.. _Interface: ================================================================================ Interface ================================================================================ Group for interface models. Available models: Fortescue_ .. _Fortescue: -------------------------------------------------------------------------------- Fortescue -------------------------------------------------------------------------------- Fortescue's symmetric component interface. This model interfaces a positive-sequence, single-phase-equivalent bus with three buses representing three phases. It is effectively a transformer with one terminal on the primary side and three on the secondary. Only the positive sequence component on the secondary winding is used for simulation. The positive-sequence voltage magnitude and angle of the secondary winding are named ``vp`` and ``ap``. The negative and zero sequence variables given in the d- and q-axis due the angle being undefined when the voltage is zero. The negative sequence voltages are ``vnd`` and ``vnq`` for the d- anx q-axis, respectively. Likewise, the zero-sequence voltages are ``vzd`` and ``vzq``. Parameters ---------- +-------+-------------+-----------------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=======+=============+=========================================+=========+========+============+ | idx | | unique device idx | | | | +-------+-------------+-----------------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +-------+-------------+-----------------------------------------+---------+--------+------------+ | name | | device name | | | | +-------+-------------+-----------------------------------------+---------+--------+------------+ | bus | | bus idx for the single-phase equivalent | | | mandatory | +-------+-------------+-----------------------------------------+---------+--------+------------+ | busa | | bus idx for phase a | | | mandatory | +-------+-------------+-----------------------------------------+---------+--------+------------+ | busb | | bus idx for phase b | | | mandatory | +-------+-------------+-----------------------------------------+---------+--------+------------+ | busc | | bus idx for phase c | | | mandatory | +-------+-------------+-----------------------------------------+---------+--------+------------+ | Sn | :math:`S_n` | Power rating | 100 | *MW* | non_zero | +-------+-------------+-----------------------------------------+---------+--------+------------+ | r | :math:`r` | resistance | 0.001 | *p.u.* | z | +-------+-------------+-----------------------------------------+---------+--------+------------+ | x | :math:`x` | short-circuit reactance | 0.025 | *p.u.* | non_zero,z | +-------+-------------+-----------------------------------------+---------+--------+------------+ | g | | iron loss | 0 | *p.u.* | y | +-------+-------------+-----------------------------------------+---------+--------+------------+ | b | | magnetizing susceptance | 0.005 | *p.u.* | y | +-------+-------------+-----------------------------------------+---------+--------+------------+ Variables --------- +------+--------------------+----------+-------------------------------------------+------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+====================+==========+===========================================+======+============+ | vp | :math:`V_{p}` | Algeb | positive sequence voltage magnitude | | v_str | +------+--------------------+----------+-------------------------------------------+------+------------+ | ap | :math:`\theta_{p}` | Algeb | positive sequence voltage phase | | v_str | +------+--------------------+----------+-------------------------------------------+------+------------+ | vnd | :math:`V_{nd}` | Algeb | negative sequence voltage on d-axis (cos) | | v_str | +------+--------------------+----------+-------------------------------------------+------+------------+ | vnq | :math:`V_{nq}` | Algeb | negative sequence voltage on q-axis (sin) | | v_str | +------+--------------------+----------+-------------------------------------------+------+------------+ | vzd | :math:`V_{zd}` | Algeb | zero sequence voltage on d-axis (cos) | | v_str | +------+--------------------+----------+-------------------------------------------+------+------------+ | vzq | :math:`V_{zq}` | Algeb | zero sequence voltage on q-axis (sin) | | v_str | +------+--------------------+----------+-------------------------------------------+------+------------+ | a | :math:`\theta_{1}` | ExtAlgeb | phase angle of single-phase eq. bus | | | +------+--------------------+----------+-------------------------------------------+------+------------+ | aa | :math:`\theta_{a}` | ExtAlgeb | phase angle of bus for phase a | | | +------+--------------------+----------+-------------------------------------------+------+------------+ | ab | :math:`\theta_{b}` | ExtAlgeb | phase angle of bus for phase b | | | +------+--------------------+----------+-------------------------------------------+------+------------+ | ac | :math:`\theta_{c}` | ExtAlgeb | phase angle of bus for phase c | | | +------+--------------------+----------+-------------------------------------------+------+------------+ | v | :math:`V_{1}` | ExtAlgeb | voltage of single-phase eq. bus | | | +------+--------------------+----------+-------------------------------------------+------+------------+ | va | :math:`V_{a}` | ExtAlgeb | voltage of bus for phase a | | | +------+--------------------+----------+-------------------------------------------+------+------------+ | vb | :math:`V_{b}` | ExtAlgeb | voltage of bus for phase b | | | +------+--------------------+----------+-------------------------------------------+------+------------+ | vc | :math:`V_{c}` | ExtAlgeb | voltage of bus for phase c | | | +------+--------------------+----------+-------------------------------------------+------+------------+ Initialization Equations ------------------------ +------+--------------------+----------+-------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +======+====================+==========+=============================================================+ | vp | :math:`V_{p}` | Algeb | :math:`\frac{V_{a}}{3} + \frac{V_{b}}{3} + \frac{V_{c}}{3}` | +------+--------------------+----------+-------------------------------------------------------------+ | ap | :math:`\theta_{p}` | Algeb | :math:`\theta_{a} + \theta_{b} + \theta_{c}` | +------+--------------------+----------+-------------------------------------------------------------+ | vnd | :math:`V_{nd}` | Algeb | :math:`0.0` | +------+--------------------+----------+-------------------------------------------------------------+ | vnq | :math:`V_{nq}` | Algeb | :math:`0.0` | +------+--------------------+----------+-------------------------------------------------------------+ | vzd | :math:`V_{zd}` | Algeb | :math:`0.0` | +------+--------------------+----------+-------------------------------------------------------------+ | vzq | :math:`V_{zq}` | Algeb | :math:`0.0` | +------+--------------------+----------+-------------------------------------------------------------+ | a | :math:`\theta_{1}` | ExtAlgeb | | +------+--------------------+----------+-------------------------------------------------------------+ | aa | :math:`\theta_{a}` | ExtAlgeb | | +------+--------------------+----------+-------------------------------------------------------------+ | ab | :math:`\theta_{b}` | ExtAlgeb | | +------+--------------------+----------+-------------------------------------------------------------+ | ac | :math:`\theta_{c}` | ExtAlgeb | | +------+--------------------+----------+-------------------------------------------------------------+ | v | :math:`V_{1}` | ExtAlgeb | | +------+--------------------+----------+-------------------------------------------------------------+ | va | :math:`V_{a}` | ExtAlgeb | | +------+--------------------+----------+-------------------------------------------------------------+ | vb | :math:`V_{b}` | ExtAlgeb | | +------+--------------------+----------+-------------------------------------------------------------+ | vc | :math:`V_{c}` | ExtAlgeb | | +------+--------------------+----------+-------------------------------------------------------------+ Algebraic Equations ----------------------------- +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+====================+==========+======================================================================================================================================================================================================================================================================================================================================+ | vp | :math:`V_{p}` | Algeb | :math:`- V_{p} + \frac{\sqrt{\left(V_{b} \sin{\left(120^{o} - \theta_{a} + \theta_{b} \right)} - V_{c} \sin{\left(120^{o} + \theta_{a} - \theta_{c} \right)}\right)^{2} + \left(V_{a} + V_{b} \cos{\left(120^{o} - \theta_{a} + \theta_{b} \right)} + V_{c} \cos{\left(120^{o} + \theta_{a} - \theta_{c} \right)}\right)^{2}}}{3}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | ap | :math:`\theta_{p}` | Algeb | :math:`\theta_{a} - \theta_{p} + \operatorname{atan}_{2}{\left(V_{b} \sin{\left(120^{o} - \theta_{a} + \theta_{b} \right)} - V_{c} \sin{\left(120^{o} + \theta_{a} - \theta_{c} \right)},V_{a} + V_{b} \cos{\left(120^{o} - \theta_{a} + \theta_{b} \right)} + V_{c} \cos{\left(120^{o} + \theta_{a} - \theta_{c} \right)} \right)}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vnd | :math:`V_{nd}` | Algeb | :math:`V_{a} \cos{\left(\theta_{a} \right)} + V_{b} \cos{\left(120^{o} - \theta_{b} \right)} + V_{c} \cos{\left(120^{o} + \theta_{c} \right)} - V_{nd}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vnq | :math:`V_{nq}` | Algeb | :math:`V_{a} \sin{\left(\theta_{a} \right)} - V_{b} \sin{\left(120^{o} - \theta_{b} \right)} + V_{c} \sin{\left(120^{o} + \theta_{c} \right)} - V_{nq}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vzd | :math:`V_{zd}` | Algeb | :math:`V_{a} \cos{\left(\theta_{a} \right)} + V_{b} \cos{\left(\theta_{b} \right)} + V_{c} \cos{\left(\theta_{c} \right)} - V_{zd}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vzq | :math:`V_{zq}` | Algeb | :math:`V_{a} \sin{\left(\theta_{a} \right)} + V_{b} \sin{\left(\theta_{b} \right)} + V_{c} \sin{\left(\theta_{c} \right)} - V_{zq}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta_{1}` | ExtAlgeb | :math:`u \left(V_{1}^{2} \left(g + g_{hk}\right) - V_{1} V_{p} \left(b_{hk} \sin{\left(\theta_{1} - \theta_{p} \right)} + g_{hk} \cos{\left(\theta_{1} - \theta_{p} \right)}\right)\right)` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | aa | :math:`\theta_{a}` | ExtAlgeb | :math:`\frac{u \left(- V_{1} V_{a} \left(- b_{hk} \sin{\left(\theta_{1} - \theta_{a} \right)} + g_{hk} \cos{\left(\theta_{1} - \theta_{a} \right)}\right) + V_{a}^{2} \left(g + g_{hk}\right)\right)}{3}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | ab | :math:`\theta_{b}` | ExtAlgeb | :math:`\frac{u \left(- V_{1} V_{b} \left(b_{hk} \sin{\left(120^{o} - \theta_{1} + \theta_{b} \right)} + g_{hk} \cos{\left(120^{o} - \theta_{1} + \theta_{b} \right)}\right) + V_{b}^{2} \left(g + g_{hk}\right)\right)}{3}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | ac | :math:`\theta_{c}` | ExtAlgeb | :math:`\frac{u \left(- V_{1} V_{c} \left(- b_{hk} \sin{\left(120^{o} + \theta_{1} - \theta_{c} \right)} + g_{hk} \cos{\left(120^{o} + \theta_{1} - \theta_{c} \right)}\right) + V_{c}^{2} \left(g + g_{hk}\right)\right)}{3}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | v | :math:`V_{1}` | ExtAlgeb | :math:`u \left(- V_{1}^{2} \left(b + b_{hk}\right) - V_{1} V_{p} \left(- b_{hk} \cos{\left(\theta_{1} - \theta_{p} \right)} + g_{hk} \sin{\left(\theta_{1} - \theta_{p} \right)}\right)\right)` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | va | :math:`V_{a}` | ExtAlgeb | :math:`\frac{u \left(V_{1} V_{a} \left(b_{hk} \cos{\left(\theta_{1} - \theta_{a} \right)} + g_{hk} \sin{\left(\theta_{1} - \theta_{a} \right)}\right) - V_{a}^{2} \left(b + b_{hk}\right)\right)}{3}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vb | :math:`V_{b}` | ExtAlgeb | :math:`\frac{u \left(V_{1} V_{b} \left(b_{hk} \cos{\left(120^{o} - \theta_{1} + \theta_{b} \right)} - g_{hk} \sin{\left(120^{o} - \theta_{1} + \theta_{b} \right)}\right) - V_{b}^{2} \left(b + b_{hk}\right)\right)}{3}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | vc | :math:`V_{c}` | ExtAlgeb | :math:`\frac{u \left(V_{1} V_{c} \left(b_{hk} \cos{\left(120^{o} + \theta_{1} - \theta_{c} \right)} + g_{hk} \sin{\left(120^{o} + \theta_{1} - \theta_{c} \right)}\right) - V_{c}^{2} \left(b + b_{hk}\right)\right)}{3}` | +------+--------------------+----------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ Services ---------- +-------+----------------+------------------------------------------------+--------------+ | Name | Symbol | Equation | Type | +=======+================+================================================+==============+ | yhk | :math:`y_{hk}` | :math:`\frac{u}{r + i x}` | ConstService | +-------+----------------+------------------------------------------------+--------------+ | ghk | :math:`g_{hk}` | :math:`\operatorname{re}{\left(y_{hk}\right)}` | ConstService | +-------+----------------+------------------------------------------------+--------------+ | bhk | :math:`b_{hk}` | :math:`\operatorname{im}{\left(y_{hk}\right)}` | ConstService | +-------+----------------+------------------------------------------------+--------------+ | d120 | :math:`120^o` | :math:`\frac{2 \pi}{3}` | ConstService | +-------+----------------+------------------------------------------------+--------------+ Config Fields in [Fortescue] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+