Impedance and Reactance Diagrams in Power Systems

Demonstrative Video

Impedance & Reactance Diagram

The impedance or reactance diagram is the equivalent circuit of the PS in which the various components are represented by their approximate or simplified equivalent circuit.
This equivalent circuit of a PS is used to analyse the performance of a system under load conditions or to analyse the condition of the system under fault.

Impedance Diagram

Impedance of a PS diagram is used for load flow studies.
The impedance diagram can be obtained from SLD by replacing all the components by their \(1\phi\) equivalent circuits.
Following approximations are made:
1. The current limiting impedances connected between the generator neutral and ground are neglected since under balance condition no current will flow through neutral.
2. The magnetizing current of a TF is very low when compared to load current the shunt branches in the equivalent circuit of the TF can be neglected.
3. If the inductive reactance of a component is very high when compared to resistance then the resistance can be omitted which introduces a little error in calculation.

Reactance Diagram

The reactance diagram is used for fault calculations
Following approximations are made (when the system is balanced)
1. The neutral to ground impedance of the generator is neglected for symmetrical faults
2. Shunt branches in the equivalent circuit of transformer are neglected
3. The resistances in the equivalent circuits of various components of the system are omitted
4. All static loads are neglected
5. Induction motors are neglected in computing fault current a few cycles after the fault occurs, because the current contributed by an IM dies very quickly after it is short-circuited
6. The capacitance of the transmission lines are neglected

Conclusion:

The reactance diagram can be obtained from impedance diagram if we omit all static loads, all residences, shunt branches of transformer, and capacitance of TL.

Impedance for reactance of various components of PS in a SLD are expressed in % or P.U. calculated by taking their ratings as base values.
When the impedance or reactance diagram is formed, all the impedances and reactances should be expressed in P.U. calculated on a common base value.
Hence it is necessary to convert all the p.u reactances to a common base.
\[X_{\text{p.u,new}} = X_{\text{p.u,old}} \times \left(\dfrac{KV_{b,old}}{KV_{b,new}}\right)^2 \times \left(\dfrac{MVA_{b,new}}{MVA_{b,old}}\right)\]
The conversion of units reactances from one base to another can be performed using the following equation

Procedure to form reactance diagram from SLD

Select a \(KVA_b\) or \(MVA_b\)
- This will be same for all sections of the PS
- In case of \(3\phi\) PS, the \(KVA_b\) or \(MVA_b\) is \(3\phi\) power rating
Select \(KV_b\) for one section of the PS
- In case of \(3\phi\) PS, the \(KV_b\) is a line value
- Various sections of PS works at different voltage levels and the voltage conversion is achieved by means of T/F
- Hence \(KV_b\) of one section of PS should be converted to a \(KV_b\) corresponding to another section using the TF voltage ratio
- In case of \(3\phi\) TF \(L-L\) voltage ratio is used to transfer the \(KV_b\) on one section to another section

\[\begin{aligned} KV_{b}~\text{on LT section} & =KV_{b}~\text{on HT section}\times\dfrac{\text{LT voltage rating}}{\text{HT voltage rating}}\\ KV_{b}~\text{on HT section} & =KV_{b}~\text{on LT section}\times\dfrac{\text{HT voltage rating}}{\text{LT voltage rating}} \end{aligned}\]

Calculation of p.u. value
- Components \(Z\) are expressed either in \(\Omega\) (actual impedance) or in p.u.
- \[\text{p.u. reactance} = \dfrac{\text{Actual rectance in ohms}}{\text{Base impedance}}\]
  If given in actual value convert to p.u values using
- \[X_{\text{p.u,new}} = X_{\text{p.u,old}} \times \left(\dfrac{KV_{b,old}}{KV_{b,new}}\right)^2 \times \left(\dfrac{MVA_{b,new}}{MVA_{b,old}}\right)\]
  In case of conversion from old base to new base