ECE 332:494:01/599:02 – Smart Grid – Spring 2021 Homework Assignment – Set 3 Solved

332:494:01/599:02 – Smart Grid – Spring 2021 
Homework Assignment – Set 3 

 

 

General guidelines for homework assignments: Homework should be submitted online (via Canvas)  

 

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.  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

  

                                                                           𝑉&A = B𝐴 𝐵F @𝑉𝐼’’A           

                                                                         @𝐼&           𝐶    𝐷

          

 

(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: 

𝑌-
=_____________________[
Ω"% ∙mile] or [Ω"% ∙ m]
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  

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?

 

332:494/599– HW Set 3                                                                                                           2