# Synchronous generator phasor diagram

• LagCompensator
In summary, the conversation discussed a problem statement involving a 4-pole, star-connected, 50 Hz, 11kV, 40 MVA turbogenerator and its connection to a power network. The relevant equation was provided, which involved the alternator terminal voltage, series reactance, and field current. A phasor diagram was drawn to illustrate the relationship between the variables, with the angle between V_t and I_a representing the lagging power factor. The question posed was about the placement of I_a and how to determine its angle, with the understanding that V_t is chosen as the reference phasor. The speaker also expressed confusion about the meaning of p.i. in relation to synchronous reactance.

#### LagCompensator

1. Problem Statement:
A 4-pole, star-connected, 50 Hz, 11kV, 40 MVA turbogenerator, with a synchronous reactance of 0.8 p.i., is connected to a power network. This power network can be represented by 11-kV infinite bus with a series reactance of j 0.5 Ω. A voltage regulator adjusts the field current such that alternator terminal voltage remains constant at 11 kV.

2. Relevant equation:
Based on the information above I can write the following equation:
$\overline{E}_ f= \underbrace{\overline{V}_{bus} + jX_{line}\overline{I}_a}_{V_t} + jX_{s}\overline{I}_a$

## The Attempt at a Solution

:[/B]
Based on the equation above I can draw the following phasor diagram. I just copied the one drawn in the book, due to my paint skills did not yield a pretty result.

The phasor diagrams draws $I_a$ lagging with respect to $V_t$, and therefore $\theta$ is the angle between them.

My question is: How do I know how to draw $I_a$? I know that $I_a$ should atleast be lagging $V_t$ at lagging power factor, but could it not also be drawn lagging with respect to $V_b$ and then $\theta$ is the angle between $V_b$ and $\theta$?

I guess $\theta$ is defined from $V_t$ is because $V_t$ is chosen as reference phasor. But I am still confused by how $I_a$ is placed.

Hope I made myself clear, and appreciate any help, best regards.

LagCompensator said:
with a synchronous reactance of 0.8 p.i.,
I'm a bit rusty on synchronous machines, what does p.i. mean?

## What is a synchronous generator phasor diagram?

A synchronous generator phasor diagram is a graphical representation of the relationship between the voltage and current in a synchronous generator. It shows the magnitude and phase angle of the generator's voltage and current at a particular instant in time.

## Why is a synchronous generator phasor diagram important?

A synchronous generator phasor diagram is important because it helps engineers and scientists understand the behavior and performance of the generator. It can also be used to analyze and troubleshoot any issues with the generator's voltage or current.

## What are the components of a synchronous generator phasor diagram?

The components of a synchronous generator phasor diagram include the stator voltage, rotor voltage, stator current, rotor current, and the phasor representing the generated voltage. It may also include the excitation voltage and load voltage if applicable.

## How do you interpret a synchronous generator phasor diagram?

To interpret a synchronous generator phasor diagram, you need to understand the relationship between the different components. The stator and rotor voltages are in phase with each other, while the stator and rotor currents are out of phase. The generated voltage is the sum of the stator and rotor voltages. The angle between the generated voltage and the stator current represents the power factor.

## What factors can affect the shape of a synchronous generator phasor diagram?

The shape of a synchronous generator phasor diagram can be affected by various factors such as the load on the generator, the excitation voltage, and the power factor. Changes in these factors can cause the phasor diagram to shift or rotate, indicating changes in the generator's performance.