Power Transfer Distribution Factor Estimate Using DC Load Flow Method Ravi Kumar, S. C. Gupta & Baseem Khan MANIT Bhopal E-mail : ravi143.96@rediffmail.com, scg.nit.09@gmail.com, baseem.khan04@gmail.com Abstract - In this paper, a DC load flow based approach has been proposed for single-transaction case using power transfer sensitivity and succeptance matrices and we seen the effect of one transaction to the other transaction. This method can be implemented for any number of transactions simultaneously. Available Transfer Capability (ATC) is a measure of the transfer capability remaining in the physical transmission network for further commercial activity over and above already committed uses. DC load flow based approach is fast computation which used to worldwide for on line implementation. Many authors have planned the ATC calculation based on DC load flow approach, though, the procedure for multi-transaction cases occurring simultaneously remains unattended using DC load flow approach The results have been determined for intact as well single transaction case. The proposed method has been applied for IEEE 6 bus system. Keywords - Available transfer capability, DC loads flow, power transfer distribution factors, single-transactions. I. INTRODUCTION In a restructure system, the information about the transfer capability will help the energy marketers in reserving the transmission services. For secure and economic supply of power, long distance bulk power transfers are vital, but the power transfer capability of a power system is limited. To operate the power system safely and to gain the advantages of bulk power transfers, computations of transport capability is essential. Transfer capability plays a very important role in liberalized electricity market [1]. All the transmission lines are utilized significantly below their physical limits due to various constraints. By rising the transfer capability the economic value of the transmission lines can be improved and also there will be an increase in overall efficiency as more energy trading can take place between the competing regions operating with different price structure. These terms, which include First Contingency Total Transfer Capability (FCTTC) and First Contingency Incremental Transfer Capability (FCITC) as defined in NERC s May 1995 Transmission Transfer Capability [2] reference document, are still applicable measures in an open transmission access environment. FERC s term Available Transmission Capacity and its definition and relationship to the industry s terminology need to be further clarified. There are three main issues in transmission management: congestion; transmission tariffs; and transmission losses [3]. The power system should be planned and operated such that these power transfers are within the limits of the system transfer Capability. So much sources available for Available Transfer Capability Definitions and Determination [4]. The electric power industries, all over the world, have been varying to a new deregulated environment due to many forces to create competitive electricity markets [5].Transfer capability of a power system is defined as the maximum power that can be transferred from one area to another area. In open access transmission system, the transmission network owners are required to provide unbundled services to support power transactions and to maintain reliable operation of the networks. In a liberalized electricity markets, to implement the open access policy North American Energy Reliability Council (NERC) in conjunction With Federal Energy Regulatory Commission (FERC) defined the term available transfer capability (ATC) to be posted in open access same time information system (OASIS) to inform all the energy market participants of the power system. The two major challenges that make the task of ATC calculation of a nonlinear power system more challenging are computing speed and accuracy due to static and dynamic security constraints. Based on the literature survey for DC load based approaches, authors have determined ATC for single transaction cases; however, simultaneous or multi-transactions cases have not been accounted for ATC determination. Since in a 155
multi-lateral market environment, multi-transactions cannot be avoided for ATC determination as it will not give accurate signal to the ISO for its quantification and reservation for commercial activity. In this paper, PTDFs based approach using DC load flow has been implemented for ATC determination in case of multitransaction environment. The results have also been obtained for single transactions. The methodology has been implemented using power flow sensitivity and succeptance matrix based on DC load flow. The results have been obtained for IEEE 6 bus system. The report is the response to NERC s Strategic Initiative on ATC and defines ATC and related terms [6].The introduction of St. Clair curves were one of the first attempts to contain thermal, voltage, and stability constraints into a single transmission line loading limitation [7]. II. METHODOLOGY FOR ATC DETERMINATION IN CASE OF MULTI-TRANSACTIONS A. Dc load flow model Following are the assumptions while DC model is in employment instead of AC model [8]- Voltage magnitudes are constant, Only angles of the complex bus voltage vary, The variation in angle is small, Transmission lines are lossless, These assumptions create a mode that is a reasonable first approximation for the real power system, which is just slightly nonlinear in normal steady state operation. The model has recompense for speed of computation, and as well has some useful properties like linearity and superposition. With these assumptions, power flow over transmission lines connecting bus i a and bus j a is given as: Where, Xlc, md =line inductive reactance in per unit Ølc = phase angle at bus lc Ømd = phase angle at bus md (1) The total power flowing into the bus ia, Pia, is the algebraic sum of generation and load at the bus and is called a bus power insertion, thus This can be articulated in matrix form as: Where, the elements of the susceptance matrix BX are functions of line reactances. One node is assigned as a location node by making its angle zero and deleting corresponding row and column in matrix. Thus, (3) (4) The dimension of obtained is. Let us augment it by adding zero columns and row corresponding to reference bus. The angles in equation (3) can be found out as (5) Thus, power flow over line lmd can be found out using equation (1). B. Power Transfer Distribution Factor (PTDF) From the power transfer point of view, a operation is a specific amount of power that is injected into the system at one bus by a generator and drawn at another bus by a load. The coefficient of linear association between the amount of a transaction and flow on a line is represented by PTDF. It is too called sensitivity because it relates the amount of one change transaction amount to another change line power flow. PTDF is the fraction of amount of a transaction from of one bus to another that flows over a transmission line. PTDF lcmd, iaja is the fraction of a transaction from bus ia to bus ja that flows over a transmission line connecting buses lc and md. C. Calculation of PTDF Using DC Model (6) Suppose these exists only one transaction in the system. Allow the transaction be of 1 MW from bus i a to bus j a. Then, the corresponding entries in equation (7) will be: P ia = 1and P ja = -1. All other entries will be zero. From equation (5), we get (2) 156
Similarly, (7) In Multi-transactions/ Simultaneous Transactions the more than one seller buses are able to flow the power to more than one buyer buses means the power flows simultaneously seller buses to buyer buses and vice-versa. A. 6-Bus Test System Thus, (8) Ø l = X lcia X lcja (9) Ø md = X mdia X mdja (10) Using equations (9), (10), (1), the PTDF can be calculated as (11) Xlc, md = Reactance of transmission line connecting buses lc and md. X lcia = Entry l c th row and i a th column of the bus reactance matrix X. III. RESULT AND DISCUSSION The results have been determined for IEEE RTS 6 bus system. The results include PTDF calculations for intact system in case of all transactions. Based on the y- bus PTDF have been calculated for all transaction cases. The transactions are chosen are: Bilateral transactions T1: transaction between seller bus 1 to buyer bus 2. T2: transaction between seller bus 3 to buyer bus 5. T3: transaction between seller bus 4to buyer bus 5. T4: transaction between seller bus 5 to buyer bus 6. T5: transaction between seller bus 1 to buyer bus 4. T5: transaction between seller bus 1 to buyer bus 5. T7: transaction between seller bus 2 to buyer bus 3. T8: transaction between seller bus 2 to buyer bus 4. T9: transaction between seller bus 2 to buyer bus 5. T10: transaction between seller bus 2to buyer bus 6. T11: transaction between seller bus 3 to buyer bus 6. TABLE-I Bus data for 6-bus system Bus Type Vm Pd Qd Pg Qg Qmn Qmx 1 1 1.05 0 0 0 0-1 2 2 2 1.05 0 0 0.5 0-1 2 3 2 1.05 0 0 0.6 0-1 2 4 0 1 0.7 0.7 0 0 0 0 5 0 1 0.7 0.7 0 0 0 0 6 0 1 0.7 0.7 0 0 0 0 In the bus data table the type column is represented by the bus type means here 1 is represented by slack bus, 2 is represented by p-v bus and 3 is represented by p-q bus. TABLE-II Line data for 6-bus system From bus To bus Rp.u. Xp.u. Bp.u. Tap 1 2 0.10 0.20 0.020 1 1 4 0.05 0.20 0.020 1 1 5 0.08 0.30 0.030 1 2 3 0.05 0.25 0.030 1 157
2 4 0.05 0.10 0.010 1 2 5 0.10 0.30 0.020 1 2 6 0.07 0.20 0.025 1 3 5 0.12 0.26 0.025 1 3 6 0.02 0.10 0.010 1 4 5 0.20 0.40 0.040 1 5 6 0.10 0.30 0.030 1 TABLE-III X-matrix for 6- bus system 0 0 0 0 0 0 0 0.0969 0.0841 0.0653 0.0674 0.0849 0 0.0841 0.1711 0.0619 0.095 0.134 0 0.0653 0.0619 0.103 0.0568 0.0621 0 0.0674 0.095 0.0568 0.1262 0.0935 0 0.0849 0.134 0.0621 0.0935 0.1684 The X- matrix is obtained by when the element of the susceptance matrix are the function of line reactances. One node is assigned as a reference node by making its angle zero and deleting corresponding row and column in [Bx] matrix and then takes the inverse of that matrix. Lines TABLE-IV PTDF for line for different transactions PTDF (P.U.) T1 T2 T3 T4 1-2 0.4844 0.0639 0.1581 0.1473 1-4 0.3263 0.0169-0.1885 0.0424 1-5 0.2248-0.0920 0.0355-0.1958 2-3 -0.0511-0.3990-0.0376-0.1616 2-4 -0.3163-0.0941-0.6933-0.2098 2-5 -0.0982-0.1346-0.0699-0.2940 2-6 -0.0601-0.3097-0.0443-0.1905 3-5 -0.0641 0.2283-0.0445-0.1838 3-6 0.0075 0.3783 0.0054 0.0230 4-5 0.0054-0.0775 0.1209-0.1680 5-6 0.0581-0.0718 0.0404 0.1670 We have determined the PTDF for different transaction of the lines. First we are determined the PTDF for transactiont1 at lines 1-2,1-4,1-5,2-3,2-4,2-5,2-6,3-5,3-6,4-5 and 5-6. In this way we have seen that the PTDF values varied from positive to negative. The same procedure is done for transactions T2, T3 and T4. When the transaction T1 is applied then we see the effect of transaction T1 on the lines with respect to buses. Fig.1 : PTDFs for transaction T1 The PTDF values for transaction T1 is shown in the negative value of PTDF with respect to line 2-5 and the line 1-2. Fig.2 : PTDFs for transaction T2 The PTDF values for transaction T2 is shown in the negative value of PTDF with respect to line 2-3 and the line 3-6. Fig.3 : PTDFs for transaction T3 158
The PTDF values for transaction T3 is shown in the negative value of PTDF with respect to line 2-4 and the line 1-2. The PTDF values for transaction T1 is shown in the negative value of PTDF with respect to line 2-5 and the line 5-6. Fig.4 : PTDFs for transaction T4 IV. CONCLUSION The methodology for PTDF determination has been suggested for simultaneous/ multi-transactions based on DC load flow approach. Results are shown in tabular form and graphical form. Active Power flows changes their patterns for different transactions. Calculation of PTDF by DC load flow is simple and it is less time consuming because this method is non iterative method. The PTDF obtained varies with simultaneous transaction case as well as multi-transaction case compared to the other transactions. V. REFERENCES [1] C. A. Cañizares, and F. L. Alvarado, Point of Collapse and Continuation Methods for AC/DC Systems, IEEE Trans. on Power Systems, vol. 8, no. 1, Feb. 1993, pp. 1-8. [2] PW.Sauer, "First Contingency Incremental Transfer Capability. (FCITC)" and "First Contingency Total Transfer... Proceedings, 30th Annual Hawaii International Conference on System Sciences, Jan. 7-10, 1997. [3] R.D. Christie, B.F. Wollenberg and I. Wangstien, Transmission Management in the Deregulated Environment, Proc. of the IEEE, vol. 88, No. 2, Feb. 2000, pp. 170-195. [4] North American Electric Reliability Council (NERC), Available Transfer Capability Definitions and Determination, NERC Report, June 1996. [5] M. Ilic, Yong. T. Yoon, and A. Zobian, Available Transmission Capacity (ATC) and its Value under Open Access, IEEE Trans. On Power Systems, vol.12, no. 2, May 1997, pp. 636-645. [6] North American Electric Reliability Council (NERC), Available Transfer Capability Definitions and Determination, NERC Report, June 1996. [7] H. P. St. Clair, "Practical Concepts in Capability and Performance of Transmission Lines," AIEE Transactions, Vol. 72, Part III, December 1953, pp. 1152-1157. [8] National programme on technology enhanced learning (NPTEL), calculation of available transfer capability electrical _engineering restructure, lecture 20. 159