You visited us 39 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Displacement

A two bus sys...

Question

A two bus system is shown below,

If 150 MW is transmitted from plant 2 to the load, a transmission loss of 15 MW is incurred. The incremental fuel costs of the two plants are:

$\frac{d C_{1}}{d P_{G 1}} = 0.04 P_{G 1} + 20 R s / M W h$

$\frac{d C_{2}}{d P_{G 2}} = 0.02 P_{G 2} + 16 R s / M W h$

The power received by load is ____ MW. (Assume system $λ$ = Rs. 25/MWh)
274.75

Open in App

Solution

The correct option is A 274.75
We know that,

Transmission loss, $P_{L} = B_{22} P_{G 2}^{2}$

$15 = B_{22} (150)^{2}$

$B_{22} = 6.6667 \times 10^{- 4} (M W^{- 1})$

$I C = λ (1 - \frac{\partial P_{L}}{\partial P_{1}})$

Now, $0.04 P_{G 1} + 20 = λ = 25$

$P_{G 1} = 125 M W$

and $0.02 P_{G 2} + 16 = λ (1 - 2 \times 6.6667 \times 10^{- 4} \times P_{G 2})$

$P_{G 2} = 168.75 M W$

$P_{L} = 6.6667 \times 10^{- 4} \times (168.75)^{2} ≅ 19 M W$

$P_{D 1} = P_{G 1} + P_{G 2} - P_{L}$

$= 125 + 168.75 - 19$

$P_{D 1} = 274.75 M W$

Suggest Corrections

Similar questions

Q. A two bus system is shown below,

If 150 MW is transmitted from plant 2 to the load, a transmission loss of 15 MW is incurred. The incremental fuel costs of the two plants are:

\frac{d C_{1}}{d P_{G 1}} = 0.04 P_{G 1} + 20 R s / M W h

\frac{d C_{2}}{d P_{G 2}} = 0.02 P_{G 2} + 16 R s / M W h

The power received by load is ____ MW. (Assume system

λ

= Rs. 25/MWh)

Q. A constant load of 300 MW is supplied by two 200 MW generators, for which incremental fuel costs are:

\frac{d C_{1}}{d P_{G 1}} = 0.10 P_{G 1} + 20.0; \frac{d C_{2}}{d P_{G 2}} = 0.12 P_{G 2} + 15

[Where

P_{G}

is in MW and C in Rs/hr]
If the most economic division of load between the generators is X and Y MW, then saving in Rs/day obtained compared to equal load sharing is Rs, _____ per day.

Q. Incremental fuel costs (in some appropriate unit) for a power plant consisting of three generating units are

I C_{1} = 20 + 0.3 P_{1}

I C_{2} = 30 + 0.4 P_{2}

I C_{3} = 30

where P

_{i}

is the power in MW generated by units for i = 1, 2 and 3.

Assume that all the three units are operating all the time. Minimum and maximum loads on each units are 50 MW and 300 MW respecitvely. If the plant is operating on economic load dispatch to supply the total power demand of 700 MW, the power generated by each unit is

Q. The figure shows a two-generator system supplying a load of P

_{D}

= 40 MW, connected at bus 2.

The fuel cost of generators G

_{1}

and G

_{2}

are:

IC

_{1}

_{G 1}

) = 10,000 Rs/MWh and

IC

_{2}

_{G 2}

) = 12,500 Rs/MWh

and the loss in the line is
P

_{l o s s (p u)}

= 0.5P

_{G 1}^{2} (p u)

, where the loss coefficient is specified in pu on a 100 MVA base. The most economic power generation schedule in MW is

Q. The incremental cost characteristic of two plant systems are

I C_{1} = 1.0 P_{1} + 85 R s / M W h r

I C_{2} = 1.2 P_{2} + 72 R s / M W h r

where $P_{1}$ and $P_{2}$ are in MW. The loss coefficient matrix in MW is $(\begin{matrix} 0.012 & - 0.001 - 0.001 & 0.04 \end{matrix}]$ the optimum scheduling for $λ = 150 R s / M W h r$ will be

Join BYJU'S Learning Program