Three Winding Transformer

See also

Unit Systems and Conventions
Standard Type Libraries

Create Function

pandapower.create_transformer3w(net, hv_bus, mv_bus, lv_bus, std_type, name=None, tp_pos=nan, in_service=True, index=None, max_loading_percent=nan, tap_at_star_point=False)

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

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

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

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_transformer3w_from_parameters(net, hv_bus, mv_bus, lv_bus, vn_hv_kv, vn_mv_kv, vn_lv_kv, sn_hv_kva, sn_mv_kva, sn_lv_kva, vsc_hv_percent, vsc_mv_percent, vsc_lv_percent, vscr_hv_percent, vscr_mv_percent, vscr_lv_percent, pfe_kw, i0_percent, shift_mv_degree=0., shift_lv_degree=0., tp_side=None, tp_st_percent=nan, tp_st_degree=nan, tp_pos=nan, tp_mid=nan, tp_max=nan, tp_min=nan, name=None, in_service=True, index=None, max_loading_percent=nan, tap_at_star_point=False)

Adds a three-winding transformer in table net[“trafo3w”].

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

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

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

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

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

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

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

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

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

pfe_kw (float) - iron losses

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*

tp_st_percent (float) - Tap step in percent

tp_st_degree (float) - Tap phase shift angle in degrees

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

tp_mid (int, nan) - default tap position

tp_min (int, nan) - Minimum tap position

tp_max (int, nan) - Maximum tap position

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

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

* only considered in loadflow if calculate_voltage_angles = True **The model currently only supports one tap-changer per 3W Transformer.

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

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_kva=40, sn_mv_kva=20, sn_lv_kva=20, vn_hv_kv=110, vn_mv_kv=20, vn_lv_kv=10, vsc_hv_percent=10,vsc_mv_percent=11, vsc_lv_percent=12, vscr_hv_percent=0.3, vscr_mv_percent=0.31, vscr_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 maximum apparent power flow. For example vsc_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_kva, sn_mv_kva). 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_kva, sn_mv_kva, sn_lv_kva). 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_kva*	float	\(>\) 0	rated apparent power on high voltage side [kVA]
sn_mv_kva*	float	\(>\) 0	rated apparent power on medium voltage side [kVA]
sn_lv_kva*	float	\(>\) 0	rated apparent power on low voltage side [kVA]
vsc_hv_percent*	float	\(>\) 0	short circuit voltage from high to medium voltage [%]
vsc_mv_percent*	float	\(>\) 0	short circuit voltage from medium to low voltage [%]
vsc_lv_percent*	float	\(>\) 0	short circuit voltage from high to low voltage [%]
vscr_hv_percent*	float	\(\geq\) 0	real part of short circuit voltage from high to medium voltage [%]
vscr_mv_percent*	float	\(\geq\) 0	real part of short circuit voltage from medium to low voltage [%]
vscr_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
tp_side	string	“hv”, “mv”, “lv”	defines if tap changer is positioned on high- medium- or low voltage side
tp_mid	integer
tp_min	integer		minimum tap position
tp_max	integer		maximum tap position
tp_st_percent	float	\(>\) 0	tap step size [%]
tp_st_degree	float		tap step size for voltage angle
tp_at_star_point	bool		whether the tap changer is modelled at terminal or at star point
tp_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:

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_kva	sn_hv_kva	sn_mv_kva	sn_lv_kva
vn_hv_kv	vn_hv_kv	vn_hv_kv	vn_hv_kv
vn_lv_kv	vn_hv_kv	vn_mv_kv	vn_lv_kv
vsc_percent	\(v_{k, t1}\)	\(v_{k, t2}\)	\(v_{k, t3}\)
vscr_percent	\(v_{r, t1}\)	\(v_{r, t2}\)	\(v_{r, t3}\)
pfe_kw	pfe_kw	0	0
i0_percent	i0_percent	0	0
shift_degree	shift_degree	0	0

The definition of the two winding transformer parameter can be found here.

To calculate the short-circuit voltages \(v_{k, t1..t3}\) and \(v_{r, t1..t3}\), first all short-circuit voltages are converted to the high voltage level:

\begin{align*} v'_{k, h} &= vsc\_hv\_percent \\ v'_{k, m} &= vsc\_mv\_percent \cdot \frac{sn\_hv\_kva}{sn\_mv\_kva} \\ v'_{k, l} &= vsc\_lv\_percent \cdot \frac{sn\_hv\_kva}{sn\_lv\_kva} \end{align*}

The short-circuit voltages of the three transformers are then calculated as follows:

\begin{align*} v'_{k, t1} &= \frac{1}{2} (v'_{k, h} + v'_{k, l} - v'_{k, m}) \\ v'_{k, t2} &= \frac{1}{2} (v'_{k, m} + v'_{k, h} - v'_{k, l}) \\ v'_{k, t3} &= \frac{1}{2} (v'_{k, m} + v'_{k, l} - v'_{k, h}) \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\_kva}{sn\_hv\_kva} \\ v_{k, t3} &= v'_{k, t3} \cdot \frac{sn\_lv\_kva}{sn\_hv\_kva} \end{align*}

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

Note

All short circuit voltages are given relative to the maximum apparent power flow. For example vsc_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_kva, sn_mv_kva). 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_kva, sn_mv_kva, sn_lv_kva). 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:

	tp_side=”hv”	tp_side=”mv”	tp_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 + (tp\_pos - tp\_mid) \cdot \frac{tp\_st\_percent}{100} \end{align*}

See also

MVA METHOD FOR 3-WINDING TRANSFORMER

Result Parameters

net.res_trafo3w

Parameter	Datatype	Explanation
p_hv_kw	float	active power flow at the high voltage transformer bus [kW]
q_hv_kvar	float	reactive power flow at the high voltage transformer bus [kVar]
p_mv_kw	float	active power flow at the medium voltage transformer bus [kW]
q_mv_kvar	float	reactive power flow at the medium voltage transformer bus [kVar]
p_lv_kw	float	active power flow at the low voltage transformer bus [kW]
q_lv_kvar	float	reactive power flow at the low voltage transformer bus [kVar]
pl_kw	float	active power losses of the transformer [kW]
ql_kvar	float	reactive power consumption of the transformer [kvar]
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]
loading_percent	float	transformer utilization [%]

\begin{align*} p\_hv\_kw &= Re(\underline{v}_{hv} \cdot \underline{i}_{hv}) \\ q\_hv\_kvar &= Im(\underline{v}_{hv} \cdot \underline{i}_{hv}) \\ p\_mv\_kw &= Re(\underline{v}_{mv} \cdot \underline{i}_{mv}) \\ q\_mv\_kvar &= Im(\underline{v}_{mv} \cdot \underline{i}_{mv}) \\ p\_lv\_kw &= Re(\underline{v}_{lv} \cdot \underline{i}_{lv}) \\ q\_lv\_kvar &= Im(\underline{v}_{lv} \cdot \underline{i}_{lv}) \\ pl\_kw &= p\_hv\_kw + p\_lv\_kw \\ ql\_kvar &= q\_hv\_kvar + q\_lv\_kvar \\ 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\_kva}, \frac{i_{mv} \cdot vn\_mv\_kv}{sn\_mv\_kva}, \frac{i_{lv} \cdot vn\_lv\_kv}{sn\_lv\_kva}) \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\_kva}, \frac{i_{mv} \cdot v_{mv}}{sn\_mv\_kva}, \frac{i_{lv} \cdot v_{lv}}{sn\_lv\_kva}) \cdot 100 \end{align*}