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EESM: Correction / Introduction of transfer ratios between rotor and stator #234

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merged 6 commits into from
May 17, 2024
Merged

EESM: Correction / Introduction of transfer ratios between rotor and stator #234

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40c3367
introduce transfer ratio k between rotor and stator windings
max-schenke Apr 23, 2024
3977a58
remove magic number
max-schenke May 13, 2024
124b7b6
fixes to EESM ODE and jacobian
max-schenke May 15, 2024
e363003
merge with current nightly
max-schenke May 15, 2024
eb00223
update python version requirement to >=3.9
max-schenke May 16, 2024
e7406f6
Merge branch 'nightly' into EESM_transformations
XyDrKRulof May 16, 2024
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127 changes: 68 additions & 59 deletions ...m_electric_motor/physical_systems/electric_motors/externally_excited_synchronous_motor.py
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Original file line number Diff line number Diff line change
Expand Up @@ -7,22 +7,23 @@

class ExternallyExcitedSynchronousMotor(SynchronousMotor):
"""
===================== ========== ============= ===========================================
===================== ========== ============= =================================================
Motor Parameter Unit Default Value Description
===================== ========== ============= ===========================================
===================== ========== ============= =================================================
r_s mOhm 15.55 Stator resistance
r_e mOhm 7.2 Excitation resistance
l_d mH 1.66 Direct axis inductance
l_q mH 0.35 Quadrature axis inductance
l_m mH 1.589 Mutual inductance
l_e mH 1.74 Excitation inductance
p 1 3 Pole pair number
k 1 65.21 Transfer ratio of number of windings (N_s / N_e)
j_rotor kg/m^2 0.3883 Moment of inertia of the rotor
===================== ========== ============= ===========================================
===================== ========== ============= =================================================

=============== ====== =============================================
=============== ====== ===========================================================================
Motor Currents Unit Description
=============== ====== =============================================
=============== ====== ===========================================================================
i_sd A Direct axis current
i_sq A Quadrature axis current
i_e A Excitation current
Expand All @@ -31,10 +32,10 @@ class ExternallyExcitedSynchronousMotor(SynchronousMotor):
i_c A Current through branch c
i_alpha A Current in alpha axis
i_beta A Current in beta axis
=============== ====== =============================================
=============== ====== =============================================
=============== ====== ===========================================================================
=============== ====== ===========================================================================
Motor Voltages Unit Description
=============== ====== =============================================
=============== ====== ===========================================================================
u_sd V Direct axis voltage
u_sq V Quadrature axis voltage
u_e V Exciting voltage
Expand All @@ -43,13 +44,13 @@ class ExternallyExcitedSynchronousMotor(SynchronousMotor):
u_c V Voltage through branch c
u_alpha V Voltage in alpha axis
u_beta V Voltage in beta axis
=============== ====== =============================================
=============== ====== ===========================================================================

======== ===========================================================
======== =========================================================================================
Limits / Nominal Value Dictionary Entries:
-------- -----------------------------------------------------------
-------- -----------------------------------------------------------------------------------------
Entry Description
======== ===========================================================
======== =========================================================================================
i General current limit / nominal value
i_a Current in phase a
i_b Current in phase b
Expand All @@ -70,7 +71,7 @@ class ExternallyExcitedSynchronousMotor(SynchronousMotor):
u_sd Voltage in direct axis
u_sq Voltage in quadrature axis
u_e Voltage in excitation circuit
======== ===========================================================
======== =========================================================================================


Note:
Expand Down Expand Up @@ -98,14 +99,15 @@ class ExternallyExcitedSynchronousMotor(SynchronousMotor):

#### Parameters taken from DOI: 10.1109/ICELMACH.2014.6960287 (C. D. Nguyen; W. Hofmann)
_default_motor_parameter = {
"p": 3,
"l_d": 1.66e-3,
"l_q": 0.35e-3,
"l_m": 1.589e-3,
"l_e": 1.74e-3,
"j_rotor": 0.3883,
"r_s": 15.55e-3,
"r_e": 7.2e-3,
'p': 3,
'l_d': 1.66e-3,
'l_q': 0.35e-3,
'l_m': 1.589e-3,
'l_e': 1.74e-3,
'j_rotor': 0.3883,
'r_s': 15.55e-3,
'r_e': 7.2e-3,
'k': 65.21,
}
HAS_JACOBIAN = True
_default_limits = dict(omega=12e3 * np.pi / 30, torque=0.0, i=150, i_e=150, epsilon=math.pi, u=320)
Expand All @@ -123,21 +125,32 @@ class ExternallyExcitedSynchronousMotor(SynchronousMotor):
def _update_model(self):
# Docstring of superclass
mp = self._motor_parameter
sigma = 1 - mp["l_m"] ** 2 / (mp["l_d"] * mp["l_e"])

# Transform rotor quantities to stator side (uppercase index denotes transformation to stator side)
mp['r_E'] = mp['k'] ** 2 * 3/2 * mp['r_e']
mp['l_M'] = mp['k'] * 3/2 * mp['l_m']
mp['l_E'] = mp['k'] ** 2 * 3/2 * mp['l_e']

mp['i_k_rs'] = 2 / 3 / mp['k'] # ratio (i_E / i_e)
mp['sigma'] = 1 - mp['l_M'] ** 2 / (mp['l_d'] * mp['l_E'])

# fmt: off

self._model_constants = np.array([
# omega, i_d, i_q, i_e, u_d, u_q, u_e, omega * i_d, omega * i_q, omega * i_e
[ 0, -mp['r_s'] / sigma, 0, mp['l_m'] * mp['r_e'] / (sigma * mp['l_e']), 1 / sigma, 0, -mp['l_m'] / (sigma * mp['l_e']), 0, mp['l_q'] * mp['p'] / sigma, 0],
[ 0, 0, -mp['r_s'], 0, 0, 1, 0, -mp['l_d'] * mp['p'], 0, -mp['p'] * mp['l_m']],
[ 0, mp['l_m'] * mp['r_s'] / (sigma * mp['l_d']), 0, -mp['r_e'] / sigma, -mp['l_m'] / (sigma * mp['l_d']), 0, 1 / sigma, 0, -mp['p'] * mp['l_m'] * mp['l_q'] / (sigma * mp['l_d']), 0],
[ mp['p'], 0, 0, 0, 0, 0, 0, 0, 0, 0],
# omega, i_d, i_q, i_e, u_d, u_q, u_e, omega * i_d, omega * i_q, omega * i_e
[ 0, -mp["r_s"] / mp["sigma"], 0, mp["l_M"] * mp["r_E"] / (mp["sigma"] * mp["l_E"]) * mp["i_k_rs"], 1 / mp["sigma"], 0, -mp["l_M"] * mp["k"] / (mp["sigma"] * mp["l_E"]), 0, mp["l_q"] * mp["p"] / mp["sigma"], 0],
[ 0, 0, -mp["r_s"], 0, 0, 1, 0, -mp["l_d"] * mp["p"], 0, -mp["p"] * mp["l_M"] * mp["i_k_rs"]],
[ 0, mp["l_M"] * mp["r_s"] / (mp["sigma"] * mp["l_d"]), 0, -mp["r_E"] / mp["sigma"] * mp["i_k_rs"], -mp["l_M"] / (mp["sigma"] * mp["l_d"]), 0, mp["k"] / mp["sigma"], 0, -mp["p"] * mp["l_M"] * mp["l_q"] / (mp["sigma"] * mp["l_d"]), 0],
[ mp["p"], 0, 0, 0, 0, 0, 0, 0, 0, 0],
])
# fmt: on

self._model_constants[self.I_SD_IDX] = self._model_constants[self.I_SD_IDX] / mp["l_d"]
self._model_constants[self.I_SQ_IDX] = self._model_constants[self.I_SQ_IDX] / mp["l_q"]
self._model_constants[self.I_E_IDX] = self._model_constants[self.I_E_IDX] / mp["l_e"]
self._model_constants[self.I_E_IDX] = self._model_constants[self.I_E_IDX] / mp["l_E"] / mp["i_k_rs"]

# fmt: on

def electrical_ode(self, state, u_dq, omega, *_):
def electrical_ode(self, state, u_dqe, omega, *_):
"""
The differential equation of the Synchronous Motor.

Expand All @@ -149,6 +162,7 @@ def electrical_ode(self, state, u_dq, omega, *_):
Returns:
The derivatives of the state vector d/dt([i_sd, i_sq, epsilon])
"""

return np.matmul(
self._model_constants,
np.array(
Expand All @@ -157,14 +171,14 @@ def electrical_ode(self, state, u_dq, omega, *_):
state[self.I_SD_IDX],
state[self.I_SQ_IDX],
state[self.I_E_IDX],
u_dq[0],
u_dq[1],
u_dq[2],
u_dqe[0],
u_dqe[1],
u_dqe[2],
omega * state[self.I_SD_IDX],
omega * state[self.I_SQ_IDX],
omega * state[self.I_E_IDX],
omega * state[self.I_E_IDX]
]
),
)
)

def _torque_limit(self):
Expand All @@ -174,46 +188,41 @@ def _torque_limit(self):
return self.torque([0, self._limits["i_sq"], self._limits["i_e"], 0])
else:
i_n = self.nominal_values["i"]
_p = mp["l_m"] * i_n / (2 * (mp["l_d"] - mp["l_q"]))
_q = -(i_n**2) / 2
_p = mp["l_M"] * i_n / (2 * (mp["l_d"] - mp["l_q"]))
_q = - i_n ** 2 / 2
if mp["l_d"] < mp["l_q"]:
i_d_opt = -_p / 2 - np.sqrt((_p / 2) ** 2 - _q)
i_d_opt = - _p / 2 - np.sqrt((_p / 2) ** 2 - _q)
else:
i_d_opt = -_p / 2 + np.sqrt((_p / 2) ** 2 - _q)
i_q_opt = np.sqrt(i_n**2 - i_d_opt**2)
i_d_opt = - _p / 2 + np.sqrt((_p / 2) ** 2 - _q)
i_q_opt = np.sqrt(i_n ** 2 - i_d_opt ** 2)
return self.torque([i_d_opt, i_q_opt, self._limits["i_e"], 0])

def torque(self, currents):
# Docstring of superclass
mp = self._motor_parameter
return (
1.5
* mp["p"]
* (mp["l_m"] * currents[self.I_E_IDX] + (mp["l_d"] - mp["l_q"]) * currents[self.I_SD_IDX])
* currents[self.I_SQ_IDX]
)
return 1.5 * mp["p"] * (mp["l_M"] * currents[self.I_E_IDX] * mp["i_k_rs"] + (mp["l_d"] - mp["l_q"]) * currents[self.I_SD_IDX]) * currents[self.I_SQ_IDX]

def electrical_jacobian(self, state, u_in, omega, *args):

mp = self._motor_parameter
sigma = 1 - mp["l_m"] ** 2 / (mp["l_d"] * mp["l_e"])
# fmt: off

return (
np.array([ # dx'/dx
[ -mp['r_s'] / mp['l_d'], mp['l_q'] / (sigma * mp['l_d']) * omega * mp['p'], mp['l_m'] * mp['r_e'] / (sigma * mp['l_d'] * mp['l_e']), 0],
[ -mp['l_d'] / mp['l_q'] * omega * mp['p'], -mp['r_s'] / mp['l_q'], -omega * mp['p'] * mp['l_e'] / mp['l_q'], 0],
[mp['l_m'] * mp['r_s'] / (sigma * mp['l_d'] * mp['l_e']), -omega * mp['p'] * mp['l_m'] * mp['l_q'] / (sigma * mp['l_d'] * mp['l_e']), -mp['r_e'] / mp['l_e'], 0],
[ 0, 0, 0, 0],
[ -mp["r_s"] / (mp["l_d"] * mp["sigma"]), mp["l_q"] / (mp["sigma"] * mp["l_d"]) * omega * mp["p"], mp["l_M"] * mp["r_E"] / (mp["sigma"] * mp["l_d"] * mp["l_E"]) * mp["i_k_rs"], 0],
[ -mp["l_d"] / mp["l_q"] * omega * mp["p"], -mp["r_s"] / mp["l_q"], -omega * mp["p"] * mp["l_M"] / mp["l_q"] * mp["i_k_rs"], 0],
[mp["l_M"] * mp["r_s"] / (mp["sigma"] * mp["l_d"] * mp["l_E"] * mp["i_k_rs"]), -omega * mp["p"] * mp["l_M"] * mp["l_q"] / (mp["sigma"] * mp["l_d"] * mp["l_E"] * mp["i_k_rs"]), -mp["r_E"] / (mp["sigma"] * mp["l_E"]), 0],
[ 0, 0, 0, 0],
]),
np.array([ # dx'/dw
mp['p'] * mp['l_q'] / mp['l_d'] * state[self.I_SQ_IDX],
-mp['p'] * mp['l_d'] / mp['l_q'] * state[self.I_SD_IDX] - mp['p'] * mp['l_m'] / mp['l_q'] * state[self.I_E_IDX],
-mp['p'],
mp['p'],
mp["p"] * mp["l_q"] / (mp["l_d"] * mp["sigma"]) * state[self.I_SQ_IDX],
-mp["p"] * mp["l_d"] / mp["l_q"] * state[self.I_SD_IDX] - mp["p"] * mp["l_M"] / mp["l_q"] * state[self.I_E_IDX] * mp["i_k_rs"],
-mp["p"] * mp["l_M"] * mp["l_q"] / (mp["sigma"] * mp["l_d"] * mp["l_E"] * mp["i_k_rs"]) * state[self.I_SQ_IDX],
mp["p"],
]),
np.array([ # dT/dx
1.5 * mp['p'] * (mp['l_d'] - mp['l_q']) * state[self.I_SQ_IDX],
1.5 * mp['p'] * (mp['l_e'] * state[self.I_E_IDX] + (mp['l_d'] - mp['l_q']) * state[self.I_SD_IDX]),
1.5 * mp['p'] * mp['l_e'] * state[self.I_SQ_IDX],
1.5 * mp["p"] * (mp["l_d"] - mp["l_q"]) * state[self.I_SQ_IDX],
1.5 * mp["p"] * (mp["l_M"] * state[self.I_E_IDX] * mp["i_k_rs"] + (mp["l_d"] - mp["l_q"]) * state[self.I_SD_IDX]),
1.5 * mp["p"] * mp["l_M"] * mp["i_k_rs"] * state[self.I_SQ_IDX],
0,
])
)
Expand Down
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