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Feasibility assessment of simultaneous bilateral and multilateral transactions
Electrical Power and Energy Systems 32 (2010) 879–885
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Feasibility assessment of simultaneous bilateral and multilateral transactions Yog Raj Sood Department of Electrical Engineering, National Institute of Technology, Hamirpur (H.P.), India
a r t i c l e
i n f o
Article history: Received 4 October 2008 Received in revised form 5 December 2009 Accepted 28 January 2010
Keywords: Transfer capability Feasibility Simultaneous bilateral transactions Multilateral transaction Deregulation ATC
a b s t r a c t The main aim in this paper is to develop algorithm for assessment of the feasibility of simultaneous bilateral and multilateral transactions and if they are not feasible then to find out the minimum amount of transacted power to be curtailed in order to make them feasible. This analysis will be a great help for the generations-loads pairs to decide whether to withdraw the unfeasible transaction completely or to make it feasible by reducing its size optimally. The proposed algorithm can also be used for determining the transfer capability and hence feasibility of a single bilateral transaction at a time. In addition to above algorithm an efficient, repeated Newton–Raphson power flow based algorithm is also developed to determine transfer capability and hence feasibility for single bilateral transaction. The results of the proposed algorithm have been compared with a method proposed by Hamoud in his paper [6]. In this paper, based on the proposed algorithm and with the extension of Hamoud’s method, different feasibility evaluation procedures for simultaneous bilateral and multilateral transactions are suggested, analyzed and applied. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction All the transactions need to be evaluated ahead of their scheduling time to check their feasibility with regard to the system conditions at the time of scheduling. ISO would have to honor and execute only those proposed transactions as far as the system design and operating conditions permit. So before we go for cost analysis, it is important to analyze the feasibility of all proposed firm transactions for a particular transmission network under prevailing system constraints. Only after passing the feasibility test the proposed firm transactions are scheduled for dispatch. This analysis will be required not only by ISO, but also by the end users of the systems to make proper decisions regarding the generations and loads to be connected at different buses of the power system. A transaction is deemed to be feasible if it can be accommodated without violating any of the system operating constraints such as equipment ratings, transmission interface limits, voltage limits etc. The feasibility of a single bilateral transaction can easily be determined from the available transfer capability (ATC) of the network between the buses where a transaction power enters and leaves the network. ATC is a measure of the transfer capability remaining in the physical transmission network for future commercial activity over and above already committed uses [1]. Transfer capability evaluation is a very wide area of research. Extensive work has already been carried out in this direction and more research is in progress in this field in order to increase its accuracy considering various factors and margins [1–4]. The transfer capability has been defined in the literature [1,5,6] in many ways E-mail address: [email protected] 0142-0615/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2010.01.025
depending upon the requirements and accuracy required for a particular analysis. It may be defined as amount of power, incremental above normal base power transfers that can be transferred over the transmission network, with all facility loading are within normal ratings and all voltages are within normal limits [5]. The literature survey [7] reveals that most of the work has been done related with determination of ATC. Ou and Singh [8] have presented a probabilistic based method to assess various factors and procedures to incorporate them into ATC. Christie et al. [9] have suggested power transfer distribution factor and line outage distribution factor for determination of transfer capability from one bus to another bus of the power system. But this method provided only the approximate results. The Information Technology applications for determination of ATC have also been given in some research papers [10]. Application software [11] is also available for ATC calculations. To render the ATC as a more realistic measure of transmission availability, a stochastic calculation of ATC has also been explained in the literature [12,13]. But most of calculation procedures reported in the literature for ATC will be useful for feasibility assessment of only bilateral transactions. But in this paper methods are proposed for feasibility assessment of simultaneous bilateral as well as simultaneous multilateral transactions. Available transfer capability is required to be posted on Open Access Same-time Information System (OASIS). The generationload pair can make reservation for the bilateral transaction whose size should be less than ATC between the points where transaction power enters and leaves the system. After including one transaction in the system, ATC between all the buses changes and reevaluated. Same procedure is repeated for second transaction. Similarly all the feasible bilateral transactions are added to the system one
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Y.R. Sood / Electrical Power and Energy Systems 32 (2010) 879–885
by one. But this procedure cannot be applied directly to simultaneous bilateral and multilateral transactions. Because the transfer capability of a transaction in a group of simultaneous transactions will depend upon the order in which the transactions are considered to be added to the transmission network.
where 8 net > < P i ðV; /Þ P i g gðV;/Þ ¼ Q i ðV; /Þ Q net i g > : P m ðV;/Þ P net m g
For each PQ bus i For each PV bus m;not including ref: bus: ð8Þ
2. Proposed algorithm for assessment of feasibility Generalized formulation of the proposed algorithm is given in this section. This algorithm can be used directly to determine the feasibility of simultaneous bilateral and multilateral transactions. In case these transactions turned out to be not feasible, then this algorithm provides an answer to the question that how much minimum amount of power has to be curtailed, in order to make them feasible.
Let there be nbt number of bilateral transactions and a transaction t is from bus i to bus j. t Let Pg ti be generation (in addition to base case) at bus i and Pdj is load (in addition to base case) at bus j for a transaction t. Base case means already committed generations, loads and transactions on transmission network. Let Tst be size of each proposed bilateral transaction t. t So Tst is equal to Pdj which is also equal to Pg ti ; considering transmission losses for the transaction being provided by the utility or pool. Let there are nmt number of groups of multilateral transactions. Let PMTk be the size of k th group of multilateral transaction. Let there be ngk number of generation points and ndk number of demand points for a group k. It may be noted that ‘ngk’ may or may not equal to ndk. Let Pgmki be the generation at a generation bus i of multilateral transaction k. k Let Pdmi be the load at a load bus i of multilateral transaction k. The objective is to maximize total power transfer PT. nbt X
Tst þ
nmt X
t¼1
PMT k
ð1Þ
k¼1
Subject to the following constraints. The bilateral transaction constraint t
Pg ti ¼ Pdj
for all bilateral transactions
for all bilateral transactions
ð3Þ
where, Tstm is maximum proposed size of transaction t. Multilateral transaction constraints ndk X
k
Pdmj ¼
ngk X
Pgmki ¼ PMT k
ð4Þ
i¼1
j¼1
Multilateral transaction generation and load constraints
Pgmki 6 Pgmpki k
k
Pdmj 6 Pdmpj
ð9Þ
Qg max i
where and are respectively minimum and maximum value of reactive power generation at PV bus i. The inequality constraint on voltage magnitude V of each PQ bus
V min 6 V i 6 V max i i
ð10Þ
where V min and V max are respectively minimum and maximum volti i age at bus i. The inequality constraint on phase angle /i of voltage at all the buses i
/min 6 /i 6 /max i i /min i
ð11Þ
/max i
where and are respectively minimum and maximum allowed value of voltage phase angle at bus i. Power limit on transmission line max
MVAfij 6 MVAf ij
ð12Þ
max
where MVAf ij is the maximum rating of transmission line connecting bus i and j. Some of these constraints are based on the anticipation of the transmission contingencies and may be due to thermal, voltage and stability problems. This optimization problem has been solved by using optimization tools explained in reference [14]. 3. Assessment of available transfer capability
ð2Þ
Bilateral transaction size constraints
Tst 6 Tstm
Qg min 6 Qg i 6 Qg max i i Qg min i
2.1. Mathematical Formulation
PT ¼
where Pi and Qi are respectively calculated real and reactive power and Q net are respectively specified real and reactive for PQ bus i. P net i i power for PQ bus i. Pm and Pnet m are respectively calculated and specified real power for PV bus m. V and / are voltage magnitude and phase angles of different buses. The inequality constraint on reactive power generation Qgi at PV buses
ð5Þ ð6Þ
The feasibility of a single bilateral transaction can easily be determined from the ATC of the transmission network between the buses, where the transaction power enters and leaves the network. Hamoud [6] has also used the same ATC for determination of feasibility of simultaneous bilateral transactions, without considering various margins like transmission reliability margin, capacity benefit margin etc. for ATC evaluation. In that case ATC is approximately equal to total transfer capability, which is a key component for ATC assessment. In order to compare the results of the proposed algorithm with the method proposed by Hamoud and for extension of his method, these margins are not considered in this analysis. In this paper two independent methods have been proposed for assessment of ATC, first method is based on optimization algorithm proposed in above Section 2 and second is based on Newton–Raphson repeated power flow (RPF) method.
Pgmpki
where, is the proposed generation at generation point i of k group k of multilateral transaction. Pdmpj is the proposed load at load point j of group k of multilateral transaction. The power flow equation of the power network
gðV; /Þ ¼ 0
ð7Þ
3.1. By proposed algorithm The proposed algorithm described in Section 2 has been used for assessment of available transfer capability for single bilateral transaction by putting number of transaction nbt = 1, number of
Y.R. Sood / Electrical Power and Energy Systems 32 (2010) 879–885
multilateral transactions nmt = 0, and taking arbitrary very high size of the transaction. All system constraints are considered, the same process is repeated for all selected contingency cases. Minimum of ATC level in all cases will be true ATC. 3.2. By repeated power flow (RPF) method Let IL is a scalar parameter representing the increase in the load as well as generation above base case. IL = 0 corresponds to no transfer (base case) and IL = ILmax corresponds to maximum transfer. IL is to be maximized by giving small increments DP in steps, subject to all transmission network constraints mentioned in Eqs. (7)–(12). ATC between any two buses of the network is the maximum value of IL satisfying all system constraints. The same process is repeated for all selected contingency cases. Minimum of ATC level in all these cases will be true ATC. The flow chart for this method for assessment of ATC from each bus to another buses of the power transmission network is shown in Fig. 1. 4. Application of proposed algorithm The proposed algorithm as explained above in Section 2, is applied to IEEE 30-bus test system. Data and single line diagram of this system is given in reference [15,16]. For simplicity of analysis we have considered only one contingency in this study i.e. outage of generator G3 at bus no. 5. However more contingencies cases can also be considered. 4.1. Feasibility of single bilateral transactions A bilateral transaction will be feasible, if it is less than or equal to available transfer capability of the network between the buses where the transaction power enters and leave the network. Table 1 shows the ATC levels calculated for single bilateral transactions by the proposed optimization method as well as by the repeated power flow (RPF) method in normal as well as in contingency case. From Table 1 it is very much clear that ATC calculated for single bilateral transaction by proposed method and RPF methods under both normal as well outage case are very much consistent. This proves the validity of the proposed method. A bilateral transaction from bus 3 to bus 10 under normal condition of the network will be feasible if it is less than or equal to 66.5383 MW. Otherwise it is unfeasible. After adding a feasibility transaction to the system. The ATC is again evaluated and hence feasibility of second transaction to be added to the systems is assessed. Same procedure is repeated for the remaining transactions. So the feasibility of a particular transaction in a group of bilateral transactions, will depend upon the order at which these transactions are added to the system. So this method can not be directly applied for feasibility assessment of simultaneous bilateral transactions and also for multilateral transactions. 4.2. Feasibility assessment of simultaneous bilateral transactions The feasibility of simultaneous bilateral transactions is determined by a method proposed by Hamoud [6] and also by the proposed methods. Two different transactions systems are considered (1) Four simultaneous wheeling transactions system In this system, four transactions shown in Table 2 are to be simultaneously applied to transmission network. It is required to find their feasibility.
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Case 1: normal case-all transmission elements in service All the transactions are added to the system. All system constraints are checked and found to be within limits. Hence it is concluded that all these transactions are feasible for their simultaneous application to the system. Case 2: contingency case-generator at bus 5 is out of service In this case generation at bus 5 is zero. The generations at other generator buses were adjusted by optimal power flow, before the application of these transactions. After simultaneous application of these four transactions, it has been observed that some of the system constraints are violated. Hence they are not feasible. Now it is desired to find out, how to serve these transactions in an optimal manner, so that maximum power can be transferred through these transactions. (2) Seven simultaneous wheeling transactions system In this system, seven transactions shown in Table 3 are to be simultaneously applied to transmission network. It is required to find their feasibility. All the transactions are added simultaneously to the system under normal conditions and system constraints are checked. It has been observed that some of the constraints are violated. Hence it is concluded that these seven simultaneous bilateral transactions system is not feasible. So it is required to find the optimal way by which these transactions may be served with minimum possible curtailment. (3) Determination of Feasibility by Hamoud’s method Hamoud [6] has proposed a method for determination of feasibility for a group of simultaneous bilateral transactions based on ATC of individual bilateral transactions. He has used a new term Available Transmission Margin (ATM) that is difference between the computed ATC and size of the transaction.
4.2.1. Application to four simultaneous transactions system Step by step procedure of calculations is illustrated below. Step1: ATC and ATM of each individual transaction are determined, the results are shown in Table 4. Step2: From Table 4, it is clear that transaction T1 has maximum ATM. So transaction T1 is accommodated first and results of ATC and ATM are shown in Table 5. Step3: In Table 5, transaction T2 has maximum ATM, so now accommodate T2 also. It has been observed that both T1 and T2 can be accommodated. The results after accommodating T1 and T2 are shown in Table 6. Step4: In Table 6, T3 has maximum ATM. So results after accommodating T3 also are given in Table 7. Since ATM of T4 is negative, so this transaction cannot be accommodated. Hence it is not feasible. The final results are given in Table 10.
4.2.2. Application to seven simultaneous transactions system The same steps are followed as illustrated for four transactions system. Results of the final step are given in Table 8. Since ATM for T3 and T4 is negative, so these transactions can not be accommodated without violating transmission system constraints. The final results are given in Table 11.
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Y.R. Sood / Electrical Power and Energy Systems 32 (2010) 879–885
Fig. 1. Flow chart for determination of ATC by RPF method.
Table 1 ATC Levels and ATC values. Transactions
T1 T2 T3 T4 T5
From bus no.
To bus no.
3 20 13 14 5
10 12 30 24 25
Normal case
Contingency case
ATC level by proposed optimization based method (MW)
ATC level by RPF based method (MW)
ATC level by proposed optimization based method (MW)
ATC level by RPF based method (MW)
66.5383 43.2780 11.3814 16.8792 23.4133
66.5 43.2 11.3 16.8 23.4
19.2535 43.4524 11.1779 16.7581 23.2384
19.2 43.4 11.1 16.7 23.2
(4) Proposed method A This method is based on proposed algorithm as explained in Section 2. All transactions are allowed to transfer maximum possi-
ATC (MW)
19.2 43.2 11.1 16.7 23.2
ble power under all system constraints. Power allocation is very much fair, without any discrimination to any individual transaction. The results of four transactions system and seven transactions system are given in Tables 10 and 11 respectively.
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Y.R. Sood / Electrical Power and Energy Systems 32 (2010) 879–885 Table 2 Four simultaneous transactions.
Table 10 Comparison results of four transactions system.
Transactions
From bus no.
To bus no.
Size (MW)
T1 T2 T3 T4
14 24 16 30
27 22 28 25
11.0 28.5 16.0 25.0
Transactions
T1 T2 T3 T4 Total transfer
Transaction amount in MW which can be accommodated Hamoud’s method
Proposed method A
Proposed method B
Proposed method C
11.0 28.5 16.0 0.00 75.5
10.67 28.50 16.0 25.00 80.17
11.0 28.5 16.0 24.40 79.9
11.0 28.5 16.0 24.40 79.9
Table 3 Seven simultaneous transactions. transactions
From bus no.
To bus no.
Size (MW)
T1 T2 T3 T4 T5 T6 T7
10 3 17 12 14 18 15
27 22 28 27 9 6 25
10.0 21.0 18.0 16.0 12.0 19.0 5.0
Table 4 ATC and ATM of all individual transaction. Transactions
ATC of each transaction (MW)
ATM (MW)
T1 T2 T3 T4
29.6 30.0 24.8 15.6
18.6 1.5 8.8 9.4
Table 5 Results after accommodating transaction T1. Transactions
ATC of each transaction (MW)
ATM (MW)
T2 T3 T4
32.2 18.7 21.0
3.7 2.7 4.0
Table 6 Results after accommodating transactions T1 and T2. Transactions
ATC of each transaction (MW)
ATM (MW)
T3 T4
16.6 24.6
0.6 0.4
Table 11 Comparison results of seven transactions system. Transactions
T1 T2 T3 T4 T5 T6 T7 Total transfer
Transaction amount in MW which can be accommodated Hamoud’s Method
Proposed Method A
Proposed Method B
Proposed Method C
10.0 21.0 0.00 0.00 12.0 19.0 5.0 67.0
8.6 21.0 11.0 11.0 12.0 19.0 1.0 83.6
10.0 21.0 15.5 0.00 12.0 19.0 5.0 82.5
10.0 21.0 13.3 3.1 12.0 19.0 5.0 83.4
(5) Proposed method B This method is an extension of Hamoud’s method. In seven transactions system, T3 and T4 are not served at all as per Hamoud’s method. However we can extend this method further to serve transactions T3 and/or T4 partially. From Table 8, ATM of T3 and T4 both are negative. But ATM of T3 is more than T2. So first of all we can allow T3 partially up to 15.5 MW equal to its ATC. After accommodating T1, T2, T5, T6, T7 and T3 equal to 15.5 MW, the results of ATC and ATM are given in Table 9. Now ATC of T4 is zero so it cannot be served at all. Final results are given in Table 11. Similarly for four transactions system, as ATC for T4 is 24.4 MW. Hence this amount may be allowed to serve in T4. So it can be partially served. Final results are given in Table 10. (6) Proposed method C
Table 7 Results after accommodating transactions T1, T2 and T3. Transactions
ATC (MW)
ATM (MW)
T4
24.4
0.6
Table 8 Results after accommodating transactions (T1, T2, T5, T6 and T7).
This is a hybrid method, a combination of the proposed algorithm and Hamoud’s method. According to this method, the proposed algorithm is applied to those transactions, which are not served by Hamoud’s method. In seven transactions system T3 and T4 are not served by Hamoud’s method. So we allocate power to T3 and T4 optimally by the proposed algorithm. Results are given in Table 11. 4.3. Comparison of proposed methods and Hamoud’s method
Transactions
ATC (MW)
ATM (MW)
T3 T4
15.5 3.5
2.5 12.5
Table 9 Results after accommodating transactions T1, T2, T5, T6, T7 and T3 = 15.5 MW. Transactions
ATC (MW)
ATM (MW)
T4
0.0
16.0
In this section a comparison of all the methods applied above for the assessment of feasibility of simultaneous bilateral transactions has been presented. The results of four and seven transactions systems are summarized in Tables 10 and 11 respectively. For four transaction system total power transfer allowed by proposed method A is (80.17 MW) more than Hamoud’s method (75.5 MW). Similarly for seven transaction system, total power transfer allowed by proposed method A (83.6 MW) is more than Hamoud’s method (67.0 MW).
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Y.R. Sood / Electrical Power and Energy Systems 32 (2010) 879–885
For large number of transactions the Hamoud’s method becomes more complicated, where as proposed method A is easy to apply using any available optimization tool. In proposed method B, the transactions, which are not served by Hamoud’s methods, are partially served. In proposed method C, the transactions, which are not served by Hamoud’s methods, are partially served in an optimal manner. In the proposed method A all the transaction are given some share of total power transfer, where as in Hamoud’s methods some transactions are fully accommodated and others are not served at all. The distribution of power among individual transactions in the proposed method A is fully and for proposed method C is partially dependent on optimization process. The Hamoud’s method can be applied only if all the transactions are non-divisible. The proposed method A can be applied if all the transactions are divisible. If it is possible to make only a least possible number of transactions to be non-divisible then either of proposed method B or C can be applied depending upon requirement of wheeling generation-load pair.
Table 14 Proposed simultaneous bilateral transactions. Transactions
From bus no.
To bus no.
Size (MW)
T1 T2 T3 T4 T5 T6 T7
11 13 12 20 16 26 5
21 24 17 19 27 13 25
15.0 7.0 5.0 13.0 17.0 6.0 5.0
Table 15 Proposed multilateral transaction. Generations
Loads
Bus no.
Maximum (MW)
Bus no.
Maximum (MW)
3 5 4 – – Total
10.0 20.0 55.0 – – 85.0
7 8 12 21 30 Total
20.0 30.0 10.0 15.0 10.0 85.0
Table 16 Feasible simultaneous bilateral transactions.
4.4. Feasibility of multilateral transaction In a multilateral transaction there are some generating companies which want to supply power jointly to some distribution companies at different buses of the transmission system. The proposed algorithm (i.e. proposed method A) has been applied for the feasibility evaluation of the multilateral transaction of Table 12. The Hamoud’s method and proposed method B and C can not be applied for multilateral transactions. It has been determined that this transaction is not feasible. Hence minimum possible curtailment has been done with proposed algorithm explained in Section 2. So the results given in Table 12 correspond to feasible values of generation and load for this multilateral transaction. From the Table 13, it may be observed that load at bus 25 has been curtailed from 69.0 MW to 23.4616 MW. Similarly generation at bus 6 has been reduced from 57.0 MW to 11.4616 MW. All other generations and loads remain unaffected. However total generation of the feasible multilateral transaction is equal to total load.
transactions
From bus no.
To bus no.
Size allowed (MW)
T1 T2 T3 T4 T5 T6 T7
11 13 12 20 16 26 5
21 24 17 19 27 13 25
12.0256 7.0000 5.0000 13.0000 17.0000 6.0000 5.0000
Table 17 Feasible multilateral transaction. Generations
Loads
Bus no.
Maximum (MW)
Bus no.
Maximum (MW)
3 5 4 – – Total
0.0000 1.1275 53.2027 – – 54.3302
7 8 12 21 30 Total
20.0000 16.8416 10.0000 0.0000 7.4886 54.3302
4.5. Feasibility of simultaneous bilateral and multilateral transaction The proposed algorithm is so general that feasibility of any number of simultaneous bilateral as well as multilateral transacTable 12 Proposed multilateral transaction. Generations
Loads
Bus no.
Maximum (MW)
Bus no.
Maximum (MW)
3 14 6 Total
30.0 22.0 57.0 109.0
12 17 25 Total
23.0 17.0 69.0 109.0
Table 13 Feasible multilateral transaction. Generations
tions can easily be determined. Seven simultaneous bilateral (Table 14) and one multilateral transaction (Table 15) are proposed for the IEEE – 30-bus system These simultaneous proposed transactions have been analyzed by the proposed algorithm. They are found to be not feasible. So the proposed algorithm has suggested the minimum possible curtailments. After these curtailments, these simultaneous transactions as shown in Tables 16 and 17 are ready for schedule. From the result of this analysis it has been observed that bilateral transaction T1 has been changed from 15 MW to 12.0256 MW. In the multilateral transaction generation at all the points has been changed from the proposed values. The load at bus no. 8 has been changed from 30 MW to 16.8416 MW, where as load at bus no. 21 has been completely eliminated. But total load remains equal to total generation. The pool is supplying losses and transactions are charged for this purpose.
Loads
Bus no.
Allowed (MW)
Bus no.
Allowed (MW)
3 14 6 Total
30.0000 22.0000 11.4616 63.4616
12 17 25 Total
23.0000 17.0000 23.4616 63.4616
5. Conclusion In this paper a new optimization based algorithm has been proposed for assessment of feasibility of simultaneous bilateral and
Y.R. Sood / Electrical Power and Energy Systems 32 (2010) 879–885
multilateral wheeling transactions. The results are compared with the existing method. It has been observed that the proposed method is fair in assessment of feasibility. It is simple and efficient to apply even when there are large numbers of bilateral and multilateral transactions. This analysis provides the information that if all simultaneous transactions are not completely feasible, then how much minimum possible curtailment of size of the transactions has to be done in an optimal manner, in order to make them feasible. The proposed algorithm has also been applied to single bilateral transaction, simultaneous bilateral transactions, multilateral transaction as well as to a combination of simultaneous bilateral and multilateral transactions. This work is a useful contribution not only for Scheduling coordinators (SCs) for scheduling various firm transactions but also for independent power producers (IPPs), bulk load centers, gencos as well as for discos to plan transfer of power from one place to other in an optimal manner. This work will also be useful for power systems of those developing countries, which are not completely deregulated, but are moving towards deregulation. Acknowledgments The author gratefully acknowledges the valuable guidance and encouragement provided by Dr. N.P. Padhy and Dr. H.O. Gupta of IIT Roorkee (India) for this research work. References [1] Phichaisawat Sotdhipong, Song YH. Transmission pricing using improved sensitivity indices. In: IEEE power engineering society 2001 winter meeting, Columbus, Ohio (USA), January 28–February 1, 2001.
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[2] Ejebe Gabriel C, Waight James G, Santos-Nieto, Tinney William F. Fast calculation of linear available transfer capability. IEEE Trans Power Syst 2000;15(3):1112–6. [3] Gisin Boris S, Obessis Manos V, Mitsche James V. Practical methods for transfer limit analysis in the power industry deregulated environment. IEEE Trans Power Syst 2000;15(3):955–60. [4] Tuglie Enrico De, Dicorato Maria, Scala Massimo La, Scarpellini Pierangelo. A Static Optimization Approach to Assess Dynamic Available Transfer Capability. IEEE Trans Power Syst 2000;15(3):1069–76. [5] Ilic M, Galiana F, Fink L, Bose A, Mallet P, Othman H. Transmission capacity in power networks. Int J Electr Power Energy Syst 1998;20(2):99–110. [6] Hamoud G. Feasibility assessment of simultaneous bilateral transactions in a deregulated environment. IEEE Trans Power Syst 2000;15(1):22–6. [7] Sood Yog Raj, Padhy Narayana Prasad, Gupta HO. Wheeling of power under deregulated environment of power industry – a bibliographical survey. IEEE Trans Power Syst 2002;17(3):870–8. [8] Ou Y, Singh C. Assessment of available transfer capability and margins. IEEE Trans Power Syst 2002;17(2):463–8. [9] Christie RD, Wollenberg BF, Wangensteen I. Transmission management in the deregulated environment. IEEE Proc 2000;88:170–95. [10] Khairuddin AB, Ahmed SS, Mustafa MW, Zin AAM, Ahmad H. A novel method for ATC computations in a large-scale power system. IEEE Trans Power Syst 2004;19(2):1150–8. [11] Sun Rong-fu, Fan Yue, Song Yong-hua, Sun Yuan-zhang. Development and application of software for ATC calculation. In: International conference on power system technology, 2006 (PowerCon 2006), Chongqing, China, October 22–26, 2006. [12] Stahlhut JW, Heydt GT. Stochastic-algebraic calculation of available transfer capability. IEEE Trans Power Syst 2007;22(2):616–23. [13] Berizzi A, Bovo C, Delfanti M, Merlo M, Pasquadibisceglie MS. A Monte Carlo approach for TTC evaluation. IEEE Trans Power Syst 2007;22(2):735–43. [14] Sood Yog Raj. Evolutionary programming based optimal power flow and its validation for deregulated power system analysis. Int J Electr Power Energy Syst 2007;29(1):65–75. [15] Alsac O, Stott B. Optimal load flow with steady state security. IEEE Trans Power Apparat Syst 1974;PAS-93(3):745–51. [16] Sood, YR. Wheeling of power under deregulated environment of power system, PhD thesis, IIT, Roorkee, India; 2003.
Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Feasibility assessment of simultaneous bilateral and multilateral transactions Yog Raj Sood Department of Electrical Engineering, National Institute of Technology, Hamirpur (H.P.), India
a r t i c l e
i n f o
Article history: Received 4 October 2008 Received in revised form 5 December 2009 Accepted 28 January 2010
Keywords: Transfer capability Feasibility Simultaneous bilateral transactions Multilateral transaction Deregulation ATC
a b s t r a c t The main aim in this paper is to develop algorithm for assessment of the feasibility of simultaneous bilateral and multilateral transactions and if they are not feasible then to find out the minimum amount of transacted power to be curtailed in order to make them feasible. This analysis will be a great help for the generations-loads pairs to decide whether to withdraw the unfeasible transaction completely or to make it feasible by reducing its size optimally. The proposed algorithm can also be used for determining the transfer capability and hence feasibility of a single bilateral transaction at a time. In addition to above algorithm an efficient, repeated Newton–Raphson power flow based algorithm is also developed to determine transfer capability and hence feasibility for single bilateral transaction. The results of the proposed algorithm have been compared with a method proposed by Hamoud in his paper [6]. In this paper, based on the proposed algorithm and with the extension of Hamoud’s method, different feasibility evaluation procedures for simultaneous bilateral and multilateral transactions are suggested, analyzed and applied. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction All the transactions need to be evaluated ahead of their scheduling time to check their feasibility with regard to the system conditions at the time of scheduling. ISO would have to honor and execute only those proposed transactions as far as the system design and operating conditions permit. So before we go for cost analysis, it is important to analyze the feasibility of all proposed firm transactions for a particular transmission network under prevailing system constraints. Only after passing the feasibility test the proposed firm transactions are scheduled for dispatch. This analysis will be required not only by ISO, but also by the end users of the systems to make proper decisions regarding the generations and loads to be connected at different buses of the power system. A transaction is deemed to be feasible if it can be accommodated without violating any of the system operating constraints such as equipment ratings, transmission interface limits, voltage limits etc. The feasibility of a single bilateral transaction can easily be determined from the available transfer capability (ATC) of the network between the buses where a transaction power enters and leaves the network. ATC is a measure of the transfer capability remaining in the physical transmission network for future commercial activity over and above already committed uses [1]. Transfer capability evaluation is a very wide area of research. Extensive work has already been carried out in this direction and more research is in progress in this field in order to increase its accuracy considering various factors and margins [1–4]. The transfer capability has been defined in the literature [1,5,6] in many ways E-mail address: [email protected] 0142-0615/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2010.01.025
depending upon the requirements and accuracy required for a particular analysis. It may be defined as amount of power, incremental above normal base power transfers that can be transferred over the transmission network, with all facility loading are within normal ratings and all voltages are within normal limits [5]. The literature survey [7] reveals that most of the work has been done related with determination of ATC. Ou and Singh [8] have presented a probabilistic based method to assess various factors and procedures to incorporate them into ATC. Christie et al. [9] have suggested power transfer distribution factor and line outage distribution factor for determination of transfer capability from one bus to another bus of the power system. But this method provided only the approximate results. The Information Technology applications for determination of ATC have also been given in some research papers [10]. Application software [11] is also available for ATC calculations. To render the ATC as a more realistic measure of transmission availability, a stochastic calculation of ATC has also been explained in the literature [12,13]. But most of calculation procedures reported in the literature for ATC will be useful for feasibility assessment of only bilateral transactions. But in this paper methods are proposed for feasibility assessment of simultaneous bilateral as well as simultaneous multilateral transactions. Available transfer capability is required to be posted on Open Access Same-time Information System (OASIS). The generationload pair can make reservation for the bilateral transaction whose size should be less than ATC between the points where transaction power enters and leaves the system. After including one transaction in the system, ATC between all the buses changes and reevaluated. Same procedure is repeated for second transaction. Similarly all the feasible bilateral transactions are added to the system one
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by one. But this procedure cannot be applied directly to simultaneous bilateral and multilateral transactions. Because the transfer capability of a transaction in a group of simultaneous transactions will depend upon the order in which the transactions are considered to be added to the transmission network.
where 8 net > < P i ðV; /Þ P i g gðV;/Þ ¼ Q i ðV; /Þ Q net i g > : P m ðV;/Þ P net m g
For each PQ bus i For each PV bus m;not including ref: bus: ð8Þ
2. Proposed algorithm for assessment of feasibility Generalized formulation of the proposed algorithm is given in this section. This algorithm can be used directly to determine the feasibility of simultaneous bilateral and multilateral transactions. In case these transactions turned out to be not feasible, then this algorithm provides an answer to the question that how much minimum amount of power has to be curtailed, in order to make them feasible.
Let there be nbt number of bilateral transactions and a transaction t is from bus i to bus j. t Let Pg ti be generation (in addition to base case) at bus i and Pdj is load (in addition to base case) at bus j for a transaction t. Base case means already committed generations, loads and transactions on transmission network. Let Tst be size of each proposed bilateral transaction t. t So Tst is equal to Pdj which is also equal to Pg ti ; considering transmission losses for the transaction being provided by the utility or pool. Let there are nmt number of groups of multilateral transactions. Let PMTk be the size of k th group of multilateral transaction. Let there be ngk number of generation points and ndk number of demand points for a group k. It may be noted that ‘ngk’ may or may not equal to ndk. Let Pgmki be the generation at a generation bus i of multilateral transaction k. k Let Pdmi be the load at a load bus i of multilateral transaction k. The objective is to maximize total power transfer PT. nbt X
Tst þ
nmt X
t¼1
PMT k
ð1Þ
k¼1
Subject to the following constraints. The bilateral transaction constraint t
Pg ti ¼ Pdj
for all bilateral transactions
for all bilateral transactions
ð3Þ
where, Tstm is maximum proposed size of transaction t. Multilateral transaction constraints ndk X
k
Pdmj ¼
ngk X
Pgmki ¼ PMT k
ð4Þ
i¼1
j¼1
Multilateral transaction generation and load constraints
Pgmki 6 Pgmpki k
k
Pdmj 6 Pdmpj
ð9Þ
Qg max i
where and are respectively minimum and maximum value of reactive power generation at PV bus i. The inequality constraint on voltage magnitude V of each PQ bus
V min 6 V i 6 V max i i
ð10Þ
where V min and V max are respectively minimum and maximum volti i age at bus i. The inequality constraint on phase angle /i of voltage at all the buses i
/min 6 /i 6 /max i i /min i
ð11Þ
/max i
where and are respectively minimum and maximum allowed value of voltage phase angle at bus i. Power limit on transmission line max
MVAfij 6 MVAf ij
ð12Þ
max
where MVAf ij is the maximum rating of transmission line connecting bus i and j. Some of these constraints are based on the anticipation of the transmission contingencies and may be due to thermal, voltage and stability problems. This optimization problem has been solved by using optimization tools explained in reference [14]. 3. Assessment of available transfer capability
ð2Þ
Bilateral transaction size constraints
Tst 6 Tstm
Qg min 6 Qg i 6 Qg max i i Qg min i
2.1. Mathematical Formulation
PT ¼
where Pi and Qi are respectively calculated real and reactive power and Q net are respectively specified real and reactive for PQ bus i. P net i i power for PQ bus i. Pm and Pnet m are respectively calculated and specified real power for PV bus m. V and / are voltage magnitude and phase angles of different buses. The inequality constraint on reactive power generation Qgi at PV buses
ð5Þ ð6Þ
The feasibility of a single bilateral transaction can easily be determined from the ATC of the transmission network between the buses, where the transaction power enters and leaves the network. Hamoud [6] has also used the same ATC for determination of feasibility of simultaneous bilateral transactions, without considering various margins like transmission reliability margin, capacity benefit margin etc. for ATC evaluation. In that case ATC is approximately equal to total transfer capability, which is a key component for ATC assessment. In order to compare the results of the proposed algorithm with the method proposed by Hamoud and for extension of his method, these margins are not considered in this analysis. In this paper two independent methods have been proposed for assessment of ATC, first method is based on optimization algorithm proposed in above Section 2 and second is based on Newton–Raphson repeated power flow (RPF) method.
Pgmpki
where, is the proposed generation at generation point i of k group k of multilateral transaction. Pdmpj is the proposed load at load point j of group k of multilateral transaction. The power flow equation of the power network
gðV; /Þ ¼ 0
ð7Þ
3.1. By proposed algorithm The proposed algorithm described in Section 2 has been used for assessment of available transfer capability for single bilateral transaction by putting number of transaction nbt = 1, number of
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multilateral transactions nmt = 0, and taking arbitrary very high size of the transaction. All system constraints are considered, the same process is repeated for all selected contingency cases. Minimum of ATC level in all cases will be true ATC. 3.2. By repeated power flow (RPF) method Let IL is a scalar parameter representing the increase in the load as well as generation above base case. IL = 0 corresponds to no transfer (base case) and IL = ILmax corresponds to maximum transfer. IL is to be maximized by giving small increments DP in steps, subject to all transmission network constraints mentioned in Eqs. (7)–(12). ATC between any two buses of the network is the maximum value of IL satisfying all system constraints. The same process is repeated for all selected contingency cases. Minimum of ATC level in all these cases will be true ATC. The flow chart for this method for assessment of ATC from each bus to another buses of the power transmission network is shown in Fig. 1. 4. Application of proposed algorithm The proposed algorithm as explained above in Section 2, is applied to IEEE 30-bus test system. Data and single line diagram of this system is given in reference [15,16]. For simplicity of analysis we have considered only one contingency in this study i.e. outage of generator G3 at bus no. 5. However more contingencies cases can also be considered. 4.1. Feasibility of single bilateral transactions A bilateral transaction will be feasible, if it is less than or equal to available transfer capability of the network between the buses where the transaction power enters and leave the network. Table 1 shows the ATC levels calculated for single bilateral transactions by the proposed optimization method as well as by the repeated power flow (RPF) method in normal as well as in contingency case. From Table 1 it is very much clear that ATC calculated for single bilateral transaction by proposed method and RPF methods under both normal as well outage case are very much consistent. This proves the validity of the proposed method. A bilateral transaction from bus 3 to bus 10 under normal condition of the network will be feasible if it is less than or equal to 66.5383 MW. Otherwise it is unfeasible. After adding a feasibility transaction to the system. The ATC is again evaluated and hence feasibility of second transaction to be added to the systems is assessed. Same procedure is repeated for the remaining transactions. So the feasibility of a particular transaction in a group of bilateral transactions, will depend upon the order at which these transactions are added to the system. So this method can not be directly applied for feasibility assessment of simultaneous bilateral transactions and also for multilateral transactions. 4.2. Feasibility assessment of simultaneous bilateral transactions The feasibility of simultaneous bilateral transactions is determined by a method proposed by Hamoud [6] and also by the proposed methods. Two different transactions systems are considered (1) Four simultaneous wheeling transactions system In this system, four transactions shown in Table 2 are to be simultaneously applied to transmission network. It is required to find their feasibility.
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Case 1: normal case-all transmission elements in service All the transactions are added to the system. All system constraints are checked and found to be within limits. Hence it is concluded that all these transactions are feasible for their simultaneous application to the system. Case 2: contingency case-generator at bus 5 is out of service In this case generation at bus 5 is zero. The generations at other generator buses were adjusted by optimal power flow, before the application of these transactions. After simultaneous application of these four transactions, it has been observed that some of the system constraints are violated. Hence they are not feasible. Now it is desired to find out, how to serve these transactions in an optimal manner, so that maximum power can be transferred through these transactions. (2) Seven simultaneous wheeling transactions system In this system, seven transactions shown in Table 3 are to be simultaneously applied to transmission network. It is required to find their feasibility. All the transactions are added simultaneously to the system under normal conditions and system constraints are checked. It has been observed that some of the constraints are violated. Hence it is concluded that these seven simultaneous bilateral transactions system is not feasible. So it is required to find the optimal way by which these transactions may be served with minimum possible curtailment. (3) Determination of Feasibility by Hamoud’s method Hamoud [6] has proposed a method for determination of feasibility for a group of simultaneous bilateral transactions based on ATC of individual bilateral transactions. He has used a new term Available Transmission Margin (ATM) that is difference between the computed ATC and size of the transaction.
4.2.1. Application to four simultaneous transactions system Step by step procedure of calculations is illustrated below. Step1: ATC and ATM of each individual transaction are determined, the results are shown in Table 4. Step2: From Table 4, it is clear that transaction T1 has maximum ATM. So transaction T1 is accommodated first and results of ATC and ATM are shown in Table 5. Step3: In Table 5, transaction T2 has maximum ATM, so now accommodate T2 also. It has been observed that both T1 and T2 can be accommodated. The results after accommodating T1 and T2 are shown in Table 6. Step4: In Table 6, T3 has maximum ATM. So results after accommodating T3 also are given in Table 7. Since ATM of T4 is negative, so this transaction cannot be accommodated. Hence it is not feasible. The final results are given in Table 10.
4.2.2. Application to seven simultaneous transactions system The same steps are followed as illustrated for four transactions system. Results of the final step are given in Table 8. Since ATM for T3 and T4 is negative, so these transactions can not be accommodated without violating transmission system constraints. The final results are given in Table 11.
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Fig. 1. Flow chart for determination of ATC by RPF method.
Table 1 ATC Levels and ATC values. Transactions
T1 T2 T3 T4 T5
From bus no.
To bus no.
3 20 13 14 5
10 12 30 24 25
Normal case
Contingency case
ATC level by proposed optimization based method (MW)
ATC level by RPF based method (MW)
ATC level by proposed optimization based method (MW)
ATC level by RPF based method (MW)
66.5383 43.2780 11.3814 16.8792 23.4133
66.5 43.2 11.3 16.8 23.4
19.2535 43.4524 11.1779 16.7581 23.2384
19.2 43.4 11.1 16.7 23.2
(4) Proposed method A This method is based on proposed algorithm as explained in Section 2. All transactions are allowed to transfer maximum possi-
ATC (MW)
19.2 43.2 11.1 16.7 23.2
ble power under all system constraints. Power allocation is very much fair, without any discrimination to any individual transaction. The results of four transactions system and seven transactions system are given in Tables 10 and 11 respectively.
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Y.R. Sood / Electrical Power and Energy Systems 32 (2010) 879–885 Table 2 Four simultaneous transactions.
Table 10 Comparison results of four transactions system.
Transactions
From bus no.
To bus no.
Size (MW)
T1 T2 T3 T4
14 24 16 30
27 22 28 25
11.0 28.5 16.0 25.0
Transactions
T1 T2 T3 T4 Total transfer
Transaction amount in MW which can be accommodated Hamoud’s method
Proposed method A
Proposed method B
Proposed method C
11.0 28.5 16.0 0.00 75.5
10.67 28.50 16.0 25.00 80.17
11.0 28.5 16.0 24.40 79.9
11.0 28.5 16.0 24.40 79.9
Table 3 Seven simultaneous transactions. transactions
From bus no.
To bus no.
Size (MW)
T1 T2 T3 T4 T5 T6 T7
10 3 17 12 14 18 15
27 22 28 27 9 6 25
10.0 21.0 18.0 16.0 12.0 19.0 5.0
Table 4 ATC and ATM of all individual transaction. Transactions
ATC of each transaction (MW)
ATM (MW)
T1 T2 T3 T4
29.6 30.0 24.8 15.6
18.6 1.5 8.8 9.4
Table 5 Results after accommodating transaction T1. Transactions
ATC of each transaction (MW)
ATM (MW)
T2 T3 T4
32.2 18.7 21.0
3.7 2.7 4.0
Table 6 Results after accommodating transactions T1 and T2. Transactions
ATC of each transaction (MW)
ATM (MW)
T3 T4
16.6 24.6
0.6 0.4
Table 11 Comparison results of seven transactions system. Transactions
T1 T2 T3 T4 T5 T6 T7 Total transfer
Transaction amount in MW which can be accommodated Hamoud’s Method
Proposed Method A
Proposed Method B
Proposed Method C
10.0 21.0 0.00 0.00 12.0 19.0 5.0 67.0
8.6 21.0 11.0 11.0 12.0 19.0 1.0 83.6
10.0 21.0 15.5 0.00 12.0 19.0 5.0 82.5
10.0 21.0 13.3 3.1 12.0 19.0 5.0 83.4
(5) Proposed method B This method is an extension of Hamoud’s method. In seven transactions system, T3 and T4 are not served at all as per Hamoud’s method. However we can extend this method further to serve transactions T3 and/or T4 partially. From Table 8, ATM of T3 and T4 both are negative. But ATM of T3 is more than T2. So first of all we can allow T3 partially up to 15.5 MW equal to its ATC. After accommodating T1, T2, T5, T6, T7 and T3 equal to 15.5 MW, the results of ATC and ATM are given in Table 9. Now ATC of T4 is zero so it cannot be served at all. Final results are given in Table 11. Similarly for four transactions system, as ATC for T4 is 24.4 MW. Hence this amount may be allowed to serve in T4. So it can be partially served. Final results are given in Table 10. (6) Proposed method C
Table 7 Results after accommodating transactions T1, T2 and T3. Transactions
ATC (MW)
ATM (MW)
T4
24.4
0.6
Table 8 Results after accommodating transactions (T1, T2, T5, T6 and T7).
This is a hybrid method, a combination of the proposed algorithm and Hamoud’s method. According to this method, the proposed algorithm is applied to those transactions, which are not served by Hamoud’s method. In seven transactions system T3 and T4 are not served by Hamoud’s method. So we allocate power to T3 and T4 optimally by the proposed algorithm. Results are given in Table 11. 4.3. Comparison of proposed methods and Hamoud’s method
Transactions
ATC (MW)
ATM (MW)
T3 T4
15.5 3.5
2.5 12.5
Table 9 Results after accommodating transactions T1, T2, T5, T6, T7 and T3 = 15.5 MW. Transactions
ATC (MW)
ATM (MW)
T4
0.0
16.0
In this section a comparison of all the methods applied above for the assessment of feasibility of simultaneous bilateral transactions has been presented. The results of four and seven transactions systems are summarized in Tables 10 and 11 respectively. For four transaction system total power transfer allowed by proposed method A is (80.17 MW) more than Hamoud’s method (75.5 MW). Similarly for seven transaction system, total power transfer allowed by proposed method A (83.6 MW) is more than Hamoud’s method (67.0 MW).
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For large number of transactions the Hamoud’s method becomes more complicated, where as proposed method A is easy to apply using any available optimization tool. In proposed method B, the transactions, which are not served by Hamoud’s methods, are partially served. In proposed method C, the transactions, which are not served by Hamoud’s methods, are partially served in an optimal manner. In the proposed method A all the transaction are given some share of total power transfer, where as in Hamoud’s methods some transactions are fully accommodated and others are not served at all. The distribution of power among individual transactions in the proposed method A is fully and for proposed method C is partially dependent on optimization process. The Hamoud’s method can be applied only if all the transactions are non-divisible. The proposed method A can be applied if all the transactions are divisible. If it is possible to make only a least possible number of transactions to be non-divisible then either of proposed method B or C can be applied depending upon requirement of wheeling generation-load pair.
Table 14 Proposed simultaneous bilateral transactions. Transactions
From bus no.
To bus no.
Size (MW)
T1 T2 T3 T4 T5 T6 T7
11 13 12 20 16 26 5
21 24 17 19 27 13 25
15.0 7.0 5.0 13.0 17.0 6.0 5.0
Table 15 Proposed multilateral transaction. Generations
Loads
Bus no.
Maximum (MW)
Bus no.
Maximum (MW)
3 5 4 – – Total
10.0 20.0 55.0 – – 85.0
7 8 12 21 30 Total
20.0 30.0 10.0 15.0 10.0 85.0
Table 16 Feasible simultaneous bilateral transactions.
4.4. Feasibility of multilateral transaction In a multilateral transaction there are some generating companies which want to supply power jointly to some distribution companies at different buses of the transmission system. The proposed algorithm (i.e. proposed method A) has been applied for the feasibility evaluation of the multilateral transaction of Table 12. The Hamoud’s method and proposed method B and C can not be applied for multilateral transactions. It has been determined that this transaction is not feasible. Hence minimum possible curtailment has been done with proposed algorithm explained in Section 2. So the results given in Table 12 correspond to feasible values of generation and load for this multilateral transaction. From the Table 13, it may be observed that load at bus 25 has been curtailed from 69.0 MW to 23.4616 MW. Similarly generation at bus 6 has been reduced from 57.0 MW to 11.4616 MW. All other generations and loads remain unaffected. However total generation of the feasible multilateral transaction is equal to total load.
transactions
From bus no.
To bus no.
Size allowed (MW)
T1 T2 T3 T4 T5 T6 T7
11 13 12 20 16 26 5
21 24 17 19 27 13 25
12.0256 7.0000 5.0000 13.0000 17.0000 6.0000 5.0000
Table 17 Feasible multilateral transaction. Generations
Loads
Bus no.
Maximum (MW)
Bus no.
Maximum (MW)
3 5 4 – – Total
0.0000 1.1275 53.2027 – – 54.3302
7 8 12 21 30 Total
20.0000 16.8416 10.0000 0.0000 7.4886 54.3302
4.5. Feasibility of simultaneous bilateral and multilateral transaction The proposed algorithm is so general that feasibility of any number of simultaneous bilateral as well as multilateral transacTable 12 Proposed multilateral transaction. Generations
Loads
Bus no.
Maximum (MW)
Bus no.
Maximum (MW)
3 14 6 Total
30.0 22.0 57.0 109.0
12 17 25 Total
23.0 17.0 69.0 109.0
Table 13 Feasible multilateral transaction. Generations
tions can easily be determined. Seven simultaneous bilateral (Table 14) and one multilateral transaction (Table 15) are proposed for the IEEE – 30-bus system These simultaneous proposed transactions have been analyzed by the proposed algorithm. They are found to be not feasible. So the proposed algorithm has suggested the minimum possible curtailments. After these curtailments, these simultaneous transactions as shown in Tables 16 and 17 are ready for schedule. From the result of this analysis it has been observed that bilateral transaction T1 has been changed from 15 MW to 12.0256 MW. In the multilateral transaction generation at all the points has been changed from the proposed values. The load at bus no. 8 has been changed from 30 MW to 16.8416 MW, where as load at bus no. 21 has been completely eliminated. But total load remains equal to total generation. The pool is supplying losses and transactions are charged for this purpose.
Loads
Bus no.
Allowed (MW)
Bus no.
Allowed (MW)
3 14 6 Total
30.0000 22.0000 11.4616 63.4616
12 17 25 Total
23.0000 17.0000 23.4616 63.4616
5. Conclusion In this paper a new optimization based algorithm has been proposed for assessment of feasibility of simultaneous bilateral and
Y.R. Sood / Electrical Power and Energy Systems 32 (2010) 879–885
multilateral wheeling transactions. The results are compared with the existing method. It has been observed that the proposed method is fair in assessment of feasibility. It is simple and efficient to apply even when there are large numbers of bilateral and multilateral transactions. This analysis provides the information that if all simultaneous transactions are not completely feasible, then how much minimum possible curtailment of size of the transactions has to be done in an optimal manner, in order to make them feasible. The proposed algorithm has also been applied to single bilateral transaction, simultaneous bilateral transactions, multilateral transaction as well as to a combination of simultaneous bilateral and multilateral transactions. This work is a useful contribution not only for Scheduling coordinators (SCs) for scheduling various firm transactions but also for independent power producers (IPPs), bulk load centers, gencos as well as for discos to plan transfer of power from one place to other in an optimal manner. This work will also be useful for power systems of those developing countries, which are not completely deregulated, but are moving towards deregulation. Acknowledgments The author gratefully acknowledges the valuable guidance and encouragement provided by Dr. N.P. Padhy and Dr. H.O. Gupta of IIT Roorkee (India) for this research work. References [1] Phichaisawat Sotdhipong, Song YH. Transmission pricing using improved sensitivity indices. In: IEEE power engineering society 2001 winter meeting, Columbus, Ohio (USA), January 28–February 1, 2001.
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