Squirrel Cage Induction Motor
Schematic
Electrical ODE
with
Torque Equation
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)[source]
Motor Parameter
Unit
Default Value
Description
r_s
Ohm
2.9338
Stator resistance
r_r
Ohm
1.355
Rotor resistance
l_m
H
143.75e-3
Main inductance
l_sigs
H
5.87e-3
Stator-side stray inductance
l_sigr
H
5.87e-3
Rotor-side stray inductance
p
1
2
Pole pair number
j_rotor
kg/m^2
0.0011
Moment of inertia of the rotor
Motor Currents
Unit
Description
i_sd
A
Direct axis current
i_sq
A
Quadrature axis current
i_sa
A
Stator current through branch a
i_sb
A
Stator current through branch b
i_sc
A
Stator current through branch c
i_salpha
A
Stator current in alpha direction
i_sbeta
A
Stator current in beta direction
Rotor flux
Unit
Description
psi_rd
Vs
Direct axis of the rotor oriented flux
psi_rq
Vs
Quadrature axis of the rotor oriented flux
psi_ra
Vs
Rotor oriented flux in branch a
psi_rb
Vs
Rotor oriented flux in branch b
psi_rc
Vs
Rotor oriented flux in branch c
psi_ralpha
Vs
Rotor oriented flux in alpha direction
psi_rbeta
Vs
Rotor oriented flux in beta direction
Motor Voltages
Unit
Description
u_sd
V
Direct axis voltage
u_sq
V
Quadrature axis voltage
u_sa
V
Stator voltage through branch a
u_sb
V
Stator voltage through branch b
u_sc
V
Stator voltage through branch c
u_salpha
V
Stator voltage in alpha axis
u_sbeta
V
Stator voltage in beta axis
Limits /
Nominal Value Dictionary Entries:
Entry
Description
i
General current limit / nominal value
i_sa
Current in phase a
i_sb
Current in phase b
i_sc
Current in phase c
i_salpha
Current in alpha axis
i_sbeta
Current in beta axis
i_sd
Current in direct axis
i_sq
Current in quadrature axis
omega
Mechanical angular Velocity
torque
Motor generated torque
u_sa
Voltage in phase a
u_sb
Voltage in phase b
u_sc
Voltage in phase c
u_salpha
Voltage in alpha axis
u_sbeta
Voltage in beta axis
u_sd
Voltage in direct axis
u_sq
Voltage in quadrature axis
Note
The voltage limits should be the peak-to-peak value of the phase voltage (\(\hat{u}_S\)). Typically the rms value for the line voltage (\(U_L\)) is given as \(\hat{u}_S=\sqrt{2/3}~U_L\)
The current limits should be the peak-to-peak value of the phase current (\(\hat{i}_S\)). Typically the rms value for the phase current (\(I_S\)) is given as \(\hat{i}_S = \sqrt{2}~I_S\)
If not specified, nominal values are equal to their corresponding limit values. Furthermore, if specific limits/nominal values (e.g. i_a) are not specified they are inferred from the general limits/nominal values (e.g. i)
- Parameters:
motor_parameter – Motor parameter dictionary. Contents specified for each motor.
nominal_values – Nominal values for the motor quantities.
limit_values – Limits for the motor quantities.
motor_initializer –
Initial motor states (currents) (‘constant’, ‘uniform’, ‘gaussian’ sampled from
given interval or out of nominal motor values)
initial_limits – limits for of the initial state-value
- CURRENTS = ['i_salpha', 'i_sbeta']
List of the motor currents names
- Type:
CURRENTS(list(str))
- CURRENTS_IDX = [0, 1]
Indices for accessing all motor currents.
- Type:
CURRENTS_IDX(list(int))
- HAS_JACOBIAN = True
Parameter indicating if the class is implementing the optional jacobian function
- VOLTAGES = []
List of the motor input voltages names
- Type:
VOLTAGES(list(str))
- electrical_jacobian(state, u_in, omega, *args)
Calculation of the jacobian of each motor ODE for the given inputs / The motors ODE-System.
Overriding this method is optional for each subclass. If it is overridden, the parameter HAS_JACOBIAN must also be set to True. Otherwise, the jacobian will not be called.
- Parameters:
state (ndarray(float)) – The motors state.
u_in (list(float)) – The motors input voltages.
omega (float) – Angular velocity of the motor
- Returns:
[0]: Derivatives of all electrical motor states over all electrical motor states shape:(states x states) [1]: Derivatives of all electrical motor states over omega shape:(states,) [2]: Derivative of Torque over all motor states shape:(states,)
- Return type:
Tuple(ndarray, ndarray, ndarray)
- electrical_ode(state, u_salphabeta, omega, *args)[source]
The differential equation of the SCIM. Sets u_ralpha = u_rbeta = 0 before calling the respective super function.
- i_in(state)
- Parameters:
state (ndarray(float)) – ODE state of the motor
- Returns:
List of all currents flowing into the motor.
- Return type:
list(float)
- property initial_limits
Returns: dict: nominal motor limits for choosing initial values
- initialize(state_space, state_positions, **__)
Initializes given state values. Values can be given as a constant or sampled random out of a statistical distribution. Initial value is in range of the nominal values or a given interval. Values are written in initial_states attribute
- Parameters:
state_space (gymnasium.Box) – normalized state space boundaries (given by physical system)
state_positions (dict) – indices of system states (given by physical system)
- property initializer
Returns: dict: Motor initial state and additional initializer parameter
- property limits
Readonly motors limit state array. Entries are set to the maximum physical possible values in case of unspecified limits.
- Returns:
Limits of the motor.
- Return type:
dict(float)
- property motor_parameter
Returns: dict(float): The motors parameter dictionary
- next_generator()
Sets a new reference generator for a new episode.
- property nominal_values
Readonly motors nominal values.
- Returns:
Current nominal values of the motor.
- Return type:
dict(float)
- static q(quantities, epsilon)
Transformation of the dq-representation into alpha-beta using the electrical angle
- Parameters:
quantities – Array of two quantities in dq-representation. Example [i_d, i_q]
epsilon – Current electrical angle of the motor
- Returns:
Array of the two quantities converted to alpha-beta-representation. Example [u_alpha, u_beta]
- static q_inv(quantities, epsilon)
Transformation of the alpha-beta-representation into dq using the electrical angle
- Parameters:
quantities – Array of two quantities in alpha-beta-representation. Example [u_alpha, u_beta]
epsilon – Current electrical angle of the motor
- Returns:
Array of the two quantities converted to dq-representation. Example [u_d, u_q]
Note
The transformation from alpha-beta to dq is just its inverse conversion with negated epsilon. So this method calls q(quantities, -epsilon).
- q_inv_me(quantities, epsilon)
Transformation of the alpha-beta-representation into dq using the mechanical angle
- Parameters:
quantities – Array of two quantities in alpha-beta-representation. Example [u_alpha, u_beta]
epsilon – Current mechanical angle of the motor
- Returns:
Array of the two quantities converted to dq-representation. Example [u_d, u_q]
Note
The transformation from alpha-beta to dq is just its inverse conversion with negated epsilon. So this method calls q(quantities, -epsilon).
- q_me(quantities, epsilon)
Transformation of the dq-representation into alpha-beta using the mechanical angle
- Parameters:
quantities – Array of two quantities in dq-representation. Example [i_d, i_q]
epsilon – Current mechanical angle of the motor
- Returns:
Array of the two quantities converted to alpha-beta-representation. Example [u_alpha, u_beta]
- property random_generator
The random generator that has to be used to draw the random numbers.
- reset(state_space, state_positions, omega=None)
Reset the motors state to a new initial state. (Default 0)
- Parameters:
state_space (gymnasium.Box) – normalized state space boundaries
state_positions (dict) – indexes of system states
- Returns:
The initial motor states.
- Return type:
numpy.ndarray(float)
- seed(seed=None)
The function to set the seed.
This function is called by within the global seed call of the environment. The environment passes the sub-seed to this component that is generated based on the source-seed of the env.
- Parameters:
seed ((np.random.SeedSequence, None)) – Seed sequence to derive new seeds and reference generators at every episode start. Default: None (a new SeedSequence is generated).
- Returns:
A list containing all seeds within this RandomComponent. In general, this list has length 1. If the RandomComponent holds further RandomComponent instances, the list has to contain also these entropies. The entropy of this instance has to be placed always at first place.
- Return type:
List(int)
- property seed_sequence
The base seed sequence that generates the sub generators and sub seeds at every environment reset.
- static t_23(quantities)
Transformation from abc representation to alpha-beta representation
- Parameters:
quantities – The properties in the abc representation like ‘’[u_a, u_b, u_c]’’
- Returns:
The converted quantities in the alpha-beta representation like ‘’[u_alpha, u_beta]’’
- static t_32(quantities)
Transformation from alpha-beta representation to abc representation
- Parameters:
quantities – The properties in the alpha-beta representation like
[u_alpha, u_beta]
- Returns:
The converted quantities in the abc representation like
[u_a, u_b, u_c]