SOFTWARE FOR CALCULATING ELECTRICAL POWER TRANSMISSION LINE PARAMETERS

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Proceedings of the OAU Faculty of Technology Conference 215 OFTWARE FOR CALCULATING ELECTRICAL POWER TRANMIION LINE PARAMETER K. N. Erinoso, F. K. Ariyo* and M. O. Omoigui Department of Electronic and Electrical Engineering Obafemi Awolowo University, Ile-Ife, Nigeria.

1 Proceedings of the OAU Faculty of Technology Conference 215 OFTWARE FOR CALCULATING ELECTRICAL POWER TRANMIION LINE PARAMETER K. N. Erinoso, F. K. Ariyo* and M. O. Omoigui Department of Electronic and Electrical Engineering Obafemi Awolowo University, Ile-Ife, Nigeria. * of Corresponding Author: ABTRACT This paper presents standalone software programmed in National Instruments-LabVIEW that calculates overhead electrical power transmission line parameters. The parameters comprise series resistance, series inductance, shunt capacitance, series impedance and shunt admittance. tate machine programming architecture of NI LabVIEW, a graphical programming environment, is employed in carrying out the routine tasks of different line parameter calculation. The calculated parameters are important in steady-state power analyses and studies such as short circuit, load flow, transient stability and steady-state stability studies. The results obtained using the developed software is consistent with previous literature results. Keywords - Transmission line parameters; series resistance; series inductance; shunt capacitance; series impedance and shunt admittance. INTRODUCTION The power system growing into a vast and complex system represents one of the most vital systems in developed as well as developing nations. The basic purpose of a transmission network, being a branch of power system, is to transfer electrical energy from generating units at various locations to the distribution system which ultimately supplies the load. Transmission line also interconnects neighboring power utilities which allows not only economic dispatch of electrical power within regions during normal conditions, but also transfer of power between regions during emergencies (Das, 26). The transmitted energy suffers power losses along the transmission line due to its series impedance. eries impedance also causes line-voltage drops, I 2 R losses, and therefore affects stability limits (Glover et al., 28). Transmitted energy is also affected by linecharging currents which inject reactive power into the power system (Glover et al., 28). Line-charging current is caused by shunt admittance of transmission lines which is primarily capacitive. hunt admittance comprises the line conductance and capacitance (Glover et al., 28). In other to achieve optimum line design that meets part of the electrical design criteria at lowest overall cost, the transmission line parameters must be taken into consideration. The basic transmission line parameters, which are often called line constants, are resistance, inductance, and capacitance. Based on the basic parameters, the series impedance and shunt admittance are derived. All of these parameters for long overhead transmission line are the focus of this paper. The standalone software programmed with NI- LabVIEW calculates these parameters with the consideration of earth effect. These parameters are important in steady-state power analyses and studies 37 such as short circuit, load flow, transient stability and steady-state stability studies. THEORETICAL DEVELOPMENT The mathematical expressions of this work is given in this section. The expressions were used in programming in NI-LabVIEW to calculate overhead electrical power transmission line parameters (aadat, 1999; Grainger and tevenson, 1994; ELEN 459, 27; EMTP, 25; Lewis and Tuttle, 1959; Carson, 1926; atsios et al, 1998). i. Transmission line Resistance ρl R = (Ω) = ac T + t 2 = R (1) A ii. R dc L P C AB k 1 T + t Transmission line Inductance and Capacitance For ingle-phase 2-wire line: λ p µ D = = ln I π GMR πε ( F / m) ln D / r [ ] 1 (2) = (3) For three-phase single and double circuit: µ D Lphase = ln (4) 2π GMRcond q A 2πε C AN = = ( F / m) (5) VAN D ln r The GMR bundle is introduced to determine the final inductance value. Assuming the same separation among

2 bundles, the equation for GMR bundle, up to three conductors per bundle, is defined as: GMR n bundle conductors n 1 1/ ( d GMR ) n = (6) stranded transition of state machines. tate machine infrastructure comprises while loop, case structure, shift register, state functionality code, and transition code (NI LabVIEW, 21). This is shown in Fig 1. For two- subconductor bundle: D ( D d ) = D d b = 4 2 (7) For a three-subconductor bundle: D b 3 2 ( D d d ) = D d = (8) 9 3 where n = number of conductors per bundle GMR = GMR of the stranded conductor stranded d = distance between bundle conductors ρ = conductor resistivity l = length of conductor A = conductor cross sectional area R = ac resistance ac R1 and R 2 = resistances at temperature, t 1 and t 2 V AN = phase a voltage T = temperature constant t1 and t 2 = conductor temperatures λ = flux linkages p I = conductor current µ = constant permeability, π 4 x 7 1 H/m 12 ε = permittivity of free space, 8.85 x 1 F/m r, D = conductor radius and diameter resp. q A = charge on conductor A GMD = geometric mean distance EXPERIMENTAL PROCEDURE A. Architecture A state programming architecture is a good choice in carrying out the routine tasks of different line parameter computation. ometimes, it may be required to change the order of the sequence, repeat one item in the sequence more often than the other items, stop a sequence immediately, or have items in the sequence that may execute only when certain conditions are met. Although a program may not have any such requirements, there is always the possibility that the program must be modified in the future. Therefore, state programming architecture makes future modification an easy task. A state machine relies on user input or in-state calculation to determine which state to go to next. Many applications require an initialization state and a default state, where many different actions can be performed. tate machines are commonly used to create user interfaces where different user actions send the user interface into different processing segments. Each processing segment acts as a state in the state machine. Each segment leads to another segment for further processing or waits for another user action. Enumerated type controls are used to control the initialization and 371 Fig. 1. ystem architecture B. Flowchart The simplified flowchart for the program is given in Fig 2. How the software works is enumerated as follows; it poses two circuit options (single-phase 2-wire line, 3-phase single circuit and 3-phase double circuit) to the user. based on the circuit type, it requests for the necessary inputs from the user; during the input request, it gives both options of a solid conductor and stranded/bundled conductor to the user; and based on the inputs, it computes and displays all the parameters. C. ystem Modules The software calculates each parameter in a separate module. These modules are interconnected in the sense that they all fetch inputs from the same source. Each module is given below. The modules are presented in graphical codes and not textual codes. NI LabVIEW is graphical programming environment that simplifies programming for users just by drag and drop routine. Due to the complexity and space-limitations of that of 3- phase single and double circuits, the modules for singlephase 2-wire line are only presented the next section. The mathematical expressions were used in programming in NI-LabVIEW to calculate overhead electrical power transmission line parameters. The NI- LabVIEW code for Resistance, Inductance, Capacitance, eries Impedance and hunt Admittance are shown in Fig 3 to Fig 6, respectively. REULT AND DICUION Tested with some sets of inputs, the software gives out following results. The snapshots are shown in Figs Fig. 7. shows result of single phase 2-wire line with the following input parameters: conductor type (hard-drawn Aluminum), earth type (average damped earth), temperature ( o C), frequency (6 Hz), line diameter (2 mm 2 ), line spacing (3 m), line height (1 m), solid or bundled (solid), long line length (25 Km).

3 Fig. 2. ystem Flowchart Fig. 3. Resistance Module 372

4 Fig. 4. Inductance Module Fig. 5. Capacitance Module 373

Fig. 6. eries Impedance and hunt Admittance for Long Lines Module Fig. 7. ingle-phase 2-Wire Line of 25 Km Length Fig. 8.

2 ), line spacing (3 m), line height (15 m), solid or bundled (bundled with 3 strands), strand spacing (1 mm), long line length (35 Km). Fig.

(2mm 2 ), line height (12 m), number of neutral or shield wire (1), solid or bundled (solid), long line length (3 Km). Fig.

5 Fig. 6. eries Impedance and hunt Admittance for Long Lines Module Fig. 7. ingle-phase 2-Wire Line of 25 Km Length Fig. 8. shows result for single-phase 2-wire line with following set of input parameters: conductor type (harddrawn Copper), earth type (dry earth), temperature (o C ), frequency (5 Hz), line diameter (15 mm 2 ), line spacing (3 m), line height (15 m), solid or bundled (bundled with 3 strands), strand spacing (1 mm), long line length (35 Km). Fig. 9 shows result of 3-phase single circuit line with the following input parameters: conductor type (annealed Copper), earth type (sandstone earth), temperature (o C ), frequency (5 Hz), line diameter (2mm 2 ), line height (12 m), number of neutral or shield wire (1), solid or bundled (solid), long line length (3 Km). Fig. 1 shows result for 3-phase single circuit line with the following input parameters: conductor type (hard-drawn Copper), earth type (dry earth), temperature (o C ), frequency (6 Hz), line diameter (2mm), line 374 height (15m), number of neutral or shield wire (2), solid or bundled (bundled with 3 strands), strand spacing (1mm 2 ), long line length (35 Km). Fig. 11 shows result for 3-phase double circuit line with the following input parameters: conductor type (hard-drawn Copper), earth type (average damped earth), temperature (o C ), frequency (6 Hz), line diameter (25 mm 2 ), line height (2 m), number of neutral or shield wire (2), solid or bundled (solid), long line length (35 Km). Fig. 12 shows result for 3-phase double circuit line with the following input parameters: conductor type (hard-drawn Copper), earth type (dry earth), temperature (o C ), frequency (5 Hz), line diameter (15mm), line height (25m), number of neutral or shield wire (2), solid or bundled (bundled with 2 strands), strand spacing (1mm 2 ), long line length (35 Km).

6 Fig. 8. ingle-phase 2-wire Line with 35 Km Length Fig. 9. Three-phase ingle Circuit Line with 3 Km Length 375

7 Fig. 1. Three-phase ingle Circuit Line with 35 Km Length Fig 11. Three-phase double circuit line with 35 Km Length Fig 12. Three-phase Double Circuit Line with 35 Km Length 376

8 CONCLUION From Figs. 7 and 8, it is observed that the parameters reduce more when dry-earth type was selected for the analysis than the average damped earth type despite increase in line length, it also shows that bundling reduces the parameters values and hence loses in the line. Figs. 9 and 1 also show that the parameters reduce more when dry-earth type was selected for the analysis than the average damped earth type despite increase in line length(sandstone/ dry-earth), though different materials were considered: annealed copper and hard-drawn copper, while Figs 11 and 12, compare hard drawn aluminum with hard-drawn copper but different earth type. The results show that copper (thou a better conductor) has high line parameters than aluminum conductor. Other factors contributing to these are: conductor diameter which increases the inductance. As evident in the result snapshots above, the standalone software is capable of calculating transmission line parameters accurately REFERENCE Das, D. Electrical Power ystems, New Age International (P) Ltd., Publishers, New Delhi, India, 26. Glover, J.D., arma, M.. and Overbye, T.J. Power ystem Analysis and Design, 4th ed. Thomson Learning, Toronto, 28.aadat, H. Power ystem Analysis, 1st ed. McGraw-Hill Companies, Inc., New York, Grainger, J.J. and tevenson (JR.), W.D. Power ystem Analysis, 1st ed. McGraw-Hill, Inc., ingapore, Transmission Line Parameter Calculation, ELEN 459 Power ystem Fault Analysis and Protection, pring 27. EMTP Reference Models for Transmission Line Relay Testing, Final-9/9/25. Lewis, W.A. and Tuttle, P.D. The Resistance and Reactance of Aluminium Conductors teel- Reinforced, AIEE Transactions, III, , Carson, J.R. Wave Propagation in Overhead Wires with Ground Return, Bell ystem Technical Journal, 5, , atsios, K.J., Labridis, D.P., and Dokopoulos, P.. Finite Element Computation of Field and Eddy Currents of a ystem consisting of a Power Transmission Line above Conductors buried in Nonhomogeneous Earth, IEEE Transaction on Power Delivery, 13, , NI LabIEW, Introduction to LabVIEW, National Instrument Corporation,

EE 740 Transmission Lines

EE 740 Transmission Lines 1 High Voltage Power Lines (overhead) Common voltages in north America: 138, 230, 345, 500, 765 kv Bundled conductors are used in extra-high voltage lines Stranded instead of