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 magnitude of three-phase fault currents at buses A and B of a power system are 10 pu and 8 pu, respectively. Neglect all resistances in the system and consider the pre-fault system to be unloaded. The pre-fault voltage at all buses in the system is 1.0 pu. The voltage magnitude at bus B during a three-phase fault at bus A is 0.8 pu. The voltage magnitude at bus A during a three-phase fault at bus B in pu, is __________.

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.

A $$3$$-bus power system network consists of $$3$$ transmission lines. The bus admittance matrix of the uncompensated system is
$$\left[ {\matrix{ { - j6} & {j3} & {j4} \cr {j3} & { - j7} & {j5} \cr {j4} & {j5} & { - j8} \cr } } \right]\,pu$$
If the shunt capacitance of all transmission lines is $$50$$% compensated, the imaginary part of the $$3$$^rd row $$3$$^rd column element (in $$pu$$) of the bus admittance matrix after compensation is