# Phase voltage and Line-Line voltage relation

• Engineering
• PhysicsTest
In summary, the conversation is about finding the phase and line-line voltage relation in a circuit using KVL. The circuit contains a wye transformer, ideal DC sources, and switches. The main question is what the circuit is supposed to do and how the switches are controlled. The conversation also includes attempts at using KVL to calculate the voltages Ua, Ub, and Uc in different switch states. The conversation ends with uncertainty about the correctness of the approach and a reference to a user guide for more information.
PhysicsTest
Homework Statement
Find the phase voltage and Line-Line voltage relation
Relevant Equations
Kirchhoff voltage and current laws
The below is the diagram i want to find the phase and line-line voltage relation

I am finding difficulty in identifying the loop and applying the KVL.
One attempt is
U_{VA} - U_R - U_L -U_O - U_L - U_R = U_VB
U_{VA} - 2(U_R+U_L) = U_VB -> eq1

UVA and UVB should actually be equal if this is a schematic of a wye transformer. They should both be 120V. The line to line voltage would be UAB.

Probably a 3Φ motor drive or inverter, since there are ideal DC sources in there. But it could be a rectifier, I guess. Much depends on the switches. Normally KVL would only be applied for a specific switch state since the network changes when switches change.

What is this circuit supposed to do? How are the switches controlled?

Yes it is inverter
 SAt SBt SCt U_VA U_VB U_VC U_AB U_BC U_CA Ua Ub Uc 1 0 0 udcbus/2 -udcbus/2 -udcbus/2 udcbus 0 -udcbus 0 1 0 -udcbus/2 udcbus/2 -udcbus/2 -udcbus udcbus 0 0 0 1 -udcbus/2 -udcbus/2 udcbus/2 0 -udcbus udcbus 1 1 0 udcbus/2 udcbus/2 -udcbus/2 0 udcbus -udcbus 1 0 1 udcbus/2 -udcbus/2 udcbus/2 udcbus -udcbus 0 0 1 1 -udcbus/2 udcbus/2 udcbus/2 -udcbus 0 udcbus
I want to calculate the voltages Ua, Ub, Uc
For the 1st case if i consider
1 0 0 the circuit will be as below

If i write KVL
a. 1 0 0
VDCBus/2 + Ua -Ub + VDCBus/2 = 0;
Ua - Ub + VDCBus=0 -> 1

b. 0 1 0
VDCBus/2 + Ub -Ua + VDCBus/2=0
-Ua + Ub + VDCBus = 0 -> 2

c. 0 0 1
VDCBus/2 + Uc - Ub + VDCBus/2 = 0 -> 3

Very confusing am i in correct direction? The document is user guide page 51.

## 1. What is the difference between phase voltage and line-line voltage?

Phase voltage refers to the voltage measured between any two phases of a three-phase electrical system. Line-line voltage, also known as line-to-line voltage, refers to the voltage measured between any two of the three lines in a three-phase system. In a balanced three-phase system, the line-line voltage is equal to the square root of three times the phase voltage.

## 2. How are phase voltage and line-line voltage related?

In a balanced three-phase system, the line-line voltage is equal to the square root of three times the phase voltage. This means that the line-line voltage is always higher than the phase voltage. For example, if the phase voltage is 120V, the line-line voltage would be approximately 208V.

## 3. Why is it important to understand the relationship between phase voltage and line-line voltage?

Understanding the relationship between phase voltage and line-line voltage is important for designing and troubleshooting three-phase electrical systems. It allows engineers and technicians to accurately measure and control the voltage in a system, ensuring its safe and efficient operation.

## 4. Can the phase voltage and line-line voltage be different in a three-phase system?

Yes, the phase voltage and line-line voltage can be different in a three-phase system if the system is unbalanced. This means that the loads on each phase are not equal, resulting in different voltages. In an unbalanced system, the line-line voltage can be higher or lower than the square root of three times the phase voltage.

## 5. How do you calculate the line-line voltage in a three-phase system?

To calculate the line-line voltage in a three-phase system, you can use the formula VLL = √3 x Vph, where VLL is the line-line voltage and Vph is the phase voltage. For example, if the phase voltage is 240V, the line-line voltage would be approximately 415V.

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