Reduced Lundell (clawpole) alternator with an external voltage regulator
Powertrain Blockset / Energy Storage and Auxiliary Drive / Alternator
The Reduced Lundell Alternator block implements a reduced Lundell (clawpole) alternator with an external voltage regulator. The backelectromotive 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 frontend 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.
To calculate voltages, the block uses these equations.
Calculation  Equations 

Alternator output voltage  $${v}_{s}={K}_{v}{i}_{f}\omega {R}_{s}{i}_{s}2{V}_{d}$$ 
Field winding voltage  ${v}_{f}={R}_{f}{i}_{f}+{L}_{f}\frac{d{i}_{f}}{dt}$ 
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  $T\left(s\right)=\frac{1}{\tau s+1}\to G\left(s\right)Gc\left(s\right)=\frac{1}{\tau s}$ ${G}_{C}\left(s\right)={K}_{g}({K}_{p}+\frac{{K}_{i}}{s})$ $G(s){G}_{C}\left(s\right)=\frac{{K}_{v}\omega}{({R}_{f}+s{L}_{f})}{K}_{g}({K}_{p}+\frac{{K}_{i}}{s})$ ${K}_{p}={L}_{f},{K}_{i}={R}_{f},and{K}_{g}=\frac{2\pi f}{{K}_{v}\omega}$ 
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  ${\tau}_{mech}={\tau}_{elec}+{\tau}_{friction}+{\tau}_{windage}+{\tau}_{start}$ 
For the power accounting, the block implements these equations.
Bus Signal  Description  Variable  Equations  



 Mechanical power  P_{mot}  ${P}_{mot}=\omega {\tau}_{mech}$ 
PwrBus  Electrical power  P_{bus}  ${P}_{bus}={v}_{s}{i}_{load}$  
 PwrLoss  Motor power loss  P_{loss}  ${P}_{loss}=({P}_{mot}+{P}_{bus}{P}_{ind})$  
 PwrInd  Electrical winding loss  P_{ind}  ${P}_{ind}={L}_{f}{i}_{f}\frac{d{i}_{f}}{dt}$ 
The equations use these variables.
v_{ref}  Alternator output voltage command 
v_{f}  Field winding voltage 
i_{f}  Field winding current 
i_{s}  Stator winding current 
V_{d}  Diode voltage drop 
R_{f}  Field winding resistance 
R_{s}  Stator winding resistance 
L_{f}  Field winding inductance 
K_{v}  Voltage constant 
F_{v}  Voltage regulator bandwidth 
F_{c}  Input current filter bandwidth 
V_{fmax}  Field control voltage upper saturation limit 
V_{fmin}  Field control voltage lower saturation limit 
K_{c}  Coulomb friction coefficient 
K_{b}  Viscous friction coefficient 
K_{w}  Windage coefficient 
ω  Motor shaft angular speed 
i_{load}  Alternator load current 
v_{s}  Alternator output voltage 
τ_{mech}, T_{mech}  Motor shaft torque 
[1] Krause, P. C. Analysis of Electric Machinery. New York: McGrawHill, 1994.