Why infinite bus frequency and voltage stay constant

An infinite bus is a bus of a very large system (ideally zero impedance and infinite inertia), so a load change at one point is negligible compared with its capacity.

• Voltage constant: Bus voltage $V = E_{th} - IZ_{th}$. For a huge interconnected system, $Z_{th}\approx0$ (very high fault level), so a change in load current produces almost no voltage drop; also many generators with AVRs share the reactive demand.
• Frequency constant: Frequency changes when the power balance changes, at a rate set by system inertia ($df/dt \propto \Delta P/H$). The total inertia of all machines is extremely large, and many governors share any load change, so $\Delta f \approx 0$.

Hence a load change that is tiny relative to the total generation leaves the voltage and frequency practically unchanged.