Two synchronous machines are connected through threephase transformers to the transmission line the ratings and reactances of
the machines and transformers are

machines 1 and 2 100 mva 20 kv x1x220x1 x2 20 x04x0 4 xr5xr 5
transformers t1

Question

Two synchronous machines are connected through three-phase transformers to the transmission line. The ratings and reactances of the machines and transformers are:

Machines 1 and 2: 100 MVA, 20 kV, $X_1 = X_2 = 20\%$ , $X_0 = 4\%$ , $X_r = 5\%$ .
Transformers T1 and T2: 100 MVA, 20Δ/345Y kV, $X = 8\%$ . Both transformers’ Y side is solidly grounded.
The transmission line has the following parameters: 100 MVA, 345 kV, $X_1 = X_2 = 15\%$ , $X_0 = 50\%$ .

Task:
Draw each of the three sequence networks.

(The diagram shows two machines, two transformers (T1 and T2), and a transmission line connecting them.)

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Kim McDonald · Answer

To get started with drawing the sequence networks for the given system, first, we need to understand each component's sequence impedance in per unit. Here's a synthesis of the information provided:

Machine Ratings and Reactances

MVA: 100 MVA
Voltage: 20 kV
Positive and Negative Sequence Reactance (X1, X2): 20%
Zero Sequence Reactance (X0): 4%
Reactance of Rotor Resistance (Xr): 5%

Transformer Ratings and Reactances

MVA: 100 MVA
Voltage: 20Δ/345Y kV
Impedance (X): 8%
Y-side: Solidly grounded

Transmission Line Parameters

MVA: 100 MVA
Voltage: 345 kV
Positive and Negative Sequence Reactance (X1, X2): 15%
Zero Sequence Reactance (X0): 50%

Given these values, let's consider the connections and draw the sequence networks:

Positive Sequence Network

Machine 1 → Transformer T1:
- Machine impedance: $j0.20 ext{ pu}$
- Transformer T1 impedance: $j0.08 ext{ pu}$
Transmission Line:
- $j0.15 ext{ pu}$
Transformer T2 → Machine 2:
- Transformer T2 impedance: $j0.08 ext{ pu}$
- Machine impedance: $j0.20 ext{ pu}$

Diagram

  [j0.20] -- [j0.08] -- [j0.15] -- [j0.08] -- [j0.20]
  Machine  Transformer   Line    Transformer  Machine
     1          T1                  T2           2

Negative Sequence Network

The negative sequence network has the same topology and similar impedances as the positive sequence network:

Machine 1 → Transformer T1:
- Machine impedance: $j0.20 ext{ pu}$
- Transformer T1 impedance: $j0.08 ext{ pu}$
Transmission Line:
- $j0.15 ext{ pu}$
Transformer T2 → Machine 2:
- Transformer T2 impedance: $j0.08 ext{ pu}$
- Machine impedance: $j0.20 ext{ pu}$

Diagram

  [j0.20] -- [j0.08] -- [j0.15] -- [j0.08] -- [j0.20]
  Machine  Transformer   Line    Transformer  Machine
     1          T1                  T2           2

Zero Sequence Network

The zero sequence network requires more care since only the Y-connected windings and transmission line zero sequence impedances are to be considered.

Machine 1:
- Impedance: $j0.04 ext{ pu}$
Transformer T1: Since it's grounded at the Y-side, consider the impedance from the Y-side. $j0.08 ext{ pu}$
Transmission Line:
- Zero sequence impedance: $j0.50 ext{ pu}$
Transformer T2: Similarly, consider the Y-side impedance. $j0.08 ext{ pu}$
Machine 2:
- Impedance: $j0.04 ext{ pu}$

Diagram

  [j0.04] -- [j0.08] -- [j0.50] -- [j0.08] -- [j0.04]
  Machine  Transformer   Line    Transformer  Machine
     1          T1                  T2           2

To summarize, for each sequence network, the machines, transformers, and transmission line reactances (per unit values) are connected end-to-end while taking care of the grounding effects on the zero-sequence network. The diagrams show series connections of the respective components' impedances.

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