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In the PWM converter-inverter system, if the converter current control is fast enough to match the inverter power at all instants, then no current flows through the DC-link capacitor, making the DC-link voltage constant, even with a very small DC-link capacitance. A matching control method making the capacitor current zero suggests the possibility of using a tiny DC-link capacitor. However, in practice, a certain amount of capacitance is required, since the matching control itself is not perfect and there are one-step delays in the PWM. In this work, the authors investigate a theoretical low bound of the DC-link capacitance, considering an extreme case in which the DC-link voltage rises to a maximum value in a single PWM period. Utilising the optimisation technique, the theoretical minimum capacitance is found to be the one that limits the voltage rise below a certain threshold value. Analytical calculation results are compared with MATLAB simulation results.