.. _StaticShunt: ================================================================================ StaticShunt ================================================================================ Static shunt compensator group. Common Parameters: u, name Available models: Shunt_, ShuntTD_, ShuntSw_ .. _Shunt: -------------------------------------------------------------------------------- Shunt -------------------------------------------------------------------------------- Phasor-domain shunt compensator Model. Parameters ---------- +-------+-------------+--------------------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=======+=============+============================================+=========+========+============+ | idx | | unique device idx | | | | +-------+-------------+--------------------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +-------+-------------+--------------------------------------------+---------+--------+------------+ | name | | device name | | | | +-------+-------------+--------------------------------------------+---------+--------+------------+ | bus | | idx of connected bus | | | mandatory | +-------+-------------+--------------------------------------------+---------+--------+------------+ | Sn | :math:`S_n` | Power rating | 100 | | non_zero | +-------+-------------+--------------------------------------------+---------+--------+------------+ | Vn | :math:`V_n` | AC voltage rating | 110 | | non_zero | +-------+-------------+--------------------------------------------+---------+--------+------------+ | g | :math:`g` | shunt conductance (real part) | 0 | | y | +-------+-------------+--------------------------------------------+---------+--------+------------+ | b | :math:`b` | shunt susceptance (positive as capacitive) | 0 | | y | +-------+-------------+--------------------------------------------+---------+--------+------------+ | fn | :math:`f_n` | rated frequency | 60 | | | +-------+-------------+--------------------------------------------+---------+--------+------------+ Variables --------- +------+----------------+----------+-------------+------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+================+==========+=============+======+============+ | a | :math:`\theta` | ExtAlgeb | | | | +------+----------------+----------+-------------+------+------------+ | v | :math:`V` | ExtAlgeb | | | | +------+----------------+----------+-------------+------+------------+ Initialization Equations ------------------------ +------+----------------+----------+---------------+ | Name | Symbol | Type | Initial Value | +======+================+==========+===============+ | a | :math:`\theta` | ExtAlgeb | | +------+----------------+----------+---------------+ | v | :math:`V` | ExtAlgeb | | +------+----------------+----------+---------------+ Algebraic Equations ----------------------------- +------+----------------+----------+-------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+================+==========+===============================+ | a | :math:`\theta` | ExtAlgeb | :math:`V^{2} g u` | +------+----------------+----------+-------------------------------+ | v | :math:`V` | ExtAlgeb | :math:`- V^{2} b u` | +------+----------------+----------+-------------------------------+ Config Fields in [Shunt] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _ShuntTD: -------------------------------------------------------------------------------- ShuntTD -------------------------------------------------------------------------------- Static shunt model with inverse transformation from phasor to time-domain. Parameters ---------- +-------+-------------+--------------------------------------------+---------+--------+------------+ | Name | Symbol | Description | Default | Unit | Properties | +=======+=============+============================================+=========+========+============+ | idx | | unique device idx | | | | +-------+-------------+--------------------------------------------+---------+--------+------------+ | u | :math:`u` | connection status | 1 | *bool* | | +-------+-------------+--------------------------------------------+---------+--------+------------+ | name | | device name | | | | +-------+-------------+--------------------------------------------+---------+--------+------------+ | bus | | idx of connected bus | | | mandatory | +-------+-------------+--------------------------------------------+---------+--------+------------+ | Sn | :math:`S_n` | Power rating | 100 | | non_zero | +-------+-------------+--------------------------------------------+---------+--------+------------+ | Vn | :math:`V_n` | AC voltage rating | 110 | | non_zero | +-------+-------------+--------------------------------------------+---------+--------+------------+ | g | :math:`g` | shunt conductance (real part) | 0 | | y | +-------+-------------+--------------------------------------------+---------+--------+------------+ | b | :math:`b` | shunt susceptance (positive as capacitive) | 0 | | y | +-------+-------------+--------------------------------------------+---------+--------+------------+ | fn | :math:`f_n` | rated frequency | 60 | | | +-------+-------------+--------------------------------------------+---------+--------+------------+ Variables --------- +------+----------------+----------+-------------+------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+================+==========+=============+======+============+ | vta | :math:`V_{ta}` | Algeb | | | v_str | +------+----------------+----------+-------------+------+------------+ | vtb | :math:`V_{tb}` | Algeb | | | v_str | +------+----------------+----------+-------------+------+------------+ | vtc | :math:`V_{tc}` | Algeb | | | v_str | +------+----------------+----------+-------------+------+------------+ | a | :math:`\theta` | ExtAlgeb | | | | +------+----------------+----------+-------------+------+------------+ | v | :math:`V` | ExtAlgeb | | | | +------+----------------+----------+-------------+------+------------+ Initialization Equations ------------------------ +------+----------------+----------+---------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | Initial Value | +======+================+==========+===================================================================================================+ | vta | :math:`V_{ta}` | Algeb | :math:`\frac{\sqrt{3} V \cos{\left(\theta + 2 \pi f_{sys} t_{dae} \right)}}{3}` | +------+----------------+----------+---------------------------------------------------------------------------------------------------+ | vtb | :math:`V_{tb}` | Algeb | :math:`- \frac{\sqrt{3} V \cos{\left(\theta + 2 \pi f_{sys} t_{dae} + \frac{\pi}{3} \right)}}{3}` | +------+----------------+----------+---------------------------------------------------------------------------------------------------+ | vtc | :math:`V_{tc}` | Algeb | :math:`- \frac{\sqrt{3} V \sin{\left(\theta + 2 \pi f_{sys} t_{dae} + \frac{\pi}{6} \right)}}{3}` | +------+----------------+----------+---------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | | +------+----------------+----------+---------------------------------------------------------------------------------------------------+ | v | :math:`V` | ExtAlgeb | | +------+----------------+----------+---------------------------------------------------------------------------------------------------+ Algebraic Equations ----------------------------- +------+----------------+----------+------------------------------------------------------------------------------------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+================+==========+============================================================================================================+ | vta | :math:`V_{ta}` | Algeb | :math:`\frac{\sqrt{3} V \cos{\left(\theta + 2 \pi f_{sys} t_{dae} \right)}}{3} - V_{ta}` | +------+----------------+----------+------------------------------------------------------------------------------------------------------------+ | vtb | :math:`V_{tb}` | Algeb | :math:`- \frac{\sqrt{3} V \cos{\left(\theta + 2 \pi f_{sys} t_{dae} + \frac{\pi}{3} \right)}}{3} - V_{tb}` | +------+----------------+----------+------------------------------------------------------------------------------------------------------------+ | vtc | :math:`V_{tc}` | Algeb | :math:`- \frac{\sqrt{3} V \sin{\left(\theta + 2 \pi f_{sys} t_{dae} + \frac{\pi}{6} \right)}}{3} - V_{tc}` | +------+----------------+----------+------------------------------------------------------------------------------------------------------------+ | a | :math:`\theta` | ExtAlgeb | :math:`V^{2} g u` | +------+----------------+----------+------------------------------------------------------------------------------------------------------------+ | v | :math:`V` | ExtAlgeb | :math:`- V^{2} b u` | +------+----------------+----------+------------------------------------------------------------------------------------------------------------+ Config Fields in [ShuntTD] +---------------+--------+-------+---------------------------------------+-----------------+ | 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) | +---------------+--------+-------+---------------------------------------+-----------------+ .. _ShuntSw: -------------------------------------------------------------------------------- ShuntSw -------------------------------------------------------------------------------- Switched Shunt Model. Parameters `gs`, `bs` and `bs` must be entered in string literals, comma-separated. They need to have the same length. For example, in the excel file, one can put :: gs = [0, 0] bs = [0.2, 0.2] ns = [2, 4] To use individual shunts as fixed shunts, set the corresponding `ns = 0` or `ns = [0]`. The effective shunt susceptances and conductances are stored in services `beff` and `geff`. Parameters ---------- +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | Name | Symbol | Description | Default | Unit | Properties | +=======+=============+==============================================================+=========+===========+=======================+ | idx | | unique device idx | | | | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | u | :math:`u` | connection status | 1 | *bool* | | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | name | | device name | | | | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | bus | | idx of connected bus | | | mandatory | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | Sn | :math:`S_n` | Power rating | 100 | | non_zero | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | Vn | :math:`V_n` | AC voltage rating | 110 | | non_zero | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | g | :math:`g` | shunt conductance (real part) | 0 | | y | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | b | :math:`b` | shunt susceptance (positive as capacitive) | 0 | | y | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | fn | :math:`f_n` | rated frequency | 60 | | | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | gs | | a list literal of switched conductances blocks | 0 | *p.u.* | y | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | bs | | a list literal of switched susceptances blocks | 0 | *p.u.* | y | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | ns | | a list literal of the element numbers in each switched block | [0] | | | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | vref | | voltage reference | 1 | *p.u.* | non_zero,non_negative | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | dv | | voltage error deadband | 0.050 | *p.u.* | non_zero,non_negative | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ | dt | | delay before two consecutive switching | 30 | *seconds* | non_negative | +-------+-------------+--------------------------------------------------------------+---------+-----------+-----------------------+ Variables --------- +------+----------------+----------+-------------+------+------------+ | Name | Symbol | Type | Description | Unit | Properties | +======+================+==========+=============+======+============+ | a | :math:`\theta` | ExtAlgeb | | | | +------+----------------+----------+-------------+------+------------+ | v | :math:`V` | ExtAlgeb | | | | +------+----------------+----------+-------------+------+------------+ Initialization Equations ------------------------ +------+----------------+----------+---------------+ | Name | Symbol | Type | Initial Value | +======+================+==========+===============+ | a | :math:`\theta` | ExtAlgeb | | +------+----------------+----------+---------------+ | v | :math:`V` | ExtAlgeb | | +------+----------------+----------+---------------+ Algebraic Equations ----------------------------- +------+----------------+----------+-------------------------------+ | Name | Symbol | Type | RHS of Equation "0 = g(x, y)" | +======+================+==========+===============================+ | a | :math:`\theta` | ExtAlgeb | :math:`V^{2} geff u` | +------+----------------+----------+-------------------------------+ | v | :math:`V` | ExtAlgeb | :math:`- V^{2} beff u` | +------+----------------+----------+-------------------------------+ Services ---------- +------+----------------+---------------------+--------------+ | Name | Symbol | Equation | Type | +======+================+=====================+==============+ | vlo | :math:`v_{lo}` | :math:`- dv + vref` | ConstService | +------+----------------+---------------------+--------------+ | vup | :math:`v_{up}` | :math:`dv + vref` | ConstService | +------+----------------+---------------------+--------------+ Discretes ----------- +------+-------------+-------------+----------------+ | Name | Symbol | Type | Info | +======+=============+=============+================+ | adj | :math:`adj` | ShuntAdjust | shunt adjuster | +------+-------------+-------------+----------------+ Config Fields in [ShuntSw] +---------------+------------------------+-------+----------------------------------------------------------+-----------------+ | 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) | +---------------+------------------------+-------+----------------------------------------------------------+-----------------+ | min_iter | :math:`sw_{iter}` | 2 | iteration number starting from which to enable switching | int | +---------------+------------------------+-------+----------------------------------------------------------+-----------------+ | err_tol | :math:`\epsilon_{tol}` | 0.010 | iteration error below which to enable switching | float | +---------------+------------------------+-------+----------------------------------------------------------+-----------------+