PYQs Based test 13: Power Systems

In the following network, the voltage magnitudes at all buses are equal to 1 pu, the voltage phase angles are very small, and the line resistances are negligible. All the line reactances are equal to j1Ω



The voltage phase angles in rad at buses 2 and 3 are

For the system below, S${}_{D1}$ and S${}_{D2}$ are complex power demands at bus 1 and bus 2 respectively. If |V₂| = 1 pu, the VAR rating of the capacitor ( Q${}_{G2}$) connected at bus 2 is

The figure shows a two – generator system applying a load of P${}_D$ = 40 MW, connected at bus 2.



The fuel cost of generators G₁ and G₂ are :

C₁(P${}_{G1}$) = 10000 Rs/MWh and C₂(P${}_{G2}$) = 12500 Rs/MWh and the loss in the line is

$P_{loss\left(Pu\right)}=0.5P_{G1\left(Pu\right)}^2$, Where the loss coefficient is specified in pu on a 100 MVA base. The most economic power generation schedule in MW is

Two generator units G₁ and G₂ are connected by 15kV line with a bus at the mid-point as shown below



G₁ = 250 MVA, 15 kV, positive sequence reactance X${}_{G1}$ = 25% on its own base

G₂ = 100 MVA, 15 kV, positive sequence reactance X${}_{G2}$ = 10% on its own base L₁ and L₂ = 10 km, positive sequence reactance X${}_L$ = 0.225 Ω/km

For the above system, the positive sequence diagram with the p.u values on the 100 MVA common base

Power is transferred from system A to system B by an HVDC link as shown in the figure. If the voltage V${}_{AB}$ and V${}_{CD}$ are as indicated in the figure, and I > 0, then