Final answer:
To derive the modelling equations for a three-phase Buck-inverter, apply Kirchhoff's laws and solve for the unknown currents using the junction and loop rules.
Step-by-step explanation:
Deriving the modelling equations for a three-phase Buck-inverter involves applying Kirchhoff's laws. We need to apply the junction and loop rules to obtain three independent equations that allow us to solve for the three unknown currents. The equations obtained by applying Kirchhoff's rules are:
a. Kirchhoff's junction rule at point A: I₁ + I₃ = 12
b. Kirchhoff's loop rule in the upper loop: E₁ - I₁R₁ - I₂R₂ - I₁r₁ = 0
c. Kirchhoff's loop rule in the lower loop: -E₂ + I₁R₁ - I₃R₃ - I₂r₂ = 0