## Tuesday, November 23, 2021

Star-triangle start

Star-delta starting
Star-delta starting is a device widely used in electrical engineering for the two-stroke starting of three-phase asynchronous electric motors.

The understanding of such a device is done simply by studying the two modes of star and delta coupling.
The comparison of the physical quantities and the mathematical approach then make it possible to understand the interest of star-delta starting.

Problem
A motor made up of three identical receivers of impedance Z, of a power factor Cos phi is connected to a three-phase network with phase-to-neutral voltage V and phase-to-phase voltage U.

For the study we perform the following tasks:

Write the formula which gives the intensity in line when we couple the three receivers in a star (I ★).
Write the formula which gives the intensity in line when we couple the three receivers in a triangle (I △).
Study the ratio I triangle by I star (I △ ÷ I ★).
Write the formula which gives the power in a star (P ★).
Write the formula which gives the power in triangle (P △).
Study the ratio Ptriangle by Petstar (P △ ÷ P ★).
Writing convention: a triangle (△) in index of a quantity means that we consider this quantity in the triangle coupling mode.
A star (★) in the index of a quantity means that this quantity is considered in the star coupling mode.

Study of star and delta couplings
Z1, Z2 and Z3 are three identical receivers (and therefore with identical Z impedances); L1, L2 and L3 are the three-phase supply lines.

Star-triangle start

Star-delta starting
Star-delta starting is a device widely used in electrical engineering for the two-stroke starting of three-phase asynchronous electric motors.

The understanding of such a device is done simply by studying the two modes of star and delta coupling.
The comparison of the physical quantities and the mathematical approach then make it possible to understand the interest of star-delta starting.

Problem
A motor made up of three identical receivers of impedance Z, of a power factor Cos phi is connected to a three-phase network with phase-to-neutral voltage V and phase-to-phase voltage U.

For the study we perform the following tasks:

Write the formula which gives the intensity in line when we couple the three receivers in a star (I ★).
Write the formula which gives the intensity in line when we couple the three receivers in a triangle (I △).
Study the ratio I triangle by I star (I △ ÷ I ★).
Write the formula which gives the power in a star (P ★).
Write the formula which gives the power in triangle (P △).
Study the ratio Ptriangle by Petstar (P △ ÷ P ★).
Writing convention: a triangle (△) in index of a quantity means that we consider this quantity in the triangle coupling mode.
A star (★) in the index of a quantity means that this quantity is considered in the star coupling mode.

Study of star and delta couplings
Z1, Z2 and Z3 are three identical receivers (and therefore with identical Z impedances); L1, L2 and L3 are the three-phase supply lines.