The expressions of fuel cost of two thermal generating units as a function of the respective power generation $${P_{G1}}$$ and $${P_{G2}}$$ are given as

$$\matrix{ {{F_1}({P_{G1}}) = 0.1aP_{G1}^2 + 40{P_{G1}} + 120\,Rs/hour} & {0\,MW \le {P_{G1}} \le 350\,MW} \cr {{F_2}({P_{G2}}) = 0.2P_{G2}^2 + 30{P_{G2}} + 100\,Rs/hour} & {0\,MW \le {P_{G2}} \le 300\,MW} \cr } $$

where $$a$$ is a constant. For a given value of $$a$$, optimal dispatch requires the total load of 290 MW to be shared as $${P_{G1}} = 175\,MW$$ and $${P_{G2}} = 115\,MW$$. With the load remaining unchanged, the value of $$a$$ is increased by 10% and optimal dispatch is carried out. The changes in $${P_{G1}}$$ and the total cost of generation, $$F( = {F_1} + {F_2})$$ in Rs/hour will be as follows

The bus admittance ($$Y_{bus}$$) matrix of a 3-bus power system is given below.

$$\quad\quad$$$$\matrix{ 1 & \quad\quad\quad2\quad\quad & 3 \cr } $$

$$\matrix{ 1 \cr 2 \cr 3 \cr } \left[ {\matrix{ { - j15} & {j10} & {j5} \cr {j10} & { - j13.5} & {j4} \cr {j5} & {j4} & { - j8} \cr } } \right]$$

Considering that there is no shunt inductor connected to any of the buses, which of the following can NOT be true?

The p.u. parameters for a $$500$$ MVA machine on its own base are:
Inertia, M = $$20$$ p.u.; reactance X = $$2$$ p.u. The p.u. values of inertia and reactance on $$100$$ MVA common base, respectively are

The three-bus power system shown in the figure has one alternator connected to bus 2 which supplies 200 MW and 40 MVAr power. Bus 3 is infinite bus having a voltage of magnitude $$|{V_3}| = 1.0$$ p.u. and angle of $$-15^\circ$$. A variable current source, $$|I|\angle \phi $$ is connected at bus 1 and controlled such that the magnitude of the bus 1 voltage is maintained at 1.05 p.u. and the phase angle of the source current, $$\phi = {\theta _1} \pm {\pi \over 2}$$, where $$\theta_1$$ is the phase angle of the bus 1 voltage. The three buses can be categorized for load flow analysis as

Two generator units $$G1$$ and $$G2$$ are connected by $$15$$ $$kV$$ line with a bus at the mid-point as shown below
$${G_1} = 250\,\,MVA.\,\,\,15kV,\,\,$$ positive sequence $$X = 25$$% on its own base
$${G_2} = 100\,\,MVA.\,\,\,15kV,\,$$ positive sequence $$X = 10$$% on its own base
$${L_1}$$ and $${L_2}$$ $$= 10$$ $$km,$$ positive sequence $$ X = 0.225$$ $$\,\,\Omega /km$$

In the above system the three-phase fault $$MVA$$ at the bus $$3$$ is

Two generator units $$G1$$ and $$G2$$ are connected by $$15$$ $$kV$$ line with a bus at the mid-point as shown below
$${G_1} = 250\,\,MVA.\,\,\,15kV,\,\,$$ positive sequence $$X = 25$$% on its own base
$${G_2} = 100\,\,MVA.\,\,\,15kV,\,$$ positive sequence $$X = 10$$% on its own base
$${L_1}$$ and $${L_2}$$ $$= 10$$ $$km,$$ positive sequence $$ X = 0.225$$ $$\,\,\Omega /km$$

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

For the power system shown in the figure below, the specifications of the components are the following:
$$G1: 25$$ $$kV,$$ $$100$$ $$MVA,$$ $$X=9$$%
$$G2: 25$$ $$kV,$$ $$100$$ $$MVA,$$ $$X=9$$%
$$T1: 25$$ $$kV/220$$ $$kV,$$ $$90$$ $$MVA,$$ $$X=12$$%
$$T2: 220$$ $$kV/ 25$$ $$kV,$$ $$90$$ $$MVA,$$ $$X=12$$%
$$Line$$ $$1: 220$$ $$kV,$$ $$X= 150$$ $$ohms$$

Choose $$25$$ $$kV$$ as the base voltage at the generator $$G1,$$ and $$200$$ $$MVA$$ as the $$MVA$$ base. The impedance diagram is

A generator is connected through a $$20$$ MVA, $$13.8/138$$ kV step up transformer, to a transmission line. At the receiving end of the line a load is supplied through a step down transformer of $$10$$ MVA, $$138/69$$ kV rating. A $$0.72$$ p.u. load, evaluated, on load side transformer ratings as base values of $$10$$ MVA and $$69$$ kV in load circuit, the value of the load (in per unit) in generator circuit will be

A new generator having $${E_g} = 1.4\,\angle {30^ \circ }\,$$ pu [ equivalent to ($$1.212 +j$$ $$0.70$$)pu ] and synchronous reactance $$'{X_s}'$$ of $$1.0$$ pu on the system base, is to be connected to a bus having voltage $${V_t}$$ in the existing power system. This existing power system can be represented by Thevenin's voltage $${E_{th}} = 0.9\angle {0^ \circ }\,\,$$ pu in series with Tjhevenin's impedance $${Z_{th}} = 0.25\angle {90^ \circ }\,\,$$ pu. The magnitude of the voltage $${V_t},$$ of the system in pu will be

A $$75$$ MVA, $$10$$ kV synchronous generator has X_d $$= 0.4$$ p.u. The X_d value (in p.u.) is a base of $$100$$ MVA, $$11$$ kV is