GATE EE 2015 Question Paper (07-Feb-2015) (Shift 1)

Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are given below:

$\begin{array}{l}{C}_1\left(P_1\right)=0.01P_1^2+30P_1+10;100MW\le P_1\le 150MW\\ C_2\left(P_2\right)=0.05P_2^2+10P_2+10;100MW\le P_2\le 180MW\end{array}$

The incremental cost (in Rs/MWh) of the power plant when it supplies 200 MW is ___________

Determine the correctness or otherwise of the following Assertion (A) and the Reason (R).

Assertion (A) : Fast decoupled load flow method gives approximate load flow solution because it uses several assumptions.

Reason (R) : Accuracy depends on the power mismatch vector tolerance

A 50 Hz generating unit has H – constant of 2 MJ/MVA. The machine is initially operating in steady-state at synchronous speed and producing 1 pu of real power. The initial value of the rotor angle δ is 5° when a bolted three-phase to ground short circuit fault occurs at the terminal of the generator. Assuming the input mechanical power to remain at 1 pu, the value of δ in degrees, 0.02 second after the fault is_________

A sustained three phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are also shown. Where is the fault located?

The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volts) is given by v(t) = 12 sin t. If the circuit is in steady-state, then the rms value of the current (in Ampere) flowing in the circuit is ____.