# Relationship between phase and line voltage

### Review of three-phase systems Single phase voltage can deliver only so much power as all power has to be For this ideal case, the relationship between Line to Neutral RMS voltage and. To derive the relations between line and phase currents and voltages of a star connected system, we have first to draw a balanced star. Where: VL is the line-to-line voltage, and VP is the phase-to-neutral voltage. . Then the relationship between line and phase voltages and currents in a.

This doubles the available power. Three Phase AC Voltage Taking this one step further, high power loads are typically powered using three phases.

### Three-phase Y and Delta Configurations | Polyphase AC Circuits | Electronics Textbook

This distributes the current over three instead of one set of wires, allowing for smaller and thus less expensive wiring. This is illustrated in Figure 2.

Phase rotation does not affect most loads except for three phase AC motors which will turn in opposite direction if the phase rotation is changed. Changing phase rotation can be accomplished by swapping any two of three phase connections. The AFX also allows phase imbalances to be programmed to study the effect of phase variations on a unit under test. This relationship between line to neutral and line to line voltage is shown in the phase diagram of Figure 3. Three Phase Phasor Diagram Figure 4 below shows two typical examples of three phase utility grid voltage configurations used in the United States.

To simulate this type of grid with an AC power source, the 3 phase load is connected as a delta between the three output phases only with no connection to the neutral output terminal.

## Relationship of Line and Phase Voltages and Currents in a Star Connected System

Thus, if any of the stated conditions are not true, you cannot just rely on this formula to determine Line to Line voltage: Identical VLN voltages on all three phases Balanced Phase angles on phase B and C Low distortion, pure sinewave A small phase shift on one or more of the three phases can have a significant impact on VLL voltages which results in load current imbalance as well. Phase voltage refers to the voltage measured across any one component source winding or load impedance in a balanced three-phase source or load.

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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.

### Relationship of Line and Phase Voltages and Currents in a Star Connected System

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.

## Three-phase Y and Delta Configurations

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.