating an artificial grid for each hour not onlydrastically increases computation time but wouldalso not reflect the real situation where one gridshould be equipped to handle demand in any hour.

For the test case, shown in Figure 2.4, the al-gorithm uses the coordinates and demand of eachnode as an input. Starting from the transformer sta-

12

3

45

67

0(1)

(0)

(2)

(4)

(6)

(3)

(5)

Figure 2.4.: Artificial grid based on the test case, num-bering of lines refers to the order in which they areconnected

tion the nodes in the system are iteratively connec-ted through direct lines based on which connectionincreases the total power distance by the least ineach step. The order in which lines are added bythe algorithm is reflected by the line numbering, i.e.line (0) is the first connection.

Each connection step performed by the al-gorithm will be described in the following:

1. Line (0)

The algorithmwill first identify node 2 to bethe closest substation to the transformerstation.

Line (0) is built between the transformerstation and node 2.

2. Line (1)

The closest free substation to the trans-former station or an already connectednode is identified at node 1.

All remaining demand is allocated to theclosest node, meaning that the demandfrom nodes 6 and 7 are allocated to thetransformer station and the demand fromnodes 3, 4 and 5 will be projected to node2 leading to a total demand of 210 kW atnode 2.



The power distance for this system is com-puted and the free node 1 will be connec-ted where the power distance increasesby the least amount. In this case, node1 is connected directly to the transformerstation because the large distance to allother nodeswould increase the total powerdistance more.

3. Line (2)

In the next step, node 3 is identified as theclosest free transformer station.

Again, the demand of all non-connectednodes is allocated to connected substa-tions and the power distance is computed.

Node 3 is connected to node 2, towhich thedemand of node 4 and 5 are allocated, vialine (2).

4. Line (3)

The next free substation is node 6,

Line (3) is built with the same approachas for previous lines. Since the distancesto the remaining connected nodes wouldincrease the power distance more, node6 is directly connected to the transformerstation via line (3).

5. Line (4)

Node 4 is identified as the closest uncon-nected node.

In this step the allocation of the remainingdemand becomes crucial to the decisionwhether it should be connected to node 3or node 2.

The demand at node 5 will be allocated tothe closest connected node, node 3. Asa result, 210 kW of power will need to bedistributed to node 2 and at least 130 kWto node 3.

The demand in node 7 is allocated to node6 and does not impact the branch towardsnode 4.

If node 4 is connected to node 3, then thetotal flow to node 3 needs to be 190 kW ofwhich 90 kW cover the demand in node 3,40 kWare transferred to node 5 and 100 kWto node 4.

Should node 4 be connected to node 2, theflow to node 3 will be 130 kW, and the flowto node 4 will be 100 kW.

When calculating the power distance forboth alternatives, one can see that the con-nection of node 4 to node 2 increases thepower distance by less than a connectionbetween node 3 and 4.

The artificial grid thus establishes a con-nection between node 2 and 4. Intuitively,by looking at the test case connecting node4 to node 3 would create a longer path forpower to flow in a radial system.

6. Line (5)

In the next step, node 7 is the closest un-connected substation.

Because of its short distance to node 6 andno close substation from where demandis allocated towards this branch, node 7 isdirectly connected to node 6.

7. Line (6)

The last node to be connected is node 5

Node 5 is connected to the closest substa-tion as there is no remaining unconnecteddemand that needs to be taken into ac-count.

For the resulting radial system, the power flowis uniquely defined by the demand at each node.From the power flow and the length per line theartificial grid based power distance can be calcu-lated. For the test case it is 14.85MW𝛼 km. Notethat the power distance on the artificial grid islower than the minimal and the power flow basedpower distance. This is a result of shorter linesin the artificial grid which will always create directconnections between nodes and does not accountfor obstacles or meshes.



2.5. Demand-distribution basedpower distance

The last approach to compute a power distanceparameter avoids using a grid - real or synthesised- altogether. Instead, the power distance is com-puted from the distribution of demand around theclosest transformer station.

The reasoning behind this is to define a highlyexogenous measure with minimal data require-ments and limited computational effort. Com-puting the demand distribution and ultimately thedemand-distribution based power distance is apurely statistical approach that only takes the geo-graphical coordinates and demand per customeras input. The resulting parameter is neither relatedto nor benchmarked against the real grid, therebyproviding an exogenous measure of the DSOs taskrather than their effort.

The demand-distribution based power dis-tance is computed in the following steps:

1. We identify the closest transformer station toevery substation and isolate areas with 𝑘 sub-stations around one transformer station as ori-gin.

2. For every substation 𝑖 within one area the dis-tance (𝑟𝑖) and angle (𝜃𝑖) to the origin is cal-culated. The radius is the euclidean distancebetween node and transformer station. Theangle is defined in degrees where 0 degreespoints North.

3. The distance between substation and origin ismultiplied with the substation demand (𝐷𝑖) toobtain a linear power distance: 𝑃𝑑𝑖 = 𝑟1/𝛼𝑖 ⋅ 𝐷𝑖.The radius is scaled down by the cost-scalingparameter to avoid double counting in step 6.

4. For each substation a normal distribution𝒩(𝜃𝑖, 𝜎), where 𝜎 = 1/𝛼, is created and scaledwith the linear power distance 𝑃𝑑𝑖 . Here thealpha parameter defines the width of the distri-bution and thereby the distance between twodemand points at which building one line be-comes more economocially favourable than

building two lines.

5. The individual distributions per substation areadded to create a continuous demand distri-bution around the transformer station 𝒟(𝜃) =∑𝑘

𝑖=0𝒩(𝜃𝑖, 𝜎)

6. The integral over the distribution (all anglesfrom 0 to 360 degrees) to the power of 𝛼 givesthe demand distribution based power distancearound the transformer station

𝑃statd = ∫360

𝜃=0𝒟(𝜃)𝛼𝑑𝜃

In the initial and most simple approach, topo-graphical constraints such as terrain steepness,water bodies and densely inhabited areas or differ-ences due to weather conditions are not accountedfor. However, correction factors can be applied tothe calculated parameter at the expense of highercomputation time. Examples for such correctionfactors are a topographical correction based onthe proportion of area types in the considered sur-rounding or a weather correction based on historicweather statistics per area.

The approach can be described in more detailwhen the test case is considered. Figure 2.5 showsthe input for the statistical methodology. For each

1 2

3

45

67

0

Figure 2.5.: Input for the statistical power distancecalculation based on the test case. Size of bubblesshows demand per node



node the geographical coordinates define the po-sition and the demand per node determines thesize of the bubbles. For each node the radius andangle to the transformer station can be calculatedas summarised in Table 2.3.

Node radius [m] angle [deg] demand [kW]1 456 267 2002 357 62 203 542 43 504 589 69 1005 726 68 406 552 175 607 632 178 50

Table 2.3.: Input per node for the statistical power dis-tance distribution

Following step 4. in the process description ascaled normal distribution of the power distanceis calculated around the angle of each node. Theindividual distributions are visualised in Figure 2.6.The colours of the curves correspond to the colourcoding of nodes in Figure 2.5 and serve as a guideto the eye. Overlaps in the individual distributionsymbolise angular proximity between two nodes.In this approach, we argue that it is more efficientto serve nodes that are in angular proximity – i.e.show overlaps – with one strong line rather thantwo individual lines.

Consequently, when the individual distributionsare summed to a continuous distributions, as de-scribed in step 5., larger peaks are visible at angleswhere multiple nodes are in close angular proxim-ity. The continuous distribution for different alphaparameters is shown in Figure 2.7. As alpha rep-resents the cost-scaling of lines with transferredpower, the economic efficiency of building one ormultiple lines depends on its value. For large al-pha values building individual lines becomes moreefficient, resulting in less overlapping of peaks inthe distribution, while small alpha values suggestbuilding strong lines to supply multiple nodes ismore cost efficient, resulting in stronger overlaps inFigure 2.7. The𝛼-parameter is defined by the actual

0 50 100 150 200 250 300 3500

10

20

30

40

50

angle

power

distan

cedistrib

ution[𝑀

𝑊𝛼𝑘𝑚

]Figure 2.6.: Normal distribution at each node adjustedfor the cost-scaled demand per node (𝑃𝛼) and theradius

0 50 100 150 200 250 300 3500

1

2

3

4

5

⋅10−3

angle

power

distan

cedistrib

ution[𝑀

𝑊𝛼𝑘𝑚

]

𝛼 = 0.6𝛼 = 0.4𝛼 = 0.2

Figure 2.7.: Total power distance distribution for thetest case for different alpha parameters (normalised)

financing conditions for assets in the distributiongrid and will be discussed in more detail in section2.7 The resulting power distance in this system is20.55MW𝛼 km .

Table 2.4 summarises the power distance res-ults for all four introduced methods. As dis-cussed, the artificial grid based power distance is



the lowest, as all grid connections are direct andnomeshes occur in the system. For the full systemtheminimal power distance is lower than the powerflow based power distance, which supports the hy-pothesis that the minimal required grid will alwaysbe a radial system. Compared to the artificial gridthe minimal radial grid has longer line lengths dueto obstacles in the real grid as simulated by lines (2)and (7). As a result, the artificial grid based powerdistance is lower than the minimal power distance.

Table 2.4.: Comparison of power distance result forthe test case

Parameter Method Power distance[MW𝛼 km]

𝑃mind Minimal 15.60

𝑃flowd Power Flow 16.68

𝑃artd Artificial grid 14.85

𝑃statd Statistical 20.55

2.6. Power distance in the low-voltage distribution system

So far and for the purpose of this study, we com-pute the power distance parameter in the high-voltage (1 to 22 kV) distribution system only. Thelastmile from the substation to the consumer is nottaken into account.

In Norway, two systems for the low voltagedistribution are used: 220V / 1-phase or 3-phaselines and 400V / 3-phase lines. Generally speaking,three-phase distribution is the technically preferredoption, while 1-phase is the historically wider usedsystem. 3-phase systems are needed for fast-charging of electric vehicles or other high-powerapplications, and are better suited to ensure equalloading of all phases. While 3-phase systems areused in both 400V and 220V systems, the mainadvantage of higher voltage lines is that they alsoallow for longer lines due to reduced losses.

Not taking into account the low-voltage dis-tribution grid can lead to distortion of the incent-

ives towards the technically inferior 220V system:since the 220V lines are usually shorter than thosein with 400V, more of the distance from a trans-former station to the consumer is covered by highvoltage lines. If only high-voltage distribution isconsidered in the benchmarking, a grid companywould be considered to have a higher output withthe 220V system, than an otherwise equal gridcompany using 400V lines. Nota bene, the sameeffect is evident in the current output parameter”length of all high voltage distribution lines” andonly partly corrected by the use of ”number ofsubstations”.

How can this be addressed? Using the ex-plicit line length or power distance for the low-voltage distribution grid may not be feasible dueto a lack of detailed grid data on this voltage level.However, the location and demand profile of eachconsumer is known thanks to the Smart Meter(SM) infrastructure. It should be feasible to takethe low-voltage distribution into account througha power distance computation, possibly similar tothe demand-distribution based power distance. Bydoing so, a grid company should not have a disad-vantage, or might ideally even have an advantagefrom using longer 400V lines.

However, a more detailed discussion and ana-lysis of how a low-voltage power distance couldbe defined and how it could be integrated into theregulatory framework is beyond the scope of thisreport.

2.7. Alpha parameter

In all proposed methods to define and calculatethe power distance, the cost scaling parameter 𝛼is used to represent the relation between cost andcapacity of a power line. To realistically capture theneeded investments to build and maintain lines atdifferent rated power, 𝛼 should be between 0 and1. For 𝛼 = 0 the power distance is equal to thesum of the length of lines and independent of thetransmitted power, for 𝛼 = 1 the relation betweencost and power is linear and suggests that building



two lines at half capacity will incur the same costsas building one line at full capacity.

In the previous study [5] the impact of differentvalues for 𝛼 was investigated, but the exact valuewas not determined. One aim of this project isto define methodologies to determine the relationbetween cost and capacity and consequently cal-culate the alpha parameter. Three methodologiesthat were investigated are described below.

After testing three methodologies we can notgive a definite answer to which value for the 𝛼-parameter should be used in calculations. Instead,the use of different methodologies has allowed usto identify a range in which the 𝛼 parameter is likelyto lie. The choicemay depend on the selected com-putationmethod for the power distance parameter.

2.7.1. Alpha based on the cost cata-logue

To verify the cost difference between building linesat different voltage levels, data from the cost cata-logue [6] can be used which specifies cost data percable type. In this approach we argue that themaindriver for cost increases related to rated power isthe cable diameter. Fundamentally, the transmittedpower in an electric cable is defined by the voltagemultiplied by the current, or after applying Ohm’slaw, by the square of the voltage divided by theresistance.

𝑃 = 𝑉 ⋅ 𝐼 = 𝑉2

𝑅 (2.9)

If we assume that the voltage on a given line isfixed, the power scales with the inverse of theresistance. The resistance 𝑅 of an electric cableis defined by

𝑅 = 𝜌 ⋅ 𝐿𝐴 (2.10)

where 𝜌 is the material specific resistivity, L isthe length and A is the cross-section area of thecable. For a given length and material, the poweron a cable will consequently be proportional to thecross-section area.

𝑃 = 𝑉2

𝐿 ⋅ 𝜌 ⋅ 𝐴 (2.11)

0 50 100 150 2000

2

4

6

8

⋅105

Cable cross-section [𝑚𝑚2]

Cost

parameter

[NOK/km

]

Figure 2.8.: Relation of cost per km to the cable crosssection.

The cost catalogue provides detailed informationon unit costs per cable type. Additionally, thematerial specific resistivity of the used materialsand the cable cross section can be extracted froma database on cable characteristics. A limitation ofthis method is, that only the capital cost for cablesis considered. The total incurred costs per linelength will also depend on other required hardware,land preparation and operation costs which mayvary significantly for different projects. However,generally we assume that overall cost of buildinglines of different voltage levels in the high-voltagedistribution grid is not expected to differ greatlyas large CAPEX components and operational costsare similar. Thus, the relation between cable costand rate power can be used to determine the 𝛼-parameter.

The calculation was performed for a FeAl over-head line without insulation. Other cable typesare described in the cost catalogue as well but wedecided to focus on the cable type with the mostavailable data. The obtained relation between thecable cross-section and the cost per unit length isshown in Figure 2.8. The cost parameter shows alogarithmic increase with cable cross-section, andconsequently with transferred power. By using alogarithmic fit on the obtained data points the 𝛼-parameter can be calculated to 𝛼 = 0.35.



2.7.2. Calculating alpha from the assetregister

A second approach to determine the alpha para-meter is to investigate the relation of total cost perDSO versus the length of lines per voltage level.The resulting linear equation system gives a solu-tion vector which is expected to show an exponen-tial trend with higher line voltage from which alphacan be obtained.

⎡⎢⎢⎢⎣

𝐿1 𝑘𝑉1 ... 𝐿11 𝑘𝑉1 𝐿22 𝑘𝑉1

... ... ... ...𝐿1 𝑘𝑉𝑛 ... 𝐿11 𝑘𝑉𝑛 𝐿22 𝑘𝑉𝑛

⎤⎥⎥⎥⎦

⋅⎡⎢⎢⎢⎣

𝑥1 𝑘𝑉

...𝑥1 𝑘𝑉

⎤⎥⎥⎥⎦

=⎡⎢⎢⎢⎣

𝐶1...𝐶𝑛

⎤⎥⎥⎥⎦

(2.12)

where 𝐿1 𝑘𝑉𝑖 is the total length of lines withvoltage 1 kV of DSO i, 𝐶𝑖 is the total incurred costuntil the present year for DSO i and 𝑥1 𝑘𝑉 is the costparameter for lines of voltage 1 kV. The size ofmatrix 𝐿 will be determined by the number of DSOs𝑛 and the number of voltage levels 1 to 22 kV.

As part of the current regulation the expensesof all DSOs are collected in an asset register.The asset register reports on the total incurredexpenses per DSO and year including new invest-ments, reinvestments and depreciation for eachgrid level and line type. For the calculation of thealpha parameter the total cost of all high voltagelines in the local distribution grid is considered.From the RME grid database the total length oflines per voltage level for eachDSOcan be obtained(within the constraints of data availability). Thelines are aggregated into three voltage levels: 5, 11and 22 kV, while reported voltages may vary.

Data from all Norwegian DSOs in the assetregister with costs > 0 are used. Therefore, the res-ulting problem becomes an overdetermined linearequation systemwhich can be solved using a least-squares approach.

For the three analysed voltage levels an in-crease in cost per km can be observed between5 kV and 11 kV (see Figure 2.9). However, for a

5 10 15 20

0.5

1

⋅106

Voltage [kV]

Cost

parameter

[NOK/km

]Figure 2.9.: Relation of cost and line voltage from theasset register calculation

higher line voltage of 22 kV the cost seems to dropto the lowest level. Based on the obtained res-ults we deem the results from this approach non-conclusive.

Limitations of this approach are that only totalinvestment costs are considered per voltage level.In the distribution grid the main expenses for build-ing a power line are location and topography spe-cific, rather than voltage dependent and the cost ofcables scales with the cable cross-section which isindependent of the voltage. Costs for land prepar-ation and general hardware components (masts,insulation, etc.) will not differ greatly betweenan 11 kV and a 22 kV line. Additionally, the linevoltage is constrained by the existing grid and doesnot necessarily reflect the actual capacity on theline. As accumulated costs until the present yearare used, historic cost developments and differentfinancing structures can not be taken into account.

2.7.3. Estimating alpha from the ideal-ised grid

When calculating the power distance based on anidealised grid the 𝛼-parameter is taken as an input.Depending on its value the connections betweensubstations, which the algorithm builds based onthe minimal increase in power distance, will differ.



With the assumption that additions to the real gridare always made under ideal economic conditions,the idealised grid which resembles the structure ofthe real grid the most should represent the existinginvestment structure. For the investigated testcases we found that an 𝛼-parameter in the range of0.3-0.5 will give the closest match to the real grid.

2.7.4. Further suggestions for calculat-ing the alpha parameter

Beyond the three investigated methods, further ap-proaches were considered and will be discussedbriefly. The implementation of these methods isbeyond the scope of this project and would requireadditional data that was not available during thisproject.

Real cases The 𝛼-parameter could also be estim-ated from project specific data of different DSOs.In this methodology, the sample size of availabledata is crucial to avoid bias from geographicaldifferences. If the sample size is small, cost dif-ferences are more likely to be caused by locationspecific constraints. Some examples are that thecost for land preparation and digging will differin rural and urban areas, installation on steeperterrain is expected to incur higher costs.Thus anadditional correction for topography would need tobe performed. We consider this approach themostchallenging due to limitations of data availabilityand bias.

Current DEA benchmarking Introducing a newbenchmarking parameter in the DEA model shouldprovide a more objective comparison of the per-formance of grid companies. At the same timea change in the regulatory structure should notmajorly change the rating of individual companiesand their positioning with respect to other DSOs.Based on computations for all grid areas in Norwayand a comparison of the power distance resultsto the current benchmarking output, it could bepossible to scale the alpha parameter to fit a sim-ilar benchmarking structure as obtained from thecurrent method. It will be interesting to investigate

how the alpha parameter impacts the rating of gridcompanies based on the power distance comparedto the current output parameters. However, we donot believe that using the current benchmark as astarting point for defining the alpha parameter is anapproach that should be pursued.


3. From power distance to energy distance


The power distance is computed for a specifichour, and can be calculated individually for all hourswithin the year. For the DEA approach, we need aselection of one ormore parameters describing thetask of the grid companies throughout the wholeyear. Selecting one individual hour might not berepresentative of or describing the task of the gridcompany, while it on the other hand would not beefficient or necessary to account for all 8760 hoursin the year.

In this chapter, we will discuss how the powerdistance can enter the DEA benchmarking usedfor the income regulation of grid companies inNorway through one or more annually aggregatedparameters. We revisit some of the challengeswithaggregating the hourly power distance into a yearlyenergy distance as described in [5], and introduceadditional concerns raised by a reference group ofgrid companies participating in this work.

The conclusion of this chapter is a selectionof recommended designs for the energy distanceparameter, that will be tested and evaluated in thecontinuation of this report.

Important questions that we address in thischapter are:

What is the actual task of a grid company?

(How) is the task of grid companies with verydifferent demand profiles comparable?

What are the main cost drivers in building andmaintaining the high voltage distribution grid?

Which aggregation methods can be used todefine energy distance parameters that accur-ately reflect the cost drivers?

3.1. Cost drivers in the distribu-tion grid

The choice of energy distance parameter(s) shouldreflect the cost drivers that a grid company is ex-posed to in the distribution grid. A DSO has theobligation to cover the demand of customers in thegrid at all times. Consequently, the grid companyhas to build andmaintain a grid that is able to serveits customers/demand at all hours - even the hourwith the highest load. This applies even though agrid can operate above limits in select hours if theyare few enough and far enough apart. In the future,a grid company serving the distribution grid needsto accommodate changes in customer patternsthat are likely to lead to higher peak loads dueto new types of demand, feed-in from distributedresidential generation and electrification of severalsectors such as onshore and offshore transporta-tion.

On the other hand, the grid companies canexpect new consumers to provide flexibility to thegrid and relieve strain on the electric infrastructurethrough demand response and flexible demandwith the increased introduction of smart homes.

The required grid infrastructure to supply cus-tomers in the distribution grid incurs high costsfor the DSOs. The costs that a grid companyfaces can be broadly divided into four categories:Investment costs, cost of energy delivered, admin-istrative costs, and cost of losses. The overallcost is directly related to the power and energysupplied but each cost component has differentdriving factors.

Investment costs: These costs represent the in-stantaneous power that a grid company needs tocover with its infrastructure. If an area has a high



peak demand, the power grid has to be built to copewith that demand regardless of the total energydelivered within a year. If an area has a high densityof vacation homes, they might be faced with highdemand in weekends and holidays, while the totalannual energy consumption is quite low. A para-meter that captures peak demand and investmentcosts is the maximum power distance – describedby the∞-norm.

Cost of energy delivered: The cost of energy de-livered, i.e. the operational cost, is driven by totalenergy delivered in a grid. A comparable measurein this context it the 1-norm – the sum of (or aver-age) kWh over the year.

Administrative costs: This includes costs re-lated to performing administrative tasks, suchas customer service, invoicing, etc. These arecosts related to the number of customers servedin the grid area, that comes in addition to thecost of delivering energy. This cost is describedseparately from the power distance approach astwo companies who deliver the same amount ofenergy, over similar distances to different amountof customers will have different tasks to cover.

Cost of losses: The losses in a power system arequadratic to the energy delivered in a grid. Asa result, losses increase quadratically with powertransferred, and two grids facing the same total oraverage energy within a year might have entirelydifferent losses. To illustrate this we describe anexemplary case of grid A and B, with 4 hours ofdemand:

Example: cost of losses

First, keep in mind that 𝑃𝑜𝑤𝑒𝑟 = 𝑈 ⋅ 𝐼 and 𝐿𝑜𝑠𝑠𝑒𝑠 =𝐼2 ⋅ 𝑅, so that with constant voltage, the currentI is increasing linearly with increasing power, andlosses are increasing quadratically with power. Thehourly demand of company A and B for four arbit-rary hours is given in Table 3.1

The sum (or average) of power is equal for thetwo companies, but the amount of losses they faceare quite different, as seen in Figure 3.1. In fact,

Company h1 h2 h3 h4 sumA 5 5 5 5 20B 5 10 2.5 2.5 20

Table 3.1.: Hourly power consumption

company B is suffering almost 40 % more lossesthan company A, due to its variable consumption.

0 1 2 3 4

0

50

100

150

hours

Accu

mulated

losses

grid Agrid B

Figure 3.1.: Accumulated losses for company A and B.

Such challenges should be accounted for in theselected of annual benchmarking parameters.

3.2. From hourly values to ayearly parameter

The tasks of the grid company are slightly morecomplex than building a grid that covers the hourlypeak demand, and that can provide for a flat ora variable profile throughout the year. The mainchallenges that grid companies are facing will bediscussed in the context of different energy dis-tance parameters. The following section gives anoverview of possible yearly aggregation methodsand their suitability as benchmarking parameters.In [5] we discussed four main options for movingfrom hourly power distance to yearly energy dis-



tance:

aggregating hourly power distances,

selecting representative hours,

averaging demand over several hours,

formulating an optimisation problem directlyfor the energy distance.

The first three are briefly revisited here, andwe referto [5] for further details.

3.2.1. Selecting parameters to describethe task of the grid company

Before we go ahead selecting parameters to de-scribe the task of the grid company, we need todecide how to account for the different concernsraised by a number of grid companies in a relatedworkshop. In order to identify challenges thatthe grid companies face in performing their task- specifically challenges that incur direct costs -we invited a selection of six grid companies toa workshop with RME, where we asked them toelaborate on how they would describe their task asa grid company. The received input was used asa knowledge base to define aggregation methodsand will be discussed in more detail in Section 3.3.

A brief summary of the main concerns and thepossible integration in the benchmarking processis given in Box 3.1.

First of all, we aim to select parameters thatboth account for investment costs and the costof losses, meaning that we will study a collectionof more parameters rather than a single one. Wewill also consider combining newand existing para-meters in order to describe the grid companies andtheir tasks.

Second, there are several concerns that we willnot recommend to reflect in the chosen parameters- either due to complexity, or because we suspectsimilar ramifications for all grid companies, as de-scribed in Box 3.1. In the following chapter wewill present a set of alternative methods of howto aggregate power distances to energy distances

Box 3.1: Concerns raised by the gridcompanies - and recommended actions

Maximum local vs. total demand: Consideredin selecting the parameters, as it can be dir-ectly handled in how we aggregate the energydistance.

Installed capacity vs. actual demand: Assum-ing this is an issue that is relevant for all gridcompanies and potentially creates systematicdifferences, this aspect requires further invest-igation.

Accounting for historical demand distribution:Not to be accounted for by the parameters de-scribing the task of the grid company. We havestated somesuggestions in how to resolve thisissue in Section 3.3.3.

Costs vary with type and area of construction:Not directly handled by the parameters, butrecommended to be adjusted for after the fact,as is already practised in the DEA.

Demand peaks of less than one hour: Couldbe handled outside of the DEA by includingspecific cases in the regulation for higher gridlevels. It could also be accounted for in theparameter by reporting maximum load for thespecific demand locations (given that they arefew enough).

describing and comparing the tasks of the gridcompanies over the full year.

3.2.2. Aggregating hourly powerdistances

The simplest approach to arrive at an energy dis-tance is to use a summation, or in generalisedterms a norm over all hourly values. Other pos-sibilities are considering the maximum value or ac-counting for variations by using a quadratic meas-ure. Typical norms would be:

1-norm This is the sumormean over the absolutevalues.1

1As all power distances are positive, it is the same as the



2-norm This is the square root of the sumover thesquares.

∞-norm The infinity norm, or largest absolutevalue in the set.

We also suggest to keep ”number of custom-ers” as a parameter, serving as a proxy for oper-ational and administrative tasks that are propor-tional to number of customers, but we do not studythis parameter in more detail.

The three norms have different interpretations.The 1-norm considers the total energy, but is in-dependent of the distribution over time. The de-mand profile might be flat or uneven, but the 1-normwould be the same2. Applying a 1-norm couldbe interpreted as representing the expected taskof the grid operator with even consumption in itssupply area. It generally provides ameasure for themean task of the grid company.

A 2-norm allows outliers to have a higher im-pact than values closer to the average. Hence,the 2-norm addresses the problem of variability indemand. When using the 2-norm, hours with a highpower distance value are, in theory, weighted morethan those with a low power distance.

The ∞-norm only looks at the largest powerdistance in the year. This ismeaningful in the sensethat this is actually the largest power distance onwhich the grid company has to dimension its grid.But at the same time it could give the grid com-pany an incentive to promote increasing the peakdemand, in order to have a higher output in the DEA.

Note that the input for all norms can be in-terpreted differently. An average value can be in-terpreted as the power distance that is calculatedfrom the average demand per node or the averageof all hourly power distances. Similarly, the max-imum value may be reflected by a real situationin the grid, i.e. the maximum demand or powerdistance in one year, or by a ”worst-case” for whichthe maximum demand at each node irrespective ofwhether they occur at the same time is used.

sum of hourly power distances. If one divides by thenumber of hours, it is the mean.

2Strictly, this holds only for 𝑎𝑙𝑝ℎ𝑎 = 1, however, the core ofthe argument also holds when considering 𝛼 < 1.

Generally, aggregating the data based on thethree new norms can be performed either beforeor after calculating the power distance, and theaggregating can either be performed on an annual,seasonal or nodal level. We elaborate on what thismeans for the different norms.

3.2.3. 1-norm

The 1-norm reflects the average situation that thegrid is exposed to. It can be expressed by theaverage or the mean value, since all benchmarkingis performed on annual basis they will only differ inmagnitudewith the proportionality to the number ofhours. Aggregating the 1-norm before calculatingthe power distance means summing or averagingover all hours for each node. As we are study-ing the sum or average for the system, it makessense to perform the aggregation on an annual,not seasonal level. There are two possibilities ofperforming the 1-norm with given hourly demanddata per node:

average demand: The power distance calculatedfor the average demand in the system. Thepower distance is only calculated once.

average 𝑃d: The average power distance in theyear. Determined after calculating the powerdistance for each hour.

Average demand

The result of the first method is a set of sums oraverages per node, and the next step is to calculatethe power distance for this summed up or averagehour.

𝐷1𝑖 =∑ℎ 𝐷𝑖ℎ𝐻

The power distance will be one value for thewhole system, which serves as an energy distance -or a parameter describing the cost of supplying theaverage demand to the system, i.e. the operationalcosts.



Average power distance

The other option is to calculate all the hourly powerdistances based on actual demand first, and thentake the sum or average of the 8760 resultingpower distances. The latter method is more de-manding in terms of computation time but mayreflect the task of the DSO more accurately.

The 1-norm parameter will be studied and com-pared for all test cases for annual aggregation bothprior to and after calculating the power distance inSection 5.5.

3.2.4. The 2-norm

The 2-norm can account for variability in demand.As describes before, uneven demand can lead tolarger losses in a system with similar maximumand average demand. In short, it should be able torepresent the difference between two systems thathave similar average demand, but where one of thesystems has a very unevenly distributed demandover time. If we aggregate the hourly demand bythe 2-norm method prior to calculating the powerdistance, we end up with one value per node. Themathematical definition of the 2-norm is

𝐷2𝑖 =√∑ℎ (𝐷𝑖ℎ − 𝐷𝑖)2

However, the losses increase quadratically withincreasing demand, meaning that losses below av-erage also decrease quadratic. The above defin-ition of the 2-norm equally rewards any demandthat is different from the average, regardless ofdirection. If we apply the 2-norm (as is) to representincreased losses due to variability in demand, wereward the grid company for having low demandand less losses.

Another property we want the parameter tohold is that it should only account for the variationaround the mean, not the level of demand, as the 1-norm is already comparing the grid companies onthe overall average demand level. If the averagelevel is also included in the 2-norm and both are

used for benchmarking, this would result in doublecounting.

Generally, the cost of losses in a system arealready indirectly accounted for in the power dis-tance calculation. The main assumption behinddefining the power distance which scales with linelength, is that transferring power over long dis-tances incurs higher costs. The increased costis related to investment and operation but also tothe losses. Additionally, applying a 2-norm ag-gregation would introduce the cost of losses in thebenchmark twice, which should be avoided.

We do not deem the 2-norm to be an idealbenchmarking parameter, as it may conflict withthe 1-norm and would need additional adjustmentsto only reward demand peaks and not variabilitythat leads to lower demand. As a result, we didnot further investigate the 2-norm on the obtainedtest cases. A consideration of an aggregationparameter that appropriately accounts for the costof losses can be included in future work.

3.2.5. The infinity-norm

One of the concerns mentioned by the grid com-panies was the difference between maximum totaldemand in the system, and maximum local de-mand. In short, a grid company can serve areas inwhich the demand peaks never occur at the sametime. The hour with the largest total demand mightbe an hour where a large area that usually havehigh demand is experiencing quite low demand.When applying an ∞-norm, we therefore need tocarefully consider the level of aggregation. Asbriefly mentioned above using a total maximum ora nodal maximum can impact the output and theway in which cost drivers are represented in thebenchmarking. In this report, four alternatives forthe infinity-norm are discussed, namely:

max demand: The power distance calculated forone hour with average demand per node. Thepower distance is only calculated once.

max 𝑃d: The maximum power distance in the



year. Determined after calculating the powerdistance for each hour.

max nodal: The power distance calculated for asystem where each substation is assigned itsmaximum yearly demand. The power distanceis only calculated once.

max flow: The power distance calculated for asystemwhere each line element is assigned itsmaximum yearly flow. The power distance isonly calculated once.

Each aggregation method and its implicationswill be discussed below:

Maximum demand

If we apply the ∞-norm prior to calculating thepower distance, we use the hour of maximum de-mand as an input to the power distance calculation.The results will require only one computation ofthe power distance output and therefore greatly re-duces computational effort. However, consideringthe hour of maximum demand in a system mayunderestimate the situation of maximum load forwhich the grid needs to be equipped. The infra-structure will have to be able to supply the max-imum demand at every node, irrespective of whenit occurs. For larger grid systems, the probabilityof the maximum demand at each node occurringat the same time will be lower than for smallersystems, while both grids theoretically need to beequipped to handle such a situation.

Maximum power distance

For the infinity-norm based on themaximum powerdistance, a computation of the output is performedfor every hour of available demand data. Afterthe computation of the power distance for eachhour, the maximum value is identified. The max-imum power distance more accurately representsthe hour in which it is most costly to supply powerto all customers, compared to using the hour ofmaximum demand. The maximum power distance

will always be at least as high as the power dis-tance in the hour ofmaximumdemand. Similar lim-itations as for themaximumdemand apply in termsof representing the actual required investment tocover the maximum demand per node at any time.

Maximum nodal demand

The third aggregation option is nodal aggregationper substation demand. We find the highest de-mand in each substation, regardless of hour, andcalculate one power distance value for the max-imum local demands. This method accounts forthe local maximum demand, but it could poten-tially overestimate the necessary investment level.In this project, only the aggregated demand persubstation is considered, which means that simul-taneity of demand for each customer is not con-sidered. It could occur that the individual cus-tomers under a substation experience their peakdemand at very different times, thereby impact-ing the maximum hour of demand per substation.Ideally, the grid should be equipped in a way thatif every customer has its annual peak demand atthe same time, power will still be supplied withoutinterruption. In the real case, such extremes areunlikely to occur and may lead to shortages whichare covered by the CENS-cost.

Maximum power flows

This method is only relevant for the power dis-tances that consider a real or constructed grid.It is described in detail in the Appendix under Al-gorithm 1, and allows us to consider the maximumflow on each line, regardless of hour.

The idea is to calculate the optimal power flowfor the grid in each hour, and find the maximumflow endured by each line segment, irrespective ofthe hour in which is occurs. This is equivalent toa nodal aggregation level per line segment. Thepower distance is then calculated for the systemwith maximum flows on all lines.

A nodal aggregation based onmaximumpowerflow on each line prior to calculating the power



distance considers themaximumflow on each line,rather than the maximum demand in each node,and is therefore less likely to be an overestimationof the (optimal) investment costs incurred by eachgrid company. Similarly to the maximum nodaldemand, this aggregation method accounts for amaximum situation in the high voltage distributiongrid but does not account for differences in peakload in the low-voltage distribution grid.

3.2.6. Selecting representative hours

To simplify any computation, one could aim atusing representative hours rather than all 8760hours of the year. For example, one could usethe hour with the highest net demand, winter peak,summer valley or the first Wednesday at 15:00 ofeach month. Dependent on how the representativehours are defined, the approach might make thetask of two grid companies less comparable. Onegrid company could be faced with high demandin the relevant hours, while the other have a lowdemand. It may also be possible for the gridcompanies to affect demand in the representativehours.

Alternatively, one could attempt to identify spe-cific demand situations and compute one rep-resentative hour for each situation, potentiallyweighted by the number of hours with a certainsituation. Such identification would rely either onmanual identification or on clustering algorithms.Another option is to perform seasonal aggrega-tions rather than only using one annual value perDSO to comapre different companies. We refrainfrom computing representative hours or seasonaloutput in this report as the data made availablefor the test cases covers different times periods.Hence, any selection of a representative hour orseasonal output would no longer be directly com-parable.

3.3. Input from the referencegroup

This section summarises the feedback receivedfrom the reference group of Norwegian grid abouttheir interpretation of the task of a DSO. The majorconcerns that were mentioned with respect to ac-curately representing cost drivers and the possibleimplementation in an energy distance parameterwill be discussed.

3.3.1. Maximum local vs. total demand

The power distance, irrespective of the chosencomputation method, is defined as the distancepower travels from point of production to pointof consumption, multiplied by the instantaneousamount of power transferred. We have earlier inthis chapter argued that the maximum load that adistribution grid has to cover is directly accountingfor the investment costs. However, a grid com-pany could serve areas in which the demand peaksnever occur at the same time. For example, therecould be a grid serving business districts, sum-mer houses, and winter cabins. These areas willexperience peak demands at completely differenttimes. It is therefore important to consider thedifference in modelling maximum power demandon nodal level, and maximum total power demandfor a full grid area. This concern is addressed byinvestigating the hour of maximum total demandand the nodal maximum demand.

3.3.2. Installed capacity vs. actualdemand

In some situations there is a gap between thepower the grid companies are obliged to deliverto a certain consumer and the power they actuallydeliver. This means that the considered fuse sizefor building a grid extension would not be reflectedby the actual supplied demand. In these situations,the local annual or seasonal peak loads will not berepresentative for the investments incurred by the



grid company.As all grid companies are subject to the same

regulations and laws, it is likely that this issue isas relevant for one as the other. In the DEA, thepower/energy distance parameter will merely serveas a means to compare the efforts made by eachgrid company in relation to its costs, and the actualvalue of the parameter is therefore only relevant inranging the companies from least tomost efficient.As long aswe are confident that this is an issue thatis faced in an equal matter by all grid companies,it is not necessary to account for the gap betweeninstalled capacity and actual demand. If it is thecase that the gap is notably more relevant for onegrid company than another and creates systematicdifferences between DSOs, it would be relevant toaccount it, inside the benchmarking parameter orseparately.

3.3.3. Accounting for historic demanddistribution

Grid infrastructure is a long-term investment, andonce built it usually serves the system for severaldecades. Most lines are built to serve the demandthat the system is currently facing with some re-spect to projected development plans in a morelong-term horizon. As time passes by, demandcentres move, old industry closes down while newindustry is established in another location. Thisdynamic could result in a system with sub-optimalinfrastructure for the present task of the DSO. Itoften makes sense to build new grid based on oldgrid rather than to redesign the entire grid. Howdo we account for grid that has been built basedon demand that no longer exists, such that itslocation/sizing is not optimal today?

An example of how extreme the consequencesmight be is a grid company being obliged to builda line serving a charging point for electric ferries.The required capacity is usually quite high, and soare the investment costs. It is also a high riskinvestment, as the charging point may be the onlyconsumption served by the line. If some years

later, the ferries switch from electricity to hydrogen,and the line becomes redundant, the grid companyis stuck with a large investment and no corres-ponding demand that is accounted for in the powerdistance calculations.

It is likely that most grid companies have areaswith sub-optimal grid infrastructure due to shiftingdemand centres. If this holds true, it is not a nuancethat needs to be captured by the power distance.However, the magnitude of impact is likely to varywith the size of a grid area, which potentially cre-ates higher risk for smaller companies. If it can beestablished that some grid companies are facingconsequences due to old and sub-optimal grid in-frastructure, we would recommend that the issueis accounted for by an adjustment factor outsidethe DEA calculation, as is done with weather ortopography today.

The extreme case that a grid company has un-dertaken a large investment in a line that becomesredundant within a few years is not likely to beequally affecting all grid companies. Even if inmany cases the majority of these investments arecovered by the customer, the full investment is con-sidered when calculating the RME efficiency. Oneway to account for these high-risk investments, isthat RME could allow the grid companies to reportthe lines separately and allow the network compan-ies to recover the full costs of these lines withoutimplications for the benchmarking (similar to theway some regional grids are regulated). However,this is also clearly an administrative issue as itwould require extra control and monitoring on thepart of RME.

3.3.4. Costs vary with type and area ofconstruction

In the power distance calculation the investmentcosts in new assets is considered through the 𝛼-parameter, that accounts for the scaling of costswith line capacity/transferred power. We arguethat installation and operation and maintenancecostswill be similar for assets of different capacity.



However, the initial investment cost and theoperational expenses are also strongly locationdependent. Location specific conditions, such astopology, existing settlements and ease of accesswill affect the choice of line and therefore the totalcost. An underground line in an urban area willnot incur the same costs as an overhead line ofthe same capacity in a sparsely populated area.In this situation the costs for the cable, whichscale exponentially with the capacity, are the samebut construction and maintenance costs will varygreatly.

This issue can be addressed through a topo-logy correction that is either introduced ex-postor in the computation of the power distance. Anex-post approach could resemble the current geo-graphical adjustments used in the DEA benchmark-ing. A possibility to include these constraints dir-ectly in the power distance calculation could bethe use of different 𝛼-parameters for different linetypes. However, as described in Section 2.7 com-puting the 𝛼-parameter is a challenging task anddefining different values per asset type may lead toa less accurate result than an adjustment after theinitial benchmarking.

3.3.5. Demand peaks of less than onehour

This is a situation that is relevant for a lot of newdemand entering the system. Themost familiar ex-ample is fast charging of electric vehicles, particu-larly public transportation, and ferries. These char-ging stations require high instantaneous power, butthe demand cycles are less than one hour. Thisis an issue as the demand data available for thepower distance calculation is reported as hourlyvalues in kWh/h, for the time being.

One example is a fast charger for an electricferry shuttle leaving port every 20 minutes. Oncearriving at the port, it charges for 5 minutes, andthen leaves for the next destination. 15 minuteslater, the next ferry arrives, charges for 5 minutes,and moves along. Within one hour, the fast charger

has only been active for 15minutes. Themaximumpower demand is 4 times as high as the reportedkWh/h, and does not reflect the size of the invest-ment in grid capacity.

As long as the demand data is reported onan hourly basis, it is difficult to account for theactual peak demand at locations such as the onedescribed above. It could be possible, as we havealready suggested for high capacity grid servinghigh-risk demand, to report these lines differently,and not include them in the DEA-calculation for thedistributional grid. Another option is to somehowflag the relevant demand location, and report themaximum output as it should be a quite constantand known value. If metering data of higher res-olution is available the infinity norm could be com-puted on the maximum demand for each node.

The two concerns of short demand peaks andhigh risk investment describe changes in the en-ergy system that calls for new parameters describ-ing the task of the grid company. In the currentregulation, these investments rarely lead to an in-crease in the output parameters (number of cus-tomers, km of line, number of substations), whilethey have a large impact on the costs incurred bythe grid company.

3.3.6. Demand decreases

Another issue is related to demand decrease,whether general or due to a specific customer redu-cing its power consumption due to e.g. bankruptcy,relocation or switch to other fuels. With the currentDEA model the output would remain unaffected(except in the cases where the number of cus-tomers is reduced), while with a power distancevariable the output is likely to be reduced, perhapssignificantly.

In some cases, connection charges may re-duce the risk for the network company as the totalcost of an investment is partly covered by thecharge. However, the benchmarking may still beaffected negatively with a power distance meas-ure instead of line length. Also, the connectioncharges generally do not apply to investments in



the meshed grid, although changes to the con-nection charging rules have been introduced from2019 to include a share of the costs in the meshedgrid as well.

It is not immediately clear how demand de-creases can be accounted for within a powerdistance-based output measure or whether it hassignificant impact overall. One may suspect thatthere are systematic differences between networkcompanies with respect to underlying demandtrends, but this has not been investigated as partof the current project. One option could be to treatsingular cases separately in line with the asset-based regional grid DEA model, but this may onthe other hand entail large administrative costs forRME and the network companies.

3.3.7. CENS and losses

Finally there is the question of whether Cost ofEnergy Not Supplied (CENS) and/or losses shouldbe considered in the benchmarking. While thesecost elements are a part of the total cost inputincluded in theDEAmodel, itmay also be discussedwhether they should be considered on the outputside as well. Networks with long line lengths andhigh power distances will naturally have higherlosses, and they will be more exposed to failuresand resulting outages that incur CENS costs.

Higher CENS and losses result in lower effi-ciency as measured by the DEA model, which isnecessary for the incentives of network compan-ies to weigh costs of network investments againstreductions in CENS and losses optimally. In thecurrentmodel, the line lengthmay be an acceptableproxy for losses and outage probability in gridswithlong lines, and a power distancemeasuremay havesimilar or even better properties. It is outside thescope of this project to consider solutions to this,but RME should consider whether further paramet-ers or adjustments are necessary. It should also benoted that the geography correction in the currentmodel may reflect CENS and losses related to linelengths as well as other factors.


4. Test cases

4. Test casesTo investigate the different computation methodsfor a benchamrking parameters, the grid compan-ies participating in the reference group of this pro-ject have provided data from real cases in theirdistribution grid. For reasons of data privacy andsecurity all grid companies are kept anonymousand each test case will be assigned a letter. Allcases are limited to substations under up to threetransformer stations from the regional to distribu-tion grid level. For each substation hourly demandand generation values are provided. The demandand generation per customer in the low-voltagedistribution grid is aggregated at the connectedsubstation. The grid data ismade available by RMEfrom a centralised database.

4.1. Description of test cases

The following sections give a short description ofeach area and provide an overview of the grid topo-logy per test case. The grid maps show all stations

Table 4.1.: Summary of grid details per test case

Test case # of trafostations

# of sub-stations

total linelength

Test Case A 1 268 426 kmTest Case B 1 321 202 kmTest Case C 1 148 109 kmTest Case D 1 106 149 kmTest Case E 1 132 86 kmTest Case F 3 398 540 km

and lines for which data was available from RME.Note that some lines and stations, marked in lightgrey, could not be connected to the grid systemeither because they are served from another trans-former station or because the grid data was miss-ing information on connections. A general over-

view of the number of substations and transformerstations as well as the total length of lines per testcase are given in Table 4.1.

Test Case A - Large geographical area withmore production than consumption

Test Case A is a large geographical area servedby one transformer station from the regional gridlevel. The test case is characterised by both centraland rural areas. It holds several small scale hydropower plants, and there are hours within the yearwith net higher production than consumption in thearea.

Figure 4.1.: Grid topology for Test Case A

The area covers around 270 substations with atotal of 4700 metering points. Demand is mostlyresidential, holiday homes, offices and servicebuildings. There are no larger industrial consumersin the area.

Compiling this test case from the available datarequired some manual handling of missing linesto the transformer station. The missing data ormismatch of coordinates requires the addition ofline elements which do not necessarily represent



the real system. Even after adding lines, uncon-nected line elements remain in the test case, thisis visualised with different colours in Figure 4.1.

The provided demand data covers the full year2018 in hourly resolution for all nodes in the testcase.

Test Case B - Combination of dense demandcentres and rural areas

Figure 4.2.: Grid topology for Test Case B

Test Case B is an area served by one trans-former station from the regional grid level. It coversboth central areas with higher demand density, andmore rural areas. There is no large-scale produc-tionwithin the selected case area, but there are cus-tomers with excess production and a small scalehydro power plant. Hourly demand data per nodewasprovided by theDSO for a timeperiod fromMay2018 to June 2019.

The area covers 320 substations and one trans-former station. The large number of substations re-quired more computation time for each parametercompared to other test cases.

Test Case C - Dense urban demand centre

Served by one transformer station from the re-gional grid level, this area is a dense demand centrewith residential buildings, a sports stadium, andseveral office and service buildings.

The area covers around 2600 metering points

Figure 4.3.: Grid topology for Test Case C

that are aggregated to approximately 150 substa-tions. The DSO provided two extensive datasets ofhourly data; one with a full year of metering datafor 2018 and another for three months fromMarch2019 to end of May 2019. For the calculationsin this project we chose to use the data for threemonths in 2019 as the dataset had consistent datafor all substations and hours whereas there wassome data missing in the full 2018 data whichcould have affected comparability.

In the dense demand centres the grid has alarge number of meshes and parallel lines. Despitethese challenges the grid data could be compiledinto a complete system. Certain lines, marked ingreywere not connected to the test case grid, eitherbecause they are served from another transformerin the region or because ofmissing lines in the data.

Test Case D - Rural with decentralised produc-tion and planned locations for shore power

Test Case D is served by one transformer from theregional grid level. It is a rural area that is subjectto typical challenges due to electrification of thetransport sector and decentralisation of power pro-duction. The area is characterised by:

A distributional grid that is mainly serving pro-duction sites

Power production on lines that are built to serveend consumers


4. Test cases

Figure 4.4.: Grid topology for Test Case D

Several planned locations for shore power

Power exchange with other grid companies

The area covers 150 substations and 1100metering points and the demand data covers a yearfrom June 2018 to June 2019 in hourly resolution.

Test Case E - Suburban region

Figure 4.5.: Grid topology for Test Case E

This case covers a suburban area served byone transformer station from the regional grid.Demand is distributed densely around the trans-former stations with some outliers in all directions.The area covers residential areas, office and retailbuildings without distributed generation or largedemand centres. The area covers 130 substationsand 5000 metering points. A full year of hourly

demand data was provided for this test case fromJanuary 2018 to end of December 2018.

Test Case F - dense rural areas and powerintensive industry

The test case represents a geographically boundedarea in the company’s grid. It is mainly served byone transformer station from the regional grid level,and partially served by two additional substations.The area is rural, with small densely populatedareas, holiday homes as well as some industry.

The area covers 390 substations and threetransformer stations. The provided hourly demanddata covers a full year from July 2018 to July 2019.The data for grid lines in the RME database differedfrom the other test cases as each line was savedas a composition of individual short line elements.The resulting large number of lines and lack ofinformation of connection points posedmajor chal-lenges when compiling the grid data.

4.1.1. Demand patterns

Each grid company in the reference group provideddemand data on hourly level for each substationin the test cases. The aggregated hourly demandprofiles are shown in Figure 4.6 on page 43. Notethat the time period of provided data varies fromtest case to test case. All test cases cover a fullyear of demand but have different start and enddates, except for Test Case C for which a datasetwith three months of demand data was used. Theresulting profiles show seasonal patterns of highdemand in winter and lower demand in summer.Minima in demand can either be related to gener-ation in the system that outweighs demand (as forTest Case D) or errors in measurement data (likelythe case for Test Case E). Without further inform-ation on the provided demand data we choose todirectly use the input data without adjustments ofpossible errors.



4.2. Data quality

The quality of available data and the ease of thenecessary data handling are essential foundationsfor any approach that is to be used for regulatorypurposes. In the following, we discuss our obser-vations and learnings gathered from importing thetest cases. We discuss grid data and demand datafrom Advanced Metering Systems (AMSs) separ-ately.

4.2.1. Grid data

RME has collected a database of all grid elementsin Norway. The database includes the locationof metering points, substations, transformers, andlines and cables of all voltage levels.

This databasewas themain source of grid datafor the project. There are big advantages of usingdata from one source, as it allows to use the exactsame algorithms to import data for each of thetest cases. Despite some of the grid companiesoffering to provide grid data in their own format, wefound it preferable to rely on the RME database toensure consistency and ease of handling.

The grid data from the RME database does nothave information about which line is connectinga certain substation to a transformer station. Wetherefore received a selection of line data from thehigh voltage distribution grid covering the area ofeach test case. We were then faced with the taskof identifying which of the lines are relevant for thepower distance. While compiling the test cases, wecame across a number of challenges related to thedata. Handling these issues involved significantmanual work and was highly time-consuming.

The following gives an non-exhaustive over-view over typical issues:

Missing lines Missing line elements, even if theyare short, are hard to solve. It is often not evid-ent where, or indeed whether, an open line endis connected to some other location. In indi-vidual cases, themissing connections could beidentified on a map and manually connected.

Such an approach is not applicable in large testcases or for the entire Norwegian distributiongrid.

Lack of connection information The line dataonly consists of the line geometry, but doesnot have any information on connection points.It is often easy to assume that two line endsare connected if they are in the same location.This approach is challenged in a number ofsituations. 1) Substations and transformerstations are represented by a point, andthe endpoints of connecting lines are oftenregistered in some distance. 2) T-junctions oflines are only recognised if all lines have anendpoint in the junction location.1

Line length The length of each line is determinedfrom the start and end coordinates. The res-ulting length is the euclidean distance betweentwo points and does not consider differencesin length due to topology or line type. Linesthat are not a direct connection between twosubstations are stored as individual line seg-ments that need to be connected as previouslydescribed. In the current DEA benchmarkingthe length of lines is reported by each DSOwhich is not necessarily the same as the lengthextracted from the RME database that is usedfor the power distance calculation.

Voltage level definitions The database providesthe voltage level formost (not all) assets. Whilethis is generally useful, the voltage definitionsdiffer and are not clearly communicated. Forexample, one line might be defined as 21 kV,another as 22 kV depending on whether typ-ical operation voltage or maximum admissiblevoltage is given.

Different meta data Even though all data comesfrom the same database, it does not alwayshold the samemeta data, or uses different tagsfor the same meta-information. For example,

1checking for any connection between all lines is computa-tionally very challenging, whereas checking closeness ofendpoints of lines is reasonable


4. Test cases

object IDs are 1) called different (objektID,lokalID, globalID, objekt_ID, ...), and 2)hold different types of IDs across data sets.

Differences in segmentation The data in somegrid areas was much more segmented than inothers, meaning that a line connecting to pointswould be split into individual line elements,each stored as an individual line. In other gridareas, the line would be stored as one longgeometrical object. Where lines are split inmany small elements, this may overload thealgorithms for connecting them.

Different data management systems Eventhough the grid data was extracted from acommon database, the original data wasprovided to RME by each grid company fromtheir data management system. There arecurrently several different data managementsystems in use that can comply to RME’s datarequirements of geographically accurate griddata. However, the line data may vary betweensystems leading to discrepancies between linesegmentation, object IDs and line lengths. Byadapting the requirements for the providedgrid data to the power distance computations,some challenges that were experienced in thisproject could potentially be overcome.

4.2.2. AMS and station data

Data on demand and generation per substationwas provided by the grid companies for each testcase. To our knowledge, the data was extractedfrom Elhub or internal measurement systems andaggregated per substation.

The provided data was generally of high qualityand easy to handle. Challenges, however, occurredin matching the demand data with the RME griddata. The main findings are

Elhub The centralisation and standardisationprovided by the metering data hub Elhubfacilitates efficient data extraction. Somecompanies in the reference group explicitlypointed out that they found it much easier

extracting the required profiles for the periodcovered by Elhub than for the preceding period.

Good data quality Where smart-meter data wasavailable, the data quality was generally verygood, with only few missing data points, usu-ally at the beginning or end of the data periodwhich could correspond to old, pre-Elhub dataor very recent data. Some extreme outlierswere also identified and only removed if it couldbe justified.

Data privacy Data privacy laws give strict ruleson data handling and data provision. Aggreg-ating data per substation alleviates the issue,and generally best practice and regulation ondata handling, non-disclosure, and limitationof data access and data storage have to befollowed. Considering that metering data holdmuch information about the customers, thesemeasures are unavoidable. We did not findthem to impede the project.

Comparability The demand and generation datawas provided individually per DSO for eachtest case. Consequently, data from differenttime periods was used as input in the calcula-tions. This may impact comparability betweenthe test cases as the peak demand can differbetween years, and datasets that cover lessthan one year will not capture all patterns andextremes.

Station ID The ID for substations differedbetween the RME grid data and the internaldata from DSOs. In some cases ID matchingwas provided by the DSOs whereas othercases required coordinate matching which willgenerally be less accurate.

Matching substations To obtain a full dataset ofgeographical coordinates, connected lines anddemand per substation the AMS data has to bematched with the RME grid data. Even whenchallenges of identifying station IDs were over-come not all stations from the AMS datasetscould be found in the RME grid data. This couldimply that new stations were added to the grid



that are not yet included in the RME database.

4.2.3. Implications of data quality

The quality of input data for the benchmarkingmethodology is crucial to ensure an objective com-parison between grid companies. Data qualityissues may even influence which power distanceparameter is most promising for regulatory pur-poses. Some considerations that should be takeninto account are:

We found that in many cases, grid data ismissing or requires extensive manual work.This may pose serious challenges for any grid-based power distance parameter.

Where line data is missing, there might besituations where provision of this data is det-rimental for the benchmarking performance ofa grid company. This would constitute a disin-centive to provide high-quality grid data.

Where station IDs cannot be matched, the as-sociated demand might not be considered inthe power distance computation. Here gridcompanies have an incentive to provide con-sistent station IDs and to ensure that all datais up to date.

Should demand data due to privacy considera-tion only be accessible on substation level, thismight imply an advantage for 220V low-voltagedistribution grids – as discussed in Section 2.6.


4. Test cases

(a) Hourly Demand Test Case A (b) Hourly Demand Test Case B

(c) Hourly Demand Test Case C (d) Hourly Demand Test Case D

(e) Hourly Demand Test Case E (f) Hourly Demand Test Case F

Figure 4.6.: Hourly demand for the six test cases



5. Results per test case and per parameter

The following section presents the results perpower distance computation method for all invest-igated test cases. For all calculations per test casean 𝛼-parameter of 0.4 was used. An analysis ofdifferent values for 𝛼 is given in Section 5.6.

5.1. Minimal power distance

In the provided test cases the number of meshes inthe test cases was too high to allow for a computa-tion. As a result, we were not able to compute theminimal power distance for any of the test cases.

As mentioned in the description of the method,the computational complexity grows exponentiallywith the number of meshes. This means that forour test cases it is not a question of parallelisationor improvements in computer technology – withover 10 × 10110 required iterations it is simply notpossible to find a solution.

Some roommight remain for reducing the num-ber of meshes, such as more precise algorithmsto recognise parallel lines, a consistent split ofthe problem along voltage levels, etc. However,it is unlikely that even such approaches will leadto a computable solution in all cases and for alldistribution grid topologies found in Norway.

We therefore have to conclude that theminimalpower distance cannot be used as a benchmarkingparameter, and will not further investigate it in thisstudy.

5.2. Power-flow based powerdistance

The power-flow based power distance is calcu-lated based on the real grid, including all meshes

in the system. The computation determines theflow on each line segment and finally calculates anhourly power distance parameter. The power-flowbased power distance could be calculated for alltest cases except for Test Case F. The use of thereal grid in the computation requires data of highquality and a significant amount of data handlingto account for unconnected substations ormissinglines. In the case of Test Case A several straightline segments had to be added manually to obtaina closed grid system. In the case of Test CaseE the transformer station needed to be manuallyconnected to the grid. For the urban grid in TestCase C simplifications of parallel lines could beapplied but required additional efforts. For the caseof Test Case F the grid data could not be compiledinto a complete grid system. Each line in the TestCase F grid was saved as a number of individualline segments without information on connectionsbetween lines and substations. The algorithmsused for all test cases to establish connections of

Figure 5.1.: Comparison of power flow based powerdistance and the total hourly demand to the power ofalpha, for 𝛼 = 0.4



lines and stations in geographical proximity couldnot compute a complete grid in this case.

Based on the demand data per substation andthe system compiled from the grid data, power-flow based power distance computationswere per-formed. The hourly results for all test cases isshown in Appendix Figure 7.1. Generally a flatten-ing trend can be observed compared to the hourlydemand data. This flattening effect is a resultof applying the alpha parameter which is below 1and therefore reduces the intensity of demand inthe calculation. Overall, the seasonal trend canstill be observed and hourly variations are visibleaccording to demand peaks.

The power-flow based power distance can becompared to the hourly demand in each system.This is illustrated in figure 5.1 with the power-flowbased power distance on the x-axis and the de-mand to the power of alpha (𝐷𝛼) on the y-axis. Foreach test case a linear relation can be observed,which is to be expected from the formulation of thepower distance in Equation 2.8. The differencesin slope is due to the differences in line lengthsin the system. For systems with longer lines, thepower distance, that scales with the length of linesto each substation, will generally be larger thanfor cases with shorter line length and meshes thatoffer multiple paths for power to flow. As a result,the more urban areas, Test Case C and Test CaseE show the steepest relation between demand andpower flow based power distance. Test cases withless meshed grids and overall longer lines show aless steep relation, as for example Test Case D andTest Case A.

For the remaining methods we will comparethe results to the results of the power-flow basedpower distance calculation. We consider thepower-flow based power distance to be the mostrealistic representation of the DSOs task based onthe existing grid infrastructure. Ideally other powerdistance parameters should show a linear relationto the power-flow based power distance to qualifyas a good proxy.

5.3. Artificial grid power dis-tance

Figure 5.2.: Comparison of power flow based powerdistance and artificial grid based power distance, for𝛼 = 0.4

The artificial grid only uses the coordinates anddemandper node anddoes not rely on the grid data.The lower data requirements made it possible tocalculate the artificial grid based power distancefor all test cases. For each case, an artificial radialgrid is built based on a representative hour fromwhich the hourly power distance can be computedby using a power flow calculation. For test caseswith more than one transformer station, individualgrid systems are created around each transformerstation. The nodes in the system are assigned tothe closest transformer station and the total powerdistance is a sum of the power distances in eachsub-system. Lines that are included in the realgrid but do not connect to a substation are notconstructed in the artifical grid.

Figure 5.3 gives a comparison of the real gridand the artificial grid for the Test CaseA. It is clearlyvisible, that the artificial grid is a radial system withno meshes. Generally the artificial grid resemblesthe real grid well, with the exception that meshesare not accounted for, which underlines the suitab-ility of the computation method for the purpose ofconstructing an idealised grid.

The hourly results for all test cases are shown



(a) real grid for Test Case A (b) Artifical grid for Test Case A

Figure 5.3.: Comparison of real and artificial grid for Test Case A, for 𝛼 = 0.4

in Appendix Figure 7.2. As for the power-flowbased power distance, a flattening compared to thedemand data can be observed. The intensity of theresulting power distance, however, varies with thetest cases. A comparison of the power-flow basedpower distance and the artificial grid based powerdistance is given in Figure 5.2. For all investigatedtest cases the artificial grid based power distanceand the power-flow based power distance showa linear relation. This indicates that the artificialgrid based power distance is a good proxy for thepower-flow based power distance.

Differences between the test cases can be ob-served in the ratio between the two parameters.Generally the artificial parameter is smaller than thepower-flow based parameter which can be attrib-uted to geographical and topographical constraintsin the real grid. The artificial grid will always createdirect connections between two nodes and theresulting grid will be radial without meshes. As aresult, the total length of lines in the grid will beshorter than in the real grid used for the powerflow calculation. The ratio is closest to 1 in ruralareas with long lines and few meshes, such asTest Case D for which lines are located on thecoast of a fjord. In urban areas, where the grid istypically more meshed and existing infrastructureconstrains the building of direct lines between two

nodes, the power-flow based parameter can bemore than twice as high as the artificial grid basedpower distance.

We further investigated the difference betweenthe power-flow based power distance and the ar-tificial parameter by comparing the total length oflines in the real and artificial grid (see Table 5.1).For all cases the artificial grid has a shorter totalline length than the real grid. This is a result ofmeshes in the real grid, lines that are built aroundobstacles and lines that do not end at a substation.The difference in total length can give a first indica-tion of the differences in power distances but doesnot fully explain the relation between the powerdistance in the real and artifical grid.

Therefore we additionally investigate the av-

Table 5.1.: Comparison of total length in real andartificial grid

Test case 𝐿𝑟𝑒𝑎𝑙 [km] 𝐿𝑎𝑟𝑡 [km]Test Case A 426 183Test Case B 202 118Test Case C 109 28Test Case D 149 106Test Case E 86 33Test Case F 540 102



erage relative line length. This means the aver-age ratio of the actual line length in the real gridcompared to the euclidean distance between twosubstations. The ratio between the two lengthscan be a indicator of topographical differences andcould be used to adjust the artificial grid basedpower distance. Table 5.2 compares the ratio ofthe power-flow based power distance and the ar-tificial grid based power distance (𝑃𝑓𝑙𝑜𝑤𝑑 /𝑃𝑎𝑟𝑡𝑑 ) tothe ratio of total line length in the real and artificialgrid (𝐿𝑟𝑒𝑎𝑙/𝐿𝑎𝑟𝑡) and the average relative line length(∑𝑖𝑗 𝑙𝑟𝑒𝑎𝑙𝑖𝑗 /𝑙𝑖𝑗). For all test cases, except for TestCase A, the ratio of power distances is inverselyproportional to the ratio of real and artificial linelength. This supports the hypothesis, that gridswith generally shorter lines in the real grid are lesswell represented by the artificial grid and the arti-ficial power distance is underestimated comparedto the power-flow based power distance.

A similar trend can be deduced from the re-lation between the power distance ratio and theaverage relative line length – the closer the linelength ratio is to 1 the closer the results for thepower distance are. This can be interpreted that theartificial grid, with its connections along the euc-lidean distance, resembles the real grid closely andthus results in a similar power distance output forthe power flow and the artificial grid basedmethod.Test Case A is an outlier in this series which maybe due to the fact that the grid has large meshesdespite substations being very spread out. As aresult power can be distributed to the most distantsubstation along several paths with lower flow per

Table 5.2.: Ratios of lengths in the real and artificialgrid

ratio ratio ratioTest case 𝑃𝑓𝑙𝑜𝑤

𝑑 /𝑃𝑎𝑟𝑡𝑑 𝐿𝑟𝑒𝑎𝑙/𝐿𝑎𝑟𝑡 ∑𝑖𝑗 𝑙𝑟𝑒𝑎𝑙𝑖𝑗 /𝑙𝑖𝑗

Test Case A 0.95 2.32 1.07Test Case B 1.48 1.71 1.17Test Case C 2.34 3.89 1.27Test Case D 1.17 1.41 1.07Test Case E 1.51 2.60 1.35

path compared to the artificial grid, where only oneconnection is established. The difference to theresults of the remaining test cases highlights thatother factors than the difference in line lengthsmayimpact the result of the artificial grid computation.A clearer investigation of other potential impactscan be performed in future work when more andlarger test cases are made available.

The differences in ratio between the two para-meters could be corrected by a geographical factor.The investigated test cases are only a limitedsample of grid areas in Norway and are thus notrepresentative for determining geographical or to-pographical correction factors. From a larger datasample and detailed geographical input it couldbe possible to investigate how the ratio changeswith the conditions in each area. As a result ageographical adjustment, similar to that used in thecurrent DEA benchmarking, can be defined.

5.4. Demand distribution basedpower distance

Figure 5.4.: Comparison of power flow based powerdistance and demand distribution based power dis-tance, for 𝛼 = 0.4

The demand distribution based power distancedoes not rely on a real or artificial grid. Insteadit uses the coordinates and demand per node tocalculate a distribution of demand around each



transformer station. This method could be appliedto all test cases without limitations due to dataquality or availability. The hourly results for all testcases is shown in Appendix Figure 7.4.

The demand distribution based power distanceand the power-flow based power distance show alinear relation for all test cases. As in the previouscomparison for the artificial parameter, the ratiobetween the two power distance parameters variesbetween test cases (see Table 5.3).

Table 5.3.: Ratios of statistical to power-flow basedpower distance

Test case ratio 𝑃𝑓𝑙𝑜𝑤𝑑 /𝑃𝑎𝑟𝑡

𝑑Test Case A 0.70Test Case B 1.17Test Case C 1.89Test Case D 0.69Test Case E 1.12

In urban areas with shorter distances betweennodes and more meshes in the system, the statist-ical power distance is lower than the power-flowbased power distance. Similarly to the artificialgrid, the statistical parameter does not accountfor meshes and indirect connections. As a result,the overall parameter is lower than the power-flow

based power distance. For less dense demanddistributions the statistical power distance is largerthan the power flow based power distance. Thiscan be attributed to the fact that nodes may notbe in angular proximity according to calculationsbut are most efficiently connected along one linee.g. in Test Case D along a fjord. As a result, thedemand distribution based power distance countsnodes with individual connections over long dis-tances whereas the real grid connects these nodesover one line for which the total length is shorter.

5.5. Comparison of yearly outputparameters - energy dis-tance

The power distance parameters described in theprevious sections are an hourly output parameterfor each grid system. To obtain a fair bench-marking parameter the hourly values need to beaggregated into one or more annual values. Asdiscussed in Section 3 different cost drivers in adistribution grid can be represented by differentaggregation parameters. Specifically the 1-norm,that accounts for the average demand or powerdistance and the infinity-norm that accounts for

Figure 5.5.: Comparison of infinity-norm and 1-norm energy distance parameters for different DSOs, from thepower-flow based power distance for 𝛼 = 0.4



the maximum. In this section we will investigatedifferent aggregationmethods for the hourly powerdistance parameters to an annual energy distancebased on the test cases. General trends can be de-duced from the results but absolute comparisonsneed to be made with caution, as the time periodsof provided data vary. All aggregations will beperformed based on the power flow based powerdistance.

The following aggregation methods are invest-igated:

1-norm:

average 𝑃d: The average power distance in theyear. Determined after calculating the powerdistance for each hour.

average nodal demand: The power distance cal-culated for the average demand at eaxch sub-station in the system. The power distance isonly calculated once.

∞-norm:

max 𝑃d: The maximum power distance in theyear. Determined after calculating the powerdistance for each hour.

max total demand: The power distance calcu-lated for one hour with maximum demand in

the system. The power distance is only calcu-lated once.

max nodal demand: The power distance calcu-lated for a systemwhere each node is assignedits maximum yearly demand. The power dis-tance is only calculated once.

max flows: The power distance calculated for asystemwhere each line element is assigned itsmaximum yearly flow. The power distance isonly calculated once.

Figure 5.6 shows a comparison of the six men-tioned methods for all test cases where the power-flow based power distance could be calculated.The two 1-norm parameters are fairly similar for allDSOs with the nodal average being slightly higherthan the average power distance. Since the de-mand is scaled with the alpha parameter its im-pact in the power distance is lower than in theoriginal demand data. Taking an average prior toapplying the power distance calculation will thuslead to a higher energy distance than performingan averaging operation after calculating the powerdistance.

For the infinity-norm parameters the max nodaldemand is consistently the highest followed by themax flows. The nodal and flow maximum tend

Figure 5.6.: Comparison of energy distance parameters for different methods of defining the maximum andaverage value, from the power-flow based power distance for 𝛼 = 0.4



to overestimate the real situation in the grid asthe demand peaks per node or flow peaks per linedo not occur in the same hour of the input data.Note that the maximum flow aggregation can onlybe performed for power distance calculations thatare based on a grid, real or synthetic. For largersystems, as for example in Test Case B, the differ-ence between themax power distance and themaxnodal demand is higher than in smaller systems.

This can be attributed to the fact that the prob-ability of the maximum demand per node to occurat the same time is lower for larger systems. There-fore the difference between the hour of maximumdemand and the maximum nodal demand will belarger. This is more clearly visible in Figure 5.6where the largest system (Test Case B) sees thelargest difference between the maximum aggreg-ation methods. The max power distance will beat least the same as the max demand – for themax power distance a power distance is calculatedfor each hour of demand, including the hour ofmaximum demand. The hour of highest demanddoes not have to correspond to the hour of thehighest power distance. It can occur that in thehour of highest demand the largest demand peaksoccur close to the transformer station, resultingin a comparably low power distance, whereas the

hour of the highest power distance may have morespread out demand.

5.6. Comparison of differentalpha parameters

In the previous sections, results were presentedfor an alpha parameter of 0.4. The chosen valueis based on the different investigated methodsto determine the 𝛼-parameter which give a rangebetween 0.3 and 0.5 (see Section 2.7). In differentcomputation methods, the alpha parameter canhave a different impact, which will be discussedbelow.

Power-flow based power distance

For the power flow based power distance compu-tation the alpha parameter has a flattening effectcompared to the demand input. For larger alphathe resulting power distance will more closely re-semble the demand profile through its peaks andvalleys, whereas for lower values the impact ofthe demand is lower in the overall result. This isillustrated in Figure 5.7 (a) for the Test Case C.An alpha of 0.6 sees large daily peaks while the

(a) Hourly power flow based power distance of TestCase C

(b) Demand distribution for different alpha parametersin one hour for Test Case D

Figure 5.7.: Comparison of results for different alpha parameters



results for alpha = 0.2 are generally flatter. In themost extreme cases an alpha of 0 would lead toa flat curve independent of demand and an alphaparameter of 1 would see the same variations asthe demand input.

Demand distribution based power distance

Thedemanddistribution that is calculated to obtainthe statistical power distance depends strongly onthe alpha parameter. Most importantly the alphaparameter is used to determine the standard de-viation of the normal distribution that is createdaround each demand node. For lower alpha para-meters the individual distributions per node willbe broader, thereby creating more overlaps with

other nodes in angular proximity. This signifies thatthe nodes can be more efficiently connected overone line with high capacity. As alpha is increasedthe peaks become sharper and less overlaps arevisible, which indicates that individual connectionsto each of the nodes are preferred. Figure 5.7 (b)shows a normalised distribution for different alphaparameters. The sharpest peaks are visible for analpha of 0.6 while the distribution for 𝛼 = 0.2 issmoother and almost shows no distinct peaks.

Artificial grid based power distance

When the artificial grid based power distance iscalculated the alpha parameter impacts the outputin two ways: (1) through the scaling of demand in

(a) real grid (b) artificial grid for 𝛼 = 0.4

(c) artificial grid for 𝛼 = 0.6 (d) artificial grid for 𝛼 = 0.8

Figure 5.8.: Comparison of real and artificial grid for different alpha parameters for Test Case E



the power distance calculation and, more import-antly, (2) through the creation of the grid basedon the minimal increase in power distance. Fig-ure 5.8 shows a comparison of the real grid ofTest Case E (top left) and the idealised grid thatis established by the algorithm for different alphavalues of 0.4, 0.6 and 0.8. It is immediately visiblethat the artificial grid has a less complex topologythan the real grid. At first sight differences in theareas with a large density of substations are notas visible. One can, however, quickly identify thatthe connections in the lower left part of the griddiffer greatly between the real and the artificialgrid for all alpha parameters. While the real gridconnects all nodes via a long U-shaped sequenceof lines, the artificial grid builds two individual lines.Which nodes to the far left are connected to eachof the two branches also differs for different alphaparameters. Depending on the value of 𝛼 the con-nection that increases the total power distance bythe least changes.

The largest differences between the artificialgrids created based on different alpha parametersare visible in the top right part of the grid. In thisarea the real grid is characterised by a large num-ber of meshes. Generally, lower alpha parametersincentivise buildingmore lineswith higher capacity.

As a result, there are more common connectionsin the artificial grid for 𝛼 = 0.4. For a higher alphaparameter building more lines with lower capacityis more efficient. This dynamic is clearly visible inthe artificial grid for 𝛼 = 0.8 where a large numberof lines branch out and supply individual nodes.Almost every substation is connected by its ownline in the 𝛼 = 0.8 grid, while the 𝛼 = 0.4 grid hasmore lines that serve multiple nodes. Overall, agrid that is established with an alpha parameterof around 0.4 resembles the real grid the most,despite being radial.

The calculation of the power distance willstrongly depend on the grid topologywhich determ-ines the length of each line and thus the path alongwhich power can be transferred to each node. Asa power flow calculation is used to determine theflow on each line and then compute the total powerdistance, the demand data is influenced by the 𝛼parameter in a similar way as described for thegrid-based computation. A lower alpha parameterreduces the total output and has a more flatteningeffect.

Energy distance

For the yearly output parameter, 𝛼 influences theresult through the hourly power distance calcula-

Figure 5.9.: Comparison of infinity-norm energy distance parameters for different alpha parameters for Test CaseC



tions. Figure 5.9 illustrates how the output for thefour infinity-norm aggregation methods changeswith the alpha parameter in the Test Case C. Forall aggregation methods, an increasing trend withalpha can be observed. A higher alpha will gener-ally increase the power distance per hour becausethe demand is flattened less compared to an alphaparameter close to zero. As the impact of demandbecomes smaller with a smaller alpha parameterit becomes less likely that the hour of maximumdemand and the hour of maximum power distanceoverlap. On the other hand, a larger contributionfrom demand in the multiplication with the linelength potentially leads to a larger spread betweenthe hour of maximum demand and the hour ofmaximum power distance. Whether the hour ofmaximum demand will also result in the highestpower distance depends most on the grid topo-logy and therefore differs from case to case. Themaximumnodal energy distance is consistently thehighest output and increases more strongly witha higher alpha parameter. The exact increase isagain determined by the grid topology where alphahas the largest impact on nodes that are located farfrom the transformer station. The long line lengthwill be multiplied with a larger value 𝑃𝛼 as alphaincreases towards one. The maximum flow en-ergy distance is always higher than the maximumhour and lower than the maximum demand. Theincrease with alpha occurs in the same scale as forthe maximum nodal demand, related to the impactof the 𝑃𝛼 term with higher alpha.



6. EvaluationIn Section 1.3 we described the most importantfactors for a suitable DEA benchmarking output.Optimally, an objective parameter should be highlyexogenous in representing the task of the grid com-pany with low requirements for data and compu-tational effort. Additionally, the parameter shouldbe intuitive to understand and comparable betweengrid companies with different external conditions.After computing the power distance using fourmethods for several test cases we can analyse thesuitability of each parameter based on the men-tioned key factors. In this section we comparethe main results for the different parameters anddiscuss feedback from the reference group on theresults. Table 6.1 summarises the suitability ofeach power distance parameter with respect tothese factors.

6.1. Discussion of key factors

6.1.1. Task representation

A benchmarking parameter should ideally reflectthe task of the DSO rather than its effort. Thetask of each grid company is to supply power tocover their customers demand at any time andlocation. An output that reflects this task shouldconsider the demand per customer and its geo-graphic distribution to account for the incurred costfor transporting power over long distances. The ex-isting grid infrastructure takes the effort of the DSO,i.e. the investments in infrastructure that the gridcompany takes to supply power to all customers,into account. Of the investigated power distanceparameters, the minimal and power-flow basedpower distance use the existing grid to investigatehow power can be ideally distributed to cover thedemand at each node. These approaches use the

existing infrastructure, which represents the DSOseffort, as well as the distribution of demand, toreflect the task of the DSO. The artificial grid basedand demand distribution based power distance areindependent of the existing grid and thus do notaccount for the effort of each grid company. In-stead these methods only consider the task of theDSO to supply demand to each node in the system,either based on an idealised grid or a statisticaldistribution. The current DEA benchmarking usesthe length of line, the number of substations andthe number of customers as output. The formertwo reflect the effort of the DSO while the latterpartly represents the task of the DSO. However, themain component of a grid company’s task lies insupplying power to cover demand for their custom-ers. The number of customers does not reflect thetotal demand or its distribution.

The annual energy distance parameter shouldreflect the task of the DSO and the different driversfor the cost that a grid company is exposed toas a result of fulfilling its task. As discussed inSection 3 different aggregation methods for hourlydata can reflect several of the most important costdrivers. We suggest using several yearly paramet-ers to account for the investment costs, the costof delivering energy and administrative costs. Thecost of delivering energy should be reflected by anaverage value, for which the average yearly demandper node or the average power distance in a yearare similarly suitable. For the administrative costswe propose to keep the number of customers in theDEA model. The representation of the investmentcosts is not as straight-forward. The DSO shouldequip its grid so that it can handle the maximumload in the system. The maximum load can besimply interpreted as the hour of maximum de-mand in a year or the maximum power distance.


6. Evaluation

Table 6.1.: Evaluation of key considerations for benchmarking parameters

𝑐ᵆ𝑟𝑟𝑒𝑛𝑡 𝐷𝐸𝐴 𝑃𝑚𝑖𝑛𝑑 𝑃𝑓𝑙𝑜𝑤

𝑑 𝑃𝑎𝑟𝑡𝑑 𝑃𝑠𝑡𝑎𝑡

𝑑Task representation medium very good very good good goodExogeneity low medium medium high highData requirements very low very high very high medium mediumComputational effort very low too high high medium mediumIntuitiveness very high high high high lowComparability mediuma very high very high higha mediuma

Overall suitability medium low high b high medium

aBefore geographical correctionbConstrained by data availability

However, the maximum demand in one year doesnot necessarily reflect the total possible maximumthat could occur in a system. We therefore con-sider it more suitable to account for the maximumdemand per substations or alternatively the max-imum flow per line segment, for methodologiesthat use a grid. If the low-voltage distribution grid isalso accounted for, the maximum demand per sub-station should be the sum of maximum demandsper customer.

6.1.2. Exogeneity

The concept of exogeneity in the context of a powerdistance parameter refers to an output that is notunder control of the benchmarked entities, i.e. in-dependent of actions taken by the DSO. The taskof the DSO should be to build and maintain a gridthat optimally supplies power to their customers,not to adapt the grid to the optimal output in thebenchmarking and accordingly receive higher rev-enues. Consequently, an ideal benchmarking para-meter should be entirely independent of the gridcompany’s investment or operational decisions. Inthe current DEA benchmarking the length of lines isa parameter that is under control of the DSO. Thiscould, in theory, lead to grid companies buildinglonger lines than necessary to improve their bench-marking output. Similarly building more substa-tions could have a positive impact on the output fora DSO. The fact that the presently used parameters

are under control of the DSO was one of the mainconcerns that motivated the definition of new out-put variables.

The grid-based power distance parameters arestill partly under control of the DSO, as the exist-ing grid infrastructure is used as input. Throughthe choice of the alpha parameter an incentive toinvestment in more substations than needed canbe avoided. However, building longer lines than re-quiredmaybe incentivised by these grid-based vari-ables as it can lead to an improved benchmarkingoutput for the grid companies. In contrast, the grid-free variables are highly exogenous and cannot beinfluenced by the grid companies. For the paramet-ers where only demand per substation and substa-tion location are used as input, the grid companiesshould not be able to impact customer demandand their location. The location of substations can,in theory, be adapted by the grid companies toimprove the benchmarking output. However, thepower distance computation for the high voltagedistribution grid should be complemented with anappropriate aggregation of demand per customerin the low voltage distribution grid around each sub-station. Through the choice of demand aggrega-tion method in the low-voltage distribution grid, theincentive for selecting a substation location basedon the benchmarking output rather than systemefficiency can be removed. Generally, the positionof a substation is constrained by multiple factorsrelated to geography and external conditions, thus



an incentive to place a substation differently doesnotmean the different placementwill be technicallypossible. The annual energy distance parameterswill be as exogenous as the hourly power distancecomputation that is used.

6.1.3. Data requirements

In the years since the introduction of the currentDEA benchmarking variables, large improvementsin available data have been made. Hourly demandand generation measurement data from smart-meters can be obtained from Elhub and RME hasbuilt a comprehensive database of the grid infra-structure in Norway. These data inputs open newpossibilities for including more detailed data inthe DEA model but also pose challenges in termsof data quality and data handling. Generally, thebenchmarking output should not pose unrealisticdata requirements on the grid companies or theregulatory authority. The data used should be ofhigh quality to avoid any adjustments that maydistort the final output. For a power distance para-meter the requirements on data quality should behigh enough to correctly account for the (hourly)demand distribution but low enough to be fulfilledfrom existing data without extensive (manual) ad-justments. For any power distance parameter,demand data per substation and substation loca-tion are crucial input. We found that geographicallocations of substations could be easily extractedfrom the RME grid data and hourly demand datafrom Elhub could be used directly. Despite somechallenges in matching the station data with thecorresponding demand, we consider the quality ofavailable data sufficient for the purpose. Hence,the grid-free power distance parameters, i.e. artifi-cial grid and statistical output, could be calculatedwithout limitations from the available data.

For power distance parameters that use theexisting grid large amounts of data needed to beprovided on the grid infrastructure. This data wasmade available as individual line segments andsubstations which had to be compiled into a com-plete grid system per test case. Despite the high

quality of available data, we encountered severalissues when compiling the grid data (see Section4.2). At present, we do not consider the availabledata to be sufficient for an objective benchmarkingthrough a grid-based power distance parameter.

The computation of an annual energy distanceoutput does not pose any additional data require-ments compared to the power distance computa-tions as long as consistent data in hourly resolutionis made available for each substation.

6.1.4. Computational effort

The benchmarking output needs to be computedfor each grid company in Norway on annual basis.Thus, it should be possible to compute any outputthat is used in the DEA benchmark with reasonablecomputational effort. In the proposed methodolo-gies in this report, it was shown that the minimalpower distance could not be solved in a reasonabletime for any of the test cases. The fact that theminimal power distance relies on an iterative op-timisation process, makes it increasingly complexwith larger and more meshed grid systems. Lo-gically, a parameter that cannot be computed forevery topology in the high voltage distribution griddoes not qualify as a benchmarking output. Forall other methodologies the computational effortwas no limitation in calculating a power distanceoutput. There were differences in the number of re-quired calculation steps and the computation timebut all parameters could be obtained in a reason-able time. Computing hourly values for any powerdistance parameter can be a time-consuming taskbut if the result for one hour can be calculated,repeating the task for each hour in the year andperforming annual aggregations is not constrainedby the computational complexity. We generallybelieve that a lower computation time should notcome at the expense of the output quality. Sincethe computation is typically only performed oncea year, we consider any parameter that can becomputed within a reasonable time to be suitablefor the purpose.

When considering the complexity of a compu-


6. Evaluation

tation all calculation steps need to be taken intoaccount. For the power distance computationsthis includes any data handling and adjustmentsneeded to compile the grid data.

6.1.5. Intuitiveness

A thorough understanding of the methodology be-hind the revenue regulation is crucial for the reg-ulatory authority that applies the benchmarkingmodel, the grid companies, whose revenues de-pend directly on the output and potentially largecustomers, who are affected by the resulting gridtariffs. While an ideal benchmarking parametershould capture the factors that affect the task ofthe DSO in detail, it should not be too complex foraffected entities to understand. In the case of theSwedish NPAM a lack of documentation and gen-eral understanding of the methodology was one ofthe reasons that the regulatory changewas notwellreceived by the grid companies. A similar outcomeshould be avoided if a new benchmarking para-meter is introduced in the DEA model. In our ex-perience and from the feedback received from thereference group, grid-based parameters are easierto understand than those that do not rely on the realgrid. In the context of grid regulation, it is intuitiveto refer to the existing topology and consider howpower can be transported in a given grid system.Though the optimisation process to compute theminimal power distance is highly complex for ameshed system, the general concept of removingline segments until a radial grid remains can beeasily understood. For a radial system the compu-tation of flows per line segment is simple. For thepower flowbasedmethod the generalmethodologyis similarly simple to grasp as it is based on the realgrid topology and physical flows – two conceptsthat anyone working in or with a grid company willlikely be familiar with. The calculation of individualflows per line segments can be less intuitive, asthere are several paths along which power can flowin a meshed grid. Overall we consider the gridbased parameters to be most easily understood.

The concept of an artificial radial grid and the

computation of power flow in the resulting sys-tem is slightly more complex. The power flowcomputation in the artificial grid itself is relativelysimple, as there are no meshes in the grid. But thecreation of the idealised grid based on the minimalincrease in power distance is more challenging tounderstand. The methodology operates in a waythat the connections between nodes are not estab-lished merely based on minimal distance but alsoaccount for the cost-scaling of lines with capacityand the remaining demand in unconnected nodes.While this approach creates a more cost effectivegrid than a grid based on minimal distances, it isalso less intuitive to understand. Nevertheless, theincreased complexity did not pose problems to theparticipants in the reference group, who developedan understanding of the concept of the artificialgrid based power distance.

The demand distribution based power distanceis the most abstract parameter analysed in thisreport. Since no real or artificial grid is used, themethodology is less intuitive to understand. Theoutput is of a similar format as for the (real or arti-ficial) grid-based parameters but calculation stepsto obtain a power distance output are founded onstatistical concepts rather than definite paths ofpower flow. Generally, the concept of angular prox-imity and its application in the demand distributionbased power distance was considered complex tounderstand by some members of the referencegroup.

6.1.6. Comparability

In order to objectively becnhmark the perform-ance of different grid companies the benchmarkingoutput should be comparable between areas withdifferent external conditions. As opposed to theSpanish RNM, where the efficiency of each DSOis determined through benchmarking a real gridagainst an artificial grid, the Norwegian DEAmodelevaluates relative efficiency between all grid com-panies. Hence, a benchmarking parameter shouldbe as objective as possible for each consideredgrid company.



Parameters that are based on the real gridwill be highly comparable between grid companiesbecause the external conditions will be reflectedboth by the total incurred cost and the resultinggrid topology. Differences in demand distribution,topographical conditions and area constraints e.g.through water bodies or natural parks, are indir-ectly accounted for through the layout of the realgrid. In contrast, the artificial grid based powerdistance and the demand distribution based powerdistance do not consider differences in topographybetween grid companies. The impact of differenttopographies for rural and urban areas could clearlybe identified in Figures 5.2 and 5.4 for the artificialand statistical power distance respectively. Wesuggest using a geographical correction factor tothese parameters ex-post. Such a correction factorcould be determined in a similar manner to thecurrent DEA benchmarking for the artificial grid andbased on a ratio of area types for the demanddistribution based power distance.

For the annual aggregation of the power dis-tance into an energy distance parameter, compar-ability is also a crucial factor. The number ofcustomers, to account for administrative costs andthe average demand per grid area, to reflect thecost of energy delivered, are comparable betweenDSO for all methods. For the infinity norm, i.e.the situation of maximum load, the selection ofthe maximum demand impacts the comparabilityof the output. For a larger grid area the prob-ability that all nodes experience their maximumload at the same time will be lower than for asmall region with few substations. Despite thelow probability, such a situation may occur andthe respective grid company will need to equipthe grid accordingly. However, when using thehour of maximum demand or the maximum powerdistance in a year DSOs with small areas and fewsubstations may have an advantage compared tothose who need to serve larger areas. We thereforepropose to use maximum demand per node or themaximum flow per line for the calculation of theinfinity norm. By using these values a ”worst-case”demand scenario is simulated which should reflect

the investments necessary to operate the grid andis therefore comparable for all DSOs.

6.1.7. Incentives

Each proposed method to calculate a power dis-tance and subsequently an energy distance maycreate different incentives for the grid companies.Ideally a benchmarking parameter should not disin-centivise any of the following; investments that im-prove security of supply, providing of accurate andupdated data, building a line in the shortest/mostefficient path, among others.

Some possible implications were alreadytouched upon in the previous paragraphs and willbe described in more detail while others are yetto be discussed. The current DEA benchmarkinguses the length of lines and number of substationsas input. Theoretically DSOs can improve theirbenchmarking output by buildingmore substationsand longer lines than what would be necessary.By taking the demand of customers and theirlocation into account power flow parametersaim at removing these incentives. The incentiveof building longer lines may still be given forthe power flow based power distance and theminimal power distance, especially for substationsthat lie at the end of a grid line. All consideredmethods may incentivise placing substations ina way that maximises the output. However, thiscan be avoided when the regulation in the highvoltage distribution grid is complemented with anappropriate aggregation of demand per customerin the low voltage distribution grid. Generally,we deem it unlikely that grid companies willchange the position of substations to improve theirbenchmarking output.

For methodologies that use a radial grid, i.e.the minimal power distance and the artificial gridbased power distance, investments that improvesecurity of supply by building ameshed systemwillnot be beneficial for the benchmarking output. Themethodologies will always identify a radial systemas the most efficient and would not promote a sys-tem that aims to improve security of supply. This


6. Evaluation

was also demonstrated in [5]. For the artificial gridbased power distance and the statistical powerdistance any investment that does not connect anew substation will not affect the output, as theartificial grid is created independently of actualgrid topology and the statistical calculation doesnot account for any grid. As a result, lines thatdo not affect the number, location or demand ofsubstations are not accounted for.

When grid data is used for a computation ithas to be ensured that grid companies are in-centivised to provide the most accurate and recentdata. Some examples for when this may not bethe case are when manual adjustments of missinglines improves the output compared to the real gridsituation, when missing demand data in hours oflow load lead to a higher annual output, when theaddition of a new substation between two trans-former stations leads to different possible flowsin the grid and not reporting the station leads to abetter relative performance.

6.2. Feedback from the referencegroup

All investigated methods and the results of the testcases were discussed with a reference group ofseven grid companies in cooperation with RME.The exchanges with Norwegian DSOs offered in-sights into common concerns and potential chal-lenges. The following is a non-exhaustive listof feedback that we received from the referencegroup:

Historic grid It was mentioned that using a grid-free parameter would not account for historicgrid developments. In many cases historicassets may not be the most efficient solutionin today’s grid but were necessary investmentsat the time of construction. In this context itwas discussed that this may apply to all gridcompanies to a similar extent.

Alpha parameter A participant mentioned thatthe cost of lines will not scale with the line

voltage, as this is often restricted by the ex-isting grid. Instead the most relevant variableis the cable diameter. This motivated our ap-proach to calculate 𝛼 from the cost catalogue.

Exogeneity The involved grid companies under-lined that it was not common to plan assetsbased on the benchmarking output as this maychange over time while infrastructure is usuallyin place for a long period. Consequently, exo-geneity in an output parameter is desired butshould not be the main focus.

Investment cost The investment cost in a gridwilldepend on the maximum load that needs tobe covered from each customer even if thesedo not occur at the same time. This feedbackindicates that using a nodal maximum demandfor the infinity norm could be the most suitableapproach.

Cost of losses The cost of losses does not de-pend on the peak demand but rather on thefluctuations in demand. At the same time thelength of lines is already a proxy for the lossesin a system. This topic should be investigatedfurther to determine whether it is sufficient toaccount for a maximum and average situationor whether and additional measure of demandfluctuations should be included.

Intuitiveness Several participants in the refer-ence group agreed that the power flow basedpower distance is the most intuitive and thatthe demand distribution based power distanceis complicated to understand.

Individual challenges Several grid companiesoutlined challenges that they were facing ina specific situation. An example was thecharging of electric ferries which leads to highdemand peaks for a shorter duration than onehour, which would not be captured by calcu-lating hourly power distance values. Anothercase was the investment in a connection toa large customer that may disconnect fromthe grid in the future. The costs would needto be covered by the DSO but if no demand is



recorded at this customer, the power distancewould not capture this investment. Theseindividual concerns are addressed in moredetail in Section 3.


7. Recommendations and conclusions

7. Recommendations and conclusionsFrom the investigations performed in this projectwe conclude that a relevant measure for the taskof a DSO is the electric power distance within itsgrid area, given an obligation to cover all loads andto handle power fed into the grid from distributedgeneration. The power distance can be computedthrough different methodologies to obtain the rel-evant distances over which the power must bedistributed to satisfy the exogenous demand. Forany computation method, the magnitude of thepower distance strongly depends on the underlyingdistribution of demand, and therefore captures thatthe task of supplying power to clients depends onthe demand distribution.

The following section analyses each power dis-tance parameter as well as the annually aggreg-ated energy distance with respect to applicabilityand regulatory implications. We then present ourrecommendations and outlook for further work.

7.1. Discussion of applicabilityand incentives per para-meter

7.1.1. Minimal power distance

The minimal power distance is calculated from theflows on all lines in theminimal grid that is requiredto supply demand within a given topology. It isbased on the assumption that an optimal grid thatminimises the electric power distance will alwaysbe a radial system, or a tree in a graph theoreticsense. An iteration over all mesh elements in a gridallows to find a globally optimal solution for anygrid system. This approach was demonstrated ontest grids in [5].

In this project the minimal power distance

could not be computed for any of the test casesdue to high computational complexity. For theoptimisation the complexity scales exponentiallywith the number of meshes in a system. In theinvestigated test cases, and likely any real grid testcase, the optimisation could not find a solution.

Besides computational challenges, the data re-quirements and need for data handling are veryhigh for the minimal power distance. Data onall lines, transformers and substations, includinghourly demand and generation need to be availablein high spatial resolution. Despite the high qualityof available data from Elhub and RME, manual ad-justments were needed to compile complete gridsystems and match stations with demand. Fora benchmarking parameter on national level, wedeem it impossible to perform any manual adjust-ments without affecting either the consistency ofthe output or the required effort.

The minimal power distance reflects the distri-bution of demand in a given grid topology and is amore exogenous parameter than the current outputin the DEA benchmarking (length of lines, numberof customers). Nevertheless, the parameter is notfully exogenous as the grid topology is partly undercontrol of the DSO through investment decisions.

It was also shown in [5] that the minimal powerdistance as a benchmarking parameter may givedisincentives to invest in grid reinforcements thatimprove security of supply. Since the resultingminimal grid will always have a radial topology, anyinvestment that creates a mesh in the grid will beconsidered inefficient.

Despite its benefits compared to the currentbenchmarking output, the computational complex-ity of this method makes it impossible to calculatea minimal power distance for all high voltage dis-tribution grids in Norway, thus disqualifying it as a



benchmarking parameter.

7.1.2. Power-flow based power dis-tance

The power-flow based power distance uses the fullmeshedgrid to compute a physically optimal powerflow along each line. Power can flow along any linesegment in the grid, for which line specificationsare kept constant, to supply the demand at everysubstations.

By using the real grid topology and consideringphysical flows, the power-flow based power dis-tance gives a good representation of the task of aDSO to supply power to each customer through theexisting grid infrastructure. The distribution of de-mand around each transformer station is accoun-ted for by themultiplication of flow per line with theline length. In contrast to the minimal power dis-tance, the power-flow based power distance doesnot remove meshes from the grid and instead usesthe full meshed system for determining the optimalpower flow. As a result, investments in lines thatenforce the grid and thereby create meshes willbe considered in the power-flow based power dis-tance.

Similarly to the minimal power distance, datarequirements for the power-flow based power dis-tance are challenging. The methodology requires afull dataset of lines and demand stations in a gridwith details on geographical location, line lengthand hourly demand/generation. At present, the griddata still requires some additional adjustments toconnect lines, substations and transformers and toremove parallel lines. These adjustments can beautomated based on typical connection patternsand require limited computational effort. However,any adjustment will lead to a less realistic repres-entation. Applying any kind of adjustment to theinput data can also lead to disincentives to providethe most accurate and updated data for the gridcompanies. In this project, some data issues couldnot be handled through automated processes. Ex-amples are the manual addition of missing lines to

connect free substations, assigning substations totransformer stations andmatching station coordin-ates to the demand data.

For the case of Test Case F, the provided griddata could not be compiled to a complete grid.Consequently the power flow based power dis-tance could not be computed. A situation were thebenchmarking parameter cannot be computed forspecific grid companies or grid areas disqualifiesthe parameter for the application on national level.

Furthermore, the use of real grid data influ-ences the exogeneity of the parameter. The topo-logy of the real grid will always be under control ofthe DSO to some extent.

Technically line specifications such as linevoltage and resistance could be used as an input tothe power flow computation to give an even morerealistic representation of the existing grid. How-ever, we consider it difficult to collect consistentdata on line specification from all grid companies.This may lead to a distortion in the benchmarkingoutput or an incentive to provide less accuratedata. Instead we would argue, that all DSOs facesimilar constraints from the grid properties and notaccounting for line parameters will not affect therelative benchmarking strongly.

Overall, the power-flow based power distanceis well suited to represent the task of the DSOand provides improved exogeneity compared to thecurrent benchmarking. For the time being, therequirements on data quality cannot be sufficientlyfulfilled to ensure an objective benchmark. Wepropose to aim at improving data quality to anextent where it becomes possible to use the power-flowbased power distance for regulatory purposes.This can be a focus of further work from the side ofthe regulatory authority.

7.1.3. Artificial grid based powerdistance

The artificial grid based power distance computesthe flows on each line of an idealised grid to supplythe demand at all nodes. The motivation behind



this method is to have an exogenous parameterthat can be computed with low data requirements.The artificial grid based power distance only usesthe location and demand per substation as an in-put. These data are presently available from Elhuband RME making it possible to compute the outputfor any given grid area.

The artificial grid is created as a radial system,as the minimal required grid to supply all nodes isalways a tree-like topology. Unless new demandnodes are added to the system, an investment innew or reinforced lines will not affect the output.This may result in disincentives to perform invest-ments that improve security of supply.

The resulting parameter is highly exogenous,as neither the location of customers nor the de-mand is under control of the DSO.

The artificial grid based power distance doesnot account for geographical or topographical con-straints, as the real grid would. This is made visibleby the different ratios between power-flow basedpower distance and artificial grid based power dis-tance for urban and rural test cases. We wantto refrain from creating an overly complex ideal-ised grid, comparable to the Swedish model, andinstead choose to compute a simple artificial gridthat captures the challenges of supplying demandto distributed nodes. Rather than including externalconstraints through topography, weather or naturalreserves in the initial computation, we suggestperforming an ex-post adjustment of such factors.Similar to the topography adjustments in the cur-rent benchmarking, the output from the artificialgrid based power distance can be adjusted in anadditional step. In Section 5.3 we described a firstapproach to compare the line lengths in the realand artificial grid as an indicator of topographicaldifferences.

If such a correction factor can be identified, andthe required data ismore easily accessible than thegrid-data needed for the power-flow based powerdistance, we suggest to use the artificial grid powerdistance in DSO income regulation.

7.1.4. Demand distribution basedpower distance

The demand distribution based power distance cal-culates an output parameter that is merely basedon the demand and location of each node. By notusing a grid altogether, the statistical parameter ishighly exogenous and has low data requirements.

The only required input data is the location ofeach substation and the demand per node whichare readily available from the grid database andElhub, respectively. The computational effort iscomparably low, as no grid needs to be createdand no power flow calculation is used. A majorlimitation of the demand distribution based powerdistance is that it is not as intuitive to understandas grid based parameters. Using a parameter thatis detached from a grid makes it harder to compareto the real grid.

The fact that only the nodes in a system areincluded in the calculation also means, that invest-ments that do not create connections to new sub-stations will not increase the output and are there-fore not considered efficient by the benchmarkingalgorithm even if they improve security of supply orenforce the grid to supply higher local demand.

Similar to the artificial grid based parameter,the statistical parameter does not account for geo-graphical differences or other limitations betweengrid areas. Potentially, a correction factor could beapplied that investigates the ratio of area types, e.g.buildings, forest, water, agricultural land, in the gridarea.

Overall, we consider the demand distributionbased power distance to be a useful statisticalparameter. For the application in a regulatory set-ting, however, it may be too complex to intuitivelyunderstand for the relevant entities. Further in-vestigations on the robustness of the method andthe exact implications of the alpha parameter arerecommended.

We propose testing a similar approach to ag-gregate demand data from individual meteringpoints to substation demand. In this context thestatistical parameter could be a useful aggregation



tool that does not disincentivise 400V lines in thelow voltage distribution grid.

7.1.5. Yearly benchmarking parameter -energy distance

The output parameter(s) in the DEA benchmark-ing should reflect different cost drivers in buildingand maintaining the grid. To reflect administrativecostswe propose to keep the number of customersas an output parameter. The costs for administrat-ive tasks will not scale with transferred power orcustomer demand but is directly proportional to thenumber of customers. The number of customersis also an exogenous parameter that is not undercontrol of the DSO.

To account for the overall cost of energy de-livered we propose to use a 1-norm energy dis-tance, which reflects the average demand suppliedto each node. Two aggregation methods wereinvestigated to calculate the 1-norm: either usingthe average demand per node and computing onepower distance from it or calculating the powerdistance for each hour and taking the annual av-erage. Taking the average of the demand prior tocalculating the power distance gives a consistentlyhigher result than the average power distance dueto the scaling of demand in the power distanceformula. The effect of the averaging operation isthe same for every DSO and calculating the averagebefore computing the power distance reduces thecomputational effort. We therefore suggest to usethe power distance from the average demand as 1-norm energy distance.

To reflect the investment cost we have lookedat maximum load situations in the grid. We argue,that a grid investment will be taken in a way thatthe maximum load in the grid can be covered atany time. In Section 5.5 we discussed that themaximum load situation in a grid can be inter-preted differently. Either by considering the hourof maximum demand in the analysed year, themaximumpower distance from the hourly output orthe maximum load per line or node irrespective of

hour. The use of the maximum flow per line or themaximum demand per node may overestimate theoutput parameter compared to calculation basedon a real situation, i.e. max demand or max powerdistance. However it needs to be considered thatjust because the combination of high demands inseveral nodes did not occur at the same time inthe considered year does not mean it cannot occurat other times. The grid should in any case beequipped to supply the requested demand to itscustomers. Thus an infinity-norm based on themaximum nodal demand or maximum flow per lineis most applicable to reflect investment costs.

7.1.6. Alpha parameter

The alpha parameter describes the scaling of costwith line capacity. An alpha parameter between 0and 1 reflects that it is more cost efficient to buildone line with high capacity rather than two lines ofhalf the capacity to supply demand.

The results shown in Chapter 5 are based oncalculation with an alpha parameter of 0.4. Ad-ditionally we performed calculations for differentalpha parameters in all methods. Generally a lowalpha parameter leads to a flattening of the res-ulting power distance compared to the demanddata. For the artificial grid, the alpha parameter isused as an input to build the grid with the smal-lest incremental increases in power distance. Wehave seen that an artificial grid created with analpha of 0.3-0.5 resembles the real grid the most,which indicates that these values reflect the realinvestment conditions in a grid most accurately.For the demand distribution based power distancethe alpha parameter influences which nodes areconsidered to be in angular proximity, i.e. for whichnodes it is more efficient to be connected to thetransformer through one strong line compared totwo individual lines.

In this project, we investigated three methodsto calculate the alpha parameter from availabledata. Our conclusion is that there is no definiteanswer as to which alpha parameter should beused. Instead we have identified a range of 𝛼 =



0.3 − 0.5 in which the alpha-parameter is likely tolie. In future work, the alpha parameter shouldbe investigated in more detail with respect to theindividual methods. It is possible that for differentmethodologies slightly different alpha parametersare most suitable.

7.2. Recommendations

In this projectwe have investigated fourmethods tocompute a parameter that reflects the distributionof demand in the high-voltage distribution grid. Themethodologies were tested on six selected testcases for representative grid companies in Norwayto obtain first conclusions on their applicability. Allrecommendations in this section are based on alimited amount of data for a small number of testcases and are thus not necessarily representativefor the distribution grid on national level. For moregeneral recommendations these methods wouldneed to be applied to full grid areas per DSO orideally the entire Norwegian high voltage distribu-tion grid. This should be the focus of futurework onthis topic, whichwill be further discussed in Section7.3.

We consider the power-flow based power dis-tance to be the most suitable parameter to repres-ent the task of the DSO. The output parameter isalso highly comparable between DSOs in regionswith different external conditions and is intuitiveto understand. Despite lower exogeneity than theartificial grid and demand distribution based powerdistance, the power-flow based power distancewould be an improvement compared to the currentbenchmarking method. From the feedback of thereference group, we also conclude that exogen-eity is not the most crucial factor in this contextas grid companies are unlikely to adapt their in-vestment decisions to influence the DEA output.Calculating the power-flow based power distanceis associated with high computational complexityand high data requirements. While the former doesnot pose limitations to its applicability in the DEAbenchmarking the data requirements disqualify the

power flow based power distance from being usedin a regulatory setting. Technically, all required datais available from Elhub and the RME grid databasebut compiling the data on individual grid assets intoa complete system calls for complex handling andmanual adjustments. We conclude that for the timebeing the available data is insufficient to reliablycompute the power-flow based power distance forall grid areas in the Norwegian distribution grid.We recommend that additional effort is put intoensuring a high quality and consistency of data forthe entire Norwegian distribution grid.

Should it not be possible to achieve a levelof data quality that is sufficient to compute anobjective power-flow based power distance, wepropose to use the artificial grid based power dis-tance with an ex-post geographical adjustments.The artificial grid based power distance has lowerdata requirements and computational complexitythan the power flow based method. Additionally,it is highly exogenous and comparability betweengrid companies can be achieved through adjust-ment factors. For this methodology, special focusshould be put on defining the representative hourand alpha parameter for which the artificial gridis created. Additional work, beyond the scope ofthis project, will be required to identify geographicaladjustment factors based on larger test cases. Op-tionally it can be investigated to use an artificial ex-tension grid, similar to the Spanish RNMbrownfieldmodel to account for historic grid infrastructure.

If only the high-voltage distribution grid is usedto compute the power distance parameters, the dis-tribution of demand in the low-voltage grid needsto be accounted for in a suitable way. The usedbenchmarkingmethod should reflect the differencein required investment depending on the neededsubstations. This could be achieved by applyingan approach similar to the demand distributionbased power distance or more simply by keepingthe number of substations as an output parameter,or a ratio of line length in different voltage levels.The choice of aggregation and output parameter inthe low-voltage distribution gridwill dependondataavailability and computational complexity, which



should be addressed in further work.In any case, we recommend testing all pro-

posed methodologies on larger test cases to com-pare the respective output to the current DEAbenchmarking. Thiswill allow analysis of how eachparameter reflects the actual investment costs thata grid company faces and how the relative ef-ficiency of grid companies changes for differentparameters, compared to the current benchmark-ing.

For the annual aggregation of hourly powerdistance parameters to a benchmarking output wepropose to use a 1-norm, that reflects the averageload situation, and an infinity-norm, that repres-ents the maximum load situation. Additionally, wesuggest to keep the number of customers as aDEA output to reflect the administration costs. Forthe 1-norm, we suggest using the average demandper substation and calculating one power distancefrom as it is the least computationally intensiveapproach. For the infinity norm, we believe that theinvestment cost is best reflected by a ”worst-case”situation of maximum possible load in a system.This is reflected by either the maximum demandper node or themaximum flow per line, irrespectiveof hour. The infinity-norm should be further invest-igated once larger test cases are made availableto compare the output to the incurred investmentcosts.

7.3. Outlook

The focus of further work should lie in identifyingadvantages and disadvantages of each parameterand the interpretation of the obtained results in thecontext of regulatory implications. Though certainaspects were covered in this report, the proposedmethodologies need to be tested on larger testcases and ideally all high voltage distribution gridsin Norway. Calculating the power distance fromlarge test cases will make it possible to comparethe different methods to each other and to theexisting DEA benchmarking model. From the ob-tained results, effects such as unwanted bias (e.g.

urban grids are depicted less effectively than ruralgrids), investment disincentives (e.g. building ad-ditional lines to increase security of supply to analready connected customer can reduce the out-put) or limited exogeneity (e.g. the result of thepower distance can be influenced by the DSO) canbe identified. The target of this analysis shouldbe to conclude which method is best suited forthe purpose of DSO revenue regulation and whichadditional adjustments to the final benchmarking,for example a topographical correction factor, maybe needed.



Appendix

Power-flow based power distance results

(a) Test Case A (b) Test Case B

(c) Test Case C (d) Test Case D

(e) Test Case E

Figure 7.1.: Hourly results for the power-flow based power distance per test case, for 𝛼 = 0.4



Artificial grid based power distance results



(e) Test Case E (f) Test Case F

Figure 7.2.: Hourly results for the artificial grid based power distance per test case, for 𝛼 = 0.4






Figure 7.3.: Artificial grid for each test case created for 𝛼 = 0.4, for test cases with more than one transformerstation each individual tree is shown in a different colour



Demand distribution based power distance results




Figure 7.4.: Hourly results for the demand distribution based power distance per test case, for 𝛼 = 0.4



Energy distance

Infinity norm algorithm

Algorithm 1∞-norm based on max PF1: procedure _ _PF(𝐷𝑖ℎ, 𝐿𝑖𝑗)2: 𝒫𝑚𝑎𝑥 ← 03: 𝑃∞𝐷 ← 04: 𝒫𝐸

5: for ℎ ← 1..𝐻 do6: Calculate OPF (𝒟ℎ, ℒ)7: 𝒫𝐸 ← 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛8: for 𝑒 ← 1..𝐸 do9: if 𝑃𝐸𝑒 ≥ 𝑃𝑚𝑎𝑥

𝑒 then10: 𝑃𝑚𝑎𝑥

𝑒 ← 𝑃𝐸𝑒11: end if12: end for13: end for14: end procedure15: 𝑃∞𝐷 ←∑𝑒∈𝐸 𝐿𝑒 ∗ |𝑃𝑚𝑎𝑥

𝑒 |𝛼16: Return 𝑃∞𝐷



A. Acronyms

AMS Advanced Metering System

CENS Cost of Energy Not Supplied

DEA Data Envelopment Analysis

DSO Distribution System Operator

NPAM Network Performance Assessment Model

RME Reguleringsmyndigheten for Energi

RNM Reference Network Model

SM Smart Meter


B. References

B. References

[1] C.M. Domingo Comillas Universidad Pontificia. RNM: Reference Network Model. : http://www.iit.comillas.edu/technology-offer/rnm (visited on 10/30/2019).

[2] A.Sanchez T. Gomez C.Mateo. “La retribucion de la distribucion de electricidad en Espana y elModelo de Red de Referencia”. In: Estudios de economica aplicada (2011).

[3] J. Wallnerström L. Bertling M. Larsson. “Review of the Swedish Network Performance AssessmentModel”. In: Electric Power Systems Research (2008).

[4] M. Larsson. The Network Performance Assessment Model. 2005.

[5] THEMA Consulting Group. Computing the power distance parameter. 2018.

[6] SINTEF Energi AS. Planleggingsbok for kraftnett - Kostnadskatalog distribusjonsnett. 2019.


http://www.iit.comillas.edu/technology-offer/rnm

http://www.iit.comillas.edu/technology-offer/rnm

Disclaimer

THEMA Consulting Group AS (THEMA) expressly disclaims any liability whatsoever to any thirdparty. THEMA makes no representation or warranty (express or implied) to any third party in relationto this Report. Any release of this Report to the public shall not constitute any permission, waiver orconsent from THEMA for any third party to rely on this report. THEMA acknowledges and agrees thatthe Client may disclose this Report (on a non-reliance basis) to the Client’s affiliates, and any of theirdirectors, officers, employees and professional advisers provided that such receiving parties, prior todisclosure, have confirmed in writing that the disclosure is on a non-reliance basis. THEMA does notaccept any responsibility for any omission or misstatement in this Report. The findings, analysis andrecommendations contained in this report are based on publicly available information and commercialreports. Certain statements contained in the Report may be statements of future expectations andother forward-looking statements that are based on THEMAs current view, modelling and assumptionsand involve known and unknown risks and uncertainties that could cause actual results, performanceor events to differ materially from those expressed or implied in such statements.

About THEMA:THEMA Consulting Group is a consulting firmfocused on electricity and energy issues, andspecializing in market analysis, market designand business strategy.

Øvre Vollgate 60158 Oslo, Norway

THEMA Consulting Group

[email protected]://www.thema.no/

Friedrichstrasse 6810117 Berlin, Germany

Berlin office

https://goo.gl/maps/dzEGQWpWC2C2

https://goo.gl/maps/dzEGQWpWC2C2

mailto:[email protected]

https://www.thema.no/

https://goo.gl/maps/SYNhSbiGGix

https://goo.gl/maps/SYNhSbiGGix

Reguleringsmyndigheten for energi

MIDDELTHUNSGATE 29 POSTBOKS 5091 MAJORSTUEN 0301 OSLOTELEFON: (+47) 22 95 95 95

www.reguleringsmyndigheten.no

Reguleringsmyndighetenfor energi – RME

RME EKSTERN RAPPORTpublikasjoner.nve.no/rme_eksternrapport/2019/rme_ekstern...Nr 01/2019 RME EKSTERN...

Documents

Transcript of RME EKSTERN RAPPORTpublikasjoner.nve.no/rme_eksternrapport/2019/rme_ekstern...Nr 01/2019 RME EKSTERN...