The Optimal Division of the Energy Market into Zones: Comparison of Two Methodologies under Variable Wind Conditions

Transcription

1 The Optmal Dvson of the Energy Market nto Zones: Comparson of Two Methodologes under Varable Wnd Condtons Karol Wawrzynak, Mchał Kłos, Grzegorz Oryńczak, Marcn Jakubek Natonal Centre for Nuclear Research, Śwerk Computng Centre Otwock-Śwerk, Poland Summary The energy market of Europe s under an ntensve process of transformaton. The man drvers for change are ntegraton of natonal markets and growng use of renewable generaton. Currently, the most popular market structures are unform, nodal, and zonal prcng. In unform prcng, there s a sngle prce of energy set on a natonal market for each hour of a day. Ths market structure s stll used n many countres manly due to hstorcal reasons. In spte of ts apparent smplcty, such an approach has serous dsadvantages manly due to the exstence of congestons [1], snce equlbrum set on the market does not take nto account safety requrements of the grd. Introducng other forms of market helps to elmnate the unform market lmtatons. In nodal prcng, each locaton of the grd has ts own prce of energy, representng the locatonal value of energy,.e. a cost of supplyng extra 1 MW of energy to ths locaton (node). Ths market structure solves congeston, snce the psychcal structure of the grd and ts transmsson lmts are taken nto account when the market equlbrum s searched for. However, such market arrangement s complcated and nsuffcently transparent for market partcpants. Zonal market, whch can be thought of as a compromse of smplcty of unform structure and accuracy of nodal one, ntroduces dfferentaton of prces between regons of dfferent costs of supplyng energy, but t mantans the transparency whch the nodal market lacks. Stll, there s no consensus n the lterature wth respect to methodology of dentfcaton of zones number and ther borders. In the proposed research we compare two competng methodologes, () consensus clusterng of Locatonal Margnal Prces and () congeston contrbuton dentfcaton [2], under the crteron of socal welfare maxmzaton, and takng nto account varable wnd generaton. Below we dscuss the two methodologes and the welfare crteron. In our prevous work [1] we presented n more detal the methodology and results already obtaned that are related to clusterng of LMP. The research related to second methodology s n ongong phase. Hence, the methodology s presented here but the complete results wll be provded shortly. () Consensus clusterng of Locatonal Margnal Prces The frst methodology s based on nodal prces, called also Locatonal Margnal Prces (LMP) [3],[4]. Nodal prcng s a method of determnng prces n all locatons of the transmsson grd. The prce at each locaton (node) represents the locatonal value of energy.e. a cost of supplyng extra 1 MW of energy to

2 node. It conssts of the cost of energy used at a node and the cost of delverng t there, whch depends on losses and congeston. Snce each occurrence of congeston leads to graduate ncrease of delvery cost [5], aggregaton (clusterng) of smlar nodal prces should result n a relable soluton to the problem of dvson of the market nto zones. However, n the lterature concernng dvson nto zones [3],[4] usually stable levels of generaton are assumed, whch remans n contradcton wth the ncreasng amount of renewable generaton for whch, as yet, wnd farms, characterzed by hghly varable power output, consttute the man source. In our prevous work [1] we found that the relatve nstablty n the amount of power njected nto the system by wnd farms sgnfcantly nfluences the energy prces even f the rate of wnd generaton to total generaton s relatvely small. Hence, we extend the clusterng of LMP method by takng nto account varable weather condtons. In essence, we conduct calculaton and clusterng of LMP for a range of dfferent wnd scenaros, and we add a thrd, aggregatng step to the method, namely, the fnal consensus clusterng, whch jons sngle clusterngs conducted for each of weather scenaros. The above procedure can be summarzed n step-wse fashon as follows: 1. On a sample of hstorcal wnd data or Monte Carlo smulatons of wnd strength, the output of wnd farms present n the energy network s estmated. 2. Each scenaro of wnd output consttutes an nput nto Drect Current Optmal Power Flow (OPF DC) [6] algorthm, to determne feasble generaton n the network and obtan set of nodal prces. In case when congeston arses, the nodal prces wll vary for ths scenaro For each scenaro, nodal prces are clustered usng a herarchcal method based on Ward s mnmal varance crteron [7], modfed to acknowledge the exstence of connecton (branch) between nodes of the clusters. 4. Snce the assgnment of nodes nto zones can vary from one scenaro to another, to derve an aggregated dvson a consensus clusterng method s used. Specfcally, we Cluster-based Smlarty Parttonng Algorthm [8] to obtan a tentatve dvson nto k 1,..., K clusters. The dvsons nto k 1,..., K clusters are then to be evaluated by a welfare-maxmzng crteron descrbed n secton (). () Congeston contrbuton dentfcaton The congeston contrbuton dentfcaton s a relatvely new approach to zonal dvson [2]. Ths method for defnng a border lne that separates zones s based on the analyss of Power Transfer Dstrbuton Factors. The dstrbuton factors reflect the nfluence of unt nodal njectons on power flow along the transmsson lnes. Thus, groupng the nodes characterzed by smlar factors nto one zone defnes a regon of desrably smlar senstvty to congeston. As the necessty for zonal dvson s the congeston 1 Neglectng the losses (a fundament of DC approxmaton) allows us to concentrate on the varaton n nodal prces whch arses only as a result of congeston cost.

3 lmtng power transfer on a transmsson lne, we focus on PTDF elements correspondng only to the connectons whch are lkely to be congested. The specfc reasonng s bult on a premse that a convenent dvson s one that mnmzes the chance of ntra-zonal congestons. Hence, borders of the zones are expected to cross the often congested lnes. PTDF elements are helpful n decdng whch nodal njecton ncreases, and whch decreases an observed congeston. The most problematc task s to concern an nconsstency resultng from arbtrary choce of a reference node whle calculatng PTDF matrx for the system. An easy way of dealng wth broken symmetry of load that affects dstrbuton factors s to use a specal type of PTDF matrx [2]. 2 Let us assume that M N H s a PTDF matrx of M-lne/N-bus system bult under assumpton that s the reference node. Decson whch node we are expected to use as the reference one s crucal when the analyss of separate matrces elements s concerned, but meanngless as long as we use H matrx only for calculatng power flows. In fact all H, {1,..., N} consttute an equvalence class wth respect to left-handed multplcaton by vectors p ( p1,..., p ) T N such that In other words, for N p n 0. (1) n1 1 2 N p H p H p H p, (2) the product remans unaffected f we apply any of H operators to a partcular vector of nodal njectons/wthdraws whch obvously satsfes the property (1). Let us prove that addng the same element to selected row of matrx H does not nfluence the lefthand sde: N N N N l ( ln l ) n ln n l n ln n n1 n1 n1 n1. (3) p H p H p p H p In the consequence, we may choose the coordnates of vector and create new PTDF operator, as the sum of PTDF matrx and a dyadc product of and N-dmensonal vector. In order to choose the proper values, we shall dscuss the role of dstrbuton factors sgns n the context of choosng a partcular reference node. 2 In [2] constructon of ths specal-form PTDF matrx was gven wthout a formal proof, whch we present here.

4 Fgure 1 Comparson of dstrbuton factors. Ther values reflect the poston of reference node. Let us consder an electrc grd consstng of two nterconnected areas [Fg 1]. The congested lne l = (n, m) defnes a row of matrx, elements of whch are pcked as objects of the followng analyss. If dstrbuton factors assgned to nodes n and m are 0.7 and -0.2, respectvely, we assume that the reference node belongs to area B. Changng zonal ascrpton of results n the need for readjustng all dstrbuton factors. Meanwhle, there s no consstent method for selectng the rght reference node, as n most cases the topology and physcal parameters of the grd do not gve an opportunty to pck a node that reflects an equvalent nfluence of power njectons at nodes n and m to power flow on the congested lne. In fact, we do not need to decde on a partcular node. The soluton s to shft all the elements of the row ( ) by the negatve average of the factors reflectng njectons n nodes n and m. It means that we should consder analyzng the l-th row of new operator S 1 k 1,, N, l n, m: Slk Hlk Hlm Hln. (4) 2 Elements of S are no longer denoted by, as the dfferental does not depend of the choce of reference bus for H. New dstrbuton factors reflect an magnary choce of the reference node, whch can be treated as stuated at electrcally equvalent dstance form nodes n and m. That leads to desred equalty of absolute values of PTDFs assgned to both ends of the congested lne. Dealng wth multple congestons, the analyss of more than one row of S s a necessty. In order to gve the equaton (4) a matrx form, we need to ntroduce some notaton. If s a matrx of absolute values of lne-node ncdence matrx denotng a system topology and dagv s an operator formng a vector from a dagonal lne of a gven matrx, defned by [dagv( M )] k M kk, the generc form of PTDF derved from any regular operator, may be expressed by: 1 T dagv T S H H A u. (5) 2

5 Then, the nodes can be easly categorzed nto two zones wth respect to a congested lne l by smply checkng the sgn of coeffcents for. When takng next congested lne, say l, to conduct the dvson, we can restran the problem only to a zone whch contans l as an ntra-zone lnk. The procedure of dvson nto zones usng congeston contrbuton dentfcaton can be summarzed n step-wse fashon as follows: 1. The generalzed PTDF matrx s computed for the network model. 2. On a sample of hstorcal wnd data or Monte Carlo smulatons of wnd strength, the output of wnd farms present n the energy network s estmated. 3. Each scenaro of wnd output consttutes an nput nto OPF DC algorthm, to determne the lnes lkely to be congested, that s, for whch the transmsson lmts were a bndng condtons n the optmzaton process. 4. Startng wth the most frequently congested lne, the network s dvded wth respect to nodes congeston contrbutons, and each of the dvson s tested accordng to the welfare crteron to evaluate ts necessty. If the dvson brngs betterment, t s appled and further congestons are treated as ntra-zonal. If not, ths lne congeston s left for the balancng market to overcome. In essence, we provde a smple proof of property referrng to matrces S and extend the dvson methodology descrbed n [2] to take nto account lnes congested n dfferent wnd generaton scenaros and to acknowledge the welfare effects of the dvson. () Welfare crteron As the welfare crteron we use the mnmzaton of the overall cost of supplyng energy. That s, a specfc dvson of a sngle market nto k zones s consdered as welfare-enhancng f the aggregated cost of supplyng energy s lower after the dvson. The cost of supplyng energy on a sngle market conssts of: value of the energy traded on the unform market, derved from the supply-demand equlbrum cost of readjustments conducted on balancng market (n order to correct for congeston and energy losses) The cost of supplyng energy on a zonal market conssts of: value of energy sold at each of k zonal markets, derved from the supply-demand equlbrum takng nto account nter-zonal tradng (defned by Market Couplng algorthm [9]) congeston rent on trades between zones cost of adjustments conducted on k balancng market (n order to correct for congeston and energy losses) In order to estmate the costs of balancng market, we frst run the OPF DC algorthm on the network model wth transmsson lmts set to nfnty, n order to fnd an unconstraned market equlbrum, wth

6 unform prce equal to the hghest margnal cost of runnng generator. Next, we run Alternatng Current Optmal Power Flow (OPF AC) wth transmsson lmts, and we compute the costs of adjustng generaton wth respect to unconstraned OPF DC soluton. The nter-zonal tradng ( market couplng ) and ntra-zone balancng markets are smulated by: 1. Runnng OPF DC algorthm wth constrants only on nter-zonal connectons. Zonal prces are determned as hghest margnal cost of runnng generator n a zone. 2. Runnng separately OPF AC wth constrants for sub-network representng each zone. The nflows/outflows on the zone border nodes are adjusted to ncorporate nter-zone flows derved by OPF DC above. The costs of adjustng generaton wth respect to unconstraned OPF DC soluton s taken as balancng market charges. Lastly, the dvson wth hghest welfare/lowest cost s treated as the most desrable (recommended) dvson nto zones. References [1] K.Wawrzynak, G.Oryńczak, M. Kłos, A. Goska, M. Jakubek, Dvson of the Energy Market nto Zones n Varable Weather Condtons usng Locatonal Margnal Prces, submtted to IECON13. [2] C.Q. Kang et al., Zonal margnal prcng approach based on sequental network partton and congeston contrbuton dentfcaton, Electrcal Power and Energy Systems, vol. 51, pp , [3] B. Burstedde, "From Nodal to Zonal Prcng A Bottom-Up Approach to the Second-Best," unpublshed, EWI Workng Paper, Dec [4] J. Balek and M. Imran, "Effectveness of zonal congeston management n the European electrcty market," n IEEE 2nd Internatonal Power and Energy Conference, PECon, [5] S. Stoft, "Transmsson prcng zones: smple or complex?" The Electrcty Journal, pp , [6] R. Zmmerman, C. Murllo-Sanchez, and R. Thomas, MATPOWER: Steady-State Operatons, Plannng and Analyss Tools for Power Systems Research and Educaton, IEEE Trans. Power Systems, vol. 26, no. 1, pp , [7] J. Ward and H. Joe, "Herarchcal groupng to optmze an objectve functon," Journal of the Amercan Statstcal Assocaton, vol. 58, no. 301, pp , [8] A. Gons, H. Mannla, and P. Tsaparas, Clusterng aggregaton," n ICDE, pp , [9] R. Djabal, J. Hoeksema, Y. Langer, COSMOS descrpton: CWE Market Couplng algorthm, Belgan Power Exchange (BELPEX) documentaton.