Reactance diagram: 100 MVA base, two parallel paths

Significance of the reactance diagram

A reactance diagram is the per-phase equivalent circuit of the system, drawn from the single line diagram, in which:

• resistances, magnetising branches and line charging are neglected
• all values are in p.u. on a common base

It is used for short-circuit (fault) calculations and stability studies, where the reactances dominate. It gives a simple network that can be reduced quickly.

Base values

• $S_b = 100$ MVA, and $V_b = 13.8$ kV at the generator (bus 1).

Both paths give 11 kV at bus 4, so the bases are consistent.

Per-unit values

$$\begin{aligned} X_G &= 0.18\times\frac{100}{90} = 0.2\\ X_{T1} = X_{T2} = X_{T3} = X_{T4} &= 0.1\times\frac{100}{50} = 0.2\\ X_{L1} &= \frac{50}{484} = 0.1033\\ X_{L2} &= \frac{70}{174.24} = 0.4017\\ X_M &= 0.2\times\frac{100}{80}\times\left(\frac{10.45}{11}\right)^2 = 0.2256 \end{aligned}$$

Load: $S = 57/100 = 0.57$ p.u. at a power factor of 0.8 lagging, and $V = 10.45/11 = 0.95$ p.u. As a series impedance:

$$Z_L = \frac{|V|^2}{S^*} = \frac{0.95^2}{0.57}\angle36.87^\circ = 1.5833\angle36.87^\circ = 1.2667 + j0.95\ \text{p.u.}$$

Reactance diagram

               T1     L1      T2
          +--j0.2--j0.1033--j0.2--+
  j0.2    |                       |
 +-/\/\---+ bus1            bus4  +---+------+
 |        |                       |   |      |
(Eg)      +--j0.2--j0.4017--j0.2--+ j0.2256 1.2667
 |             T3     L2      T4     |   +j0.95
 |                                  (Em)  |
 +------------- reference -----------+----+