Externally Excited Synchronous Motor

Schematic

\[\begin{split}L_{\sigma \mathrm{d}} &= L_\mathrm{d} - L_\mathrm{m} \\ L_{\sigma \mathrm{e}} &= L_\mathrm{e} - L_\mathrm{m} \\ \psi_\mathrm{d} &= L_\mathrm{d} i_\mathrm{sd} + L_\mathrm{m} i_\mathrm{e} \\ \psi_\mathrm{q} &= L_\mathrm{q} i_\mathrm{sq}\end{split}\]

Electrical ODE

\[\sigma = \frac{L_\mathrm{d} L_\mathrm{e} - L_\mathrm{m}^2}{L_\mathrm{d} L_\mathrm{e}}\]

\[\begin{split}\frac{\mathrm{d} i_\mathrm{sd}}{\mathrm{d} t} &= - \frac{ R_\mathrm{s} }{ \sigma L_{\mathrm{d} } } i_\mathrm{sd} + \frac{L_\mathrm{q}}{\sigma L_\mathrm{d}} p \omega_\mathrm{me} i_\mathrm{sq} + \frac{L_\mathrm{m} R_\mathrm{e}}{\sigma L_\mathrm{d} L_\mathrm{e}} i_\mathrm{e} + \frac{1}{\sigma L_\mathrm{d}} u_\mathrm{d} - \frac{L_\mathrm{m}}{\sigma L_\mathrm{d} L_\mathrm{e}} u_\mathrm{e} \\ \frac{\mathrm{d} i_\mathrm{sq}}{\mathrm{d} t} &= -\frac{L_\mathrm{d}}{L_\mathrm{q}} p \omega_\mathrm{me} i_\mathrm{sd} - \frac{R_\mathrm{s}}{L_\mathrm{q}} i_\mathrm{sq} - \frac{L_\mathrm{m}}{L_\mathrm{q}} p \omega_\mathrm{me} i_\mathrm{e} + \frac{1}{L_\mathrm{q}} u_\mathrm{q} \\ \frac{\mathrm{d} i_\mathrm{e}}{\mathrm{d} t} &= \frac{L_\mathrm{m} R_\mathrm{s}}{\sigma L_\mathrm{d} L_\mathrm{e}} i_\mathrm{sd} - \frac{L_\mathrm{m} L_\mathrm{q}}{ \sigma L_\mathrm{d} L_\mathrm{e}} p \omega_\mathrm{me} i_\mathrm{sq} - \frac{R_\mathrm{s}}{ \sigma L_\mathrm{e}} i_\mathrm{e} - \frac{L_\mathrm{m}}{\sigma L_\mathrm{d}L_\mathrm{e}} u_\mathrm{d} + \frac{1}{\sigma L_\mathrm{e}} u_\mathrm{e} \\ \frac{\mathrm{d} \varepsilon_\mathrm{el}}{\mathrm{d} t} &= p \omega_\mathrm{me} \\\end{split}\]

Torque Equation

\[T = 1.5 p (L_\mathrm{m} i_\mathrm{e} + (L_\mathrm{d} - L_\mathrm{q}) i_\mathrm{sd}) i_\mathrm{sq}\]

Code Documentation

class gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor(motor_parameter=None, nominal_values=None, limit_values=None, motor_initializer=None)

Bases: SynchronousMotor

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.

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API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.

Note

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electrical_jacobian(state, u_in, omega, *args)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.electrical_jacobian.

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electrical_ode(state, u_dqe, omega, *_)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.electrical_ode.

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i_in(state)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.i_in.

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initialize(state_space, state_positions, **__)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.initialize.

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next_generator()

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.next_generator.

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static q(quantities, epsilon)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.q.

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static q_inv(quantities, epsilon)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.q_inv.

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q_inv_me(quantities, epsilon)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.q_inv_me.

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q_me(quantities, epsilon)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.q_me.

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reset(state_space, state_positions, **__)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.reset.

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seed(seed=None)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.seed.

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static t_23(quantities)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.t_23.

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static t_32(quantities)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.t_32.

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torque(currents)

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.torque.

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CURRENTS = ['i_sd', 'i_sq', 'i_e']

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.CURRENTS.

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CURRENTS_IDX = [0, 1, 2]

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.CURRENTS_IDX.

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EPSILON_IDX = 3

HAS_JACOBIAN = True

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.HAS_JACOBIAN.

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IO_CURRENTS = ['i_a', 'i_b', 'i_c', 'i_sd', 'i_sq', 'i_e']

IO_VOLTAGES = ['u_a', 'u_b', 'u_c', 'u_sd', 'u_sq', 'u_e']

I_E_IDX = 2

I_SD_IDX = 0

I_SQ_IDX = 1

VOLTAGES = ['u_sd', 'u_sq', 'u_e']

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.VOLTAGES.

Note

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property initial_limits

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.initial_limits.

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property initializer

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.initializer.

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property limits

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.limits.

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property motor_parameter

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.motor_parameter.

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property nominal_values

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.nominal_values.

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property random_generator

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.random_generator.

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property seed_sequence

API for gym_electric_motor.physical_systems.electric_motors.ExternallyExcitedSynchronousMotor.seed_sequence.

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