Real Power Allocation in Open Access Environment

Transcription

1 Real Power Allocaton n Open Access Envronment Debdeep Saha Grjananda Chowdhury Insttute of Management and Technology Dr. Sarmla Patra Assam Engneerng College Abstract Tracng the flow of electrcty becomes an mportant ssue under transmsson open access. In practce, power flow follows the physcal laws of electrcty and therefore t s not straght forward to map out how the partcpants make use of the system. Ths artcle focuses on presentng an analyss of the performance of major power tracng methods based on proportonal sharng prncple namely the Graph Theory. The power transmsson costs, whch are charged to the market partcpants, are a central ssue of the new deregulated electrcty markets. The artcle mplements a methodology for transmsson cost allocaton based on the prncple of proportonal sharng states that any power flow leavng a bus s made up of the flows enterng that bus n a proportonal manner, thus satsfyng Krchhoff frst law. To carry out the computer tests, IEEE 6 and 30 bus systems are taken to allocate real power as a part of transmsson loss allocaton. It also allows the assessment of contrbutons of ndvdual generators (or load) to ndvdual lne flows. Index Terms Transmsson loss allocaton, Graph theory, deregulaton, monopolstc. I. INTRODUCTION Transmsson loss allocaton s the process of assgnng to each ndvdual generaton and load the responsblty of payng for a part of the system transmsson losses. Although no power system varable s affected by ths process, the revenue and payment reconclaton are dependent on the crteron adopted for ths purpose Transmsson loss allocaton s not an easy task. Even n a smple two-node system wth one generator supplyng a sngle load, loss allocaton between the generator and the load has to be agreed upon as there s no physcal measurement or mathematcal method that determnes the loss shares n a unque manner. In a real system, matters obtan more complcated because of two facts. The frst s that the determnaton of the lne flows caused by each load through each transmsson lne has a good degree of arbtrarness. The second s that the transmsson lne loss s a nonlnear functon of the lne flow, and hence cannot be separated between partal flows through the same lne n a unque convncng way [3]. Contnung trend towards deregulaton and unbundlng of transmsson servces has resulted n the need to assess what the mpact of a partcular generator or load s on the power system. A new method of tracng the flow of electrcty n meshed electrcal networks s proposed whch may be appled to both real and reactve power flows. The method allows assessment of how much of the real and reactve power output from a partcular staton goes to a partcular load. It also allows the assessment of contrbutons of ndvdual generators (or load) to ndvdual lne flows [6]. In a compettve envronment, usage allocaton questons must be answered clearly and unequvocally. To help answer such questons, ths artcle practces a proposed method for determnng how much of the actve and reactve power output of each generator s contrbuted by each load. Ths method takes as ts startng pont a solved power flow soluton. Havng determned where the power goes, one can compute how much power flows from a gven generator to each load or from all generators to a partcular load. It s also possble to determne how many MWs each load or generator contrbutes to the actve flow n a branch. These physcal contrbutons form a bass upon whch the cost of buldng and mantanng each component of the network could be allocated among ts users Computaton of the contrbutons defned and used n s possble only f the quanttes beng allocated are lnearly addtve. Ths mples that actve and reactve powers should be consdered separately. Power flows of generators and loads are traced to determne the transmsson system usage by each generator and load. Then, transmsson losses caused by each generator or load are determned. Based on power flow tracng methodology, topologcal generaton and load dstrbuton factors are determned n through matrx nverson, wth addtonal nodes added to represent lne losses. Vol. 5 Issue 3 May ISSN: X

2 II. POWER TRACING The monopolstc, vertcally ntegrated power system has now become market drven. In ths new operatng envronment, determnng the mpact of ndvdual market players on the system has become very sgnfcant. To ensure far competton among the players, all fnancal transactons should be transparent, and none of the costs should be allowed to be subsdzed or cross-subsdzed. In such a structure a transmsson system s beng used by multple generaton and load enttes that do not own the transmsson system. In vew of market operaton t becomes more mportant to know the role of ndvdual generators and loads to transmsson wres and power transfer between ndvdual generators to loads. Transparency can be accomplshed only when the power-flow path of a generator and ts flow extent are known. Ths nformaton, whch can be determned by power-flow tracng, not only enables the ndependent system operators (ISOs) to pay proper revenue to the generators, but t also proves to be a very mportant tool for dfferent analytcal purposes [8]. Usage allocaton refers to power contrbuton of each generator to each load. The advantage of knowng the usage allocaton ncludes loss allocaton assocated to each path, cost assgnment to transmsson lne prcng, congeston management, ancllary servces and decson on schedulng of generators. To acheve the above mentoned advantages several schemes have been developed to solve the allocaton problem. Methods based on dc load flow and senstvty analyss cannot consder accurately, the reactve power transfer allocaton and system non lnearty. The blateral transacton approach ams at assgnng the transmsson cost of any specfc transacton between two nodes. Research has been carred out by unbundlng the flow of electrcty based on ndvdual transactons takng place whch s theoretcally very dffcult. Other commonly used approaches nclude applcaton of superposton theorem and power tracng methods. The proportonal sharng prncple bascally amounts to assumng that the network node s a perfect mxer of ncomng flows so that t s mpossble to tell whch partcular nflowng electron goes nto whch partcular outgong lne. Ths seems to agree wth common sense and wth the generally accepted vew that electrcty s ndstngushable. The concept of power flow tracng between generators and transmsson has been dscussed for determnng wheelng rates of new users under deregulated envronments [6]. III. FUNDAMENTALS OF LOAD FLOW TRACING In order to smplfy the problem, we frst make the followng basc assumptons: a) An ac load flow soluton s avalable from on-lne state estmaton or off-lne system analyss. The studed system has fnte number of buses. It s operated properly and there s no loop flow n the system. b) Real power and reactve power requred by Transmsson lne resstance, reactance and chargng capactance have been moved to the lne termnal buses (see Secton III for detals) and modelled as equvalent loads accordng to ac load flow soluton. Therefore the lne actve and reactve power flows keep constant along the lne, each edge has a defnte drecton and the network s lossless. c) A generator has the prorty to provde power to the load on the same bus. The remanng power wll enter the network to supply other loads n the network to avod unnecessary losses. It s true even accordng to a transacton contract a generator does not sell electrcty to the local load. Ths s because electrcty has no label and system operators have the authorty to dspatch the power flow. Therefore the buses of a network can be classfed as generator buses, load buses and network buses based on ther net njecton to the system. Ths concept can be appled to both actve and reactve power flows. d) The flows of electrcty obey the proportonal-sharng Rule. The above assumpton leads to the followng lemmas- Lemma 1: A lossless, fnte-nodes power system wthout loop flow has at least one pure source,.e. a generator bus wth all ncdent lnes carryng outflows. Ths lemma wll be proved below. It guarantees to start and contnue a downstream tracng from an exstng pure source. Lemma 2: A lossless, fnte-nodes power system wthout loop flow has at least one pure snk,.e. a load bus wth all ncdent lnes carryng nflows [8]. IV. PROPORTIONAL SHARING PRINCIPLE The proportonal sharng prncple s based on Krchhoff s current law. It deals wth a general transportaton problem and assumes that the network node s a perfect mxer of ncomng flows. Practcally the only requrement for the nput data s that Krchhoff s current law must be satsfed for all the nodes n the network. In ths respect the method s equally applcable to ac as well as dc power flow. As electrcty s ndstngushable and each of the outflows down the lne from node s dependent only on the voltage gradent and mpedance of Vol. 5 Issue 3 May ISSN: X

3 the lne, t may be assumed that each MW leavng the node contans the same proporton of the nflows as the total nodal flow P [6]. The nodal sum.e. total ncomng and total outgong power at node s equal. The man prncple used to trace the flow of electrcty wll be that of proportonal sharng s shown n Fg 1(a). In ths, four lnes are connected to node a, wth two nflows and wth two wth outflows. The total power flow through the node s Pa = = l00mw of whch 40% s suppled by lne j-a and 60% by lne k-a. Accordng to proportonal sharng prncple- The 70MW outflowng n lne a-m conssts of 70*40/100=28 MW. suppled by lne j-a and 70*60/100=42MW suppled by lne k-a. Smlarly the 30MW outflowng n lne a-n conssts of 30*40/100=12MW suppled by lne j-a and 30*60/100=18 MW suppled by lne k-a. The proportonal sharng prncple bascally amounts to assumng that the network node s a perfect mxer of ncomng flows so that t s mpossble to tell whch partcular n flowng electron goes nto whch partcular outgong lne. The prncple s far as t treats all the ncomng and out-flowng flows n the same way. Fg 1(a): Representaton of Proportonal Sharng Prncple V. DOWNSTREAM LOOKING ALGORITHM Now consder the dual, downstream-lookng, problem when the nodal through-flow P, s expressed as the sum of outflows P P P l L P Cl P P L where alpha() d s, as before, the set of nodes suppled drectly from node and C l P l / Pl Ths equaton can be rewrtten as P C P P l A P D P L Where A d s the (n x n) downstream dstrbuton matrx and P, s the vector of nodal demands. The element of A d s equal to L (.l) A d Cl P l / Pl l 1 0 Vol. 5 Issue 3 May ISSN: X

4 Note that A, s also sparse and non symmetrc. Addng and gves a symmetrc matrx whch has the same -1-1 structure as the nodal. Admttance matrx. If A d exsts then P= A d P L and ts th element s equal to P [ A ] P for =1,2..n l 1 k Ths equaton shows how the nodal power P, dstrbuted between all the loads n the system. On the other hand, the same P s equal to the sum of the generaton at node and all the nflows n lnes enterng the node. Hence the nflow to node from lne -j can be calculated usng the proportonal sharng prncple as l 1 P l / P P P l / P [ Al k Pk P ] j k D,k L P LK Where j D,k flows n lne -j. L P LK s the topologcal load dstrbuton factor that s the porton of kth load demand that Ths defnton s agan smlar to that of the generalzed load dstrbuton factor based on DC load-flow senstvty analyss. However, the topologcal factor represents the share (whch s always postve) of the load n a lne flow whle the generalzed factor determnes the mpact of the load on a lne flow and may be negatve. The generaton at a node s also an nflow and can be calculated usng the proportonal sharng prncple as G PG / P P ( PG / P ) [ Ad k Pk 1 P ] Ths equaton shows that the share of the output of the th generator used to supply the kth load demand s equal to P G P LK [A d -1 ] k / P and can be used to trace where the power of a partcular generator goes to[6]. VI. RESULTS AND DISCUSSIONS (A) An applcaton wth IEEE 6 bus system To make the appled method easy to understand, a small test system was selected to explan the steps nvolved. The one-lne dagram of the system s shown n Fgure 7(a), and the system data can be found. From the power-flow results, the drecton of power flows through the lnes can be determned. The real power-flow drecton s ndcated by the arrows placed under the branches. Fg2 (a): Sngle lne dagram of 6 bus system Three generators are connected to buses 1, 3, 6. From the power-flow drectons shown n the fgure, t can be seen that only bus 1 s the start buses, as the bus has all the outgong power. All other generator buses, namely buses 3 and 6, do not get power only from the generators connected to that bus through the transmsson lnes. For nstance, bus 3 gets power from bus 1, whle. Agan, bus 6 s only the bus where all of the connectng lnes carry ncomng power, and no lne carres power out of ths bus. So, bus 6 s the only end bus n ths system. Ths process of selectng start and end buses should be repeated for reactve power flow also, as ths mght result nto a dfferent set of start and end buses. In ths case, there wll be a sngle start bus for reactve Vol. 5 Issue 3 May ISSN: X

5 power flow at bus 1.Once the start and end buses are selected, the flow drecton matrx (F ) s formed. Matrx F for actve power allocaton of the test system s shown below: Table 1(a): Flow Incdence Matrx of 6 bus system The elements of F havng value 1 ndcate a drect connecton between the correspondng buses. As bus 1 s drectly connected to bus 2 and 3 only, and the drecton of the power flow s from bus 1 to bus 2, so the frst row of F has a double 1 value n column 2 and 3. In bus 6, although there are three lnes connected, power flow n all of these buses s toward ths bus, so all of the elements n the last row of F are 0. The total nflow for each of the buses s calculated, followed by the calculaton of the contrbuton for each of the generator buses on tself. Ths s taken as 1 f the generator s a start generator. So, for the sx-bus system, the contrbuton of generators 1 toward tself wll be 1. For all other generators at buses 3 and 6, ther contrbutons on the bus where they are connected wll be calculated as C 33 = P G3 / P 3 where PG3 s the output of the generator at bus 3, and P3 s the total nflow at bus 3. Once the contrbuton of generators toward ther own buses are over, any of the start buses s selected (1, here), and the contrbuton of ths bus s calculated for all the buses (j) havng a non-zero element of F correspondng to ths new bus. From the flow-drecton matrx shown above, t s seen that, correspondng to bus 1, only bus 2 has a non-zero element. So, the contrbuton of bus 1 on bus 2 wll be C 12 = P 12 / P 2 where P12 s the power flow from bus 1 to bus 2, and P2 s the total nflow at bus 2. Bus 2 wll now be consdered as the start bus, and the process wll be repeated for all other buses untl t reaches any one of the end buses. These steps are repeated for all generators. The resultng contrbuton matrx, whch gves the contrbuton of each bus Table 1 (b): Contrbuton matrx If any bus has a contrbuton value of less than 1 toward tself (here buses 2, 3, 4, and 6), then ts contrbuton for all other buses gets modfed by multplyng each of the contrbuton value for that bus by ts selfcontrbuton, whch s less than 1 (as per Step 11 of the algorthm). The fnal contrbuton matrx of the generators toward the actve load for the test system s Table1 (c): Fnal contrbuton Matrx Vol. 5 Issue 3 May ISSN: X

6 The contrbuton of a generator toward a bus s consdered to be same as the generator s contrbuton to all branches connected to that bus and havng an outward power flow drecton from the bus nto the branch. So, determnng the bus from whch power s sent nto the branch wll lead to the contrbuton of generators on the branch loss as well as branch flow. Smlarly, the contrbuton of any load on branch loss wll be the same as the contrbuton of the load on the bus that s connected to the branch and carres power n an outward drecton from the branch toward the load. The contrbuton of ndvdual generators on the load s represented by the followng graph- Fg 1(c): Graphcal Representaton of generator contrbuton to loa From the fgure, t s clear that () Generator 1 s supplyng 100% power to Bus 1. () Generator 3 s supplyng 9.09% power to Bus 1 and 90.9% power to Bus3 () Generator 6 s supplyng 60.3% power to Bus 1, 25.05% power to Bus 3 and 14.29% power to Bus 6. (B) An applcaton wth IEEE 30 bus system Fg 3(a): Sngle lne dagram of 30 bus system Vol. 5 Issue 3 May ISSN: X

7 Consderng bus 1 as the start bus, reactve power s traced n the above system. Startng wth the flow-ncdence matrx, the connectons are checked between each lnes are contrbuton s analyzed by proportonal sharng prncple. Followng the smlar steps of Downstream Lookng Algorthm, the above system s traced for reactve power and the updated contrbuton matrx s shown n Table 5 The contrbuton of ndvdual generators on load buses can be represented as- Fg 3 (b): Graphcal representaon of contrbuton of ndvdual generators to load The fnal contrbuton matrx whch shows the contrbuton of the 6 generators on the 30 ndvdual buses s as follows- Table 2(a): Fnal contrbuton matrx of 30 bus system on the 6 generators VII. CONCLUSION Ths Artcle uses a method for power-flow tracng and allocaton of transmsson losses based on the powerflow results. It employs the graph theoretc methods drectly to determne the contrbuton of the generators to ndvdual loads or lne flows. Unlke other graph theory based approaches, the method does not requre subgroupng of the system buses. Ths makes the method very smple to mplement, and also t sgnfcantly Vol. 5 Issue 3 May ISSN: X

8 decreases the computaton tme. The method allocates loads and losses to the generators avodng any possblty of cross-subsdy. So, ncreased accuracy and mproved speed wth the very smple approach of the method are ts man advantages over the other smlar methods, consderng the premum value of the power and energy losses. REFERENCES [1] Janusz balek Tracng the flow of electrcty IEE Proc.-Gener. Transm. Dstrh., Vol. 143, No 4, July 1996 [2] Danel Krschen Ron Allan Goran Strbac Contrbutons of Indvdual Generators to Loads and Flows IEEE Transactons on Power Systems, Vol. 12, No. 1, February [3] Ya-Chn Chang*, Chan-Nan Lu An electrcty tracng method wth applcaton to power loss allocaton Electrcal Power and Energy Systems 23 (2001) [4] C.-T. Su, J.-H. Law and C.-M. L Power-flow tracng and wheelng costng consderng complex power and convecton lnes IEEE Proc.-Gener. Transm. Dstrb., Vol. 153, No. 1, January [5] M. W. Mustafa, Member, IEEE and H. Shareef, Student Member, IEEE A Comparson of Electrc Power Tracng Methods Used n Deregulated Power Systems. Frst Internatonal Power and Energy Conference PECon 2006 November 28-29, 2006, Putra. [6] Sobhy M. Abdelkader, Transmsson Loss Allocaton Through Complex Power Flow Tracng 2240 IEEE Transactons on power system, VOL. 22, NO. 4, November [7] M.DE1 and S. K. GOSWAMI1. A Drect and Smplfed Approach to Power-flow Tracng and Loss Allocaton Usng Graph Theory Electrc Power Components and Systems, 38: , 2010 Vol. 5 Issue 3 May ISSN: X