Reduced Lundell Alternator

Reduced Lundell (claw-pole) alternator with an external voltage regulator

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  • Powertrain Blockset / Energy Storage and Auxiliary Drive / Alternator

Description

The Reduced Lundell Alternator block implements a reduced Lundell (claw-pole) alternator with an external voltage regulator. The back-electromotive force (EMF) voltage is proportional to the input velocity and field current. The motor operates as a source torque to the internal combustion engine.

Use the Reduced Lundell Alternator block:

  • To model an automotive electrical system

  • In an engine model with a front-end accessory drive (FEAD)

The calculated motor shaft torque is in the opposite direction of the engine speed. You can:

  • Tune the external voltage regulator to a desired bandwidth. The stator current and two diode drops reduce the stator voltage.

  • Filter the load current to desired bandwidth. The load current has a lower saturation of 0 A.

The Reduced Lundell Alternator block implements equations for the electrical, control, and mechanical systems that use these variables.

Electrical

To calculate voltages, the block uses these equations.

CalculationEquations
Alternator output voltagevs=KvifωRsis2Vd
Field winding voltagevf= Rfif+Lfdifdt

Control

The controller assumes no resistance or voltage drop.

CalculationEquations

Field winding voltage transform

Vf(s)=RfIf(s)+sLfIf(s)

Field winding current transform

If(s)=Vf(s)(Rf+sLf)

Open loop electrical transfer function

G(s)= Vs(s)Vf(s)= Kvω(Rf+sLf)

Open loop voltage regulator transfer function

GC(s)=  Vf(s)Vref(s)

Closed loop transfer function

 T(s)= G(s)Gc(s)1+G(s)Gc(s)

Closed loop controller design

T(s)=1τs+1 G(s)Gc(s)= 1τs

GC(s)= Kg (Kp+ Kis)

G(s)GC(s)= Kvω(Rf+sLf)Kg (Kp+ Kis)

Kp=Lf  ,Ki=Rf ,and Kg=2πfKvω

Mechanical

To calculate torques, the block uses these equations.

CalculationEquations
Electrical torque

τelec= (Kvifω)iload

Frictional torque

 τfriction= Kbω

Windage torque

τwindage=Kwω2

Torque at start

τstart=Kc when ω=0

Motor shaft torque

τmech=τelec+τfriction+τwindage+τstart

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal DescriptionVariableEquations

PwrInfo

PwrTrnsfrd — Power transferred between blocks

  • Positive signals indicate flow into block

  • Negative signals indicate flow out of block

PwrMtr

Mechanical power

Pmot

Pmot= ωτmech

PwrBus

Electrical power

Pbus

Pbus=  vsiload

PwrNotTrnsfrd — Power crossing the block boundary, but not transferred

  • Positive signals indicate an input

  • Negative signals indicate a loss

PwrLoss

Motor power loss

Ploss

Ploss= (Pmot+PbusPind)

PwrStored — Stored energy rate of change

  • Positive signals indicate an increase

  • Negative signals indicate a decrease

PwrInd

Electrical winding loss

Pind

Pind= Lfifdifdt

The equations use these variables.

vref

Alternator output voltage command

vf

Field winding voltage

if

Field winding current

is

Stator winding current

Vd

Diode voltage drop

Rf

Field winding resistance

Rs

Stator winding resistance

Lf

Field winding inductance

Kv

Voltage constant

Fv

Voltage regulator bandwidth

Fc

Input current filter bandwidth

Vfmax

Field control voltage upper saturation limit

Vfmin

Field control voltage lower saturation limit

Kc

Coulomb friction coefficient

Kb

Viscous friction coefficient

Kw

Windage coefficient

ω

Motor shaft angular speed

iload

Alternator load current

vs

Alternator output voltage

τmech, Tmech

Motor shaft torque

Ports

Inputs

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Alternator output voltage command, in V.

Motor shaft input angular speed, in rad/s.

Alternator load current, in A.

Output

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Bus signal containing these block calculations.

SignalDescriptionUnits

FldVolt

Field winding voltage

A

FldFlux

Field flux

Wb

PwrInfo

PwrTrnsfrd

PwrMtr

Mechanical power

W
PwrBus

Electrical power

W

PwrNotTrnsfrd

PwrLoss

Motor power loss

W

PwrStored

PwrInd

Electrical winding loss

W

Alternator output voltage, in V.

Motor shaft torque, in N·m.

Parameters

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Machine Configuration

Voltage constant, in V/rad/s.

Field winding resistance, in ohm.

Field winding inductance, in H.

Stator winding resistance, in ohm.

Diode voltage drop, in V.

Voltage Regulator

The regulator bandwidth, in Hz.

The current filter bandwidth, in Hz.

The maximum field voltage, in V.

The minimum field voltage, in V.

Mechanical Losses

Coulomb friction, in N·m.

Viscous friction, in N·m/rad/s.

Windage, in N·m/rad2/s2.

References

[1] Krause, P. C. Analysis of Electric Machinery. New York: McGraw-Hill, 1994.

Extended Capabilities

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

See Also

Introduced in R2017a