Energy Curtailment Regulation Impact on. Distributed Generation Integration

Transcription

1 Energy Curailmen Regulaion Impac on 1 Disribued Generaion Inegraion Yalin Huang and Lennar Söder Absrac This paper invesigaes he relaionship beween energy curailmen regulaion and invesmens in disribuion neworks in a deregulaed elecric power sysem wih disribued generaion. Curailmen due o he nework consrains is he ineres of he paper. The nework invesmen can be based on accommodaing he energy produced from disribued generaion wihou curailmen; however, a par of hese invesmens is only relevan for a few hours annually when he generaion is oo high compared o he demand. Therefore, energy curailmen is generally allowed. The curailed generaion owners are compensaed according o he curailmen regulaion. In his paper, he opimal curailmen and invesmen are obained by a proposed mehod under differen energy curailmen regulaions. The mehod is based on a nework invesmen opimizaion model including flucuaing load and generaion, invesmen iming, curailmen and regulaory impac. Case sudies of German and Swedish energy curailmen regulaions are performed. All he coss are obained by a nework invesmen model, which considers nework consrains, flucuaions of generaion and load and regulaory seings. The reference oal social cos is assumed o be he minimum of he combined grid invesmen and energy curailmen coss. Resuls show ha deep connecion charge scheme for DG sends ou srong locaional signals for he DG connecion and which reduces he oal social cos compared o shallow connecion charge scheme. Also he pre-agreed maximum curailmen level and high compensaion price can lead o high oal social cos. Index Terms Nework invesmen, disribued generaion, curailmen regulaion, curailmen compensaion. The auhors are wih he School of Elecrical Engineering, Royal Insiue of Technology KTH, Sockholm, SE-10044, Sweden. yalin.huang@ee.kh.se

2 2 1) Ses L N NOMENCLATURE All fixed and possible branches, e.g. L1,L2,L3...; All nodes in he nework, e.g. N1,N2,N3...; N S The subsaion node, subse of N; F Se of fixed branches, subse of L; R Se of reinforcemen branches, subse of L; K Se of all connecion branches for all DG unis, subse of L; AL Se of alernaives; N LD Se of load nodes, subse of N; N DG Se of DG nodes, subse of N; K dg 2) Parameers Se of connecion branches for connecion of dg in N DG, subse of K T δ Number of periods in he planning horizon; The annual discoun rae; δ cap, δ oper Presen value facors for he invesmen and operaion coss in planning period ; n sc V N min, V N max I L,AL max R L,AL, X L,AL A P N,sc, Q N,sc C R,AL C K,AL C N S,AL λ loss λ cur Number of scenarios; Minimum and maximum node volage limis; Maximum curren limis on each branch; Resisance and reacance of he alernaives of each branch; node-branch incidence marix; Acive and reacive power of demand or supply on each node in planning period scenario sc; Vecor of invesmen coss of he alernaives of he replacemen branches in R; connecion branches in K; subsaions in N s respecively; Price of power losses; Price of DG curailmen; P b,sc Probabiliy of scenario sc in in planning period ; V N re,,sc V N im,,sc γ 3) Binary variables Real par and imaginary par of volage in planning period scenario sc; Maximum curailmen percenage; E L,AL D R,AL, D Kdg,AL 4) Variables Vecor of exisence of alernaives of he replacemen branches and connecion branches in planning period ; Vecor of binary decision on invesmen of alernaives of he upgrading or insallaion in planning period ;

3 3 P cur,sc P loss,sc I L,AL re,,sc, I L,AL im,,sc P N DG,cur,sc P N DG,cm I N re,,sc, I N im,,sc Q N DG,cur,sc Q N DG,cm V N re,,sc, V N im,,sc C cap, C oper Toal curailed power in planning period scenario sc; Loss in he sysem in planning period scenario sc; Real par and imaginary par of curren flows in all alernaives for each branch in planning period scenario sc; Real par and imaginary par of curailed power from DG in planning period scenario sc; Real par and imaginary par of excessive curailed power from DG in planning period ; Real par and imaginary par of curren injecion from he load poin or DG connecion poin in planning period scenario sc; Real par and imaginary par of all nodal volages in planning period scenario sc; Capial expendiure (CAPEX) and operaional expendiure (OPEX) in planning period ; C loss, C cur Cos of losses and curailmen in planning period ; C oal Ne presen value (NPV) of he oal cos. I. INTRODUCTION The increasing amoun of disribued generaion (DG) of all sizes, ypes, and wih he unexpeced sies for he grid operaors is adding complexiy o disribuion grid. This is especially challenging for renewable energy due o heir high flucuaions in generaion. The grid invesmen can be based on accommodaing he energy produced from renewables wihou curailmen; however, a par of hese invesmens is only relevan for a few hours annually when he generaion is oo high compared o he demand. Therefore, energy curailmen in some siuaions is an opion o decrease he invesmen. However, curailed producers suffer economic losses. Furhermore, curailing renewable energy is inuiively viewed as a wase given he low marginal cos of i. Therefore, curailed producers may receive compensaion according o energy curailmen regulaion, which defines he compensaion rules in he erms of he price, he quaniy and he payer. Energy curailmen can be due o nework consrains, securiy consrains in he grid, low elecriciy price and sraegic bidding [Jacobsen and Schröder, 2012]. The curailmen of DG due o nework consrains is he focus of his paper. Generaion curailmen, including convenional generaion and renewable generaion, is a common pracice in ransmission levels [Lew e al., 2013]. Curailmen can also occur in he disribuion sysem due o he increasing DG peneraion level. If curailmen is allowed by

4 4 regulaion, i would affec he planning decision of DSOs and DG owners. On one hand, if he nework were dimensioned according o he exreme scenario, he invesmen cos could be high wihou curailmen and he nework would be redundan mos of he ime. On he oher hand, high permissible curailmen would lead o under-inves in he nework, less renewable energy and possibly more losses. A qualiaive analysis of differen nowadays energy curailmen regulaions in EU counries is presened in [Ropenus e al., 2009]. I explains he inerplay beween he curailmen coss and nework invesmen. Energy curailmen regulaion combined wih a new acive nework managemen is proposed in [Kane and Aul, 2014]. By acceping curailmen in combinaion wih acive conrol more renewable generaion capaciy can be accommodaed in a disribuion grid. Paper [Brandsä e al., 2011] argues ha he use of volunary curailmen agreemens is a good approach o efficienly inegrae large-scale renewables in Germany. Energy curailmen of inermien renewable energy sources in relaion o oher generaion unis are analysed in [Henrio, 2015]. The opimal level of curailmen is defined as he level when he oal generaion cos (including oher generaion sources) is minimized. The analyical model developed in [Henrio, 2015] considers he generaion availabiliy, generaor limis and compensaion schemes for renewables. The considered schemes are feed-in premium and marke-based remuneraion. The analysis focuses on shor-erm operaion opimaliy. Opimal curailmen level in he longerm perspecive is analysed in [Jacobsen and Schröder, 2012]. Pros and cons of differen compensaion rules, nowadays and newly proposed, for renewable curailmen are discussed wih saisics for some counries. I poins ou ha equilibrium beween nework invesmen and energy curailmen is reached when he marginal nework invesmen cos due o DG is equal o he marginal expeced compensaion for he curailmen over he lifeime of he nework invesmen. However, hese coss have no been quanified in he reviewed sudies. The challenge o quanify he equilibrium lies in esimaing he cos of reinforcing and expanding he grid o accommodae he energy and he value of he curailed energy under differen energy curailmen regulaions. This paper addresses he challenge from engineering and economic poins of view. The engineering perspecive ackles he nework consrains, he power flow and he amoun of energy curailmen in he grid. The economic perspecive conains he regulaion regarding compensaion for curailed energy and nework long-erm invesmen. Opimal soluions are obained from he

5 5 economic perspecive and a he same ime respec he engineering consrains. II. BACKGROUND Curailmen in his paper is defined as he difference beween he energy ha is poenially available from he generaion uni and he energy ha is acually produced. The reasons of curailmen can be caegorized ino four kinds: nework consrains, securiy consrains in he grid, excess generaion relaive o load and sraegic bidding [Jacobsen and Schröder, 2012]. The securiy consrains are relaed o he reserve capaciy cos and up- or down-regulaion. The excess generaion relaive o load is relaed o he capaciy marke and elecriciy marke. The sraegic bidding is relaed o marke power. In he disribuion level, he mos relevan reason ha causes curailmen is he nework consrains. Curailmen due o nework consrains can be inerpreed as underinvesmen of he nework or excess generaion. Grid invesmen for DG is only economically raional when he expeced curailmen exceeds a cerain level. To reach his level curailmen regulaion plays an imporan role. The amoun of curailmen is also affeced by he nework hosing capaciy. The nework hosing capaciy is defined as he capaciy ha can be inegraed ino he nework wihou reinforcemen. The available hosing capaciy is differen in differen poins of he grid. The DG owner can choose o connec o a poin which has higher available hosing capaciy or o a poin which requires reinforcemen. The decision is evaluaed by DG owner given he limiaion from he generaion iself, for example wind power generaion is dependen on he resources, he cos of he connecion; he remuneraion of he generaion and he compensaion of he curailed energy. The limiaion from he generaion iself is exogenous and is acknowledged. The laer hree are discussed below. The DG inegraion and curailmen also affec DSO s invesmen decisions. Aspecs of he cos of grid connecion invesmen and opimal curailmen are inroduced in deail below as well. A. Connecion charges There are in general hree ypes of connecion charges depending on how he cos of he nework connecion for DG is shared beween he DSO and he DG owners [Frias e al., 2009]. One is called shallow connecion charge, which means ha he DG owner only pays for he invesmen beween he grid connecion poin o he DG. One is called deep connecion charge,

6 6 which means ha he DG owner pays for he connecion line and he necessary reinforcemen in he upper sream nework. The hird one is called he shallowish charge, which means ha he DG owner pays he connecion line and par of he reinforcemen in he upper sream nework. The lower connecion charge is, he more likely he DG owner would need o curail he generaion. For example, if i is he shallow connecion charge applied in he sysem, he DG owner only need o inves enough capaciy for he connecion line wihou considering he hosing capaciy of he res of he nework. If he nework is no able o ransfer all he generaion, he DG owner would need o curail heir generaion. However, if i is he deep connecion charge applied, he DG owner pays for he necessary reinforcemen. The DG owner would evaluae differen connecion poins by he available hosing capaciy. Therefore, he deep connecion charge sends ou a srong locaional signal for he DG owners. The shallow connecion charge can also send ou locaional signals by adding a locaional compensaion [Jacobsen and Schröder, 2012]. The compensaion a he same ime can incenivise he DSO o inves in he grid o inegrae more renewable disribued generaion. Thus, by applying deep connecion charge he DG owner chooses a rade-off beween he grid connecion invesmen and he curailmen. Higher invesmen allows higher generaion inegraion in he life ime; on he oher hand, higher curailmen reduces invesmen. By applying shallow connecion charge, he DSO chooses a rade-off beween he grid reinforcemen invesmen and he curailmen wih compensaion. B. Remuneraion of DG producers In order o increase he renewable peneraion level in he grid, many counries implemened suppor mechanisms for renewable DG [Ropenus e al., 2011]. In general, he suppor mechanisms can be divided ino invesmen suppor and operaional suppor [Ropenus e al., 2011]. Invesmen suppor comprises capial grans and fiscal incenives or exempions. Operaional suppor comprises feed-in ariff (FiT), price premiums and green cerificaes. Under he feed-in ariff scheme, he producer receives a fixed price per kwh of energy fed ino he grid. This fixed price is se higher han average marke price and graned for a cerain period o reduce he risk in invesing renewables. Under he price premiums scheme, he producer is guaraneed a fixed premium addiion o he marke price. This scheme aims o suppor he renewables a he same ime o adjus he renewable generaion according o he demand. Under he green cerificae

7 7 scheme, he price of he energy is no regulaed bu he quaniy of he energy. The renewable energy fed ino he nework receives green cerificaes depending on he amoun of he energy (MWh). I is ofen implemened ogeher wih an obligaion of green quoa for he producers or he consumers. The renewable producers can sell heir cerificae o he ones ha do no have enough green energy. The income of he producer depends on he elecriciy energy price and he green cerificae rading. In he case of producion being curailed, he producer receives compensaion for curailmen which is equivalen o he los income in some cases. C. Compensaion schemes for curailmen Curailed energy is no compensaed all he ime. The energy can be curailed due o he low price, eiher low elecriciy marke price or green cerificae price or high price o down regulae. This kind of curailmen is generally referred o as volunary curailmen which is no compensaed. Examples of volunary shor-erm curailmen are shown in [Jacobsen and Schröder, 2012, Brandsä e al., 2011]. Compensaion is relevan when he curailmen is due o he grid limiaion. This kind of curailmen is generally referred o as involunarily curailmen [Jacobsen and Schröder, 2012]. The curailed energy can be valued by he los income or he avoided cos of grid reinforcemen. The los income in his case is he value by selling he curailed energy o he marke and/or los subsidy. Due o he grid limiaion, he producer should be compensaed for heir losses. The avoided cos of grid reinforcemen is he cos o reinforce he grid in order o inegrae he curailed energy. Due o he curailmen, he invesmen cos is reduced. The invesmen cos can be paid by he DSO or he DG owner depending on he connecion charge scheme. The compensaion should be so low ha he DG has he incenive o connec in he area where his is higher hosing capaciy. However, he compensaion should also be so high ha he DSO is moivaed o inves in he grid reinforcemen. In he case ha compensaion is se o cover he los income, for example he feed-in ariff for renewables or on elecriciy marke price, i is usually combined wih a pre-agreed maximum curailmen level beween he DSO and he DG owner [Jacobsen and Schröder, 2012]. If he curailmen is higher han he level, i is fully compensaed by a fixed subsidy. By seing differen pre-agreed maximum curailmen level, he DG owner has an incenive o locae he invesmen o he area wih higher hosing capaciy. Differen connecion poin has differen hosing capaciies, since he hosing capaciy is deermined by he nework consrains, he load profiles and

8 8 reinforcemen invesmen which is eiher paid by he DG owner or he DSO (depending on he connecion charge policy). The DSO also may se a higher maximum curailmen level o reduce he amoun of compensaion. If i is compensaed based on marke price wihou pre-agreed maximum curailmen level, his can resul in a faser connecion process when he elecriciy price is high. This compensaion is usually parial in order o send ou locaional incenives [Jacobsen and Schröder, 2012]. If he compensaion also serves he aim o increase renewables, i can be se based on generaion cos. The compensaion can be se high enough o incenivise invesmen in renewables. D. Cos of grid connecion invesmen In order o achieve efficien DG inegraion, opimal involunary curailmen levels in power disribuion sysems should be deermined ogeher wih opimal nework expansion in he long erm. In he ideal power sysem where he oal social cos is minimised, he nework expansion in he long erm should ake ino accoun he DG inegraion and he usage of he nework. If he nework is buil o saisfy he possible highes generaion from DG, he usage of he nework will be very low for he res of he ime. For example, for wind power, he oupu ha is above 80 % of i s capaciy level can be less han 20% of he ime in a year. A cerain maximum curailmen level can be allowed in order o increase he capaciy usage and decrease he invesmen of grid. This level can be se by a pre-defined quaniy or compensaion price. The pre-defined quaniy can be se from wo poins of view. One is se from he DSO s poin of view. The allowed maximum curailmen can be se based on he available hosing capaciy in he grid. In order o incenivise he grid company o speed up he reinforcemen, his level should be so low ha he DSOs need o reinforce heir neworks and inves enough capaciy for he connecion. The oher one is se from he DG poin of view. The allowed maximum curailmen can be se based on he producion densiy funcion o ensure a cerain amoun of inegraion level. For example, if he probabiliy of producion below 80 % of i s capaciy level is 90%, he maximum curailmen can be se as 20%. If he curailmen level is deermined by he compensaion price, hen he nework invesmen will increase unil he marginal nework invesmen is equal o he compensaion price.

9 9 E. Opimal curailmen The opimal curailmen level considered in he presen paper is deermined by he long-erm invesmen model. The focus of he opimal curailmen is on he involunary curailmen due o he grid limi. If he grid is under-invesed, he curailed energy is high and no opimal for furher expansion of he grid or he power qualiy deerioraes. If he grid is over-invesed, some grid capaciy will be only used in a few percenage ime in he life ime. On he one hand, if he curailmen is opimal wih regard o he nework invesmen cos and he los income of DG, changing he pricing scheme for generaion from DG ogeher wih he compensaion scheme can affec he opimal curailmen level. On he oher hand, one of he aims of remuneraion and compensaion schemes for DG is o reach an opimal curailmen as well as an opimal expansion of he nework. From he DG owner s perspecive, given a cerain connecion charge scheme, a cerain compensaion scheme and remuneraion scheme, he opimal curailmen due o he grid limi is when he marginal los income of expeced curailed energy over he lifeime is equal o he marginal cos of increasing he capaciy of he connecion line (or including increasing he capaciy of he res of he grid). From he DSO s perspecive, given a cerain compensaion scheme and connecion charge policy, he opimal expansion of he nework is when he marginal nework cos is equal o he marginal expeced compensaion for curailmen over he lifeime of he nework invesmen. This is under he condiion ha he DSO minimizes he cos and here is no oher moneary incenives for DG inegraion applied. If here is such incenive, he marginal nework cos should be he ne cos. III. METHOD In he presen paper, we propose a model o evaluae differen curailmen regulaions in he conex of disribuion sysems wih DG. The model considers he flucuaion of load and DG, he nework consrains and he ime of invesmen decisions. The flucuaion of load and DG is modelled by muli-scenarios for each year. The invesmen decisions are modelled o be made in he beginning of each year. The curailmen regulaion, DG connecion charge policy and DG inegraion incenives are also considered in he model. The DSO is assumed o be under a cerain incenive regulaion, which resuls ha he DSO minimizes he oal cos. The opimal curailmen level is deermined ogeher wih opimal nework long-erm expansion by using he proposed nework invesmen model.

10 10 The impac of differen energy curailmen regulaions is evaluaed by applying differen curailmen regulaions on he same disribuion grid wih disribued wind generaion and load. The impac on he DSO s decision, he DG curailmen level and he cos are presened. A. Proposed model The model is used o opimize he nework invesmen decisions considering DG connecion in he fuure. The invesmen decisions are upgrading ransformers, exising lines and building connecion lines for DG for a planning period. The connecion lines for DG can be he decision of he DSO or DG owners depending on he regulaion. These decisions should be feasible, which means ha he nework consrains are fulfilled during he whole planning period wih flucuaing load and DG, and economically opimal, which means ha he cos is he lowes among all he possible invesmen plans. The mahemaical formulaion are as following: The nework is divided ino hree differen pars: replacemen branches(r), fixed nework(f), addiional branches(k). Replacemen branches is he par of he nework ha would require reinforcemen in he exising nework. Fixed nework is he remaining par of he exising nework. Addiional branches is he par of new connecions in he nework. This classificaion is useful o define differen logical consrains in order o narrow down he searching area. 1) Objecive: The objecive is o minimize he oal cos in he nework for he long-erm planning period. The oal cos of he DSO considered in his paper conains he cos of building new connecion lines, replacing exising lines and he operaional coss of he all nework. The operaional cos includes he purchase of losses from he upsream grid and he curailmen compensaion if i is applicable. I is assumed ha he mainenance cos of a line is consan, herefore i is no included in he opimizaion.

11 11 C oal = C cap C oper C loss = T =1 [δ cap C cap = (C R,AL ) D R,AL + (C N S,AL ) D N S,AL = C loss n sc sc=1 + C cur + δ oper C oper ] (1a) + (C K,AL ) D K,AL (1b) (1c) P loss,sc λ loss P b,sc (1d) N DG C cur = P N DG,cm λ cur (1e) 2) Consrains: Physical, logical and economical consrains all considered. For each scenario (sc) in any year () he power flow and operaion consrains (3)-(5)and (7) are he same. Therefore he subscripion and sc in hese consrains are ignored in he presenaion for he readabiliy. However, he logical consrains (6) and he curailmen consrains (8) (9) depend on he sage or scenarios, so he subscripion or sc is presened. The mehod o linearise he consrains (3)-(5) is based on mehods proposed in [O Neill e al., 2012]. i Radial configuraion A radial feeder wih N +1 nodes (N nodes for he nework plus one node for he subsaion) always leads o a ree having a mos N branches [Haffner e al., 2008]. nr(f ) represens he number of fixed branches. ii Power balance j,al D R,AL j + k,al D K,AL k + nr(f ) N (2) The power balance of each node is ha he power flow ino a node is equal o he power flow ou of a node. iii Kirchhoff s circui laws (V N re + j V N im)(i N re j I N im) = (P N P N,cur ) + j (Q N Q N,cur ) The balance of he sysem is guaraneed by KCL and KVL. KCL implies ha he sum of currens flowing ino a node should be equal o he sum of currens flowing ou of i. KVL (3)

12 12 implies ha he sum of he elecrical volage differences around any closed nework is zero. Equaion (4a) applies o boh he real par and imaginary par of currens. I should be noed ha he KVL only applies o he lines ha exis in he nework. The incidence marix A shows he relaionship beween he node wih all branches, so he case in which no new line is buil beween wo nodes should be excluded from Equaion (4b) and Equaion (4c). Therefore, he equaion is muliplied by he corresponding binary variable which represen ha he line exiss. AI L = I s N (A V N re + V 0 )E L,AL (RI L re XI X im)e L,AL = 0 (A V N im)e L,AL (RI L im + XI L re)e L,AL = 0 (4a) (4b) (4c) iv The capaciy limis of subsaions, lines and volage limis The volage a each node should be wihin he he minimum and maximum limi. Moreover, he curren flowing hrough he subsaion is limied by he capaciy of he subsaion as well. The capaciy limi of he subsaion is represened by he curren flowing hrough since he volage is assumed o be 1p.u. a he subsaion. V min V N V max I S I S max (5a) (5b) I L I max E L,AL (5c) v The logical consrains The model also akes logical consrains ino accoun and predefines DG connecion alernaives o reduce he search space. Equaion (6a) shows ha maximum one invesmen on each branch (and subsaion) is permied in he planning horizon. Equaion (6b) shows ha he alernaives for replacemen or connecion branches (and subsaion) exiss only afer he corresponding invesmen has been done. Equaion (6c) shows ha only one alernaive of replacemen branches exiss in a period. Equaion (6d) shows ha a mos one branch among he connecion branches is buil o connec DG in one period. Equaion (6e) shows ha all

13 13 DG should be conneced in he end of he planning period. AL,T K dg,al K dg,al,t AL D L,AL 1 (6a) E L,AL E L,AL 1 + D L,AL (6b) E R,AL = 1 (6c) E Kdg,AL 1 (6d) E Kdg,AL 1 (6e) where K dg represens all he roues of connecion one DG unis. vi The curailmen consrains The curailmen should no be more han he producion in each scenario: P N DG,cur P N DG Q N DG,cur Q N DG (7a) (7b) The curailed energy in he sysem is assumed o be eiher a) associaed wih a cos; or b) discouraged by a cerain quoa. The cos of curailmen is he compensaion for curailmen as discussed in Secion II-C. In (1e) cos of curailmen (C cur ) is based on he curailmen ha is above he pre-agreed maximum curailmen level. This excess par is modelled by posiive variables P N DG,cm, Q N DG,cm as shown in (8). (8) is valid for each DG uni. The model can however be readily adaped o pu a hreshold on curailmen by removing he cos of curailmen (C cur ) in (1e) from he objecive funcion and adding consrain (9) insead. n sc P N DG,cur,sc sc=1 n sc Q N DG,cur,sc sc=1 P b sc P N DG,cm γ 1 n sc sc=1 n sc P b sc Q N DG,cm γ 2 sc=1 P N DG,sc P b sc (8a) Q N DG,sc P b sc (8b) n sc P N DG,cur,sc P b sc γ 1 sc=1 n sc Q N DG,cur sc=1,sc P b sc γ 2 n sc sc=1 n sc sc=1 P N DG,sc P b sc (9a) Q N DG,sc P b sc (9b) where γ is a parameer for he highes permissible curailmen level as a share of available DG.

14 14 vii The connecion charge scheme The connecion charge schemes considered in he model are a) deep connecion charge and b) shallow connecion charge. In he deep connecion charge scheme DG owners choose a connecion plan which has he leas price offered by DSOs. The plan is assumed o be decided by he oal cos of DSOs o inegrae i. Therefore, in his case he lines o connec DG are deermined by he leas cos for DSOs, which is as he model presened above. The model can however be readily adaped o consider shallow connecion charge scheme by defining decision variable which represens he connecion lines (D K,AL ) as parameers. This enables he model o minimize reinforcemen cos on he nework given he connecion lines ha DG owners propose. IV. CASE STUDY To apply he proposed model considering differen regulaory cases, a radial nework where DG plans have asked for connecion is creaed. The sysem deails (node daa and line daa) can be found in [Huang, 2014]. The nework is a disribuion sysem wih 21 load nodes displayed in Fig. 1. The nework operaes a 24.9 kv. Two wind farms are in he pipeline o be conneced. For each wind farm, hree possible connecion roues are predefined. In he figure, he square node represens he feeding subsaion, he wind urbines represen wind farms, and he circles are he load poins and wind farm locaions (N22 and N23). The branches beween nodes represen he elecrical connecions beween nodes. Coninuous lines denoe he exising nework and dashed lines are candidae roues for new connecions. The base values for he whole nework are 2.5 MVA and 24.9 kv. The volages are limied beween [ ] kv (±5 %). Invesmen for one planning period of four years is considered in he case sudy. A DG owner applies for a connecion o N22 a he year 2 and anoher DG owner applies for a connecion o N23 a year 3. The wo DG unis are assumed o mainain a power facor 1 and 0.95 respecively, and hey ac as negaive load. All he values are in per uni (p.u.) and he coss of lines are discouned o he beginning of he planning horizon. The insalled capaciy of he wo DG unis accouns for 47% of he oal load. In his grid, all lines have wo alernaives for upgrade, AL1 is he iniial line and AL2 AL3 are he alernaives o upgrade, and here are hree pahs o connec each new wind farm ino

15 15 he nework. L8, L13, and L21 are for N22. L9, L15, and L24 are for N23. Each new pah has hree alernaives. The decisions of alernaives (oal hree) of each line (oal 26) are made in he beginning of each year, herefore, he opimizaion problem has = 312 binary variables for invesmen and anoher 312 binaries o represen he exisence of each line in each year. L14 L16 L L5 L15 23 L L23 L25 L9 L1 L2 L L6 L10 L11 21 L3 L8 L7 6 L18 L19 L L12 7 L20 L13 22 L L26 Fig. 1. Diagram of he 23-node nework The applicaion looks ino he impac of curailmen regulaion on DSO s invesmen decisions ogeher wih connecion charge schemes and renewable energy suppor schemes. Case I is based on he Germany energy regulaion. The maximum curailmen level is regulaed o hree percen of he annual energy ha can be produced and shallow connecion charge is applied. Full compensaion o he generaor is sill under discussion in Germany [for Economic Affairs and Energy, 2014]. Differen compensaion prices are applied o show he impac on curailmen and invesmen. Case II is based on he Swedish energy regulaion. Deep connecion charge for DG is applied, and no specified maximum curailmen level from he regulaion. However, he DG owner and he DSO can have an agreemen on he curailmen level before he connecion. The curailed energy is compensaed. For his case, differen compensaion prices are also applied o show he impac.

16 16 A. Case I In his case we model he regulaion for renewable DG in Germany. Grid operaors mus connec renewable energy plans o heir grid and remunerae generaors for all he energy hey feed ino he grid according o he fixed FiT sysem. The FiT sysem applies for 20 years and for he year of commissioning. Furhermore, a marke premium sysem for renewable energy sources is saed in he Renewable Energy Sources Ac [for Economic Affairs and Energy, 2014]. Since he DG owners only pay for he invesmen of connecion lines (shallow connecion charge), he connecion line is decided from he DG owners ineres no considering he reinforcemen of he res of he grid. In his model, we assume ha L21.AL2.T2 (AL 2 of he line L21 is buil a year 2) and L9.AL2.T3 (AL 2 of he line L9 is buil a year 3) are chosen. The cos is 3.75 Me and 3.75 Me respecively. The producion is paid by FiT and is compensaed by he same price if applicable. Two annual maximum levels of curailmen, 3% and 10% of he annual producion, are analysed. The compensaion price is se as he cos for losses, which is 0.09e /kwh. Given hese consrains, he DSO invess he grid wih he leas cos opion. TABLE I RESULTS FOR CASE I Case I Maximum curailmen <3% Maximum curailmen <10% Wih Compens. Wihou Compens. Wih Compens. Wihou Compens. Toal cos Capex Connecion cos Compensaion(N22,N23) 0,0-0,0 - Curailmen(N22,N23) 2.9%, 0.4% 2.9%, 0.4% 8.6%,0 8.6%,0 In able I he resuls for differen maximum curailmen level are presened. For each maximum curailmen level, wo compensaion rules are applied. One is o compensae he par which is above he maximum level, he oher one is ha here is no compensaion and he maximum level should be fulfilled. The presened resuls include he ne presen value (NPV) of oal cos, capial expendiure (capex), connecion cos for he DG, he compensaion paid o he DG and he average curailmen during he planning period for each DG. Resuls show ha he oal cos is lower when he maximum curailmen level is higher. Furhermore, he oal cos does

17 17 no change by wheher he curailmen is compensaed or no. This is because he compensaion price is so high ha i is no worh i o curailmen more. The opimal curailmen levels are differen when he pre-agreed maximum curailmen levels are differen. The opimal curailmen level is higher when he pre-agreed maximum curailmen level is higher. Furhermore, he opimal oal cos of he DSO is sensiive o he compensaion price as shown in Table II. In his able, differen compensaion prices are applied o he case where he preagreed maximum curailmen level is 3% and compensaion is only applies o he par ha is above his level. By seing he compensaion price, he opimal curailmen level is deermined. Lowering down he he curailmen compensaion price, he curailmen level may increase. I does no always increase because ha he nework expansion opimisaion by naure is an ineger problem. The cos increases wih he DG inegraion in a sep-wise manner. Moreover, i does no necessarily increase because he higher inegraion level of DG can reduce he losses and delay some of he reinforcemen. In his case, when here is no DG, he opimal oal cos is M e. TABLE II DIFFERENT COMPENSATION PRICE FOR MAXIMUM CURTAILMENT <3% IN CASE I Case I Compens. = El. price Compens. = 0.5*El. price Compens. = 0.25 El. price Toal cos Capex Compensaion(N22,N23) 0,0 0.38,0 0.19,0 Curailmen(N22,N23) 2.9%, 0.4% 10.7%,3% 10.7%,3% B. Case II In Sweden, he main incenive for he use of renewable energy sources is a quoa sysem in erms of quoa obligaions and a cerificae rading sysem. The Elecriciy Cerificaes Ac obliges energy suppliers o prove ha a cerain quoa of he elecriciy supplied by hem was generaed from renewable energy sources. Energy suppliers shall provide his evidence by presening cerificaes allocaed o he producers of elecriciy from renewable sources. Furhermore, elecriciy generaed from wind energy is eligible for ax privileges as auhorised by he Energy Tax Ac [res, 2015].

18 18 TABLE III RESULTS FOR CASE II Case I Compens. = El price Compens. = 0.5*El price Compens. = 0.25 El price Wihou DG Toal cos Capex Curailmen(N22,N23) 6.3%,3.6% 6.3%,3.6% 6.3%,3.6% - Compensaion Connecion lines L21,AL2,T2 L21,AL2,T2 L21,AL2,T2 L15,AL2,T3 L15,AL2,T3 L15,AL2,T3 - Connecion cos Loss 3.7% 3.7% 3.7% 3.8% Since he DG owners pay he deep connecion charge, he cos of reinforcemen due o DG connecion is covered by he DG owners. From he DG owners s perspecive, he connecion decision is chosen based on max (E o DG Ecur DG ) λ el + E cur DG λ cm C oal. λ el is he price for selling he elecriciy and λ cm is he compensaion received due o curailmen. Given he λ el, λ cm are exernal, he decision will be based on he les nework connecion cos opion. Differen compensaion price can impac on he opimal curailmen level and connecion decisions as shown in Table III. In Table III NPV of he oal cos for he DSO, capex including he connecion lines, he opimal curailmen level, he compensaion for he curailmen, he connecion lines, NPV of he cos for connecion lines and losses are presened for differen compensaion prices. Wih he decrease of he compensaion price, he curailmen level does no increase. This is parly because ha he losses may increase if he curailmen level is oo high; parly because ha he DG delays he reinforcemen of he nework, so he invesmen is lower when here is less curailmen. DG delays he reinforcemen of he nework can be furher examined by assuming no DG inegraion in he same nework. In he case of no DG inegraion he reinforcemen cos is much higher han he case of DG inegraion. Therefore, he impac of he compensaion price on he curailmen level is lile in his case sudy. The higher he compensaion price jus leads o he higher he oal cos of he DSO. Comparing he connecion lines and capex in Case I and Case II, he cos is much lower in Case II and he decisions on connecion lines are differen. This confirms ha he deep connecion

19 19 charge gives locaional incenives for he DG connecion. The DG connecs a he poins where causes less reinforcemen in he nework. However, he opimal curailmen level in Case II is higher han 3%. I means he oal cos would increase if he maximum curailmen level is se o 3%. Therefore, if he pre-agreed maximum curailmen level is se lower han he opimal curailmen level, i resuls higher cos for he DSO. V. CONCLUSION This paper concludes ha he energy curailmen regulaion has o srike a balance beween he grid invesmen and he curailed energy compensaion. In order o evaluae he balance, he cos analysis from he grid operaor s and he generaor s perspecive is necessary. Using he proposed mehod, he opimal nework invesmen and energy curailmen is obained under differen DG regulaions. Furhermore, he DG or renewable energy suppor regulaions should be consisen wih he curailmen regulaion o send ou incenives for DG and grid operaors o minimize he oal social cos. The resuls show ha he deep connecion charge scheme sends ou locaional incenives for he DG connecion and herefore decreases he oal social cos. Las bu no he leas, he compensaion rules for curailmen has big impac on he opimal curailmen level. In he case sudy i is shown ha high pre-agreed maximum curailmen level or high compensaion price does no lead o lower oal social cos. In he presen paper, he opimal invesmen and curailmen is obained under a given regulaion. However, wheher he regulaion is opimal or no requires furher sudies. Moreover, shor-erm benefis from energy curailmen, for example from up-regulaion and down-regulaion prices, can be added in he fuure sudies. REFERENCES [res, 2015] (2015). Legal sources on renewable energy. hp:// Accessed: [Brandsä e al., 2011] Brandsä, C., Brunekreef, G., and Jahnke, K. (2011). How o deal wih negaive power price spikes?flexible volunary curailmen agreemens for large-scale inegraion of wind. Energy Policy, 39(6): [for Economic Affairs and Energy, 2014] for Economic Affairs, F. M. and Energy (2014). An elecriciy marke for germany s energy ransiion. [Frias e al., 2009] Frias, P., Gomez, T., Cossen, R., and Rivier, J. (2009). Improvemens in curren European nework regulaion o faciliae he inegraion of disribued generaion. Inernaional Journal of Elecrical Power and Energy Sysems, 31(9):

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