ECE 332:494:01/599:02 – Smart Grid – Homework Assignment – Set 1 Solved

  


 

332:494:01/599:02 – Smart Grid – 
Homework Assignment – Set 1 

 

General guidelines for homework assignments: Homework should be submitted online (via Canvas under the ‘assignment’ Homework 1)  

 

Question 1: 

For the single-phase system in Figure 1, it is given that the load 𝑍!"#$ is consuming 16𝑘𝑉𝐴 at a 𝑝𝑓 = 0.6 𝑙𝑒𝑎𝑑𝑖𝑛𝑔. The voltage across the load 𝑽!"#$ = 120∠0°𝑉(𝑟𝑚𝑠).

The line impedance is 𝑍!&’( = 1 + 𝑗2Ω

 

Figure 1
 

(a)     For the load impedance, 𝑍!"#$, draw the power triangle and find (include units for each of the first three values):  𝑃!"#$;      𝑄!"#$;    |𝑆!"#$|; 𝑆!"#$ and the power factor angle 𝜃)*

(b)     Find the load impedance: 𝑍+"#$  

(c)     Find the power losses on the line impedance 𝑆+&’((𝑍+&’()

 

Question 2: 

 Given the single-phase system in Figure 2, given that:

-   𝑉!"#$ = 13,800∠0°𝑉,-.

-   Load 1: 60kW at 0.8 power factor lead;  

-   Load 2: 160 kVA at 0.5 power factor lag;  

  

Figure 2
(a)       Find and draw the power triangle for load 𝑍!"#$/: what is the real power 𝑃!"#$/ and reactive power 𝑄!"#$/ consumed by load 𝑍!"#$/   

(b)       Find and draw the power triangle for load 𝑍!"#$0: what is the real power 𝑃!"#$0 and reactive power 𝑄!"#$0 consumed by load 𝑍!"#$0   

(c)       Find the power factor (pf) for the total load 𝑍!"#$_(2 = 𝑍!"#$/||𝑍!"#$0  and the total apparent power H𝑆!"#$_(2H in Figure 3

 

  

 

Figure 3
(d)       Find the line current phasor Iline     

(e)       A capacitor is added in parallel to ZLoad_eq (see figure 4). If the power grid frequency is f=60Hz, calculate the size of the capacitor  𝐶3"-)                      required in order to correct the power factor for the load to 0.95 lag  

 

  

Figure 4
332:494/599 HW 1                                                                                                                  2

Question 3: 

 A small manufacturing plant is located 3km down a transmission line, which has a series reactance of j0.4 Ω/km. The line resistance is negligible. The plant is a three-phase load with a line voltage of 690V (Assume a positive sequence and a phase voltage Van that serves as reference with angle ∠0 ). It consumes 200 kW at 0.85 power factor lagging. (a)  Determine the line voltage at the source  

(b)  Determine the 3-phase complex power generated by the source

 

   

Question4: 

The following three-phase loads are connected in parallel across a 3,800 V (line-line;

(Assume a positive sequence and a phase voltage Van that serves as reference with angle
∠0  )
 balanced three-phase power network:  
Load 1: 120 kVA at 0.9 power factor lag;  Load 2: 180 kW at 0.55 power factor lead;  Load 3: 30 kW at unity power factor.

(a)    Find the total complex power of the three loads

(b)   Find the overall power factor

(c)    Find line current in the supply line