Game-theoretic Modeling of Curtailment Rules and their Effect on Transmission Line Investments Andoni, Merlinda; Robu, Valentin; Fruh, Wolf-Gerrit

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1 Heriot-Watt University Heriot-Watt University Researh Gateway Game-theoreti Modeling of Curtailment Rules and their Effet on Transmission Line Investments Andoni, Merlinda; Robu, Valentin; Fruh, Wolf-Gerrit Published in: Proeedings of the IEEE Power Engineering Soiety 6th Innovative Smart Grid Tehnologies Europe Conferene Publiation date: 16 Doument Version Peer reviewed version Link to publiation in Heriot-Watt University Researh Gateway Citation for published version (APA): Andoni, M., Robu, V., & Fruh, W-G. (16). Game-theoreti Modeling of Curtailment Rules and their Effet on Transmission Line Investments. In Proeedings of the IEEE Power Engineering Soiety 6th Innovative Smart Grid Tehnologies Europe Conferene IEEE.

2 Game-theoreti Modeling of Curtailment Rules and their Effet on Transmission Line Investments Merlinda Andoni, Valentin Robu and Wolf-Gerrit Früh Heriot-Watt University, Edinburgh, UK Abstrat This paper provides a study of the impat of urtailment shemes, applied when generation exeeds demand, on the Capaity Fator (CF) of wind generators, inluding the effet of spatial wind orrelation among different loations. Moreover, we disuss how a round-robin urtailment rule ould be implemented to guarantee approximately equally urtailment ratio for generators of unequal rated apaity. Next, we onsider a two-loation problem, where exess renewable energy generation and demand are not o-loated. We study the ombined effet that urtailment shemes and line aess rules have on the deision to invest in new transmission lines. In partiular, we show that, for ommon aess rules, this an lead to a Stakelberg game between transmission and loal generation apaity investors, and we haraterise the equilibrium of this game. Finally, we apply and exemplify our model to a onrete problem of building a transmission link in western Sotland, and we propose a mehanism for setting transmission harges that assures both that the transmission line gets built, but investors from the loal ommunity an also benefit from investing in renewable energy. I. INTRODUCTION Integrating energy generated from renewable energy soures (RES) into existing grids is one of the key fators for ensuring a sustainable, arbon-free energy future [1], yet sets a new set of hallenges to eletriity networks []. A key problem is that loations whih are best suited for installing new apaity due to favourable resoure onditions or soial approval, e.g. large wind turbines, are typially remote loations (suh as windy islands), situated far from population/industry entres. Hene, a lot of new RES apaity installed is subjet to generation urtailment, a strategy where distributed generators are granted non-firm grid aess and are required to adjust their outputs aording to the system operator s instrutions, foremost due to network onstraints, low loal demand or insuffiient distribution or transmission network apaity. Tehnial and regulatory aspets of urtailment have been extensively studied [3], however, it is beoming inreasingly lear, that espeially in areas of network ongestion, eah loation s urtailment level (and the urtailment poliy applied) an play a ruial role on the total installed generation apaity, due to their effet on investor deisions [4] and might therefore disourage future RES investment. The long term solution is to build or reinfore transmission and distribution lines, between remote and areas of high demand. Network upgrade often presents prohibitively high osts and is traditionally performed, or partially supported by publi investment means, usually through the transmission system or loal distribution network operator (TSO/DNO). From a publi poliy standpoint, it would be highly desirable to inentivise private investors to undertake part of the required grid infrastruture investment. An approah would be that power lines are built under a ommon aess priniple, where the line investors may be given a liense under the obligation to allow line aess from third parties, subjet to a transmission fee per unit of energy transported, the level of whih is subjet to a ap set by the regulator. The interplay between urtailment rules and priniples of aess applied to power lines, raises potentially omplex issues, espeially as the line investor, regulator and loal RES investors may have different underlying goals [5]. In this paper, we use the tools from game theory to examine these interations and show that a omplex Stakelberg game an our, in whih the deision to build a transmission line depends on the equilibrium strategy of loal investors to invest in additional generation apaity. Various ommerial and aademi studies [3], [4], [6], [7] disuss the appliation of urtailment strategies, primarily fousing on their tehnial, legal and regulatory impliations, rather than their impat on investor s deision-making, regarding generation or transmission assets, whih is the fous of our work. In the ontext of deregulated eletriity markets, transmission planning tehniques need to adopt optimisation [8] and strategi modeling of market partiipants [9], as opposed to intuitive approahes, adopted by utility ompanies in the past [1]. This is where game theory tools an play a signifiant role. Strategial behaviour of energy investors has been simulated, with agent-based modeling [11], [1], or by examining alternative market strutures, where network upgrade is performed by system operators or private investors, leading to different optimal results [13]. In [14], oalition formation is used to oordinate privately developed power grid lines, in order to redue ineffiienies and transmission losses, while transmission planning and expansion at areas of network ongestion were studied in [15]. Curtailment strategies or line aess rules were not onsidered in these works. However, as the profitability of any sheme is diretly affeted by suh rules, we fous on this fator for our work. Stakelberg games have been used to model transmission upgrade, using eonomi analysis with soial welfare [16], Loational Marginal Priing [17] or highlighting the unertainties of RES generation [18]. Reent works on the renewable energy /16/$ IEEE

3 domain, use Stakelberg game analysis to desribe energy trading of mirogrids [19], [] or propose novel funding shemes for RES investment [1]. In summary, the ontribution of this work to the state of the art an be stated as follows: First, we formalise the effet of ommonly-used urtailment rules on the RES apaity installed at a partiular loation. We show that the resulting apaity built and profitability of different generators an differ widely under different urtailment models or wind orrelation, and we propose a new round-robin rule. Seond, we study the network upgrade as a Stakelberg game between the line and loal RES investors, for ommon aess rules, and we derive the amounts generated and profits in the equilibrium of this game. Finally, we exemplify our analytial results for the ase of a grid reinforement and the finanial parameters of the Kintyre-Hunterston link, in the UK, and determine a feasible range of the transmission harges. The remainder of this paper is organised as follows: Setion II elaborates on urtailment strategies. Effets on transmission investment are shown in Setion III. Numerial results of a line upgrade ase-study are presented in Setion IV, while Setion V onludes. II. CURTAILMENT STRATEGIES The seletion of a urtailment strategy (see [7], [] for an extensive review) needs to aount for several assessment riteria, suh as fairness, transpareny, effiieny or reliability. The shemes proposed take into onsideration: the tehnial harateristis of the generators, their size, loation, expeted response time, and ruially, the order of onnetion to the power grid. In this paper, we fous our attention to the main mehanisms found in the literature or applied to ommerial Ative Network Management (ANM) shemes 1 :last-in-firstout (LIFO), Pro Rata (or proportional) and Rota. In LIFObased urtailment, generators are urtailed based on the inverse order in whih they were granted the right to onnet to the distribution network. By ontrast, Pro Rata shares urtailment equally among installed generators, proportionally to the rated apaity or atual power output at the time of urtailment. Finally, Rota urtails generators at a rotational basis or a predetermined rota, as speified by the system operator. To illustrate the effets and operation of these shemes, we onsider a simple network of three wind generators of P N1 = 7 MW, P N = MW and P N3 = 3 MW rated apaity, where the subsript denotes the hronologial order of their onnetion to the power grid. For simpliity, we assume there is no export apability and the demand is onstant and equal to P D,t = 6 MW, t. For a given time interval t, if all generators are produing their nominal output power, a total of P C,t = 6 MW needs to be urtailed. The alloation of this 1 LIFO is used in: and Pro Rata is used in: Projets/tier--projets/Flexible-Plug-and-Play-(FPP)/ power to the generators depends on the sheme seleted: With LIFO, the third and seond generator are ompletely urtailed and the first is urtailed by 1 MW. On the other hand, when Rota is implemented, the generators take turns, resulting here in the first generator being urtailed by 6 MW, while the other generators are not affeted. In the next urtailment event, the seond generator is required to be urtailed and so on. By ontrast, with Pro Rata the allowed export is alloated proportionally to the generator s output, resulting in 3.5 MW, 1 MW and 1.5 MW urtailed power, respetively. If Pro Rata is not always desirable (tehnially speaking, it may require modified pith-ontrolled wind turbines, suh that their output an be adjusted as needed, whih may be more expensive), we an think of an equivalent Rota-type strategy with the same fairness properties, a strategy we all Frational Round Robin (FRR). With FRR, the power urtailed is distributed sequentially on a rotation basis, aording to the number of rated apaity units installed, so that larger generators are hosen proportionally more times, in diret relation to their size. This means for instane that, on average, every 1 times a urtailment of 6 MW is needed, the first generator will be urtailed 7 times, the seond times and the third 3 times. Being aware in advane of the urtailment order, the unertainty of short-term power output predition of a generator an be redued. Moreover, for a suffiiently long period of time (i.e. many years, the typial lifetime of a wind turbine), the urtailment rate under FRR onverges to the proportional urtailment rate with Pro Rata. We implement a simulation proess, in the ourse of one year, to ompute the apaity fators of the wind generators, under different shemes. However, sine network onstraints are usually appliable to a partiular geographial area of the grid, where wind onditions may be similar, the power output of the generators presents a level of spatial orrelation, whih is signifiant for the required urtailment level at this area. To model orrelation, we apply the tehnique developed by Früh (15) [3]. First of all, we generate 876 data points of wind speed u rand,i for i = generators, from three random and independent samples of a Weibull distribution (one for eah generator), using the typial UK values of = 9 m/s and k = 1.8. We set the wind speed at the first generator s loation as a referene u Ref and we produe random, yet rossorrelated wind data series u i at eah generator s loation, by the following equations: u i (t) = r u Ref (t) + (1 r ) u rand,i (t) (1) r = 1 aros(1 r) () π where r is the Pearson s orrelation oeffiient. The data series are then onverted to power outputs, using a generi model of a wind turbine. If the aggregate power at time t exeeds the power demanded, then urtailment is required, whih is alloated to the generators aording to the strategy imposed. Based on the power urve of Eneron E44 ommerial wind turbine.

4 Average apaity fator variane Capaity fator (%) Average apaity fator (%) 35 LIFO Rota Pro Rata FRR 3 LIFO Rota Pro Rata FRR Generators Pearson oeffiient r Fig. 1. Curtailment mehanisms effets on the CF of wind generators under LIFO, Rota, Pro Rata and FRR Fig. 3. Correlation effets on average CF under different urtailment shemes LIFO Rota Pro Rata FRR Average number of urtailment events Fig.. Fairness under different urtailment shemes Fig. 1 shows the CF results for eah generator under the four different shemes for onditions of perfet orrelation (r = 1). LIFO learly favours early onnetions, while the third generator suffers a redution of 67.4%. Rota an disadvantage smaller-sized generators. On the ontrary, Pro Rata produes equal CF redution for all generators, while FRR produes similar results to Pro Rata, as expeted. A measure of fairness is the variane of the average CF for eah strategy. In Fig., we illustrate, for r = 1, this variane with the average of the number of urtailment events required. LIFO presents a poor performane with respet to fairness, as opposed to Pro Rata, whih requires the largest number of urtailment events. FRR an present similar fairness properties to Pro Rata, while reduing signifiantly the number of urtailment events per generator. Finally, Rota is fairer than LIFO and requires the smallest number of urtailment events ompared to all shemes. Finally, as shown in Fig.3, the required total urtailment inreases, as we proeed from no orrelation to perfet orrelation, resulting in lower CFs. In the following setion, we turn our attention to modeling the grid infrastruture investment, at areas where generation urtailment is applied. III. CURTAILMENT & NETWORK UPGRADE Here, we study how the applied urtailment influenes the deision to build or reinfore transmission lines. We onsider two loations: A is a net onsumer (where demand exeeds supply, e.g. a mainland loation with industry or signifiant population density) and B is a net energy produer (favourable RES onditions, e.g. a remote region rih in wind resoure). In pratie, there would be some loal demand and supply, onsidered here negligible, and installation of new RES apaity is not be feasible without a network upgrade. Loation A has a net demand of E D,A, equal to loal demand minus loal generation. Moreover, we onsider two players: the line investor, who an be merhant-type or a utility ompany and is building the A B interonnetion and possibly renewable generation apaity at B, equal to E G1,B, and a loal player, who represents the loal RES generators or investors loated at B, E G,B. This seond player an be thought of as investors from the loal ommunity, who do not have the tehnial/finanial apaity to build a line, but may have aess to heaper land, find it easier to get ommunity permission to build turbines et., hene may have a lower per-unit generation ost 3. Essentially, E Gi represents the expeted energy units, for the projet lifetime, aording to the resoure on the site s loation, without enountering urtailment. Note that, while for a partiular time period, suh as an hour or a day, the expeted generation is unertain, for the overall lifetime of a RES projet, it an be estimated with relatively high ertainty from the weather and wind patterns at this loation. For simpliity, we assume there is no RES apaity installed at loation B prior to the onstrution of the power line. However, the deision of building the power line will eliit a reation from loal investors. This two-stage proess is analysed as a Stakelberg game. Cruially, the line investor 3 Note that in Sotland, or other ountries suh as Denmark, loal groups often at together to make land available and invest in RES projets. Community Energy Sotland (CES) is an umbrella organisation of suh groups.

5 has a first mover advantage, as only he an build the grid infrastruture, whih is expensive, tehnially hallenging and only a limited set of investors (e.g. DNO-approved) have the expertise and regulatory approval to arry it out. The power line ost is estimated as C T = I T + M T over the projet lifetime, where I T is the ost of building the line (or initial investment) and M T the ost of operation and maintenane. The monetary value of the power line is proportional to the energy flowing from B to A, harged under ommon aess rules with p T transmission fee per energy unit. Moreover, the ost of expeted generation per unit Gi (for onstant depreiation) is Gi = (I G,i + M Gi )/E Gi, where I Gi the ost of building the plant and M Gi the operation and maintenane osts, and we assume that the energy generated by a RES unit is sold at a onstant feed-in-tariff prie (FIT), equal to p G. The line investor or leader an assess and evaluate the reation of other investors to determine his strategy (i.e. the line and RES apaity to be installed), aiming to influene the equilibrium prie. Loal generators or followers an only at after observing the leader s strategy. The equilibrium of the game is found by bakward indution. First, the leader estimates the best response of loal generators, given its own output and then deides his strategy aiming to maximise his profit. At a seond stage, the follower observes this strategy and deides his generation apaity, as his best response, i.e. maximising his own profit, as antiipated by the leader. The network aess arrangements play here a ruial role for the market equilibrium formed. Hene, we define a new parameter, whih quantifies the urtailment imposed to eah generator. If the expeted urtailed energy units are E Ci, then the urtailment rate CR i of i generator, is defined as the ratio of expeted urtailment to expeted generation, over the projet lifetime CR i = E Ci /E Gi and it is ruial for the viability of existing and future RES investment. Here, CR i < 1 and an be interpreted as CF redution, e.g. CR i = 5% results in a 5% CF redution. Next, we fous and present the equilibrium results for LIFO and a fair urtailment sheme, whih an be an expression of either Pro Rata or FRR. A. LIFO sheme Under a LIFO sheme, the leader is proteted from any urtailment, hene he an build all generation apaity to serve E D,A himself and maximise his profits. The loal investors have to provide all urtailment required, as late onnetions, thus there is no inentive for them to invest in new apaity. Lemma 1: The transmission investment game between the line investor and loal generators with LIFO urtailment results in the expeted generation and profits, at Stakelberg equilibrium: E G 1,B = E DA (3) E G,B = (4) Π 1 = (p G G1 ) E DA (5) Π = (6) Proof: The apaity of the transmission line is bound by the demand at mainland, therefore total generation apaity at loation B, (E G1,B + E G,B ) annot exeed E DA. Any generation apaity built exeeding the demanded energy, has to be urtailed. Taking this into aount, the profit funtions of the two players are Π 1 = p T E DA + (p G p T G1 ) E G1,B C T Π = (E DA E G1,B ) (p G p T G ) Aounting for the leader s market advantage, we derive the desired equations. B. Pro Rata or FRR sheme The main differene from LIFO, is that proportional rules are imposed to all generators, regardless of their order of onnetion. Therefore, more total apaity E G,B = E G1,B + E G,B than the energy demanded at A an potentially be installed, as long as the urtailment rate or energy urtailed E C,B = E G,B E D,A allows for the investments to be profitable. The urtailment rate at loation B is given by E D,A CR B = 1 E G1,B + E G,B Given this, the general profit funtions of the players, whih are funtions of both players energy outputs Π(E G1,B, E G,B), an be expressed as: ( pg E D,A Π 1 = E G1,B + E G,B G1 ) E G1,B (7) + p T E D,A E G,B C T (8) E G1,B + E [ G,B ] (pg p T ) E D,A Π = G E G,B (9) E G1,B + E G,B Before stating our main Stakelberg equilibrium results, we need to define the players best responses. Proposition 1: Given the output of the leader E G1,B, the follower s best response is: E G,B = (p G p T ) E D,A E G1,B G E G1,B (1) Proof: Let the value of E G,B, whih maximises the profit of the follower, be E G,B = argmax Π. Setting as E G,B zero the partial derivative of Π in (9), with respet to E G,B and rearranging, we get (1). Proposition : Given the output of the follower EG, the,b leader s best response is: E G 1,B = (p G p T ) G E D,A 4 G1 (11) Proof: Let the value of E G1,B, whih maximises the profit of the follower, be E G1,B = argmax Π 1. Substituting E G1,B (1) in (8) and then setting as zero the partial derivative of Π 1 with respet to E G1,B gives the stated expression. Lemma : The transmission investment game between the line investor and loal generators with a proportional sheme

6 results in expeted generation and assoiated profits, at Stakelberg equilibrium: E G 1,B = (p G p T ) G E D,A 4 G1 (1) E G,B = (p G p T ) ( G1 G ) E D,A 4 G1 (13) Π 1 = (p G p T ) G E D,A 4 G1 + p T E D,A C T (14) Π = ( G 1 G ) (p G p T ) E D,A 4 (15) G 1 Proof: Replaing Prop. in (1), the optimum output of loal generators EG,B is found, i.e. (13). Finally, substituting the energy outputs at equilibrium (1) and (13), in (8) and (9), we derive the equilibrium profits Π 1 = max Π 1 and Π = max Π. Finally, note that this strategi interation requires the total generation apaity to exeed the demand at A, i.e. E G1,B + E G,B > E D,A. This onstraint yields the following onditions, whih must hold for the setting to atually be game-theoreti (and for our analysis to be relevant): G < p G p T (16) G1 < p G p T IV. CASE STUDY (17) In this setion, we apply the theoretial framework of the Stakelberg game with Pro Rata (.f. Lemma ) to the onrete ase-study of Kintyre-Hunterston grid reinforement projet 4, urrently under development in the UK. Grid infrastruture in the Kintyre peninsula was originally designed and built to serve a typial rural area of low demand. Wind generation rapid growth, due to substantial inentives, quikly led to high volumes of renewable investment in the region. RES apaity was expeted to reah 454 MW by the end of 15, and future onnetions estimations exeed 793 MW. The neessity for large transmission investment soon beame apparent, therefore the loal DNO proeeded in a 3m network upgrade projet onneting existing Hunterston substation, partially through a sub-sea link to Crossaig, thus reating headroom for additional 15 MW renewable apaity estimated to provide a net lifetime benefit of 5m [4]. Based on these projet figures, we onsider a simplified two-node network, in whih the energy demand in the mainland, met by generation in Kintyre, equals the energy transmitted through the power line. With the majority of investment being wind projets, we estimate the total energy demand as E D,A = 9, 855, MWh for 5 years projet lifetime. As urrently valid in UK for medium size wind projets, the FIT prie was set to p G = 8.6/MWh. In Figure 4, we summarise the results of our model, namely the generation apaity built and assoiated profits at Stakelberg equilibrium, for three senarios: Senario 1 orresponds to the plots of the first olumn and shows the effet of varying the loal investors generation ost, keeping all other parameters at onstant values (set as G1 = p T =.3p G and 4 G =... G1 ), Senario in the seond olumn shows the effet of varying the line investor s generation ost (with settings: G = p T =.3p G and G1 =.15p G....35p G ) and Senario 3 in the third olumn shows the effet of varying the transmission fee (with other parameters set at G1 =.3p G, G =.9 G1 and p T =....4p G ). For eah senario, the range of the free parameter (fixing the others) is determined from the onstraints in (16) and (17). Given a ertain FIT (this parameter is ontrolled by the regulatory authority), the line investment feasibility depends diretly on the generation ost G1 and transmission fee p T. If the line is built, it sets up a level of total feasible generation investment at B whih, ombined with Pro Rata aess rule, leads to larger volumes of apaity being built than atual demand (see 1st row of Fig. 4), as long as the urtailment rate is kept under reasonable levels. Note the level of total generation does not depend on the generation osts of loal investors, sine they annot at without the existene of the line (see Fig. 4 1st row, 1st olumn). For all settings, the size of G relative to G1 determines how exportable level of generation apaity is shared. Cheaper generation has an advantage in all 3 sets of results (.f. Fig. 4 first row), although as the graphs show, the dependeny is not neessarily linear. Another onlusion is that transmission harges, agreed by the line investor and an independent regulatory authority, has to be set within a speifi range. Low values of p T may lead to transmission investment being aborted, somewhat larger values might theoretially be suffiient to ahieve profitability for the line investor, however, hide the risk of free-riding from loal investors, who benefit from the leader s investment at ost muh less than to leader s himself. What the result in Fig. 4 (row, ol. 3) shows is that there exists a range in whih p T an be set suh as to assure the line gets built (i.e. when the leader s profits are above in our ase, transmission harges need to be at least 8/MWh), but also not disourage other loal renewable investors. V. CONCLUSIONS & FUTURE WORK To our knowledge, this is the first work examining the ombined effets of urtailment strategies and transmission aess rules on RES apaity investment and network expansion. Our researh foused on the effets of the urtailment shemes to investment deisions and market behaviour. We model grid reinforement, as a two-stage strategi game between the line investor and loal generators and determine generation apaities and profits at equilibrium. Based on a UK grid reinforement projet, we propose a method to alulate transmission harges, under ommon aess rules, whih enables the implementation of both transmission and loal generation investments. Future work inludes expanding the developed two-loation model to more omplex settings and multiple loations. We also plan to expand the equilibrium results to settings with partial orrelation.

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