Connection of Two Power Elements
A Commutation cell connects two power elements, often referred to as sources, although they can either produce or absorb power.
Some requirements to connect power sources exist. The impossible configurations are listed in figure 1. They are basically:
- a voltage source cannot be shorted, as the short circuit would impose a zero voltage which would contradict the voltage generated by the source;
- in an identical way, a current source cannot be placed in an open circuit;
- two (or more) voltage sources cannot be connected in parallel, as each of them would try to impose the voltage on the circuit;
- two (or more) current sources cannot be connected in series, as each of them would try to impose the current in the loop.
This applies to classical sources (battery, generator), but also to capacitors and inductors: At a small time scale, a capacitor is identical to a voltage source, and an inductor to a current source. Connecting two capacitors with different voltage level in parallel therefore corresponds to connecting two voltage sources, one of the forbidden connections of figure 1.
The figure 2 illustrates the poor efficiency of such connection. One capacitor is charged to a voltage V, and is connected to a capacitor with the same capacity, but discharged.
Before the connection, the energy in the circuit is, and the quantity of charges Q is equal to .
After the connection has been made, the quantity of charges is constant, and the total capacitance is . Therefore the voltage across the capacitances is . The energy in the circuit is then . Therefore half of the energy has been dissipated during the connection.
The same applies with the connections in series of two inductances. The magnetic flux remains constant before and after the commutation. As the total inductance after the commutation is 2L, the current becomes (see figure 2). The energy before the commutation is . After, it is . Here again, half of the energy is dissipated during the commutation.
As a result, it can be seen that a commutation cell can only connect a voltage source to a current source (and vice versa). However, using inductors and capacitors, it is possible to transform the behaviour of a source: for example two voltage sources can be connected through a converter if it uses an inductor to transfer energy.
Read more about this topic: Commutation Cell
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