Synchronous generator#

The Synchronous generator block is a model of a synchronousgenerator that describes the mechanical motion of its rotor,as well as the processes in the stator winding in a simplified form.

This model includes:

The equation of motion of the generator, presented in the form (1):

(1)#\[ \frac{\Delta \mathrm{s}}{\Delta \mathrm{t}}=\frac{1}{T_{J}}\left(\frac{P_{\mathrm{т}\mathrm{у}\mathrm{р}\mathrm{б}}}{\left(1+s_{u}\right)\cdot P_{\mathrm{н}\mathrm{о}\mathrm{м}}}-\frac{P_{\mathrm{э}\mathrm{л}}}{\left(1+s_{u}\right)\cdot P_{\mathrm{н}\mathrm{о}\mathrm{м}}}-D\cdot s\right); \]

where:

\(s\) - rotor sliding;

\(P_{turb}\) - turbine power (can be set bothas a function via external port and constant by entering a specificvalue in the block parameters), [W];

\(P_{el}\) - electrical power of the generator, [W];

\(P_{rat}\) - rated electric power of the generator, [W];

\(s_{u}\) - voltage module slipping, r.u.;

\(D\) - Damping factor,s.u.

Rotor inertia constant in s, calculated by the formula (2):

(2)#\[ T_{J}=\frac{J\cdot \omega _{0}^{2}}{S_{\mathrm{н}\mathrm{о}\mathrm{м}}}=\frac{J\cdot \left(2\cdot \pi \cdot f_{0}\right)^{2}\cdot \mathrm{c}\mathrm{o}\mathrm{s}\phi _{\mathrm{н}\mathrm{о}\mathrm{м}}}{P_{\mathrm{н}\mathrm{о}\mathrm{м}}} \]

where:

\(\omega _{0}\) - synchronous angular frequency of rotor rotation, [rad/s];

\(\omega\) - angular frequency of rotor rotation, [rad/s], (3) :

(3)#\[\omega =\omega_{0} \cdot (1+s)\]

Stator winding voltage equation (4):

(4)#\[ U=E_{q}+ I_{q}\cdot \mathrm{j}\cdot \mathrm{X}_{d}. \]

where:

\(U\) - generator output voltage, [V];

\(E_{q}\) - synchronous Efficiency, [V] (can be set both as a function via external port and constantby entering a specific value in the block parameters. In the lattercase, it will be automatically assigned the rated voltage value);

\(I_{q}\) - stator winding current, [A];

\(X_d\) - longitudinal resistanceof the stator winding, [Ohm]. It is calculated as follows based on the source data (5):

(5)#\[ X_{d}=X_{\mathrm{d}.\mathrm{о}.\mathrm{е}.}\cdot \frac{U_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}}{S_{\mathrm{н}\mathrm{о}\mathrm{м}}}=X_{\mathrm{d}.\mathrm{о}.\mathrm{е}.}\cdot \frac{U_{\mathrm{н}\mathrm{о}\mathrm{м}}^{2}\cdot \mathrm{c}\mathrm{o}\mathrm{s}\phi _{\mathrm{н}\mathrm{о}\mathrm{м}}}{P_{\mathrm{н}\mathrm{о}\mathrm{м}}}. \]

1. Properties#

Property	Default value	Description	Units of measurement
Mechanical power of a prime mover	2e6	–	W
Rotor moment of inertia	3250	–	kg\(\cdot \) m\(^2\)
Damping factor	5	–	–
Rated active power	2e6	–	W
Rated power factor	0.9	–	–
Rated voltage	10000	–	V
Stator winding resistance along the direct axis	2	–	r.u.
[SC] Subtransient resistance	0	For SC calculation	Ohm
[SC] Subtransient reactance	0	For SC calculation	r.u.

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Mechanical power of a prime mover	Input	–	W	Automation
EMF	Input	–	V	Automation
Electrical port	Output	–	–	Elecrocity

In order to see the connection capabilities of the block, you need to go to page Description of block ports