.. _Motor: ================================================================================ Motor ================================================================================ Induction Motor group Common Parameters: u, name Available models: Motor3_, Motor5_ .. _Motor3: -------------------------------------------------------------------------------- Motor3 -------------------------------------------------------------------------------- Third-order induction motor model. See "Power System Modelling and Scripting" by F. Milano. To simulate motor startup, set the motor status ``u`` to ``0`` and use a ``Toggle`` to control the model. Parameters ---------- +-------+----------------+---------------------------+---------+-----------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=======+================+===========================+=========+===========+============+ | idx | | unique device idx | | | | +-------+----------------+---------------------------+---------+-----------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +-------+----------------+---------------------------+---------+-----------+------------+ | name | | device name | | | | +-------+----------------+---------------------------+---------+-----------+------------+ | bus | | interface bus id | | | mandatory | +-------+----------------+---------------------------+---------+-----------+------------+ | Sn | :math:`S_n` | Power rating | 100 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | Vn | :math:`V_n` | AC voltage rating | 110 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | fn | :math:`f` | rated frequency | 60 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | rs | :math:`r_s` | rotor resistance | 0.010 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | xs | :math:`x_s` | rotor reactance | 0.150 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | rr1 | :math:`r_{R1}` | 1st cage rotor resistance | 0.050 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | xr1 | :math:`x_{R1}` | 1st cage rotor reactance | 0.150 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | rr2 | :math:`r_{R2}` | 2st cage rotor resistance | 0.001 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | xr2 | :math:`x_{R2}` | 2st cage rotor reactance | 0.040 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | xm | :math:`x_m` | magnetization reactance | 5 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | Hm | :math:`H_m` | Inertia constant | 3 | *kWs/KVA* | power | +-------+----------------+---------------------------+---------+-----------+------------+ | c1 | :math:`c_1` | 1st coeff. of Tm(w) | 0.100 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | c2 | :math:`c_2` | 2nd coeff. of Tm(w) | 0.020 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | c3 | :math:`c_3` | 3rd coeff. of Tm(w) | 0.020 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | zb | :math:`z_b` | Allow working as brake | 1 | | | +-------+----------------+---------------------------+---------+-----------+------------+ Variables --------- +-------+--------------+----------+------------------------------------+------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=======+==============+==========+====================================+======+============+ | slip | :math:`slip` | State | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | e1d | :math:`e1d` | State | real part of 1st cage voltage | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | e1q | :math:`e1q` | State | imaginary part of 1st cage voltage | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | vd | :math:`vd` | Algeb | d-axis voltage | | | +-------+--------------+----------+------------------------------------+------+------------+ | vq | :math:`vq` | Algeb | q-axis voltage | | | +-------+--------------+----------+------------------------------------+------+------------+ | p | :math:`p` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | q | :math:`q` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | Id | :math:`Id` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | Iq | :math:`Iq` | Algeb | | | | +-------+--------------+----------+------------------------------------+------+------------+ | te | :math:`te` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | tm | :math:`tm` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +-------+--------------+----------+------------------------------------+------+------------+ | v | :math:`v` | ExtAlgeb | Bus voltage magnitude | | | +-------+--------------+----------+------------------------------------+------+------------+ Initialization Equations ------------------------ +-------+--------------+----------+------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=======+==============+==========+======================================================+ | slip | :math:`slip` | State | :math:`1.0 u` | +-------+--------------+----------+------------------------------------------------------+ | e1d | :math:`e1d` | State | :math:`0.05 u` | +-------+--------------+----------+------------------------------------------------------+ | e1q | :math:`e1q` | State | :math:`0.9 u` | +-------+--------------+----------+------------------------------------------------------+ | vd | :math:`vd` | Algeb | | +-------+--------------+----------+------------------------------------------------------+ | vq | :math:`vq` | Algeb | | +-------+--------------+----------+------------------------------------------------------+ | p | :math:`p` | Algeb | :math:`u \left(Id vd + Iq vq\right)` | +-------+--------------+----------+------------------------------------------------------+ | q | :math:`q` | Algeb | :math:`u \left(Id vq - Iq vd\right)` | +-------+--------------+----------+------------------------------------------------------+ | Id | :math:`Id` | Algeb | :math:`1` | +-------+--------------+----------+------------------------------------------------------+ | Iq | :math:`Iq` | Algeb | | +-------+--------------+----------+------------------------------------------------------+ | te | :math:`te` | Algeb | :math:`u \left(Id e1d + Iq e1q\right)` | +-------+--------------+----------+------------------------------------------------------+ | tm | :math:`tm` | Algeb | :math:`u \left(aa + bb slip + c_{2} slip^{2}\right)` | +-------+--------------+----------+------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +-------+--------------+----------+------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | | +-------+--------------+----------+------------------------------------------------------+ Differential Equations ----------------------------- +-------+--------------+-------+---------------------------------------------------------------------------------------------+-----------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +=======+==============+=======+=============================================================================================+===========+ | slip | :math:`slip` | State | :math:`u \left(- te + tm\right)` | :math:`M` | +-------+--------------+-------+---------------------------------------------------------------------------------------------+-----------+ | e1d | :math:`e1d` | State | :math:`u \left(e1q slip wb - \frac{Iq \left(x_{0} - x_{1}\right) + e1d}{T_{10}}\right)` | | +-------+--------------+-------+---------------------------------------------------------------------------------------------+-----------+ | e1q | :math:`e1q` | State | :math:`u \left(- e1d slip wb - \frac{- Id \left(x_{0} - x_{1}\right) + e1q}{T_{10}}\right)` | | +-------+--------------+-------+---------------------------------------------------------------------------------------------+-----------+ Algebraic Equations ----------------------------- +------+------------+----------+-------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+============+==========+=============================================================+ | vd | :math:`vd` | Algeb | :math:`- u v \sin{\left(a \right)} - vd` | +------+------------+----------+-------------------------------------------------------------+ | vq | :math:`vq` | Algeb | :math:`u v \cos{\left(a \right)} - vq` | +------+------------+----------+-------------------------------------------------------------+ | p | :math:`p` | Algeb | :math:`- p + u \left(Id vd + Iq vq\right)` | +------+------------+----------+-------------------------------------------------------------+ | q | :math:`q` | Algeb | :math:`- q + u \left(Id vq - Iq vd\right)` | +------+------------+----------+-------------------------------------------------------------+ | Id | :math:`Id` | Algeb | :math:`u \left(- Id rs + Iq x_{1} - e1d + vd\right)` | +------+------------+----------+-------------------------------------------------------------+ | Iq | :math:`Iq` | Algeb | :math:`u \left(- Id x_{1} - Iq rs - e1q + vq\right)` | +------+------------+----------+-------------------------------------------------------------+ | te | :math:`te` | Algeb | :math:`- te + u \left(Id e1d + Iq e1q\right)` | +------+------------+----------+-------------------------------------------------------------+ | tm | :math:`tm` | Algeb | :math:`- tm + u \left(aa + bb slip + c_{2} slip^{2}\right)` | +------+------------+----------+-------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`p` | +------+------------+----------+-------------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | :math:`q` | +------+------------+----------+-------------------------------------------------------------+ Services ---------- +------+------------------+--------------------------------------------+--------------+ | Name | Symbol | Equation | Type | +======+==================+============================================+==============+ | wb | :math:`\omega_b` | :math:`2 \pi fn` | ConstService | +------+------------------+--------------------------------------------+--------------+ | x0 | :math:`x_0` | :math:`xm + xs` | ConstService | +------+------------------+--------------------------------------------+--------------+ | x1 | :math:`x'` | :math:`\frac{xm xr_{1}}{xm + xr_{1}} + xs` | ConstService | +------+------------------+--------------------------------------------+--------------+ | T10 | :math:`T'_0` | :math:`\frac{xm + xr_{1}}{rr_{1} wb}` | ConstService | +------+------------------+--------------------------------------------+--------------+ | M | :math:`M` | :math:`2 Hm` | ConstService | +------+------------------+--------------------------------------------+--------------+ | aa | :math:`\alpha` | :math:`c_{1} + c_{2} + c_{3}` | ConstService | +------+------------------+--------------------------------------------+--------------+ | bb | :math:`\beta` | :math:`- c_{2} - 2 c_{3}` | ConstService | +------+------------------+--------------------------------------------+--------------+ Config Fields in [Motor3] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _Motor5: -------------------------------------------------------------------------------- Motor5 -------------------------------------------------------------------------------- Fifth-order induction motor model. See "Power System Modelling and Scripting" by F. Milano. To simulate motor startup, set the motor status ``u`` to ``0`` and use a ``Toggle`` to control the model. Parameters ---------- +-------+----------------+---------------------------+---------+-----------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=======+================+===========================+=========+===========+============+ | idx | | unique device idx | | | | +-------+----------------+---------------------------+---------+-----------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +-------+----------------+---------------------------+---------+-----------+------------+ | name | | device name | | | | +-------+----------------+---------------------------+---------+-----------+------------+ | bus | | interface bus id | | | mandatory | +-------+----------------+---------------------------+---------+-----------+------------+ | Sn | :math:`S_n` | Power rating | 100 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | Vn | :math:`V_n` | AC voltage rating | 110 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | fn | :math:`f` | rated frequency | 60 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | rs | :math:`r_s` | rotor resistance | 0.010 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | xs | :math:`x_s` | rotor reactance | 0.150 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | rr1 | :math:`r_{R1}` | 1st cage rotor resistance | 0.050 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | xr1 | :math:`x_{R1}` | 1st cage rotor reactance | 0.150 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | rr2 | :math:`r_{R2}` | 2st cage rotor resistance | 0.001 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | xr2 | :math:`x_{R2}` | 2st cage rotor reactance | 0.040 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | xm | :math:`x_m` | magnetization reactance | 5 | | non_zero,z | +-------+----------------+---------------------------+---------+-----------+------------+ | Hm | :math:`H_m` | Inertia constant | 3 | *kWs/KVA* | power | +-------+----------------+---------------------------+---------+-----------+------------+ | c1 | :math:`c_1` | 1st coeff. of Tm(w) | 0.100 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | c2 | :math:`c_2` | 2nd coeff. of Tm(w) | 0.020 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | c3 | :math:`c_3` | 3rd coeff. of Tm(w) | 0.020 | | | +-------+----------------+---------------------------+---------+-----------+------------+ | zb | :math:`z_b` | Allow working as brake | 1 | | | +-------+----------------+---------------------------+---------+-----------+------------+ Variables --------- +-------+--------------+----------+------------------------------------+------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +=======+==============+==========+====================================+======+============+ | slip | :math:`slip` | State | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | e1d | :math:`e1d` | State | real part of 1st cage voltage | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | e1q | :math:`e1q` | State | imaginary part of 1st cage voltage | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | e2d | :math:`e2d` | State | real part of 2nd cage voltage | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | e2q | :math:`e2q` | State | imag part of 2nd cage voltage | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | vd | :math:`vd` | Algeb | d-axis voltage | | | +-------+--------------+----------+------------------------------------+------+------------+ | vq | :math:`vq` | Algeb | q-axis voltage | | | +-------+--------------+----------+------------------------------------+------+------------+ | p | :math:`p` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | q | :math:`q` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | Id | :math:`Id` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | Iq | :math:`Iq` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | te | :math:`te` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | tm | :math:`tm` | Algeb | | | v_str | +-------+--------------+----------+------------------------------------+------+------------+ | a | :math:`a` | ExtAlgeb | Bus voltage phase angle | | | +-------+--------------+----------+------------------------------------+------+------------+ | v | :math:`v` | ExtAlgeb | Bus voltage magnitude | | | +-------+--------------+----------+------------------------------------+------+------------+ Initialization Equations ------------------------ +-------+--------------+----------+------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +=======+==============+==========+======================================================+ | slip | :math:`slip` | State | :math:`1.0 u` | +-------+--------------+----------+------------------------------------------------------+ | e1d | :math:`e1d` | State | :math:`0.05 u` | +-------+--------------+----------+------------------------------------------------------+ | e1q | :math:`e1q` | State | :math:`0.9 u` | +-------+--------------+----------+------------------------------------------------------+ | e2d | :math:`e2d` | State | :math:`0.05 u` | +-------+--------------+----------+------------------------------------------------------+ | e2q | :math:`e2q` | State | :math:`0.9 u` | +-------+--------------+----------+------------------------------------------------------+ | vd | :math:`vd` | Algeb | | +-------+--------------+----------+------------------------------------------------------+ | vq | :math:`vq` | Algeb | | +-------+--------------+----------+------------------------------------------------------+ | p | :math:`p` | Algeb | :math:`u \left(Id vd + Iq vq\right)` | +-------+--------------+----------+------------------------------------------------------+ | q | :math:`q` | Algeb | :math:`u \left(Id vq - Iq vd\right)` | +-------+--------------+----------+------------------------------------------------------+ | Id | :math:`Id` | Algeb | :math:`0.9 u` | +-------+--------------+----------+------------------------------------------------------+ | Iq | :math:`Iq` | Algeb | :math:`0.1 u` | +-------+--------------+----------+------------------------------------------------------+ | te | :math:`te` | Algeb | :math:`u \left(Id e2d + Iq e2q\right)` | +-------+--------------+----------+------------------------------------------------------+ | tm | :math:`tm` | Algeb | :math:`u \left(aa + bb slip + c_{2} slip^{2}\right)` | +-------+--------------+----------+------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | | +-------+--------------+----------+------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | | +-------+--------------+----------+------------------------------------------------------+ Differential Equations ----------------------------- +-------+--------------+-------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +=======+==============+=======+=========================================================================================================================================================================================+===========+ | slip | :math:`slip` | State | :math:`u \left(- te + tm\right)` | :math:`M` | +-------+--------------+-------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+ | e1d | :math:`e1d` | State | :math:`u \left(e1q slip wb - \frac{Iq \left(x_{0} - x_{1}\right) + e1d}{T_{10}}\right)` | | +-------+--------------+-------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+ | e1q | :math:`e1q` | State | :math:`u \left(- e1d slip wb - \frac{- Id \left(x_{0} - x_{1}\right) + e1q}{T_{10}}\right)` | | +-------+--------------+-------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+ | e2d | :math:`e2d` | State | :math:`u \left(e1q slip wb - slip wb \left(e1q - e2q\right) + \frac{- Iq \left(x_{1} - x_{2}\right) + e1d - e2d}{T_{20}} - \frac{Iq \left(x_{0} - x_{1}\right) + e1d}{T_{10}}\right)` | | +-------+--------------+-------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+ | e2q | :math:`e2q` | State | :math:`u \left(- e1d slip wb + slip wb \left(e1d - e2d\right) + \frac{Id \left(x_{1} - x_{2}\right) + e1q - e2q}{T_{20}} - \frac{- Id \left(x_{0} - x_{1}\right) + e1q}{T_{10}}\right)` | | +-------+--------------+-------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------+ Algebraic Equations ----------------------------- +------+------------+----------+-------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+============+==========+=============================================================+ | vd | :math:`vd` | Algeb | :math:`- u v \sin{\left(a \right)} - vd` | +------+------------+----------+-------------------------------------------------------------+ | vq | :math:`vq` | Algeb | :math:`u v \cos{\left(a \right)} - vq` | +------+------------+----------+-------------------------------------------------------------+ | p | :math:`p` | Algeb | :math:`- p + u \left(Id vd + Iq vq\right)` | +------+------------+----------+-------------------------------------------------------------+ | q | :math:`q` | Algeb | :math:`- q + u \left(Id vq - Iq vd\right)` | +------+------------+----------+-------------------------------------------------------------+ | Id | :math:`Id` | Algeb | :math:`u \left(- Id rs + Iq x_{2} - e2d + vd\right)` | +------+------------+----------+-------------------------------------------------------------+ | Iq | :math:`Iq` | Algeb | :math:`u \left(- Id x_{2} - Iq rs - e2q + vq\right)` | +------+------------+----------+-------------------------------------------------------------+ | te | :math:`te` | Algeb | :math:`- te + u \left(Id e2d + Iq e2q\right)` | +------+------------+----------+-------------------------------------------------------------+ | tm | :math:`tm` | Algeb | :math:`- tm + u \left(aa + bb slip + c_{2} slip^{2}\right)` | +------+------------+----------+-------------------------------------------------------------+ | a | :math:`a` | ExtAlgeb | :math:`p` | +------+------------+----------+-------------------------------------------------------------+ | v | :math:`v` | ExtAlgeb | :math:`q` | +------+------------+----------+-------------------------------------------------------------+ Services ---------- +------+------------------+-----------------------------------------------------------------------------+--------------+ | Name | Symbol | Equation | Type | +======+==================+=============================================================================+==============+ | wb | :math:`\omega_b` | :math:`2 \pi fn` | ConstService | +------+------------------+-----------------------------------------------------------------------------+--------------+ | x0 | :math:`x_0` | :math:`xm + xs` | ConstService | +------+------------------+-----------------------------------------------------------------------------+--------------+ | x1 | :math:`x'` | :math:`\frac{xm xr_{1}}{xm + xr_{1}} + xs` | ConstService | +------+------------------+-----------------------------------------------------------------------------+--------------+ | T10 | :math:`T'_0` | :math:`\frac{xm + xr_{1}}{rr_{1} wb}` | ConstService | +------+------------------+-----------------------------------------------------------------------------+--------------+ | M | :math:`M` | :math:`2 Hm` | ConstService | +------+------------------+-----------------------------------------------------------------------------+--------------+ | aa | :math:`\alpha` | :math:`c_{1} + c_{2} + c_{3}` | ConstService | +------+------------------+-----------------------------------------------------------------------------+--------------+ | bb | :math:`\beta` | :math:`- c_{2} - 2 c_{3}` | ConstService | +------+------------------+-----------------------------------------------------------------------------+--------------+ | x2 | :math:`x''` | :math:`\frac{xm xr_{1} xr_{2}}{xm xr_{1} + xm xr_{2} + xr_{1} xr_{2}} + xs` | ConstService | +------+------------------+-----------------------------------------------------------------------------+--------------+ | T20 | :math:`T''_0` | :math:`\frac{\frac{xm xr_{1}}{xm + xr_{1}} + xr_{2}}{rr_{2} wb}` | ConstService | +------+------------------+-----------------------------------------------------------------------------+--------------+ Config Fields in [Motor5] +---------------+--------+-------+---------------------------------------+-----------------+ | Option | Symbol | Value | Info | Accepted values | +===============+========+=======+=======================================+=================+ | allow_adjust | | 1 | allow adjusting upper or lower limits | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_lower | | 0 | adjust lower limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+ | adjust_upper | | 1 | adjust upper limit | (0, 1) | +---------------+--------+-------+---------------------------------------+-----------------+