pydynamicestimator.devices.inverter

Parameters:: dae (pydynamicestimator.system.Dae) – DAE object
Returns:: Vswd (ndarray): d-component of the switching block voltage Vswq (ndarray): q-component of the switching block voltage ifd_ext (ndarray): d-component of the filter current in the network (external) dq-reference frame ifq_ext (ndarray): q-component of the filter current in the network (external) dq-reference frame Vfd_ext (ndarray): d-component of the filter voltage in the network (external) dq-reference frame Vfq_ext (ndarray): q-component of the filter voltage in the network (external) dq-reference frame itd_ext (ndarray): d-component of the terminal current in the network (external) dq-reference frame itq_ext (ndarray): q-component of the terminal current in the network (external) dq-reference frame
Return type:: Tuple

frequency_estimator_init(Vfd_ext: numpy.ndarray, Vfq_ext: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray][source]

Steady-state initialization of the frequency estimator. Based on methods used in https://github.com/NREL-Sienna/PowerSimulationsDynamics.jl

Parameters:

Vfd_ext (ndarray) – d-component of the filter voltage in the network (external) dq-reference frame
Vfq_ext (ndarray) – q-component of the filter voltage in the network (external) dq-reference frame

Returns:

Vfq_pll (ndarray): q-component of the filter voltage in the PLL’s dq-reference frame epsilon (ndarray): integrator state of the PLL delta_pll (ndarray): angle difference between the dq-reference frame of the PLL and the network

Return type:

Tuple

outer_loop_init(dae: pydynamicestimator.system.Dae, Vfd_ext: numpy.ndarray, Vfq_ext: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray][source]

Steady-state initialization of the inverter outer loop. Based on methods used in https://github.com/NREL-Sienna/PowerSimulationsDynamics.jl

Parameters:

dae (pydynamicestimator.system.Dae) – DAE object
Vfd_ext (ndarray) – d-component of the filter voltage in the network (external) dq-reference frame
Vfq_ext (ndarray) – q-component of the filter voltage in the network (external) dq-reference frame

Returns:

Pref (ndarray): active power reference Qref (ndarray): reactive power reference

Return type:

Tuple

inner_loop_init(dae: pydynamicestimator.system.Dae, ifd_ext: numpy.ndarray, ifq_ext: numpy.ndarray, Vfd_ext: numpy.ndarray, Vfq_ext: numpy.ndarray, Vswd: numpy.ndarray, Vswq: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray][source]

Steady-state initialization of the inverter inner loop. Based on methods used in https://github.com/NREL-Sienna/PowerSimulationsDynamics.jl

Parameters:

dae (pydynamicestimator.system.Dae) – DAE object
ifd_ext (numpy.ndarray)
ifq_ext (numpy.ndarray)
Vfd_ext (numpy.ndarray)
Vfq_ext (numpy.ndarray)
Vswd (numpy.ndarray)
Vswq (numpy.ndarray)

Returns:

delta_c Vref xi_d xi_q gamma_d gamma_q Pc_tilde Qc_tilde

Return type:

Tuple

finit(dae: pydynamicestimator.system.Dae)[source]

Parameters:: dae (pydynamicestimator.system.Dae)
Returns:: None

class pydynamicestimator.devices.inverter.GridFollowing[source]

Bases: Inverter

Grid-Following Inverter (with Droop) Based on the grid-following inverter model in https://doi.org/10.1109/TPWRS.2021.3061434

The dynamic behavior of the grid-following converter is described by the following differential equations:

Converter Voltage Dynamics

\[\dot{v}_{fd_{ext}} = \frac{\omega_{b}}{c_{f}}(i_{fd_{ext}} - i_{td_{ext}}) + \omega_{net}\omega_{b}v_{fq_{ext}}\]

\[\dot{v}_{fq_{ext}} = \frac{\omega_{b}}{c_{f}}(i_{fq_{ext}} - i_{tq_{ext}}) - \omega_{net}\omega_{b}v_{fd_{ext}}\]

Converter Current Dynamics

\[\dot{i}_{fd_{ext}} = \frac{\omega_{b}}{l_{f}}(v_{swd} - v_{fd_{ext}}) - \frac{\omega_{b}r_{f}}{l_{f}}i_{fd_{ext}} + \omega_{net}\omega_{b}i_{fq_{ext}}\]

\[\dot{i}_{fq_{ext}} = \frac{\omega_{b}}{l_{f}}(v_{swq} - v_{fq_{ext}}) - \frac{\omega_{b}r_{f}}{l_{f}}i_{fq_{ext}} - \omega_{net}\omega_{b}i_{fd_{ext}}\]

Grid-Side Current Dynamics

\[\dot{i}_{td_{ext}} = \frac{\omega_b}{l_t}(v_{fd_{ext}} - v_{n_{re}}) - \frac{\omega_b r_t}{l_t}i_{td_{ext}} + \omega_{net} \omega_b i_{tq_{ext}}\]

\[\dot{i}_{tq_{ext}} = \frac{\omega_b}{l_t}(v_{fq_{ext}} - v_{n_{im}}) - \frac{\omega_b r_t}{l_t}i_{tq_{ext}} - \omega_{net} \omega_b i_{td_{ext}}\]

Phase-Locked Loop (PLL) Dynamics

\[\dot{\epsilon} = v_{fq_{pll}}\]

\[\delta\dot{\theta}_{pll} = \omega_{b}\delta\omega_{pll}\]

Power and Frequency Dynamics

\[\dot{\tilde{p}}_{c} = \omega_{f}(p_{c} - \tilde{p}_{c})\]

\[\delta\dot{\theta}_{c} = \omega_{b}\delta\omega_{c}\]

\[\dot{\tilde{q}}_{c} = \omega_{f}(q_{c} - \tilde{q}_{c})\]

Control Dynamics

\[\dot{\xi}_{d} = v_{fd^{*}} - v_{fd_{int}}\]

\[\dot{\xi}_{q} = v_{fq^{*}} - v_{fq_{int}}\]

\[\dot{\gamma}_{d} = i_{fd^{*}} - i_{fd_{int}}\]

\[\dot{\gamma}_{q} = i_{fq^{*}} - i_{fq_{int}}\]

_type = 'Inverter'

_name = 'GridFollowing_inverter_model'

epsilon

delta_pll

Kpll_p

Kpll_i

fgcall(dae: pydynamicestimator.system.Dae) → None[source]

A method that executes the differential and algebraic equations of the model and adds them to the appropriate places in the Dae class

Parameters:: dae – an instance of a class Dae
Returns:: None
Return type:: None

finit(dae: pydynamicestimator.system.Dae) → None[source]

Parameters:: dae (pydynamicestimator.system.Dae)
Returns:: None
Return type:: None

class pydynamicestimator.devices.inverter.GridForming[source]

Bases: Inverter

Grid-Forming Inverter (Droop-Based) Based on the grid-forming inverter model in https://doi.org/10.1109/TPWRS.2021.3061434 The dynamic behavior of the grid-forming converter is described by the following differential equations:

Converter Voltage Dynamics

\[\dot{v}_{fd_{ext}} = \frac{\omega_{b}}{c_{f}}(i_{fd_{ext}} - i_{td_{ext}}) + \omega_{net}\omega_{b}v_{fq_{ext}}\]

\[\dot{v}_{fq_{ext}} = \frac{\omega_{b}}{c_{f}}(i_{fq_{ext}} - i_{tq_{ext}}) - \omega_{net}\omega_{b}v_{fd_{ext}}\]

Converter Current Dynamics

\[\dot{i}_{fd_{ext}} = \frac{\omega_{b}}{l_{f}}(v_{swd} - v_{fd_{ext}}) - \frac{\omega_{b}r_{f}}{l_{f}}i_{fd_{ext}} + \omega_{net}\omega_{b}i_{fq_{ext}}\]

\[\dot{i}_{fq_{ext}} = \frac{\omega_{b}}{l_{f}}(v_{swq} - v_{fq_{ext}}) - \frac{\omega_{b}r_{f}}{l_{f}}i_{fq_{ext}} - \omega_{net}\omega_{b}i_{fd_{ext}}\]

Grid-Side Current Dynamics

\[\dot{i}_{td_{ext}} = \frac{\omega_b}{l_t}(v_{fd_{ext}} - v_{n_{re}}) - \frac{\omega_b r_t}{l_t}i_{td_{ext}} + \omega_{net} \omega_b i_{tq_{ext}}\]

\[\dot{i}_{tq_{ext}} = \frac{\omega_b}{l_t}(v_{fq_{ext}} - v_{n_{im}}) - \frac{\omega_b r_t}{l_t}i_{tq_{ext}} - \omega_{net} \omega_b i_{td_{ext}}\]

Power and Frequency Dynamics

\[\dot{\tilde{p}}_{c} = \omega_{f}(p_{c} - \tilde{p}_{c})\]

\[\delta\dot{\theta}_{c} = \omega_{b}\delta\omega_{c}\]

\[\dot{\tilde{q}}_{c} = \omega_{f}(q_{c} - \tilde{q}_{c})\]

Control Dynamics

\[\dot{\xi}_{d} = v_{fd^{*}} - v_{fd_{int}}\]

\[\dot{\xi}_{q} = v_{fq^{*}} - v_{fq_{int}}\]

\[\dot{\gamma}_{d} = i_{fd^{*}} - i_{fd_{int}}\]

\[\dot{\gamma}_{q} = i_{fq^{*}} - i_{fq_{int}}\]

_type = 'Inverter'

_name = 'GridForming_inverter_model'

fgcall(dae: pydynamicestimator.system.Dae) → None[source]

A method that executes the differential and algebraic equations of the model and adds them to the appropriate places in the Dae class

Parameters:: dae – an instance of a class Dae
Returns:: None
Return type:: None

finit(dae) → None[source]

Parameters:: dae (pydynamicestimator.system.Dae)
Returns:: None
Return type:: None