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DC Link Capacitor Voltage Ripple

The transient fluctuation in the DC bus voltage (VdcV_{dc}) caused by the switching action. It is inversely proportional to the capacitance CC and the switching frequency fswf_{sw}.
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The statement of the theorem

The DC link capacitor voltage ripple ΔVdc\Delta V_{dc} is the transient fluctuation in VdcV_{dc} caused by the ripple current Δidc\Delta i_{dc} flowing through the capacitor CC. Assuming a switching period TswT_{sw}, the ripple is approximated by: ΔVdc≈Δidc2πfswC \Delta V_{dc} \approx \frac{\Delta i_{dc}}{2 \pi f_{sw} C} where Δidc\Delta i_{dc} is the peak-to-peak ripple current, which is proportional to the output current IoutI_{out} and the switching period TswT_{sw}. The relationship is fundamentally governed by the capacitor charge balance: ∫tt+Tswidc(t)dt=CdVdcdt\int_{t}^{t+T_{sw}} i_{dc}(t) dt = C \frac{d V_{dc}}{dt}.