Comparison of Transmission oss Allocation s in Deregulated ower System. Srinivasa Varma & V. Sankar Research Scholar, Department of Electrical Engineering, JNTUACEA, Anantapur, Andhra radesh, ndia e-mail: pinnivarma@ieee.org, sankarvelamury@ieee.org Astract - The prolem of Transmission oss Allocation (TA) among the power system agents has ecome more important with the increase of the competition level in electricity markets. n this paper different Transmission oss Allocation methodologies are considered. The comparison etween them, which is not availale in the literature, has een made. The methods considered in this paper are; ostage Stamp (S), roportional Sharing rinciple (S) and oss Function Decomposition (FD) methods. Algorithms have een implemented for these methods. These methodologies are illustrated on EEE 5-us system and EEE-4 us system. The theoretical values are verified with the simulation results otained from the MATAB programming. Keywords: ostage Stamp, roportional Sharing rinciple, oss Function Decomposition, Transmission oss Allocation.. NTRODUCTON The economic ackground of the electric power utility sector is changing; all over the world, the power system is under restructuring. The main ojective of this restructured power system is to create the competition in the electricity market. One of the key issues of this restructured power system is Transmission oss Allocation. The transmission loss allocation can ensure an efficient utilisation of the existing network, its security and e a device to send correct signals concerning the development of new generating capacities [9]. Transmission loss allocation is a suject of considerale deate among various customers in the electricity industry. From the viewpoint of state regulators and load interests, loss allocation raises questions of increased or reduced electricity rates for end-use customers. This paper descries a variety of transmission loss allocation methodologies and evaluates their respective properties. A description of transmission planning, including how studies are conducted, is essential to understanding the kinds of enefits transmission planning identifies and places loss allocation methodologies into context [3, 5, 6]. n this paper, three different loss allocation methods are discussed; ostage Stamp method (S), roportional Sharing rinciple (S) method and oss Function Decomposition (FD) method. The ostage Stamp method does not take into account the network and produces sustantially different results than other methods. The proportional sharing procedure takes into account the network [7]. The oss Function Decomposition method provides fair, efficient and accurate loss allocation to the transmission system customers. n this paper, the applications of S, S and FD methods are illustrated y using sample 5 -Bus system and EEE 4-Bus test system to perform the loss allocation to the transmission customers.. OSTAE STAM METHOD The S method allocates the transmission system losses to the generators and loads proportional to their active generation or load consumption. However, the network topology is not taken into account. t will not e apt for two identical loads, which locate near generators and far away from generators respectively, to e allocated with the same amount of loss [7]. A. Transmission oss Allocation Based on main assumption the S method proportionally allocates 5% of losses to the generator and 5% to the demands, that is nternational Journal on Advanced Electrical and Electronics Engineering, (JAEEE), SSN (rint): 78-8948, Volume-, ssue-, 7
Comparison of Transmission oss Allocation s in Deregulated ower System where, i i () Dj Dj () D i, Dj - Real ower eneration and oad at uses i and j, D - Total ower eneration and oad of the System i - osses allocated to the generator i Dj - osses allocated to the demand j and - Total losses of the system.. ROORTONA SHARN RNCE METHOD S method, sometimes is also called flow-tracing scheme. n this method, it is assumed that nodal inflows are shared proportionally among nodal outflows. This method uses a topological approach to determine the contriution of individual generators or loads to every line flow ased on the calculation of topological distriution factors. This method can deal with oth dcpower flow and ac power flows; i.e., it can e used to find contriutions of oth active and reactive power flows [4, 8]. A. Formation of Branch ncidence Matrix (B) Consider a network consisting of n nodes and m ranches and define, Q,, Q, D and Q D as (n ) vectors of nodal flows, nodal real and reactive power generations and nodal demands respectively, and F and F q as (m) vectors of real and reactive ranch power flows. The (m n) incidence matrix B can e formed y considering + for sending end node and - for receiving end node. f there is any node, that does not elongs to particular ranch can e assigned zero. This matrix B can e split into matrix B u consisting of - s and B d consisting of + s. B. Transmission oss Allocation The adjacency matrix (D) is defined as (nn) matrix with [D] ij = if there is a flow from node i to node j. The adjacency matrix can e expressed as follows. D = B d T B u (3) The ranch flow matrix (F d ) with (nn) size, such that its (ij) element is equal to the flow in line i-j towards node j (i.e., downstream). F d can e expressed as follows, F d = B d T diag(f)b u (4) where, F is power flow vector which is taken from the Newton Raphson oad Flow method. The element (ij) of F d T is equal to the flow in line i- j towards i (ie, upstream). The Kirchhoff Current aw (KC) can e expressed to compute nodal powers as, = +F d T. (5) where, is (n ) vector of ones. The upstream allocation matrix (A u ) is the sparse and non-symmetric matrix and it can e expressed as, A u = + B u T diag(f)b d [diag()] - (6) where, is an dentity matrix. Similarly, the downstream allocation matrix (A d ) can e expressed as, A d = + B d T diag(f)b u [diag()] - (7) The roportional Sharing rinciple method can also express ranch flows as the sum of components supplied from individual generators or to individual loads. i-j (gross) = ij i n k [ A for j u( i, k ) ] k (8) d i where, i d = set of nodes supplied directly from node i i k = Nodal power k = Buses (enerator us) = enerating power at us k ij = Branch power flow (iupstream, j downstream) i-j (net) where, n ij u = [ Ad ( i, k )] Dk for j i (9) i k Dk = load at us k k = Buses (oad us) ij = Branch power flow (jupstream, i downstream) i u = Set of nodes supplying node i n order to assign 5% of losses to the generation and 5% to the demand, the final generation and demand per us are computed as, i net i j i () nternational Journal on Advanced Electrical and Electronics Engineering, (JAEEE), SSN (rint): 78-8948, Volume-, ssue-, 7
Comparison of Transmission oss Allocation s in Deregulated ower System Dj gross i j Di () Finally the real power losses allocated to every generator and demand are computed as, i Dj () i Dj i (3) V. OSS FUNCTON DECOMOSTON METHOD Dj oss Function Decomposition (FD) method is a different method for allocating transmission losses among loads and generators y using Current rojection concept for ool ased markets. This is the est method for allocating losses which in turn fix the costs among loads and generators. n this method, first, loss function is decomposed into two components, load losses and no load losses. Therefore, y using current projection concept, share on ranch current due to loads and generators are determined. Finally, after otaining the ranch current contriutions, the losses can e allocated to each participant. t has een represented that transmission losses can e considered as consisting of two parts. The first is due to line flows caused y load currents only when the generator voltages are all equal in oth magnitude and angles, i.e., there is no circulating current flow. This part will e referred to as load losses. The second part is due to the circulating current resulting from differences in generator voltages. Being caused y mismatch in generator s voltages, this part will e referred to as no load losses. This oss Function Decomposition method is classified into to types, susidized method and un-susidized method. Some times the susidized method can allocate the negative losses to the generators and loads. To avoid this prolem the un-susidized method can e used to allocate only positive losses [, ]. A. Susidized FD i) Transmission oss Allocation to oads oss due to load currents are otained y assuming that all generators act as ideal voltage sources with no circulating currents etween them. n such a case, generation nodes are short circuited and the load nodes are considered as current sources. Considering the node equations of the power system and y proper partitioning of Y BUS, the power system equations can e written as: Y Y Y Y V V (4) The current injection at load us is represented y, the contriution of to the generator us voltage is zero and its contriutions to the load us voltage will e calculated as: V k = Y - e, k =,, n (5) where, is numer of loads and e is an dimension vector with value of at position and all the others equal to. The contriution of to the voltage drop across ranch is computed as: ΔV = V f - V t (6) where, the suscripts f, t represent the from us and the to us of ranch, respectively. The contriution of to the current through ranch can e computed as: V (7) z where Z = R + jx is the complex serial impedance of ranch. Here the shunt elements of lines are not taken into account ecause it is only focused on active loss allocation. load. is the ranch current contriution due to According to the superposition principle, the ranch current contriution due to each current injection is as follow: l (8) et p denote the projection vector of in the direction of, which is defined to e the current projection component of ranch produced y the current injection at load and it is calculated as: p j cos( ) e (9) where, Ф, Ф are phase angles of,. After otaining the ranch current contriutions due to load current injections, its allocated loss of ranch is accordingly given y the following formula: ( V f V t ) * p ) j cos( e z () cos( ) z nternational Journal on Advanced Electrical and Electronics Engineering, (JAEEE), SSN (rint): 78-8948, Volume-, ssue-, 7
Comparison of Transmission oss Allocation s in Deregulated ower System cos( ) r oss () where, r = Resistance of a ranch Therefore, the total transmission loss allocation to injection attriuted to load is computed as follows: m T oss oss () ii) Transmission oss Allocation to enerators oss due to mismatch in generators voltages are otained y setting the load currents to zero. Setting in Eqn. (4) to zero, and keeping the generator voltage as otained from the power flow solution. The current injection at generator us is shown y, its contriutions to the load us voltage will e calculated according to elow: V k = -(Y -.Y.Z )e (3) where, Z = [[Y ] [Y ][Y ] - [Y ]] - Also the contriution of to the generator us voltage can e computed as: V k = Z e (4) The contriution of to the current through ranch can e computed as: V (5) z According to Superposition principle the ranch current contriutions due to each generator current injection is calculated as: g (6) n this stage, like the previous one, p denote the projection vector of in the direction of, which is defined to e the current projection component of ranch produced y the current injection at generator and it is calculated as: p j cos( ) e (7) Consequently, allocated loss of ranch due to mismatch in generator s voltage derived as: cos( ) r oss (8) where, Ф, Ф are phase angles of,. Therefore, the total transmission loss allocation to injection attriuted to generator is computed as follows: m T oss oss B. Un-Susidized FD i) Transmission oss Allocation to oads (9) f losses allocated y susidized method ( s ) to any load us is less than i.e., negative value, then, β = / (-K i ) (3) where, K i is the negative loss of i th ranch allocated to the load uses and u = s β + (- β) (3) where, u is loss allocated y un-susidized method u (new) = u ( Ts / Tu ) (3) where, Ts = Total susidized losses at particular ranch Tu = Total unsusidized losses at particular ranch Now, sum( s ) = sum( u(new) ) ii) Transmission oss Allocation to enerators f losses allocated y susidized method ( s ) to any generator us is less than i.e., negative value, then, =/(-K i ) (33) where, K i is the negative loss of i th ranch allocated to the generator uses and u = s +(- ) (34) where, u is loss allocated y un-susidized method where, u (new) = u ( Ts / Tu ) (35) Ts = Total susidized losses at particular ranch Tu = Total unsusidized losses at particular ranch Now, sum( s ) = sum( u(new) ) V. CASE STUDY : EEE 5-BUS SYSTEM The EEE 5 Bus System shown in Fig. is used to compare the transmission loss allocation methods considered in this paper. t consists of two generators ( and ) and three loads ( 3, 4 and 5 ) respectively. The 5 us system represented y the us power injections, line power flows and line power losses nternational Journal on Advanced Electrical and Electronics Engineering, (JAEEE), SSN (rint): 78-8948, Volume-, ssue-, 73
Comparison of Transmission oss Allocation s in Deregulated ower System nternational Journal on Advanced Electrical and Electronics Engineering, (JAEEE), SSN (rint): 78-8948, Volume-, ssue-, 74 otained from the ase case solution i. e., Newton Raphson load flow analysis. Fig. EEE 5 Bus System A. Theoretical calculations for S The transmission losses can e allocated to the generators using Eqn. (), i.e., oss Allocation to enerators = (/)*3.36*(3.36/83.36) =.947 MW Similarly, loss allocation to enerator is.733 MW The transmission losses can e allocated to the loads using Eqn. (), i.e., oss Allocation to oad 3 = (/)* 3.36* (6/8) =.56 MW Similarly, loss allocation to load 4 and 5 are.47 MW and.65 MW B. Theoretical Calculations for S The adjacency matrix (D) can e formed using Eqn. (3) as follows D The ranch flow matrix (F d ) can e calculated using Eqn. (4) as follows 4.6796 8.8456 9.734 4.43 84.3434 9.75 F d 4.6796 8.8456 9.734 4.43 84.3434 9.75 The nodal powers can e calculated using Eqn. (5) as follows 7. 9.6796 6. 8. 3.369 4.6796 8.8456 9.734 4.43 84.3434 9.75 7 5 6 The upstream and downstream allocation matrices otained from the Eqns. (6) and (7) are.465.366.7.86.578.84 A u.5984.46.43.6874.8957.36 A d Using Eqn. (8), allocation of generators to all loads are computed as ower from en. to oad 3 75MW 9. 3.369.84 6 6 3 Similarly, 4 = 45.57 MW, 5 = 38.847 MW 3 = 4.43MW, 4 = 5.55MW, 5 = 33.38 MW Using Eqn. (9), allocation of loads to all generators are computed as D 7569MW 8. 6.36 3.369 3.369 3 Similarly, D3 = 4.43 MW, D4 = 44.7863 MW D4 = 5.37MW, D5 = 37.54MW, D5 = 3.4796 MW Now, the gross power injected to the generators and loads are computed as = D3 + D4 + D5 = 8.7569 +44.7863+37.54 =.636 MW
Comparison of Transmission oss Allocation s in Deregulated ower System = D3 + D4 + D5 = 4.43+5.37+3.4796 = 78.9364 MW DD = 3 + 3 = 9.75 + 4.43 = 6.4378 MW DD4 = 4 + 4 = 45.57 + 5.55 = 5.754 MW DD5 = 5 + 5 = 38.847 + 33.38 = 7.689 MW Using Eqns. () and () the final generation and load per us are computed as.636 3.369. MW Similarly, 79. 468MW DD3 D 3 6.4378 6 D 3 6. 89MW Similarly, D 4 5.377MW, D 7. 844MW 5 Using Eqns. () and (3) transmission loss allocation to generators and demands is computed as 3.369.. 487MW 8 79.468. 538MW D3 D 3 D 3 6.89 6. 89MW Similarly, 4.377MW, D D. 844MW 5 C. Theoretical Calculations for FD oss Allocation to oads: Y-Bus is formed for 5-us system shown in Fig. as follows Y-Bus = The current injection values to the loads can e calculated y using Eqn. (4) and keeping V = 3 4 5 6.5 j8.695.5 j3.75.97 j38.695 j3.5 j3.75 j3.5 j33.75 5 j5.6667 j5.5 j3.75.5 j33.7 9.6 j7.43.5 j7.5. j.3.5 j7.5 3.75 j. Now the current injection values are 5 j5.6667 j5 9.667 j7.435.5 j7.5. j.7 3 = -.567+j.4, 3 = -.47+j.7, 5 = -.67+j.359.5 j3.75.5 j7.5 3.75 j..57 j.5 The contriution of load us currents to the load us voltages can e calculated using Eqn. (5) Now the contriution of 3 to the load us voltages is as follows V V V 3 3 3 4 3 5 Now,.89 j.6.3 j.4.9 j.7.567 j.4.9 j.6.33 j.98 3 3 3 V 3 = -.8-j.3, V 4 = +j, V 5 = +j The contriution of 3 to the voltage drop across ranch is computed using Eqn. (6) as ΔV 3 = V V 3 ΔV 4 = V V 4 = +j =.8+j.3, ΔV 3 = V V 3 =.8+j.3, ΔV 4 = V V 4 = +j ΔV 5 = V V 5 = +j and ΔV 45 = V 4 V 5 = +j The contriution of 3 to the current through ranch can e computed using Eqn. (7) as: = ΔV 3 /Z 3 =.634-j.38, 3 = ΔV 4 /Z 4 = +j 3 = ΔV 3 /Z 3 =.55-j.9, 3 3 = ΔV 4 /Z 4 = +j 3 4 = ΔV 5 /Z 5 = +j and 3 5 = ΔV 45 /Z 45 = +j 3 6 Similarly the contriution of 4 to the load us voltages is as follows V 3 4 = +j, V 4 4 = -.-j.8, V 5 4 = -.76- j.7 The contriution of 4 to the voltage drop across ranch is ΔV 3 = V V 3 = +j, ΔV 4 = V V 4 =.+j.8 ΔV 3 = V V 3 = +j, ΔV 4 = V V 4 =.+j.8 ΔV 5 = V V 5 =.76-j.7and ΔV 45 =V 4 V 5 =-.36-j.58 The contriution of 4 to the current through ranch is as follows 4 = ΔV 3 /Z 3 = +j, 4 = ΔV 4 /Z 4 =.39-j.78 3 4 = ΔV 3 /Z 3 = +j, 4 4 = ΔV 4 /Z 4 =.6-j.6 5 4 = ΔV 5 /Z 5 =.53-j.3 and 6 4 =ΔV 45 /Z 45 = -.5+j.9 Similarly the contriution of 5 to the load us voltages is as follows V 3 5 = +j, V 4 5 -.5-j.4, V 5 5 = -.57-j.54 nternational Journal on Advanced Electrical and Electronics Engineering, (JAEEE), SSN (rint): 78-8948, Volume-, ssue-, 75
Comparison of Transmission oss Allocation s in Deregulated ower System The contriution of 5 to the voltage drop across ranch is ΔV 3 = V V 3 = +j, ΔV 4 = V V 4 =.5+j.4 ΔV 3 = V V 3 = +j, ΔV 4 = V V 4 =.5+j.4 ΔV 5 = V V 5 =.57+j.54 and ΔV 45 =V 4 V 5 =.4+j.39 The contriution of 5 to the current through ranch is as follows 5 = ΔV /Z = +j, 5 = ΔV 3 /Z =.3-j.6 3 5 = ΔV 4 /Z 4 = +j, 4 5 = ΔV 5 /Z 5 =.-j.53 5 5 = ΔV 34 /Z 34 =.75-j.47 and 6 5 = ΔV 45 /Z 45 =.399-j.4 The ranch current contriution due to each current injection can e evaluated using Eqn. (8) is as follow = 3 + 4 + 5 =.63-j.3, = 3 + 4 + 5 =.69-j.4 3 = 3 3 + 3 4 + 3 5 =.55-j.9, 4 = 4 3 + 4 4 + 4 5 =.7-j.8 5 = 5 3 + 5 4 + 5 5 =.38-j.6 & 6 = 6 3 + 6 4 + 6 5 =.347-j. Now, the loss (in MW) allocation to all the ranches can e calculated using Eqn. () For current injection at load 3 3 loss =.94, 3 loss =, 3 loss3 =.7, 3 loss4 =, 3 loss5 =, 3 loss6 =. For current injection at load 4: loss 4 =, loss 4 =.537, loss3 4 =, loss4 4 =.67, loss5 4 =.3, loss6 4 = -.95. For current injection at load 5: loss 5 =, loss 5 =.534, loss3 5 =, loss4 5 =.73, loss5 5 =.755, loss6 5 =.84. The total transmission loss allocation to each load is computed using Eqn. () as follows oss allocation to load 3: T loss 3 = loss 3 + loss 3 + loss3 3 + loss4 3 + loss5 3 + loss6 3 =.94 + +.7 + + + =.3 MW oss allocation to load 4: T loss 4 = loss 4 + loss 4 + loss3 4 + loss4 4 + loss5 4 + loss6 4 = +.537+ +.67 +.3.95 =.639 MW oss allocation to load 5: T loss 5 = loss 5 + loss 5 + loss3 5 + loss4 5 + loss5 5 + loss6 5 = +.534 ++.73 +.755 +.84 =.66 MW oss Allocation to enerators: The current injections at generator uses are as follows: =.9+j.7 and = -.87+j.37 The contriution of to the load us voltages using Eqn. (3) are: V 3 =.58-j.7,V 4 =.58-j.64, V 5 =.587-j.79 The voltage contriutions of generator due to generator current injections are computed using Eqn. (4) as follows: V V. j3.96.6 j4.9 V =.57-j.5 and V =.58-j.7.6 j.39.9 j.7. j3.967 Now the contriution of to the voltage drop across ranch is computed as ΔV 3 =V V 3 = -.6+j.7, ΔV 4 = V V 4 = -.+j. ΔV 3 =V V 3 =.8-j.9, ΔV 4 = V V 4 =.6-j.77 ΔV 5 =V V 5 =.6-j. and ΔV 45 =V 4 V 5 = -.6+j.68 The contriutions of to the current through each ranch are computed using Eqn. (5) as = ΔV 3 /Z 3 =.65+j.8, = ΔV 4 /Z 4 =.6+j.7 3 = ΔV 3 /Z 3 = -.6-j., 4 = ΔV 4 /Z 4 = -.37-j.6 5 =ΔV 5 /Z 5 = -.9-j. & 6 = ΔV 45 /Z 45 =.49+j. Similarly, the contriution of to the load us voltages and generator us voltages are V =.55+j.5, V =.54+j.4 V 3 =.54-j.4,V 4 =.55-j.5 & V 5 =.55-j.5 nternational Journal on Advanced Electrical and Electronics Engineering, (JAEEE), SSN (rint): 78-8948, Volume-, ssue-, 76
Comparison of Transmission oss Allocation s in Deregulated ower System Now the contriution of to the voltage drop across ranch is given as: ΔV 3 = V V 3 =.+j., ΔV 4 = V V 4 =.6+j.63 ΔV 3 = V V 3 =.38-j.4, ΔV 4 = V V 4 =.8-j.5 ΔV 5 = V V 5 =.9-j.5 & ΔV 45 = V 4 V 5 =.9+j.8 The contriution of ranch is given as: = ΔV 3 /Z 3 =.58-j.4, = ΔV 4 /Z 4 =.3-j.6 3 = ΔV 3 /Z 3 = -.9+j.44, 4 = ΔV 4 /Z 4 = -.78+j.37 5 = ΔV 5 /Z 5 = -.55+j.6 & 6 = ΔV 45 /Z 45 =.86-j.4 to the current through each The ranch current contriution due to each current injection can e evaluated using Eqn. (6) is as follow = + + 3 =.574+j.4, = + + 3 =.8+j.64 3 = 3 + 3 + 3 3 =-.7+.3, 4 = 4 + 4 + 4 3 =-.6+j. 5 = 5 + 5 + 5 3 =-.58+j.5 & 6 = 6 + 6 + 6 3 =.58+j.7 Now, the loss (in MW) allocation to all the ranches can e calculated using Eqn. (8) For current injection at enerator loss =.89, loss =.33, loss3 = -.7, loss4 = -.4, loss5 = -.5, loss6 =.64. For current injection at enerator : loss =.76, loss =., loss3 = -.4, loss4 = -.56, loss5 = -.47, loss6 =.7. The total transmission loss allocation to each generator is computed using Eqn. (9) as follows oss allocation to enerator : T loss = loss + loss + loss3 + loss4 + loss5 + loss6 =.89 +.33 -.7 -.4 -.5 +.64 =.36 MW oss allocation to enerator : T loss = loss + loss + loss3 + loss4 + loss5 + loss6 =.7 +. -.4 -.56 -.47 +.7=-.3 MW From the aove calculations the negative loss i.e., -.3MW is allocated to the generator. To convert it into positive value the unsusidized method is followed as follows For the generator- the value of K i from ranch 3 is -.4MW Now, using Eqn. (33), = /(+.4) =.9596 Using Eqn. (34), U =(-.7.9596) +(-.9596) =.33 MW U =(-.4.9596)+(-.9596) =. MW Using Eqn. (35), U(new) = (-.7-.4) (.33)/(.33+.) = -.5 MW U (new) = (-.7-.4) (.)/(.33+.) =. MW Similarly, for the generator- the value of K i from ranch 4 is -.56 MW, and =.9468 U =.394 MW, U =. MW U(new) = -.7 MW, U (new) =. MW Similarly, for the generator- the value of K i from ranch 5 is -.47 MW, and =.878 U =.4 MW, U =. MW U(new) = -.5 MW, U (new) =. MW Now, the total loss allocated to generator and generator are oss allocation to enerator : T loss = loss + loss + loss3 + loss4 + loss5 + loss6 =.89 +.33 -.5 -.7 -.5 +.64 =. MW oss allocation to enerator : T loss = loss + loss + loss3 + loss4 + loss5 + loss6 =.76 +. -.+. -. +.7 =. MW D. Transmission oss Allocation Results The results otained for the three loss allocation methods are shown in the tales. Tale shows the transmission power losses allocated to the generators and the Tale shows the transmission power losses allocated to the loads using three loss allocation methods. nternational Journal on Advanced Electrical and Electronics Engineering, (JAEEE), SSN (rint): 78-8948, Volume-, ssue-, 77
Comparison of Transmission oss Allocation s in Deregulated ower System TABE OSS (in MW) AOCATON TO ENERATORS enerator No. S S FD Susidized Unsusidized.95.5.36..73.53 -.3. TABE OSS (in MW) AOCATON TO OADS oad No. S S FD Susidized Unsusidized 3.56..3.3 4.47.38.64.64 5.65.8.7.7 From the aove results, it can e oserved that S method could not consider the network into account, it allocate the losses to the generators and demands with respect to their capacities with out considering the power flows etween them, from the results it is can e seen that the S method allocates the losses of.95mw to the enerator -, ut its contriution of power flow to the other demands apart from its own demand is only 3.36MW and it allocates the losses of.73mw to the generator with its contriution of 8MW power flow to the other demands. The S method is considering the network into account; it allocates the losses to the generators and demands according to their power flow contriution. From the results it shows that the S method allocates the losses of.5mw to the generator- as it contriutes the 3.36MW to the other demands and it allocates the.53mw losses to the generator as it contriutes the 8MW power flow to the other demands. So, from this analysis it is oserved that, with the S method, the entire transmission network customers are convincingly enefited ut with the S method some customers with more contriution of power may gets more enefit and customers with less contriution may gets less enefit y allocating the huge amount of loss allocation. From the results, it is oserved that the FD method allocates the losses with respect to losses occurred in each segment. This method will not consider the assumption of allocating 5% losses to the generators and 5% to the loads. The loss allocated to all generators is.3mw and loads are 3.3MW. So, from this analysis it is oserved that, with the FD method the entire transmission network customers are reasonaly enefited. The FD method may produce negative loss allocations. They could e physically understandale with the concept of counter flows and dominant flows. Whether the negative loss allocations are acceptale or not, they depend on the market and its participants. f they are acceptale, they could actually send out signals to help reducing system losses. However, this prolem can e avoided y using unsusidized method. V. CASE STUDY : EEE 4-BUS SYSTEM A case study ased on the EEE, shown in Fig., is presented in this section. Fig. EEE 4 Bus System A. Transmission oss Allocation Results The results of EEE 4 us system otained for the three loss allocation methods are shown in the tales. Tale shows the transmission power losses allocated to the generators and the Tale V shows the transmission power losses allocated to the loads using three cost allocation methods. TABE OSS AOCATON TO ENERATORS enerator No. S S Susidized FD Unsusidized 5.76 6.7 7.44 3.6.99.58 -.33.58 nternational Journal on Advanced Electrical and Electronics Engineering, (JAEEE), SSN (rint): 78-8948, Volume-, ssue-, 78
Comparison of Transmission oss Allocation s in Deregulated ower System oad No. TABE V : OSS AOCATON TO OADS S S Susidized FD Unsusidized.56.4 -.34.58 3.45.79 3.88 3.3 4.5.3.54.6 5.9.6.9.6 6.9.3.3.37 7.4 8...3.7 9.77.76.94.7.3.4.3.36.9.9..5.5.6..5 3.35.37.5.53 4.38.49.7.67 V. CONCUSONS The roportional Sharing rinciple method provides fair and efficient loss allocation to the users when compare to ostage Stamp which allocates fixed costs to the users. But, this S method follows the assumption of allocating 5% losses to the generators and 5% to the loads. The FD method will not consider this assumption. The ostage Stamp method does not take into account the network and produces sustantially different results than other methods. The proportional sharing procedure takes into account the network. The oss Function Decomposition method provides fair, efficient and accurate loss allocation to the transmission system customers when compare to the ostage Stamp method which allocates fixed and equal loss to oth generators and loads. This method will not consider the assumption of allocating 5% losses to the generators and 5% to the loads. ostage Stamp method is not advisale ecause it is unfair for specific group of generators and demands. enerators close to load centre are unfairly treated with respect to generators far away from load center. Similarly, demands close to generating areas are unfairly treated with respect to demands far away from those areas. REFERENCES [] M. R. Erahim, Z. hofrani and M. Ehas, Transmission oss Allocation via oss Function Decomposition and Current njection Concept, World Academy of Science, Engineering and Technology 6, pp. 675-678,. [] S. Adelkader, A new method for transmission loss allocation considering the circulating currents etween generators, EEE ower Systems Conference th nternational Middle-East, pp. 8-86, March 8. [3] S. N. Kkeshmiri and M. Ehsan, Transmission oss Allocation using Normalized oss weight Factors, nt. Conf. on Electric Utility Deregulation and Restructuring and ower Technologies (DRT), pp. 43-435, April 8. [4] Ansyari, C. S. Ozveren and D. King, Allocation of Transmission osses using Three Different roportional Sharing s, nt. Conf. on Universities ower Engineer, pp. 34-38, 7. [5] Juan Carlos Mateus and alo Cuervo Franco, Transmission oss Allocation Through Equivalent Bilateral Exchanges and Economical Analysis, EEE Transactions on ower Systems, Vol., No. 4, pp. 799-87, Novemer 5. [6] Francisco D. aliana, Antonio J. Conejo, and Hugo A. il, Transmission Network Cost Allocation Based on Equivalent Bilateral Exchanges, EEE Transactions on ower Systems, Vol. 8, No. 4, pp. 45-43, Novemer 3. [7] A. J. Conejo, J. M. Arroyo, N. Alguacil and A.. uijarro, Transmission oss Allocation: A Comparison of Different ractical Algorithms, EEE Transactions on ower Systems, Vol. 7, No. 3, August. [8] Janusz Bialek, Topological eneration and oad Distriution Factors for Supplement Charge Allocation in Transmission Open Access, EEE Transactions on ower Systems, Vol., No. 3, August 997. [9] Mohammad Shahidehpour, Hatim Yamin and Zuyi i, Market Operations in Electric ower Systems Forecasting, Scheduling, and Risk Management, A John Wiley & Sons, nc., ulication. nternational Journal on Advanced Electrical and Electronics Engineering, (JAEEE), SSN (rint): 78-8948, Volume-, ssue-, 79