Three Winding Transformer

See also

Unit Systems and Conventions
Standard Type Libraries

Create Function

pandapower.create.create_transformer3w(net, hv_bus, mv_bus, lv_bus, std_type, name=None, tap_pos=nan, in_service=True, index=None, max_loading_percent=nan, tap_at_star_point=False, tap_dependent_impedance=nan, vk_hv_percent_characteristic=None, vkr_hv_percent_characteristic=None, vk_mv_percent_characteristic=None, vkr_mv_percent_characteristic=None, vk_lv_percent_characteristic=None, vkr_lv_percent_characteristic=None, **kwargs)

Creates a three-winding transformer in table net[“trafo3w”]. The trafo parameters are defined through the standard type library.

INPUT:

net - The net within this transformer should be created

hv_bus (int) - The bus on the high-voltage side on which the transformer will be connected to

mv_bus (int) - The medium voltage bus on which the transformer will be connected to

lv_bus (int) - The bus on the low-voltage side on which the transformer will be connected to

std_type - The used standard type from the standard type library

OPTIONAL:

name (string) - A custom name for this transformer

tap_pos (int, nan) - current tap position of the transformer. Defaults to the medium position (tap_neutral)

tap_at_star_point (boolean) - Whether tap changer is located at the star point of the 3W-transformer or at the bus

in_service (boolean) - True for in_service or False for out of service

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

max_loading_percent (float) - maximum current loading (only needed for OPF)

tap_at_star_point (bool) - whether tap changer is modelled at star point or at the bus

tap_dependent_impedance (boolean) - True if transformer impedance must be adjusted dependent on the tap position of the trabnsformer. Requires the additional columns “vk_percent_characteristic” and “vkr_percent_characteristic” that reference the index of the characteristic from the table net.characteristic. A convenience function pandapower.control.create_trafo_characteristics can be used to create the SplineCharacteristic objects, add the relevant columns and set up the references to the characteristics. The function pandapower.control.trafo_characteristics_diagnostic can be used for sanity checks.

vk_hv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vkr_hv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vk_mv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vkr_mv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vk_lv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vkr_lv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

OUTPUT:

index (int) - The unique ID of the created transformer

EXAMPLE:

create_transformer3w(net, hv_bus = 0, mv_bus = 1, lv_bus = 2, name = “trafo1”, std_type = “63/25/38 MVA 110/20/10 kV”)

pandapower.create.create_transformer3w_from_parameters(net, hv_bus, mv_bus, lv_bus, vn_hv_kv, vn_mv_kv, vn_lv_kv, sn_hv_mva, sn_mv_mva, sn_lv_mva, vk_hv_percent, vk_mv_percent, vk_lv_percent, vkr_hv_percent, vkr_mv_percent, vkr_lv_percent, pfe_kw, i0_percent, shift_mv_degree=0.0, shift_lv_degree=0.0, tap_side=None, tap_step_percent=nan, tap_step_degree=nan, tap_pos=nan, tap_neutral=nan, tap_max=nan, tap_min=nan, name=None, in_service=True, index=None, max_loading_percent=nan, tap_at_star_point=False, vk0_hv_percent=nan, vk0_mv_percent=nan, vk0_lv_percent=nan, vkr0_hv_percent=nan, vkr0_mv_percent=nan, vkr0_lv_percent=nan, vector_group=None, tap_dependent_impedance=nan, vk_hv_percent_characteristic=None, vkr_hv_percent_characteristic=None, vk_mv_percent_characteristic=None, vkr_mv_percent_characteristic=None, vk_lv_percent_characteristic=None, vkr_lv_percent_characteristic=None, **kwargs)

Adds a three-winding transformer in table net[“trafo3w”]. The model currently only supports one tap-changer per 3W Transformer.

Input:

net (pandapowerNet) - The net within this transformer should be created

hv_bus (int) - The bus on the high-voltage side on which the transformer will be connected to

mv_bus (int) - The bus on the middle-voltage side on which the transformer will be connected to

lv_bus (int) - The bus on the low-voltage side on which the transformer will be connected to

vn_hv_kv (float) rated voltage on high voltage side

vn_mv_kv (float) rated voltage on medium voltage side

vn_lv_kv (float) rated voltage on low voltage side

sn_hv_mva (float) - rated apparent power on high voltage side

sn_mv_mva (float) - rated apparent power on medium voltage side

sn_lv_mva (float) - rated apparent power on low voltage side

vk_hv_percent (float) - short circuit voltage from high to medium voltage

vk_mv_percent (float) - short circuit voltage from medium to low voltage

vk_lv_percent (float) - short circuit voltage from high to low voltage

vkr_hv_percent (float) - real part of short circuit voltage from high to medium voltage

vkr_mv_percent (float) - real part of short circuit voltage from medium to low voltage

vkr_lv_percent (float) - real part of short circuit voltage from high to low voltage

pfe_kw (float) - iron losses in kW

i0_percent (float) - open loop losses

OPTIONAL:

shift_mv_degree (float, 0) - angle shift to medium voltage side*

shift_lv_degree (float, 0) - angle shift to low voltage side*

tap_step_percent (float) - Tap step in percent

tap_step_degree (float) - Tap phase shift angle in degrees

tap_side (string, None) - “hv”, “mv”, “lv”

tap_neutral (int, nan) - default tap position

tap_min (int, nan) - Minimum tap position

tap_max (int, nan) - Maximum tap position

tap_pos (int, nan) - current tap position of the transformer. Defaults to the medium position (tap_neutral)

tap_at_star_point (boolean) - Whether tap changer is located at the star point of the 3W-transformer or at the bus

name (string, None) - Name of the 3-winding transformer

in_service (boolean, True) - True for in_service or False for out of service

max_loading_percent (float) - maximum current loading (only needed for OPF)

tap_dependent_impedance (boolean) - True if transformer impedance must be adjusted dependent on the tap position of the trabnsformer. Requires the additional columns “vk_percent_characteristic” and “vkr_percent_characteristic” that reference the index of the characteristic from the table net.characteristic. A convenience function pandapower.control.create_trafo_characteristics can be used to create the SplineCharacteristic objects, add the relevant columns and set up the references to the characteristics. The function pandapower.control.trafo_characteristics_diagnostic can be used for sanity checks.

vk_hv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vkr_hv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vk_mv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vkr_mv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vk_lv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vkr_lv_percent_characteristic (int) - index of the characteristic from net.characteristic for the adjustment of the parameter “vk_percent” for the calculation of tap dependent impedance.

vk0_hv_percent (float) - zero sequence short circuit voltage from high to medium voltage

vk0_mv_percent (float) - zero sequence short circuit voltage from medium to low voltage

vk0_lv_percent (float) - zero sequence short circuit voltage from high to low voltage

vkr0_hv_percent (float) - zero sequence real part of short circuit voltage from high to medium voltage

vkr0_mv_percent (float) - zero sequence real part of short circuit voltage from medium to low voltage

vkr0_lv_percent (float) - zero sequence real part of short circuit voltage from high to low voltage

vector_group (list of String) - Vector group of the transformer3w

OUTPUT:

trafo_id - The unique trafo_id of the created 3W transformer

Example:

create_transformer3w_from_parameters(net, hv_bus=0, mv_bus=1, lv_bus=2, name=”trafo1”, sn_hv_mva=40, sn_mv_mva=20, sn_lv_mva=20, vn_hv_kv=110, vn_mv_kv=20, vn_lv_kv=10, vk_hv_percent=10,vk_mv_percent=11, vk_lv_percent=12, vkr_hv_percent=0.3, vkr_mv_percent=0.31, vkr_lv_percent=0.32, pfe_kw=30, i0_percent=0.1, shift_mv_degree=30, shift_lv_degree=30)

Note

All short circuit voltages are given relative to the minimum apparent power flow. For example vk_hv_percent is the short circuit voltage from the high to the medium level, it is given relative to the minimum of the rated apparent power in high and medium level: min(sn_hv_mva, sn_mv_mva). This is consistent with most commercial network calculation software (e.g. PowerFactory). Some tools (like PSS Sincal) however define all short ciruit voltages relative to the overall rated apparent power of the transformer: max(sn_hv_mva, sn_mv_mva, sn_lv_mva). You might have to convert the values depending on how the short-circuit voltages are defined.

Input Parameters

net.trafo3w

Parameter	Datatype	Value Range	Explanation
name	string		name of the transformer
std_type	string		transformer standard type name
hv_bus*	integer		high voltage bus index of the transformer
mv_bus	integer		medium voltage bus index of the transformer
lv_bus*	integer		low voltage bus index of the transformer
vn_hv_kv*	float		rated voltage at high voltage bus [kV]
vn_mv_kv*	float	\(>\) 0	rated voltage at medium voltage bus [kV]
vn_lv_kv*	float	\(>\) 0	rated voltage at low voltage bus [kV]
sn_hv_mva*	float	\(>\) 0	rated apparent power on high voltage side [kVA]
sn_mv_mva*	float	\(>\) 0	rated apparent power on medium voltage side [kVA]
sn_lv_mva*	float	\(>\) 0	rated apparent power on low voltage side [kVA]
vk_hv_percent*	float	\(>\) 0	short circuit voltage from high to medium voltage [%]
vk_mv_percent*	float	\(>\) 0	short circuit voltage from medium to low voltage [%]
vk_lv_percent*	float	\(>\) 0	short circuit voltage from high to low voltage [%]
vkr_hv_percent*	float	\(\geq\) 0	real part of short circuit voltage from high to medium voltage [%]
vkr_mv_percent*	float	\(\geq\) 0	real part of short circuit voltage from medium to low voltage [%]
vkr_lv_percent*	float	\(\geq\) 0	real part of short circuit voltage from high to low voltage [%]
pfe_kw*	float	\(\geq\) 0	iron losses [kW]
i0_percent*	float	\(\geq\) 0	open loop losses [%]
shift_mv_degree	float		transformer phase shift angle at the MV side
shift_lv_degree	float		transformer phase shift angle at the LV side
tap_side	string	“hv”, “mv”, “lv”	defines if tap changer is positioned on high- medium- or low voltage side
tap_neutral	integer
tap_min	integer		minimum tap position
tap_max	integer		maximum tap position
tap_step_percent	float	\(>\) 0	tap step size [%]
tap_step_degree	float		tap step size for voltage angle
tap_at_star_point	bool		whether the tap changer is modelled at terminal or at star point
tap_pos	integer		current position of tap changer
in_service*	boolean	True/False	specifies if the transformer is in service.

*necessary for executing a power flow calculation.

Note

Three Winding Transformer loading can not yet be constrained with the optimal power flow.

Electric Model

Three Winding Transformers are modelled by three two-winding transformers in \(Y\)-connection:

The parameters of the three transformers are defined as follows:

	T1	T2	T3
hv_bus	hv_bus	auxiliary bus	auxiliary bus
lv_bus	auxiliary bus	mv_bus	lv_bus
sn_mva	sn_hv_mva	sn_mv_mva	sn_lv_mva
vn_hv_kv	vn_hv_kv	vn_hv_kv	vn_hv_kv
vn_lv_kv	vn_hv_kv	vn_mv_kv	vn_lv_kv
vk_percent	\(v_{k, t1}\)	\(v_{k, t2}\)	\(v_{k, t3}\)
vkr_percent	\(v_{r, t1}\)	\(v_{r, t2}\)	\(v_{r, t3}\)
shift_degree	0	shift_mv_degree	shift_lv_degree

The iron loss (pfe_kw) and open loop loss (i0_percent) of the 3W transformer is by default attributed to T1 (‘hv’). The parameter ‘trafo3w_losses’ in the runpp function however also allows to assign the losses to T2 (‘mv’), T3(‘lv’) or to the star point (‘star’).

To calculate the short-circuit voltages \(v_{k, t1..t3}\) and \(v_{r, t1..t3}\), first all short-circuit voltages are converted from side based values to branch based values

\begin{align*} v'_{k, hm} &= vk\_hv\_percent \cdot \frac{sn\_hv\_mva}{min(sn\_hv\_mva, sn\_mv\_mva)} \\ v'_{k, ml} &= vk\_mv\_percent \cdot \frac{sn\_hv\_mva}{min(sn\_mv\_mva, sn\_lv\_mva)} \\ v'_{k, lh} &= vk\_lv\_percent \cdot \frac{sn\_hv\_mva}{min(sn\_hv\_mva, sn\_lv\_mva)} \end{align*}

These transformer now represent a \(\Delta\) connection of the equivalent transformers. A \(\Delta-Y\) conversion is therefore applied to recieve the parameters in \(Y\)-connection:

\begin{align*} v'_{k, T1} &= \frac{1}{2} (v'_{k, hm} + v'_{k, lh} - v'_{k, ml}) \\ v'_{k, T2} &= \frac{1}{2} (v'_{k, ml} + v'_{k, hm} - v'_{k, lh}) \\ v'_{k, T3} &= \frac{1}{2} (v'_{k, ml} + v'_{k, lh} - v'_{k, hm}) \end{align*}

Since these voltages are given relative to the high voltage side, they have to be transformed back to the voltage level of each transformer:

\begin{align*} v_{k, T1} &= v'_{k, t1} \\ v_{k, T2} &= v'_{k, t2} \cdot \frac{sn\_mv\_mva}{sn\_hv\_mva} \\ v_{k, T3} &= v'_{k, t3} \cdot \frac{sn\_lv\_mva}{sn\_hv\_mva} \end{align*}

The real part of the short-circuit voltage is calculated in the same way.

The definition of how impedances are calculated for the two winding transformer from these parameters can be found here.

Note

All short circuit voltages are given relative to the maximum apparent power flow. For example vk_hv_percent is the short circuit voltage from the high to the medium level, it is given relative to the minimum of the rated apparent power in high and medium level: min(sn_hv_mva, sn_mv_mva). This is consistent with most commercial network calculation software (e.g. PowerFactory). Some tools (like PSS Sincal) however define all short circuit voltages relative to the overall rated apparent power of the transformer: max(sn_hv_mva, sn_mv_mva, sn_lv_mva). You might have to convert the values depending on how the short-circuit voltages are defined.

The tap changer adapts the nominal voltages of the transformer in the equivalent to the 2W-Model:

	tap_side=”hv”	tap_side=”mv”	tap_side=”lv”
\(V_{n, HV, transformer}\)	\(vnh\_kv \cdot n_{tap}\)	\(vnh\_kv\)	\(vnh\_kv\)
\(V_{n, MV, transformer}\)	\(vnm\_kv\)	\(vnm\_kv \cdot n_{tap}\)	\(vnm\_kv\)
\(V_{n, LV, transformer}\)	\(vnl\_kv\)	\(vnl\_kv\)	\(vnl\_kv \cdot n_{tap}\)

with

\begin{align*} n_{tap} = 1 + (tap\_pos - tap\_neutral) \cdot \frac{tap\_st\_percent}{100} \end{align*}

The variable tap_side controls if the tap changer is located at T1 (‘hv’), T2 (‘mv’) or T3 (‘lv’). The tap_at_star_point variable controls if the tap changer is located at the star point of the three winding transformer or at the terminal side (hv/mv/lv bus).

See also

MVA METHOD FOR 3-WINDING TRANSFORMER

Result Parameters

net.res_trafo3w

Parameter	Datatype	Explanation
p_hv_mw	float	active power flow at the high voltage transformer bus [MW]
q_hv_mvar	float	reactive power flow at the high voltage transformer bus [kVar]
p_mv_mw	float	active power flow at the medium voltage transformer bus [MW]
q_mv_mvar	float	reactive power flow at the medium voltage transformer bus [kVar]
p_lv_mw	float	active power flow at the low voltage transformer bus [MW]
q_lv_mvar	float	reactive power flow at the low voltage transformer bus [kVar]
pl_mw	float	active power losses of the transformer [MW]
ql_mvar	float	reactive power consumption of the transformer [Mvar]
i_hv_ka	float	current at the high voltage side of the transformer [kA]
i_mv_ka	float	current at the medium voltage side of the transformer [kA]
i_lv_ka	float	current at the low voltage side of the transformer [kA]
vm_hv_pu	float	voltage magnitude at the high voltage bus [pu]
vm_mv_pu	float	voltage magnitude at the medium voltage bus [pu]
vm_lv_pu	float	voltage magnitude at the low voltage bus [pu]
va_hv_degree	float	voltage angle at the high voltage bus [degrees]
va_mv_degree	float	voltage angle at the medium voltage bus [degrees]
va_lv_degree	float	voltage angle at the low voltage bus [degrees]
loading_percent	float	transformer utilization [%]

\begin{align*} p\_hv\_mw &= Re(\underline{v}_{hv} \cdot \underline{i}_{hv}) \\ q\_hv\_mvar &= Im(\underline{v}_{hv} \cdot \underline{i}_{hv}) \\ p\_mv\_mw &= Re(\underline{v}_{mv} \cdot \underline{i}_{mv}) \\ q\_mv\_mvar &= Im(\underline{v}_{mv} \cdot \underline{i}_{mv}) \\ p\_lv\_mw &= Re(\underline{v}_{lv} \cdot \underline{i}_{lv}) \\ q\_lv\_mvar &= Im(\underline{v}_{lv} \cdot \underline{i}_{lv}) \\ pl\_mw &= p\_hv\_mw + p\_lv\_mw \\ ql\_mvar &= q\_hv\_mvar + q\_lv\_mvar \\ i\_hv\_ka &= i_{hv} \\ i\_mv\_ka &= i_{mv} \\ i\_lv\_ka &= i_{lv} \end{align*}

The definition of the transformer loading depends on the trafo_loading parameter of the power flow.

For trafo_loading=’current’, the loading is calculated as:

\begin{align*} loading\_percent &= max(\frac{i_{hv} \cdot vn\_hv\_kv}{sn\_hv\_mva}, \frac{i_{mv} \cdot vn\_mv\_kv}{sn\_mv\_mva}, \frac{i_{lv} \cdot vn\_lv\_kv}{sn\_lv\_mva}) \cdot 100 \end{align*}

For trafo_loading=’power’, the loading is defined as:

\begin{align*} loading\_percent &= max( \frac{i_{hv} \cdot v_{hv}}{sn\_hv\_mva}, \frac{i_{mv} \cdot v_{mv}}{sn\_mv\_mva}, \frac{i_{lv} \cdot v_{lv}}{sn\_lv\_mva}) \cdot 100 \end{align*}