Ask question

Ask question

All categories

3 years ago

12

The line voltage of a balanced three-phase transmission line is 4200 V rms. The transmission line has an impedance of 4 6 Z j l

  per phase. Assuming that the load receives a total of 1 MVA at 0.75 power factor lagging, determine (a) the complex power, (b) the power loss in the three-phase line, (c) the line voltage at the sending end of the transmission line.

1 answer:

balu736 [363]3 years ago

4 0

Answer:

1.23MVA, 226.74kW, 5.16kV

Explanation:

Parameters Given

line impedance, Zl = (4 + j6) ohms per phase

load voltage, Vl = 4200V

received complex power, S = 1 × 10⁶VA

power factor, cosФ = 0.75

Ф = 41.41°

sinФ = 0.66

Solution:

S = √3 * Vl * I (that is √3 × line voltage × line current)

1 × 10⁶ = √3 × 4200 × I

I = 137.46A

Vl = 4200∠0

I = 137.46∠- 41.41° lagging

source voltage, Vs = load voltage, Vl + voltage drop along the line, Vd

Vd = Zl * I where ( Zl = 4 + j6, = √(4² + 6²)∠tan⁻¹(6/4), = 7.21∠56.31° )

Vd = 7.21∠56.31° × 137.46∠- 41.41°

= 991.22∠14.9°

Vs = Vl + Vd

= 4200∠0° + 991.22∠14.9°

= 4200(cos 0° + j sin 0°) + 991.22(cos 14.9° + jsin 14.9°)

= 4200 + 957.68 + j254.88

= 5157.68 + j254.88

or

= 5163.97∠2.83° V (line voltage at the sending end of the transmission line)

Sending end current, I = 137.46∠-41.41 A

(a) Complex power = √3 × Vs × I

= √3 × 5163.97∠2.83° ×137.46∠-41.41

= 1229477.76∠-38.58°VA

= 1.23∠-38.58MVA

complex power = 1.23MVA

(b) power loss in the three phase line, Pl = 3 × square of line current, I × line impedance, Rl

Pl =3 × I² × Rl where Zl = R + j X = 4 + j6 hence R = 4

= 3 × 137.46² × 4

= 226743.02W

= 226.74kW

(c) from the above, the line voltage at the sending end of the transmission line is = 5163.97V

= 5.16kW

You might be interested in

Part of the basic procedures is the vehicle check. What does that mean?

saul85 [17]

The choices are:

a. bringing it to a mechanic for a tune-up

b. checking to make sure it is in working order

c. making sure you are entering your vehicle

d. giving the tires a good kick to check traction

Answer:

The answer is: letter b, checking to make sure it is in working order.

Explanation:

A "vehicle check" is essential for everyone involved. It makes the driver and the passengers safe, and also extends that safety to the people in the environment. Before driving, you need to check your car for the following: <em>fluids, wipers, spare wheels, leaks and the like</em>. This will ensure that your vehicle is in proper working order and <u>will lessen the possibility of car accident in the future.</u>

Thus, this explains the answer, letter b.

5 0

3 years ago

You have been assigned to design an open cylindrical storage tank 4 meters tall with a diameter of 8 meters to be made out of A-

Katen [24]

Answer:

The required wall thickness is $1.506 \times 10^{-3}$ m

Explanation:

Given:

Fluid density $\rho = 1200$ $\frac{kg}{m^{3} }$

Diameter of tank $d = 8$ m

Length of tank $l = 4$ m

F.S = 4

For A-36 steel yield stress $\sigma = 250$ MPa,

Allowable stress $\sigma _{allow} = \frac{\sigma}{F.S}$

$\sigma _{allow} = \frac{250}{4} = 62.5$ MPa

Pressure force is given by,

$P = \rho gh$

$P = 1200 \times 9.8 \times 4$

$P = 47088$ Pa

Now for a vertical pipe,

$\sigma _{allow} = \frac{Pd}{4t}$

Where $t =$ required thickness

$t = \frac{Pd}{4 \sigma _{allow} }$

$t = \frac{47088 \times 8 }{4 \times 62.5 \times 10^{6} }$

$t = 1.506 \times 10^{-3}$ m

Therefore, the required wall thickness is $1.506 \times 10^{-3}$ m

8 0

3 years ago

¿Cuál era probablemente el activo más valioso de Persia?

laila [671]

Answer:

su suministro de aceite

Explanation:

(it's oil supply)

8 0

4 years ago

Read 2 more answers

When do you know if you start volly ball

igomit [66]

Answer You ask your coach

7 0

3 years ago

A continuous random variable, X, whose probability density function is given by f(x) = ( λe−λx , if x ≥ 0 0, otherwise is said t

Ganezh [65]

Answer:

a) $F(x) = \lambda \int_0^{\infty} e^{-\lambda x} dx= -e^{-\lambda x} \Big|_0^{\infty} = 1- e^{-\lambda x} \$

b) $P(10 < X$

Explanation:

Previous concepts

The cumulative distribution function (CDF) F(x),"describes the probability that a random variableX with a given probability distribution will be found at a value less than or equal to x".

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution".

Part a

Let X the random variable of interest. We know on this case that $X\sim Exp(\lambda)$

And we know the probability denisty function for x given by:

$f(x) = \lambda e^{-\lambda x} , x\geq 0$

In order to find the cdf we need to do the following integral:

$F(x) = \lambda \int_0^{\infty} e^{-\lambda x} dx= -e^{-\lambda x} \Big|_0^{\infty} = 1- e^{-\lambda x} \$

Part b

Assuming that $X \sim Exp(\lambda =0.1)$ , then the density function is given by:

$f(x) = 0.1 e^{-0.1 x} dx , x\geq 0$

And for this case we want this probability:

$P(10 < X$

And evaluating the integral we got:

$P(10 < X$

4 0

4 years ago