# Star delta voltage and current relationship

### Voltage and Currents in Star- and Delta-Connected Loads | Introduction to AC Circuits | InformIT

The voltage and current relationships in three-phase ac circuits can be simplified by using the rms values (I and V) of the quantities. Refer to Fig. Three Phase Transformer Star and Delta Configurations . The secondary current in each phase of a star-connected group of transformers is the Then the relationship between line and phase voltages and currents in a three-phase system. Relationship of Line and Phase Voltages and Currents in a Star Connected System is perfectly balanced, the magnitude of current and voltage of each phase is the same. Three Phase Circuit | Star and Delta System.

### Voltage and Current Relationships for Different Types of Connection ~ your electrical home

For the circuit shown above, the phase voltage is volts. The terms line current and phase current follow the same logic: Y-connected sources and loads always have line voltages greater than phase voltages, and line currents equal to phase currents.

If the Y-connected source or load is balanced, the line voltage will be equal to the phase voltage times the square root of 3: Take close notice of the polarity for each winding in Figure below. At first glance it seems as though three voltage sources like this would create a short-circuit, electrons flowing around the triangle with nothing but the internal impedance of the windings to hold them back. Due to the phase angles of these three voltage sources, however, this is not the case.

If they do, then there will be no voltage available to push current around and around that loop, and consequently, there will be no circulating current.

Starting with the top winding and progressing counter-clockwise, our KVL expression looks something like this: Indeed, if we add these three vector quantities together, they do add up to zero. Another way to verify the fact that these three voltage sources can be connected together in a loop without resulting in circulating currents is to open up the loop at one junction point and calculate voltage across the break: Sure enough, there will be zero voltage across the break, telling us that no current will circulate within the triangular loop of windings when that connection is made complete.

Conversely, because each line conductor attaches at a node between two windings, the line current will be the vector sum of the two joining phase currents. With each load resistance receiving volts from its respective phase winding at the source, the current in each phase of this circuit will be So each line current in this three-phase power system is equal to The answer is no.

With a Y-connected system, a neutral wire was needed in case one of the phase loads were to fail open or be turned offin order to keep the phase voltages at the load from changing.

This is not necessary or even possible!

Two three-phase load connections that are commonly used in the ac circuits were given in Fig. In this section, the voltage and the current functions are examined while the three-phase loads are connected to the star-connected three-phase supplies, shown in Fig.

Two common balanced-load connections in three-phase ac circuits.

## Three-phase Y and Delta Configurations

Similarly, i1p, i2p, i3p, i12p, i23p, and i31p are the phase currents, and i1L, i2L, and i3L are the line currents. The phase voltages of a three-phase supply can be given as Equation 3. In a balanced three-phase system, there is a very simple relationship between the line and phase quantities, which can be obtained from the phasor quantities or the time-varying expressions of the voltages and the currents. The voltage and current relationships in three-phase ac circuits can be simplified by using the rms values I and V of the quantities.

Voltage and current relationships in three-phase circuits.

Star-Connected Balanced Load Phase current: The VI provides a visual aid to understanding the definitions of phase and line voltages and phase and line currents in the delta- and the star-connected ac systems that contain the loads as well as the ac supplies. In addition, the instantaneous voltage and currents are displayed in the front panel of the VI.

Show that the line voltage Vline in the three-phase system is times the phase voltage Vphase, and verify the result by using the VI for a given phase voltage. Study the concept in question 1 this time for the line currents and the phase currents in the case of a delta-connected three-phase load.