$$a_s$$magnetical axis of phase a in the stator

aphase a in a three-phase system

arotational unit vector of 120°

$${\underset{\_}{a}}^2$$rotational unit vector of 240°

[A]phase transformation matrix

bphase b in a three-phase system

cphase c n a three-phase system

Ccondenser capacity

Dfixed of stator-oriented direct axis

Ddiode

[D]rotational matrix operator of a two-phase axis system

$$d\lambda$$arbitrarily rotating of field-oriented direct axis

$$d{\lambda }_m$$air-gap field-oriented direct axis

$$d{\lambda }_r$$resultant rotor field-oriented direct axis

$$d{\lambda }_s$$resultant stator field-oriented direct axis

$$d\theta$$rotor-oriented direct axis

$$\underset{\_}{e}$$space phasor of the electromotive force

$$f_s$$stator voltage and stator current frequency

$$d{\epsilon }_s$$stator current oriented direct axis

$$\underset{\_}{i}$$space vector or space phasor of a current

$$i_a$$armature current in a DC machine

$$i_A$$active component of the current space phasor

$$i_d$$$$$$DC link current

$$i_m$$magnetizing current

$$i_{mr}$$rotor-flux based magnetizing current

$$i_{ms}$$stator-flux based magnetizing current

Rereal axis of the complex plane and real part of the complex expression

Imimaginary axis of the complex plane and imaginary part of the complex expression

$$i{}_r$$rotor current

$$i_R$$reactive component of the current space phasor

$$i_s$$stator current

jrotational unit vector of 90°

[j]rotational matrix operator of 90° for a two-phase system of magnitudes without zero-sequence component

Jtotal equivalent moment of inertia

$$k_i$$proportional coefficient between the magnitude of the stator current space phasor and the d.c. link current

Ktorque constant of a DC machine

[K]rotational matrix operator of 90° for a three-phase system of magnitudes

$$K_F$$space phasor definition (constant) coefficient

$$K_I$$referring constant of the currents and magneto motoric force

$$K_M$$torque constant of an AC machine

$$K_{Mr}$$torque constant of the induction machine containing the rotor leakage coefficient

$$K_{Ms}$$torque constant of the induction machine containing the stator leakage coefficient

$$\left[K_p\right]$$power coefficient matrix

$$K_R$$referring constant of the resistances and inductances

$$K_{SC}$$scale coefficient of the space phasor

$$K_u$$reffering constant of the voltages and electro motoric force

$$l_m$$inductance of the main magnetic circuit

$$l_r$$useful inductance of the rotor-phase winding

$$l_{rr}$$total per-phase inductance of the rotor

$$l_s$$useful inductance of the stator-phase winding

$$l_{ss}$$total per-phase inductance of the stator

$$l_{\sigma r}$$rotor’s own per-phase leakage inductance

$$l_{\sigma s}$$stator’s own per-phase leakage inductance

$$L_B$$inductance of the thyristor commutation coil

$$L_F$$DC link current filtering inductance

$$L_m$$three-phase resultant mutual (useful) inductance

$$L_r$$three-phase resultant (total) rotor inductance

$$L_{ro}$$zero-sequence inductance of the rotor

$$L_s$$three-phase resultant (total) stator inductance

$$L_{so}$$zero-sequence inductance of the stator

$$L_{\sigma r}$$resultant leakage inductance of the rotor

$$L_{\sigma s}$$resultant leakage inductance of the stator

mmutual inductance between a stator and a rotor phase

$$m_e$$electromagnetic torque

$$m_j$$dynamic torque

$$m_r$$resistent load torque

$$m_{\sigma r}$$mutual leakage inductance between two rotor phases

$$m_{\sigma s}$$mutual leakage inductance between two stator phases

$$N_r$$number of rotor phases

$$N_s$$number of stator phases

[q]matrix of the oscillator output quantities

pinstantaneous power or power losses

$$p_m$$instantaneous mechanical power

$$p_{roj}$$projection of a space vector or space phasor

qfixed or stator-oriented quadrature axis

[Q]rotational matrix of 90° for a two-phase system of magnitudes including the zero-sequence component

$$q{\in }_s$$stator-current oriented quadrature axis

$$q\lambda$$arbitrarily rotating or field-oriented quadrature axis

$$q{\lambda }_m$$air-gap field-oriented quadrature axis

$$q{\lambda }_r$$resultant rotor field-oriented quadrature axis

$$q{\lambda }_s$$resultant stator field-oriented quadrature axis

$$q\theta$$rotor-oriented quadrature axis

Rereal axis of the complex plane

Rereal part of a complex expression

$$R_D$$resistance of diode

$$R_r$$rotor per-phase resistance

$$R_S$$stator per-phase resistance

$$R_T$$resistance of thyristor or transistor

ttime

[t]three-phase projection matrix

[T]rotational matrix operator of three-phase axis system

$$\underset{\_}{u}$$space phasor of voltage

$$\Delta u$$voltage drop

$$u_d$$DC link output/inverter input voltage

$$u_r$$rotor voltage

$$u_{red}$$rectifier output/DC link input voltage

$$u_s$$stator voltage

Nturn number of winding

$$z_p$$number of the poli-pairs

$${\epsilon }_m$$angular position of the magnetizing-current space phasor

$${\epsilon }_r$$angular position of the rotor-current space phasor

$${\epsilon }_s$$angular position of the stator-current space phasor

$$\lambda$$angular position of an arbitrarily rotating direct axis or of a field-oriented axis

$${\lambda }_m$$angular position of the air-gap resultant flux space phasor

$${\lambda }_r$$angular position of the rotor resultant flux space phasor

$${\lambda }_s$$angular position of the stator resultant flux space phasor

$$\theta$$electrical angular position of the rotor $$a_r$$ axis

$${\theta }_r$$mechanical angular position of the rotor $$a_r$$ axis

$$\sigma$$resultant (total) leakage coefficient

$${\sigma }_r$$rotor leakage coefficient

$${\sigma }_s$$stator leakage coefficient

$$\underset{\_}{\psi }$$space vector or space phasor of flux linkage

$${\underset{\_}{\psi }}_a$$space vector of armature reaction flux in DC machine

$${\underset{\_}{\psi }}_c$$space vector of compensating flux in DC machine

$${\underset{\_}{\psi }}_e$$space vector of exciting flux

$${\psi }_m$$air-gap flux

$${\psi }_m$$resultant rotor flux

$${\psi }_s$$resultant stator flux

$${\psi }_{\sigma r}$$rotor leakage flux

$$\left[\tau \right]$$rotational matrix of three-phase axis system, when the zero-sequence component is missing

$${\tau }_r$$time constant of the rotor

$${\tau }_s$$time constant of the stator

$$\omega$$electrical angular speed of the rotor

$${\omega }_o$$synchronous electrical angular speed

$${\omega }_r$$mechanical angular speed of the rotor

$${\omega }_{{\epsilon }_m}$$rotational speed of the magnetizing-current space phasor

$${\omega }_{{\epsilon }_r}$$rotational speed of the rotor-current space phasor

$${\omega }_{{\epsilon }_s}$$rotational speed of the stator-current space phasor

$${\omega }_{\lambda }$$angular speed of an arbitrarity rotating axis system or of a field-oriented axis

$${\omega }_{{\lambda }_m}$$rotational speed of the air-gap flux space phasor

$${\omega }_{{\lambda }_r}$$rotational speed of the resultant rotor flux space phasor

$${\omega }_{\lambda }$$rotational speed of the resultant stator flux space phasor