International Journal of Latest Research in Science and Technology Volume 4, Issue 5: Page No.4-8, September-October 2015 http://www.mnkjournals.com/ijlrst.htm ISSN (Online):2278-5299 SIGNIFICANCE OF TRANSPOSITION FOR 220KV TOWER 1 G.Radhika, 2 Dr.M.Suryakalavathi & 3 K.Vamshi 1 Sr.Assistant Professor, VNRVJIET, Hyderabad, India 2 Professor, JNTUH, Hyderabad, India 3 VNRVJIET, Hyderabad, India 1 Email: radlalitha.g@gmail.com, 2 mungala@yahoo.com, 3 kondavamshi327@gmail.com Abstract- Economy is becoming increasingly dependent on electricity as a basic input. Transmission lines provide the means of connecting the generating capacities to the load centres.knowledge of the parameters of multi-conductor transmission lines is necessary in analysing a number of problems in power-transmission systems. These parameters under power frequency i.e. 50Hz are required in order to study load flow, system stability and fault levels. Transmission lines are electrically short at power frequency and it is permissible to calculate series and shunt parameters separately. As the number of conductors increase, the complexity in calculating the matrices increases with the use of classical methods. The complexity of the mathematical expressions involved in multi-conductor line problems is reduced with the aid of digital computer program. The objective of this paper is to study the effect of transposition for a chosen 220kV twin bundled over head transmission line with two ground wires having asymmetrical spacing between the conductors by representing with a digital computer program using MATLAB. The Phase impedance matrix (3X3) calculated by eliminating earth wires contains unbalanced impedances of (5x5) and also its corresponding sequence impedance matrix (3X3) contains intersequence mutual couplings and are eliminated by doing Perfect Phase Transposition. The comparison shows the closer agreement between calculated values and those obtained by the digital program. The same technique is valid for tower with any number of conductors. Keywords - Transmission Line, Transposition, Phase Impedance Matrix, Sequence Impedance Matrix, MATLAB I. INTRODUCTION Untransposed lines are reckoned to be the main source of current unbalance in the transmission systems. To evaluate the unbalanced conditions on transmission lines, method of symmetrical components [4] is applied by expressing the impedance of a transmission line as a positive, negative and zero sequence components. The advantage of the application of sequence components is that the size of the problem is effectively reduced in compared to phase components approach. The asymmetrical spacing of lines results in the unbalance of line self and mutual impedances in phase frame of reference and hence unequal voltage drops even though the currents are balanced and they can be made equal with the help of transposition. It is defined as interchanging the position of the line conductors at regular intervals along the line so that each conductor occupies the original position of every other conductor [1]. It is an effective way to equalize the phase impedances and reduce the induction from normal operating currents and voltages In this paper, 220kV Overhead line with two ground wires is presented with a horizontal phase conductor configuration. Generally, Bundled conductors with two, four, six and eight sub conductors are used for many reasons for voltages exceeding 220kV.Twin Bundled Conductors are chosen for this type of transmission line to present lesser reactance per phase. Modern computer technology gives an opportunity to prevent the difficulties occurred during the calculation of unbalance caused by transmission lines as well as to implement the new approach in relation to operational speed and accuracy of calculations [2]. The average height of the conductor including sag with respect to earth is calculated by using [1]. Meters (1) Where, H av is the average Height in mt H t is the total Height in mt S av is the average sag in mt II. PHASE AND SEQUENCE IMPEDANCES Figure shows 220kV single-circuit overhead line with a symmetrical horizontal phase conductor configuration and two earth wires. The cross numbered 1-5 represents the mid span conductor positions due to conductor sag. Figure 1: The 220KV S/C OH line geometry ISSN:2278-5299 4
The spacing s of the conductors relative to the centre of the tower and earth [3], are given in the table. Table 1: Spacing s of the Conductors with respect to tower and earth International Journal of Latest Research in Science and Technology. So, after eliminating the earth wires the matrix size reduces to 3x3 as shown, a 9.91m m 6.75m H1 25.9m H2 19.86m Average sag for 10.74m phase conductors Average sag for earth 8.25m conductors Average Height of phase conductors is calculated using equation (1) Z Phase is the phase impedance matrix of the unbalanced three phase mutually coupled line. The matrix is symmetric but the self or diagonal terms are unequal to each other, and the mutual or off-diagonal terms on a given row or column are unequal to each other. The impedance matrix in the sequence frame of reference obtained by transforming the phase impedance matrix by using eq (4).The Sequence impedance matrix is calculated by assuming phase rotation of RYB by using Where H is the sequence to phase transformation matrix. Average Height of earth conductors= The Self impedance of every individual conductor and ground wire is given as, (2) And the mutual impedances between the conductors i & j is given as, Where, D erc is depth of equivalent earth return conductor. The calculated self and mutual impedances are shown in a matrix form, Currents flowing in any one conductor will induce voltage drops in the other two conductors and these may be unequal even if the currents are balanced. This is because the mutual impedances, which are dependent on the physical spacing s of the conductors, are unequal. The 5x5 partitioned Z matrix obtained as shown below including earth wires, (3) The sequence impedance matrix is full, non-diagonal and non-symmetric. A non diagonal matrix means that mutual coupling in the sequence circuits exist. The conversion to sequence reference frame still produces a full and even asymmetric sequence impedance matrix that includes intersequence mutual couplings. Where this intersequence mutual coupling is to be eliminated, the circuit has to be perfectly transposed. III. TRANSPOSITION The calculated sequence series impedance matrices include full intersequence mutual couplings. To eliminate the intersequence mutual couplings, the line is to be perfectly transposed. The objective of transposition is to produce equal series self-impedances, and equal series mutual impedances in the phase frame of reference. Perfect phase transposition means that each phase conductor occupies successively the same physical positions as the other two conductors in two successive line sections for equal length. Case-1: Forward Successive Phase Transposition: Figure 2: Forward Phase Transposition In large-scale power system short-circuit analysis, we are interested in the calculation of short-circuit currents on the faulted phases R, Y or B or a combination of these but generally not in the currents flowing in the earth wires. The Figure.2 shows three sections of a transposed line. This represents a perfect transposed line where the three sections have equal length. Perfect transposition results in the same total voltage drop for each phase conductor and hence equal average series self-impedances of each phase conductor and series phase mutual impedances. ISSN:2278-5299 5
Shows a complete forward transposition cycle, i.e. three transpositions where the line is divided into three sections and t (top), m (middle) and b (bottom) are used to designate the conductor physical positions on the tower. If the three conductors of the circuit are designated C1, C2 and C3, then a forward transposition is defined as one where the conductor positions for the three sections are C1C2C3, C3C1C2 then C2C3C1 as shown. Z Phase is the phase impedance matrix of the perfectly transposed line, noting that the individual conductor impedances are symmetric. International Journal of Latest Research in Science and Technology. Figure 3: Reverse Phase Transposition The sectional matrices formed by general matrix approach for reverse transposition cycle are shown below, (8) The above section matrics are formed by general matrix analysis approach which is more suitable for modern calculations by digital computers. Where T is the transposition matrix given by, (5) (9) The effect of pre-multiplying matrix Z Section-1 by matrix T t is to shift its row 2elements up to row 1, row 3 elements up to row 2 and row 1 elements to row 3.Also, the effect of post-multiplying matrix Z Section-1 by matrix T is to shift its column 2 elements to column 1, column 3 elements to column 2 and column 1elements to column 3. (6) Using eq.7 Z Phase is the phase impedance matrix of a balanced or perfectly transposed line. Where, (10) (11) (7) Case-2: Reverse Successive Phase Transposition The Figure.3 shows Reverse transposition cycle which is defined as one where the conductor positions for the three sections are C1C2C3, C2C3C1 and C3C1C2. For R, Y, B electrical phase rotation of conductors 1, 2 and 3 respectively, the sequence impedance matrix is calculated using, (12) ISSN:2278-5299 6
International Journal of Latest Research in Science and Technology. H is the Sequence to phase transformation matrix given by, The below Figure s 4,5, represents the Untransposed phase impedance matrix showing that, the diagonal and off diagonal elements are not equal and their corresponding sequence impedance matrix contains inter circuit mutual couplings which are made to zero. and In the sequence reference frame, only diagonal elements are present and off diagonal elements are all made to zero. Also, the positive and negative sequence components are equal in the sequence impedance matrix. Where, Figure 4: Untransposed phase impedance matrix (13) (14) In this sequence impedance matrix, mutual sequence coupling is eliminated completely i.e., all the off diagonal elements are made to zero. IV. SUMMARY OF THE PROGRAM (i) As explained the input data are read in. These include physical geometry of the line, earth resistivity, stranding factors appropriate to the bundling arrangements, sag, resistivity and frequency. Let p be the number of phase conductors and q be the number of earth wires. (ii) Calculating the average heights with respect to earth using the formula [eq.1]. (iii) Calculating the distances between the conductors and substituting the values in self and mutual impedances. (iv) The Z matrix of size 5x5 is formed and by eliminating the earth wires get reduced to 3x3 by using the formula [A]-[B -1 ] [C] [D]. (v) Sequence matrix is formed from the phase matrix by [eq.4]. (vi) Transposed phase and sequence impedance matrices are formed by using [eq.7]. Figure 5: Corresponding sequence impedance matrix Figure. 6 show the perfectly transposed or balanced phase impedance matrix, showing the bars of equal length in the self and off diagonal positions. Figure 6: Perfectly transposed phase impedance matrix And figure 7 contains only diagonal elements i.e., Positive, negative and zero sequence components only which shows that the mutual coupling is eliminated completely. V. RESULTS AND DISCUSSIONS To overcome the complexity of manual iterative calculations, a program is coded to generate phase and sequence impedance matrices showing the effect of transposition of 220 kv, double ground wired, single circuit transmission tower. ISSN:2278-5299 7
International Journal of Latest Research in Science and Technology. Figure 7: Corresponding Sequence impedance matrix VI. CONCLUSION Thus three transpositions are sufficient to produce balanced mutual phase impedance matrix and mutual sequence couplings are entirely eliminated in the sequence impedance matrix. The transposed phase and sequence impedance matrices for both forward and reverse phase transpositions obtained the same result. The output and mathematical calculation hence shows an excellent resemblance in similarity by which it is proved that the impedance calculation has been reduced the complexity by using programming technique. The same program can be used for any tower configurations i.e. for multiple circuit lines. REFERENCES 1. Nasser Tleis, Power system modeling and fault analysis, newness publications, 2008. 2. R.H.Galloway, W.B.Shorrocks and L.M.Wedepohl, Calculation of electrical parameters for short and long polyphase transmission lines, Institution of Electrical Engineers, Vol.11, No.12, pp.2051-2059, 1964. 3. G.Radhika, Dr.M.Suryakalavathi, Back flashover analysis improvement of a 220kV transmission line, International journal of Engineering Research and Applications, Vol.3, Issue.1, pp.533-536, 2013. 4. Fortescue.C.L, Method of Symmetrical Coordinates applied to the solution of polyphase networks, Transactions of AIEE, Vol.37, pp.1027-1140, 1918. 5. Arif M.Gashimov, Aytek R.Babayeva, Ahmet Nayir, Transmission Line Transposition, International Conference on Electrical & Electronics Engineering, pp.364-367, 2009. ISSN:2278-5299 8