Final answer:
To derive the algebraic relations in a three-phase converter circuit, Kirchhoff's voltage and current laws are applied to determine currents and voltages across the circuit. The junction rule and loop rule form a set of linear equations that are solved to find the unknowns, and components like IGBTs, MOSFETs, and thyristors can serve as switches.
Step-by-step explanation:
The algebraic relations between the inputs and outputs of a three-phase converter can be derived using Kirchhoff's voltage and current laws. According to Kirchhoff's first rule, also known as the junction rule, the sum of all currents entering a junction must be equal to the sum of all currents leaving that junction. Kirchhoff's second rule, the loop rule, states that the algebraic sum of potential changes around any closed circuit path must be zero, which is a result of energy conservation.
Applying the junction rule at a point 'a' in the circuit might look something like: I1 = I2 + I3, where I1, I2, and I3 are the currents at the junction.
For the loop rule, consider a closed loop in the circuit and write down the sum of voltage drops and rises which should equal zero. This generates a set of linear equations corresponding to each loop. By solving these equations simultaneously, we can find the unknown currents in the circuit. Semiconductor devices such as IGBTs (Insulated Gate Bipolar Transistors), MOSFETs (Metal Oxide Semiconductor Field-Effect Transistors), or thyristors can be employed as switching elements in the converter circuit. The relations in matrix form will contain coefficients for resistances, inductances, and the known voltages from sources Vg1 and Vg2.