Flexible AC transmission system

In the case of a no-loss line, voltage magnitude at the receiving end is the same as voltage magnitude at the sending end: V_s = V_r = V. Transmission results in a phase lag ${\displaystyle \delta }$ that depends on line reactance X.

${\displaystyle {\begin{aligned}{\underline {V_{s}}}&=V\cos \left({\frac {\delta }{2}}\right)+jV\sin \left({\frac {\delta }{2}}\right)\\[3pt]{\underline {V_{r}}}&=V\cos \left({\frac {\delta }{2}}\right)-jV\sin \left({\frac {\delta }{2}}\right)\\[3pt]{\underline {I}}&={\frac {{\underline {V_{s}}}-{\underline {V_{r}}}}{jX}}={\frac {2V\sin {\left({\frac {\delta }{2}}\right)}}{X}}\end{aligned}}}$

As it is a no-loss line, active power P is the same at any point of the line:

${\displaystyle P_{s}=P_{r}=P=V\cos \left({\frac {\delta }{2}}\right)\cdot {\frac {2V\sin {\left({\frac {\delta }{2}}\right)}}{X}}={\frac {V^{2}}{X}}\sin(\delta )}$

Reactive power at sending end is the opposite of reactive power at receiving end:

${\displaystyle Q_{s}=-Q_{r}=Q=V\sin \left({\frac {\delta }{2}}\right)\cdot {\frac {2V\sin \left({\frac {\delta }{2}}\right)}{X}}={\frac {V^{2}}{X}}(1-\cos \delta )}$

As ${\displaystyle \delta }$ is very small, active power mainly depends on ${\displaystyle \delta }$ whereas reactive power mainly depends on voltage magnitude.

Examples of FACTS for series compensation (schematic)

• Static synchronous series compensator (SSSC)
• Thyristor-controlled series capacitor (TCSC): a series capacitor bank is shunted by a thyristor-controlled inductor reactor
• Thyristor-controlled series reactor (TCSR): a series reactor bank is shunted by a thyristor-controlled reactor
• Thyristor-switched series capacitor (TSSC): a series capacitor bank is shunted by a thyristor-switched reactor
• Thyristor-switched series reactor (TSSR): a series reactor bank is shunted by a thyristor-switched reactor

Examples of FACTS for shunt compensation (schematic)

• Static synchronous compensator (STATCOM); previously known as a static condenser (STATCON)
• Static VAR compensator (SVC). Most common SVCs are:
  • Thyristor-controlled reactor (TCR): reactor is connected in series with a bidirectional thyristor valve. The thyristor valve is phase-controlled. Equivalent reactance is varied continuously.
  • Thyristor-switched reactor (TSR): Same as TCR but thyristor is either in zero- or full- conduction. Equivalent reactance is varied in stepwise manner.
  • Thyristor-switched capacitor (TSC): capacitor is connected in series with a bidirectional thyristor valve. Thyristor is either in zero- or full- conduction. Equivalent reactance is varied in stepwise manner.
  • Mechanically-switched capacitor (MSC): capacitor is switched by circuit-breaker. It aims at compensating steady state reactive power. It is switched only a few times a day.

• Static synchronous series compensator
• HVDC
• Dynamic line rating for electric utilities

In-line references

General references