Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

Appendices
⎡ ⎤
⎢ 1 0 ⎥
⎡K
A ⎤ ⎢ ⎥
⎢ 1 3 K
K
⎥ ⎢ ⎥ ⎡ α ⎤
⎢ B ⎥
=
⎢
−
2 2 ⎥⎢ K
⎥
β
⎢K
⎣ ⎦
⎣ ⎥
C ⎦ ⎢ ⎥
⎢ 1 3⎥
⎢
− −
⎣ 2 2 ⎥⎦
xy , ⇒ α,
β
Kα = Kxcosθ K
+ Kycos( π / 2 + θK) = KxcosθK − KysinθK
Kβ = Kxcos( π / 2 − θK) + KycosθK = KxsinθK + KycosθK
⎡Kα
⎤ ⎡cosθK
−sinθ
K
K⎤⎡ x ⎤
⎢
K
⎥ = ⎢
β sinθK
cosθ
⎥⎢ K
⎥
⎣ ⎦ ⎣
K ⎦⎣ y ⎦
α, β ⇒ x,
y
Kx = Kα cosθ K
+ Kβ cos( π / 2 − θK) = Kα cosθK + Kβ
sinθK
Ky = Kα cos( π / 2 + θK) + Kβ cosθK =− Kα sinθK + Kβ
cosθK
⎡Kx ⎤ ⎡ cosθK sinθ
K
K ⎤⎡ α ⎤
⎢
K
⎥ = ⎢
y sinθK cosθ
⎥⎢ K
⎥
⎣ ⎦ ⎣−
K⎦⎣ β ⎦
A3 Model of PM synchronous motor
# This template models the permanent magnet synchronous motor(pmsm)
# t1,t2 and t3 are motor input terminals
# rotor speed (in rad/s) is the output
# rs-Stator windings' resistence per phase(in Ohms)
# ld-d_axis inductance(in H)
# lq-q_axis inductance(in H)
# pm-Rotor magnet flux(Wb)
# j-Moment of inertia(in kgm2)
# d- Damping constant (Nm/rad/s)
# tl-motor load (Nm)
# p-Number of pole pairs
# power-The total input power (W)
# Assumptions:No core losses,no saturation,thermal effects
#(rs,ld,lq and pm values are constants)
element template pmsm_dtc t1 t2 t3 t0 speed out_me out_psi out_thetam out_ualf out_ubet out_psia
out_psib out_ialf out_ibet out_theta
out_tl=rs,ld,lq,pm,d,tl,j,p,init_theta_m,init_omega_m,omega_m_const
electrical t1,t2,t3,t0 # motor input terminals and stator neutral point
output nu speed,
out_me,out_psi,out_thetam,out_ualf,out_ubet,out_psia,out_psib,out_ialf,out_ibet,out_theta,out_tl
number rs=0.692,ld=6m,lq=6m,pm=0.26379,d=0.002044,tl=0.0,j=0.003,p=3.0,
init_theta_m=0.0,init_omega_m=0.0,omega_m_const=0.0
{
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