A $$3$$-bus power system is shown in the figure below, where the diagonal elements of $$Y$$-bus matrix are: $${Y_{11}} = - j12\,pu,\,\,\,{Y_{22}} = - j15\,pu\,\,$$ and $$\,{Y_{33}} = - j7\,pu.$$

The per unit values of the line reactance's $$p, q$$ and $$r$$ shown in the figure are

In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is $$\,100\,\, \times \,\,100.$$ If there are $$20$$ PV buses in addition to PQ buses and a slack bus, the total number of buses in the system is ________.

The figure show the per-phase representation of a phase-shifting transformer connected between buses $$1$$ and $$2,$$ where $$\alpha $$ is a complex number with non-zero real and imaginary parts.
For the given circuit, $${Y_{bus}}$$ and $${Z_{bus}}$$ are bus admittance matrix and bus impedance matrix, respectively, each of size $$2\, \times \,2$$. Which one of the following statements is true?

In a 100 bus power system, there are 10 generators. In a particular iteration of Newton Raphson load flow technique (in polar coordinates), two of the PV buses are converted to PQ type. In this iteration.