Transformer

Create Function

Transformers can be either created from the standard type library (create_transformer) or with custom values (create_transformer_from_parameters).

Input Parameters

net.trafo

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
lv_bus*	integer		low voltage bus index of the transformer
sn_mva*	float	\(>\) 0	rated apparent power of the transformer [MVA]
vn_hv_kv*	float	\(>\) 0	rated voltage at high voltage bus [kV]
vn_lv_kv*	float	\(>\) 0	rated voltage at low voltage bus [kV]
vk_percent*	float	\(>\) 0	short circuit voltage [%]
vkr_percent*	float	\(\geq\) 0	real component of short circuit voltage [%]
pfe_kw*	float	\(\geq\) 0	iron losses [kW]
i0_percent*	float	\(\geq\) 0	open loop losses in [%]
vk0_percent***	float	\(\geq\) 0	zero sequence relative short-circuit voltage
vkr0_percent***	float	\(\geq\) 0	real part of zero sequence relative short-circuit voltage
mag0_percent***	float	\(\geq\) 0	z_mag0 / z0 ratio between magnetizing and short circuit impedance (zero sequence)
mag0_rx***	float		zero sequence magnetizing r/x ratio
si0_hv_partial***	float	\(\geq\) 0	zero sequence short circuit impedance distribution in hv side
vector_group***	String	‘Dyn’,’Yyn’,’Yzn’,’YNyn’	Vector Groups ( required for zero sequence model of transformer )
shift_degree*	float		transformer phase shift angle
tap_side	string	“hv”, “lv”	defines if tap changer is at the high- or low voltage side
tap_neutral	integer		rated tap position
tap_min	integer		minimum tap position
tap_max	integer		maximum tap position
tap_step_percent	float	\(>\) 0	tap step size for voltage magnitude [%]
tap_step_degree	float	\(\geq\) 0	tap step size for voltage angle
tap_pos	integer		current position of tap changer
tap_phase_shifter	bool		defines whether the transformer is an ideal phase shifter
parallel	int	\(>\) 0	number of parallel transformers
max_loading_percent**	float	\(>\) 0	Maximum loading of the transformer with respect to sn_mva and its corresponding current at 1.0 p.u.
df	float	1 \(\geq\) df \(>\) 0	derating factor: maximal current of transformer in relation to nominal current of transformer (from 0 to 1)
in_service*	boolean	True / False	specifies if the transformer is in service
oltc*	boolean	True / False	specifies if the transformer has an OLTC (short-circuit relevant)
power_station_unit*	boolean	True / False	specifies if the transformer is part of a power_station_unit (short-circuit relevant).

*necessary for executing a balanced power flow calculation
**optimal power flow parameter
***necessary for executing a three phase power flow / single phase short circuit

Note

The transformer loading constraint for the optimal power flow corresponds to the option trafo_loading=”current”:

Note

vkr_percent can be calculated as follow :

\begin{align*} vkr\_percent &= \frac{P\_cu}{S\_trafo} \cdot 100 \end{align*}

Where
P_cu is the power loss in the copper in kW
S_trafo is the rated apparent power of the transformer in kW

Electric Model

The equivalent circuit used for the transformer can be set in the power flow with the parameter “trafo_model”.

trafo_model=’t’:

sequence = 0:

trafo_model=’pi’:

Transformer Ratio

The magnitude of the transformer ratio is given as:

\begin{align*} n &= \frac{V_{ref, HV, transformer}}{V_{ref, LV, transformer}} \cdot \frac{V_{ref, LV bus}}{V_{ref, HV bus}} \end{align*}

The reference voltages of the high- and low voltage buses are taken from the net.bus table. The reference voltage of the transformer is taken directly from the transformer table:

\begin{align*} V_{ref, HV, transformer} &= vn\_hv\_kv \\ V_{ref, LV, transformer} &= vn\_lv\_kv \end{align*}

If the power flow is run with voltage_angles=True, the complex ratio is given as:

\begin{align*} \underline{n} &= n \cdot e^{j \cdot \theta \cdot \frac{\pi}{180}} \\ \theta &= shift\_degree \end{align*}

Otherwise, the ratio does not include a phase shift:

\begin{align*} \underline{n} &= n \end{align*}

Impedance Values

The short-circuit impedance is calculated as:

\begin{align*} z_k &= \frac{vk\_percent}{100} \cdot \frac{net.sn\_mva}{sn\_mva} \\ r_k &= \frac{vkr\_percent}{100} \cdot \frac{net.sn\_mva}{sn\_mva} \\ x_k &= \sqrt{z^2 - r^2} \\ \underline{z}_k &= r_k + j \cdot x_k \end{align*}

The magnetising admittance is calculated as:

\begin{align*} y_m &= \frac{i0\_percent}{100} \\ g_m &= \frac{pfe\_kw}{sn\_mva \cdot 1000} \cdot \frac{net.sn\_mva}{sn\_mva} \\ b_m &= \sqrt{y_m^2 - g_m^2} \\ \underline{y_m} &= g_m - j \cdot b_m \end{align*}

The values calculated in that way are relative to the rated values of the transformer. To transform them into the per unit system, they have to be converted to the rated values of the network:

\begin{align*} Z_{N} &= \frac{V_{N}^2}{S_{N}} \\ Z_{ref, trafo} &= \frac{vn\_lv\_kv^2 \cdot net.sn\_mva}{sn\_mva} \\ \underline{z} &= \underline{z}_k \cdot \frac{Z_{ref, trafo}}{Z_{N}} \\ \underline{y} &= \underline{y}_m \cdot \frac{Z_{N}}{Z_{ref, trafo}} \\ \end{align*}

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

Tap Changer

Longitudinal regulator

A longitudinal regulator can be modeled by setting tap_phase_shifter to False and defining the tap changer voltage step with tap_step_percent.

The reference voltage is then multiplied with the tap factor:

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

On which side the reference voltage is adapted depends on the \(tap\_side\) variable:

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

Note

The variables tap_min and tap_max are not considered in the power flow. The user is responsible to ensure that tap_min < tap_pos < tap_max!

Cross regulator

In addition to tap_step_percent a value for tap_step_degree can be defined to model an angle shift for each tap, resulting in a cross regulator that affects the magnitude as well as the angle of the transformer ratio.

Ideal phase shifter

If tap_phase_shifter is set to True, the tap changer is modeled as an ideal phase shifter, meaning that a constant angle shift is added with each tap step:

\begin{align*} \underline{n} &= n \cdot e^{j \cdot (\theta + \theta_{tp}) \cdot \frac{\pi}{180}} \\ \theta &= shift\_degree \end{align*}

The angle shift can be directly defined in tap_step_degree, in which case:

\begin{align*} \theta_{tp} = tap\_st\_degree \cdot (tap\_pos - tap\_neutral) \end{align*}

or it can be given as a constant voltage step in tap_step_percent, in which case the angle is calculated as:

\begin{align*} \theta_{tp} = 2 \cdot arcsin(\frac{1}{2} \cdot \frac{tap\_st\_percent}{100}) \cdot (tap\_pos - tap\_neutral) \end{align*}

If both values are given for an ideal phase shift transformer, the power flow will raise an error.

Result Parameters

net.res_trafo

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 [MVar]
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 [MVar]
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_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_lv_pu	float	voltage magnitude at the low voltage bus [pu]
va_hv_degree	float	voltage angle at the high voltage bus [degrees]
va_lv_degree	float	voltage angle at the low voltage bus [degrees]
loading_percent	float	load utilization relative to rated power [%]

\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\_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\_lv\_ka &= i_{lv} \end{align*}

net.res_trafo_3ph

Parameter	Datatype	Explanation
p_a_hv_mw	float	active power flow at the high voltage transformer bus : Phase A [MW]
q_a_hv_mvar	float	reactive power flow at the high voltage transformer bus : Phase A [MVar]
p_b_hv_mw	float	active power flow at the high voltage transformer bus : Phase B [MW]
q_b_hv_mvar	float	reactive power flow at the high voltage transformer bus : Phase B [MVar]
p_c_hv_mw	float	active power flow at the high voltage transformer bus : Phase C [MW]
q_c_hv_mvar	float	reactive power flow at the high voltage transformer bus : Phase C [MVar]
p_a_lv_mw	float	active power flow at the low voltage transformer bus : Phase A [MW]
q_a_lv_mvar	float	reactive power flow at the low voltage transformer bus : Phase A [MVar]
p_b_lv_mw	float	active power flow at the low voltage transformer bus : Phase B [MW]
q_b_lv_mvar	float	reactive power flow at the low voltage transformer bus : Phase B [MVar]
p_c_lv_mw	float	active power flow at the low voltage transformer bus : Phase C [MW]
q_c_lv_mvar	float	reactive power flow at the low voltage transformer bus : Phase C [MVar]
pl_a_mw	float	active power losses of the transformer : Phase A [MW]
ql_a_mvar	float	reactive power consumption of the transformer : Phase A [Mvar]
pl_b_mw	float	active power losses of the transformer : Phase B [MW]
ql_b_mvar	float	reactive power consumption of the transformer : Phase B [Mvar]
pl_c_mw	float	active power losses of the transformer : Phase C [MW]
ql_c_mvar	float	reactive power consumption of the transformer : Phase C [Mvar]
i_a_hv_ka	float	current at the high voltage side of the transformer : Phase A [kA]
i_a_lv_ka	float	current at the low voltage side of the transformer : Phase A [kA]
i_b_hv_ka	float	current at the high voltage side of the transformer : Phase B [kA]
i_b_lv_ka	float	current at the low voltage side of the transformer : Phase B [kA]
i_c_hv_ka	float	current at the high voltage side of the transformer : Phase C [kA]
i_c_lv_ka	float	current at the low voltage side of the transformer : Phase C [kA]
loading_percent	float	load utilization relative to rated power [%]

\begin{align*} p\_hv\_mw_{phase} &= Re(\underline{v}_{hv_{phase}} \cdot \underline{i}^*_{hv_{phase}}) \\ q\_hv\_mvar_{phase} &= Im(\underline{v}_{hv_{phase}} \cdot \underline{i}^*_{hv_{phase}}) \\ p\_lv\_mw_{phase} &= Re(\underline{v}_{lv_{phase}} \cdot \underline{i}^*_{lv_{phase}}) \\ q\_lv\_mvar_{phase} &= Im(\underline{v}_{lv_{phase}} \cdot \underline{i}^*_{lv_{phase}}) \\ pl\_mw_{phase} &= p\_hv\_mw_{phase} + p\_lv\_mw_{phase} \\ ql\_mvar_{phase} &= q\_hv\_mvar_{phase} + q\_lv\_mvar_{phase} \\ i\_hv\_ka_{phase} &= i_{hv_{phase}} \\ i\_lv\_ka_{phase}&= i_{lv_{phase}} \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\_mva}, \frac{i_{lv} \cdot vn\_lv\_kv}{sn\_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\_mva}, \frac{i_{lv} \cdot v_{lv}}{sn\_mva}) \cdot 100 \end{align*}