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
* delta : Load 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