Electrical Engineering BMT & UFC › Energy Storage › Electrical Energy Storage

Capacitor

Capacitors are introduced in the tutorial Fundamentals of Electrical Engineering. Please read through this chapter again beforehand. The behaviour of voltage and current at the capacitor is described intuitively in this chapter.

For the capacitor, the following applies:

\[ \begin{gathered} u_C = U_{C0} + \frac{1}{C} \int i_C(t)\,dt \\[6pt] i_C(t) = C \cdot \frac{du(t)}{dt} \end{gathered} \]

In power electronics, capacitors are used to smooth voltages. If the current changes strongly at a point in a circuit, the voltage there often changes particularly strongly as a result. If the current flows through a resistor, the voltage changes by ΔU = R ∙ ΔI. Capacitors ensure that the voltage changes only slightly despite a large change in current. There are two ways of looking at the smoothing effect:

For the voltage across a capacitor to change in the form of dU/dt, current must flow into or out of it. The current at the capacitor is proportional to the change in voltage, i.e. the derivative of the voltage du/dt. The more the voltage changes, the more current must flow. The larger the capacitance C, the more current must flow per change in voltage. So for a fixed current, the voltage changes less with a high capacitance than with a low capacitance.

When current is drawn from a capacitor or flows into it, the voltage changes according to the integral equation. The change in voltage caused by this current is proportional to the integral – i.e. the sum – of the current. The more current flows, the greater the change in voltage. The factor 1/C ensures that the voltage changes less with a higher capacitance C.

Next, we return to the analogy of the capacitor as a water store. The electric current corresponds to the inflow or outflow of water. The voltage corresponds to the fill level and the capacitance to the base area of the water store. When water flows into or out of the water store per unit of time, the fill level changes less, the larger the base area of the store. With a swimming pool, the fill height changes less than with a water glass for the same inflow. In power electronics, we use capacitors the size of a swimming pool so that the inflow or outflow of water (current) affects the fill level (voltage) as little as possible.

If we provide a large capacitance C, a capacitor in a circuit ensures that the voltage changes only slightly, even if the current changes strongly. Please keep this behaviour in mind as you continue working through the tutorial.