32
Flexible AC Transmission Systems
Electrical Engineering Department, COPPE/Federal University of Rio de Janeiro, Brazil, South America
Electrical Engineering Department, Polytechnic School and COPPE/Federal University of Rio de Janeiro, Brazil, South America
Electrical Engineering Department, Federal University of Juiz de Fora, Brazil, South America
Electrical Engineering Department, Federal University of Ceara, Brazil, South America
Pos-doctoral Fellow at Toronto University supported by Capes Foundation, Ministry of Education, Brazil, South America
Eneltec- Energia Elétrica e Tecnologia, Brazil, South America
32.1 Introduction
32.4 Synthesis of FACTS Devices
This chapter presents the basic operation principles of FACTS devices. Starting with a brief introduction on the concept and its origin, the text then focuses on the ideal behavior of each basic shunt and series of FACTS device. Guidelines on the synthesis of the first generation of these devices based on thyristors are presented, followed by the newer generations of FACTS devices based on self-commutated semiconductor switches.
32.1 Introduction
In 1988, Hingorani [1] published a paper entitled “Power Electronics in Electric Utilities: Role of Power Electronics in Future Power Systems,” which proposed the extensive use of power electronics for the control of ac systems, which resulted in the flexible ac transmission system or the FACTS concepts [2]. The basic idea was to obtain ac systems with a high level of control flexibility, as in high-voltage direct current (HVDC) systems [3] based on the use of the thyristor and the self-commutated (controllable turn-on and turn-off) semiconductor devices, such as gate turn-off thyristors (GTOs), insulated gate bipolar transistors (IGBTs), and integrated gate controlled thyristors (IGCTs) [4, 5], which were not yet developed at that time.
The switching characteristics of thyristors –controlled turn-on and natural turn-off –are appropriate for using in line-commutated converters, such as in conventional HVDC transmission systems with a current source in the dc side. In this application, the technology for series connection of thyristors is very important due to the high-voltage characteristics of the transmission voltage. This is a well-known technology. Maximum breakdown voltage and current conduction capabilities are around 8 kV and 4 kA, respectively. These are some features that make thyristors important for very high-power applications, although they present some serious drawbacks, such as the lack of controlled turn-off capability and low switching speeds.
Self-commutated switches are adequate for use in converters where turn-off capability is necessary. The device with highest ratings in this group was, for a long time, the GTO with maximum switching capability of 6 kV and 6 kA. At present, there are IGBTs with ratings in the range of 6.5 kV to 3 kA and IGCTs with switching capability of about 6 kV and 4 kA. The GTOs and IGCTs are devices that normally need small inductor for limiting the rate of change of turn-on current (di/dt). Normally, GTOs also need a snubber circuit for limiting the rate of change of voltage (dv/dt).
The GTOs, IGCTs, and IGBTs are the most used options for self-commutated high-power converters. Because the switching time of these devices is in the microsecond range (or below), their series connection is more complicated than in the case of thyristors. However, there are examples of series connections of various GTOs or IGCTs and, in the case of IGBTs, the number of series connected devices can go as high as 32 [6].
Because of the commutation nature of the thyristors, the converters used in HVDC systems are of the current source type [7]. On the other hand, the force-commutated converters using the self-commutated devices are basically of the voltage source type. More details about current source and voltage source converters can be found in many power electronics books, e.g. [3, 7].
32.2 Ideal Shunt Compensator
A simple and lossless ac system is composed of two ideal generators, and a short transmission line, as shown in Fig. 32.1, is considered as basis to the discussion of the operating principles of a shunt compensator [8]. The transmission line is modeled by an inductive reactance XL. In the circuit, a continuously controlled voltage source is connected in the middle of the transmission line. It is assumed that the voltage phasors Vs and VR have the same magnitude and are phase-shifted by δ. The subscript “S” stands for “Source” and “R” stands for “Receptor.” Figure 32.2 shows the phasor diagram of the system given in Fig. 32.1 in which the compensation voltage phasor VM has also the same magnitude as VS and VR, and its phase is exactly (–δ/2) with respect to VS and (+δ/2) with respect to VR.
FIGURE 32.1 Ideal shunt compensator connected in the middle of a transmission line.
FIGURE 32.2 Phasor diagram of the system with shunt reactive power compensation.
In this situation, the current ISM flows from the source and the current Imr flows into the receptor. The phasor IM is the resulting current flowing through the ideal shunt compensator; Fig. 32.2 shows that this current ImR, in this case, is orthogonal to the voltage Vm, which means that the ideal shunt compensator voltage source does not has to generate or absorb active power and have only reactive power in its terminals.
From Fig. 32.2 and knowing that no active power flows to or from the ideal shunt compensator, it is possible to calculate the power transferred from Vs to Vr that is given by
(32.1)
where Ps is the active power flowing from the source, V is the magnitude of the voltages Vs and Vr.
If the ideal shunt compensator were not present, the transferred power would be given by
(32.2)
Since 2 sin(δ/2) is always greater than sin δ for δ in the range of [0, 2π], the ideal shunt compensator does improve the power transfer capability of the transmission line. This voltage source is in fact operating as an ideal reactive power shunt compensator.
If the phase angle between Vm and Vs is different from δ/2 (as shown in Fig. 32.3), the power flowing through Vm has both active and reactive components.
FIGURE 32.3 Phasor diagram of the system with shunt reactive and active power compensation.
With the characteristics of the ideal shunt compensator, presented above, it is possible to synthesize power electronics-based devices to operate as active or reactive power compensators. This is discussed in the following sections. It will be seen that the requirements of the device synthesis with actual semiconductor switches for the situations of reactive or active power compensation are different because of the need of energy storage element or energy source if active power is to be drained or generated by the shunt compensator.
32.3 Ideal Series Compensator
Similar to the previous section, the ideal series compensator is modeled by a voltage source for which the phasor is VC connected in the middle of a lossless transmission line as shown in Fig. 32.4.
FIGURE 32.4 Ideal series compensator connected in the middle of a transmission line.
The current flowing through the transmission line is given by
(32.3)
where Vsr = Vs –Vr.
If the ideal series compensator voltage is generated in such a way that its phasor VC is in quadrature with line current I, this series compensator neither supplies nor absorbs active power. As discussed earlier, power at the series source is only reactive and the voltage source may, in this particular case, be replaced by capacitive or inductive equivalent impedance. Then, the equivalent impedance is given by
(32.4)
where
(32.5)
is the compensation factor and XComp is the series equivalent compensation reactance, negative if capacitive and positive if inductive. In this case, the compensation voltage is given by
(32.6)
and the transmitted power is equal to
(32.7)
Equation (32.7) shows that the transmitted power can be considerably increased by series compensation, choosing a proper compensation factor s. The reactive power at the series source is given by
(32.8)
The left-hand side of the Fig. 32.5a shows the phasor diagram of the system shown in Fig. 32.4 without the ideal series compensator. On the right-hand side of the Fig. 32.5a, the voltage phasor Vl on the line reactance XL and the compensator voltage phasor VC are shown for a given compensation level, assuming that this voltage VC corresponds to a capacitive compensation. In this case, the line current phasor leads voltage phasor VC by 90°, and the total voltage drop in the line VZ = Vs –Vr –VC is larger than the original voltage drop Vl. The current flowing in the line is larger after compensation than before. This situation shows the case where the series compensator is used to increase power flow.
FIGURE 32.5 Phasor diagram of the series reactive compensator: (a) capacitive and (b) reactive mode.
The left-hand side of the Fig. 32.5b shows the same non-compensated situation as in the previous case. On the right-hand side, the case of an equivalent inductive compensation is shown. In this case, the compensation voltage VC is in phase with the line drop voltage Vl, producing an equivalent total voltage drop Vz smaller than in the original case. As a result, the current phasor I flowing in the line is smaller than before compensation. This kind of compensation might be interesting in the case that the power flowing through the line has to be decreased. In either capacitive or inductive compensation modes, no active power is absorbed or generated by the ideal series compensator.
Figure 32.6 shows an ac system with an ideal generic series compensation voltage source VC for the general case where it may not be in quadrature with the line current. In this case, the compensator can fully control the phase difference between the two systems, thus controlling the active and reactive power exchanged between them. However, in this case, the compensation voltage source VC may have to absorb or generate active power (PC), as well as control the reactive power (QC).
FIGURE 32.6 Ideal generic series compensator.
Figure 32.7 shows the phasor diagram of this ideal generic series compensator. This figure also shows a dashed-line circle with the locus of all the possible positions that the compensation voltage VC could take, assuming that the magnitude shown for this voltage is its maximum. Naturally, if the sum of the compensation voltage and the source voltage VS is on the circle, the magnitude of Vs1 may be smaller or larger than the magnitude of VS.
FIGURE 32.7 Phasor diagram of the ac system compensated with an ideal generic series compensator.
The compensation voltage VC can be added to the VS in a way that the resultant voltage VS1 has the same magnitude of VS but with a phase shifted by an angle α. In this case, the series compensator can be called as a phase-shifter compensator and the power flowing through the transmission line (see Fig. 32.6) is expressed below:
(32.9)
Equation (32.9) shows that transmitted power increases as the phase difference (δ –α) reaches 90°. However, its maximum value is the same as in the case of no compensation. The difference is that with this compensator, the system power angle, and angle difference between the two voltage sources at the terminals of the line can be controlled faster than the conventional way, i.e., by controlling the synchronous generator.
In Fig. 32.7, voltage VC may have any phase angle with respect to line current. Therefore, it may have to supply or absorb active power, as well as control reactive power. As in the case of the shunt device, this feature must also be taken into account in the synthesis of the actual devices. As a first approximation, when the goal is to control active power flowing through the medium- or short-length transmission lines, compensator location seems to be a question of convenience.
Figure 32.8 summarizes the active power transfer characteristics in a transmission line as a function of the power angle, δ, as shown in Figs. 32.1 and 32.2, for the cases of the line without compensation, line with series or shunt compensation, and line with phase-shift compensation. These characteristics are drawn on the assumption that the source voltages Vs and Vr (see Fig. 32.2) have the same magnitude. A 50% series compensation (s=0.5) as defined in Eq. (32.4) presents a significant increase in the line power transfer capability.
FIGURE 32.8 Power transfer characteristics for the case of shunt, series, and no compensation.
As shown in Fig. 32.8, in general, series compensation is the best choice for increasing power transfer capability. The phase-shifter compensator is important to connect two systems with excessive or uncontrollable phase difference. It does not increase power transfer capability significantly; however, it may allow the adjustment of large or highly variable phase differences. The shunt compensator does not increase power transfer capability in a significant way in its normal operating region, where the angle δ is naturally below 90° and in general around 30°. The great importance of the shunt compensator is the increase in the stability margin, as explained in Fig. 32.9.
FIGURE 32.9 Stability margin characteristics — stable situation.
Figure 32.9 shows the power transfer characteristics (Pδ × δ) of a transmission line, which is first assumed to be transmitting power Ps0 at phase angle δ0. If a problem happens in the line (a fault, for example) the turbine that drives the generator cannot change its mechanical power input immediately even if there is no power transmission for a short time. This situation accelerates the generator, increasing its frequency and leading to an increase of the phase angle δ to δ1. If the line restarts operation at the instant corresponding to this phase angle δ1, the transmitted power will be P1, which is larger than P0 and decelerates the turbine or generator. The area A1 corresponds to the energy that accelerated the turbine. As the frequency gets higher than the rated frequency at (PS1, δ1 ), the phase angle will increase up to δ2, where the area A2 is equal to the area A1. If the area given by the A2 plus A3 is larger than A1, the system is said to be dynamically stable. On the contrary, if it is not possible to have an area A2 equal to A1, the system is said to be unstable. An unstable situation is shown in Fig. 32.10 in which the system is the same as in Fig. 32.9 but assuming a longer interval with no power transmission. In this case, the turbine or generator accelerates more than that in Fig. 32.9 and the phase angle δ increases above its critical value δc, which is slightly less than 90° reaching δ1. Therefore, the area below the Pδ curve to decelerate the system is not enough leading to an unstable system because A2 is smaller than A1.
FIGURE 32.10 Stability margin characteristics — unstable situation.
Looking at Fig. 32.8, it is possible to see that depending on the operating point, all three compensation methods increase the stability margin as the area under the curve of transmitted power Pg versus phase angle 5 is increased. The ideal shunt compensator is the one that most increases this area, and thus it is said to be the best option to increase the stability margin.
32.4 Synthesis of FACTS Devices
It has been stated that the synthesis of the compensators presented in Sections 32.2 and 32.3 can be achieved with thyristors or self-commutated switches, such as GTO, IGBT, or IGCT. Each type of switches leads to devices with different operating principles and synthesis concepts, and hence they should be discussed separately. Terms and definitions for most of the FACTS devices are given in [9].
Thyristor-based FACTS devices use line or natural commutation together with large energy storage elements (capacitors or reactors). On the other hand, devices based on self-commutating switches, such as GTOs, IGCTs, or IGBTs, use gate-controlled commutation. In general, it is said that the first generation of FACTS devices is based on conventional line-commutated thyristors, and the subsequent generations are based on gate-controlled devices or self-commutated switches. The most important FACTS devices based on thyristors and self-commutating devices are presented in the following sections.
32.4.1 Thyristor-Based FACTS Devices
32.4.1.1 Thyristor-Controlled Reactor
The most used thyristor-based FACTS device is the thyristor-controlled reactor (TCR) as shown in Fig. 32.11a. This is a shunt compensator that produces an equivalent continuous variable inductive reactance by using phase-angle control. Figure 32.11b shows the voltage and current waveforms of the TCR. The current is controlled by the firing angle α -the magnitude of the fundamental current component can be larger or smaller depending on the angle α, which can vary from 90 to 180° measured from the zero-crossing of the voltage. At α = 90°, the reactor is fully inserted in the circuit and for α = 180°, the reactor is completely out of the circuit. Figure 32.12 shows the equivalent admittance of the TCR as function of the firing angle α. Naturally, this admittance is always inductive.
FIGURE 32.11 (a) TCR and (b) its voltage and current waveforms.
FIGURE 32.12 Equivalent admittance of a TCR as a function of the firing angle a.
32.4.1.2 Thyristor-Switched Capacitor
Figure 32.13 shows the thyristor-switched capacitor (TSC). The word “controlled” used in the case of the reactor is substituted by “switched” because the thyristor is turned on only when zero-voltage switching (ZVS) condition is achieved. This means that the voltage across the thyristor terminals has to be zero at the turn-on instant. In practical cases, it maybe slightly positive because thyristors need positive anode-cathode voltages to be triggered (large anode-cathode voltage during turn-on); however, it can produce a large current spike that can damage the thyristors. Therefore, due to this switching characteristic, the thyristors can only connect the capacitor to the grid or disconnect it. Consequently, only step-like control is possible, and therefore a continuous control is not possible. The capacitor connection to or disconnection from the grid is normally performed at very low frequencies, and the harmonics, when they appear, are not a serious concern.
FIGURE 32.13 Thyristor-switched capacitor.
32.4.1.3 Static Var Compensator
The use of the TCR shown in Fig. 32.11 or the TSC shown in Fig. 32.13 allows only continuous inductive compensation or discontinuous capacitive compensation. However, in most applications, it is desirable to have continuous capacitive or inductive compensation. The static var compensator (SVC) is generally designed to operate in both inductive and capacitive continuous compensation [10, 11]. It maybe used for reactive power compensation for either voltage regulation or power factor correction. The basic three-phase SVC scheme is comprised by a three-phase TCR parallel connected to a capacitor bank. In some cases this capacitor bank can be a TSC. The TCR serves as the controller basis for the conventional SVC.
Figure 32.14 shows a single-line diagram of a SVC, where the TCRs are Δ connected and the capacitors are Y connected. The circuit does not show the filters that are normally needed due to the switching-generated harmonics. In some cases, the fixed capacitor can be replaced by a TSC to get more flexibility in terms of control range.
FIGURE 32.14 Six-Pulse SVC.
The capacitance of the SVC is calculated in such a way as to generate the maximum capacitive reactive power that it has to control. This condition is achieved when the thyristors are turned off (α = 180°). On the other hand, the maximum reactive power of the TCR inductor has to be greater than the reactive power of the capacitor bank. In this way, the SVC can control the reactive power from capacitive to inductive.
The maximum inductive reactive power is given for the case when the thyristors are turned on at minimum firing angle (α = 90°). The SVC can control reactive power from maximum capacitive for α = 180° to maximum inductive for α = 90°. Thus the SVC represents an adjustable fundamental frequency susceptance to the ac network, controlled by the firing-angle of the TCR thyristors (90° < α < 180°).
The SVC is well known, and many examples of successful applications can be found around the world.
Due to the once-per-cycle thyristor firing with phase-angle control, current with low-order harmonic components appears and Y-Δ transformers and passive filters may be needed to eliminate them. Three sets of TCRs connected in the δ side of Y-Δ transformers form a conventional six-pulse TCR. To minimize harmonic generation, it is common to have two sets of transformers connected in Y-Δ and δ-δ with the TCR connected in the δ side forming a 12-pulse TCR.
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-gered so as to connect the capacitors in series with the transmission line. If the thyristors are turned on, the capacitor is bypassed. Thyristors must be turned on at a zero-voltage condition (ZVS), as it occurs in the case of the TSC, to avoid current spikes in the switches. An example of an application based on this concept is presented in [12].
FIGURE 32.15 Thyristor-switched series capacitors.
This compensation system has the advantage of being very simple. However, it does not allow continuous control. If the connection or disconnection of the capacitors is to be made at sporadic switching, no harmonic problem occurs. Depending on the frequency, the thyristors are switched and harmonic or subharmonics may appear. In this arrangement, it is interesting to choose the value of the capacitors in such a way that many different combinations can be achieved. For example, if the total number of capacitors is three, they could have values proportional to 1, 2, and 3. Therefore, by combining these values it is possible to obtain equivalent capacitor proportional to 1, 2, 3, 4, 5, and 6.
32.4.1.5 Thyristor-Controlled Series Capacitor (TCSC)
Figure 32.16 shows the thyristor-controlled series capacitor (TCSC). In this figure, the transmission line and the voltage sources in at its ends are represented by a current source because this is the actual behavior of most of the transmission system. This compensator is also based on the TCR that was first developed for shunt connection. When the TCR is used connected in series with the line, it has to be always connected in parallel with a capacitor because it is not possible to control the current if the equivalent of the transmission line and the sources is a current source. This circuit is similar to the conventional SVC with the difference that the TCSC is connected in series with the line. In this compensator, the equivalent value of the series connected reactor can be continuously controlled by adjusting the firing angle of the thyristors. As a consequence, this device presents a continuously controllable series capacitor. Various practical systems based on this concept are under operation around the world [12–14]. This device has been used for power flow control and power oscillation damping.
FIGURE 32.16 Thyristor-controlled series capacitors.
Figure 32.17 presents the current and voltage waveforms in the TCSC, showing that although there is a large amountof harmonics in the capacitor and reactor currents, capacitor voltage is almost sinusoidal. In actual applications, these harmonics are not a serious concern, and they are filtered by the capacitor itself and by the transmission line impedance.
FIGURE 32.17 TCSC voltage and current waveforms.
Figure 32.18 shows the equivalent impedance of the TCSC as a function of the firing-angle α. This figure shows that this device has both capacitive and inductive characteristic regions divided by a resonant region. In the example shown in this figure, the resonance happens for α around 145°. In normal operation, the TCSC is controlled in the capacitive compensation region where its impedance varies from its minimum value Zmin for firing-angle α = 180° and its maximum safe value Zmax for α around 150°. Operation with α close to the resonance region is not safe. This device can operate also in the inductive region, but in this case, normally it is used only when α = 90° to decrease power transfer capability of the transmission line.
FIGURE 32.18 TCSC equivalent reactance.
32.4.1.6 Thyristor-Controlled Phase Angle Regulator
The thyristor-controlled phase angle regulator (TCPAR), shown in Fig. 32.19, as an example may improve considerably the controllability of a utility of power transmission system.
FIGURE 32.19 Thyristor-controlled phase angle regulator (TCPAR).
In this figure, only control of phase “a” is detailed. The series voltage generated in phase “a” comes from three secondary windings of a transformer whose primary side is connected between phases “b” and “c.” Each of the three secondary windings can be connected in series with the line through the thyristors’ switching. The thyristors are connected in antipar-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 chosen as to decrease harmonic content of the series compensation voltage.
The TCPAR in Fig. 32.19 has some peculiarities that should be pointed out. One of them is that active power can only flow from the shunt to the series windings. The compensation voltage phasor, as shown in Fig. 32.20, has a limited range of variation; in the case of phase “a,” its locus is along a line orthogonal to Va because the injected voltage is in phase with the voltage (Vb — Vc). As a consequence, it is not possible for the TCPAR to generate a compensating voltage phasor whose locus is a circle, as shown in Fig. 32.7, for the case of an ideal generic series compensator.
FIGURE 32.20 Phasor diagram of the TCPAR in Fig. 32.19.
Other configuration of phaseshifters can be found in the literature, e.g., [15, 16].
32.4.2 FACTS Devices Based on Self-Commutated Switches
There are various different types of FACTS devices based on self-commutated switches, and the names used here are in accordance with the names published in [9]. Some of them are newer devices and are not in that reference. In this case, the name used is the same as it appears in the literature. In [2], it is possible to find most of the details of FACTS devices.
32.4.2.1 The Static Synchronous Compensator
The development of high-power self-commutated devices, such as GTOs, IGBTs, and IGCTs, has led to the development of high-power voltage source converters (VSC), such as the six-pulse two-level VSC shown in Fig. 32.21a [4] or the three-level neutral point clamped VSC shown in Fig. 32.21b [17]. In the figures, the switches are GTOs (they could be IGBTs, IGCTs, or other self-commutating switches) with an antiparallel-connected diode, which operates with a unidirectional voltage-blocking capability and a bidirectional current 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.
FIGURE 32.21 (a) Basic six-pulse VSI two-level var compensator and (b) basic three-level var compensator.
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 source maybe replaced by a capacitor. If active power has tobe absorbed or generated by the compensator, an energy storage system has to be connected at the dc side of the VSC.
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.
The first high-rating STATCOM is under operation since 1991 [18] in Japan and uses three single-phase VSCs to form one three-phase, six-pulses, 10-MVA converter. To guarantee low losses, the switching frequency is equal to the line frequency 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 converters are connected in series through a zigzag transformer to eliminate low-frequency voltage harmonics. The device with compensation capability of 80 MVA was developed to increase the transient stability margin of the system, and it has allowed a 20% increase of the transmitted power above the previous stability limit. Since it was developed for improving transient stability margin, it normally operates in standby mode without reactive compensation and, consequently, low losses. During transient situation, this STATCOM operates for a short time until the system is stable.
The development of a ± 100-Mvar STATCOM in United States was reported in [19]. It is based on eight sets of three-phase bridge converters, similar to that shown in Fig. 32.21b; it was developed for reactive power control, so it can operate continuously with acceptable losses. The switching frequency is equal to line frequency, and the number of pulses is 48; therefore, the output voltage waveform is almost sinusoidal and harmonic filters are not used in both cases referred in [18, 19].
32.4.2.1.1 Basic Switching Control Techniques
In FACTS applications, the power ratings of the converters are in the range of some MW to hundreds of MW and the switching frequency is lower when compared with the switching frequency used in industrial application converters to avoid excessive switching losses. However, there are various switching control types. The most known so far are as follows:
32.4.2.1.2 Multipulse Converters Switched at Line Frequency
The multipulse converter was the first choice for STATCOM application because it presents low losses and low harmonic 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 produce phase differences of 15, 30, 45, and 60°. With this arrangement, the resulting output voltage and its harmonic spectrum are as shown in Fig. 32.23. The first two harmonics components are the 23rd- and 25th-order harmonics. Figure 32.24 shows the voltage waveform for a 48-pulse converter and its respective harmonic spectrum. In this case, the first two harmonic components are the 47th- and 49th-order harmonics. The total harmonic distortion (THD) for the 24-pulse and 48-pulse converters is 7 and 3.3%, respectively. These converters can also be built by using three-level converters. However, one drawback of the multipulse converter is the complexity of the transformers, which have to operate with high harmonic content in their voltage and various different turns ratio.
FIGURE 32.22 6-Pulse 2-level VSI-based 24-pulse var compensator.
FIGURE 32.23 (a) 24-Pulse converter voltage waveform and (b) its harmonie spectrum.
FIGURE 32.24 (a) 48-Pulse converter voltage waveform and (b) its harmonie spectrum.
32.4.2.1.3 PWM (Pulse Width Modulation) with Harmonic Elimination Technique
One way to avoid the complexity of the multipulse converters is to use PWM with harmonic elimination technique [20]. With this approach, it is possible to use relatively low switching frequency and, consequently, have low switching losses. The PWM modulation is obtained by off-line 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” instants calculated in such a way as to eliminate the 5th-, 7th-, 11th-, and 13th-order harmonics. This voltage corresponds to the voltage between one phase of the converter and the negative terminal of the dc side. Figure 32.25b shows the control angle as a function of the modulation index ma. Figure 32.26 shows the harmonic spectrum for the phase-to-phase voltage waveform corresponding to that shown in Fig. 32.25a. Here, it is considered that the RMS value of the fundamental component of the voltage in Fig. 32.25 is equal to unity. In Fig. 32.26, the magnitude of the fundamental component is equal to 
. The higher-order harmonics in the voltage waveform can be eliminated by a relatively small passive filter, so the voltage and the current at the converter terminals are practically harmonic-free; therefore, the transformer that connects a PWM-controlled STATCOM to the grid maybe a conventional transformer designed for sinusoidal operation.
FIGURE 32.25 (a) Example of one-phase voltage with the harmonie elimination technique and (b) the control angle as function of the modulation index.
FIGURE 32.26 Line voltage harmonic spectrum for the voltage waveform in Fig. 32.25a.
32.4.2.1.4 Sinusoidal PWM
The sinusoidal PWM control technique is possibly the simplest to implement and can be synthesized by comparing a sinusoidal reference voltage with a triangular carrier [4]. This switching control method needs 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 content at low frequencies is negligible; however, there is a relatively high harmonic content at the switching frequency, which is eliminated by a passive filter.
32.4.2.1.5 Cascade Converter
The basic cascade converter [21] topology is shown in Fig. 32.27. Only two single-phase full bridge converters are shown, the first and the nth. However, in actual application, several of them are connected in series and switched at line frequency. The resulting voltage waveform can be similar to the multipulse converter waveform with the advantage that there is no need of transformers to sum up the converters output voltage. Due to the line frequency switching, the switching losses are very low. The resulting voltage waveform can be almost sinusoidal depending on the number of series converters, and the transformer used to connect them to the grid can be a conventional sinusoidal waveform transformer, if necessary. One drawback of this converter topology 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 number of single-phase converters; and the capacitance of each capacitor has to be much higher when compared with three-phase converters. This is because the instantaneous power in the single-phase converter has a large oscillating component at double of the line frequency and it would force a large voltage ripple in the capacitors if they were small.
FIGURE 32.27 Cascade converter basic topology.
32.4.2.1.6 STATCOM Control Techniques
The control of reactive power in the STATCOM is done by controlling its terminal voltage. Figure 32.28 shows a simplified circuit in which the ac grid is represented by a voltage source Vs behind an impedance XL and the STATCOM is represented by its fundamental voltage VI. Figure 32.29a shows the case when the ac grid phasor voltage VS is in phase with the STATCOM voltage VI and both have the same magnitude. In this case, the line current IL is zero. Figure 32.28b shows the case when VS is little larger than VI. In this case, the line current IL, which lags the voltage VL by 90°, is also lagging the ac grid phasor voltage VS, and therefore, the STATCOM produces an inductive reactive power. On the other hand, Fig. 32.29c shows the case when VS is little smaller than VI. Hence, the line current IL, which lags the voltage VL by 90°, leads the voltage VS, and therefore, the STATCOM produces a capacitive reactive power. In summary, the STATCOM reactive power can be controlled if the magnitude of its VI voltage is controlled, assuming that it is in phase with VS.
FIGURE 32.28 Simplified circuit for the ac grid and the STATCOM.
FIGURE 32.29 Reactive power control in a STATCOM.
• If Vs is equal to VI, there is no reactive power and no active power in the STATCOM;
• If Vs is larger than VI, the STATCOM reactive power is inductive;
• If Vs is smaller than VI, 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 VI. There are two basic principles: in the case of multipulse converters, the output voltage magnitude can only be controlled by controlling the dc side voltage that is the dc capacitor voltage; 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 phase difference δ between Vs and VI is positive. The resulting line current is in such a way that produces an active power flowing into the converter, charging the dc capacitor. Figure 32.30b shows the phasor diagram for a negative phase angle δ. In this case, the dc capacitor is discharged. Therefore, by controlling the phase angle δ, it is possible to control the dc capacitor voltage.
FIGURE 32.30 Active power control in a STATCOM.
In general, STATCOM based on multipulse converter without 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.
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 reference frame where they can be controlled in such a way as to regulate the quadrature component of the current, which controls reactive power. The direct component of the current is used to control the dc capacitor voltage as it represents the active power.
Another way to control the STATCOM is by using the instantaneous power theory [23, 24]. This theory was first proposed 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 or fundamental reactive component.
32.4.2.1.7 STATCOM DC Side Capacitor
Theoretically, the dc side capacitor of a STATCOM based on three-phase converters operating in a balanced system and controlling only the reactive power could have a capacitance equal to zero Farad, once the three-phase instantaneous reactive power does not contribute to the energy transfer between the dc and ac side [25]. However, in actual STATCOMs, a finite capacitor has to be used with the objective of keeping constant or controlled dc voltage as it tends to vary due to the converter switching.
One parameter commonly used in synchronous machine is the inertia constant H defined by
(32.10)
where J and ω are the rotor moment of inertia and angular speed and S is the machine apparent power. A similar parameter for the STATCOM, Hst, can be defined by
(32.11)
where C and VDC are the dc capacitance and its voltage and S is the STATCOM apparent power.
In both cases, the constants H and Hst are values in time units corresponding to the relation of the amount of energy stored in the rotor inertia, or in the capacitor, and the machine, or STATCOM, apparent power, respectively. In the case of synchronous machines, the value of H is in the range of few seconds (generally, in the range of 1-3 s), and in the case of the STATCOM, Hst value is in the range of milliseconds or below (0.5–5 ms) if only reactive power is to be controlled. These numbers show that the STATCOM based on three-phase converters and designed only for reactive power control (which is the general case) has almost no stored energy in its dc capacitor. On the other hand, STATCOM based on single-phase converters without a common dc link may have larger capacitors as in the case of cascade converters due to the power oscillations at double of the line frequency.
There are STATCOMs (in some cases with different names) that are designed for operation with unbalanced loads. In this case, the dc capacitor has to be also much larger than in the case of balanced systems to avoid large voltage ripple on the dc voltage due to power oscillations at twice the line frequency, which appears naturally in unbalanced systems [26, 27] or unbalanced voltages [28] or system with flicker problem [29, 30]. In this case, the STATCOM compensates reactive power and the instantaneous oscillating active power due to the negative sequence current components. In fact, this is an extension of the shunt active power filter application where the goal is the current harmonic compensation, which includes negative sequence currents even at the fundamental frequency. If sub-harmonics are present, the device is able to filter them out as well.
32.4.2.1.8 STATCOM with Energy Storage
In general, the STATCOM is designed for reactive power compensation and it does not need large energy storage elements. However, there are some applications where it may be interesting to have some energy stored in the dc side, for example to compensate for active power for a short time. In these applications, the dc-side capacitor has to be substituted by a voltage source energy storage device like a battery [31] or a double-layer capacitor (super capacitor). Another possibility is to store energy in superconducting magnetic energy storage (SMES) systems [32, 33]. A natural solution for the use of the superconducting reactor would be the connection to the ac grid through a current source converter (CSC) instead of the voltage source converter. However, this has not been the case found in the literature. Figure 32.31 shows a block diagram of a typical STATCOM/SMES system, where the SMES is connected to the dc side of the STATCOM through a dc-dc converter, which converts the direct current in the superconductor magnet to dc voltage in the STATCOM dc side and vice versa. This STATCOM can control reactive power continuously, as well as active power for a short time, depending on the amount of energy stored in the superconducting magnet.
FIGURE 32.31 STATCOM with SMES.
32.4.2.1.9 Comparison between SVC and STATCOM
Figure 32.32a shows the steady-state volt-ampere characteristics for the SVC shown in Fig. 32.14, whereas Fig. 32.32b shows the same characteristics for a STATCOM. For operation at rated voltage, both devices can present similar characteristics in terms of control range. However, current compensation capability of SVC for lower voltages becomes smaller, whereas in the STATCOM, it does not change significantly for voltages lower than rated (but approximately above 0.2 pu). This is explained by the fact that the SVC is based on impedance control, whereas the STATCOM is based on voltage source control. Therefore, in the SVC, the current decreases with a corresponding voltage decrease, whereas in the STATCOM, the current capability of the converters depends only on the switching device used, so the maximum current can be kept unchanged even for a low voltage condition. This is an important characteristic, especially in applications where the voltage may drop (as in most cases), where the STATCOM presents a better performance.
FIGURE 32.32 Comparison between SVC and STATCOM.
32.4.2.2 Adjustable Speed Synchronous Condenser
The adjustable speed synchronous condenser is not exactly a FACTS device, as it contains an electrical machine. However, it may be an interesting shunt device to compensate reactive power continuously and relatively large amounts of active power for a short time. The basic topology of this device is shown in Fig. 32.33. It is based on a double-fed induction machine with a conventional three-phase winding in the stator and a three-phase winding in the rotor. The latter is supplied by a three-phase converter connected back-to-back to a second converter, which is connected to the grid.
FIGURE 32.33 Adjustable speed synchronous condenser.
This configuration allows the generation of a rotating magnetic flux in the rotor, which depends on the rotor converter frequency. When the machine is rotating at synchronous speed, the rotor converter operates at zero frequency and the magnetic flux in the rotor is stationary with respect to the rotor itself. In this case, the compensator operates as a conventional synchronous condenser.
However, when the rotor speed is lower or higher than the synchronous speed (normally during transients), the rotor converter generates a field current with the necessary frequency to keep the stator and rotor fluxes synchronized –if the synchronous frequency is 60 Hz and the rotor is running at 58 Hz, the rotor converter has to supply voltage or current at 2 Hz so as to synchronize the fluxes. Naturally, it would be more interesting to use field-oriented control [34] instead of scalar control to get a better performance.
This hybrid compensator may supply energy to the ac system, if rotor speed is decreased. This machine is designed to have relatively large rotor inertia so as to present a large inertia constant (which may be in the range of more than 10 s). It is also called adjustable speed rotary condenser [35]. Operation at speeds higher than the synchronous speed is also possible, if it is necessary to absorb energy from the grid.
One of the advantages of this device is that a compensator with power in the range of 400 MVA may be synthesized with power electronics converter rated at a small fraction of this power and with a large capability to supply both active (for a few seconds) and reactive power (continuously) [35].
32.4.2.3 Static Synchronous Series Compensator
In contrast to the STATCOM, which is a shunt FACTS device, it is possible to build a converter-based compensator for series compensation. Figure 32.34 shows the basic diagram of a static synchronous series compensator (SSSC) based on voltage source converter (VSC) with a capacitor in its dc side and connected in series with the transmission line through a transformer [36]. The inputs to the SSSC controller shown in this figure are the line current and voltage, as well as the active and reactive power references p*SE and q*SE, respectively. In general, only reactive power is compensated, and in this case, the active power reference p*SE is zero and q*SE is chosen so as to control power flow. Naturally, in the case of power flow control, it is necessary to have another control loop for this purpose and this is not shown in the figure.
FIGURE 32.34 Static synchronous series compensator (SSSC).
One should note that if current is flowing in the transmission line, the SSSC controls reactive power by generating voltage vC in quadrature with the line current. The device then shows capacitive or inductive equivalent impedance by increasing or decreasing the power flow, respectively. The compensation characteristic is, as shown in Fig. 32.8, for the case of series compensation where the transmitted power is always positive for 0 < δ < 180°. That is, with reactive power control, it is only possible to transmit in one direction. However, if instead of controlling q*SE, voltage vC is controlled, it is possible to have power flow reversion. Figure 32.35 shows the power flow characteristics of a transmission line with an SSSC using constant voltage control. The voltage is in quadrature with the current, and its magnitude is kept constant. The figure shows that it is possible to have power flow reversion for small values of δ with a constant compensation voltage vC.
FIGURE 32.35 Power flow characteristics for voltage-controlled SSSC.
It should be noted that the discussion presented with respect to the converters for the case of the STATCOM is also valid for the case of the SSSC. The SSSC can be used for power flow control and for power oscillation damping as well.
32.4.2.4 Gate-Controlled Series Capacitor
Figure 32.16 shows the TCSC, which is basically a TCR in parallel with a capacitor and both connected in series with a transmission line. The combination is effective in continuously controlling the equivalent capacitive reactance presented to the system, mainly for power flow control and oscillation damping purposes. It was also pointed out that the device has the disadvantage of a resonance area due to the association capacitor or TCR (see Fig. 32.18).
In [37], the continuously regulated series capacitor using GTO thyristors to directly control capacitor voltage is presented. Figure 32.36 shows the GTO thyristor-controlled series capacitor (GCSC) [38], hereafter renamed as the gate-controlled series capacitor because it may also be built using other self-commutated switches such as IGBTs or IGCTs.
FIGURE 32.36 Gate-controlled series capacitor.
The GCSC circuit consists of a capacitor and a pair of self-commutated switches in antiparallel connection. As the switches operate under ac voltage, they must be able to block both direct and reverse voltages and allow current control in both directions.
Figure 32.37 shows the voltage and current waveforms for the GCSC, where the current in the transmission line is assumed to be sinusoidal. If the switches are kept turned on, the capacitor is bypassed and does not present any compensation effect. If they are kept off, the capacitor is fully inserted in the line. On the other hand, if the switches are conducting and are turned off at a given blocking angle γ counted from the zero-crossings of the line current, the capacitor voltage vC appears as a result of the integration of the line current passing through it. The next time the capacitor voltage crosses zero, the switches are turned on again, to be turned off at the next turn-off angle y. With this switching control sequence, it must be clear that the switches always switch at zero voltage. This is an interesting feature for the series connection of the switches under high-voltage operation [39].
FIGURE 32.37 GCSC voltage and current waveforms.
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 vc. Also, it can be smaller than the TCSC [40]. Moreover, the dynamic response of the GCSC is generally better than that of 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.
FIGURE 32.38 GCSC équivalent fundamental impedance.
32.4.2.5 Unified Power Flow Controller
The unified power flow controller (UPFC) is a more complete transmission line compensator [42], shown as a simplified block diagram in Fig. 32.39. This device can be understood as a STATCOM and an SSSC with a common dc link. The energy storing capacity of the DC capacitor is generally small, and so the shunt converter has to draw drain (or generate) active power from the grid in exactly the same amount as the active power being generated (or drained) by the series converter. If this is not followed, the dc link voltage may increase or decrease with respect to the rated voltage, depending on the net power being absorbed or delivered by both converters. On the other hand, the reactive power in the shunt or series converter can be controlled independently, giving a great flexibility to the power flow control.
FIGURE 32.39 UPFC block diagram.
The phasor diagram in Fig. 32.40 shows that the UPFC can be controlled in such a way as to produce any voltage phasor in series with the transmission line that fits inside the dashed line circle on top of the phase voltage phasors. The maximum radius of the circle is limited by the voltage limitation of the series converter. The fact that the locus of vC is a circle is one of the greatest advantages of the UPFC when compared with the thyristor-based phase shifter. If the UPFC injects or absorbs reactive power in parallel with the system, the magnitude of voltage Vs will be increased or decreased, respectively. This extra characteristic increases the locus of the series voltage vC. Of course, this effect is only possible if an inductive impedance is present in series with the voltage source Vs, which is normally the case.
FIGURE 32.40 Phasor diagram for a system with a UPFC.
The shunt compensator of the UPFC is normally used with two objectives. The first is to control the reactive power in the point of connection, and therefore controlling the voltage at this point. The second is to control active power in such a way as to control the dc link voltage. The control technique to be used can be similar to the one used in STATCOM. The series compensator can be controlled in the same way as the SSSC, with the difference that in this case, it may control active and reactive power. Naturally, the active power control in the series compensator would change the capacitor voltage that should be controlled by the shunt compensator.
32.4.2.6 Interline Power Flow Controller
The interline power flow controller (IPFC) [43] is a UPFC-derived device with the objective of controlling power flow between lines instead of one line as in the UPFC. Figure 32.41 shows a basic block diagram of an IPFC with two converters to control the power flow in lines 1 and 2. The minimum number of converters connected back-to-back is two, but there may be more. Each converter should be connected in series with a different transmission line and should control power flow in this line with the following conditions:
• The reactive power control can be totally independent in each converter;
• The active power flowing into or out of each converter has to be coordinated in such a way that the dc link voltage is kept controlled.
FIGURE 32.41 Block diagram of IPFC with two converters.
The dc link voltage control can be achieved in a similar way as in the case of the UPFC. In this case, one of the series converters can control the compensation voltage freely and it may produce active power flowing into or from the dc link, which would charge or discharge the dc link capacitor. Therefore, the other converter has to be controlled to regulate this dc voltage. If there are n converters with n greater than two, (n – 1) converters can absorb or generate active power, whereas one converter has to control the dc link voltage. Anyway, all n converters can control reactive power freely. For instance, this concept allows the control of the power flow in n lines and it is possible to transfer active power from one line to another to balance power flow in n parallel transmission lines.
32.4.2.7 Convertible Static Converter
Following the IPFC, a more generic concept is the convertible static converter (CSC) [44, 45], which is based on the connection of a voltage source converter in various different topologies. Considering one simple case of two transmission lines and two converters with apparent power each equals to S, it is possible to have the following topologies:
• Two converters connected in shunt operating as a STAT-COM rated at 2S apparent power;
• Two converters connected in series with one transmission line forming an SSSC with 2S apparent power;
• One converter connected in shunt and the other in series forming a UPFC;
• One converter connected in series with one line and the other connected in series with the other line forming an IPFC.
Other topologies are possible depending on how the converters are connected in the system. The basic control of each converter depends on how it is being used if, as a STATCOM, SSSC, UPFC, or IPFC.
32.5 Voltage Source Converter (VSC)-Based HVDC Transmission
The VSC-based HVDC technology is a suitable solution for dc transmission systems through underground or undersea dc cables. The basic circuit configuration for a VSC-based HVDC system is shown in Fig. 32.42. It comprises two VSCs connected back-to-back through dc cables. The dc capacitors are used at the dc side of both converters for smoothing of the dc voltage [46]. One of the main advantages of the VSC-HVDC system is that it allows independent active and reactive power control in each terminal, and thus it can be connected to weak power systems and to passive networks [47, 48]. Beyond that, the VSCs have a faster dynamic response when compared with the conventional current source converter (CSC)-based HVDC, and thus it can increase the system stability, improve the power flow control, and isolate the transients from one side to the other. These features provide more flexibility to the systems where the VSC-HVDC is connected, and hence the VSC-HVDC is addressed in this Chapter.
FIGURE 32.42 Voltage source converter HVDC system.
The VSC-HVDC system can also be seen as an extension of the IPFC concept, keeping in mind that the main idea is to transfer active power from one bus to another through a dc link. The main differences are that the IPFC is connected in series with the line and both converters are directly connected in a back-to-back configuration, i.e., without the dc cables, whereas the VSC-HVDC system is shunt connected to the bus and the converters are connected through dc cables. The VSC-HVDC system can also be connected in back-to-back configuration, and one application can be the control of the power flow in a transmission line. In this case, the VSC-HVDC can be seen as an extension of the UPFC. The difference is that the transmission line is segmented by the VSC-HVDC system and whole power flows through the converters, whereas the UPFC does not segment the line and only a fraction of the main power flows through the converters. Another application that the back-to-back VSC-HVDC can be applied is the (full converter) connection of wind turbine units to the ac grid [47, 49].
The VSC-based dc transmission has an exactly dual configuration of the conventional HVDC transmission system, which is based on the thyristor-controlled CSC. The duality can be explained by the fact that the thyristor-controlled HVDC system controls the dc link current, whereas the system based on VSC controls the dc link voltage. This concept can be used for the connection of asynchronous systems, systems with different frequencies or located in places where cable transmission is more applicable than conventional transmission lines (as in congested urban areas or underwater transmission). The number of VSCs can be two for point-to-point transmission or more for multipoint transmission.
Although the CSC-HVDC transmission can be synthesized for higher power as compared with the VSC-HVDC system, it can only control active power and may need large quantity of reactive power. This means that reactive power compensation equipment is normally necessary, which does not happen to the VSC-HVDC system.
There are different VSC topologies suitable for the dc power transmission. The most often used topologies are the two-level three-phase converter followed by the three-level three-phase converter (neutral point clamped [NPC]), both are similar to the converters shown in Fig. 32.21. New topologies for VSC-HVDC application are emerging, as in the case of the modular multilevel converter (MMC) [50]. The MMC is suitable for high-voltage or high-power application and thus it is suitable for either HVDC transmission or FACTS applications [51, 52].
For very high-power applications, a MMC is also an alternative, and potentially preferable, to a multilevel converter [53]. The MMC is being presented as the preferred potential candidate for VSC-HVDC system applications [54]. Features like modularity and capability of a multimodule VSC to handle high power or high voltage indicate that a MMC may also be an option to high-power STATCOM, SSSC, UPFC, or IPFC.
Figure 32.43 shows the basic topology of a three-phase MMC. Each leg is comprised of n submodules, which are composed of two self-commutated switches and a storage capacitor. Depending on the application, a full-bridge submodule might be necessary instead of the half-bridge shown in this figure. The submodule can be seen as a voltage source with two possible stages 0 or +VC, where VC is the voltage over the capacitor. Thus, each arm can be understood as a controllable voltage with n possible voltage steps, and the higher the number of sub modules the more-approximated sine waveform can be achieved at the ac side. The main advantages of the MMC are low switching losses, low dv/dt over individual switch, modularity, reconfigurable design, and increased energy storage [53]. Beyond that, the MMC can also be directly connected to the power system, i.e., without any power transformer [55], which can reduce the overall substation footprint and cost, resulting in a compact-area HVDC substation.
FIGURE 32.43 Modular multilevel converter topology.
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