流感x-Based PMSM

流感x-based permanent magnet synchronous motor

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Library:
动力总成设备 /推进 /电动机和逆变器

Description

The流感x-Based PMSMblock implements a flux-based three-phase permanent magnet synchronous motor (PMSM) with a tabular-based electromotive force. The block uses the three-phase input voltages to regulate the individual phase currents, allowing control of the motor torque or speed.

流感x-based motor models take into account magnetic saturation and iron losses. To calculate the magnetic saturation and iron loss, the流感x-Based PMSMblock uses the inverse of the flux linkages. To obtain the block parameters, you can use finite-element analysis (FEA) or measure phase voltages using a dynamometer.

By default, the block sets theSimulation Typeparameter toContinuous在模拟过程中使用连续的样品时间。如果要为固定步骤的双重和单精度目标生成代码，请考虑将参数设置为Discrete. Then specify aSample Time, Tsparameter.

To enable power loss calculations suitable for code generation targets that limit memory, selectEnable memory optimized 2D LUT.

三相正弦模型电气系统

The block implements equations that are expressed in a stationary rotor reference (dq) frame. Thed-axis aligns with thea-axis. All quantities in the rotor reference frame are referred to the stator.

The block uses these equations.

Calculation	Equation
q- andd- 轴电压	$\begin{array}{l} v_{d} = \frac{d ψ_{d}}{d t} + R_{s} i_{d} - ω_{e} ψ_{q} \\ v_{q} = \frac{d ψ_{q}}{d t} + R_{s} i_{q} + ω_{e} ψ_{d} \end{array}$
q- andd-axis current	$\begin{array}{l} i_{d} = f (ψ_{d}, ψ_{q}) \\ i_{q} = g (ψ_{d}, ψ_{q}) \end{array}$
Electromechanical torque	$T_{e} = 1.5 P [ψ_{d} i_{q} - ψ_{q} i_{d}]$

The equations use these variables.

ω_m	Rotor mechanical speed
ω_e	Rotor electrical speed
θ_da	dq stator electrical angle with respect to the rotor a-axis
R_s,R_r	Resistance of the stator and rotor windings, respectively
i_q,i_d	q- andd-axis current, respectively
v_q,v_d	q- andd- 轴电压, respectively
ψ_q,ψ_d	q- andd-axis magnet flux, respectively
P	杆对数
T_e	电磁转矩

Transforms

计算平衡三相的电压和电流（a,b）数量，正交两相（α,β) quantities, and rotating (d,q) reference frames, the block uses the Clarke and Park Transforms.

In the transform equations.

$\begin{array}{l} ω_{e} = P ω_{m} \\ \frac{d θ_{e}}{d t} = ω_{e} \end{array}$

Transform	Description	Equations
Clarke	Converts balanced three-phase quantities (a,b) into balanced two-phase quadrature quantities (α,β).	$\begin{array}{l} x_{α} = \frac{2}{3} x_{a} - \frac{1}{3} x_{b} - \frac{1}{3} x_{c} \\ x_{β} = \frac{\sqrt{3}}{2} x_{b} - \frac{\sqrt{3}}{2} x_{c} \end{array}$
Park	转换平衡的两相正交固定量（α,β) into an orthogonal rotating reference frame (d,q).	$\begin{array}{l} x_{d} = x_{α} \cos θ_{e} + x_{β} \sin θ_{e} \\ x_{q} = - x_{α} \sin θ_{e} + x_{β} \cos θ_{e} \end{array}$
Inverse Clarke	Converts balanced two-phase quadrature quantities (α,β）成平衡的三相量（a,b).	$\begin{array}{l} x_{a} = x_{a} \\ x_{b} = - \frac{1}{2} x_{α} + \frac{\sqrt{3}}{2} x_{β} \\ x_{c} = - \frac{1}{2} x_{α} - \frac{\sqrt{3}}{2} x_{β} \end{array}$
逆公园	Converts an orthogonal rotating reference frame (d,q) into balanced two-phase orthogonal stationary quantities (α,β).	$\begin{array}{l} x_{α} = x_{d} \cos θ_{e} - x_{q} \sin θ_{e} \\ x_{β} = x_{d} \sin θ_{e} + x_{q} \cos θ_{e} \end{array}$

The transforms use these variables.

ω_m	Rotor mechanical speed
P	电动杆对
ω_e	Rotor electrical speed
θ_e	Rotor electrical angle
x	Phase current or voltage

Mechanical System

The rotor 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 rotor and load
F	Combined viscous friction of rotor and load
θ_m	Rotor mechanical angular position
T_m	Rotor shaft torque
T_e	电磁转矩
T_f	转子和负载摩擦扭矩
ω_m	Rotor mechanical speed

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	多变的	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 正信号表示输入 Negative signals indicate a loss	`PwrElecLoss`	Resistive power loss	P_电子	$P_{e l e c} = - \frac{3}{2} (R_{s} i_{s d}^{2} + R_{s} i_{s q}^{2})$
		`PwrMechLoss`	Mechanical power loss	P_机械	什么时候端口配置被设定为`扭矩`: $P_{m e c h} = - (ω_{m}^{2} F + \| ω_{m} \| T_{f})$ 什么时候端口配置被设定为`Speed`: $P_{m e c h} = 0$
	`PwrStored`- 存储的能源变化速率 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	定子电阻
i_a,i_b,i_c	Stator phase a, b, and c current
i_sq,i_sd	Stator q- and d-axis currents
v_an,v_bn,v_cn	Stator phase a, b, and c voltage
ω_m	Angular mechanical velocity of the rotor
F	Combined motor and load viscous damping
T_e	电磁转矩
T_f	Combined motor and load friction torque

Lookup Table Memory Optimization

The data for theCorresponding d-axis current, idandCorresponding q-axis current, iqlookup tables are functions of thed- andq-axis flux.

To enable current calculations suitable for code generation targets that limit memory, selectEnable memory optimized 2D LUT. The block uses linear interpolation to optimize the current lookup table values for code generation. This table summarizes the optimization implementation.

Use Case		Implementation
d- andq-axis flux aligns with the lookup table breakpoint values.		Memory-optimized current is current lookup table value at intersection of flux values.
d- andq-axis flux does not align with the lookup table breakpoint values, but is within range.		内存优化的电流是相应的通量值之间的线性插值。
d- andq- 轴通量与查找表断点值不符，并且不超出范围。		Cannot compute an memory-optimized current. Block uses extrapolated data.

外推

The lookup tables optimized for code generation do not support extrapolation for data that is out of range. However, you can include pre-calculated extrapolation values in the power loss lookup table by selectingSpecify Extrapolation.

该块使用端点参数调整表数据大小。

User Input	外推

Ports

输入

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`LdTrq`— Rotor shaft torque
`scalar`

Rotor shaft input torque,T_m, in N·m.

Dependencies

To create this port, select扭矩为了端口配置parameter.

`Spd`- 转子轴速度
`scalar`

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

Dependencies

To create this port, selectSpeed为了端口配置parameter.

`相伏`— Stator terminal voltages
`1`-经过-`3`大批

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

Dependencies

To create this port, selectSpeedor扭矩为了端口配置parameter.

Output

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`Info`— Bus signal
bus

The bus signal contains these block calculations.

Signal			Description	多变的	单位
`IaStator`			Stator phase current A	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 rotor	ω_m	rad/s
`MtrPos`			Rotor mechanical angular position	θ_m	rad
`Mtrtrq`			电磁转矩	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_电子	W
	`PwrNotTrnsfrd`	`PwrMechLoss`	Mechanical power loss	P_机械	W
	`PwrStored`	`pwrmtrstored`	Stored motor power	P_str	W

`PhaseCurr`— Phase a, b, c current
`1`-经过-`3`大批

A阶段A，B，C电流，i_a,i_b, andi_c，在一个。

`Mtrtrq`— Motor torque
`scalar`

Motor torque,T_mtr, in N·m.

Dependencies

To create this port, selectSpeed为了Port configurationparameter.

`mtrspd`— Motor speed
`scalar`

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

Dependencies

To create this port, select扭矩为了Port configurationparameter.

Parameters

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块的选择

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

By default, 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

环境Simulation TypetoDiscretecreates theSample Time, Tsparameter.

`Sample time, Ts`— Sample time for discrete integration
`0.001`(default) |`scalar`

Integration sample time for discrete simulation, in s.

Dependencies

环境Simulation TypetoDiscretecreates theSample Time, Tsparameter.

`端口配置`— Select port configuration
`扭矩`(default) |`Speed`

This table summarizes the port configurations.

端口配置	Creates Input Port	Creates Output Port
`扭矩`	`LdTrq`	`mtrspd`
`Speed`	`Spd`	`Mtrtrq`

`Enable memory optimized 2D LUT`— Selection
`off`(default) |`on`

Enable generation of optimized lookup tables, suitable code generation targets that limit memory.

`Vector of d-axis flux, flux_d`— Flux breakpoints
`1`-经过-`M`vector

d-axis flux,ψ_d, breakpoints, in Wb.

`重新取样flux_d存储大小,n1`— Flux bit size
`2`(default) |`4`|`8`|`16`|`32`|`64`|`128`|`256`

流感x breakpoint storage size,n1, dimensionless. The block resamples theCorresponding d-axis current, idandCorresponding q-axis current, iqdata based on the storage size.

Dependencies

To create this parameter, selectEnable memory optimized 2D LUT.

`Vector of q-axis flux, flux_q`— Flux breakpoints
`1`-经过-`N`vector

q-axis flux,ψ_q, breakpoints, in Wb.

`Resample storage size for flux_q, n2`— Flux bit size
`2`(default) |`4`|`8`|`16`|`32`|`64`|`128`|`256`

流感x breakpoint storage size,n2, dimensionless. The block resamples theCorresponding d-axis current, idandCorresponding q-axis current, iqdata based on the storage size.

Dependencies

To create this parameter, selectEnable memory optimized 2D LUT.

`Corresponding d-axis current, id`— 2D lookup table
`M`-经过-`N`大批

Array of values ford-axis current,i_d, as a function ofMd-fluxes,ψ_d, andNq-fluxes,ψ_q，在A中，每个值都指定了特定组合的电流d- andq-axis flux. The array size must match the dimensions defined by the flux vectors.

If you setEnable memory optimized 2D LUT, the block converts the data to single precision.

`Corresponding q-axis current, iq`— 2D lookup table
`M`-经过-`N`大批

Array of values forq-axis current,i_d, as a function ofMd-fluxes,ψ_d, andNq-fluxes,ψ_q，在A中，每个值都指定了特定组合的电流d- andq-axis flux. The array size must match the dimensions defined by the flux vectors.

If you setEnable memory optimized 2D LUT, the block converts the data to single precision.

`flux_d max endpoint, u1max`— Flux breakpoint
`0.22457`(default) |`scalar`

流感x breakpoint maximum extrapolation endpoint,u1max, in Wb.

Dependencies

To create this parameter, selectEnable memory optimized 2D LUTandSpecify Extrapolation.

`flux_d min endpoint, u1min`— Flux breakpoint
`-0.22607`(default) |`scalar`

流感x breakpoint minimum extrapolation endpoint,u1min, in Wb.

Dependencies

To create this parameter, selectEnable memory optimized 2D LUTandSpecify Extrapolation.

`flux_q max endpoint, u2max`— Flux breakpoint
`0.42959`(default) |`scalar`

流感x breakpoint maximum extrapolation endpoint,u2max, in Wb.

Dependencies

To create this parameter, selectEnable memory optimized 2D LUTandSpecify Extrapolation.

`flux_q min endpoint, u2min`— Flux breakpoint
`-0.4296`(default) |`scalar`

流感x breakpoint minimum extrapolation endpoint,u2min, in Wb.

Dependencies

To create this parameter, selectEnable memory optimized 2D LUTandSpecify Extrapolation.

`Stator phase resistance, Rs`— Resistance
`0.02`(default) |`scalar`

Stator phase resistance,R_s, in ohm.

`杆对数，p`— Pole pairs
`4`(default) |`scalar`

电动杆对,P.

`Initial flux, fluxdq0`— Flux
`[0 0]`(default) |`vector`

Initiald- andq-axis flux,ψ_q0andψ_d0, in Wb.

`Initial mechanical position, theta_init`— Angle
`0`(default) |`scalar`

Initial rotor angular position,θ_m0, in rad.

`Initial mechanical speed, omega_init`— Speed
`0`(default) |`scalar`

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

Dependencies

要启用此参数，请选择扭矩configuration parameter.

`Physical inertia, viscous damping, and static friction, mechanical`- 惯性，阻尼，摩擦
`[0.0027，4.924e-4，0]`(default) |`vector`

Mechanical properties of the rotor:

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

Dependencies

要启用此参数，请选择扭矩configuration parameter.

参考

[1] Hu, Dakai, Yazan Alsmadi, and Longya Xu. “High fidelity nonlinear IPM modeling based on measured stator winding flux linkage.”IEEE^®Transactions on Industry Applications，卷。51, No. 4, July/August 2015.

[2] Chen, Xiao, Jiabin Wang, Bhaskar Sen, Panagiotis Lasari, Tianfu Sun. “A High-Fidelity and Computationally Efficient Model for Interior Permanent-Magnet Machines Considering the Magnetic Saturation, Spatial Harmonics, and Iron Loss Effect.”IEEE Transactions on Industrial Electronics，卷。62，第7号，2015年7月。

[3] Ottosson, J., M. Alakula. “A compact field weakening controller implementation.”国际电力电子，电动驱动器，自动化和运动研讨会, July, 2006.

Extended Capabilities

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

Version History

Introduced in R2017b

流感x-Based PMSM

Description

三相正弦模型电气系统

Transforms

Mechanical System

Power Accounting

Lookup Table Memory Optimization

Ports

输入

LdTrq— Rotor shaft torquescalar

Dependencies

Spd- 转子轴速度scalar

Dependencies

相伏— Stator terminal voltages1-经过-3大批

Dependencies

Output

Info— Bus signalbus

PhaseCurr— Phase a, b, c current1-经过-3大批

Mtrtrq— Motor torquescalar

Dependencies

mtrspd— Motor speedscalar

Dependencies

Parameters

Simulation type— Select simulation typeContinuous(default) |Discrete

Dependencies

Sample time, Ts— Sample time for discrete integration0.001(default) |scalar

Dependencies

端口配置— Select port configuration扭矩(default) |Speed

Enable memory optimized 2D LUT— Selectionoff(default) |on

Vector of d-axis flux, flux_d— Flux breakpoints1-经过-Mvector

重新取样flux_d存储大小,n1— Flux bit size2(default) |4|8|16|32|64|128|256

Dependencies

Vector of q-axis flux, flux_q— Flux breakpoints1-经过-Nvector

Resample storage size for flux_q, n2— Flux bit size2(default) |4|8|16|32|64|128|256

Dependencies

Corresponding d-axis current, id— 2D lookup tableM-经过-N大批

Corresponding q-axis current, iq— 2D lookup tableM-经过-N大批

flux_d max endpoint, u1max— Flux breakpoint0.22457(default) |scalar

Dependencies

flux_d min endpoint, u1min— Flux breakpoint-0.22607(default) |scalar

Dependencies

flux_q max endpoint, u2max— Flux breakpoint0.42959(default) |scalar

Dependencies

flux_q min endpoint, u2min— Flux breakpoint-0.4296(default) |scalar

Dependencies

Stator phase resistance, Rs— Resistance0.02(default) |scalar

杆对数，p— Pole pairs4(default) |scalar

Initial flux, fluxdq0— Flux[0 0](default) |vector

Initial mechanical position, theta_init— Angle0(default) |scalar

Initial mechanical speed, omega_init— Speed0(default) |scalar

Dependencies

Physical inertia, viscous damping, and static friction, mechanical- 惯性，阻尼，摩擦[0.0027，4.924e-4，0](default) |vector

Dependencies

参考

Extended Capabilities

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

Version History

See Also

Topics

`LdTrq`— Rotor shaft torque
`scalar`

`Spd`- 转子轴速度
`scalar`

`相伏`— Stator terminal voltages
`1`-经过-`3`大批

`Info`— Bus signal
bus

`PhaseCurr`— Phase a, b, c current
`1`-经过-`3`大批

`Mtrtrq`— Motor torque
`scalar`

`mtrspd`— Motor speed
`scalar`

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

`Sample time, Ts`— Sample time for discrete integration
`0.001`(default) |`scalar`

`端口配置`— Select port configuration
`扭矩`(default) |`Speed`

`Enable memory optimized 2D LUT`— Selection
`off`(default) |`on`

`Vector of d-axis flux, flux_d`— Flux breakpoints
`1`-经过-`M`vector

`重新取样flux_d存储大小,n1`— Flux bit size
`2`(default) |`4`|`8`|`16`|`32`|`64`|`128`|`256`

`Vector of q-axis flux, flux_q`— Flux breakpoints
`1`-经过-`N`vector

`Resample storage size for flux_q, n2`— Flux bit size
`2`(default) |`4`|`8`|`16`|`32`|`64`|`128`|`256`

`Corresponding d-axis current, id`— 2D lookup table
`M`-经过-`N`大批

`Corresponding q-axis current, iq`— 2D lookup table
`M`-经过-`N`大批

`flux_d max endpoint, u1max`— Flux breakpoint
`0.22457`(default) |`scalar`

`flux_d min endpoint, u1min`— Flux breakpoint
`-0.22607`(default) |`scalar`

`flux_q max endpoint, u2max`— Flux breakpoint
`0.42959`(default) |`scalar`

`flux_q min endpoint, u2min`— Flux breakpoint
`-0.4296`(default) |`scalar`

`Stator phase resistance, Rs`— Resistance
`0.02`(default) |`scalar`

`杆对数，p`— Pole pairs
`4`(default) |`scalar`

`Initial flux, fluxdq0`— Flux
`[0 0]`(default) |`vector`

`Initial mechanical position, theta_init`— Angle
`0`(default) |`scalar`

`Initial mechanical speed, omega_init`— Speed
`0`(default) |`scalar`

`Physical inertia, viscous damping, and static friction, mechanical`- 惯性，阻尼，摩擦
`[0.0027，4.924e-4，0]`(default) |`vector`

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