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Optimized 'power flow tracing based contract path method' for transmission pricing.

INTRODUCTION

Wheeling is defined as the "use of transmission and/or distribution facilities of a system to transmit power of and for another entity or entities". It may also be defined as the "use of some party's transmission system(s) for the benefit of the other parties". More precisely, wheeling refers to the "transmission of real and reactive powers from a seller to a buyer through the transmission network of a third party" (Wenjuan Zhang, Fangxing Li and Leon M. Tolbert, 2008).

In the regulated electric power market, wheeling transactions have accounted for a minor portion of the overall transmission network capacity usage. However, the wheeling company in the deregulated market plays a vital role due to its involvement in the wheeling charge evaluation (R. D. Christie, B. F. Wollenberg and I. Wangensteen, 2000).

The determination of transmission pricing for wheeling transactions is due to re-dispatching of generators and transmission losses. The transmission pricing scheme must be implemented easily, recovery both capital cost and operating cost, provide equal opportunity among all users, offer a simple and understandable price structure and encourage towards efficient usage and investment (Pavlos S. Georgilakis, George A. Orfanos and Nikos D. Hatziargyriou, 2014).

Wheeling Cost Methodologies:

Different methods proposed to evaluate the cost of wheeling transactions are broadly classified as incremental or marginal cost methods and embedded cost methods (G Jain, K Singh and D.K. Palwalia, 2012).

Incremental wheeling cost methodologies:

Incremental wheeling cost methods involve Short Run Marginal Cost (SRMC) method and Long Run Incremental Cost (LRIC) method (Syarifuddin Nojeng, Mohammad Yusri Hassan, Dalila Mat Said, Md. Pauzi Abdullah and Faridah Hussin, 2014).

SRMC pricing of transmission service is highly volatile. Also it fails to recover the overall incurred network costs and it provides wrong economic signals to both owners and customers of transmission company. On the other hand, LRIC pricing of transmission service involves more assumptions about the costs and scenarios of expansion (M. W. Mustafa and H. Shareef, 2006).

Embedded wheeling cost methodologies:

Alternate to the marginal cost methods due to its drawbacks, embedded wheeling cost methods are widely used. These methods offer several benefits such as fair to all parties and provision of an adequate remuneration to transmission systems.

The embedded cost methods are classified as Postage stamp method, Contract path method, MW-Mile methods and Boundary flow methods (Ferdinand Gubina, David G. and Ivo B., 2000). In this paper, Contract path method is presented.

Contract path method:

In the contract path method, transmission service provider and the customer agree on a fictitious path called "contract path" for the transmission service. However the selection of the contract path is not usually based on the power flow study to identify the transmission facilities actually involved in the transaction. In other words, the contract path interconnects the points of injection and receipt virtually without power flow studies. The path chosen must have "sufficient unused capacity" to carry out the amount of power to be transported (D. Kirschen, R. AlIan and G. Strbac, 1997).

Once the contract path is determined, all or a part of the transmission cost related to the specified path is assigned to the transaction and wheeling charges are calculated according to the equation:

W[C.sub.t] = [summation over (k)] W[C.sub.k]/[MD.sub.system] [P.sub.t]

where

[MD.sub.system] = System maximum demand in MW

[P.sub.t] = Power transacted for transaction t in MW

W[C.sub.t] = Wheeling cost for transaction t in Rs. / hr.

W[C.sub.k] = Wheeling cost of contract path k in Rs. / hr.

This method is also simple like postage stamp method and provides a distinct way of settling financial liabilities to influenced parties along the contract path (J. Bialek, 1996). However, it overlooks the possibility of outages occurring in the contract path, which would impose additional power flows on neighboring systems which are not parties of the contract path.

Bialek's power flow tracing methodology:

Bialek's power flow tracing methodology determines each generator's contribution based on the calculation of topological distribution factors using either the upstream looking algorithm or the downstream looking algorithm (Oana Pop, Stefan Kilyeni, Petru Andea, Constantin Barbulescu and Cristian Craciun, 2010).

The Bialek's tracing procedure is as follows:

B = (mxn) sized matrix called 'Incidence matrix' with its elements values equal to 1 when power flows from 'm' bus to 'n' bus, -1 when power flows from 'n' bus to 'm' bus and 0 when no power flows between 'm' bus and 'n' bus.

[B.sub.d] = (mxn) sized matrix derived from incidence matrix, consisting of 1's and other element values equal to zero.

[B.sub.u] = (mxn) sized matrix derived from incidence matrix, consisting of -1's and other elements values equal to zero.

[F.sup.d] = -[B.sup.T.sub.d] x diag(F) x [B.sub.u] (1)

[A.sub.d] = I + [B.sup.T.sub.d] x diag(F) [B.sub.u] x diag([P.sup.-1]) (2)

[A.sub.u] = I + [B.sup.T.sub.u] x diag(F) x [B.sub.d] x diag([P.sup.-1]) (3)

Equation (1) results in an (nxn) sized matrix with the (i, j) element indicating line flow from ith bus to jth bus. Equations (2) and (3) provide two nonsingular matrices, each of size (nxn) [M.Y. Hassan, N.H. Radzi , M.P Abdullah, F. Hussin and M.S. Majid, 2011].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Equations (4) and (5) can be used to determine the transmission network usage for line power flows and load demand contributions due to individual generators (B. Saravanan, Siddharth Das, Surbhi Sikri and D. P. Kothari, 2013).

Proposed algorithm for optimal power flow:

A technique similar to heuristic technique is employed to achieve the reduction of wheeling cost. The reduction of wheeling cost of some generators would raise that of other generators, to maintain meeting the load.

The stepwise procedure in the technique proposed is as follows:

1. Assuming N = 0, solve a normal optimal power flow with all limits in place.

2. Save the solution as the current best.

3. Increment N.

4. Using the best solution from previous stage as the base case for current stage, form a candidate list of generators with minimum generation limits binding.

5. If there are no candidates, return the current best solution as the final solution.

6. If there are candidates, for each generator on the candidate list, solve an optimal power flow to find the total system cost with this generator shut down. If the total system cost is reduced further, replace the current best solution with the solution obtained. If any of the candidate solutions produces an improvement, return to step 3.

Application example:

A six-bus eleven-line bus system whose single-line diagram is shown in Fig. 1 is considered for the effect of improvement of generation dispatch on the wheeling cost to be paid by each generator for utilizing the contract path in the wheeling network for power transfer. The bus data, generator data and the line data of the bus system considered are presented in Tables numbered 1, 2 and 3 respectively (Appendix-'A').

[FIGURE 1 OMITTED]

The wheeling cost is calculated by contract path method excluding and including the algorithm proposed for OPF to reduce the wheeling cost, with buyers at buses-4, 5 and 6 demanding same amount of power from a group of sellers available at buses-1, 2 and 3 respectively. The generators available at the buses-1, 2 and 3 are assumed to have the same lower and upper reactive power generation limits of -150 MVAr and 150 MVAr respectively.

Table 4 shows the transmission line numbers in the contract paths selected by the buyers in the agreements assumed to be made with different sellers.

Tables numbered 5 and 6 present the 'active' and 'reactive' line power flows as well as 'active' and 'reactive' line power losses excluding and including the improvement of generation dispatch respectively.

Tables numbered 7 and 8 present the contribution of each generator to the bus power demands including line power losses and the contribution of each generator to the line power flows, excluding and including the OPF technique proposed respectively.

Discussion:

It can be observed that the inclusion of generation dispatch improvement reduces the gross 'active' line power loss magnitude. It can be perceived that the generation dispatch improvement enclosure reduces the total 'reactive' line power loss magnitude. It can be found that the relaxation of some generators from power generation due to generation dispatch improvement leads to the overloading of few generators when compared to their loading under the case of exclusion of power generation dispatch. It can be observed that the relaxation of some generators from 'loss' power generation due to generation dispatch improvement leads to the extra 'loss' power generation of few generators when compared to their loading prior to power generation dispatch.

Conclusions:

The 'contract path' methodology can be used to determine the wheeling cost for power trading between the seller and buyer only when the demanded power flows through the electrical path contracted between both. However, majority of the transacted power may actually flow outside the contracted path and hence the actual operating environment may be ignored thereby providing incorrect economic signals to the transmission system users.

Table 9 presents the generator-wise wheeling costs determined by contract path methodology for bus-wise load demands. Table 10 presents the same with all lines assumed to be in the contract.
Nomenclature:

no.                           number
hr.                           hour
p.u.                          per unit
V                             Bus voltage magnitude in p.u.
[delta]                       Bus voltage phase angle in degrees.
[V.sub.l] and [V.sub.u]       Lower and upper limits of V in p.u.
[P.sub.d] and [Q.sub.d]       Demanded active & reactive powers in MW
                                and MVAr.
[P.sub.g] and [Q.sub.g]       Generated active and reactive powers in
                                MW and MVAr.
[P.sub.1] and [P.sub.u]       Lower and upper limits of Pg in MW.
[gamma], [beta] and [alpha]   Generator fuel cost coefficients in
                                Rs./MW2, Rs./MW & Rs.
p and q                       Sending-end and receiving-end bus no.s.
R                             Line resistance in p.u.
X                             Line inductive reactance in p.u.
B                             Half total line charging susceptance in
                                p.u.
l                             Line length in km.
P_pq and P_qp                 Active power flow from pth bus to qth
                                bus and vice versa in MW.
Q_pq and Q_qp                 Reactive power flow from pth bus to qth
                                bus and vice versa in MVAr.
P_L and Q_L                   Active and reactive power losses in MW
                                and MVAr.
Rs.                           Rupees
N                             Stage no. with same no. of generators
                                shut down.


ARTICLE INFO

Article history:

Received 23 July 2015

Accepted 28 August 2015

Available online 25 September 2015

Appendix- 'A '

The system data of the six-bus eleven-line system considered is as follows:
Table 1: Bus data.

Bus no.   Bus type    V     [delta]   [V.sub.1]   [V.sub.u]

1          Slack     1.05      0        0.94       1.06
2            PV      1.05      0        0.94       1.06
3            PV      1.07      0        0.94       1.06
4            PQ      1.00      0        0.94       1.06
5            PQ      1.00      0        0.94       1.06
6            PQ      1.00      0        0.94       1.06

Bus no.   [P.sub.d]   [Q.sub.d]

1           0            0
2           0            0
3           0            0
4           70           70
5           70           70
6           70           70

Table 2: Generator data.

PV bus no.   [P.sub.g]   [P.sub.1]   [P.sub.u]   [Q.sub.g]   [gamma]

1                0          10          85           0        0.008
2               50          10          80           0        0.009
3               60          10          70           0        0.007

PV bus no.   [beta]   [alpha]

1             7.0       200
2             6.3       180
3             6.8       140

Table 3: Line data.

Line no.   p   q    R      X       B      l

1          1   2   0.10   0.20   0.020   578
2          1   4   0.05   0.20   0.020   289
3          1   5   0.08   0.30   0.030   463
4          2   3   0.05   0.25   0.030   289
5          2   4   0.05   0.10   0.010   289
6          2   5   0.10   0.30   0.020   578
7          2   6   0.07   0.20   0.025   405
8          3   5   0.12   0.26   0.025   694
9          3   6   0.02   0.10   0.010   116
10         4   5   0.20   0.40   0.040   1156
11         5   6   0.10   0.30   0.030   578


REFERENCES

Wenjuan Zhang, Fangxing Li and Leon M. Tolbert, 2008. Sensitivity of Var Compensation Economic Benefits Considering Generator Marginal Cost. Proc. of 3rd IEEE International Conference on Electric Utility Deregulation, Restructuring, and Power Technology, China, pp: 650-656.

Christie, R.D., B.F. Wollenberg and I. Wangensteen, 2000. Transmission management in deregulated environment, Proc. of IEEE, 88(2): 449-451.

Pavlos S. Georgilakis, George A. Orfanos and Nikos D. Hatziargyriou, 2014. Computer-assisted interactive learning for teaching transmission pricing methodologies. IEEE Transactions on Power Systems, pp: 1-9.

Jain, G., K. Singh and D.K. Palwalia, 2012. Transmission wheeling cost evaluation using MW-Mile methodology. Proc. of Nirma University International Conference on Engineering (NUICONE), Ahmedabad, pp: 1-6.

Syarifuddin Nojeng, Mohammad Yusri Hassan, Dalila Mat Said, Md. Pauzi Abdullah and Faridah Hussin, 2014. Improving the MW-Mile method using the power factor-based approach for pricing the transmission services. IEEE Transactions on Power Systems, pp: 1-7.

Mustafa, M.W. and H. Shareef, 2006. A Comparison of Electric Power Tracing Methods Used in Deregulated Power Systems. Proc. of First International Power and Energy Conference PECon 2006, Malaysia, pp: 156-160.

Ferdinand Gubina, David G. and B. Ivo, 2000. A Method for Determining the Generators' Share in a Consumer Load. IEEE Transactions on Power Systems, 15(4): 1376-1381.

Kirschen, D., R. AlIan and G. Strbac, 1997. Contributions of Individual Generators to Loads and Flows. IEEE Transactions on Power Systems, 12: 52-60.

Bialek, J., 1996. Tracing the flow of electricity. IEE Proc. of Generation, Transmission and Distribution, 143(4): 313-320.

Oana Pop, Stefan Kilyeni, Petru Andea, Constantin Barbulescu and Cristian Craciun, 2010. Power flow tracing method for electricity transmission and wheeling pricing. Journal of Sustainable Energy, 1(4): 63-70.

Hassan, M.Y., N.H. Radzi, M.P. Abdullah, F. Hussin and M.S. Majid, 2011. Wheeling Charges Methodology for Deregulated Electricity Markets using Tracing-based Postage Stamp Methods. International Journal of Integrated Engineering, 3(2): 39-46.

Saravanan, B., Siddharth Das, Surbhi Sikri and D.P. Kothari, 2013. A solution to the unit commitment problem - A review. Frontiers in Energy (Springer link), 7(2): 223-236.

[1] Irinjila Kranthi Kiran and [2] Dr. Askani Jaya Laxmi

[1] Associate Professor, Dept. of EEE, MVGR College of Engineering, Chinthalavalasa, Vizianagaram (Dt.)-535005 Andhra Pradesh, India.

[2] Professor, Dept. of EEE & Coordinator, Centre for Energy Studies, JNTUH College of Engineering, Kukatpally, Hyderabad-500085, Telangana, India.

Corresponding Author: Irinjila Kranthi Kiran, Associate Professor, Dept. of EEE, MVGR College of Engineering, Chinthalavalasa, Vizianagaram (Dt.)-535005 Andhra Pradesh, India.
Table 4: Contract paths between different sellers and buyers.

Load                 Contract path' line no.s
bus
no.       PV bus-1          PV bus-2           PV bus-3

4      1, 2, 3, 5, 10   1, 2, 3, 5, 6, 10    2, 3, 8, 10
5      1, 2, 3, 6, 10    1, 3, 6, 7, 11        8, 9, 11
6      1, 3, 6, 7, 11    4, 6, 7, 9, 11     4, 7, 8, 9, 11

Table 5: 'Active' line power flows & 'Active' line power losses
before & after the improvement of generation dispatch.

Line no.    Before improvement      After improvement

           P_pq     P_qp    P_L    P_pq     P_qp    P_L

1          29.12   -28.19   0.93   11.01   -10.90   0.11
2          43.70   -42.57   1.12   30.58   -29.78   0.80
3          35.63   -34.51   1.12   25.53   -24.72   0.81
4          2.98    -2.94    0.04   0.38    -0.38    0.00
5          33.28   -31.64   1.64   45.60   -43.76   1.84
6          15.50   -14.93   0.57   18.74   -18.05   0.69
7          26.43   -25.81   0.62   26.18   -25.46   0.72
8          19.33   -18.10   1.23   23.33   -22.23   1.10
9          43.62   -42.55   1.07   47.05   -46.07   0.98
10         4.21    -4.17    0.04   3.54    -3.51    0.03
11         1.71    -1.65    0.06   -1.49    1.52    0.03
                   Total    8.45           Total    7.12

Table 6: 'Reactive' line power flows & 'Reactive' line power losses
before & after improvement of generation dispatch.

Line     Before improvement        After improvement
no.
        Q_pq     Q_qp     Q_L    Q_pq     Q_qp     Q_L

1      -14.50   14.16    -0.34   -3.77    1.77    -2.01
2      22.73    -20.31   2.42    28.37   -27.26   1.11
3      14.89    -13.78   1.11    20.35   -20.44   -0.09
4      -10.63    7.46    -3.17   -3.91    0.57    -3.34
5      49.60    -47.35   2.25    44.37   -41.74   2.64
6      18.47    -18.84   -0.37   19.19   -19.21   -0.02
7      15.27    -16.13   -0.86   20.09   -20.67   -0.57
8      26.88    -26.84   0.04    20.68   -20.89   -0.22
9      64.50    -60.21   4.29    56.99   -53.13   3.86
10     -2.34    -1.45    -3.79   -1.00   -2.83    -3.83
11     -9.10     6.34    -2.75   -6.64    3.80    -2.84
                Total    -1.19           Total    -5.32

Table 7: Generator-wise contribution to bus power demands including
line power losses before and after the improvement of generation
dispatch.

Bus   PV         Before improvement
no.   bus
      no.   Pg      Total   Qg      Total
                    (MW)            (MVAr)

4     1     52.90   72.98   13.77   68.83
      2     20.07           51.33
      3     0.00            3.72
5     1     43.85   73.26   9.34    67.29
      2     11.42           23.05
      3     17.98           34.89
6     1     11.68   72.20   0.00    72.68
      2     18.50           12.47
      3     42.01           60.21

Bus   PV        After improvement
no.   bus
      no.   Pg      Total   Qg      Total
                    (MW)            (MVAr)

4     1     34.36   72.57   26.55   70.80
      2     38.20           43.95
      3     0.00            0.30
5     1     29.62   72.84   18.39   61.50
      2     19.02           19.37
      3     24.19           23.74
6     1     3.13    71.70   0.00    72.37
      2     22.76           18.18
      3     45.80           54.18

Table 8: Generator-wise contribution to line power flows before and
after the improvement of generation dispatch.

Line    PV               Before improvement
no.     bus
        no.    Pg     Total (MW)    Qg     Total (MVAr)

1        1    29.11     29.11      0.00       13.69
         2    0.00                 12.61
         3    0.00                 1.08
2        1    43.69     43.69      13.96      22.24
         2    0.00                 7.62
         3    0.00                 0.65
3        1    35.63     35.63      9.15       14.57
         2    0.00                 4.99
         3    0.00                 0.42
4        1    1.11       3.02      0.00        7.45
         2    1.90                 0.00
         3    0.00                 7.45
5        1    12.39     33.67      0.00       47.98
         2    21.28                44.19
         3    0.00                 3.79
6        1    5.77      15.67      0.00       17.86
         2    9.90                 16.45
         3    0.00                 1.41
7        1    9.84      26.74      0.00       14.77
         2    16.90                13.60
         3    0.00                 1.16
8        1    0.34      19.35      0.00       26.87
         2    0.58                 0.00
         3    18.42                26.87
9        1    0.77      43.67      0.00       64.49
         2    1.32                 0.00
         3    41.57                64.49
10       1    3.18       4.38      -0.19      -1.39
         2    1.20                 -0.47
         3    0.00                 -0.72
11       1    1.07       1.78      0.00        6.58
         2    0.27                 1.13
         3    0.43                 5.45

Line    PV               After improvement
no.     bus
        no.    Pg     Total (MW)    Qg     Total (MVAr)

1        1    11.01     11.01      0.00        1.69
         2    0.00                 1.68
         3    0.00                 0.01
2        1    30.58     30.58      26.17      27.15
         2    0.00                 0.98
         3    0.00                 0.00
3        1    25.53     25.53      18.77      19.47
         2    0.00                 0.70
         3    0.00                 0.00
4        1    0.04       0.38      0.00        0.56
         2    0.33                 0.00
         3    0.00                 0.56
5        1    5.52      45.66      0.00       42.63
         2    40.13                42.34
         3    0.00                 0.29
6        1    2.26      18.75      0.00       18.43
         2    16.48                18.31
         3    0.00                 0.12
7        1    3.17      26.21      0.00       19.30
         2    23.03                19.17
         3    0.00                 0.13
8        1    0.01      23.32      0.00       20.67
         2    0.11                 0.00
         3    23.20                20.67
9        1    0.03      47.05      0.00       56.98
         2    0.22                 0.00
         3    46.79                56.98
10       1    1.73       3.66      -0.38      -1.01
         2    1.93                 -0.63
         3    0.00                 -0.00
11       1    0.06       1.55      0.00        3.92
         2    0.49                 0.98
         3    0.99                 2.93

Table 9: Generator-wise wheeling costs under different contract paths
before and after the improvement of generation dispatch.

Load          Wheeling cost (Rs.)
bus
no.           Before improvement

       PV bus-1    PV bus-2    PV bus-3

4      54,387.43   38,582.04   23,836.09
5      54,141.00   30,164.07   34,678.49
6      41,803.89   21,267.68   37,306.49

Load          Wheeling cost (Rs.)
bus
no.            After improvement

       PV bus-1    PV bus-2    PV bus-3

4      36,321.14   35,034.81   21,577.31
5      36,036.37   28,319.46   31,915.26
6      23,672.05   27,143.26   32,132.52

Table 10: Generator-wise wheeling costs before and after the
improvement of generation dispatch under a single contract path
including all lines.

Load         Wheeling cost (Rs.)
bus
no.          Before improvement

       PV bus-1    PV bus-2    PV bus-3

4      62,975.44   49,153.61   41,068.04
5
6

Load          Wheeling cost (Rs.)
bus
no.           After improvement

       PV bus-1    PV bus-2    PV bus-3

4      38,984.05   48,012.02   32,306.83
5
6
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Author:Kiran, Irinjila Kranthi; Laxmi, Askani Jaya
Publication:Advances in Natural and Applied Sciences
Date:Nov 1, 2015
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