.. _DCLink: ================================================================================ DCLink ================================================================================ Basic DC links Common Parameters: u, name Available models: Ground_, R_, L_, C_, RCp_, RCs_, RLs_, RLCs_, RLCp_ .. _Ground: -------------------------------------------------------------------------------- Ground -------------------------------------------------------------------------------- Ground model that sets the voltage of the connected DC node. Parameters ---------- +----------+-------------+------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +==========+=============+==============================+=========+========+============+ | idx | | unique device idx | | | | +----------+-------------+------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +----------+-------------+------------------------------+---------+--------+------------+ | name | | device name | | | | +----------+-------------+------------------------------+---------+--------+------------+ | node | | Node index | | | mandatory | +----------+-------------+------------------------------+---------+--------+------------+ | voltage | :math:`V_0` | Ground voltage (typically 0) | 0 | *p.u.* | | +----------+-------------+------------------------------+---------+--------+------------+ Variables --------- +------+-------------+----------+------------------------------------------+------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+=============+==========+==========================================+======+============+ | Idc | :math:`Idc` | Algeb | Ficticious current injection from ground | | v_str | +------+-------------+----------+------------------------------------------+------+------------+ | v | :math:`v` | ExtAlgeb | | | | +------+-------------+----------+------------------------------------------+------+------------+ Initialization Equations ------------------------ +------+-------------+----------+---------------+ | Name | Symbol | Type | Initial Value | +======+=============+==========+===============+ | Idc | :math:`Idc` | Algeb | :math:`0` | +------+-------------+----------+---------------+ | v | :math:`v` | ExtAlgeb | | +------+-------------+----------+---------------+ Algebraic Equations ----------------------------- +------+-------------+----------+------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+=============+==========+====================================+ | Idc | :math:`Idc` | Algeb | :math:`u \left(v - voltage\right)` | +------+-------------+----------+------------------------------------+ | v | :math:`v` | ExtAlgeb | :math:`- Idc` | +------+-------------+----------+------------------------------------+ Config Fields in [Ground] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _R: -------------------------------------------------------------------------------- R -------------------------------------------------------------------------------- Resistive dc line Parameters ---------- +--------+------------------+-----------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+=============================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+-----------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | node1 | | Node 1 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | node2 | | Node 2 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn1 | :math:`V_{dcn1}` | DC voltage rating on node 1 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn2 | :math:`V_{dcn2}` | DC voltage rating on node 2 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Idcn | :math:`I_{dcn}` | DC current rating | 1 | *kA* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | R | | DC line resistance | 0.010 | *p.u.* | non_zero,r | +--------+------------------+-----------------------------+---------+--------+------------+ Variables --------- +------+---------------+----------+--------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+===============+==========+==========================+========+============+ | Idc | :math:`Idc` | Algeb | Current from node 2 to 1 | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | v1 | :math:`v_{1}` | ExtAlgeb | DC voltage on node 1 | | | +------+---------------+----------+--------------------------+--------+------------+ | v2 | :math:`v_{2}` | ExtAlgeb | DC voltage on node 2 | | | +------+---------------+----------+--------------------------+--------+------------+ Initialization Equations ------------------------ +------+---------------+----------+--------------------------------------------------+ | Name | Symbol | Type | Initial Value | +======+===============+==========+==================================================+ | Idc | :math:`Idc` | Algeb | :math:`\frac{u \left(- v_{1} + v_{2}\right)}{R}` | +------+---------------+----------+--------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | | +------+---------------+----------+--------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | | +------+---------------+----------+--------------------------------------------------+ Algebraic Equations ----------------------------- +------+---------------+----------+----------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+===============+==========+==========================================================+ | Idc | :math:`Idc` | Algeb | :math:`- Idc + \frac{u \left(- v_{1} + v_{2}\right)}{R}` | +------+---------------+----------+----------------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- Idc` | +------+---------------+----------+----------------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`Idc` | +------+---------------+----------+----------------------------------------------------------+ Config Fields in [R] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _L: -------------------------------------------------------------------------------- L -------------------------------------------------------------------------------- Inductive dc line Parameters ---------- +--------+------------------+-----------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+=============================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+-----------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | node1 | | Node 1 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | node2 | | Node 2 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn1 | :math:`V_{dcn1}` | DC voltage rating on node 1 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn2 | :math:`V_{dcn2}` | DC voltage rating on node 2 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Idcn | :math:`I_{dcn}` | DC current rating | 1 | *kA* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | L | | DC line inductance | 0.001 | *p.u.* | non_zero,r | +--------+------------------+-----------------------------+---------+--------+------------+ Variables --------- +------+---------------+----------+----------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+===============+==========+======================+========+============+ | IL | :math:`IL` | State | Inductance current | *p.u.* | v_str | +------+---------------+----------+----------------------+--------+------------+ | v1 | :math:`v_{1}` | ExtAlgeb | DC voltage on node 1 | | | +------+---------------+----------+----------------------+--------+------------+ | v2 | :math:`v_{2}` | ExtAlgeb | DC voltage on node 2 | | | +------+---------------+----------+----------------------+--------+------------+ Initialization Equations ------------------------ +------+---------------+----------+---------------+ | Name | Symbol | Type | Initial Value | +======+===============+==========+===============+ | IL | :math:`IL` | State | :math:`0` | +------+---------------+----------+---------------+ | v1 | :math:`v_{1}` | ExtAlgeb | | +------+---------------+----------+---------------+ | v2 | :math:`v_{2}` | ExtAlgeb | | +------+---------------+----------+---------------+ Differential Equations ----------------------------- +------+------------+-------+----------------------------------------+---------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +======+============+=======+========================================+=========+ | IL | :math:`IL` | State | :math:`- u \left(v_{1} - v_{2}\right)` | | +------+------------+-------+----------------------------------------+---------+ Algebraic Equations ----------------------------- +------+---------------+----------+-------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+===============+==========+===============================+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- IL` | +------+---------------+----------+-------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`IL` | +------+---------------+----------+-------------------------------+ Config Fields in [L] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _C: -------------------------------------------------------------------------------- C -------------------------------------------------------------------------------- Capacitive dc branch Parameters ---------- +--------+------------------+-----------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+=============================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+-----------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | node1 | | Node 1 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | node2 | | Node 2 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn1 | :math:`V_{dcn1}` | DC voltage rating on node 1 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn2 | :math:`V_{dcn2}` | DC voltage rating on node 2 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Idcn | :math:`I_{dcn}` | DC current rating | 1 | *kA* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | C | | DC capacitance | 0.001 | *p.u.* | non_zero,g | +--------+------------------+-----------------------------+---------+--------+------------+ Variables --------- +------+---------------+----------+--------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+===============+==========+==========================+========+============+ | vC | :math:`vC` | State | Capacitor current | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | Idc | :math:`Idc` | Algeb | Current from node 2 to 1 | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | v1 | :math:`v_{1}` | ExtAlgeb | DC voltage on node 1 | | | +------+---------------+----------+--------------------------+--------+------------+ | v2 | :math:`v_{2}` | ExtAlgeb | DC voltage on node 2 | | | +------+---------------+----------+--------------------------+--------+------------+ Initialization Equations ------------------------ +------+---------------+----------+---------------+ | Name | Symbol | Type | Initial Value | +======+===============+==========+===============+ | vC | :math:`vC` | State | :math:`0` | +------+---------------+----------+---------------+ | Idc | :math:`Idc` | Algeb | :math:`0` | +------+---------------+----------+---------------+ | v1 | :math:`v_{1}` | ExtAlgeb | | +------+---------------+----------+---------------+ | v2 | :math:`v_{2}` | ExtAlgeb | | +------+---------------+----------+---------------+ Differential Equations ----------------------------- +------+------------+-------+----------------------------------+---------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +======+============+=======+==================================+=========+ | vC | :math:`vC` | State | :math:`- Idc u` | | +------+------------+-------+----------------------------------+---------+ Algebraic Equations ----------------------------- +------+---------------+----------+----------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+===============+==========+======================================================================+ | Idc | :math:`Idc` | Algeb | :math:`Idc \left(1 - u\right) + u \left(- v_{1} + v_{2} + vC\right)` | +------+---------------+----------+----------------------------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- Idc` | +------+---------------+----------+----------------------------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`Idc` | +------+---------------+----------+----------------------------------------------------------------------+ Config Fields in [C] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _RCp: -------------------------------------------------------------------------------- RCp -------------------------------------------------------------------------------- Parameters ---------- +--------+------------------+-----------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+=============================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+-----------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | node1 | | Node 1 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | node2 | | Node 2 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn1 | :math:`V_{dcn1}` | DC voltage rating on node 1 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn2 | :math:`V_{dcn2}` | DC voltage rating on node 2 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Idcn | :math:`I_{dcn}` | DC current rating | 1 | *kA* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | R | :math:`R` | DC line resistance | 0.010 | *p.u.* | non_zero,r | +--------+------------------+-----------------------------+---------+--------+------------+ | C | :math:`C` | DC capacitance | 0.001 | *p.u.* | non_zero,g | +--------+------------------+-----------------------------+---------+--------+------------+ Variables --------- +------+---------------+----------+--------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+===============+==========+==========================+========+============+ | vC | :math:`vC` | State | Capacitor current | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | Idc | :math:`Idc` | Algeb | Current from node 2 to 1 | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | v1 | :math:`v_{1}` | ExtAlgeb | DC voltage on node 1 | | | +------+---------------+----------+--------------------------+--------+------------+ | v2 | :math:`v_{2}` | ExtAlgeb | DC voltage on node 2 | | | +------+---------------+----------+--------------------------+--------+------------+ Initialization Equations ------------------------ +------+---------------+----------+-----------------------------------+ | Name | Symbol | Type | Initial Value | +======+===============+==========+===================================+ | vC | :math:`vC` | State | :math:`v_{1} - v_{2}` | +------+---------------+----------+-----------------------------------+ | Idc | :math:`Idc` | Algeb | :math:`\frac{- v_{1} + v_{2}}{R}` | +------+---------------+----------+-----------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | | +------+---------------+----------+-----------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | | +------+---------------+----------+-----------------------------------+ Differential Equations ----------------------------- +------+------------+-------+---------------------------------------------+-----------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +======+============+=======+=============================================+===========+ | vC | :math:`vC` | State | :math:`- u \left(Idc - \frac{vC}{R}\right)` | :math:`C` | +------+------------+-------+---------------------------------------------+-----------+ Algebraic Equations ----------------------------- +------+---------------+----------+----------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+===============+==========+======================================================================+ | Idc | :math:`Idc` | Algeb | :math:`Idc \left(1 - u\right) + u \left(- v_{1} + v_{2} + vC\right)` | +------+---------------+----------+----------------------------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- Idc` | +------+---------------+----------+----------------------------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`Idc` | +------+---------------+----------+----------------------------------------------------------------------+ Config Fields in [RCp] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _RCs: -------------------------------------------------------------------------------- RCs -------------------------------------------------------------------------------- Parameters ---------- +--------+------------------+-----------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+=============================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+-----------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | node1 | | Node 1 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | node2 | | Node 2 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn1 | :math:`V_{dcn1}` | DC voltage rating on node 1 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn2 | :math:`V_{dcn2}` | DC voltage rating on node 2 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Idcn | :math:`I_{dcn}` | DC current rating | 1 | *kA* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | R | :math:`R` | DC line resistance | 0.010 | *p.u.* | non_zero,r | +--------+------------------+-----------------------------+---------+--------+------------+ | C | :math:`C` | DC capacitance | 0.001 | *p.u.* | non_zero,g | +--------+------------------+-----------------------------+---------+--------+------------+ Variables --------- +------+---------------+----------+--------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+===============+==========+==========================+========+============+ | vC | :math:`vC` | State | Capacitor current | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | Idc | :math:`Idc` | Algeb | Current from node 2 to 1 | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | v1 | :math:`v_{1}` | ExtAlgeb | DC voltage on node 1 | | | +------+---------------+----------+--------------------------+--------+------------+ | v2 | :math:`v_{2}` | ExtAlgeb | DC voltage on node 2 | | | +------+---------------+----------+--------------------------+--------+------------+ Initialization Equations ------------------------ +------+---------------+----------+-----------------------------------+ | Name | Symbol | Type | Initial Value | +======+===============+==========+===================================+ | vC | :math:`vC` | State | :math:`v_{1} - v_{2}` | +------+---------------+----------+-----------------------------------+ | Idc | :math:`Idc` | Algeb | :math:`\frac{- v_{1} + v_{2}}{R}` | +------+---------------+----------+-----------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | | +------+---------------+----------+-----------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | | +------+---------------+----------+-----------------------------------+ Differential Equations ----------------------------- +------+------------+-------+----------------------------------+-----------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +======+============+=======+==================================+===========+ | vC | :math:`vC` | State | :math:`- Idc u` | :math:`C` | +------+------------+-------+----------------------------------+-----------+ Algebraic Equations ----------------------------- +------+---------------+----------+------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+===============+==========+==============================================================================+ | Idc | :math:`Idc` | Algeb | :math:`Idc \left(1 - u\right) + u \left(- Idc R - v_{1} + v_{2} + vC\right)` | +------+---------------+----------+------------------------------------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- Idc` | +------+---------------+----------+------------------------------------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`Idc` | +------+---------------+----------+------------------------------------------------------------------------------+ Config Fields in [RCs] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _RLs: -------------------------------------------------------------------------------- RLs -------------------------------------------------------------------------------- Parameters ---------- +--------+------------------+-----------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+=============================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+-----------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | node1 | | Node 1 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | node2 | | Node 2 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn1 | :math:`V_{dcn1}` | DC voltage rating on node 1 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn2 | :math:`V_{dcn2}` | DC voltage rating on node 2 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Idcn | :math:`I_{dcn}` | DC current rating | 1 | *kA* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | R | :math:`R` | DC line resistance | 0.010 | *p.u.* | non_zero,r | +--------+------------------+-----------------------------+---------+--------+------------+ | L | :math:`L` | DC line inductance | 0.001 | *p.u.* | non_zero,r | +--------+------------------+-----------------------------+---------+--------+------------+ Variables --------- +------+---------------+----------+--------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+===============+==========+==========================+========+============+ | IL | :math:`IL` | State | Inductance current | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | Idc | :math:`Idc` | Algeb | Current from node 2 to 1 | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | v1 | :math:`v_{1}` | ExtAlgeb | DC voltage on node 1 | | | +------+---------------+----------+--------------------------+--------+------------+ | v2 | :math:`v_{2}` | ExtAlgeb | DC voltage on node 2 | | | +------+---------------+----------+--------------------------+--------+------------+ Initialization Equations ------------------------ +------+---------------+----------+--------------------------------------------------+ | Name | Symbol | Type | Initial Value | +======+===============+==========+==================================================+ | IL | :math:`IL` | State | :math:`\frac{v_{1} - v_{2}}{R}` | +------+---------------+----------+--------------------------------------------------+ | Idc | :math:`Idc` | Algeb | :math:`- \frac{u \left(v_{1} - v_{2}\right)}{R}` | +------+---------------+----------+--------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | | +------+---------------+----------+--------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | | +------+---------------+----------+--------------------------------------------------+ Differential Equations ----------------------------- +------+------------+-------+-----------------------------------------------+-----------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +======+============+=======+===============================================+===========+ | IL | :math:`IL` | State | :math:`u \left(- IL R + v_{1} - v_{2}\right)` | :math:`L` | +------+------------+-------+-----------------------------------------------+-----------+ Algebraic Equations ----------------------------- +------+---------------+----------+-------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+===============+==========+===============================+ | Idc | :math:`Idc` | Algeb | :math:`- IL u - Idc` | +------+---------------+----------+-------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- Idc` | +------+---------------+----------+-------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`Idc` | +------+---------------+----------+-------------------------------+ Config Fields in [RLs] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _RLCs: -------------------------------------------------------------------------------- RLCs -------------------------------------------------------------------------------- Parameters ---------- +--------+------------------+-----------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+=============================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+-----------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | node1 | | Node 1 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | node2 | | Node 2 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn1 | :math:`V_{dcn1}` | DC voltage rating on node 1 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn2 | :math:`V_{dcn2}` | DC voltage rating on node 2 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Idcn | :math:`I_{dcn}` | DC current rating | 1 | *kA* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | R | :math:`R` | DC line resistance | 0.010 | *p.u.* | non_zero,r | +--------+------------------+-----------------------------+---------+--------+------------+ | L | :math:`L` | DC line inductance | 0.001 | *p.u.* | non_zero,r | +--------+------------------+-----------------------------+---------+--------+------------+ | C | :math:`C` | DC capacitance | 0.001 | *p.u.* | non_zero,g | +--------+------------------+-----------------------------+---------+--------+------------+ Variables --------- +------+---------------+----------+--------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+===============+==========+==========================+========+============+ | IL | :math:`IL` | State | Inductance current | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | vC | :math:`vC` | State | Capacitor current | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | Idc | :math:`Idc` | Algeb | Current from node 2 to 1 | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | v1 | :math:`v_{1}` | ExtAlgeb | DC voltage on node 1 | | | +------+---------------+----------+--------------------------+--------+------------+ | v2 | :math:`v_{2}` | ExtAlgeb | DC voltage on node 2 | | | +------+---------------+----------+--------------------------+--------+------------+ Initialization Equations ------------------------ +------+---------------+----------+-----------------------+ | Name | Symbol | Type | Initial Value | +======+===============+==========+=======================+ | IL | :math:`IL` | State | :math:`0` | +------+---------------+----------+-----------------------+ | vC | :math:`vC` | State | :math:`v_{1} - v_{2}` | +------+---------------+----------+-----------------------+ | Idc | :math:`Idc` | Algeb | :math:`0` | +------+---------------+----------+-----------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | | +------+---------------+----------+-----------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | | +------+---------------+----------+-----------------------+ Differential Equations ----------------------------- +------+------------+-------+----------------------------------------------------+-----------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +======+============+=======+====================================================+===========+ | IL | :math:`IL` | State | :math:`u \left(- IL R + v_{1} - v_{2} - vC\right)` | :math:`L` | +------+------------+-------+----------------------------------------------------+-----------+ | vC | :math:`vC` | State | :math:`IL u` | :math:`C` | +------+------------+-------+----------------------------------------------------+-----------+ Algebraic Equations ----------------------------- +------+---------------+----------+-------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+===============+==========+===============================+ | Idc | :math:`Idc` | Algeb | :math:`- IL - Idc` | +------+---------------+----------+-------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- Idc` | +------+---------------+----------+-------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`Idc` | +------+---------------+----------+-------------------------------+ Config Fields in [RLCs] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _RLCp: -------------------------------------------------------------------------------- RLCp -------------------------------------------------------------------------------- Parameters ---------- +--------+------------------+-----------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +========+==================+=============================+=========+========+============+ | idx | | unique device idx | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +--------+------------------+-----------------------------+---------+--------+------------+ | name | | device name | | | | +--------+------------------+-----------------------------+---------+--------+------------+ | node1 | | Node 1 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | node2 | | Node 2 index | | | mandatory | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn1 | :math:`V_{dcn1}` | DC voltage rating on node 1 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Vdcn2 | :math:`V_{dcn2}` | DC voltage rating on node 2 | 100 | *kV* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | Idcn | :math:`I_{dcn}` | DC current rating | 1 | *kA* | non_zero | +--------+------------------+-----------------------------+---------+--------+------------+ | R | :math:`R` | DC line resistance | 0.010 | *p.u.* | non_zero,r | +--------+------------------+-----------------------------+---------+--------+------------+ | L | :math:`L` | DC line inductance | 0.001 | *p.u.* | non_zero,r | +--------+------------------+-----------------------------+---------+--------+------------+ | C | :math:`C` | DC capacitance | 0.001 | *p.u.* | non_zero,g | +--------+------------------+-----------------------------+---------+--------+------------+ Variables --------- +------+---------------+----------+--------------------------+--------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+===============+==========+==========================+========+============+ | IL | :math:`IL` | State | Inductance current | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | vC | :math:`vC` | State | Capacitor current | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | Idc | :math:`Idc` | Algeb | Current from node 2 to 1 | *p.u.* | v_str | +------+---------------+----------+--------------------------+--------+------------+ | v1 | :math:`v_{1}` | ExtAlgeb | DC voltage on node 1 | | | +------+---------------+----------+--------------------------+--------+------------+ | v2 | :math:`v_{2}` | ExtAlgeb | DC voltage on node 2 | | | +------+---------------+----------+--------------------------+--------+------------+ Initialization Equations ------------------------ +------+---------------+----------+-----------------------------------+ | Name | Symbol | Type | Initial Value | +======+===============+==========+===================================+ | IL | :math:`IL` | State | :math:`0` | +------+---------------+----------+-----------------------------------+ | vC | :math:`vC` | State | :math:`v_{1} - v_{2}` | +------+---------------+----------+-----------------------------------+ | Idc | :math:`Idc` | Algeb | :math:`\frac{- v_{1} + v_{2}}{R}` | +------+---------------+----------+-----------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | | +------+---------------+----------+-----------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | | +------+---------------+----------+-----------------------------------+ Differential Equations ----------------------------- +------+------------+-------+----------------------------------------------------+-----------+ | Name | Symbol | Type | RHS of Equation "T x' = f(x, y)" | T (LHS) | +======+============+=======+====================================================+===========+ | IL | :math:`IL` | State | :math:`u vC` | :math:`L` | +------+------------+-------+----------------------------------------------------+-----------+ | vC | :math:`vC` | State | :math:`- u \left(- IL + Idc - \frac{vC}{R}\right)` | :math:`C` | +------+------------+-------+----------------------------------------------------+-----------+ Algebraic Equations ----------------------------- +------+---------------+----------+----------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+===============+==========+======================================================================+ | Idc | :math:`Idc` | Algeb | :math:`Idc \left(1 - u\right) + u \left(- v_{1} + v_{2} + vC\right)` | +------+---------------+----------+----------------------------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- Idc` | +------+---------------+----------+----------------------------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`Idc` | +------+---------------+----------+----------------------------------------------------------------------+ Config Fields in [RLCp] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+