Squirrel Cage Induction Motor

Schematic

Electrical ODE

\[\begin{split}\frac{\mathrm{d} i_\mathrm{s \alpha}}{\mathrm{d} t}&= -\frac{1}{\tau_\sigma} i_\mathrm{s \alpha} + \frac{R_\mathrm{r} L_\mathrm{m}}{\sigma L_\mathrm{r}^2 L_\mathrm{s}} \psi_\mathrm{r \alpha} + p \omega_{\text{me}} \frac{L_\mathrm{m}}{\sigma L_\mathrm{r} L_\mathrm{s}} \psi_\mathrm{r \beta} + \frac{1}{\sigma L_\mathrm{s}} u_\mathrm{s \alpha}\\ \frac{\mathrm{d} i_\mathrm{s \beta}}{\mathrm{d} t}&= -\frac{1}{\tau_\sigma} i_\mathrm{s \beta} - p \omega_{\text{me}} \frac{L_\mathrm{m}}{\sigma L_\mathrm{r} L_\mathrm{s}} \psi_\mathrm{r \alpha} + \frac{R_\mathrm{r} L_\mathrm{m}}{\sigma L_\mathrm{r}^2 L_\mathrm{s}} \psi_\mathrm{r \beta} + \frac{1}{\sigma L_\mathrm{s}} u_\mathrm{s \beta}\\ \frac{\mathrm{d} \psi_\mathrm{r \alpha}}{\mathrm{d} t}&= \frac{L_\mathrm{m}}{\tau_\mathrm{r}} i_\mathrm{s \alpha} - \frac{1}{\tau_\text{r}} \psi_\mathrm{r \alpha} - p \omega_{\text{me}} \psi_\mathrm{r \beta} \\ \frac{\mathrm{d} \psi_\mathrm{r \beta}}{\mathrm{d} t}&= \frac{L_\mathrm{m}}{\tau_\mathrm{r}} i_\mathrm{s \beta} + p \omega_{\mathrm{me}} \psi_\mathrm{r \alpha} - \frac{1}{\tau_\mathrm{r}} \psi_\mathrm{r \beta} \\ \frac{\mathrm{d} \varepsilon_\mathrm{el}}{\mathrm{d} t}&= p \omega_\mathrm{me}\end{split}\]

with

\[\begin{split}L_\mathrm{s} &= L_\mathrm{m} + L_\mathrm{\sigma s}, & L_\mathrm{r} &= L_\mathrm{m} + L_\mathrm{\sigma r}\\ \sigma &= \frac{L_\mathrm{r} L_\mathrm{s} - L_\mathrm{m}^2}{L_\mathrm{r} L_\mathrm{s}}, & \tau_\mathrm{r} &=\frac{L_\mathrm{r}}{R_\mathrm{r}}, & \tau_\sigma &= \frac{\sigma L_\mathrm{s}}{R_\mathrm{s} + R_\mathrm{r} \frac{L_\mathrm{m}^2}{L_\mathrm{r}^2}}\end{split}\]

Torque Equation

\[T=\frac{3}{2} p \frac{L_\mathrm{m}}{L_\mathrm{r}} (\psi_\mathrm{r \alpha} i_\mathrm{s \beta} - \psi_\mathrm{r \beta} i_\mathrm{s \alpha})\]

Code Documentation

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

Bases: InductionMotor

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.

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API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.

Note

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electrical_jacobian(state, u_in, omega, *args)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.electrical_jacobian.

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electrical_ode(state, u_salphabeta, omega, *args)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.electrical_ode.

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i_in(state)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.i_in.

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initialize(state_space, state_positions, **__)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.initialize.

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next_generator()

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.next_generator.

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static q(quantities, epsilon)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.q.

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static q_inv(quantities, epsilon)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.q_inv.

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q_inv_me(quantities, epsilon)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.q_inv_me.

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q_me(quantities, epsilon)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.q_me.

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reset(state_space, state_positions, omega=None)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.reset.

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seed(seed=None)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.seed.

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static t_23(quantities)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.t_23.

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static t_32(quantities)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.t_32.

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torque(states)

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.torque.

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CURRENTS = ['i_salpha', 'i_sbeta']

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.CURRENTS.

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CURRENTS_IDX = [0, 1]

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.CURRENTS_IDX.

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EPSILON_IDX = 4

FLUXES = ['psi_ralpha', 'psi_rbeta']

FLUX_IDX = [2, 3]

HAS_JACOBIAN = True

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.HAS_JACOBIAN.

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IO_CURRENTS = ['i_sa', 'i_sb', 'i_sc', 'i_salpha', 'i_sbeta', 'i_sd', 'i_sq']

IO_VOLTAGES = ['u_sa', 'u_sb', 'u_sc', 'u_salpha', 'u_sbeta', 'u_sd', 'u_sq']

I_SALPHA_IDX = 0

I_SBETA_IDX = 1

PSI_RALPHA_IDX = 2

PSI_RBETA_IDX = 3

STATOR_VOLTAGES = ['u_salpha', 'u_sbeta']

VOLTAGES = []

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.VOLTAGES.

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property initial_limits

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.initial_limits.

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property initializer

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.initializer.

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property limits

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.limits.

Note

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property motor_parameter

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.motor_parameter.

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property nominal_values

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.nominal_values.

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property random_generator

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.random_generator.

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property seed_sequence

API for gym_electric_motor.physical_systems.electric_motors.SquirrelCageInductionMotor.seed_sequence.

Note

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