JCT College of Engineering Technology Pichanur Coimbatore 641
JCT College of Engineering & Technology, Pichanur, Coimbatore- 641 105. Transmission & Distribution Faculty Name : M. D. Saravanan Designation : Asso. Professor Year/Sem : II/IV Dept : EEE ACT - 0 1539 pk 0
Performance Equations and Parameters of Transmission Lines A transmission line is characterized by four parameters: ◦ series resistance (R) due to conductor resistivity ◦ shunt conductance (G) due to currents along insulator strings and corona; effect is small and usually neglected ◦ series inductance (L) due to magnetic field surrounding the conductor ◦ shunt capacitance (C) due to the electric field between the conductors These are distributed parameters. The parameters and hence the characteristics of cables differ significantly from those of overhead lines because the conductors in a cable are ◦ much closer to each other ◦ surrounded by metallic bodies such as shields, lead or aluminum sheets, and steel pipes ◦ separated by insulating material such as impregnated paper, oil, or inert gas ACT - 1 1539 pk 1
For balanced steady-state operation, the performance of transmission lines may be analyzed in terms of singlephase equivalents. Fig. 6. 1 Voltage and current relationship of a distributed parameter line (6. 8) (6. 9) The general solution for voltage and where current at a distance x from the receiving end (see book: page 202) is: ACT - 2 1539 pk 2
The constant Z C is called the characteristic impedance and K is called the propagation constant. The constants K and Z C are complex quantities. The real part of the propagation constant K is called the attenuation constant α, and the imaginary part the phase constant β. If losses are completely neglected, ACT - 3 1539 pk 3
For a lossless line, Equations 6. 8 and 6. 9 simplify to (6. 17) (6. 18) When dealing with lightening/switching surges, HV lines are assumed to be lossless. Hence, ZC with losses neglected is commonly referred to as the surge impedance. The power delivered by a line when terminated by its surge impedance is known as the natural load or surge impedance load. where V 0 is the rated voltage At SIL, Equations 6. 17 and 6. 18 further simplify to (6. 20) (6. 21) ACT - 4 1539 pk 4
Hence, for a lossless line at SIL, ◦ V and I have constant amplitude along the line ◦ V and I are in phase throughout the length of the line ◦ The line neither generates nor absorbs VARS As we will see later, the SIL serves as a convenient reference quantity for evaluating and expressing line performance Typical values of SIL for overhead lines: nominal (k. V): 230 SIL (MW): 140 345 420 500 1000 765 2300 Underground cables have higher shunt capacitance; hence, Z C is much smaller and SIL is much higher than those for overhead lines. ◦ for example, the SIL of a 230 k. V cable is about 1400 MW ◦ generate VARs at all loads ACT - 5 1539 pk 5
Typical Parameters Table 6. 1 Typical overhead transmission line parameters Note: 1. Rated frequency is assumed to be 60 Hz 2. Bundled conductors used for all lines listed, except for the 230 k. V line. 3. R, x. L, and b. C are per-phase values. 4. SIL and charging MVA are three-phase values. Table 6. 2 Typical cable parameters * direct buried paper insulated lead covered (PILC) and high pressure pipe type (PIPE) ACT - 6 1539 pk 6
Voltage Profile of a Radial Line at No-Load With receiving end open, IR = 0. Assuming a lossless line from Equations 6. 17 and 6. 18, we have (6. 31) (6. 32) At the sending end (x = l), (6. 33) where θ = βl. The angle θ is referred to as the electrical length or the line (6. 35) angle, and is expressed in radians. From Equations 6. 31, 6. 32, and(6. 36) 6. 33 ACT - 7 1539 pk 7
As an example, consider a 300 km, 500 k. V line with β = 0. 0013 rads/km, ZC = 250 ohms, and ES = 1. 0 pu: Base current is equal to that corresponding to SIL. Voltage and current profiles are shown in Figure 6. 5. The only line parameter, other than line length, that affects the results of Figure 6. 5 is β. Since β is practically the same for overhead lines of all voltage levels (see Table 6. 1), the results are universally applicable, not just for a 500 k. V line. The receiving end voltage for different line lengths: - for l = 300 km, VR = 1. 081 pu - for l = 600 km, VR = 1. 407 pu - for l = 1200 km, VR = infinity Rise in voltage at the receiving end is because of capacitive charging current flowing through line inductance. ◦ known as the "Ferranti effect". ACT - 8 1539 pk 8
(a) Schematic Diagram (b) Voltage Profile (c) Current Profile Figure 6. 5 Voltage and current profiles for a 300 km lossless line with receiving end open-circuited 9
Voltage - Power Characteristics of a Radial Line Corresponding to a load of P R +j. Q R at the receiving end, we have Assuming the line to be lossless, from Equation 6. 17 with x = l Fig. 6. 7 shows the relationship between V R and P R for a 300 km line with different loads and power factors. The load is normalized by dividing P R by P 0, the natural load (SIL), so that the results are applicable to overhead lines of all voltage ratings. From Figure 6. 7 the following fundamental properties of ac transmission are evident: a) There is an inherent maximum limit of power that can be transmitted at any load power factor. Obviously, there has to be such a limit, since, with ES constant, the only way to increase power is by lowering the load impedance. This will result in increased current, but decreased V R and large line losses. Up to a certain point the increase of current dominates the decrease of V R , thereby resulting in an increased P R. Finally, the decrease in V R is such that the trend reverses. ACT - 10 1539 pk 10
Figure 6. 7 Voltage-power characteristics of a 300 km lossless radial line ACT - 11 1539 pk 11
Voltage - Power Characteristics of a Radial Line (cont'd) b) Any value of power below the maximum can be transmitted at two different values of V R. The normal operation is at the upper value, within narrow limits around 1. 0 pu. At the lower voltage, the current is higher and may exceed thermal limits. The feasibility of operation at the lower voltage also depends on load characteristics, and may lead to voltage instability. c) The load power factor has a significant influence on V R and the maximum power that can be transmitted. This means that the receiving end voltage can be regulated by the addition of shunt capacitive compensation. Fig. 6. 8 depicts the effect of line length: ◦ For longer lines, VR is very sensitive to variations in P R. ◦ For lines longer than 600 km ( θ > 45°), V R at natural load is the lower of the two values which satisfies Equation 6. 46. Such operation is likely to be unstable. ACT - 12 1539 pk 12
Figure 6. 8 Relationship between receiving end voltage, line length, and load of a lossless radial line ACT - 13 1539 pk 13
Voltage-Power Characteristic of a Line Connected to Sources at With Ends E and E assumed to be equal, the following Both conditions exist: S R ◦ the midpoint voltage is midway in phase between ES and ER ◦ the power factor at midpoint is unity ◦ with P R >P 0, both ends supply reactive power to the line; with P R <P 0, both ends absorb reactive power from the line. Fig. 6. 9 Voltage and current phase relationships with ES equal to ER, and PR less than Po Fig. 6. 8 (developed for a radial line) may be used to analyze how V m varies with P R. ◦ with the length equal to half that of the actual line, plots of V R shown in Figure 6. 8 give V m. ACT - 14 1539 pk 14
Power Transfer and Stability Considerations Assuming a lossless line, from Equation 6. 17 with x = l, we can show that (6. 51) where θ = βl is the electrical length of line and is the angle by which ES leads ER , i. e. the load angle. If ES = ER = rated voltage, then the natural load is and Equation 6. 51 becomes The above is valid for synchronous as well as asynchronous load at the receiving end. Fig. 6. 10(a) shows the δ - P R relationship for a 400 km line. For comparison, the V m - P R characteristic of the line is shown in Fig. 6. 10(b). ACT - 15 1539 pk 15
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