332:494:01/599:02 – Smart Grid Homework Assignment – Set 3

Description

Question 1:
A three-phase overhead transmission line is designed to deliver 100 𝑀𝑉𝐴 at 220 𝑘𝑉 line
voltage over a distance of 100 𝑘𝑚.
If the 𝐼!𝑅 losses need to be kept to a maximum of 3% of the rated line MVA, given the
resistivity of the conductor material to be 2.84 × 10″# Ω ∙ 𝑚, determine the required
conductor diameter (in inches or mils) and the conductor size in circular mils.
Remark: neglect any other line losses (other than resistivity)
Question 2:
A 230𝑘𝑉 three phase transmission line has a per phase series impedance of 𝑧 = 0.05 +
𝑗0.45W per km and a per phase shunt admittance of 𝑦 = 𝑗3.4 × 10″$ Ω”% 𝑝𝑒𝑟 𝑘𝑚. The
line is 80𝑘𝑚 long. Using the medium line p model:
(a) Determine the transmission line model: 𝑍 and 𝑌/2
Medium Line (50-150 mi)
• the shunt admittance must be included in calculations. However, the
total admittance is usually modeled (π model) as two capacitors of
equal values (each corresponding to a half of total admittance)
placed at the sending and receiving ends.
• The total series resistance and series reactance are calculated as
before. Similarly, the total shunt admittance is given by
@
𝑉&
𝐼&
A = B
𝐴 𝐵
𝐶 𝐷F @
𝑉’
𝐼’
A
332:494/599– HW Set 3 2
(b) Determine the constants 𝐴, 𝐵, 𝐶, and 𝐷 for:
(c) Find the sending end (generating) voltage 𝑉&, current 𝐼&, and generated power 𝑆&()*+,
when the line delivers to a load of:
1. 200 𝑀𝑉𝐴 with 0.8 lagging power factor at 220 𝑘𝑉
2. 306 𝑀𝑉𝐴 with unity power factor at 220 𝑘𝑉
Question 3:
a. Given that the external diameter of a cable is 0.84” and the cables are located
horizontally such that 𝐷𝑎𝑏 = 10𝑓𝑡, 𝐷𝑏𝑐 = 10𝑓𝑡 and 𝐷𝑐𝑎 = 20𝑓𝑡, what is the shunt
capacitor per mile 𝑌-=_____________________[Ω”% ∙mile] or [Ω”% ∙ m]
b. Given that the GMR of a cable is 0.16𝑓𝑡 and the cables are located horizontally
such that 𝐷𝑎𝑏 = 10𝑓𝑡, 𝐷𝑏𝑐 = 10𝑓𝑡 and 𝐷𝑐𝑎 = 20𝑓𝑡, what is the line inductive
reactance per mile per phase 𝑋.=_____________________[ Ω /mile] or [Ω /m]
Remark: the grid frequency is assumed to be 𝑓 = 60𝐻𝑧.
Question 4:
Consider a 3-phase hydropower generator feeding power into the grid bus, which is held
at line voltage of 26𝑘𝑉. The internal reactance is 0.8𝑝𝑢 for a rated power of 30𝑀𝑉𝐴.
(a) Choose as base value 𝑆/,1∅ = 30𝑀𝑉𝐴 and 𝑉/,.. = 26𝑘𝑉 and calculate the per-unit
values for the power and grid voltage.
(b) Assume the generator initially runs overexcited with |𝐸| = 1.3 𝑝𝑢 and a real power
output of 𝑃, = 0.32𝑝𝑢. Compute the reactive power and the apparent power output
of the generator as measured at the grid bus.
(c) For the case in (b) find the power factor
(d) Assume the steam valve is opened to generate a 50% increase in power 𝑃,, what are
the new power angle, the reactive power, and the new power factor?
(e) What can be done to bring back the power factor to the previous value? Explain.
(f) Assume that from the original initial state we increase the field current such that the
armature voltage amplitude is increased by 15%, what will be the resulting reactive
power? What will be the resulting power factor?