# Derive the relationship between phase and line voltages mathematically

### Voltage and Currents in Star- and Delta-Connected Loads | Introduction to AC Circuits | InformIT The NI is connected between each phase and neutral: visualize the phasor math required to convert from line-to-neutral voltages to line-to-line voltages. Magnitude and phase relationship of all voltages in system. In a star connection the line current is equal to the phase current. http://www. ddttrh.info It actually simply follows from the derivation from how three phase circuits are. To derive the relations between line and phase currents and voltages of a star connected system, we have first to draw a balanced star.

It is very convenient to carry out the calculations in a per-phase star-connected line to neutral basis. 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. 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.

## Transmission Line Analysis

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. The NI is rated to Vrms from channel to earth, so the measurement is within the safety specifications. Assuming a perfectly balanced system, each phase is separated by degrees and the line-to-neutral voltage on each phase is the same.

As long as these two assumptions hold true, then the magnitude of the line to line voltage is 1.

### Transmission Line Analysis

If the line-to-neutral voltage is Vrms, then the line-to-line voltage will be Vrms. The NI is rated for V ch-ch isolation, so this voltage is within the safety specifications.

Back to Top 2. Measuring line-to-line Voltages - The Most General Case The connection scheme shown above in figure 1 can be used to indirectly measure the line-to-line voltages on a Y-connected systems.

The line-to-line voltage is the vector sum of the line to neutral voltages. So, for example, if we know Van, Vbn, and Vcn defined as in the diagram belowwe can find the line to line voltages as follows: The following phasor diagram diagram 1 will help visualize the phasor math required to convert from line-to-neutral voltages to line-to-line voltages. Line-to-line calculation phasors We will start with an example showing how to measure Vab.

### Power in Three-Phase AC Circuits | Introduction to AC Circuits | InformIT

As has been described above, the line-to-line voltage is the phasor sum of the line-to-neutral voltages, so Nominally, each phase in a three phase system is spaced exactly degrees apart. However, since our intent is to perform measurements in the system, we cannot assume it to be ideal.

Breaking up Vbn into rectangular components results in the following: Subtracting the in-phase component of Vbn from Van: