ECE 332:494:01/599:02 – Smart Grid – Homework Assignment – Set 2 Solved

332:494:01/599:02 – Smart Grid – Homework Assignment – Set 2 (updated) 

 

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

 

Question 1: 

A balanced Y-connected voltage source with a phase voltage 𝑉!" = 277∠0°𝑉 delivers to a balanced delta connected load with impedance 𝑍#$%&! = 45 − 𝑗18Ω that is in parallel with a Yconnected load with impedance 𝑍’ = 30 + 𝑗15Ω.  

(a)   Calculate the total current deliver to the loads 

(b)   Calculate the total real and reactive power for the loads  

 

Question 2: 

Consider the three-phase system in Figure 1. From the generator bus (marked as B1) power is delivered to a load of 150MW and 60Mvar at bus 3 and a load of 120MW and 60Mvar at bus 4 (all values in 3-Phase). The line voltage magnitude at bus 4 (B4) for load 2 needs is kept at 69 kV. 

(a)   Find the per-unit representation of the system with a power base value of: 

•       Option one: single-phase value of 100MVA for the power and phase voltage base value of 23/ at bus B1 

•       Option two: three-phase value of 300MVA for the power and line voltage base value of 23 kV at bus B1 Per the option you chose: 

1.     Find the base values for the systems in figure 1 

2.     Find all per-unit line impedances: transformers T1 and T2 impedances 

3.     Find all per-unit values for all given powers, impedances, and voltages 

(b)   What is the line voltage magnitude at the generating source at bus 1 (magnitude of the line voltage at B1)? 

(c)   Find the real and reactive power for the generator (remember, it’s a three phase system). 

  

 

 

Figure 1(a): one line diagram for system in question 2 

  

Figure 1(b): one-line diagram for system in question 2 in per-unit 

 

Question 3: 

The three-phase power and line-line voltage. are given for the electric power system in figure 2. For the per-unit analysis, a base value of 100MVA is chosen for the three-phase power and a base value of 20kV is chosen for the line voltage on generator 1 end.   

(a)  Find the base values for the systems in figure 2 

(a)     Find all per-unit line impedances: transformers T1 and T2 impedances; generators G1 and G2 impedances.  

(b)     Find all per-unit values for all given powers, and voltages 

(c) Find load1 impedance  (d) Find the current flow through the load
 

         

 

 

332:494/599– HW Set 2                                                                                                            2 

                         

Figure 2 (a): one-line diagram for system in question 3  
 

 

  

 

Figure 2 (b): one-line diagram for system in question 3 in per-unit
 

 

  

Figure 2 (c): OR another representation… one-line diagram for system in question 3 in per-unit