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:

Dampers	Up to 3 damper winding, one on d-axis and two on q-axis
Magnetic saturation	Total, independent or only on the d axis.
Stator connection	Wye with neutral, Wye grounded, or delta.
Shaft	Maximum 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 current	Field 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
Xf	Field reactance	pu
Rf	Field resistance	pu
XD	D-Damper reactance (must be defined when including the d-axis dampers - ignored otherwise)	pu
RD	D-Damper resistance (must be defined when including the d-axis dampers - ignored otherwise)	pu
XQ1	Q1-Damper reactance (must be defined when including 1 q-axis dampers - ignored otherwise)	pu
RQ1	Q1-Damper resistance (must be defined when including 1 q-axis dampers - ignored otherwise)	pu
XQ2	Q2-Damper reactance (must be defined when including 2 q-axis dampers - ignored otherwise)	pu
RQ2	Q2-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
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
K_d	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
K_ij	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
D_ij	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: LPB turbine LPA turbine IP turbine 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
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
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

Name	Description
S	AC side stator connector (supports only 3-phase connections)
N	AC side neutral connector (supports only 1-phase connections)

Inputs

Name	Description	Unit
Vfd_i	Speed independent field Voltage
Tm_i	Mechanical torque
Pm_i	Mechanical power
Efd_i	Speed 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_i	Mechanical torque of the machine	Nm
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 Value	Description
	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,

X_c = Canay Reactance (pu)

W_r = 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 W_exc 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 is the unsaturated inductance in pu.

In HYPERSIM, we define the field voltage independent of the variation of the speed (field voltage independent of speed deviation):

Thus, the field voltage dependent on the variation of the speed (field voltage dependent on speed deviation) is given by :

At steady state and at the fundamental frequency ωr=1, we have :

NOTE: When the machine is used in motor mode, the mechanical torque is negative and positive in generator T_im mode.

Limitations

This model does not take into account hysteresis. Under certain conditions some models of the machine may differ since the model of the synchronized machine-implemented is non-iterative.

References

[1] Power System Stability and Control, P. Kundur, McGraw-Hill 1994

[2] G. Sybille, Tarik Zabaiou, " Emergency Diesel-Generator and Asynchronous Motor", Mathworks demo example, version: 2017B

[3] Power System Control and Stability, 2^nd edition, P. Mr. Anderson, A.A.Fouad, IEEE press 2003

HYPERSIM Documentation

Synchronous Machine (pu Fundamental)