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Synchronous Machine (pu Fundamental)


The Synchronous Machine (SM) component is a Norton equivalent (non-iterative) model. The machine's electrical parameters must be specified with fundamental parameters (in per unit). Additionally, the control of the SM can only be done externally through the mechanical power or the mechanical torque and the excitation input.

The model has the following features:

DampersUp to 3 damper winding, one on d-axis and two on q-axis
Magnetic saturationTotal, independent or only on the d axis.
Stator connectionWye with neutral, Wye grounded, or delta.
ShaftMaximum 6 masses including the mass of the exciter.


The synchronous machine participates in the load flow as a source behind an impedance. The machine may be a reference node (swing bus), PV node or PQ node.


Mask and Parameters

Electrical Parameters

Parameter

Description

Unit          

Variable = {Possible Values}

Base power

Nominal power

MVA


Base voltage

Nominal voltage (line to line)

kV


Frequency

Nominal frequency

Hz


Number of poles

Number of poles

-


d-axis damper

Number of dampers on d-axis (up to 1)

-


q-axis damper

Number of dampers on q-axis (up to 1)

-


Stator connection

Stator windings connection (wye or delta)

-


Field currentField current which will produced 1 pu voltage on the air gap line used to calculate the pu value of current values input to the saturation table (not available in the current version)A

Rs

Stator resistance

pu


Xl

Stator leakage reactance

pu


X0

Zero sequence reactance

pu


Xc

Canay reactance

pu


Xd

d-axis synchronous reactance

pu


Xq

q-axis synchronous reactance

pu


XfField reactancepu
RfField resistancepu
XDD-Damper reactance (must be defined when including the d-axis dampers - ignored otherwise)pu
RDD-Damper resistance (must be defined when including the d-axis dampers - ignored otherwise)pu
XQ1Q1-Damper reactance (must be defined when including 1 q-axis dampers - ignored otherwise)pu
RQ1Q1-Damper resistance (must be defined when including 1 q-axis dampers - ignored otherwise)pu
XQ2Q2-Damper reactance (must be defined when including 2 q-axis dampers - ignored otherwise)pu
RQ2Q2-Damper resistance (must be defined when including 2 q-axis dampers - ignored otherwise)pu

Mechanical Data Parameters

Number of mass allows addition of up to 5 masses on the machine shaft. Selection of 1 mass is default meaning only 1 mass shaft is simulated corresponding to the machine itself. Selection of 2 masses means the machine and the Low Pressure Turbine A (corresponding to mass 2 in the following figure) is simulated. Similarly selection of additional masses adds the next mass shown in the figure below. 

Parameter

Description

Unit

Variable = {Possible Values}

Number of mass

Number of mass

-


H

Depending on the number of mass, the table of inertia constants is as follows:

  • Generator
  • Low Pressure Turbine B (LPB)
  • Low Pressure Turbine A (LPA)
  • Intermediate Pressure (IP) Turbine
  • High Pressure (HP) Turbine

s


Kd

Depending on the number of mass, the table of absolute damping coefficients is as follows:

  • Generator
  • Turbine LPB
  • LPA Turbine
  • Ip Turbine
  • Turbine HP

Nm/rad/s


Kij

Depending on the number of mass, the table of stiffness coefficients is as follows:

  • Generator-Turbine LPB
  • LPB-Turbine LPA Turbine
  • Turbine LPA-Turbine IP
  • Turbine IP-Turbine HP

Nm/rad


D

Depending on the number of mass, the table of self damping coefficients is as follows:

  • Generator
  • Turbine LPB,
  • LPA Turbine,
  • Ip Turbine,
  • Turbine HP

Nm/rad/s


Dij

Depending on the number of mass, the table of mutual speed deviation damping coefficients is as follows:

  • Generator-Turbine LPB,
  • LPB-Turbine LPA Turbine,
  • Turbine LPA-Turbine IP,
  • Turbine IP-Turbine HP

Nm/rad/s


F

Depending on the number of masses, the table of fraction of external torque is defined as the fraction of the total external torque applied to each mass as follows:

  1. LPB turbine
  2. LPA turbine
  3. IP turbine
  4. HP turbine

Note that the sum of F must always be equal to 1.

-

Exciter Type

Type of exciter (rotating or static)

-


H (Exciter)

Inertia constant

s


Kd (Exciter)

Absolute damping coefficient

Nm/rad/s


D (Exciter)

Self damping coefficient

Nm/rad/s


D(Generator-Exciter)

Mutual deviation speed damping coefficient

Nm/rad/s


K(Generator-Exciter)

Stiffness coefficient

Nm/rad


Control Parameters

Parameter

Description

Unit

Variable = {Possible Values}

Excitation control

The excitation is controlled as follows:

  • Constant: constant field voltage from loadflow
  • External: Field voltage (Efd) from exciter
  • External: Field voltage (Vfd) from exciter

pu


Mechanical control

The mechanical control can be done as follows:

  • Constant: constant mechanical power from load flow
  • Mechanical power: mechanical power from prime mover
  • Mechanical torque: mechanical torque from prime mover

pu


Saturation Parameters

Parameter

Description

Unit

Variable = {Possible Values}

Saturation

User can disable or enable independent, total or only d-axis saturation

-


d-axis saturation curve points

Number of d-axis saturation curve points (max 10 points can be added)

-


Imd

d-axis magnetizing current points of saturation curve.

pu


Fluxmd

d-axis magnetizing flux points of saturation curve.

pu


q-axis saturation curve points

Number of q-axis saturation curve points (max 10 points can be added)

-


Imq

q-axis magnetizing current points of saturation curve.

pu


Fluxmq

q-axis magnetizing flux points of saturation curve.

pu


Note: The magnetizing current of axis d or q are defined in p.u of the exciter i.e. base of the rotor current. For example if a field current of 1000 A produces an air gap flux of 1 pu then this current is equal to 1 p.u. A 1500 A current producing an air gap flux of 1.1 pu then this current is = 1.5 p.u.

Load Flow Parameters

Parameter

Description

Unit

Variable = {Possible Values}

Type of bus

The bus can be:

  • Swing
  • PV
  • PQ

-


Voltage

Desired voltage at the terminal of the machine

pu


Angle

Desired voltage angle at the terminal of the machine

Deg


Active power

Desired active power output at the terminal of the machine

MW


Reactive power

Desired reactive power output at the terminal of the machine

MVAr


Minimum power reactive

Minimum reactive output at the terminal of the machine

MVAr


Maximum power reactive

Maximum reactive output at the terminal of the machine

MVAr


Ports, Inputs, Outputs and Signals Available for Monitoring

Ports

NameDescription

S

AC side stator connector (supports only 3-phase connections)

N

AC side neutral connector (supports only 1-phase connections)

Inputs

NameDescriptionUnit
Vfd_iSpeed independent field Voltage
Tm_iMechanical torque
Pm_iMechanical power
Efd_iSpeed dependent field voltage

Outputs

None

Sensors

Last name

Description

Unit

Efd

Speed-dependent field voltage

pu

Efd_i

Speed-dependent field voltage of the exciter

pu

Efd_ss

The exciter’s field voltage calculated during load flow. It is used to initialize the blocks of the exciter. ss: steady state.

pu

Flux0s

Zero-sequence Stator flux

pu

Fluxds

d-axis stator flux

pu

Fluxm

Mutual Magnetization flux

pu

Fluxmd

Mutual magnetization flux of d-axis

pu

Fluxmq

Mutual magnetization flux of q-axis

pu

Fluxqs

q-axis stator flux

pu

I0s

Zero-sequence stator current

pu

ID

d-axis damper current

pu

IQ1

Q1 axis damper current

pu

IQ2

Q2 axis damper current

pu

Ias

stator current of phase A

pu

Ibs

stator current of phase B

pu

Ics

stator current of phase C

pu

Ids

d-axis stator current

pu

If

field current

pu

Im

Magnetizing current

pu

Imd

d-axis magnetizing current

pu

Imq

q-axis magnetizing current

pu

Iqs

q-axis stator current

pu

Pm_i

Mechanical power of the turbine

pu

Pmec

Mechanical power of the turbine

Nm

Pmec_pu

Mechanical power of the turbine

pu

Pmec_ss

Mechanical power of the turbine calculated during load flow. It is used to initialize the blocks of the turbine

pu

PowerAngle

The load angle of the machine

rad

Ps

active power

W

Ps_pu

active power

pu

Qs

reactive power

VAr

RotorAngle

Rotor angle (relative to synchronous reference frame) of the synchronous machine

rad

RotorAngle_EXC

Rotor angle (relative to synchronous reference frame) of the mass (exciter)

rad

RotorAngle_HP

Rotor angle (relative to a synchronous reference frame) of the mass (HP turbine)

rad

RotorAngle_IP

Rotor angle (relative to a synchronous reference frame) of the mass (IP turbine)

rad

RotorAngle_LPA

Rotor angle (relative to a synchronous reference frame) of the mass (LPA turbine)

rad

RotorAngle_LPB

Rotor angle (relative to a synchronous reference frame) of the mass (turbine LPB)

rad

Tem

electromagnetic torque of the synchronous machine

Nm

Tem_pu

electromagnetic torque of the synchronous machine

pu

Texc

electromagnetic torque of the exciter

pu

ThetaS

Electrical angle of rotor (angle between the axis of phase A and d)

rad

Tm_iMechanical torque of the machineNm

Tmec

mechanical torque of the turbine

Nm

Tmec_GEN_EXC

mechanical torque between the synchronous machine mass and the exciter

pu

Tmec_HP

mechanical torque applied to the mass (HP turbine)

pu

Tmec_HP_IP

mechanical torque between HP and IP turbine masses

pu

Tmec_IP

mechanical torque applied to the mass (IP turbine)

pu

Tmec_IP_LPA

mechanical torque between the turbine masses IP and LPA

pu

Tmec_LPA

mechanical torque applied to the mass (LPA turbine)

pu

Tmec_LPA_LPB

mechanical torque between the turbine masses LPA and LPB

pu

Tmec_LPB

mechanical torque applied to the mass (turbine LPB)

pu

Tmec_LPB_GEN

mechanical torque between the masses LPB turbine and the synchronous machine

pu

Tmec_pu

mechanical torque of the turbine

pu

V0s

zero sequence stator voltage

pu

Vds

d-axis stator voltage

pu

Vqs

q axis stator voltage

pu

Vfd

Speed independent field Voltage

pu

Vfd_i

Speed independent field voltage of the exciter

pu

Vt

Terminal voltage of the machine

pu

Wm

mechanical or electrical speed of the machine

pu

Wm_EXC

mechanical or electrical speed of the exciter

pu

Wm_HP

mechanical or electrical speed of the turbine HP

pu

Wm_IP

mechanical or electrical speed of the IP turbine

pu

Wm_LPA

mechanical or electrical speed of the turbine LPA

pu

Wm_LPB

mechanical or electrical speed of the turbine LPB

pu

Wrpm

Mechanical speed of the machine

r / min

Additional Information & Model Equations

Additional Information

In the q-axis, the machine has 2 damper windings Q1, Q2. In the d-axis (the axis of the magnetic field), one d-axis damper winding. The rotor reference is such that the q axis leads the d axis.

Base Values for PU Conversion

Base ValueDescription

Base power

Base stator voltage (peak) for wye connection

Base stator voltage (peak) for delta connection

Base stator current (peak)

Base rotor current

Base mechanical torque

Base flux (peak)


Model Equations

Park's transformation is defined as follows:

Where is the angle between the axis of phase a and d.

The equations of the electrical system (p.u. with generating convention) are given by:

Where,

Xc = Canay Reactance (pu)

Wr = Electrical speed (Rad/s)

The electromagnetic torque (p.u.) developed by the synchronous machine is given by:

The torque (p.u.) developed by the excitor is given by:

Where Wexc is the mechanical speed (pu) of the exciter

The mechanical (general) equation of mass i is described as follows:

Where,

The mechanical torque developed on the ith mass (Nm)

: The electromagnetic torque developed by the PMSM (Nm)

: The torque developed by the exciter (Nm)

: The mechanical speed of mass i (rad / s)

: Mechanical synchronous speed (rad / s)

: The mechanical angle of mass i with respect to a frame of reference

: Absolute damping coefficient (Nm / mechanical rad / s)

: Self damping coefficient (Nm / mechanical rad / s)

: Mutual damping coefficient (Nm / mechanical rad / s)

: Angular stiffness (Nm / mechanical rad)

: Inertia constant (s)

At no load, the rotor voltage (in p.u) seen from the stator is given by


Where is the electrical speed in pu and