## Synchronous Generator P-Q Curve

Version 1.2 (111 KB) by
Synchronous Generator Capability Curve (P-Q Curve) using MATLAB

Updated 14 Apr 2022

From GitHub

# Synchronous Generator Capability Curve (P-Q Curve) using MATLAB

The generator operating limits is expressed in the form of the generator P-Q diagram. In other words, generator P-Q diagram provides a safe boundary in which the generator can operate without exceeding thermal limitations.

In this publication, practical steps for drawing Generator Capability Curve using MATLAB is presented .

Assumptions:

``````* Synchronous Generator
* Round Rotor
* Armature Winding Resistance is neglected
* Quantities are expressed based on Per Unit (P.U.) system
``````

Parameters and Quantities definitions:

``````* Sn	: Nominal Apparent Power
* P 	: Active Power
* Q 	: Reactive Power
* Ea	: Induced voltage in stator windings
* V 	: Terminal Voltage
* I 	: Armature Current
* PF	: Power Factor
* Xs	: Synchronous Reactance
* theta	: Power factor angle
``````

In the following, three main limits of generator capability is presented:

## 1. Armature Current Limit

Armature Current Limitation will resulted in the following equations for P and Q:

## 2. Field Current Limit

Field Current Limitation will resulted in the following equations for P and Q:

## 3. Stability Limit

Stability of the turbogenerator is the ability to stay in synchronous operation under slow load changes.

Stability limitation will resulted in the following equations for P and Q:

## Usage:

Just define the required parameters as follows and run the script

```%% Synchronous Generator P-Q Curve

%% Parameter Definition
Sn = 1;                 % Rated apparent power [P.U.]
PF = 0.85;              % Power Factor
V = [1.05, 0.95, 1];    % Terminal Voltage (+-5% Voltage Variation) [P.U.]
I = Sn./V;              % Nominal Current [P.U.]
Xs = 2;                 % Synchronous Reactance
```

## Usage:

Synchronous Generator P-Q Curve:

## Contact

Email: smtoraabi@ymail.com

### Cite As

mansour torabi (2023). Synchronous Generator P-Q Curve (https://github.com/Mansourt/Synchronous-Generator-P-Q-Curve_MATLAB/releases/tag/v1.2), GitHub. Retrieved .

##### MATLAB Release Compatibility
Created with R2022a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.2

See release notes for this release on GitHub: https://github.com/Mansourt/Synchronous-Generator-P-Q-Curve_MATLAB/releases/tag/v1.2

1.1

See release notes for this release on GitHub: https://github.com/Mansourt/Synchronous-Generator-P-Q-Curve_MATLAB/releases/tag/v1.1

1.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.