Synchronous Machine Salient Pole

Salient-pole synchronous machine with fundamental or standard parameterization

Library:
Simscape / Electrical / Electromechanical / Synchronous

Description

The Synchronous Machine Salient Pole block models a salient-pole synchronous machine using fundamental or standard parameters.

Synchronous Machine Initialization Using Load-Flow Target Values

If the block is in a network that is compatible with the frequency-time simulation mode, you can perform a load-flow analysis on the network. A load-flow analysis provides steady-state values that you can use to initialize the machine.

For more information, see Perform a Load-Flow Analysis Using Simscape Electrical and Frequency and Time Simulation Mode. For an example that shows how initialize an synchronous machine using data from a load flow analysis, see Synchronous Machine Initialization with Loadflow.

Equations

The synchronous machine equations are expressed with respect to a rotating reference frame, defined by

$θ_{e} (t) = N θ_{r} (t),$

where:

θ_e is the electrical angle.
N is the number of pole pairs.
θ_r is the rotor angle.

The Park transformation maps the synchronous machine equations to the rotating reference frame with respect to the electrical angle. The Park transformation is defined by

$P_{s} = \frac{2}{3} [\begin{matrix} \cos θ_{e} & \cos (θ_{e} - \frac{2 π}{3}) & \cos (θ_{e} + \frac{2 π}{3}) \\ - \sin θ_{e} & - \sin (θ_{e} - \frac{2 π}{3}) & - \sin (θ_{e} + \frac{2 π}{3}) \\ \frac{1}{2} & \frac{1}{2} & \frac{1}{2} \end{matrix}] .$

The Park transformation is used to define the per-unit synchronous machine equations. The stator voltage equations are defined by

$e_{d} = \frac{1}{ω_{b a s e}} \frac{d ψ_{d}}{d t} - Ψ_{q} ω_{r} - R_{a} i_{d},$

$e_{q} = \frac{1}{ω_{b a s e}} \frac{d ψ_{q}}{d t} + Ψ_{d} ω_{r} - R_{a} i_{q},$

and

$e_{0} = \frac{1}{ω_{b a s e}} \frac{d Ψ_{0}}{d t} - R_{a} i_{0},$

where:

e_d, e_q, and e₀ are the d-axis, q-axis, and zero-sequence stator voltages, defined by

$[\begin{matrix} e_{d} \\ e_{q} \\ e_{0} \end{matrix}] = P_{s} [\begin{matrix} v_{a} \\ v_{b} \\ v_{c} \end{matrix}] .$

v_a, v_b, and v_c are the stator voltages measured from port ~ to neutral port n.
ω_base is the per-unit base electrical speed.
ψ_d, ψ_q, and ψ₀ are the d-axis, q-axis, and zero-sequence stator flux linkages.
ω_r is the per-unit rotor rotational speed.
R_a is the stator resistance.
i_d, i_q, and i₀ are the d-axis, q-axis, and zero-sequence stator currents, defined by

$[\begin{matrix} i_{d} \\ i_{q} \\ i_{0} \end{matrix}] = P_{s} [\begin{matrix} i_{a} \\ i_{b} \\ i_{c} \end{matrix}] .$

i_a, i_b, and i_c are the stator currents flowing from port ~ to port n.

The rotor voltage equations are defined by

$e_{f d} = \frac{1}{ω_{b a s e}} \frac{d Ψ_{f d}}{d t} + R_{f d} i_{f d},$

$e_{1 d} = \frac{1}{ω_{b a s e}} \frac{d Ψ_{1 d}}{d t} + R_{1 d} i_{1 d} = 0,$

and

$e_{1}_{q} = \frac{1}{ω_{b a s e}} \frac{d Ψ_{1 q}}{d t} + R_{1 q} i_{1 q} = 0,$

where:

e_fd is the field voltage.
e_1d, and e_1q are the voltages across the d-axis damper winding 1 and q-axis damper winding 1. They are equal to 0.
ψ_fd, ψ_1d, and ψ_1q are the magnetic fluxes linking the field circuit, d-axis damper winding 1, and q-axis damper winding 1.
R_fd, R_1d, and R_1q are the resistances of rotor field circuit, d-axis damper winding 1, and q-axis damper winding 1.
i_fd, i_1d, and i_1q are the currents flowing in the field circuit, d-axis damper winding 1, and q-axis damper winding 1.

The saturation equations are defined by

$ψ_{a d} = ψ_{d} + L_{l} i_{d},$

$ψ_{a q} = ψ_{q} + L_{l} i_{q},$

$ψ_{a t} = \sqrt{ψ_{a d}^{2} + ψ_{a q}^{2}},$

$K_{s} = 1$ (if saturation is disabled),

$K_{s} = f (ψ_{a t})$ (if saturation is enabled),

and

$L_{a d} = K_{s} * L_{a d u},$

where:

ψ_ad is the d-axis air-gap or mutual flux linkage.
ψ_aq is the q-axis air-gap or mutual flux linkage.
ψ_at is the air-gap flux linkage.
K_s is the saturation factor.
L_adu is the unsaturated mutual inductance of the stator d-axis.
L_ad is the mutual inductance of the stator d-axis.

The saturation factor function, f, is calculated from the per-unit open-circuit lookup table as:

$L_{a d} = \frac{d ψ_{a t}}{d i_{f d}},$

$V_{a g} = g (i_{f d}),$

and

$L_{a d} = \frac{d g (i_{f d})}{d i_{f d}} = \frac{d V_{a g}}{d i_{f d}},$

where:

V_ag is the per-unit air-gap voltage.

In per-unit,

$K_{s} = \frac{L_{a d}}{L_{a d u}},$

and

$ψ_{a t} = V_{a g}$

can be rearranged to

$K_{s} = f (ψ_{a t}) .$

The stator flux linkage equations are defined by

$Ψ_{d} = - (L_{a d} + L_{l}) i_{d} + L_{a d} i_{f d} + L_{a d} i_{1 d},$

$Ψ q = - (L_{a q} + L_{l}) i_{q} + L_{a q} i_{1 q},$

and

$Ψ_{0} = - L_{0} i_{0},$

where:

L_l is the stator leakage inductance.
L_ad and L_aq are the mutual inductances of the stator d-axis and q-axis.

The rotor flux linkage equations are defined by

$ψ_{f d} = L_{f f d} i_{f d} + L_{f 1 d} i_{1 d} - L_{a d} i_{d},$

$ψ_{1 d} = L_{f 1 d} i_{f d} + L_{11 d} i_{1 d} - L_{a d} i_{d},$

and

$ψ_{1 q} = L_{11 q} i_{1 q} - L_{a q} i_{q},$

where:

L_ffd is the self-inductance of the rotor field circuit.
L_11d is the self-inductance of the d-axis damper winding 1.
L_11q is the self-inductance of the q-axis damper winding 1.
L_f1d is the roto field circuit and d-axis damper winding 1 mutual inductance.

The inductances are defined by these equations:

$L_{f f d} = L_{a d} + L_{f d}$

$L_{f 1 d} = L_{f f d} - L_{f d}$

$L_{11 d} = L_{f 1 d} + L_{1 d}$

$L_{11 q} = L_{a q} + L_{1 q}$

The inductance equations assume that per-unit mutual inductance L_12q = L_aq, that is, the stator and rotor currents in the q-axis all link a single mutual flux represented by L_aq.

The rotor torque is defined by

$T_{e} = Ψ_{d} i_{q} - Ψ_{q} i_{d} .$

Plotting and Display Options

You can perform plotting and display actions using the Electrical menu on the block context menu.

Right-click the block and, from the Electrical menu, select one of these options:

Display Base Values — Displays the machine per-unit base values in the MATLAB^® Command Window.
Display Associated Base Values — Displays associated per-unit base values in the MATLAB Command Window.
Display Associated Initial Conditions — Displays associated initial conditions in the MATLAB Command Window.
Plot Open-Circuit Saturation (pu) — Plots air-gap voltage, V_ag, versus field current, i_fd, both measured in per-unit, in a MATLAB figure window. The plot contains three traces:
- Unsaturated — Stator d-axis mutual inductance (unsaturated), Ladu you specify
- Saturated — Per-unit open-circuit lookup table (Vag versus ifd) you specify
- Derived — Open-circuit lookup table (per-unit) derived from the Per-unit open-circuit lookup table (Vag versus ifd) you specify. This data is used to calculate the saturation factor,K_s, versus magnetic flux linkage, ψ_at, characteristic.
Plot Saturation Factor (pu) — Plots saturation factor,K_s, versus magnetic flux linkage, ψ_at, both measured in per-unit, in a MATLAB figure window using the present machine parameters. This parameter is derived from other parameters that you specify:
- Stator d-axis mutual inductance (unsaturated), Ladu
- Per-unit field current saturation data, ifd
- Per-unit air-gap voltage saturation data, Vag

Variables

The Variables settings allow you to specify the priority and initial target values for block variables before simulation. For more information, see Set Priority and Initial Target for Block Variables.

For this block, the Variables settings are visible only if, in the Initial Conditions settings, the Initialization option parameter is set to Set targets for rotor angle and Park's transform variables.

Ports

Output

expand all

`pu` — Machine per-unit measurements
physical

Physical signal vector port associated with the machine per-unit measurements. The vector elements are:

Field voltage (field circuit base, Efd), pu_fd_Efd
Field current (field circuit base, Ifd), pu_fd_Ifd
Electrical torque, pu_torque
Rotor velocity, pu_velocity
Stator d-axis voltage, pu_ed
Stator q-axis voltage, pu_eq
Stator zero-sequence voltage, pu_e0
Stator d-axis current, pu_id
Stator q-axis current, pu_iq
Stator zero-sequence current, pu_i0
Rotor electrical angle, electrical_angle_out

To connect to this port, use the Synchronous Machine Measurement block.

Conserving

expand all

`fd+` — Field winding positive terminal
electrical

Electrical conserving port associated with the field winding positive terminal.

`fd-` — Field winding negative terminal
electrical

Electrical conserving port associated with the field winding negative terminal.

`R` — Machine rotor
mechanical

Mechanical rotational conserving port associated with the machine rotor.

`C` — Machine case
mechanical

Mechanical rotational conserving port associated with the machine case.

`~` — Stator windings
electrical

Expandable three-phase port associated with the stator windings.

`n` — Neutral phase
electrical

Electrical conserving port associated with the neutral point of the wye winding configuration.

Parameters

expand all

Main

`Rated apparent power` — Rated apparent power
`300e6` `V*A` (default)

Rated apparent power.

`Rated voltage` — RMS rated line-line voltage
`24e3` `V` (default)

RMS rated line-line voltage.

`Rated electrical frequency` — Nominal electrical frequency
`60` `Hz` (default)

Nominal electrical frequency at which rated apparent power is quoted.

`Number of pole pairs` — Number of pole pairs
`10` (default)

Number of machine pole pairs.

`Specify parameterization by` — Block parameterization
`Fundamental parameters` (default) | `Standard parameters`

Block parameterization method. Options are:

Fundamental parameters — Specify impedance using fundamental parameters.
Standard parameters — Specify impedance using fundamental parameters and specify d-axis and q-axis time constants.

Dependencies

If this parameter is set to Fundamental parameters:

Fundamental parameters in the Impedances settings are visible.
Time Constant settings are visible.

If this parameter is set to Standard parameters:

Standard parameters in the Impedances settings are visible.
Time Constant settings are not visible.

`Specify field circuit input required to produce rated terminal voltage at no load by` — Specify field circuit input required to produce rated terminal voltage at no load by
`Field circuit current` (default) | `Field circuit voltage`

Field circuit parameterization method. Options are:

Field circuit voltage — Specify the field circuit in terms of voltage.
Field circuit current — Specify the field circuit in terms of current.

This parameter affects the visibility of the Field circuit voltage and Field circuit current parameters.

Dependencies

If this parameter is set to Field circuit voltage.

The Field circuit voltage parameter is visible.
The Field circuit current parameter is not visible.

If this parameter is set to Field circuit current:

The Field circuit current parameter is visible.
The Field circuit voltage parameter is not visible.

`Field circuit voltage` — Field circuit voltage
`216.54` `V` (default)

Voltage across field circuit which produces rated voltage at machine terminals.

Dependencies

This parameter is visible only if the Specify field circuit input required to produce rated terminal voltage at no load by parameter is set to Field circuit voltage.

`Field circuit current` — Field circuit current
`1000` `A` (default)

Current in field circuit which produces rated voltage at machine terminals.

Dependencies

This parameter is visible only if the Specify field circuit input required to produce rated terminal voltage at no load by parameter is set to Field circuit current.

`Zero sequence` — Zero-sequence model
`Include` (default) | `Exclude`

Zero-sequence model:

Include — Prioritize model fidelity. This model is the default zero-sequence model. An error occurs if you Include zero-sequence terms for simulations that use the Partitioning solver. For more information, see Increase Simulation Speed Using the Partitioning Solver.
Exclude — Prioritize simulation speed for desktop simulation or real-time deployment.

Dependencies

If this parameter is set to:

Include and Specify parameterization by is set to Fundamental parameters — The Stator zero-sequence inductance, L0 parameter in the Impedances settings is visible.
Include and Specify parameterization by is set to Standard parameters — The zero-sequence reactance, X0 parameter in the Impedances settings is visible.
Exclude — The zero-sequence parameter in the Impedances settings is not visible.

`Rotor angle definition` — Reference point for the rotor angle measurement
`Angle between the a-phase magnetic axis and the d-axis` (default) | `Angle between the a-phase magnetic axis and the q-axis`

Reference point for the rotor angle measurement.

When you select the default value, the rotor d-axis and stator a-phase magnetic axis are aligned when the rotor angle is zero.

The other value you can choose for this parameter is Angle between the a-phase magnetic axis and the q-axis. When you select this value, the rotor q-axis and stator a-phase magnetic axis are aligned when the rotor angle is zero.

Impedances

`Stator d-axis mutual inductance (unsaturated), Ladu` — Stator d-axis mutual inductance (unsaturated)
`0.9` (default) | positive scalar

Unsaturated stator d-axis mutual inductance. If Magnetic saturation representation is set to None, this is equivalent to the stator d-axis mutual inductance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter is set to Fundamental parameters.

`Stator q-axis mutual inductance, Laq` — Stator q-axis mutual inductance
`0.55` (default) | positive scalar

Stator q-axis mutual inductance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter is set to Fundamental parameters.

`Stator zero-sequence inductance, L0` — Stator zero-sequence inductance
`0.15` (default) | positive scalar

Stator zero-sequence inductance. This parameter must be greater than 0.

Dependencies

This parameter is visible if the Specify parameterization by parameter is set to Fundamental parameters and the Zero Sequence parameter is set to Include.

`Stator leakage inductance, Ll` — Stator leakage inductance
`0.15` (default) | positive scalar

Stator leakage inductance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter is set to Fundamental parameters.

`Stator resistance, Ra` — Stator resistance
`0.011` (default) | positive scalar

Stator resistance. This parameter must be greater than 0.

`Rotor field circuit inductance, Lfd` — Rotor field circuit inductance
`0.2571` (default) | positive scalar

Rotor field circuit inductance. This parameter must be greater than 0.

`Rotor field circuit resistance, Rfd` — Rotor field circuit resistance
`0.0006` (default) | positive scalar

Rotor field circuit resistance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter is set to Fundamental parameters.

`Rotor d-axis damper winding 1 inductance, L1d` — Rotor d-axis damper winding 1 inductance
`0.2` (default) | positive scalar

Rotor d-axis damper winding 1 inductance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter to Fundamental parameters.

`Rotor d-axis damper winding 1 resistance, R1d` — Rotor d-axis damper winding 1 resistance
`0.0354` (default) | positive scalar

Rotor d-axis damper winding 1 resistance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter is set to Fundamental parameters.

`Rotor q-axis damper winding 1 inductance, L1q` — Rotor q-axis damper winding 1 inductance
`0.2567` (default) | positive scalar

Rotor q-axis damper winding 1 inductance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter is set to Fundamental parameters.

`Rotor q-axis damper winding 1 resistance, R1q` — Rotor q-axis damper winding 1 resistance
`0.0428` (default) | positive scalar

Rotor q-axis damper winding 1 resistance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter is set to Fundamental parameters.

`Stator leakage reactance, Xl` — Stator leakage reactance
`0.15` (default) | positive scalar

Stator leakage reactance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter to Standard parameters.

`d-axis synchronous reactance, Xd` — d-axis synchronous reactance
`1.05` (default) | positive scalar

d-axis synchronous reactance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter to Standard parameters.

`q-axis synchronous reactance, Xq` — q-axis synchronous reactance
`0.7` (default) | positive scalar

q-axis synchronous reactance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter to Standard parameters.

`zero-sequence reactance, X0` — Zero-sequence reactance
`0.15` (default) | positive scalar

Zero-sequence reactance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter to Standard parameters and the Zero Sequence parameter is set to Include.

`d-axis transient reactance, Xd'` — d-axis transient reactance
`0.35` (default) | positive scalar

d-axis transient reactance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter is set to Standard parameters.

`d-axis subtransient reactance, Xd''` — d-axis subtransient reactance
`0.25` (default) | positive scalar

d-axis subtransient reactance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter is set to Standard parameters.

`q-axis subtransient reactance, Xq''` — q-axis subtransient reactance
`0.325` (default) | positive scalar

q-axis subtransient reactance. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify parameterization by parameter is set to Standard parameters.

Time Constants

`Specify d-axis time constant` — Specify d-axis time constant
`Open circuit` (default) | `Short circuit`

Select between Open circuit and Short circuit.

The setting for this parameter affects the visibility of the d-axis time constant parameters.

`d-axis transient open-circuit, Td0'` — d-axis transient open-circuit
`5.25` `s` (default) | positive scalar

d-axis transient open-circuit time constant. This parameter must be:

Greater than 0.
Greater than d-axis subtransient open-circuit, Td0''.

Dependencies

This parameter is visible only if the Specify d-axis transient time constant parameter is set to Open circuit.

`d-axis transient short-circuit, Td'` — d-axis transient short-circuit
`1.75` `s` (default) | positive scalar

d-axis transient short-circuit time constant. This parameter must be:

Greater than 0.
Greater than d-axis subtransient short-circuit, Td''.

Dependencies

This parameter is visible only if the Specify d-axis transient time constant parameter is set to Short circuit.

`d-axis subtransient open-circuit, Td0''` — d-axis subtransient open-circuit
`0.03` `s` (default) | positive scalar

d-axis subtransient open-circuit time constant. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify d-axis transient time constant parameter is set to Open circuit.

`d-axis subtransient short-circuit, Td''` — d-axis subtransient short-circuit
`0.0214` `s` (default) | positive scalar

d-axis subtransient short-circuit time constant. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify d-axis transient time constant parameter is set to Short circuit.

`Specify q-axis time constant` — Specify q-axis time constant
`Open circuit` (default) | `Short circuit`

Select between Open circuit and Short circuit.

The setting for this parameter affects the visibility of the q-axis time constant parameters.

`q-axis subtransient open-circuit, Tq0'` — q-axis subtransient open-circuit
`0.05` `s` (default) | positive scalar

q-axis subtransient open-circuit time constant. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify q-axis transient time constant parameter is set to Open circuit.

`q-axis subtransient short-circuit, Tq'` — q-axis subtransient short-circuit
`0.0232` `s` (default) | positive scalar

q-axis subtransient short-circuit time constant. This parameter must be greater than 0.

Dependencies

This parameter is visible only if the Specify q-axis transient time constant parameter is set to Short circuit.

Saturation

`Magnetic saturation representation` — Magnetic saturation representation
`None` (default) | `Open-circuit lookup table (v versus i)`

Block magnetic saturation model:

None
Open-circuit lookup table (v versus i)

Dependencies

If you set this parameter to Open-circuit lookup table (v versus i), related parameters are visible.

`Per-unit field current saturation data, ifd` — Per-unit field current saturation data
`[0, .48, .76, 1.38, 1.79]` (default)

Field current, i_fd, data that populates the air-gap voltage, V_ag, versus field current, i_fd, lookup table. This parameter must contain a vector with at least five elements.

Dependencies

This parameter is visible only if the Magnetic saturation representation parameter is set to Open-circuit lookup table (v versus i).

`Per-unit air-gap voltage saturation data, Vag` — Per-unit air-gap voltage saturation data
`[0, .8, 1.08, 1.31, 1.4]` (default)

Air-gap voltage, V_ag, data that populates the air-gap voltage, V_ag, versus field current, i_fd, lookup table. This parameter must contain a vector with at least five elements.

Dependencies

This parameter is visible only if the Magnetic saturation representation parameter is set to Open-circuit lookup table (v versus i).

Initial Conditions

`Initialization option` — Initialization option
`Set real power, reactive power, terminal voltage, and terminal phase` (default) | `Set targets for rotor angle and Park's transform variables` | `Set targets for load flow variables`

Model for specifying values for certain parameters and variables at the start of simulation. To:

Set an operating point regardless of the connected network, select Set real power, reactive power, terminal voltage and terminal phase.

Specify the priority and initial target values for block variables before simulation using the Variables settings, select Set targets for rotor angle and Park's transform variables. For more information, see Set Priority and Initial Target for Block Variables.
Select a bus type and specify the related parameters for a load-flow analysis in the Initial Conditions settings, select Set targets for load flow variables.

Dependencies

If you set this parameter to:

Set targets for rotor angle and Park's transform variables — The Variables settings become visible.
Set real power, reactive power, terminal voltage, and terminal phase — Related parameters become visible.
Set targets for load flow variables — Related parameters become visible.

`Source type` — Voltage source model
`Swing bus` (default) | `Voltage source with series impedance` | `PV bus` | `PQ bus`

Type of voltage source that the block models.

Dependencies

This parameter is visible only if the Initialization option parameter is set to Set targets for load flow variables and the Source type parameter is set to Swing bus or PV bus.

The visibility of Terminal voltage magnitude, Terminal voltage angle, Active power generated, Reactive power generated, Minimum terminal voltage magnitude (pu, Phase search range at terminals, and Phase search range at terminals depend on the value that you choose for this parameter.

`Terminal voltage magnitude` — Terminal voltage magnitude
`24e3` `V` (default)

Terminal voltage magnitude.

Dependencies

This parameter is visible only if the Initialization option parameter is set to Set real power, reactive power, terminal voltage, and terminal phase or if the Initialization option parameter is set to Set targets for load flow variables and the Source type parameter is set to Swing bus or PV bus.

`Terminal voltage angle` — Terminal voltage angle
`0` `deg` (default)

Terminal voltage angle.

Dependencies

`Active power generated` — Active power generated
`270e6` `V*A` (default)

Active power generated.

Dependencies

`Reactive power generated` — Reactive power generated
`0` `V*A` (default)

Reactive power generated.

Dependencies

`Minimum terminal voltage magnitude (pu)` — Minimum terminal voltage magnitude
`0.95` (default)

Per-unit minimum steady-state voltage magnitude.

Dependencies

This parameter is visible only if the Initialization option parameter is set to Set targets for load flow variables and the Source type parameter is set to PQ bus.

`Phase search range at terminals` — Phase search range at terminals
`[-inf, inf]` `deg` (default)

Vector that defines the phase angle search range.

Dependencies

This parameter is visible only if the Initialization option parameter is set to Set targets for load flow variables and the Source type parameter is set to PV bus or PQ bus.

`Parasitic conductance to electrical reference` — Parasitic conductance to electrical reference
`1e-6` `S` (default)

Parasitic conductance to the electrical reference.

Dependencies

This parameter is visible only if the Initialization option parameter is set to Set targets for load flow variables.

Model Examples

Synchronous Machine Initialization with Loadflow

Initialize synchronous machine as part of a load flow analysis. When initializing a synchronous machine there are two degrees of freedom which can be set by any two of rotor angle, active power, reactive power and terminal voltage. The pair of variables that are constrained is set by the source type drop-down menu, this having options of Swing bus, PV bus and PQ bus. Here the machine is configured for a swing bus with a 1.02 per-unit voltage and zero degrees phase.

SM Torque Control

Control the torque in a synchronous machine (SM) based electrical-traction drive. A high-voltage battery feeds the SM through a controlled three-phase converter for the stator windings and a controlled four quadrant chopper for the rotor winding. An ideal angular velocity source provides the load. The Control subsystem uses an open-loop approach to control the torque and a closed-loop approach to control the current. At each sample instant, the torque request is converted to relevant current references. The current control is PI-based. The simulation uses several torque steps in both motor and generator modes. The task scheduling is implemented as a Stateflow® state machine. The Visualization subsystem contains scopes that allow you to see the simulation results.

SM Velocity Control

Control the rotor angular velocity in a synchronous machine (SM) based electrical-traction drive. A high-voltage battery feeds the SM through a controlled three-phase converter for the stator windings and a controlled four quadrant chopper for the rotor winding. An ideal torque source provides the load. The Control subsystem includes a multi-rate PI-based cascade control structure which has an outer angular-velocity-control loop and three inner current-control loops. The task scheduling in the Control subsystem is implemented as a Stateflow® state machine. The Visualization subsystem contains scopes that allow you to see the simulation results.

References

[1] Kundur, P. Power System Stability and Control. New York, NY: McGraw Hill, 1993.

[2] Lyshevski, S. E. Electromechanical Systems, Electric Machines and Applied Mechatronics. Boca Raton, FL: CRC Press, 1999.

Documentation

Synchronous Machine Salient Pole

Description

Synchronous Machine Initialization Using Load-Flow Target Values

Equations

Plotting and Display Options

Variables

Ports

Output

pu — Machine per-unit measurements physical

Conserving

fd+ — Field winding positive terminal electrical

fd- — Field winding negative terminal electrical

R — Machine rotor mechanical

C — Machine case mechanical

~ — Stator windings electrical

n — Neutral phase electrical

Parameters

Main

Rated apparent power — Rated apparent power 300e6 V*A (default)

Rated voltage — RMS rated line-line voltage 24e3 V (default)

Rated electrical frequency — Nominal electrical frequency 60 Hz (default)

Number of pole pairs — Number of pole pairs 10 (default)

Specify parameterization by — Block parameterization Fundamental parameters (default) | Standard parameters

Dependencies

Specify field circuit input required to produce rated terminal voltage at no load by — Specify field circuit input required to produce rated terminal voltage at no load by Field circuit current (default) | Field circuit voltage

Dependencies

Field circuit voltage — Field circuit voltage 216.54 V (default)

Dependencies

Field circuit current — Field circuit current 1000 A (default)

Dependencies

Zero sequence — Zero-sequence model Include (default) | Exclude

Dependencies

Rotor angle definition — Reference point for the rotor angle measurement Angle between the a-phase magnetic axis and the d-axis (default) | Angle between the a-phase magnetic axis and the q-axis

Impedances

Stator d-axis mutual inductance (unsaturated), Ladu — Stator d-axis mutual inductance (unsaturated) 0.9 (default) | positive scalar

Dependencies

Stator q-axis mutual inductance, Laq — Stator q-axis mutual inductance 0.55 (default) | positive scalar

Dependencies

Stator zero-sequence inductance, L0 — Stator zero-sequence inductance 0.15 (default) | positive scalar

Dependencies

Stator leakage inductance, Ll — Stator leakage inductance 0.15 (default) | positive scalar

Dependencies

Stator resistance, Ra — Stator resistance 0.011 (default) | positive scalar

Rotor field circuit inductance, Lfd — Rotor field circuit inductance 0.2571 (default) | positive scalar

Rotor field circuit resistance, Rfd — Rotor field circuit resistance 0.0006 (default) | positive scalar

Dependencies

Rotor d-axis damper winding 1 inductance, L1d — Rotor d-axis damper winding 1 inductance 0.2 (default) | positive scalar

Dependencies

Rotor d-axis damper winding 1 resistance, R1d — Rotor d-axis damper winding 1 resistance 0.0354 (default) | positive scalar

Dependencies

Rotor q-axis damper winding 1 inductance, L1q — Rotor q-axis damper winding 1 inductance 0.2567 (default) | positive scalar

Dependencies

Rotor q-axis damper winding 1 resistance, R1q — Rotor q-axis damper winding 1 resistance 0.0428 (default) | positive scalar

Dependencies

Stator leakage reactance, Xl — Stator leakage reactance 0.15 (default) | positive scalar

Dependencies

d-axis synchronous reactance, Xd — d-axis synchronous reactance 1.05 (default) | positive scalar

Dependencies

q-axis synchronous reactance, Xq — q-axis synchronous reactance 0.7 (default) | positive scalar

Dependencies

zero-sequence reactance, X0 — Zero-sequence reactance 0.15 (default) | positive scalar

Dependencies

d-axis transient reactance, Xd' — d-axis transient reactance 0.35 (default) | positive scalar

Dependencies

d-axis subtransient reactance, Xd'' — d-axis subtransient reactance 0.25 (default) | positive scalar

Dependencies

q-axis subtransient reactance, Xq'' — q-axis subtransient reactance 0.325 (default) | positive scalar

Dependencies

Time Constants

Specify d-axis time constant — Specify d-axis time constant Open circuit (default) | Short circuit

d-axis transient open-circuit, Td0' — d-axis transient open-circuit 5.25 s (default) | positive scalar

Dependencies

d-axis transient short-circuit, Td' — d-axis transient short-circuit 1.75 s (default) | positive scalar

Dependencies

d-axis subtransient open-circuit, Td0'' — d-axis subtransient open-circuit 0.03 s (default) | positive scalar

Dependencies

d-axis subtransient short-circuit, Td'' — d-axis subtransient short-circuit 0.0214 s (default) | positive scalar

Dependencies

Specify q-axis time constant — Specify q-axis time constant Open circuit (default) | Short circuit

`pu` — Machine per-unit measurements
physical

`fd+` — Field winding positive terminal
electrical

`fd-` — Field winding negative terminal
electrical

`R` — Machine rotor
mechanical

`C` — Machine case
mechanical

`~` — Stator windings
electrical

`n` — Neutral phase
electrical

`Rated apparent power` — Rated apparent power
`300e6` `V*A` (default)

`Rated voltage` — RMS rated line-line voltage
`24e3` `V` (default)

`Rated electrical frequency` — Nominal electrical frequency
`60` `Hz` (default)

`Number of pole pairs` — Number of pole pairs
`10` (default)

`Specify parameterization by` — Block parameterization
`Fundamental parameters` (default) | `Standard parameters`

`Specify field circuit input required to produce rated terminal voltage at no load by` — Specify field circuit input required to produce rated terminal voltage at no load by
`Field circuit current` (default) | `Field circuit voltage`

`Field circuit voltage` — Field circuit voltage
`216.54` `V` (default)

`Field circuit current` — Field circuit current
`1000` `A` (default)

`Zero sequence` — Zero-sequence model
`Include` (default) | `Exclude`

`Rotor angle definition` — Reference point for the rotor angle measurement
`Angle between the a-phase magnetic axis and the d-axis` (default) | `Angle between the a-phase magnetic axis and the q-axis`

`Stator d-axis mutual inductance (unsaturated), Ladu` — Stator d-axis mutual inductance (unsaturated)
`0.9` (default) | positive scalar

`Stator q-axis mutual inductance, Laq` — Stator q-axis mutual inductance
`0.55` (default) | positive scalar

`Stator zero-sequence inductance, L0` — Stator zero-sequence inductance
`0.15` (default) | positive scalar

`Stator leakage inductance, Ll` — Stator leakage inductance
`0.15` (default) | positive scalar

`Stator resistance, Ra` — Stator resistance
`0.011` (default) | positive scalar

`Rotor field circuit inductance, Lfd` — Rotor field circuit inductance
`0.2571` (default) | positive scalar

`Rotor field circuit resistance, Rfd` — Rotor field circuit resistance
`0.0006` (default) | positive scalar

`Rotor d-axis damper winding 1 inductance, L1d` — Rotor d-axis damper winding 1 inductance
`0.2` (default) | positive scalar

`Rotor d-axis damper winding 1 resistance, R1d` — Rotor d-axis damper winding 1 resistance
`0.0354` (default) | positive scalar

`Rotor q-axis damper winding 1 inductance, L1q` — Rotor q-axis damper winding 1 inductance
`0.2567` (default) | positive scalar

`Rotor q-axis damper winding 1 resistance, R1q` — Rotor q-axis damper winding 1 resistance
`0.0428` (default) | positive scalar

`Stator leakage reactance, Xl` — Stator leakage reactance
`0.15` (default) | positive scalar

`d-axis synchronous reactance, Xd` — d-axis synchronous reactance
`1.05` (default) | positive scalar

`q-axis synchronous reactance, Xq` — q-axis synchronous reactance
`0.7` (default) | positive scalar

`zero-sequence reactance, X0` — Zero-sequence reactance
`0.15` (default) | positive scalar

`d-axis transient reactance, Xd'` — d-axis transient reactance
`0.35` (default) | positive scalar

`d-axis subtransient reactance, Xd''` — d-axis subtransient reactance
`0.25` (default) | positive scalar

`q-axis subtransient reactance, Xq''` — q-axis subtransient reactance
`0.325` (default) | positive scalar

`Specify d-axis time constant` — Specify d-axis time constant
`Open circuit` (default) | `Short circuit`

`d-axis transient open-circuit, Td0'` — d-axis transient open-circuit
`5.25` `s` (default) | positive scalar

`d-axis transient short-circuit, Td'` — d-axis transient short-circuit
`1.75` `s` (default) | positive scalar

`d-axis subtransient open-circuit, Td0''` — d-axis subtransient open-circuit
`0.03` `s` (default) | positive scalar

`d-axis subtransient short-circuit, Td''` — d-axis subtransient short-circuit
`0.0214` `s` (default) | positive scalar

`Specify q-axis time constant` — Specify q-axis time constant
`Open circuit` (default) | `Short circuit`

`q-axis subtransient open-circuit, Tq0'` — q-axis subtransient open-circuit
`0.05` `s` (default) | positive scalar

`q-axis subtransient short-circuit, Tq'` — q-axis subtransient short-circuit
`0.0232` `s` (default) | positive scalar

`Magnetic saturation representation` — Magnetic saturation representation
`None` (default) | `Open-circuit lookup table (v versus i)`

`Per-unit field current saturation data, ifd` — Per-unit field current saturation data
`[0, .48, .76, 1.38, 1.79]` (default)

`Per-unit air-gap voltage saturation data, Vag` — Per-unit air-gap voltage saturation data
`[0, .8, 1.08, 1.31, 1.4]` (default)

`Initialization option` — Initialization option
`Set real power, reactive power, terminal voltage, and terminal phase` (default) | `Set targets for rotor angle and Park's transform variables` | `Set targets for load flow variables`

`Source type` — Voltage source model
`Swing bus` (default) | `Voltage source with series impedance` | `PV bus` | `PQ bus`

`Terminal voltage magnitude` — Terminal voltage magnitude
`24e3` `V` (default)

`Terminal voltage angle` — Terminal voltage angle
`0` `deg` (default)

`Active power generated` — Active power generated
`270e6` `V*A` (default)

`Reactive power generated` — Reactive power generated
`0` `V*A` (default)

`Minimum terminal voltage magnitude (pu)` — Minimum terminal voltage magnitude
`0.95` (default)

`Phase search range at terminals` — Phase search range at terminals
`[-inf, inf]` `deg` (default)

`Parasitic conductance to electrical reference` — Parasitic conductance to electrical reference
`1e-6` `S` (default)

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.