A load center of 120 MW derives power from two power stations connected by 220 kV transmission lines of 25 km and 75 km as shown in the figure below. The three generators G1,G2 and G3 are of 100 MW capacity each and have identical fuel cost characteristics. The minimum loss generation schedule for supplying the 120 MW load is

A negative sequence relay is commonly used to protect

A three–bus network is shown in the figure below indicating the p.u. impedances of each element

The bus admittance matrix, $$Y$$-$$bus,$$ of the network 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 $$ X = 0.225$$ $$\,\,\Omega /km$$

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