GATE EE 2014 Question Paper (01-Mar-2014) (Shift 2)

A two bus power system shown in the figure supplies load of 1.0 + j 0.5 p.u.



The values of V₁ in p.u. and δ₂ respectively are

The fuel cost functions of two power plants are

Plant $P1:C_1=0.05P{g}_1^2+AP{g}_1+B$

Plant $P_2:C_2=0.10P{g}_2^2+3AP{g}_2+2B$

Where, P${}_{g1}$ and P${}_{g2}$ are the generated powers of two plants, and A and B are the constants. If the two plants optimally share 1000 MW load at incremental fuel cost of 100 Rs/MWh, the ratio of load shared by plants P₁ and P₂ is

The overcurrent relays for the line protection and loads connected at the buses are shown in the figure.



The relays are IDMT in nature having the characteristic

$t_{op}=\frac{0.14\times TimeMultiplierSetting}{{\left(PlugSettingMultiplier\right)}^{0.02}-1}$

The maximum and minimum fault currents at bus B are 2000 A and 500 A respectively. Assuming the time multiplier setting and plug setting for relay RB to be 0.1 and 5A respectively, the operating time of RB (in seconds) is_______

For the given system, it is desired that the system be stable. The minimum value of α for this condition is _______________.

The Bode magnitude plot of the transfer function $G\left(s\right)=\frac{K\left(1+0.5s\right)\left(1+as\right)}{s\left(1+\frac{s}{8}\right)\left(1+bs\right)\left(1+\frac{s}{36}\right)}$ is shown below. Note that – 6dB/octave = -20 dB/decade. The value of $\frac{a}{bK}$ is ___________