AC/DC Converter¶

Asymmetrical monopolar converter configuration¶

Symmetrical monopolar converter configuration¶

Equivalent converter model is taken from [1].

(1)¶\[\begin{split}\begin{align} P_s &= -V_i^2 G_{tf}+ V_iV_f[G_{tf} \cos(\theta_i-\theta_f)+B_{tf} \sin(\theta_i-\theta_f)] \\ Q_s &= V_i^2 B_{tf}+ V_iV_f[G_{tf} \sin(\theta_i-\theta_f)-B_{tf} \cos(\theta_i-\theta_f)] \end{align}\end{split}\]

(2)¶\[\begin{split}\begin{align} P_c &= V_c^2 G_{pr}- V_fV_c[G_{pr} \cos(\theta_f-\theta_c)-B_{pr} \sin(\theta_f-\theta_c)] \\ Q_c &= -V_c^2 B_{pr}+ V_fV_c[G_{pr} \sin(\theta_f-\theta_c)+B_{pr} \cos(\theta_f-\theta_c)] \end{align}\end{split}\]

(3)¶\[\begin{split}\begin{align} P_{cf}-P_{sf} &= 0 \\ Q_{cf}-Q_{sf}-Q_f &= 0 \end{align}\end{split}\]

(4)¶\[P_{c_{AC}} + P_{cn_{loss}} + P_{cn_{DC}} = 0\]

(5)¶\[P_{cn_{loss}} = a\cdot p_{cn} +b \frac{\sqrt{P_{c_{AC}}^2+Q_{c_{AC}}^2}}{V_{c_{AC}}} + \frac{c}{p_{cn}} \left( \frac{P_{c_{AC}}^2+Q_{c_{AC}}^2} {V_{c_{AC}}^2} \right)\]

(6)¶\[\begin{split}p_{cn} = \begin{cases} 1, & \text{for asymmetrical or symmetrical monopolar} \\ 2, & \text{for bipolar} \end{cases}\end{split}\]

(7)¶\[\begin{split}\begin{align} P_{s_{AC}}^2+Q_{s_{AC}}^2 &\leq S_{cn_{rating}}^2 \qquad \forall cn \in \mathcal{C}n \\ |P_{cn_{DC}}| &\leq S_{cn_{rating}} \qquad \forall cn \in \mathcal{C}n \end{align}\end{split}\]

Class Reference: pyflow_acdc.Classes.AC_DC_converter

class AC_DC_converter(AC_type, DC_type, AC_node, DC_node, P_AC=0, Q_AC=0, P_DC=0, Transformer_resistance=0, Transformer_reactance=0, Phase_Reactor_R=0, Phase_Reactor_X=0, Filter=0, Droop=0, kV_base=345, MVA_max=1.05, nConvP=1, polarity=1, lossa=1.103, lossb=0.887, losscrect=2.885, losscinv=4.371, Ucmin=0.85, Ucmax=1.2, arm_res=0.001, S_base=100, name=None)¶

AC/DC converter station (e.g. VSC) linking an AC and a DC node.

Parameters:

AC_type (str) – AC-side control mode: 'Slack', 'PV', or 'PQ'.
DC_type (str) – DC-side control mode: 'Slack', 'P', 'Droop', or 'PAC' (stored as type).
AC_node (Node_AC) – AC bus (stored as Node_AC).
DC_node (Node_DC) – DC bus (stored as Node_DC).
P_AC (float, optional) – Active power injection at the AC side in pu.
Q_AC (float, optional) – Reactive power injection at the AC side in pu.
P_DC (float, optional) – Active power injection at the DC side in pu.
Transformer_resistance (float, optional) – Transformer resistance in pu (scaled by polarity).
Transformer_reactance (float, optional) – Transformer reactance in pu.
Phase_Reactor_R (float, optional) – Phase-reactor resistance in pu.
Phase_Reactor_X (float, optional) – Phase-reactor reactance in pu.
Filter (float, optional) – Filter susceptance in pu.
Droop (float, optional) – Droop rate (stored as Droop_rate).
kV_base (float, optional) – AC-side base voltage in kV (stored as AC_kV_base).
MVA_max (float, optional) – Maximum MVA rating of one converter.
nConvP (float, optional) – Number of parallel converters (stored as np_conv).
polarity (int, optional) – Converter polarity, 1 or -1 (stored as cn_pol).
lossa (float, optional) – No-load loss coefficient for active power.
lossb (float, optional) – Linear current loss coefficient.
losscrect (float, optional) – Switching loss coefficient for rectifier operation.
losscinv (float, optional) – Switching loss coefficient for inverter operation.
Ucmin (float, optional) – Minimum converter voltage in pu.
Ucmax (float, optional) – Maximum converter voltage in pu.
arm_res (float, optional) – Arm resistance in pu (stored as ra).
S_base (float, optional) – Per-unit power base in MVA.
name (str, optional) – Converter identifier.

References