Thyristor-Switched Series Capacitor

32.4.1.4 Thyristor-Switched Series Capacitor

Figure 32.15 shows the thyristor-switched series capacitor (TSSC). In this device, the thyristors should be kept untrig-

FIGURE 32.13 Thyristor-switched capacitor. gered so as to connect the capacitors in series with the trans- mission line. If the thyristors are turned on, the capacitor is bypassed. Thyristors must be turned on at a zero-voltage condi-

The circuit does not show the filters that are normally needed tion (ZVS), as it occurs in the case of the TSC, to avoid current due to the switching-generated harmonics. In some cases, the spikes in the switches. An example of an application based on fixed capacitor can be replaced by a TSC to get more flexibility this concept is presented in [12]. in terms of control range.

This compensation system has the advantage of being very The capacitance of the SVC is calculated in such a way as simple. However, it does not allow continuous control. If the to generate the maximum capacitive reactive power that it has connection or disconnection of the capacitors is to be made to control. This condition is achieved when the thyristors are at sporadic switching, no harmonic problem occurs. Depend- turned off (α = 180 ◦ ). On the other hand, the maximum reac- ing on the frequency, the thyristors are switched and harmonic tive power of the TCR inductor has to be greater than the or subharmonics may appear. In this arrangement, it is inter- reactive power of the capacitor bank. In this way, the SVC esting to choose the value of the capacitors in such a way that can control the reactive power from capacitive to inductive. many different combinations can be achieved. For example, if

32 Flexible AC Transmission Systems 859

FIGURE 32.14 Six-Pulse SVC.

FIGURE 32.15 Thyristor-switched series capacitors.

the total number of capacitors is three, they could have values proportional to 1, 2, and 3. Therefore, by combining these val- ues it is possible to obtain equivalent capacitor proportional to

FIGURE 32.16 Thyristor-controlled series capacitors.

1, 2, 3, 4, 5, and 6. of harmonics in the capacitor and reactor currents, capacitor

32.4.1.5 Thyristor-Controlled Series

voltage is almost sinusoidal. In actual applications, these har-

monics are not a serious concern, and they are filtered by the Figure 32.16 shows the thyristor-controlled series capacitor capacitor itself and by the transmission line impedance. (TCSC). In this figure, the transmission line and the volt-

Capacitor (TCSC)

Figure 32.18 shows the equivalent impedance of the TCSC age sources in at its ends are represented by a current source as a function of the firing-angle α. This figure shows that this

because this is the actual behavior of most of the transmission device has both capacitive and inductive characteristic regions system. This compensator is also based on the TCR that was divided by a resonant region. In the example shown in this first developed for shunt connection. When the TCR is used figure, the resonance happens for α around 145 ◦ . In normal connected in series with the line, it has to be always connected operation, the TCSC is controlled in the capacitive compen- in parallel with a capacitor because it is not possible to control sation region where its impedance varies from its minimum

the current if the equivalent of the transmission line and the ◦ = 180 and its maximum safe sources is a current source. This circuit is similar to the con- ◦ value Z max for α around 150 . Operation with α close to

value Z min for firing-angle α

ventional SVC with the difference that the TCSC is connected the resonance region is not safe. This device can operate also in series with the line. In this compensator, the equivalent value in the inductive region, but in this case, normally it is used of the series connected reactor can be continuously controlled only when α = 90 ◦ to decrease power transfer capability of the by adjusting the firing angle of the thyristors. As a consequence, transmission line. this device presents a continuously controllable series capaci- tor. Various practical systems based on this concept are under operation around the world [12–14]. This device has been used

32.4.1.6 Thyristor-Controlled Phase Angle Regulator

for power flow control and power oscillation damping. The thyristor-controlled phase angle regulator (TCPAR), Figure 32.17 presents the current and voltage waveforms shown in Fig. 32.19, as an example may improve considerably in the TCSC, showing that although there is a large amount the controllability of a utility of power transmission system.

860 E. H. Watanabe et al.

Capacitor voltage

Capacitor current

Reactor current FIGURE 32.17 TCSC voltage and current waveforms.

Equivalent Impedance

Firing angle, α FIGURE 32.18 TCSC equivalent reactance.

In this figure, only control of phase “a” is detailed. The series the voltage (V b −V c ). As a consequence, it is not possible for voltage generated in phase “a” comes from three secondary the TCPAR to generate a compensating voltage phasor whose windings of a transformer whose primary side is connected locus is a circle, as shown in Fig. 32.7, for the case of an ideal between phases “b” and “c.” Each of the three secondary wind- generic series compensator. ings can be connected in series with the line through the

Other configuration of phaseshifters can be found in the thyristors’ switching. The thyristors are connected in antipar- literature, e.g., [15, 16]. allel, forming bidirectional naturally commutated switches. By turning on a set of thyristors, a voltage whose magnitude can

be controlled by phase control is connected in series with the transmission line. The number of secondary windings is cho-

32.4.2 FACTS Devices Based on

sen as to decrease harmonic content of the series compensation

Self-Commutated Switches

voltage. The TCPAR in Fig. 32.19 has some peculiarities that should There are various different types of FACTS devices based on

be pointed out. One of them is that active power can only self-commutated switches, and the names used here are in flow from the shunt to the series windings. The compensa- accordance with the names published in [9]. Some of them are tion voltage phasor, as shown in Fig. 32.20, has a limited range newer devices and are not in that reference. In this case, the of variation; in the case of phase “a,” its locus is along a line name used is the same as it appears in the literature. In [2], it is

orthogonal to V a because the injected voltage is in phase with possible to find most of the details of FACTS devices.

32 Flexible AC Transmission Systems 861

FIGURE 32.19 Thyristor-controlled phase angle regulator (TCPAR).

V c c antiparallel-connected diode, which operates with a unidi- rectional voltage-blocking capability and a bidirectional cur- rent flow. In contrast, the current source converters (CSC) used in HVDC transmission systems use switches (thyristors) operating with unidirectional current flow and bidirectional

voltage-blocking capabilities.

In a conventional VSC, for industrial applications, a voltage source is connected at the converter dc side. However, in the case that only reactive power has to be controlled, the dc voltage

V a source may be replaced by a capacitor. If active power has to be absorbed or generated by the compensator, an energy storage

V ′ a system has to be connected at the dc side of the VSC. α

In practical applications, small reactors (L) are necessary to connect the VSC to the ac network. This is necessary to avoid current peaks during switching transients. In most cases, these reactors are the leakage inductance of the coupling

transformers.

V b The first high-rating STATCOM is under operation since 1991 [18] in Japan and uses three single-phase VSCs to form FIGURE 32.20 Phasor diagram of the TCPAR in Fig. 32.19.

one three-phase, six-pulses, 10-MVA converter. To guarantee low losses, the switching frequency is equal to the line fre- quency and a total of eight sets of three-phase converters are used to form a 48-pulse converter. All the converters have a

common dc capacitor in their dc side. In the ac side, the con- The development of high-power self-commutated devices, verters are connected in series through a zigzag transformer such as GTOs, IGBTs, and IGCTs, has led to the develop- to eliminate low-frequency voltage harmonics. The device with ment of high-power voltage source converters (VSC), such as compensation capability of 80 MVA was developed to increase the six-pulse two-level VSC shown in Fig. 32.21a [4] or the the transient stability margin of the system, and it has allowed three-level neutral point clamped VSC shown in Fig. 32.21b

32.4.2.1 The Static Synchronous Compensator

a 20% increase of the transmitted power above the previous [17]. In the figures, the switches are GTOs (they could be stability limit. Since it was developed for improving transient IGBTs, IGCTs, or other self-commutating switches) with an stability margin, it normally operates in standby mode without

862 E. H. Watanabe et al.

(b) FIGURE 32.21 (a) Basic six-pulse VSI two-level var compensator and (b) basic three-level var compensator.

reactive compensation and, consequently, low losses. During it was developed for reactive power control, so it can operate transient situation, this STATCOM operates for a short time continuously with acceptable losses. The switching frequency until the system is stable.

is equal to line frequency, and the number of pulses is 48; The development of a ±100-Mvar STATCOM in United therefore, the output voltage waveform is almost sinusoidal States was reported in [19]. It is based on eight sets of three- and harmonic filters are not used in both cases referred phase bridge converters, similar to that shown in Fig. 32.21b; in [18, 19].

32 Flexible AC Transmission Systems 863 32.4.2.1.1 Basic Switching Control Techniques In FACTS Fig. 32.26, the magnitude of the fundamental component is √

applications, the power ratings of the converters are in the equal to

3. The higher-order harmonics in the voltage wave- range of some MW to hundreds of MW and the switching fre- form can be eliminated by a relatively small passive filter, so the quency is lower when compared with the switching frequency voltage and the current at the converter terminals are practi- used in industrial application converters to avoid excessive cally harmonic-free; therefore, the transformer that connects a switching losses. However, there are various switching control PWM-controlled STATCOM to the grid may be a conventional types. The most known so far are as follows:

transformer designed for sinusoidal operation. • Multipulse converters switched at line frequency, as in

[18, 19]; 32.4.2.1.4 Sinusoidal PWM The sinusoidal PWM control • Pulse width modulation (PWM) with harmonic elimina- technique is possibly the simplest to implement and can be tion technique [20];

synthesized by comparing a sinusoidal reference voltage with • Sinusoidal PWM [6];

a triangular carrier [4]. This switching control method needs • Cascade converters [21].

a relatively high switching frequency, which is in the range of 1–2 kHz and consequently produces higher switching losses when compared with multipulse STATCOM. The harmonic

32.4.2.1.2 Multipulse Converters Switched at Line Frequency content at low frequencies is negligible; however, there is a rela- The multipulse converter was the first choice for STATCOM tively high harmonic content at the switching frequency, which application because it presents low losses and low harmonic is eliminated by a passive filter. content [18,19]. Figure 32.22 shows a 24-pulse converter based on three-phase, two-level and six-pulse converters. In this case, the zigzag transformers are connected in such a way as to pro- 32.4.2.1.5 Cascade Converter The basic cascade converter duce phase differences of 15, 30, 45, and 60 ◦ . With this arrange- [21] topology is shown in Fig. 32.27. Only two single-phase full ment, the resulting output voltage and its harmonic spectrum bridge converters are shown, the first and the nth. However, are as shown in Fig. 32.23. The first two harmonics components in actual application, several of them are connected in series are the 23rd- and 25th-order harmonics. Figure 32.24 shows and switched at line frequency. The resulting voltage waveform the voltage waveform for a 48-pulse converter and its respec- can be similar to the multipulse converter waveform with the tive harmonic spectrum. In this case, the first two harmonic advantage that there is no need of transformers to sum up the components are the 47th- and 49th-order harmonics. The total converters output voltage. Due to the line frequency switching, harmonic distortion (THD) for the 24-pulse and 48-pulse con- the switching losses are very low. The resulting voltage wave- verters is 7 and 3.3%, respectively. These converters can also be form can be almost sinusoidal depending on the number of built by using three-level converters. However, one drawback series converters, and the transformer used to connect them of the multipulse converter is the complexity of the transform- to the grid can be a conventional sinusoidal waveform trans- ers, which have to operate with high harmonic content in their former, if necessary. One drawback of this converter topology voltage and various different turns ratio.

is that it is not possible to have a back-to-back connection. The need to have one dc capacitor for each single-phase converter has two consequences: the number of capacitors is equal to the

32.4.2.1.3 PWM (Pulse Width Modulation) with Harmonic number of single-phase converters; and the capacitance of each Elimination Technique One way to avoid the complexity of capacitor has to be much higher when compared with three- the multipulse converters is to use PWM with harmonic elimi- phase converters. This is because the instantaneous power in nation technique [20]. With this approach, it is possible to use the single-phase converter has a large oscillating component at relatively low switching frequency and, consequently, have low double of the line frequency and it would force a large voltage switching losses. The PWM modulation is obtained by off-line ripple in the capacitors if they were small. calculation of the switches at “on” and “off ” instants in such a way as to eliminate the low-frequency harmonics. Figure 32.25a shows an example of voltage waveform with “on” and “off ” 32.4.2.1.6 STATCOM Control Techniques The control of instants calculated in such a way as to eliminate the 5th-, 7th-, reactive power in the STATCOM is done by controlling its ter- 11th-, and 13th-order harmonics. This voltage corresponds to minal voltage. Figure 32.28 shows a simplified circuit in which the voltage between one phase of the converter and the neg- the ac grid is represented by a voltage source V S behind an ative terminal of the dc side. Figure 32.25b shows the control impedance X L and the STATCOM is represented by its funda-

angle as a function of the modulation index m a . Figure 32.26 mental voltage V I . Figure 32.29a shows the case when the ac shows the harmonic spectrum for the phase-to-phase volt- grid phasor voltage V S is in phase with the STATCOM volt- age waveform corresponding to that shown in Fig. 32.25a. age V I and both have the same magnitude. In this case, the line Here, it is considered that the RMS value of the fundamental current I L is zero. Figure 32.28b shows the case when V S is little component of the voltage in Fig. 32.25 is equal to unity. In larger than V I . In this case, the line current I L , which lags the

864 E. H. Watanabe et al.

FIGURE 32.22 6-Pulse 2-level VSI-based 24-pulse var compensator.

32 Flexible AC Transmission Systems 865 v (t )

• If V S is larger than V I , the STATCOM reactive power is

inductive;

• If V S is smaller than V I , the STATCOM reactive power is

capacitive.

Therefore, the reactive power control in a STATCOM is a problem of how to control the magnitude of its voltage V I .

(a)

There are two basic principles: in the case of multipulse con- verters, the output voltage magnitude can only be controlled

by controlling the dc side voltage that is the dc capacitor volt- age; in the case of PWM control, the dc capacitor voltage can be

kept constant, and the voltage can be controlled by the PWM

controller itself.

Figure 32.30a shows the phasor diagram for the case when a

Voltage phase-neutral (pu)

phase difference δ between V S and V I is positive. The resulting

line current is in such a way that produces an active power flow-

Harmonic order

ing into the converter, charging the dc capacitor. Figure 32.30b shows the phasor diagram for a negative phase angle δ. In this

(b)

FIGURE 32.23 (a) 24-Pulse converter voltage waveform and (b) its case, the dc capacitor is discharged. Therefore, by controlling harmonic spectrum.

the phase angle δ, it is possible to control the dc capacitor voltage.

In general, STATCOM based on multipulse converter with- v (t )

out PWM has to control its voltage by charging or discharging the dc capacitor, and this voltage has to be variable. On the other hand, STATCOM based on a PWM-controlled converter has to control dc side capacitor voltage only to maintain it

constant. In both cases, the principle shown in Fig. 32.30 is valid.

(a)

The STATCOM control technique presented above illustrates the basic scalar control concepts. However, this compensator

can be also controlled by a vector technique [22]. In this case,

the three-phase voltages are transformed to a synchronous ref- erence frame where they can be controlled in such a way as

to regulate the quadrature component of the current, which

0.25 Voltage phase-neutral (pu)

controls reactive power. The direct component of the current is used to control the dc capacitor voltage as it represents the

Harmonic order

active power.

Another way to control the STATCOM is by using the instan- FIGURE 32.24 (a) 48-Pulse converter voltage waveform and (b) its

(b)

taneous power theory [23, 24]. This theory was first proposed harmonic spectrum.

for controlling active power filters and is used in the design of the compensators operating with unbalanced systems. If a high frequency PWM converter is used, this theory allows the design of active filters to compensate for harmonic components

voltage V L by 90 ◦ , is also lagging the ac grid phasor voltage V S , or fundamental reactive component. and therefore, the STATCOM produces an inductive reactive

power. On the other hand, Fig. 32.29c shows the case when V S 32.4.2.1.7 STATCOM DC Side Capacitor

Theoretically, the is little smaller than V I . Hence, the line current I L , which lags

dc side capacitor of a STATCOM based on three-phase con- the voltage V L by 90 ◦ , leads the voltage V S , and therefore, the verters operating in a balanced system and controlling only the STATCOM produces a capacitive reactive power. In summary, reactive power could have a capacitance equal to zero Farad, the STATCOM reactive power can be controlled if the magni- once the three-phase instantaneous reactive power does not tude of its V I voltage is controlled, assuming that it is in phase contribute to the energy transfer between the dc and ac side with V S . [25]. However, in actual STATCOMs, a finite capacitor has to

be used with the objective of keeping constant or controlled active power in the STATCOM;

• If V S is equal to V I , there is no reactive power and no

dc voltage as it tends to vary due to the converter switching.

866 E. H. Watanabe et al.

0.4 PWM control angle,

Modulation index, m a (pu)

(a)

(b)

FIGURE 32.25 (a) Example of one-phase voltage with the harmonic elimination technique and (b) the control angle as function of the modulation index.

0.50 Phase-to-phase voltage, (pu) 0.25

1 1 17 17 19 19 23 23 25 25 Harmonic order

FIGURE 32.26 Line voltage harmonic spectrum for the voltage waveform in Fig. 32.25a.

One parameter commonly used in synchronous machine is the where C and V DC are the dc capacitance and its voltage and S inertia constant H defined by

is the STATCOM apparent power.

In both cases, the constants H and H ST are values in time

Jω 2 /2

units corresponding to the relation of the amount of energy

(32.10) stored in the rotor inertia, or in the capacitor, and the machine,

or STATCOM, apparent power, respectively. In the case of syn- chronous machines, the value of H is in the range of few

where J and ω are the rotor moment of inertia and angu- seconds (generally, in the range of 1–3 s), and in the case of the lar speed and S is the machine apparent power. A similar STATCOM, H ST value is in the range of milliseconds or below parameter for the STATCOM, H ST , can be defined by (0.5–5 ms) if only reactive power is to be controlled. These

numbers show that the STATCOM based on three-phase con-

CV DC 2 /2

verters and designed only for reactive power control (which is

H ST =

the general case) has almost no stored energy in its dc capacitor.

32 Flexible AC Transmission Systems 867

C d n FIGURE 32.30 Active power control in a STATCOM.

of balanced systems to avoid large voltage ripple on the dc volt- FIGURE 32.27 Cascade converter basic topology. age due to power oscillations at twice the line frequency, which

appears naturally in unbalanced systems [26, 27] or unbal-

anced voltages [28] or system with flicker problem [29, 30]. ac grid

STATCOM

In this case, the STATCOM compensates reactive power and V L

the instantaneous oscillating active power due to the nega-

C d tive sequence current components. In fact, this is an extension

jX L of the shunt active power filter application where the goal is

I L the current harmonic compensation, which includes negative sequence currents even at the fundamental frequency. If sub-

V I harmonics are present, the device is able to filter them out FIGURE 32.28 Simplified circuit for the ac grid and the STATCOM.

as well. 32.4.2.1.8 STATCOM with Energy Storage In general, the

On the other hand, STATCOM based on single-phase convert- STATCOM is designed for reactive power compensation and it ers without a common dc link may have larger capacitors as in does not need large energy storage elements. However, there the case of cascade converters due to the power oscillations at are some applications where it may be interesting to have double of the line frequency.

some energy stored in the dc side, for example to compen- There are STATCOMs (in some cases with different names) sate for active power for a short time. In these applications, that are designed for operation with unbalanced loads. In this the dc-side capacitor has to be substituted by a voltage source case, the dc capacitor has to be also much larger than in the case energy storage device like a battery [31] or a double-layer

FIGURE 32.29 Reactive power control in a STATCOM.

868 E. H. Watanabe et al.

ac bus Coupling

transformer

Superconducting magnetic energy storage Voltage

source

V d dc-dc

P and Q references

FIGURE 32.31 STATCOM with SMES.

Transient operation

Transient operation

FIGURE 32.32 Comparison between SVC and STATCOM.

capacitor (super capacitor). Another possibility is to store depending on the amount of energy stored in the supercon- energy in superconducting magnetic energy storage (SMES) ducting magnet. systems [32, 33]. A natural solution for the use of the super- conducting reactor would be the connection to the ac grid 32.4.2.1.9 Comparison between SVC and STATCOM Figure through a current source converter (CSC) instead of the volt- 32.32a shows the steady-state volt–ampere characteristics for age source converter. However, this has not been the case the SVC shown in Fig. 32.14, whereas Fig. 32.32b shows the found in the literature. Figure 32.31 shows a block dia- same characteristics for a STATCOM. For operation at rated gram of a typical STATCOM/SMES system, where the SMES voltage, both devices can present similar characteristics in is connected to the dc side of the STATCOM through a terms of control range. However, current compensation capa- dc–dc converter, which converts the direct current in the bility of SVC for lower voltages becomes smaller, whereas in the superconductor magnet to dc voltage in the STATCOM dc STATCOM, it does not change significantly for voltages lower side and vice versa. This STATCOM can control reactive than rated (but approximately above 0.2 pu). This is explained power continuously, as well as active power for a short time, by the fact that the SVC is based on impedance control, whereas

32 Flexible AC Transmission Systems 869

ac system

Coupling transformer

Slip rings V d

Back-to-back converter

3-phase field winding FIGURE 32.33 Adjustable speed synchronous condenser.

the STATCOM is based on voltage source control. There- However, when the rotor speed is lower or higher than fore, in the SVC, the current decreases with a corresponding the synchronous speed (normally during transients), the rotor voltage decrease, whereas in the STATCOM, the current capa- converter generates a field current with the necessary frequency bility of the converters depends only on the switching device to keep the stator and rotor fluxes synchronized – if the syn- used, so the maximum current can be kept unchanged even chronous frequency is 60 Hz and the rotor is running at 58 Hz, for a low voltage condition. This is an important character- the rotor converter has to supply voltage or current at 2 Hz so as istic, especially in applications where the voltage may drop to synchronize the fluxes. Naturally, it would be more interest- (as in most cases), where the STATCOM presents a better ing to use field-oriented control [34] instead of scalar control performance.

to get a better performance.

This hybrid compensator may supply energy to the ac sys- tem, if rotor speed is decreased. This machine is designed to

have relatively large rotor inertia so as to present a large inertia The adjustable speed synchronous condenser is not exactly a constant (which may be in the range of more than 10 s). It is

32.4.2.2 Adjustable Speed Synchronous Condenser

FACTS device, as it contains an electrical machine. However, also called adjustable speed rotary condenser [35]. Operation it may be an interesting shunt device to compensate reac- at speeds higher than the synchronous speed is also possible, if tive power continuously and relatively large amounts of active it is necessary to absorb energy from the grid. power for a short time. The basic topology of this device is

One of the advantages of this device is that a compensator shown in Fig. 32.33. It is based on a double-fed induction with power in the range of 400 MVA may be synthesized with

machine with a conventional three-phase winding in the stator power electronics converter rated at a small fraction of this and a three-phase winding in the rotor. The latter is supplied power and with a large capability to supply both active (for a by a three-phase converter connected back-to-back to a second few seconds) and reactive power (continuously) [35]. converter, which is connected to the grid.

This configuration allows the generation of a rotating mag- netic flux in the rotor, which depends on the rotor converter

32.4.2.3 Static Synchronous Series Compensator

frequency. When the machine is rotating at synchronous speed, In contrast to the STATCOM, which is a shunt FACTS device, the rotor converter operates at zero frequency and the mag- it is possible to build a converter-based compensator for series netic flux in the rotor is stationary with respect to the rotor compensation. Figure 32.34 shows the basic diagram of a itself. In this case, the compensator operates as a conventional static synchronous series compensator (SSSC) based on volt- synchronous condenser.

age source converter (VSC) with a capacitor in its dc side

870 E. H. Watanabe et al.

(VSI)

Source C d Load

SE *

Series compensator

control

q SE *

FIGURE 32.34 Static synchronous series compensator (SSSC).

and connected in series with the transmission line through a

32.4.2.4 Gate-Controlled Series Capacitor

transformer [36]. The inputs to the SSSC controller shown in Figure 32.16 shows the TCSC, which is basically a TCR in this figure are the line current and voltage, as well as the active parallel with a capacitor and both connected in series with a and reactive power references p ∗ SE and q ∗ SE , respectively. In gen- transmission line. The combination is effective in continuously eral, only reactive power is compensated, and in this case, the controlling the equivalent capacitive reactance presented to the active power reference p ∗ SE is zero and q SE ∗ is chosen so as to con- system, mainly for power flow control and oscillation damping trol power flow. Naturally, in the case of power flow control, it purposes. It was also pointed out that the device has the disad- is necessary to have another control loop for this purpose and vantage of a resonance area due to the association capacitor or this is not shown in the figure.

TCR (see Fig. 32.18).

One should note that if current is flowing in the trans- In [37], the continuously regulated series capacitor using mission line, the SSSC controls reactive power by generating GTO thyristors to directly control capacitor voltage is pre- voltage v C in quadrature with the line current. The device sented. Figure 32.36 shows the GTO thyristor-controlled then shows capacitive or inductive equivalent impedance by series capacitor (GCSC) [38], hereafter renamed as the gate- increasing or decreasing the power flow, respectively. The com- controlled series capacitor because it may also be built using pensation characteristic is, as shown in Fig. 32.8, for the case other self-commutated switches such as IGBTs or IGCTs. of series compensation where the transmitted power is always

The GCSC circuit consists of a capacitor and a pair of positive for 0 < δ < 180 ◦ . That is, with reactive power control, it self-commutated switches in antiparallel connection. As the is only possible to transmit in one direction. However, if instead switches operate under ac voltage, they must be able to block

of controlling q ∗ SE , voltage v C is controlled, it is possible to have both direct and reverse voltages and allow current control in power flow reversion. Figure 32.35 shows the power flow char- both directions. acteristics of a transmission line with an SSSC using constant

Figure 32.37 shows the voltage and current waveforms for voltage control. The voltage is in quadrature with the current, the GCSC, where the current in the transmission line is and its magnitude is kept constant. The figure shows that it is assumed to be sinusoidal. If the switches are kept turned on, possible to have power flow reversion for small values of δ with the capacitor is bypassed and does not present any compensa-

tion effect. If they are kept off, the capacitor is fully inserted It should be noted that the discussion presented with respect in the line. On the other hand, if the switches are conducting to the converters for the case of the STATCOM is also valid and are turned off at a given blocking angle γ counted from for the case of the SSSC. The SSSC can be used for power flow the zero-crossings of the line current, the capacitor voltage v C control and for power oscillation damping as well.

a constant compensation voltage v C .

appears as a result of the integration of the line current passing

32 Flexible AC Transmission Systems 871

2 v C = − 0.707 pu

1.5 v C =0

(pu)

v C = + 0.707 pu

P s 0.5

0 Power flow reversion

(degree) FIGURE 32.35 Power flow characteristics for voltage-controlled SSSC.

V C through it. The next time the capacitor voltage crosses zero, i (t)

the switches are turned on again, to be turned off at the next turn-off angle γ . With this switching control sequence, it must

C d be clear that the switches always switch at zero voltage. This is an interesting feature for the series connection of the switches

G 1 under high-voltage operation [39].

The GCSC has some advantages when compared with the TCSC – the blocking angle can be continuously varied, which in turn varies the fundamental component of the voltage v C . Also, it can be smaller than the TCSC [40]. Moreover, the

G 2 dynamic response of the GCSC is generally better than that of FIGURE 32.36 Gate-controlled series capacitor.

the TCSC [41].

The fundamental impedance of the GCSC as a function of the blocking angle γ is shown in Fig. 32.38. A blocking angle of

90 ◦ means the capacitor is fully inserted in the circuit, whereas

a value of 180 ◦ corresponds to a situation where the capacitor is bypassed and no compensation occurs. Line current