Reactive Power Compensation

Transmission System

Two-bus steady-state transmission-line model

POWER FLOW ACTIVE

Calculated Operating Point

RECEIVING VOLTAGE

1.000 pu

SOURCE REACTIVE POWER

0.000 pu

REAL POWER LOSS

0.000 pu

MAX POWER TRANSFER

2.500 pu

POWER ANGLE

0.0°

EFFICIENCY

100.0 %

LOAD POWER FACTOR

0.894

EFFECTIVE X

0.400 pu

Receiving-End Voltage vs Active Power

Selected compensation

Uncompensated

Power-Angle Characteristic

Selected X

Uncompensated

Phasor Diagram

Receiving-end voltage as reference; lagging-load transmission-line phasor construction

Mathematical Model

1. Effective reactance

X_{eff} = X_{L} (1 - k_{s})

Series compensation inserts a capacitive reactance in series with the transmission line. The resulting effective line reactance is smaller than the uncompensated reactance.

2. Net reactive power

Q_{net} = Q_{L} - Q_{sh}

3. Receiving-end power

S = P_{L} + j Q_{net}

4. Transmission equation

\bar{V_{s}} = \bar{V_{r}} + (R + j X_{eff}) I

5. Current

I = \frac{\bar{S}}{\bar{V_{r}}}

6. Power-angle relation

P \approx \frac{V_{s}}{X_{eff}} V_{r} \sin δ

7. Approximate maximum power

P_{\max} \approx \frac{V_{s}^{2}}{X_{eff}}

Learning Objectives

Observe the effect of shunt compensation on receiving-end voltage.

Study reduction in line reactance using series compensation.

Compare compensated and uncompensated P–δ characteristics.

Understand reactive-power flow in a transmission system.

Interpret the transmission-line phasor relationship.

Reactive Power Compensation in Transmission System

Transmission System

Calculated Operating Point

Phasor Diagram

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