Question 1 - A 275 kV, 450 km, 50-Hz three-phase uncompensated overhead transmission line, assumed to be loss-less, is composed of three conductors per phase with flat horizontal spacing of 10.5 m. The bundle spacing is 32 cm and conductors' diameter and GMR are 4 cm and 1.2 cm, respectively.
NOTE: Please keep at least four significant decimal points during calculation in this assignment in order to obtain more accurate results for the practical part.
(1) Determine the phase constant β, the surge impedance Zc, velocity of propagation v, and the wavelength λ of the line.
(2) Determine the ABCD parameters.
(3) Calculate voltage, current, real and reactive power at the sending end, and the percent voltage regulation of the line if the receiving end load is 900MW at 0.95 power factor lagging and at 275kV ( |VR| ≡ 275kV).
(4) What will the load be to maintain |VS| = |VR| with zero reactive power loss along the transmission line? Also calculate the load power. (Hint: Investigate the meaning of Zc in Glover and Sharma's "Power System Analysis and Design" Book).
(5) What is the maximum amount of real power that can be transferred to the load at unity power factor if the required receiving end voltage should always be no less than 0.88, per unit (|VS| ≡ 275kV)?
(6) For the original uncompensated system, if a unity power factor load of 1200MW is connected to the receiving end, the receiving end voltage will drop. Therefore, a shunt capacitor needs to be placed in the receiving end bus to support its voltage magnitude if the required receiving end voltage is 1 per unit. (|VS|≡ 275kV).
a) Calculate the value of the capacitor in Micro Farad.
b) Calculate the new ABCD matrix in this case.
c) Calculate voltage and can at the receiving end and the sending end after compensation.
(7) Series capacitive compensation of 55% of the line inductance is installed in the middle of the line.
a) What is the maximum amount of real power (unity power factor load) that can be transferred by this compensated line?
b) What are the new ABCD parameters?
c) What is the line current at this maximum loading?
d) Name two other practical methods for increasing real power transfer. (NOTE: the required receiving end voltage should always be no less than 0.88 per unit (|VS| ≡ 275kV)).
Question 2 - Write a brief report for the following questions. You MUST show your graphic results clearly in your report. An example of a Power World figure is shown as follows. Make sure you have indicated the necessary parameters. Please do not copy or forge your graphs. We will check your Power World program. If the results do not match, you will get ZERO marks. (NOTE: you do not have to do the calculation. You should use Power World to help you solve these problems.
(1) Use Power World to check your calculation in questions (4). (5), (6) and (7) in Question 1. Require 4 graphs.
(2) For the original uncompensated system in Question 1, if the load drops to one fourth of that during the day time (daytime load: 1200MW at unity power factor):
- What is the magnitude of the receiving end voltage (assume |VS| ≡ 275kV)? Require 1 graph.
- What can we do to maintain |VR| = 1.01 p. u.? What kind of compensation do we need? What are the parameters for the compensation? Require 1 graph.
(3) For the original uncompensated system in Question 1:
What will happen if the load is 900MW at 0.9 power factor lagging (|VS| ≡ 275 kV)? Require 1 graph.
Generally, a capacitor bank is installed at the receiving end for voltage support, in which the capacitor value is selected to improve the power factor to a value between 0.95 lagging and 0.866 leading. In this case however, receiving end voltage may fall outside of the range of 0.94 p. u. ≤ |VR| ≤ 1.04 p. u. To maintain this voltage range, what range of capacitor/inductance values are required? Require several graphs.
Question 3 - From a nuclear power plant, 10 GW are to be transmitted to a load center located 600 km away. Determine the number of three-phase, 50 Hz lines required to transmit this power for the following cases: (a) 330 kV lines with surge impedance Zc = 320 Ω; (b) 500 KV lines with Zc = 280 Ω; (c) 765 KV lines with surge impedance Zc = 270 Ω.
Assume the voltage magnitudes of both sending and receiving ends are 1 pu and the angle difference between sending and receiving voltage is 30 degree. Line mutual coupling is assumed to be negligible. All lines are also assumed to be lossless. You may need following equation about power transfer in terms of SIL
P = VSpuVRpu (SIL) (sinδ/sin(2πl/λ)) Watt
where voltages are in per unit, l is the length of the transmission line and λ is the wavelength. For the sake of simplicity, use the wavelength from Question 1 - (1) for all transmission lines. To calculate the reactance of the equivalent π circuit of a long line, you may use
X = SIL sin 2πl/λ
1) What do you think about the result? Which line configuration is more economical?
2) Intermediate stations are often built to support long transmission lines. Use your best line configuration from Question 3 - (1). Assume there are two intermediate substations that divide each line into three 200 km line sections. Based on given assumptions if one line section close to the sending end and one line section close to the receiving end are out of service, what is the amount of real power that can still be transmitted?
3) Same as Question 3 - (2). What if this time three line sections in series are out of service (one close to the generator, one in the middle and one dose to the load)? Such kind of line outage is similar to an entire long line outage without any intermediate substations. So, what do you think about the benefit of intermediate substations as compared with the situation that no intermediate substations are installed?
Question 4 - Intermediate stations are often built to support long transmission lines. Use your best line configuration from Question 3. Assume there are two intermediate substations that divide each line into three 200 km line sections. Each line segment is represented by π model with parameters R: 0, X: 0.04674, B: 0.9151 to match those for a 200 km distributed line. Use Power World to do following simulations:
1) If the load bus voltage is greater than or equal to 730 KV even with any line segment out of service, what is the maximum amount of real power that can be delivered to the load? Figures from power world showing the result are needed.
2) Same as 1). What is the maximum amount of real power transfer if any two line segments are out of service? Figures from power world showing the result are needed.
3) Same as 2). What is the maximum amount of real power transfer if any three line segments are out of service? Figures from power world showing the result are needed.