Impedance

Create Function

Input Parameters

net.impedance

Parameter	Datatype	Value Range	Explanation
name	string		name of the impedance
from_bus*	integer		index of bus where the impedance starts
to_bus*	integer		index of bus where the impedance ends
rft_pu*	float	\(>\) 0	resistance of the impedance from ‘from’ to ‘to’ bus [p.u.]
xft_pu*	float	\(>\) 0	reactance of the impedance from ‘from’ to ‘to’ bus [p.u.]
rtf_pu*	float	\(>\) 0	resistance of the impedance from ‘to’ to ‘from’ bus [p.u.]
xtf_pu*	float	\(>\) 0	reactance of the impedance from ‘to’ to ‘from’ bus [p.u.]
rft0_pu*	float	\(>\) 0	zero-sequence resistance of the impedance from ‘from’ to ‘to’ bus [p.u.]
xft0_pu*	float	\(>\) 0	zero-sequence reactance of the impedance from ‘from’ to ‘to’ bus [p.u.]
rtf0_pu*	float	\(>\) 0	zero-sequence resistance of the impedance from ‘to’ to ‘from’ bus [p.u.]
xtf0_pu*	float	\(>\) 0	zero-sequence reactance of the impedance from ‘to’ to ‘from’ bus [p.u.]
gf_pu*	float	\(>\) 1	conductance at the ‘from_bus’ [p.u.]
bf_pu*	float	\(>\) 2	susceptance at the ‘from_bus’ [p.u.]
gt_pu*	float	\(>\) 3	conductance at the ‘from_bus’ [p.u.]
bt_pu*	float	\(>\) 4	susceptance at the ‘from_bus’ [p.u.]
gf0_pu*	float	\(>\) 1	zero-sequence conductance at the ‘from_bus’ [p.u.]
bf0_pu*	float	\(>\) 2	zero-sequence susceptance at the ‘from_bus’ [p.u.]
gt0_pu*	float	\(>\) 3	zero-sequence conductance at the ‘from_bus’ [p.u.]
bt0_pu*	float	\(>\) 4	zero-sequence susceptance at the ‘from_bus’ [p.u.]
sn_mva*	float	\(>\) 0	reference apparent power for the impedance per unit values [MVA]
in_service*	boolean	True / False	specifies if the impedance is in service.

*necessary for executing a power flow calculation.

Electric Model

The impedance is modelled as a longitudinal per unit impedance with \(\underline{z}_{ft} \neq \underline{z}_{tf}\) :

The per unit values given in the parameter table are assumed to be relative to the rated voltage of from and to bus as well as to the apparent power given in the table. The per unit values are therefore transformed into the network per unit system:

\begin{align*} \underline{z}_{ft} &= (rft\_pu + j \cdot xft\_pu) \cdot \frac{S_{N}}{sn\_mva} \\ \underline{z}_{tf} &= (rft\_pu + j \cdot xtf\_pu) \cdot \frac{S_{N}}{sn\_mva} \\ \end{align*}

where \(S_{N}\) is the reference power of the per unit system (see Unit Systems and Conventions).

The asymmetric impedance results in an asymmetric nodal point admittance matrix:

\begin{bmatrix} Y_{00} & \dots & \dots & Y_{nn} \\ \vdots & \ddots & \underline{y}_{ft} & \vdots \\ \vdots & \underline{y}_{tf} & \ddots & \vdots \\ \underline{Y}_{n0} & \dots & \dots & \underline{y}_{nn}\\ \end{bmatrix}

Optionally, the impedance element can also have conductance and susceptance at the “from” and “to” buses. In this case, the electric model becomes similar to the line model. It is possible to have different values of susceptance and conductance for the “from” and “to” bus, as is in the case of the resistance and reactance. This provides for flexibility in modeling an impedance branch element, which will be especially useful when modeling grid equivalents.

Result Parameters

net.res_impedance

Parameter	Datatype	Explanation
p_from_mw	float	active power flow into the impedance at “from” bus [MW]
q_from_mvar	float	reactive power flow into the impedance at “from” bus [MVAr]
p_to_mw	float	active power flow into the impedance at “to” bus [MW]
q_to_mvar	float	reactive power flow into the impedance at “to” bus [MVAr]
pl_mw	float	active power losses of the impedance [MW]
ql_mvar	float	reactive power consumption of the impedance [MVar]
i_from_ka	float	current at from bus [kA]
i_to_ka	float	current at to bus [kA]

\begin{align*} i\_from\_ka &= i_{from}\\ i\_to\_ka &= i_{to}\\ p\_from\_mw &= Re(\underline{v}_{from} \cdot \underline{i}^*_{from}) \\ q\_from\_mvar &= Im(\underline{v}_{from} \cdot \underline{i}^*_{from}) \\ p\_to\_mw &= Re(\underline{v}_{to} \cdot \underline{i}^*_{to}) \\ q\_to\_mvar &= Im(\underline{v}_{to} \cdot \underline{i}^*_{to}) \\ pl\_mw &= p\_from\_mw + p\_to\_mw \\ ql\_mvar &= q\_from\_mvar + q\_to\_mvar \\ \end{align*}