Question

The following single-line diagram of a three-phase power system shows the impedances in per unit on a 100-MVA, 400-kV base. The load at bus 2 is $2 = 14.85 MW -j32.4 Mvar, and at bus 3 is $3 = 75 MW 18.6 Mvar. It is required to maintain the voltage at bus 3 at 410 ∠0° kV. Determine the voltage at buses 1 and 2.

Vi Va Vs
| | |
|--------|-----------|------------|
| 50.4 pu | 70.5 pu | |
| | | 1 ∠0° |
| | | |
|--------- S2 S3

Answer 1

To determine the voltage at buses 1 and 2 in the given three-phase power system, calculate the apparent power at bus 2 using the load information, calculate the voltage at bus 2 using the apparent power and impedance between buses 1 and 2, and then calculate the voltage at bus 1 using the apparent power and impedance between buses 1 and 3.

Step-by-step explanation:

To determine the voltage at buses 1 and 2, we need to use the information provided about the load at bus 2 and the desired voltage at bus 3. First, let's calculate the apparent power at bus 2 using the given load values. The apparent power is calculated using the formula S = P + jQ, where P is the real power (in MW) and Q is the reactive power (in Mvar). For bus 2, S2 = 14.85 - j32.4 MVA.

Next, we can calculate the voltage at bus 2 using the formula |Vi| = |Vs| - (|S2| / |Z12|), where |Vi| is the absolute value of the voltage at bus i, |Vs| is the desired voltage at bus 3, |S2| is the modulus of the apparent power at bus 2, and |Z12| is the impedance between buses 1 and 2. From the given diagram, we can see that |Z12| is equal to 50.4 pu.

After calculating the voltage at bus 2, we can then determine the voltage at bus 1 using the formula |V1| = |Vs| - (|S2| / |Z13|), where |V1| is the absolute value of the voltage at bus 1, |Z13| is the impedance between buses 1 and 3, and all other variables are defined as before. From the given diagram, we can see that |Z13| is equal to 70.5 pu.