Renewable Energy Sources and Responsive Demand. Do We Need Congestion Management in the...

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE TRANSACTIONS ON POWER SYSTEMS 1

Renewable Energy Sources and Responsive Demand.Do We Need Congestion Management

in the Distribution Grid?Remco A. Verzijlbergh, Laurens J. De Vries, and Zofia Lukszo, Member, IEEE

Abstract—Possible congestion management mechanisms forprice-responsive electric vehicle demand in electricity distri-bution networks are investigated. Because a high penetrationof renewable energy sources weakens the correlation betweenwholesale electricity prices and network demand, cost-minimizingelectric vehicles may cause high peaks in network load. Man-aging congestion is not costly in theory but difficult to implementefficiently. Grid tariffs that are fixed ex ante, based on networkload, were found to make the problem worse compared to thebase-case scenario of flat tariffs. An optimal dynamic grid tariffyields desirable outcomes but is difficult to determine in caseof realistic forecasting uncertainties. An iterative approach of adistribution grid capacity market has practical barriers relatedto IT infrastructure and computational requirements. Advancecapacity allocation is more straightforward to implement, but theinter-temporal constraints of the electric vehicles continue to posea challenge.

Index Terms—Congestion management, electric vehicles, net-work tariffs, power distribution, smart grid.

I. INTRODUCTION

T WO major technological trends that may play an im-portant role in a transition towards a low-carbon energy

system are the introduction of renewable energy sources (RES)and the advent of electric vehicles (EVs). As the penetrationof RES progresses, electricity will increasingly be supplied byfluctuating, weather-driven sources like solar and wind energy.This has consequences for the functioning of the electricitysystem. One paradigm for dealing with variable RES is theconcept of a smart grid, which may facilitate demand respon-siveness. Currently, the price-elasticity of electricity demandis low and the ability to shift load is, especially for smallconsumers, limited. EVs, on the contrary, could form a flexibleload of significant magnitude. They are therefore capable ofreacting to and influencing wholesale electricity prices. Bydoing so they have the potential to support renewable energysources [1].

Manuscript received May 22, 2013; revised June 25, 2013, September 27,2013, and December 02, 2013; accepted January 13, 2014. This work was sup-ported by the Next Generation Infrastructures Foundation. Paper no. TPWRS-00641-2013.The authors are with the Energy & Industry Group, Delft University of Tech-

nology, 2600 GA Delft, The Netherlands (e-mail: [email protected];[email protected]; [email protected]).Digital Object Identifier 10.1109/TPWRS.2014.2300941

However, when fleets of EVs are reacting to wholesale prices,they will do so in a correlated way, since they react to the sameelectricity price. When EVs postpone charging until the elec-tricity price is at its lowest, they will create a peak demand atthat moment. Of course there is a feedback mechanism: whenthe EVs are expected to add to demand significantly at that mo-ment, the resulting price increase will be taken into consider-ation ex ante and EV demand will spread to some extent, see,e.g., [2]. However, as was for example shown in [3], when theshare of variable renewables increases, electricity demand andthe wholesale price become increasingly decorrelated becausethe wholesale price depends on the instantaneous load and pro-duction of electricity. In other words, when wind and/or solargeneration are high, there could be relatively low wholesaleprices even if electricity demand is high.Owing to the potentially large impacts of a high share of

EVs in power systems, a large body of literature on this topichas been developed in recent years. A broad overview of EVstudies was given in [4]. The problem of an aggregator whomin-imizes the charging costs of EVs by reacting on time varyingprices (potentially driven largely by renewable energy produc-tion) was studied in, e.g., [2], and in combination with providingfrequency regulation in, e.g., [5]. EVs also received much at-tention because of the potential role in supporting renewableenergy sources, e.g., in [6] and [1]. There has also been a strongfocus on the grid impacts of EVs and how charging can be con-trolled in order to alleviate potentially severe impacts, such as[7]–[10].A common finding of many of these studies is that controlled

charging of EVs can have significant value for various actorsin the power system. Only a few studies, however, have an-alyzed the problem of satisfying different objectives such asminimizing the cost of vehicle charging, frequency regulationand providing balancing services, in combination with grid con-straints.In [11], the problem of EV charging under grid constraints

was investigated. The essence of the method that was appliedin this paper was first to minimize the cost of charging, then toevaluate if all grid constraints are satisfied, and if not, then tocommunicate available grid capacity to the EV aggregator who,finally, performs the charging cost optimization again, now in-cluding the EV power constraints that follow from the grid con-ditions. It was shown that this method is successful in not ex-ceeding grid limitations and can even be applied to quite com-plex grid topologies.

0885-8950 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


2 IEEE TRANSACTIONS ON POWER SYSTEMS

Reference [12] investigates how dynamic day-ahead grid tar-iffs can be used to alleviate distribution grid congestion causedby electric vehicle charging. In this case, the exact congestiontariff is set by the distribution system operator (DSO) using fore-casts of wholesale prices and EV trips. In this formulation ofthe problem, the DSO first mimics the EV aggregator and com-putes theminimum-cost EV charging profile. Next, he computesthe congestion tariff based on the locational marginal price for-mulation using the shadow price of grid congestion in the grid.However, this approach does not take into account the inter-tem-poral constraints of EV charging. A somewhat heuristic methodfor determining the appropriate “congestion” level was appliedto circumvent the problem that arises when inter-temporal con-straints are ignored: if one only charges a congestion fee on theexpected time of congestion, then the EVs will adjust their be-havior and congestion will likely occur just before and after thetime with a congestion fee.Reference [13] provides a comprehensive overview of dif-

ferent methods for relieving distribution grid congestion causedby EV charging. Three methods are discussed: 1) a distribu-tion grid capacity market, 2) advance capacity allocation and3) a dynamic grid tariff. Of the two formerly discussed papers,[11] falls in category 1 and [12] in category 3. Reference [13]concludes that there is always a trade-off between complexities,values and risks for the stakeholders. No single strategy has aclear advantage over the others.The goal of this paper is to investigate possible mechanisms

for aligning EV responsive demand with constraints resultingfrom limited distribution grid capacity more thoroughly. To thisend, we first present a mathematical description of optimal EVcharging in the current situation and analyze the problem thatarises when the share of variable renewable energy increases.We then describe and formalize a number of congestion man-agement mechanisms that could alleviate the problem. We an-alyze the different mechanisms in a case study in which wemake use of empirical data on renewable energy production anddriving behavior. We will also comment briefly on the chal-lenges caused by uncertainty and on the IT requirements of thedifferent congestion management mechanisms.This paper adds a number of novel aspects to the scientific

literature. The first is that, as the paper title suggests, we focusexplicitly on power systems with a high share of renewable en-ergy sources, because especially in these systems price-respon-sive demand is expected to play an important role. A centraltheme of this paper is that the influence of variable RES on theelectricity price makes the need for congestion management inthe distribution grid more urgent. Secondly, we present a math-ematical formalization of different distribution grid congestionmanagement methods in relation to EV charging, whichmay be-come the single largest source of flexible electricity demand athousehold level. In addition, we perform a numerical case studyin order to compare the performance of the different congestionmanagement mechanisms, producing new insights into the ad-vantages and limitations of the various methods. Because thecase study is based on empirical data of driving patterns, elec-tricity prices, renewable energy production and network load,we are able to evaluate the congestion management methods inrealistic situations.

II. PROBLEM ANALYSIS

A. Need for Congestion Management Due to the WeakeningCorrelation Between Wholesale Electricity Prices and Demand

In an electricity system without much variable renewable en-ergy, electricity prices rise when demand is high. This providesan incentive for EVs to be charged during off-peak hours, so thecharging of EVs should not add significantly to the peak flowsthrough the electricity network. However, in the presence of asignificant volume of wind energy, which will likely be the caseby the time that these large numbers of EVs have been intro-duced, this dynamic can be expected to change.A consequence of a large volume of wind energy will be that

the current correlation between the wholesale electricity priceand network flow will become weaker. This means that if thecharging of electric vehicles is driven by wholesale electricityprices, this may lead to network flows in excess of the capacityof distribution grids. A typical case is when wind output is max-imal during peak consumption hours. This may result in lowwholesale prices despite the fact that consumption is high, andresponsive demand reacting to the price could therefore causeeven higher network loads. For a typical time period, Fig. 1shows how system load, wind generation, the electricity priceand network load are correlated. The data are taken from theDutch electricity system [14], but we expanded the current elec-tricity generation portfolio with two different installed wind ca-pacities. For the network load we use the standard householdload profile that is used for net planning purposes in The Nether-lands [15]. During the observed period, there is a distinct peakin wind power production that lasts roughly one day. It is im-portant to observe how wind generation reduces the electricityprice significantly in the case with 15 GW of wind generatingcapacity and, as a result, the electricity price profile shows quitea different shape than the network load profile: at somemomentswith high network load the electricity price is low. In the casewith only 2 GW of wind, the electricity price follows the de-mand curve more closely. One could argue that this phenom-enon of decoupling, due to the specific timing of the wind powerproduction and demand, is a relatively rare event, but since thenetworks need to accommodate the maximum demand, even afew hours per year can be problematic.In the case that price-responsive EV demand will react to a

low wholesale price while network load is high, a congestionmanagement mechanism will be necessary in order to preventnetwork congestion. This mechanism will need to influence EVcharging behavior in such a way that network constraints arenot violated. An additional objective is that it should minimizethe additional cost to EV owners as compared to charging whenwholesale prices are lowest. A final consideration is the feasi-bility in terms of information, computation and communicationrequirements.

B. Minimum Cost EV Charging Formulation

Wewill first summarize our EV chargingmodel. Amore elab-orate description of the optimization formulation of an aggre-gator that minimizes charge costs of a fleet of EVs is providedin [3].


VERZIJLBERGH et al.: RENEWABLE ENERGY SOURCES AND RESPONSIVE DEMAND 3

Fig. 1. From top to bottom: total system demand, wind generation, net demand,electricity price and distribution network load. All graphs are for the same 5-dayperiod. The second, third and fourth figures show the differences between theinstalled wind power capacity of 2 GW and 15 GW.

We assume that real-time pricing of electricity will have beenimplemented and that EV owners, represented by an aggregatorwho manages a fleet of EVs, therefore have their vehicles pro-grammed to minimize the electricity cost of charging. The ag-gregate demand of the EVs is assumed to be large enough to thewholesale electricity price. (See also [2].) We differentiate be-tween electricity consumed by EVs and electricity consumed forother purposes. We will refer to the latter as ‘baseline electricityconsumption’, which we assume to be perfectly price-inelastic.Demand of electricity is given by

(1)

where is the baseline demand and is the extra de-mand of the EVs.We include an EV-load dependent part in the electricity price

(2)

where is the baseline electricity price at time andthe EV dependent part. As outlined in [3], the idea is to linearizethe electricity price around a certain average price and use themerit order of power plants to estimate the sensitivity parameter. This approximation allows for a quadratic programming for-mulation of the EV charging problem, while it still includes thefeedback of EV charging on the electricity prices. If this feed-

back would not be taken into account, all EV demand wouldbe programmed in a short time interval with the lowest pricesin the optimization period, causing unrealistically high peaks indemand.In addition to the electricity price we will also consider

the time-dependent network tariff . Then the minimum-costcharging problem takes the following form:

(3)

(4)

(5)

(6)

(7)

where optimization variable denotes the charging rate ofvehicle out of a total of at time and state variabledenotes the battery state-of-charge (actually state-of-energy).The vehicles are characterized by the following technical pa-rameters: denotes the charging efficiency per vehicle,and the minimum and maximum state-of-charge and thecharging power limits are given by and . Equation(7) relates the battery state to the charging rate. This implicitlycontains the assumption that vehicles do not deliver energy backto the grid: . The term represents the dischargesdue to driving and thus depends on the driving patterns of theEV owners. In a way, this term can be considered to reflect in-dividual consumer preferences, since it determines the level offlexibility of each EV. Drivers covering large daily distancescan not afford to wait several days to recharge.

C. Simulation of the Current Situation (Flat Grid Tariff)

To demonstrate why there could be a need for congestionmanagement in distribution grids, we run a simulation where afleet of EVs charges according to the formulation above. Part ofthis fleet is connected to a certain distribution grid with a certaincapacity and, in addition to the price-responsive EV demand, aperfectly inelastic electricity load that represents roughly 1000households. We assume that 50% of the households owns an EVand we represent the resulting fleet of approximately 500 EVsby 25 typical driver profiles. Details of the construction of thedriver profiles can be found in [16]. A similar method was usedin [2]. Furthermore, we assume that the cable has a peak load(occurring during only one hour of the simulated year) that is ex-actly equal to the cable’s safe capacity. This means we assumea minimally dimensioned cable—an extreme case compared tothe typical cable loadings that are observed in practice.In order to clearly observe the effect of wind energy influ-

encing the electricity price and the resulting price-responsiveEV load, we consider two scenarios for wind penetration: onewith 2 GW of wind generation installed and one with 15 GWof wind installed. The first reflects the current installed capacitywhile the latter means to represent a high wind penetration sce-nario which is likely to materialize by the time EVs reach sub-stantial numbers. We furthermore assume that no wind genera-tion capacity is assumed to be installed on the distribution cable



Fig. 2. Comparison between load profiles resulting from minimum cost EVcharging for two wind capacities and uncontrolled EV charging.

under consideration, so the only aspect of wind that is rele-vant in this case study is its influence on wholesale electricityprice. To give an impression of the relative size of the assumedwind generation capacity: with 15 GW wind capacity and a ca-pacity factor of close to 22%, the yearly wind energy productionamounts to roughly 28% of the yearly system demand (17 GWpeak, 11 GW average).The simulation spans a period of a year in a so-called rolling

horizon optimization scheme. This means we solve the opti-mization problem described by (3)–(7) for a period of 5 days(120 time-steps), then implement the control actions for thefirst day, then move the horizon by one day, etc. The rollinghorizon optimization has two important advantages: there areno end-point effect towards the end of each optimization periodand secondly, this formulation allows for an easier adaptation toinclude uncertain forecasts that are updated each day. We em-phasize that this uncertainty is not taken into account in thispaper, which implicitly means we assume perfect wind, loadand electricity price forecasts. In reality, especially the wind,and thus also price forecasts are known to be prone to signifi-cant forecast errors, so this is an important aspect that will needto be addressed in future work. Although such detailed analysisare considered out of the scope of this paper, we briefly discussimplication issued related to uncertainty in subsection D of theresults and discussion section.We run a simulation of a year. The EVs are charged as de-

scribed above and the network tariff is assumed not to de-pend on time. For comparison, we also simulate an uncontrolledcharging profile that occurs if EVs simply start charging uponarrival at home. (See [3] for more information on the construc-tion of the uncontrolled charging profile.) Fig. 2 shows the net-work load that results from the minimum cost charging formu-lation described above for the same period that was shown inFig. 1. One observes a strong peak in network demand in theevening of day 2. This is the result of the fact that the EVs post-pone their charging until the period with the lowest price. In thecase with only 2 GW of wind installed, this peak is absent. Onealso observes how theminimum-cost charging strategy can evenlead to a higher network peak than the uncontrolled chargingscenario.

III. CONGESTION MANAGEMENT MECHANISM DESIGN

We will analyze the effectiveness and implementation issuesof the main three congestion management mechanisms that arediscussed in the literature: a dynamic grid tariff, advance ca-pacity allocation and a distribution grid capacity market. In thissection we will discuss how we modeled these mechanisms.A congestion management mechanism would limit the com-

bined load of the EVs plus the inelastic baseline load to the ca-pacity of a certain distribution asset, say a cable . The math-ematical formulation of this constraint reads

(8)

where denotes the subset of EVs connected to a partic-ular cable and the inelastic baseline load. The minimiza-tion of (3) in combination with constraints (4)–7) and this extraconstraint leads to the theoretically minimal energy costs of agroup of EVs on a certain cable, while respecting the cablelimits. An optimal congestion management mechanism, eitherprice-based or capacity-based, is thus expected to yield the sameEV charging profile and costs.

A. Dynamic Network Tariff

The first mechanism that we discuss is a dynamic(time-varying) network tariff. The theoretically optimalnetwork tariff would be the lowest tariff that would cause theEV load plus baseline demand to be just lower than networkcapacity. This can be formulated as a bi-level programmingproblem of the following form:

(9)

(10)

(11)

(12)

(13)

(14)

(15)

This problem formulation states that the task of the DSO(the leader) is to find the lowest time-varying tariff such thatwhen the EV aggregator (the follower) minimizes his chargingcosts, the sum of inelastic demand and EV demand does notexceed line capacity . Note that this formulation assumes awelfare-maximizing DSO, which is an approximation of a per-fectly regulated or an ideal publicly owned DSO. Relaxation ofthis assumption is outside the scope of this paper, as networkregulation is a different and well-developed line of research.In, e.g., [17], it is shown that even the linear version of

a bi-level programming problem is NP-hard and generally



requires sophisticated algorithms to solve. In this case, how-ever, because the follower problem is quadratic in nature,the complexity increases further, even in the case of perfectinformation on the leader’s side. The presence of inevitableuncertainties makes this a stochastic problem that could rendersome solution approaches infeasible. We therefore considertwo alternative approaches that have certain practical advan-tages: a capacity-based approach and a distributed and iterativeprice-based approach.

B. Advance Capacity Allocation

The idea behind the advance capacity allocation method isthat the DSO announces the volume of available network ca-pacity for vehicle charging ahead of real time. A practical im-plementation of this formulation would involve the network op-erator communicating the forecasted time-dependent availablecapacity to the EV aggregator ex-ante. Another possi-bility would be for the network operator to take on the role ofthe EV aggregator himself, but this would constitute a departurefrom the principle of unbundling network-related and commer-cial activities. In case of a single aggregator, the aggregator cansimply include the announced free capacity in the optimizationformulation. Essentially he thus includes constraint (8) in theoptimization problem described by (3)–(7).In a case with multiple EV aggregators, matters become more

complicated. A natural approach would be for the DSO to col-lect the demand bids (for each time-step) for network capacityby the aggregators and to auction the free network capacity (thecapacity that is not needed to serve inelastic demand). Once themarket is cleared, the DSO communicates the allocated capacityper time step to each aggregator. An issue that complicates theallocation by auction is that the demand bid for capacity in acertain time-step depends on what would be allocated in pre-vious and future time-steps. It would thus require iterations tocircumvent this problem, which increases the complexity of thismechanism significantly. In the next section we will discuss asolution approach that is more suitable for multiple aggregators.Other allocation methods may also be possible, for instance

on the basis of the maximum willingness to pay for network ca-pacity. If the aggregators would submit their demand for net-work capacity ex ante (computed periodically, e.g., once peryear) to the DSO, in case of congestion he would allocate theavailable network capacity based on these bids. The aggrega-tors could be asked to submit bid functions, but perhaps a singlemaximum willingness to pay could also work. They would notneed to update their demand function frequently, as in principletheir maximum willingness to pay should remain constant. Thismethod has simplicity and transparency as advantages, but doesnot guarantee that all EVs always have enough energy in theirbatteries for making all intended vehicle trips. As we take thedriving behavior as a constraint in our analysis, we will notpursue this option any further.

C. Distribution Grid Capacity Market

The problem of finding the optimal dynamic grid tariffdescribed by (9)–(15) can also be approached in an iterative

and distributed way. Essentially, this approach consists of thefollowing steps: first the aggregators perform the optimiza-tion without a network tariff and communicate the chargingschedule to the DSO. The DSO then evaluates whether thenetwork constraints are satisfied; if not, he raises the networktariff during the moments when network capacity is exceeded.The aggregators re-calculate the charging schedule based onthe new grid tariff, communicate their demand to the DSO, etc.This procedure is repeated until it converges, which results in acertain grid tariff and a binding charging schedule.This scheme was labeled a distribution grid capacity market

in [13] and was also investigated by [18], who shows that thisalso works in a situation with multiple aggregators and yieldsthe optimal load profiles without the need for informationsharing between the aggregators. We use the same algorithm as[18], which is briefly described below. For notational conve-nience, instead of using subscript , we now use bold fonts todenote vectors with a length of the number of time-steps in theoptimization. Furthermore, we drop superscript to denotethe network tariff, so

Solve (3) s.t. (4)–(7) to obtain

Stop if

In [18] it is shown that, because the optimization problemhas a convex objective function with affine constraints, the tariffleading to the optimal EV charging profile can be found by thismethod. Although it is considered out of the scope of this paperto give a mathematical proof that the tariff that results fromthis algorithm is equal to the optimal tariff as it was definedin Section III-A, we will nevertheless refer to it as the “op-timal tariff” to clearly distinguish it from the proxy tariffs. Itshould therefore be noted that “optimality” in a strict mathe-matical sense is not claimed, but rather that this tariff leads toan EV load profile that turns out to be identical to the optimalEV profile in the capacity-constrained optimization problem.

D. Proxies for the Optimal Tariff

The three congestion management mechanisms that we dis-cussed so far should, in theory, all lead to the same optimal EVprofile. They have, however, certain practical difficulties asso-ciated with their implementation that will be discussed in thenext sections, so we will also investigate a number of proxiesfor the optimal tariff that are simpler and easier to implement.We consider three possible proxies and discuss them in the orderof increasing complexity. We add a constant part to all tariffs,including the tariffs described above, in order to make the av-erage tariff equal to 0.04EUR/kWh, which is equal to the currentnetwork-related part in the Dutch electricity tariff. This is irrel-evant, however, for the optimization since this constant part ofthe tariff drops out of the optimization objective.

a) Day-night tariff: The simplest time-dependent networktariff is a day-night tariff. In the Netherlands, the night tariff isin effect from 11 PM to 7 AM, so we assume the same period.



A second degree of freedom is the price difference between theperiods. Here we assume a value of 0.02 EUR/kWh.This tariff structure has a number of desirable features. Day-

night electricity tariffs are already in place in many countriesand consumers are therefore familiar with it. In addition, it istransparent for consumers since it is always the same. Further-more, it does not require network load to be metered or forecast.At most, onemight adjust the starting hours of the different tariffperiods and the price difference periodically.

b) Time of use tariff based on historical network load: Amore differentiated time of use (ToU) tariff would take into ac-count the shape of the network load profile. This varies day today, depending on many factors such as the weather, the compo-sition of the loads connected to the network (residential, com-mercial, etc.), type of houses, etc. Ignoring these variations, onecould simply take the average load profile over a period in thepast and base the tariff on that profile.The reason for taking the load profile into account is the fol-

lowing: the tariff should be high when network load is high andvice versa. We take a simple approach and scale the load pro-file (measured in kW) linearly with a conversion factor (unit:EUR/h) to obtain a time-differentiated tariff in EUR/kWh. Thevalue of the conversion factor is chosen such that the averagetariff again equals 0.04 EUR/kWh.This tariff, although a bit more sophisticated, has most of the

positive features of the day-night tariff: it is transparent for con-sumers since it is the same every day and easy to implement (asit does not require an IT infrastructure). In addition, it only re-quires past network load measurements.

c) Time of use tariff based on real network load: A nextstep in the complexity of a proxy tariff is to base the tariff onexpected real network load. It is the same as the previous tariff,except that now we use the real network load profile, instead ofa historic average. This should give a more precise economicsignal, but requires more enabling IT infrastructure. The mostserious requirement is that now it becomes necessary to forecastnetwork load, because the tariffs need to be announced aheadof time. How far ahead exactly is a point that deserves furtherstudy that we consider outside the scope of this paper. We em-phasize that we assume perfect network load forecasts in oursimulations (which we present in the next section). In reality,one needs to find a balance between forecasting as far ahead aspossible, which allows consumers to adjust their demand in atimely fashion and accepting larger forecast errors.This tariff also requires a more sophisticated IT infrastruc-

ture, because forecasts need to be announced to the consumersfrequently. One can think of a variety of possibilities to do this,ranging from announcements on web pages to dedicated IT sys-tems. We consider discussion on this theme important, but out-side our scope. For consumers, this tariff is the least transparentof the proxy tariffs, since it changes every day.

E. Comparison

Fig. 3 schematically compares the information flows betweenthe DSO and the aggregator(s) in the three different congestionmanagement schemes and the proxy tariffs. The variables thatthe stakeholders are required to forecast in the different schemesare indicated as grey boxes. We distinguish between network

Fig. 3. Schematic representation of the different congestion managementschemes. denotes a time varying network tariff,available network capacity, a demand function for network capacityat time and denotes EV load. The gray blocks denote forecasting ofinformation that has to be done by the stakeholders. Arrows denote informationflows. Dashed lines indicate an arrow or block that may not be necessary. (a)Dynamic grid tariff. (b) Advance capacity allocation. (c) Iterative distributiongrid capacity market. (d) Proxies for grid tariff.

Fig. 4. Comparison of the different network tariffs.

load (indicated with load), electricity wholesale prices (price)and all EV related information, i.e., planned trips and technicalEV parameters, which determine the demand for EV charging.Fig. 4 shows the optimal tariff as well as the three proxy tar-

iffs that we consider in this paper. One observes how the threeproxies give a strong signal in comparison with the optimaltariff, which is constant most of the time except when conges-tion occurs. This observation suggests that the proxies may per-form well in terms of reducing the peak load, but will influencethe economic signal of the wholesale market prices and there-fore result in higher energy costs.

IV. RESULTS AND DISCUSSION

We will now discuss the results of the simulations with whichwe evaluated the various congestion management methods. Inthe presentation of the results we focus on two output param-eters: 1) the peak load, which is a measure of the extent towhich the congestion management mechanism was able to pre-vent congestion and 2) the total costs of charging the EVs, which



Fig. 5. Comparison of the different load profiles. The upper panels shows the yearly load duration curve (a detail of the first part in the left panel) and the lowerpanel shows a typical period of three days.

is measure of the economic efficiency of the congestion man-agement mechanism. The unilaterally determined dynamic net-work tariff (Section III-A) is not simulated explicitly because ofthe difficulties of its application in practice. However, the op-timal tariff that was found using the iterative distribution gridcapacity market (Section III-C) can be considered to approxi-mate it closely. In the presentation of the simulation results, themethod labeled “optimal tariff” can hence be considered to rep-resent both the dynamic network tariff from Section III-A andthe distribution grid capacity market from Section III-C.

A. Simulation Setup

We evaluated the various congestion management mecha-nisms discussed above with our simulation model. The generalsetup is similar to the one described in Section II-C, except wenow only consider the 15 GW wind case. In the cases of theproxy tariffs, the tariffs are contained in the term in (3) andthe minimization problem described by (3)–(7) was solved toobtain the EV load. In the case of the distribution grid capacitymarket, the iterative algorithm described in Section III-C wasperformed to obtain the for this case. In the algorithm, theconvergence criterion was set to 0.01 EUR. The same problemdescribed by (3)–(7) was then solved to obtain the EV load. Inthe simulation of the advance capacity allocation method it wasassumed that there is only one aggregator on the network underconsideration. Hence, the allocation of the capacity could be

done in a straightforward manner by directly including the net-work constraint (8) in the optimization problem (3)–(7).

B. Simulation Results

The lower panel of Fig. 5 shows the resulting load profilesfor the simulated distribution cable for a typical period. One ob-serves several interesting features. Most notably, we see that thedashed lines that correspond to the proxy tariffs all show net-work peaks similar to the flat tariff. These tariffs therefore per-form poorly with respect to network peak reduction. Secondly,the load profile resulting from the optimal tariff and the loadprofile representing the advance capacity allocation method areidentical. This suggests that both methods indeed converge tothe same EV charging profile.Load profiles for an entire year are commonly summarized in

a load-duration curve. The upper panels of Fig. 5 show the loadduration curves for all mechanisms. The left side of the figureis an enlargement of the first 400 hours of the full load-durationcurve, which is shown on the right. The figure confirms that theload-duration curve that results from an optimal tariff, as ob-tained through an iterative capacity market, is practically iden-tical to the advance capacity allocation case. We also note howthe three proxy tariffs all lead to a higher load peak. The reasonis that the proxy network tariffs do not make use of feedbackbetween the network tariff and EV load [like the quadratic termin (3)] so, as a result, EV load concentrates in moments with



TABLE ICOMPARISON OF SIMULATION RESULTS

low tariffs. This result is similar to what one observes when thedependence between EV load and the electricity price is not in-cluded in a minimum electricity cost formulation, as was, e.g.,shown by [3].The second important performance criterion of the different

tariffs, in addition to the peak load on the cable, is economic ef-ficiency. This can be evaluated from the total yearly electricitycosts for EV charging. We emphasize that these do not con-tain the network costs. Table I shows the total yearly energycosts for the EV fleet. We note that the charging costs for a fleetof approximately 500 EVs are 58 600 EUR in case of uncon-trolled charging (when EVs do not respond to wholesale pricesnor any network tariff signal), whereas the flat tariff with EVsminimizing their costs in response to the wholesale price signal,without consideration for grid constraints, yields the lowest costof 41 900 EUR. Interestingly, the application of an efficient con-gestion management method causes the charging costs to beonly slightly higher (42 100 EUR) than the unconstrained flattariff case. We draw the important conclusion that the networkconstraint is a “cheap constraint”, much cheaper than investingin the additional network capacity that would be needed to avoidthe congestion. This may not always be the case, but given thefact that we started with a minimally-dimensioned network (justlarge enough to match current peak demand) and a high volume(15 GW) of wind generation and EVs, it is likely to be true inmany other cases.We observe that the proxies perform considerably worse with

respect to charging costs, approximately 20% higher than in theoptimal tariff case. This is due to the fact that the proxy networktariff always adds a network component to the electricity pricesignal, while this is not needed most of the time. Combining thefact that the proxies lead to a higher network peak and higherenergy costs, we can only conclude that they do not work. Thebusiness-as-usual option (a flat tariff) is even preferable to proxynetwork tariffs.

C. Comparison of Results to the Literature

An assumption that underlies the “dynamic grid tariff” thatwas proposed in [12] and also discussed in [13] is that the DSOcan accurately forecast the electricity price, network load andEV preferences, and correctly compute the optimal grid tariffsfrom them. The stochastic, nonlinear bi-level optimizationproblem that is the mathematical formalization of this schememay actually be very difficult, if not impossible, to solve with

acceptable accuracy and computing time. Future researchshould shed more light on the practical implementation of this.Furthermore, one may question if a DSO should even engagein the forecasting and optimization tasks that are involved withthis scheme because they are fundamentally different from hiscore tasks of network operation and maintenance.The iterative distribution grid capacity market was described

in [13], [18] and [11]. As already pointed out in [13], this ap-proach also creates a large computational and communicativeburden for both the DSO and EV aggregator(s). The conver-gence of this procedure is an issue that is worthwhile discussing,as was also done in [18], who illustrated it with a numerical ex-ample of a small conceptual system. The system studied in thispaper can be considered somewhat richer (with 25 EVs and a120 time-step optimization horizon), so it is interesting to eval-uate the convergence of the algorithm in this particular setting.In 166 out of the 360 simulations we performed there was gridcongestion. In the majority of the cases the algorithm convergedwithin 10 iterations and the highest number of iterations re-quired to converge was 33. This is in line with [18] who alsofind convergence after approximately 10 iterations.The advance capacity allocation method described in this

paper is straightforward if one assumes the presence of a singleEV aggregator on each distribution network branch. It seems,however, unlikely but also undesirable from a competitionpoint of view that this is the case. In the case of multipleaggregators, the DSO could allocate the free capacity accordingto some distribution ratio. How this ratio should be chosen ina fair and economically efficient way is an important ques-tion. Alternatively, free capacity could be auctioned amongthe various aggregators who will need to communicate theirdemand function for network capacity to the DSO at everytime step. It is important to mention here again that the freenetwork capacity is not a single quantity but a function of time(the free capacity is given by ). Combined with theinter-temporal constraints associated with the demand responseoptimization by the EVs, this makes the advance allocation byex-ante communication of demand complicated. A secondarymarket in which capacity rights can be traded could prove tobe a helpful mechanism in this respect. An allocation based onan offline computed maximum willingness to pay is anotherpossibility.The congestion management schemes investigated in this

paper are also interesting in the light of proposed methods forintegrating price-responsive energy demand with electricitygeneration such as the ones discussed by [19]. The main dif-ference in scope is that [19] discusses methods for matchingsupply and demand of energy whereas we concern ourselvesmainly with supply and demand of network capacity. Reference[19] proposes to replace point by point iterations between sup-pliers and demand of electricity with the exchange of demandfunctions, which are constructed by varying energy prices uni-formly and calculating corresponding values for demand. Thisapproach could also be of interest for the grid capacity marketdiscussed here, but the inter-temporal constraints remain anissue to be investigated further.



D. Uncertainty

The optimizations that were formulated in the previous sec-tions are all deterministic: all actors had perfect knowledge offuture electricity prices, driving behavior and inelastic networkload. In reality this is not the case and all of the above optimiza-tion tasks are questions of decision making under uncertainty.This motivates us to ask the question which of the proposed con-gestion management schemes performs best under the assump-tion of imperfect information.A dynamic grid tariff set by the DSO requires forecasts of EV

driving schedules, technical EV parameters, electricity pricesand inelastic network load, as one can see from the optimiza-tion formulation of (9)–(15) and schematically in Fig. 3. There-fore many uncertainties enter the problem. Except for inelasticnetwork load, it seems difficult for a DSO to forecast these vari-ables since they do not belong to its core business. The distri-bution grid capacity market appears more promising becauseit requires actors only to forecast variables in their own “do-main”, i.e., inelastic network load for the DSO and EV parame-ters and electricity prices for the EV aggregator. The advancecapacity allocation mechanism appears to create the smallestforecasting burden: the DSO only needs to forecast inelastic net-work load. Of course, if network capacity is auctioned, the EVaggregator needs to forecast price and EV parameters, but in thiscase wrong forecasts only lead to economic inefficiency, not tonetwork overloads. Given the limited number of hours with con-gestion these costs will probably be limited.

E. IT Infrastructure Requirements

Another implementation issue is the requirement for IT in-frastructure that is associated with the different schemes. Thenumber of distribution network assets that a DSO handles istypically large. Depending on the method of bookkeeping, oron what network level the congestion management is to be ap-plied, this can be in the orders of tens of thousands of networks.The costs related to the IT infrastructure may therefore be sub-stantial and should be an important criterion in the assessmentof different congestion management schemes.For the ex-ante determined dynamic grid tariff, the IT re-

quirements appear to be rather modest. The main burden in thisscheme is for the DSO, who can perform the optimizations “offline” and only needs to communicate the resulting grid tariff.There does not need to be any communication from aggregatorto DSO.In the case of advance capacity allocation, the DSO commu-

nicates the volume of free network capacity to the aggregator(s).In case of only one aggregator, this is everything that is needed,but in case of multiple aggregators they need to send their de-mand functions to the DSO, who then clears the market. Here,too, the IT requirements do not appear to be excessive.By far the heaviest requirements on IT infrastructure are

associated with the iterative network capacity market. In thisscheme, information has to flow iteratively between DSOand aggregator. Also, on the aggregators’ side, each iterationrequires a new optimization. With large amounts of EVs andespecially when stochastic optimization methods are applied,this is a large computational effort in itself. The entire scheme

could thus take considerable time, during which information isconstantly flowing between the actors.

V. CONCLUSIONS

This study presents an analysis of methods for managing thecongestion of distribution networks that may arise when a largequantity of responsive EV demand reacts to wholesale elec-tricity prices which are influenced by a large share of variablerenewable energy sources. We present a mathematical formula-tion of the EV optimization problem and analyze a number ofpossible congestion management methods. The most importantconclusions from this study can be summarized as follows:• Variable renewable energy generation weakens the corre-lation between wholesale electricity prices and electricitydemand. As a consequence, large network flows caused bycost-minimizing EV demand may cause distribution net-work overload.

• The constraint that limited network capacity puts on EVcharging has a low cost associated with it. Shifting demandpeaks through an optimal congestion management mecha-nism increases the energy costs of EV charging only mar-ginally.

• Tariffs that are fixed ex ante, based on historic networkload profiles, do not solve congestion efficiently and maynot be effective at all. They influence the economic signalof the wholesale electricity price, leading to unnecessarilyhigh electricity costs for EV charging. The reason is thatnetwork capacity is only a constraint during a limitednumber of hours per year, while these tariffs force con-tinuous changes in EV charging. Therefore we do notrecommend the use of grid tariffs that are fixed ex-ante formanaging network congestion that is caused by EVs.

• The unilateral determination of an optimal dynamic gridtariff can be formulated as a non-linear bi-level program-ming problem where the leader’s task is to find the lowestpossible network tariff added to the wholesale prices butkeeps network loads within bounds. Even in the case ofperfect information this is a difficult problem to solve.The additional complexity of uncertainty may render thismechanism infeasible.

• An algorithm for an iterative grid capacity market maysolve congestion in an economically efficient way, but itsimplementation requires frequent exchange of informa-tion between DSO and aggregator(s) and therefore posesa heavy computational burden to both the DSO and theEV aggregator.

• Advance capacity allocation is a straightforward methodfor dealing with network constraints if there is only a singleEV aggregator. If more aggregators are active in the samedistribution network, a capacity auction could be a possiblemechanism, but the existence of inter-temporal constraintsfor the EV optimization complicates such an auction. Pos-sibly, a secondary market in which capacity rights can betraded among aggregators could contribute to this solution.

We summarize the answer to the question raised in the title ofthis paper as follows: due to the limited additional costs of thenetwork constraint on EV charging and the poor performance ofgrid tariffs that are determined ex ante, an efficient congestion



management mechanism will likely be needed for the distribu-tion grid. The introduction of a such a mechanism will post-pone or even avoid the need for more costly network capacityupgrades. The design of this mechanism depends on many fac-tors that need to be addressed carefully in future research, forwhich we recommend a number of possible directions. Most im-portantly, uncertainties in electricity prices which are stronglyrelated to imperfect RES forecasts, as well as uncertainties innetwork load and EV driving schedules need to be taken into ac-count. Furthermore, adding a large share of solar energy wouldbe a valuable addition to the wind-based analysis performedhere. Two factors make this particularly interesting: solar energyhas a more regular and markedly different timing than wind,and, secondly, it is largely embedded at the distribution levelitself. Other important issues to be investigated concern the re-lations between congestion management on the one hand andinvestment in new distribution assets and capital cost recoveryon the other hand. Another topic that deserves more attention isthe question how to embed the distribution grid congestion man-agement mechanisms in the new energy market designs as dis-cussed in [19]. Finally, we recommend more detailed studies ofthe exact design of the different congestion management mech-anisms. The specifics of capacity allocation by auctioning, de-mand functions for network capacity, bids representing willing-ness to pay, the iterative grid capacity market, etc, should beinvestigated in such studies.

ACKNOWLEDGMENT

The authors would like to thankM. van Blijswijk for his com-ments on the manuscript.

REFERENCES

[1] H. Lund and W. Kempton, “Integration of renewable energy into thetransport and electricity sectors through v2g,” Energy Policy, vol. 36,no. 9, pp. 3578–3587, 2008.

[2] T. Kristoffersen, K. Capion, and P. Meibom, “Optimal charging ofelectric drive vehicles in a market environment,” Appl. Energy, vol.88, no. 5, pp. 1940–1948, 2011.

[3] R. Verzijlbergh, Z. Lukszo, and M. Ilic, “Comparing different evcharging strategies in liberalized power systems,” in Proc. 2012 9thInt. Conf. Eur. Energy Market (EEM), May 2012, pp. 1–8.

[4] D. B. Richardson, “Electric vehicles and the electric grid: A reviewof modeling approaches, impacts, and renewable energy integration,”Renew. Sustain. Energy Rev., vol. 19, no. 0, pp. 247–254, 2013.

[5] E. Sortomme and M. A. El-Sharkawi, “Optimal combined bidding ofvehicle-to-grid ancillary services,” IEEE Trans. Smart Grid, vol. 3, no.1, pp. 70–79, Mar. 2012.

[6] W. Kempton and J. Tomic, “Vehicle-to-grid power implementation:From stabilizing the grid to supporting large-scale renewable energy,”J. Power Sources, vol. 144, no. 1, pp. 280–294, Jun. 2005.

[7] J. Peças Lopes, F. Soares, and P. Almeida, “Integration of electric ve-hicles in the electric power system,” Proc. IEEE, vol. 99, no. 1, pp.168–183, 2010.

[8] K. Clement-Nyns, E. Haesen, and J. Driesen, “The impact of chargingplug-in hybrid electric vehicles on a residential distribution grid,” IEEETrans. Power Syst., vol. 25, no. 1, pp. 371–380, Feb. 2010.

[9] R. Verzijlbergh, M. Grond, Z. Lukszo, J. Slootweg, and M. Ilic, “Net-work impacts and cost savings of controlled ev charging,” IEEE Trans.Smart Grid, vol. 3, no. 3, pp. 1203–1212, Sep. 2012.

[10] R. C. Green II, L. Wang, and M. Alam, “The impact of plug-in hy-brid electric vehicles on distribution networks: A review and outlook,”Renew. Sustain. Energy Rev., vol. 15, pp. 544–553, 2011.

[11] O. Sundstrom and C. Binding, “Flexible charging optimization forelectric vehicles considering distribution grid constraints,” IEEETrans. Smart Grid, vol. 3, no. 1, pp. 26–37, Mar. 2012.

[12] N. O’Connell, Q. Wu, J. Stergaard, A. Nielsen, S. Cha, and Y. Ding,“Day-ahead tariffs for the alleviation of distribution grid congestionfrom electric vehicles,” Elect. Power Syst. Res., vol. 92, pp. 106–114,2012.

[13] P. Bach Andersen, J. Hu, and K. Heussen, “Coordination strategies fordistribution grid congestion management in a multi-actor, multi-objec-tive setting,” in Proc. 2012 3rd IEEE PES Int. Conf. Exhib. InnovativeSmart Grid Technologies (ISGT Europe), Oct. 2012, pp. 1–8.

[14] TenneT, Dutch Transmission System Operator [Online]. Available:http://www.tennet.org

[15] Energie Data Services Nederland, Dutch Consumption Profiles [On-line]. Available: http://www.edsn.nl/verbruiksprofielen (last accessedSep. 2013)

[16] R. Verzijlbergh, “The power of electric vehicles. Exploring the value offlexible electricity demand in amulti-actor context,” Ph.D. dissertation,Delft Univ. Technol., Delft, The Netherlands, 2013.

[17] J. Bard, Practical Bilevel Optimization. Norwell, MA, USA: Kluwer,1998.

[18] B. Biegel, P. Andersen, J. Stoustrup, and J. Bendtsen, CongestionMan-agement in a Smart Grid via Shadow Prices, ser. IFAC Workshop Se-ries. New York, NY, USA: Elsevier Science, 2012, pp. 518–523.

[19] M. Ilic, L. Xie, and J.-Y. Joo, “Efficient coordination of wind powerand price-responsive demand—Part I: Theoretical foundations,” IEEETrans. Power Syst., vol. 26, no. 4, pp. 1875–1884, Nov. 2011.

Remco A. Verzijlbergh received the M.Sc. degreein applied physics from the Delft University of Tech-nology, The Netherlands, and the Ph.D. degree at theEnergy and Industry group at the Delft University ofTechnology, The Netherlands.His research interests include operations and eco-

nomics of power systems, with a special focus on theintegration of electric vehicles and renewable energysources in power systems.

Laurens J. De Vries received the Ph.D. degree fromthe Faculty of Technology, Policy and Managementof Delft University of Technology, The Netherlands.He is an Assistant Professor at the Faculty of Tech-

nology, Policy and Management of Delft Universityof Technology. He performs research and teaches inthe field of electricity market design, analyzing themutual relationships between the physical infrastruc-ture and its (economic) organization and regulation.He focuses on long-term issues, such as generationadequacy and, more in general, the process of restruc-

turing power sectors in OECD as well as in developing countries.

Zofia Lukszo (M’10) received the Ph.D. degreefrom Eindhoven University of Technology, TheNetherlands.She is an Associate Professor at Delft University

of Technology, The Netherlands. Her researchfocuses on operations management, mainly in theprocess industry and infrastructure sectors. She hasextensive experience in the application of mathe-matical modelling, optimization and quality controlin decision making at the operation and control levelin the process industry. She is also a leader of the

program Intelligent Infrastructures within the international research programof the Next Generation Infrastructures ( http://www.nginfra.nl).

Renewable Energy Sources and Responsive Demand. Do We Need Congestion Management in the...

Documents

Transcript of Renewable Energy Sources and Responsive Demand. Do We Need Congestion Management in the...