.. _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:`I_{dc}` | Algeb | Ficticious current injection from ground | | v_str | +------+----------------+----------+------------------------------------------+------+------------+ | v | :math:`v` | ExtAlgeb | | | | +------+----------------+----------+------------------------------------------+------+------------+ Initialization Equations ------------------------ +------+----------------+----------+---------------+ | Name | Symbol | Type | Initial Value | +======+================+==========+===============+ | Idc | :math:`I_{dc}` | Algeb | :math:`0` | +------+----------------+----------+---------------+ | v | :math:`v` | ExtAlgeb | | +------+----------------+----------+---------------+ Algebraic Equations ----------------------------- +------+----------------+----------+------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+================+==========+====================================+ | Idc | :math:`I_{dc}` | Algeb | :math:`u \left(- V_{0} + v\right)` | +------+----------------+----------+------------------------------------+ | v | :math:`v` | ExtAlgeb | :math:`- I_{dc}` | +------+----------------+----------+------------------------------------+ 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:`I_{dc}` | 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:`I_{dc}` | 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:`I_{dc}` | Algeb | :math:`- I_{dc} + \frac{u \left(- v_{1} + v_{2}\right)}{R}` | +------+----------------+----------+-------------------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- I_{dc}` | +------+----------------+----------+-------------------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`I_{dc}` | +------+----------------+----------+-------------------------------------------------------------+ 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:`I_{L}` | 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:`I_{L}` | 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:`I_{L}` | 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:`- I_{L}` | +------+---------------+----------+-------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`I_{L}` | +------+---------------+----------+-------------------------------+ 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:`v_{C}` | State | Capacitor current | *p.u.* | v_str | +------+----------------+----------+--------------------------+--------+------------+ | Idc | :math:`I_{dc}` | 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:`v_{C}` | State | :math:`0` | +------+----------------+----------+---------------+ | Idc | :math:`I_{dc}` | 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:`v_{C}` | State | :math:`- I_{dc} u` | | +------+---------------+-------+----------------------------------+---------+ Algebraic Equations ----------------------------- +------+----------------+----------+----------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+================+==========+============================================================================+ | Idc | :math:`I_{dc}` | Algeb | :math:`I_{dc} \left(1 - u\right) + u \left(- v_{1} + v_{2} + v_{C}\right)` | +------+----------------+----------+----------------------------------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- I_{dc}` | +------+----------------+----------+----------------------------------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`I_{dc}` | +------+----------------+----------+----------------------------------------------------------------------------+ 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:`v_{C}` | State | Capacitor current | *p.u.* | v_str | +------+----------------+----------+--------------------------+--------+------------+ | Idc | :math:`I_{dc}` | 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:`v_{C}` | State | :math:`v_{1} - v_{2}` | +------+----------------+----------+-----------------------------------+ | Idc | :math:`I_{dc}` | 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:`v_{C}` | State | :math:`- u \left(I_{dc} - \frac{v_{C}}{R}\right)` | :math:`C` | +------+---------------+-------+---------------------------------------------------+-----------+ Algebraic Equations ----------------------------- +------+----------------+----------+----------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+================+==========+============================================================================+ | Idc | :math:`I_{dc}` | Algeb | :math:`I_{dc} \left(1 - u\right) + u \left(- v_{1} + v_{2} + v_{C}\right)` | +------+----------------+----------+----------------------------------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- I_{dc}` | +------+----------------+----------+----------------------------------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`I_{dc}` | +------+----------------+----------+----------------------------------------------------------------------------+ 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:`v_{C}` | State | Capacitor current | *p.u.* | v_str | +------+----------------+----------+--------------------------+--------+------------+ | Idc | :math:`I_{dc}` | 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:`v_{C}` | State | :math:`v_{1} - v_{2}` | +------+----------------+----------+-----------------------------------+ | Idc | :math:`I_{dc}` | 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:`v_{C}` | State | :math:`- I_{dc} u` | :math:`C` | +------+---------------+-------+----------------------------------+-----------+ Algebraic Equations ----------------------------- +------+----------------+----------+---------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+================+==========+=======================================================================================+ | Idc | :math:`I_{dc}` | Algeb | :math:`I_{dc} \left(1 - u\right) + u \left(- I_{dc} R - v_{1} + v_{2} + v_{C}\right)` | +------+----------------+----------+---------------------------------------------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- I_{dc}` | +------+----------------+----------+---------------------------------------------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`I_{dc}` | +------+----------------+----------+---------------------------------------------------------------------------------------+ 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:`I_{L}` | State | Inductance current | *p.u.* | v_str | +------+----------------+----------+--------------------------+--------+------------+ | Idc | :math:`I_{dc}` | 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:`I_{L}` | State | :math:`\frac{v_{1} - v_{2}}{R}` | +------+----------------+----------+--------------------------------------------------+ | Idc | :math:`I_{dc}` | 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:`I_{L}` | State | :math:`u \left(- I_{L} R + v_{1} - v_{2}\right)` | :math:`L` | +------+---------------+-------+--------------------------------------------------+-----------+ Algebraic Equations ----------------------------- +------+----------------+----------+-------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+================+==========+===============================+ | Idc | :math:`I_{dc}` | Algeb | :math:`- I_{L} u - I_{dc}` | +------+----------------+----------+-------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- I_{dc}` | +------+----------------+----------+-------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`I_{dc}` | +------+----------------+----------+-------------------------------+ 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:`I_{L}` | State | Inductance current | *p.u.* | v_str | +------+----------------+----------+--------------------------+--------+------------+ | vC | :math:`v_{C}` | State | Capacitor current | *p.u.* | v_str | +------+----------------+----------+--------------------------+--------+------------+ | Idc | :math:`I_{dc}` | 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:`I_{L}` | State | :math:`0` | +------+----------------+----------+-----------------------+ | vC | :math:`v_{C}` | State | :math:`v_{1} - v_{2}` | +------+----------------+----------+-----------------------+ | Idc | :math:`I_{dc}` | 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:`I_{L}` | State | :math:`u \left(- I_{L} R + v_{1} - v_{2} - v_{C}\right)` | :math:`L` | +------+---------------+-------+----------------------------------------------------------+-----------+ | vC | :math:`v_{C}` | State | :math:`I_{L} u` | :math:`C` | +------+---------------+-------+----------------------------------------------------------+-----------+ Algebraic Equations ----------------------------- +------+----------------+----------+-------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+================+==========+===============================+ | Idc | :math:`I_{dc}` | Algeb | :math:`- I_{L} - I_{dc}` | +------+----------------+----------+-------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- I_{dc}` | +------+----------------+----------+-------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`I_{dc}` | +------+----------------+----------+-------------------------------+ 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:`I_{L}` | State | Inductance current | *p.u.* | v_str | +------+----------------+----------+--------------------------+--------+------------+ | vC | :math:`v_{C}` | State | Capacitor current | *p.u.* | v_str | +------+----------------+----------+--------------------------+--------+------------+ | Idc | :math:`I_{dc}` | 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:`I_{L}` | State | :math:`0` | +------+----------------+----------+-----------------------------------+ | vC | :math:`v_{C}` | State | :math:`v_{1} - v_{2}` | +------+----------------+----------+-----------------------------------+ | Idc | :math:`I_{dc}` | 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:`I_{L}` | State | :math:`u v_{C}` | :math:`L` | +------+---------------+-------+-------------------------------------------------------------+-----------+ | vC | :math:`v_{C}` | State | :math:`- u \left(- I_{L} + I_{dc} - \frac{v_{C}}{R}\right)` | :math:`C` | +------+---------------+-------+-------------------------------------------------------------+-----------+ Algebraic Equations ----------------------------- +------+----------------+----------+----------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+================+==========+============================================================================+ | Idc | :math:`I_{dc}` | Algeb | :math:`I_{dc} \left(1 - u\right) + u \left(- v_{1} + v_{2} + v_{C}\right)` | +------+----------------+----------+----------------------------------------------------------------------------+ | v1 | :math:`v_{1}` | ExtAlgeb | :math:`- I_{dc}` | +------+----------------+----------+----------------------------------------------------------------------------+ | v2 | :math:`v_{2}` | ExtAlgeb | :math:`I_{dc}` | +------+----------------+----------+----------------------------------------------------------------------------+ 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) | +---------------+--------+-------+---------------------------------------+-----------------+