Surface Mount PMSM

Three-phase exterior permanent magnet synchronous motor with sinusoidal back electromotive force

expand all in page

库:
Powertrain Blockset / Propulsion / Electric Motors and Inverters
Motor Control Blockset / Electrical Systems / Motors

Description

TheSurface Mount PMSMblock implements a three-phase exterior permanent magnet synchronous motor (PMSM) with sinusoidal back electromotive force. The block uses the three-phase input voltages to regulate the individual phase currents, allowing control of the motor torque or speed.

默认情况下, the block sets theSimulation typeparameter toContinuousto use a continuous sample time during simulation. If you want to generate code for fixed-step double- and single-precision targets, considering setting the parameter toDiscrete. Then specify aSample Time, Tsparameter.

On theParameterstab, if you selectBack-emforTorque constant, the block implements one of these equations to calculate the permanent flux linkage constant.

Setting	Equation
`Back-emf`	$λ_{p m} = \frac{1}{\sqrt{3}} \cdot \frac{K_{e}}{1000 P} \cdot \frac{60}{2 π}$
`Torque constant`	$λ_{p m} = \frac{2}{3} \cdot \frac{K_{t}}{P}$

Motor Construction

This figure shows the motor construction with a single pole pair on the motor.

The motor magnetic field due to the permanent magnets creates a sinusoidal rate of change of flux with motor angle.

For the axes convention, thea-phase and permanent magnet fluxes are aligned when motor angleθ_ris zero.

Three-Phase Sinusoidal Model Electrical System

The block implements these equations, expressed in the motor flux reference frame (dq frame). All quantities in the motor reference frame are referred to the stator.

$\begin{array}{l} ω_{e} = P ω_{m} \\ \frac{d}{d t} i_{d} = \frac{1}{L_{d}} v_{d} - \frac{R}{L_{d}} i_{d} + \frac{L_{q}}{L_{d}} P ω_{m} i_{q} \end{array}$

$\frac{d}{d t} i_{q} = \frac{1}{L_{q}} v_{q} - \frac{R}{L_{q}} i_{q} - \frac{L_{d}}{L_{q}} P ω_{m} i_{d} - \frac{λ_{p m} P ω_{m}}{L_{q}}$

$T_{e} = 1.5 P [λ_{p m} i_{q} + (L_{d} - L_{q}) i_{d} i_{q}]$

TheL_qandL_dinductances represent the relation between the phase inductance and the motor position due to the saliency of the motor magnets. For the surface mount PMSM, $L_{d} = L_{q}$ .

The equations use these variables.

L_q,L_d	q- and d-axis inductances (H)
R	Resistance of the stator windings (ohm)
i_q,i_d	q- and d-axis currents (A)
v_q,v_d	q- and d-axis voltages (V)
ω_m	Angular mechanical velocity of the motor (rad/s)
ω_e	Angular electrical velocity of the motor (rad/s)
λ_pm	Permanent magnet flux linkage (Wb)
K_e	Back electromotive force (EMF) (Vpk_LL/krpm, where Vpk_LL is the peak voltage line-to-line measurement)
K_t	Torque constant (N·m/A)
P	Number of pole pairs
T_e	Electromagnetic torque (Nm)
Θ_e	Electrical angle (rad)

Mechanical System

The motor angular velocity is given by:

$\begin{matrix} \frac{d}{d t} ω_{m} = \frac{1}{J} (T_{e} - T_{f} - F ω_{m} - T_{m}) \\ \frac{d θ_{m}}{d t} = ω_{m} \end{matrix}$

The equations use these variables.

J	Combined inertia of motor and load (kgm^2)
F	Combined viscous friction of motor and load (N·m/(rad/s))
θ_m	Motor mechanical angular position (rad)
T_m	Motor shaft torque (Nm)
T_e	Electromagnetic torque (Nm)
T_f	Motor shaft static friction torque (Nm)
ω_m	Angular mechanical velocity of the motor (rad/s)

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	Variable	Equations
`PwrInfo`	`PwrTrnsfrd`— Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	`PwrMtr`	Mechanical power	P_mot	$P_{m o t} = - ω_{m} T_{e}$
		`PwrBus`	Electrical power	P_bus	$P_{b u s} = v_{a n} i_{a} + v_{b n} i_{b} + v_{c n} i_{c}$
	`PwrNotTrnsfrd`— Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	`PwrElecLoss`	Resistive power loss	P_elec	$P_{e l e c} = - \frac{3}{2} (R_{s} i_{s d}^{2} + R_{s} i_{s q}^{2})$
		`PwrMechLoss`	Mechanical power loss	P_mech	WhenPort Configurationis set to`Torque`: $P_{m e c h} = - (ω_{m}^{2} F + \| ω_{m} \| T_{f})$ WhenPort Configurationis set to`Speed`: $P_{m e c h} = 0$
	`PwrStored`— Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	`PwrMtrStored`	Stored motor power	P_str	$P_{s t r} = P_{b u s} + P_{m o t} + P_{e l e c} + P_{m e c h}$

The equations use these variables.

R_s	Stator resistance (ohm)
i_a,i_b,i_c	Stator phase a, b, and c current (A)
i_sq,i_sd	Stator q- and d-axis currents (A)
v_an,v_bn,v_cn	Stator phase a, b, and c voltage (V)
ω_m	Angular mechanical velocity of the motor (rad/s)
F	Combined motor and load viscous damping N·m/(rad/s)
T_e	Electromagnetic torque (Nm)
T_f	Combined motor and load friction torque (Nm)

Ports

Input

expand all

`LdTrq`— Load torque on motor
`scalar`

Load torque on the motor shaft,T_m, in N·m.

Dependencies

To create this port, selectTorquefor thePort Configurationparameter.

`Spd`— Motor shaft speed
`scalar`

Angular velocity of the motor,ω_m, in rad/s.

Dependencies

To create this port, selectSpeedfor thePort Configurationparameter.

`PhaseVolt`— Stator terminal voltages
`1`-by-`3`array

Stator terminal voltages,V_a,V_b, andV_c, in V.

Output

expand all

`Info`— Bus signal
bus

The bus signal contains these block calculations.

Signal			Description	Variable	Units
`IaStator`			定子相电流一	i_a	A
`IbStator`			Stator phase current B	i_b	A
`IcStator`			Stator phase current C	i_c	A
`IdSync`			Direct axis current	i_d	A
`IqSync`			Quadrature axis current	i_q	A
`VdSync`			Direct axis voltage	v_d	V
`VqSync`			Quadrature axis voltage	v_q	V
`MtrSpd`			Angular mechanical velocity of the motor	ω_m	rad/s
`MtrPos`			Motor mechanical angular position	θ_m	rad
`MtrTrq`			Electromagnetic torque	T_e	N·m
`PwrInfo`	`PwrTrnsfrd`	`PwrMtr`	Mechanical power	P_mot	W
	`PwrTrnsfrd`	`PwrBus`	Electrical power	P_bus	W
	`PwrNotTrnsfrd`	`PwrElecLoss`	Resistive power loss	P_elec	W
	`PwrNotTrnsfrd`	`PwrMechLoss`	Mechanical power loss	P_mech	W
	`PwrStored`	`PwrMtrStored`	Stored motor power	P_str	W

`PhaseCurr`— Phase a, b, c current
`1`-by-`3`array

Phase a, b, c current,i_a,i_b, andi_c, in A.

`MtrTrq`——电动机转矩
`scalar`

Motor torque,T_mtr, in N·m.

Dependencies

To create this port, selectSpeedfor theMechanical input configurationparameter.

`MtrSpd`— Motor speed
`scalar`

Angular speed of the motor,ω_mtr, in rad/s.

Dependencies

To create this port, selectTorquefor theMechanical input configurationparameter.

Parameters

expand all

块的选择

`Mechanical input configuration`— Select port configuration
`Torque`(default) |`Speed`

This table summarizes the port configurations.

Port Configuration	Creates Input Port	Creates Output Port
`Torque`	`LdTrq`	`MtrSpd`
`Speed`	`Spd`	`MtrTrq`

`Simulation type`— Select simulation type
`Continuous`(default) |`Discrete`

默认情况下, the block uses a continuous sample time during simulation. If you want to generate code for single-precision targets, considering setting the parameter toDiscrete.

Dependencies

SettingSimulation typetoDiscretecreates theSample Time, Tsparameter.

`Sample Time (Ts)`— Sample time for discrete integration
`scalar`

Integration sample time for discrete simulation, in s.

Dependencies

SettingSimulation typetoDiscretecreates theSample Time, Tsparameter.

Load Parameters

`File`— Path to motor parameter ".m" or ".mat" file
`scalar`

Enter the path to the motor parameter ".m" or ".mat" file that you saved using the Motor Control Blockset™ parameter estimation tool. You can also click theBrowsebutton to navigate and select the ".m" or ".mat" file, and updateFileparameter with the file name and path. For details related to the motor parameter estimation process, seeEstimate PMSM Parameters Using Recommended Hardware.

Load from file- Click this button to read the estimated motor parameters from the ".m" or ".mat" file (indicated by theFileparameter) and load them to the motor block.
Save to file- Click this button to read the motor parameters from the motor block and save them into a ".m" or ".mat" file (with a file name and location that you specify in theFileparameter).

Note

在你点击Save to filebutton, ensure that the target file name in theFileparameter has either ".m" or ".mat" extension. If you use any other file extension, the block displays an error message.

Parameters

`Number of pole pairs (P)`— Pole pairs
`scalar`

Motor pole pairs,P.

`Stator phase resistance per phase (Rs)`— Resistance
`scalar`

Stator phase resistance per phase,R_s, in ohm.

`Stator d-axis inductance (Ldq_)`— Inductance
`scalar`

Stator inductance,L_dq, in H.

`Permanent flux linkage constant (lambda_pm)`— Flux
`scalar`

Permanent flux linkage constant,λ_pm, in Wb.

`Back-emf constant (Ke)`— Back electromotive force
`scalar`

Back electromotive force, EMF,K_e, in peak Vpk_LL/krpm. Vpk_LL is the peak voltage line-to-line measurement.

To calculate the permanent flux linkage constant, the block implements this equation.

$λ_{p m} = \frac{1}{\sqrt{3}} \cdot \frac{K_{e}}{1000 P} \cdot \frac{60}{2 π}$

`Torque constant (Kt)`— Torque constant
`scalar`

Torque constant,K_t, in N·m/A.

To calculate the permanent flux linkage constant, the block implements this equation.

$λ_{p m} = \frac{2}{3} \cdot \frac{K_{t}}{P}$

`Physical inertia, viscous damping, and static friction (mechanical)`— Inertia, damping, friction
`vector`

Mechanical properties of the motor:

Inertia,J, in kg.m^2
Viscous damping,F, in N·m/(rad/s)
Static friction,T_f, in N·m

Dependencies

To enable this parameter, select theTorqueconfiguration parameter.

Initial Values

`Initial d-axis and q-axis current (idq0)`— Current
`vector`

Initial q- and d-axis currents,i_q, i_d, in A.

`Initial mechanical position (theta_init)`— Angle
`scalar`

Initial motor angular position,θ_m0, in rad.

`Initial mechanical speed (omega_init)`— Speed
`scalar`

Initial angular velocity of the motor,ω_m0, in rad/s.

Dependencies

To enable this parameter, select theTorqueconfiguration parameter.

References

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

[2] Anderson, P. M.Analysis of Faulted Power Systems.Hoboken, NJ: Wiley-IEEE Press, 1995.

Extended Capabilities

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

版本History

Introduced in R2017a

Surface Mount PMSM

Description

Motor Construction

Three-Phase Sinusoidal Model Electrical System

Mechanical System

Power Accounting

Ports

Input

LdTrq— Load torque on motorscalar

Dependencies

Spd— Motor shaft speedscalar

Dependencies

PhaseVolt— Stator terminal voltages1-by-3array

Output

Info— Bus signalbus

PhaseCurr— Phase a, b, c current1-by-3array

MtrTrq——电动机转矩scalar

Dependencies

MtrSpd— Motor speedscalar

Dependencies

Parameters

Mechanical input configuration— Select port configurationTorque(default) |Speed

Simulation type— Select simulation typeContinuous(default) |Discrete

Dependencies

Sample Time (Ts)— Sample time for discrete integrationscalar

Dependencies

File— Path to motor parameter ".m" or ".mat" filescalar

Number of pole pairs (P)— Pole pairsscalar

Stator phase resistance per phase (Rs)— Resistancescalar

Stator d-axis inductance (Ldq_)— Inductancescalar

Permanent flux linkage constant (lambda_pm)— Fluxscalar

Back-emf constant (Ke)— Back electromotive forcescalar

Torque constant (Kt)— Torque constantscalar

Physical inertia, viscous damping, and static friction (mechanical)— Inertia, damping, frictionvector

Dependencies

Initial d-axis and q-axis current (idq0)— Currentvector

Initial mechanical position (theta_init)— Anglescalar

Initial mechanical speed (omega_init)— Speedscalar

Dependencies

References

Extended Capabilities

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

版本History

`LdTrq`— Load torque on motor
`scalar`

`Spd`— Motor shaft speed
`scalar`

`PhaseVolt`— Stator terminal voltages
`1`-by-`3`array

`Info`— Bus signal
bus

`PhaseCurr`— Phase a, b, c current
`1`-by-`3`array

`MtrTrq`——电动机转矩
`scalar`

`MtrSpd`— Motor speed
`scalar`

`Mechanical input configuration`— Select port configuration
`Torque`(default) |`Speed`

`Simulation type`— Select simulation type
`Continuous`(default) |`Discrete`

`Sample Time (Ts)`— Sample time for discrete integration
`scalar`

`File`— Path to motor parameter ".m" or ".mat" file
`scalar`

`Number of pole pairs (P)`— Pole pairs
`scalar`

`Stator phase resistance per phase (Rs)`— Resistance
`scalar`

`Stator d-axis inductance (Ldq_)`— Inductance
`scalar`

`Permanent flux linkage constant (lambda_pm)`— Flux
`scalar`

`Back-emf constant (Ke)`— Back electromotive force
`scalar`

`Torque constant (Kt)`— Torque constant
`scalar`

`Physical inertia, viscous damping, and static friction (mechanical)`— Inertia, damping, friction
`vector`

`Initial d-axis and q-axis current (idq0)`— Current
`vector`

`Initial mechanical position (theta_init)`— Angle
`scalar`

`Initial mechanical speed (omega_init)`— Speed
`scalar`

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