[SOLVED] ECE599-Homework 1

Description

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

• 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_)*
• Find the load impedance: 𝑍_+”#$
• 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

• Find and draw the power triangle for load 𝑍_!”#$/: what is the real power 𝑃_!”#$/ and reactive power 𝑄_!”#$/ consumed by load 𝑍_!”#$/
• 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_!”#$0
• Find the power factor (pf) for the total load 𝑍_{!”#$_(2} = 𝑍_!”#$/||𝑍_!”#$0 and the total apparent power H𝑆_{!”#$_(2}H in Figure 3

Figure 3

• Find the line current phasor I_line
• A capacitor is added in parallel to Z_{Load_eq} (see figure 4). If the power grid frequency is f=60Hz, calculate the size of the capacitor 𝐶_3″-)                         required in order to correct the power factor for the load to 0.95 lag

Figure 4

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 V_an 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;

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.

• Find the total complex power of the three loads
• Find the overall power factor
• Find line current in the supply line