Reduced Lundell Alternator

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

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Libraries:
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.

Calculation	Equations
Alternator output voltage	$$v_s=K_v{i}_f\omega -R_s{i}_s-2V_d$$
Field winding voltage	$v_f= R_f{i}_f+L_f\frac{d{i}_f}{dt}$

Control

The controller assumes no resistance or voltage drop.

Calculation	Equations
Field winding voltage transform	$V_f\left(s\right)=R_f{I}_f\left(s\right)+s{L}_f{I}_f\left(s\right)$
Field winding current transform	$I_f\left(s\right)=\frac{V_f\left(s\right)}{(R_f+s{L}_f)}$
Open loop electrical transfer function	$G\left(s\right)= \frac{V_s\left(s\right)}{V_f\left(s\right)}= \frac{K_v\omega }{(R_f+s{L}_f)}$
Open loop voltage regulator transfer function	$G_C\left(s\right)= \frac{V_f\left(s\right)}{Vref\left(s\right)}$
Closed loop transfer function	$$T\left(s\right)= \frac{G\left(s\right)Gc\left(s\right)}{1+G\left(s\right)Gc\left(s\right)}$$
Closed loop controller design	$T\left(s\right)=\frac{1}{\tau s+1}\to G\left(s\right)Gc\left(s\right)= \frac{1}{\tau s}$ $G_C\left(s\right)= K_g (K_p+ \frac{K_i}{s})$ $G(s)G_C\left(s\right)= \frac{K_v\omega }{(R_f+s{L}_f)}{K}_g (K_p+ \frac{K_i}{s})$ $K_p=L_{f },K_i=R_{f },and K_g=\frac{2\pi f}{K_v\omega }$

Mechanical

To calculate torques, the block uses these equations.

Calculation	Equations
Electrical torque	${\tau }_{elec}= (K_v{i}_f\omega )i_{load}$
Frictional torque	$${\tau }_{friction}= K_b\omega$$
Windage torque	${\tau }_{windage}=K_w{\omega }^2$
Torque at start	$${\tau }_{start}=K_c$$ when $$\omega =0$$
Motor shaft torque	${\tau }_{mech}={\tau }_{elec}+{\tau }_{friction}+{\tau }_{windage}+{\tau }_{start}$

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	Pmot	$P_{mot}= \omega {\tau }_{mech}$
		PwrBus	Electrical power	Pbus	$P_{bus}= - v_s{i}_{load}$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrLoss	Motor power loss	Ploss	$P_{loss}= -(P_{mot}+P_{bus}-P_{ind})$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrInd	Electrical winding loss	Pind	$P_{ind}= L_f{i}_f\frac{d{i}_f}{dt}$

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

Examples

Build Conventional Vehicle Model

Build a vehicle with an internal combustion engine using the conventional vehicle reference application.

Ports

Inputs

RefVolt — Alternator output voltage command

scalar

Alternator output voltage command, in V.

AltSpd — Angular speed

scalar

Motor shaft input angular speed, in rad/s.

LdCurr — Alternator load current

scalar

Alternator load current, in A.

Do not connect the port to the alternator rated current, which is a constant value. The block uses the alternator load current as the stator winding current, i_s, to determine the alternator voltage and motor torque. If you connect the port to the rated alternator current, the block does not model the dynamic effect of load current changes on the voltage and motor torque.

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal			Description	Units
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

AltVolt — Alternator output voltage

scalar

Alternator output voltage, in V.

LdTrq — Motor shaft torque

scalar

Motor shaft torque, in N·m.

Parameters

Machine Configuration

Voltage constant, Kv — Constant

.1 (default) | scalar

Voltage constant, in V/rad/s.

Field winding resistance, Rf — Resistance

0.2 (default) | scalar

Field winding resistance, in ohm.

Field winding inductance, Lf — Inductance

0.002 (default) | scalar

Field winding inductance, in H.

Stator winding resistance, Rs — Resistance

0.01 (default) | scalar

Stator winding resistance, in ohm.

Diode voltage drop, Vd — Voltage

0.7 (default) | scalar

Diode voltage drop, in V.

Voltage Regulator

Regulator bandwidth, Fv — Bandwidth

2000 (default) | scalar

The regulator bandwidth, in Hz.

Current filter bandwidth, Fc — Bandwidth

1000 (default) | scalar

The current filter bandwidth, in Hz.

Field voltage max, Vfmax — Maximum field voltage

100 (default) | scalar

The maximum field voltage, in V.

Field voltage min, Vfmin — Minimum field voltage

-100 (default) | scalar

The minimum field voltage, in V.

Mechanical Losses

Coulomb friction, Kc — Friction

0 (default) | scalar

Coulomb friction, in N·m.

Viscous friction, Kb — Friction

0 (default) | scalar

Viscous friction, in N·m/rad/s.

Windage, Kw — Windage

0 (default) | scalar

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™.

Version History

Introduced in R2017a