# DC bus capacitance design for SPWM inverter

I am working on a 5kW grid-connected inverter where I need to find the DC bus capacitance value. I understand that the capacitor serves 2 purposes: 1) to provide a low impedance path for the high frequency currents from the device, and 2) To reduce voltage ripple in the DC bus.

Some specifications:

DC bus voltage = 800 V

Phase voltage = 240 V

So I first thought of finding out the ripple current that flows into the capacitor, so that it can be used to find the required capacitance for a given voltage ripple specification. I found the equation for the DC bus capacitor current in SPWM inverter from a paper. I have 2 questions, one mathematical and one relating to the design.

Question 1:

Here, $$\ \hat{A}_{0n} \$$ and $$\ \hat{B}_{0n} \$$ are zero (proved by the paper for SPWM inverters). The resulting equation has a dc component and a bunch of other components. Now, if I were to find the frequency spectrum of this series, will the magnitude of $$\ i_C(t) \$$ at frequency $$\ m \omega_c + n\omega_o \$$ equal to $$\ \sqrt{\hat{A}_{mn}^2 + \hat{B}_{mn}^2 }\$$? Given that I wanted to find the rms ripple current, I wanted to find the rms value of all the components except the DC term.

Question 2:

After finding the rms ripple current through the capacitor, I used: $$\frac{i_{ripple, rms}}{C} = \frac{dV}{dt}$$ If the voltage ripple specification ($$\ dV \$$) is given, can this be rearranged as: $$C = \frac{dV}{i_{ripple, rms} \cdot f_{sw}}$$ where $$\ f_{sw} \$$ is the switching frequency?

• If you are working on a design then sure, it may be of some interest to some folk to derive a simplistic version of the math but, why aren't you using a simulator to model the circuit and find all the nuances that maths isn't going to show up. Commented Jul 1, 2023 at 15:08
• @Andyaka I am trying to do it on Simulink and am working on that model as well, but thought whether this theoretical design would make sense. Commented Jul 1, 2023 at 15:31
• What are A and B? Just Fourier coefficients, no waveform yet defined? Commented Jul 1, 2023 at 20:14
• @TimWilliams They are Fourier coeficients that depend on a bunch of factors related to the inverter; I am able to evaluate them (there were equations for the coefficients in the paper I mentioned). Commented Jul 2, 2023 at 1:03

If the voltage ripple specification ($$\ dV \$$) is given, can this be rearranged as: $$C = \frac{dV}{i_{ripple, rms} \cdot f_{sw}}$$ where $$\ f_{sw} \$$ is the switching frequency?
Which, since the harmonics are AC sinusoidal steady-state, you should use that form: $$\\frac{V}{I} = \frac{1}{2 \pi F C}\$$.
• Do you mean evaluate $C_h = \frac{I_h}{2 \cdot \pi \cdot f_h \cdot V_{ripple}}$ and then sum the capacitor value over the range of harmonics? Commented Jul 2, 2023 at 1:12