Line

See also

Unit Systems and Conventions
Standard Type Libraries

Create Function

Lines can be either created from the standard type library (create_line) or with custom values (create_line_from_parameters).

Note

Lines for 3 phase load flow uses zero sequence parameters which can be provided through a custom standard type using pandapower.create_std_type() and pandapower.add_zero_impedance_parameters()

Zero sequence parameters (Added through std_type For Three phase load flow) :

-r0_ohm_per_km (float) - zero sequence line resistance in ohm per km

-x0_ohm_per_km (float) - zero sequence line reactance in ohm per km

-c0_nf_per_km (float) - zero sequence line capacitance in nano Farad per km

pandapower.create_line(net, from_bus, to_bus, length_km, std_type, name=None, index=None, geodata=None, df=get_default_value('line', 'df'), parallel=get_default_value('line', 'parallel'), in_service=get_default_value('line', 'in_service'), max_loading_percent=nan, alpha=nan, temperature_degree_celsius=nan, **kwargs)

Creates a line element in net[“line”] The line parameters are defined through the standard type library.

Parameters:

• net (pandapowerNet) – The net within this line should be created

• from_bus (int | integer) – ID of the bus on one side which the line will be connected with

• to_bus (int | integer) – ID of the bus on the other side which the line will be connected with

• length_km (float) – The line length in km

• std_type (str) – Name of a standard line type: - Pre-defined in standard_linetypes - Customized std_type made using create_std_type()

• name (str | None) – A custom name for this line

• index (int | integer | None) – Force a specified ID if it is available. If None, the index one higher than the highest already existing index is selected.

• geodata (Iterable[tuple[float, float]] | None) – Iterable[Tuple[int, int]|Tuple[float, float]], The geodata of the line. The first element should be the coordinates of from_bus and the last should be the coordinates of to_bus. The points in the middle represent the bending points of the line

• in_service (bool) – True for in_service or False for out of service

• df (float) – derating factor: maximum current of line in relation to nominal current of line (from 0 to 1)

• parallel (int) – number of parallel line systems

• max_loading_percent (float) – maximum current loading (only needed for OPF)

• alpha (float) – temperature coefficient of resistance: R(T) = R(T_0) * (1 + alpha * (T - T_0))

• temperature_degree_celsius (float) – line temperature for which line resistance is adjusted

Keyword Arguments:

• tdpf (bool) – whether the line is considered in the TDPF calculation

• wind_speed_m_per_s (float) – wind speed at the line in m/s (TDPF)

• wind_angle_degree (float) – angle of attack between the wind direction and the line (TDPF)

• conductor_outer_diameter_m (float) – outer diameter of the line conductor in m (TDPF)

• air_temperature_degree_celsius (float) – ambient temperature in °C (TDPF)

• reference_temperature_degree_celsius (float) – reference temperature in °C for which r_ohm_per_km for the line is specified (TDPF)

• solar_radiation_w_per_sq_m (float) – solar radiation on horizontal plane in W/m² (TDPF)

• solar_absorptivity – Albedo factor for absorptivity of the lines (TDPF)

• emissivity (float) – Albedo factor for emissivity of the lines (TDPF)

• r_theta_kelvin_per_mw (float) – thermal resistance of the line (TDPF, only for simplified method)

• mc_joule_per_m_k (float) – specific mass of the conductor multiplied by the specific thermal capacity of the material (TDPF, only for thermal inertia consideration with tdpf_delay_s parameter)

Returns:

The unique ID of the created line

Return type:

int | integer

Example

>>> create_line(net, from_bus=0, to_bus=1, length_km=0.1,  std_type="NAYY 4x50 SE", name="line1")

pandapower.create_line_from_parameters(net, from_bus, to_bus, length_km, r_ohm_per_km, x_ohm_per_km, c_nf_per_km, max_i_ka, name=None, index=None, type=None, geodata=None, in_service=get_default_value('line', 'in_service'), df=get_default_value('line', 'df'), parallel=get_default_value('line', 'parallel'), g_us_per_km=get_default_value('line', 'g_us_per_km'), max_loading_percent=nan, alpha=nan, temperature_degree_celsius=nan, r0_ohm_per_km=nan, x0_ohm_per_km=nan, c0_nf_per_km=nan, g0_us_per_km=get_default_value('line', 'g0_us_per_km'), endtemp_degree=nan, **kwargs)

Creates a line element in net[“line”] from line parameters.

Parameters:

• net (pandapowerNet) – The net within this line should be created

• from_bus (int | integer) – ID of the bus on one side which the line will be connected with

• to_bus (int | integer) – ID of the bus on the other side which the line will be connected with

• length_km (float) – The line length in km

• r_ohm_per_km (float) – line resistance in ohm per km

• x_ohm_per_km (float) – line reactance in ohm per km

• c_nf_per_km (float) – line capacitance (line-to-earth) in nano Farad per km

• r0_ohm_per_km (float) – zero sequence line resistance in ohm per km

• x0_ohm_per_km (float) – zero sequence line reactance in ohm per km

• c0_nf_per_km (float) – zero sequence line capacitance in nano Farad per km

• max_i_ka (float) – maximum thermal current in kilo Ampere

• name (str | None) – A custom name for this line

• index (int | integer | None) – Force a specified ID if it is available. If None, the index one higher than the highest already existing index is selected.

• in_service (bool) – True for in_service or False for out of service

• type (Literal['ol', 'cs'] | None) – type of line (“ol” for overhead line or “cs” for cable system)

• df (float) – derating factor: maximum current of line in relation to nominal current of line (from 0 to 1)

• g_us_per_km (float) – dielectric conductance in micro Siemens per km

• g0_us_per_km (float) – zero sequence dielectric conductance in micro Siemens per km

• parallel (int) – number of parallel line systems

• geodata (Iterable[tuple[float, float]] | None) – The geodata of the line. The first row should be the coordinates of bus a and the last should be the coordinates of bus b. The points in the middle represent the bending points of the line

• max_loading_percent (float) – maximum current loading (only needed for OPF)

• alpha (float) – temperature coefficient of resistance: R(T) = R(T_0) * (1 + alpha * (T - T_0)))

• temperature_degree_celsius (float) – line temperature for which line resistance is adjusted

• endtemp_degree (float)

Keyword Arguments:

• tdpf – whether the line is considered in the TDPF calculation

• wind_speed_m_per_s – wind speed at the line in m/s (TDPF)

• wind_angle_degree – angle of attack between the wind direction and the line (TDPF)

• conductor_outer_diameter_m – outer diameter of the line conductor in m (TDPF)

• air_temperature_degree_celsius – ambient temperature in °C (TDPF)

• reference_temperature_degree_celsius – reference temperature in °C for which r_ohm_per_km for the line is specified (TDPF)

• solar_radiation_w_per_sq_m – solar radiation on horizontal plane in W/m² (TDPF)

• solar_absorptivity – Albedo factor for absorptivity of the lines (TDPF)

• emissivity – Albedo factor for emissivity of the lines (TDPF)

• r_theta_kelvin_per_mw – thermal resistance of the line (TDPF, only for simplified method)

• mc_joule_per_m_k – specific mass of the conductor multiplied by the specific thermal capacity of the material (TDPF, only for thermal inertia consideration with tdpf_delay_s parameter)

Returns:

The unique ID of the created line

Return type:

int | integer

Example

>>> create_line_from_parameters(net, from_bus=0, to_bus=1, length_km=0.1,
>>>   r_ohm_per_km=.01, x_ohm_per_km=0.05, c_nf_per_km=10, max_i_ka=0.4, name="line1"
>>> )

Table Structure

net.line

Parameter	Datatype	Value Range	Explanation	nullable	required	optimal power flow	short circuit	3ph	tdpf
name			name of the line	✓
std_type			standard type which can be used to easily define line parameters with the pandapower standard type library	✓
from_bus	int	>=0	Index of bus where the line starts		✓
to_bus	int	>=0	Index of bus where the line ends		✓
length_km	float	>0	length of the line [km]		✓
r_ohm_per_km	float	>=0	resistance of the line [Ohm per km]		✓
x_ohm_per_km	float	>=0	reactance of the line [Ohm per km]		✓
c_nf_per_km	float	>=0	capacitance of the line (line-to-earth) [nano Farad per km]		✓
g_us_per_km	float	>=0	dielectric conductance in micro Siemens per km		✓
r0_ohm_per_km	float	>=0	zero sequence resistance of the line [Ohm per km]	✓			✓	✓
x0_ohm_per_km	float	>=0	zero sequence reactance of the line [Ohm per km]	✓			✓	✓
c0_nf_per_km	float	>=0	zero sequence capacitance of the line [nano Farad per km]	✓			✓	✓
g0_us_per_km	float	>=0	dielectric conductance of the line [micro Siemens per km]	✓			✓	✓
max_i_ka	float	>0	maximal thermal current [kilo Ampere]		✓
parallel	int	>=1	number of parallel line systems		✓
df	float	[0, 1]	derating factor (scaling) for max_i_ka		✓
type			type of line normally “ol” - overhead line “cs” - underground cable system	✓
max_loading_percent	float	>0	Maximum loading of the line	✓		✓
endtemp_degree	float	>-273	Short-Circuit end temperature of the line in degree Celsius	✓			✓		✓
in_service	bool		specifies if the line is in service.		✓
geo			geojson.LineString object or its string representation	✓
alpha	float		temperature coefficient of resistance: R(T) = R(T_0) * (1 + alpha * (T - T_0))	✓
temperature_degree_celsius	float	>-273	line temperature for which line resistance is adjusted	✓
tdpf	bool		whether the line is considered in the TDPF calculation	✓					✓
wind_speed_m_per_s	float	>=0	wind speed at the line in m/s (TDPF)	✓					✓
wind_angle_degree	float	[0, 360]	angle of attack between the wind direction and the line (TDPF)	✓					✓
conductor_outer_diameter_m	float		outer diameter of the line conductor in m (TDPF)	✓					✓
air_temperature_degree_celsius	float		ambient temperature in °C (TDPF)	✓					✓
reference_temperature_degree_celsius	float	>-273	reference temperature in °C for which r_ohm_per_km for the line is specified (TDPF)	✓					✓
solar_radiation_w_per_sq_m	float		solar radiation on horizontal plane in W/m² (TDPF)	✓					✓
solar_absorptivity	float		Albedo factor for absorptivity of the lines (TDPF)	✓					✓
emissivity	float		Albedo factor for emissivity of the lines (TDPF)	✓					✓
r_theta_kelvin_per_mw	float		thermal resistance of the line (TDPF, only for simplified method)	✓					✓
mc_joule_per_m_k	float		specific mass of the conductor multiplied by the specific thermal capacity of the material (TDPF, only for thermal inertia consideration with tdpf_delay_s parameter)	✓					✓

Note

Defining a line with length zero leads to a division by zero in the power flow and is therefore not allowed. Lines with a very low impedance might lead to convergence problems in the power flow for the same reason. If you want to directly connect two buses, please use the switch element instead of a line with a small impedance!

Electric Model

Lines are modelled with the \(\pi\)-equivalent circuit:

Three phase line model

The elements in the equivalent circuit are calculated from the parameters in the net.line dataframe as:

\begin{align*} \underline{Z_{1 or 2}} &= (r\_ohm\_per\_km + j \cdot x\_ohm\_per\_km) \cdot \frac{length\_km}{parallel} \\ \underline{Y_{1 or 2}}&= (g\_us\_per\_km \cdot 1 \cdot 10^-6 + j \cdot 2 \pi f \cdot c\_nf\_per\_km \cdot 1 \cdot 10^-9) \cdot length\_km \cdot parallel\\ \underline{Z_{0}} &= (r0\_ohm\_per\_km + j \cdot x0\_ohm\_per\_km) \cdot \frac{length\_km}{parallel} \\ \underline{Y_{0}} &= (g0\_us\_per\_km \cdot 1 \cdot 10^-6 + j \cdot 2 \pi f \cdot c0\_nf\_per\_km \cdot 1 \cdot 10^-9) \cdot length\_km \cdot parallel \end{align*}

The power system frequency \(f\) is defined when creating an empty network, the default value is \(f = 50 Hz\).

Note

For three phase load flow, three decoupled sequence networks ( zero , positive and negative) are considered.

Positive and Negative sequence impedances are given by r_ohm_per_km, x_ohm_per_km, and c_nf_per_km

Zero sequence impedances are given by r0_ohm_per_km, x0_ohm_per_km, and c0_nf_per_km

The parameters are then transformed in the per unit system:

\begin{align*} Z_{N} &= \frac{V_{N}^2}{S_{N}} \\ \underline{z} &= \frac{\underline{Z}}{Z_{N}} \\ \underline{y} &= \underline{Y} \cdot Z_{N} \\ \end{align*}

Where the reference voltage \(V_{N}\) is the nominal voltage at the from bus and the rated apparent power \(S_{N}\) is defined system wide in the net object (see Unit Systems and Conventions).

Note

pandapower assumes that nominal voltage of from bus and to bus are equal, which means pandapower does not support lines that connect different voltage levels. If you want to connect different voltage levels, either use a transformer or an impedance element.

Result Tables

net.res_line

Parameter	Datatype	Explanation	nullable	required
p_from_mw	float	active power flow into the line at “from” bus [MW]	✓	✓
q_from_mvar	float	reactive power flow into the line at “from” bus [MVar]	✓	✓
p_to_mw	float	active power flow into the line at “to” bus [MW]	✓	✓
q_to_mvar	float	reactive power flow into the line at “to” bus [MVar]	✓	✓
pl_mw	float	active power losses of the line [MW]	✓	✓
ql_mvar	float	reactive power consumption of the line [MVar]	✓	✓
i_from_ka	float	Current at from bus [kA]	✓	✓
i_to_ka	float	Current at to bus [kA]	✓	✓
i_ka	float	Maximum of i_from_ka and i_to_ka [kA]	✓	✓
vm_from_pu	float	voltage magnitude at from bus	✓	✓
vm_to_pu	float	voltage magnitude at to bus	✓	✓
va_from_degree	float	voltage angle at from bus [degrees]	✓	✓
va_to_degree	float	voltage angle at to bus [degrees]	✓	✓
loading_percent	float	line loading [%]	✓	✓

The power flow results in the net.res_line table are defined as:

\begin{align*} 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 \\ i\_from\_ka &= i_{from} \\ i\_to\_ka &= i_{to} \\ i\_ka &= max(i_{from}, i_{to}) \\ loading\_percent &= \frac{i\_ka}{imax\_ka \cdot df \cdot parallel} \cdot 100 \end{align*}

net.res_line_3ph

Parameter	Datatype	Explanation	nullable	required
p_a_from_mw	float	active power flow into the line at from bus: Phase A [MW]	✓	✓
q_a_from_mvar	float	reactive power flow into the line at from bus : Phase A [MVar]	✓	✓
p_b_from_mw	float	active power flow into the line at from bus: Phase B [MW]	✓	✓
q_b_from_mvar	float	reactive power flow into the line at from bus : Phase B[MVar]	✓	✓
p_c_from_mw	float	active power flow into the line at from bus: Phase C [MW]	✓	✓
q_c_from_mvar	float	reactive power flow into the line at from bus : Phase C[MVar]	✓	✓
p_a_to_mw	float	active power flow into the line at to bus: Phase A [MW]	✓	✓
q_a_to_mvar	float	reactive power flow into the line at to bus : Phase A[MVar]	✓	✓
p_b_to_mw	float	active power flow into the line at to bus: Phase B [MW]	✓	✓
q_b_to_mvar	float	reactive power flow into the line at to bus : Phase B[MVar]	✓	✓
p_c_to_mw	float	active power flow into the line at to bus: Phase C [MW]	✓	✓
q_c_to_mvar	float	reactive power flow into the line at to bus : Phase C[MVar]	✓	✓
pl_a_mw	float	active power losses of the line: Phase A [MW]	✓	✓
ql_a_mvar	float	reactive power consumption of the line: Phase A [MVar]	✓	✓
pl_b_mw	float	active power losses of the line: Phase B [MW]	✓	✓
ql_b_mvar	float	reactive power consumption of the line: Phase B [MVar]	✓	✓
pl_c_mw	float	active power losses of the line: Phase C [MW]	✓	✓
ql_c_mvar	float	reactive power consumption of the line: Phase C [MVar]	✓	✓
i_a_from_ka	float	Current at from bus: Phase A [kA]	✓	✓
i_a_to_ka	float	Current at to bus: Phase A [kA]	✓	✓
i_a_ka	float	Current at Phase A [kA]	✓	✓
i_b_from_ka	float	Current at from bus: Phase B [kA]	✓	✓
i_b_to_ka	float	Current at to bus: Phase B [kA]	✓	✓
i_b_ka	float	Current at Phase B [kA]	✓	✓
i_c_from_ka	float	Current at from bus: Phase C [kA]	✓	✓
i_c_to_ka	float	Current at to bus: Phase C [kA]	✓	✓
i_c_ka	float	Current at Phase C [kA]	✓	✓
i_n_from_ka	float	Current at from bus: Neutral [kA]	✓	✓
i_n_to_ka	float	Current at to bus: Neutral [kA]	✓	✓
i_ka	float	Maximum of i_from_ka and i_to_ka [kA]	✓	✓
i_n_ka	float	Current Neutral [kA]	✓	✓
loading_a_percent	float	line a loading [%]	✓	✓
loading_b_percent	float	line b loading [%]	✓	✓
loading_c_percent	float	line c loading [%]	✓	✓
loading_n_percent	float	line loading [%]	✓	✓

The power flow results in the net.res_line_3ph table are defined as:

\begin{align*} p\_from\_mw_{phase} &= Re(\underline{v_{phase}}_{from} \cdot \underline{i_{phase}}^*_{from}) \\ q\_from\_mvar_{phase} &= Im(\underline{v_{phase}}_{from} \cdot \underline{i_{phase}}^*_{from}) \\ p\_to\_mw_{phase} &= Re(\underline{v_{phase}}_{to} \cdot \underline{i_{phase}}^*_{to}) \\ q\_to\_mvar_{phase} &= Im(\underline{v_{phase}}_{to} \cdot \underline{i_{phase}}^*_{to}) \\ pl\_mw_{phase} &= p\_from\_mw_{phase} + p\_to\_mw_{phase} \\ ql\_mvar_{phase} &= q\_from\_mvar_{phase} + q\_to\_mvar_{phase} \\ i\_from\_ka_{phase} &= i_{from_{phase}} \\ i\_to\_ka_{phase} &= i_{to_{phase}} \\ i\_ka &= max(i_{from}, i_{to}) \\ i\_from\_ka_{neutral} &= |i_{from_{phaseA}}| + |i_{from_{phaseB}}| + |i_{from_{phaseC}}|\\ i\_to\_ka_{neutral} &= |i_{to_{phaseA}}| + |i_{to_{phaseB}}| + |i_{to_{phaseC}}| \\ loading\_percent &= \frac{i\_ka}{imax\_ka \cdot df \cdot parallel} \cdot 100 \end{align*}

net.res_line_est

The state estimation results are put into net.res_line_est with the same definition as in net.res_line.

Parameter	Datatype	Explanation	nullable	required
p_from_mw	float	active power flow into the line at “from” bus [MW]	✓	✓
q_from_mvar	float	reactive power flow into the line at “from” bus [MVar]	✓	✓
p_to_mw	float	active power flow into the line at “to” bus [MW]	✓	✓
q_to_mvar	float	reactive power flow into the line at “to” bus [MVar]	✓	✓
pl_mw	float	active power losses of the line [MW]	✓	✓
ql_mvar	float	reactive power consumption of the line [MVar]	✓	✓
i_from_ka	float	Current at from bus [kA]	✓	✓
i_to_ka	float	Current at to bus [kA]	✓	✓
i_ka	float	Maximum of i_from_ka and i_to_ka [kA]	✓	✓
vm_from_pu	float	voltage magnitude at from bus	✓	✓
vm_to_pu	float	voltage magnitude at to bus	✓	✓
va_from_degree	float	voltage angle at from bus [degrees]	✓	✓
va_to_degree	float	voltage angle at to bus [degrees]	✓	✓
loading_percent	float	line loading [%]	✓	✓

net.res_line_sc

The short-circuit (SC) results are put into net.res_line_sc with following definitions:

Parameter	Datatype	Explanation	nullable	required
ikss_ka	float	initial short-circuit current value [kA]	✓	✓
ikss_from_ka	float	magnitude of the initial SC current at “”from”” bus [kA]	✓	✓
ikss_from_degree	float	degree of the initial SC current at “”from”” bus [degrees]	✓	✓
ikss_to_ka	float	magnitude of the initial SC current at “”to”” bus [kA]	✓	✓
ikss_to_degree	float	degree of the initial SC current at “”to”” bus [degrees]	✓	✓
p_from_mw	float	active SC power flow into the line at “”from”” bus [MW]	✓	✓
q_from_mvar	float	reactive SC power flow into the line at “”from”” bus [MVar]	✓	✓
p_to_mw	float	active SC power flow into the line at “”to”” bus [MW]	✓	✓
q_to_mvar	float	reactive SC power flow into the line at “”to”” bus [MVar]	✓	✓
vm_from_pu	float	voltage magnitude at “”from”” bus [p.u.]	✓	✓
vm_to_pu	float	voltage magnitude at “”to”” bus [p.u.]	✓	✓
va_from_degree	float	voltage angle at “”from”” bus [degrees]	✓	✓
va_to_degree	float	voltage angle at “”to”” bus [degrees]	✓	✓
ip_ka	float	peak value of the short-circuit current [kA]	✓	✓
ith_ka	float	equivalent thermal short-circuit current [kA]	✓	✓