Skip to content

Latest commit

 

History

History
54 lines (40 loc) · 3.26 KB

two_winding_transformer_model.md

File metadata and controls

54 lines (40 loc) · 3.26 KB
Raw

(two_winding_transformer_model)=

Two winding transformer

Attributes, Units and Remarks

Input and Result Attributes and Units are defined at PowerSystemDataModel. Please refer to:

  • Input: {doc}PowerSystemDataModel - Two Winding Transformer Model <psdm:models/input/grid/transformer2w>
  • Result: {doc}PowerSystemDataModel - Two Winding Transformer Model <psdm:models/result/grid/transformer2w>

Calculation of basic equivalent circuit elements

... based on derived values. All values are given with regard to the high voltage side.

  1. Reference Impedance: $Z_{Ref}=\frac{V^{2}{Ref}}{S{Ref}},Z_{Ref}=\Omega$ based on externally given reference voltage $V_{Ref}$ and reference apparent power $S_{Ref}$
  2. Reference Impedance regarding the transformer's reference system: $Z_{Ref,Transf} = \frac{V^{2}{HV}}{S{Rated}}, [Z_{Ref,Transf}] = \Omega$
  3. Reference Current:$I_{Ref,Transf} = \frac{S_Ref,Transf}{\sqrt{3} \cdot V_{HV}}, [I_{Ref,Tranf}] = A$
  4. Short circuit impedance: $Z_{SC} = v_{SC} \cdot Z_{Ref,Transf}, [Z_{SC}] = \Omega$ with $[v_{SC}] = %$
  5. Short circuit resistance:$R_{SC} = \frac{P_{C_{u}}}{3 \cdot I^{2}{Ref,Transf}}, [R{SC}] = \Omega$
  6. Short circuit reactance: $X_{SC} = \sqrt{Z^{2}{SC} - R^{2}{SC}}, [X_{SC}] = \Omega$
  7. Main field impedance: $Z_{M} = \frac{V_{HV}}{\sqrt{3} \cdot i_{noLoad \cdot I_{Ref,Transf}}}, Z_{M} = \Omega$
  8. Main field resistance: $R_{M} = \frac{V^{2}{HV}}{P{F_{e}}}, [R_{M}] = \Omega$
  9. Main field reactance: $X_{M} = \frac{1}{\sqrt{\frac{1}{Z^{2}{M}} - \frac{1}{R^{2}{M}}}}, [R_{M}] = \Omega$

When the load flow calculation asks for the values with regard to the low voltage side, each Impedance has to be divided by square of the transformers default transmission ration $\gamma = \frac{V_{HV}}{V_{LV}}$:

  1. Short circuit resistance: $R_{SC,LV} = \frac{R_{SC}}{\gamma^{2}}$
  2. Short circuit reactance: $X_{SC,LV} = \frac{X_{SC}}{\gamma^{2}}$
  3. Main field resistance: $R_{M,LV} = \frac{R_{M}}{\gamma^{2}}$
  4. Main field reactance: $X_{M,LV} = \frac{X_{M}}{\gamma^{2}}$

Finally all values are delivered as per unit-values and ready to use in the fundamental $\pi$circuit:

  1. Short circuit conductance: $g_{ij} = \frac{Z_{Ref}}{R_{SC}}$
  2. Short circuit susceptance: $b_{ij} = \frac{Z_{Ref}}{X_{SC}}$
  3. Phase to ground conductance: $g_{0} = \frac{Z_{Ref}}{2 \cdot R_{M}}$
  4. Phase to ground susceptance: $B_{0} = \frac{Z_{Ref}}{2 \cdot X_{M}}$

If there is a tap changer, this has to be taken into account as well:

  1. Tap ratio:$\tau = 1 - (t_{actual}-t_{neutral}) \cdot \frac{dV}{100}$
  2. Tap changer is on low voltage side:
  3. Short circuit conductance: $g_{ij} = \frac{Z_{Ref}}{R_{SC}} \cdot \tau$
  4. Short circuit susceptance: $b_{ij} = \frac{Z_{Ref}}{X_{SC}} \cdot \tau$
  5. Phase to ground conductance: $g_{0} = \frac{Z_{Ref}}{2 \cdot R_{M}}$
  6. Phase to ground susceptance: $b_{0} = \frac{Z_{Ref}}{2 \cdot X_{M}} \cdot \tau^{2}$
  7. Tap changer is on highvoltage side:
  8. Short circuit conductance:$g_{ij} = \frac{Z_{Ref}}{R_{SC} \cdot \tau}$
  9. Short circuit susceptance:$b_{ij} = \frac{Z_{Ref}}{X_{SC} \cdot \tau}$
  10. Phase to ground conductance:$g_{0} = \frac{Z_{Ref}}{2 \cdot R_{M}}$
  11. Phase to ground susceptance:$b_{0} = \frac{Z_{Ref}}{2 \cdot X_{M} \cdot \tau^{2}}$