**Thyristor-controlled reactor (TCR)**

Thyristor-controlled reactor (TCR) is defined as: a shunt-connected thyristorcontrolled inductor whose effective reactance is varied in a continuous manner by partial conduction control of the thyristor valve.

Thyristor-switched reactor (TSR) is defined as: a shunt-connected, thyristorswitched inductor whose effective reactance is varied in a stepwise manner by full- or zero-conduction operation of the thyristor valve.

**Principles of operation of the TCR**

The basis of the TCR is shown in Figure 6.1. The controlling element is the thyristor controller, shown here as two back-to-back thyristors which conduct on alternate half-cycles of the supply frequency. If the thyristors are gated into conduction precisely at the peaks of the supply voltage, full conduction results in the reactor, and the current is the same as though the thyristor controller were short-circuited.

The current is essentially reactive, lagging the voltage by nearly 90°. It contains a small in-phase component due to the power losses in the reactor, which may be of the order of 0.5-2% of the reactive power. Full conduction is shown by the current waveform in Figure 6.2(a).

If the gating is delayed by equal amounts on both thyristors, a series of current waveforms is obtained, such as those in Figure 6.2(a) through (d). Each of these corresponds to a particular value of the gating angle α, which is measured from the zero-crossing of the voltage. Full conduction is obtained with a gating angle of 90°. Partial conduction is obtained with gating angles between 90° and 180°. The effect of increasing the gating angle is to reduce the fundamental harmonic component of the current. This is equivalent to an increase in the inductance of the reactor, reducing its reactive power as well as its current. So far as the fundamental component of current is concerned, the TCR is a controllable susceptance, and can therefore be applied as a static compensator.

Fig. 6.1 Basic thyristor-controlled reactor.

Fig. 6.2 Voltage ant line current waveforms of a basic single-phase TCR for various firing ankles. (a) α = 90°, σ = 180°; (b) α = 100°, σ = 160°; (c) α = 130°, σ = 100°; (d) α = 150°, σ = 60°.

Fig. 6.3 Control law of a basic TCR.

The instantaneous current

(6.1)*i*is given by
where

*V*is the rms voltage; X_{L}= ωL is the fundamental-frequency reactance of the reactor (in Ohms); ω = 2π*f*; and α is the gating delay angle. The time origin is chosen to coincide with a positive-going zero-crossing of the voltage. The fundamental component is found by Fourier analysis and is given by
(6.2)

where σ is the conduction angle, related to α by the equation
(6.3)

Equation 6.2 can be written as
(6.4)

where B

_{L}(σ) is an adjustable fundamental-frequency susceptance controlled by the conduction angle according to the law
(6.5)

This control law is shown in Figure 6.3. The maximum value of B

_{L}is 1/X_{L}, obtained with σ = π or 180, that is, full conduction in the thyristor controller. The minimum value is zero, obtained with σ = 0 (α=180°). This control principle is called phase control.**Fundamental voltage/current characteristic**

The TCR has to have a control system that determines the gating instants (and therefore σ), and that issues the gating pulses to the thyristors. In some designs the control system responds to a signal that directly represents the desired susceptance B

_{L}. In others, the control algorithm processes various measured parameters of the compensated system (e.g. the voltage) and generates the gating pulses directly with- out using an explicit signal for B_{L}. In either case the result is a voltage/current characteristic of the form shown in Figure 6.4. Steady-state operation is shown at the point of intersection with the system load line. In the example, the conduction angle is shown as 130°, giving a voltage slightly above 1.0 p.u., but this is only one of an infinite number of possible combinations, depending on the system load line, the control settings, and the compensator rating. The control characteristic in Figure 6.4 can be described by the equation
(6.6)

where *I*is normally the rated current of the reactors shown here as 1 put.

_{max}
Fig. 6.4 Fundamental voltage/current characteristic in the TCR compensator.

**Harmonics**

Increasing the gating angle (reducing the conduction angle) has two other important effects. First, the power losses decrease in both the thyristor controller and the reactor. Second, the current waveform becomes less sinusoidal; in other words, the TCR generates harmonic currents. If the gating argles are balanced, (i.e. equal for both thyristors), all odd order harmonics are generated, and the rms value of the

*nth*harmonic component is given by
(6.7)

Figure 6.5(a) shows the variation of the amplitudes of some of the major (lower- order) harmonics with the conduction angles, and Figure 6.5(b) the variation of the total harmonic content.
Table 6.2 gives the maximum amplitudes of the harmonics down to the 37th. (Note that the maxima do not all occur at the same conduction angle.)

The TCR described so far is only a single-phase device. For three-phase systems the preferred arrangement is shown in Figure 6.6; i.e. three single-phase TCRs connected in delta. When the system is balanced, all the triples harmonics circulate in the closed delta and are absent from the line currents. All the other harmonics are present in the line currents and their amplitudes are in the same proportions as shown in Figure 6.5 and Table 6.2. However, the waveforms differ from those ones presented in Figure 6.2.

It is important in the TCR to ensure that the conduction angles of the two back-to- back thyristors are equal. Unequal conduction angles would produce even harmonic components in the current, including DC. They would also cause unequal thermal stresses in the thyristors. The requirement for equal conduction also limits σ to a maximum of 180°. However, if the reactor in Figure 6.1 is divided into two separate reactors (Figure 6.7), the conduction angle in each leg can be increased to as much as 360°. This arrangement has lower harmonics than that of Figure 6.1, but the power losses are increased because of currents circulating between the two halves.

Fig. 6.5 TCR Harmonics. (a) major harmonic current components of TCR. Each is shown as a percentage of the fundamental component at full conduction. The percentages are the same for both phase and line currents; and (b) total harmonic content of TCR current, as a fraction of the fundamental component at full conduction. The percentages are the same for both phase and line currents.

Table 6.2 Maximum amplitudes of harmonic currents in TCR^{a}

Harmonic order | Percentage |

1 | 100.00 |

3 | (13.78)^{b} |

5 | 5.05 |

7 | 2.59 |

9 | (1.57) |

11 | 1.05 |

13 | 0.75 |

15 | (0.57) |

17 | 0.44 |

19 | 0.35 |

21 | (0.29) |

23 | 0.24 |

25 | 0.20 |

27 | (0.17) |

29 | 0.15 |

31 | 0.13 |

33 | (0.12) |

35 | 0.10 |

37 | 0.09 |

^{a}Values are expressed as a percentage of the amplitude of the fundamental component at full conduction.

^{b}The values apply to both phase and line currents, except that triples harmonics do not appear in the line currents. Balanced conditions are assumed.

Fig. 6.6 Three-phase TCR with shunt capacitors. The split arrangement of the reactors in each phase provides extra protection to the thyristor controller in the event of a reactor fault.

Fig. 6.7 TCR with more than 180° of conduction in each leg to reduce harmonic currents.

As already noted, TCR harmonic currents are sometimes removed by filters (Figure 6.6). An alternative means for eliminating the 5th and 7th harmonics is to split the TCR into two parts fed from two secondaries on the step-down transformer, one being in wye and the other in delta, as shown in Figure 6.8. This produces a 30° phase shift between the voltages and currents of the two TCRs and virtually eliminates the 5th and 7th harmonics from the primary-side line current. It is known as a 12-pulse arrangement because there are 12 thyristor eatings every period. The same phase-multiplication technique is used in conventional HVDC rectifier transformers for harmonic cancellation. With the 12-pulse scheme, the lowest-order characteristic harmonics are the 11th and 13th. It can be used without filters for the 5th and 7th harmonics, which is an advantage when system resonances occur near these frequencies. For higher-order harmonics a plain capacitor is often sufficient, connected on the low-voltage side of the step-down transformer. Otherwise a high-pass filter may be used. The generation of third-harmonic currents under unbalanced conditions is similar to that in the six-pulse arrangement (Figure 6.6).

Fig. 6.8 Arrangement of 12-pulse TCR configuration with double-secondary transformer.

With both 6-pulse and 12-pulse TCR compensators, the need for filters and their frequency responses must be evaluated with due regard to the possibility of unbalanced operation. The influence of other capacitor balks and sources of harmonic currents in the electrical neighbourhood of the compensator must also be taken into account. For this purpose, several software packages are available and some examples with a specific one will be provided later.

The 12-pulse connection has the further advantage that if one half is faulted the other may be able to continue to operate normally. The control system must take into account the 30° phase shift between the two TCRs, and must be designed to ensure accurate harmonic cancellation. A variant of the 12-pulse TCR uses two separate transformers instead of one with two secondaries.

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