27.1.1.1 Evaluation of Transmission Costs

The cost of a transmission line comprises the capital investment required for the actual infrastructure (i.e., right of way (RoW), towers, conductors, insulators, and terminal equipment) and costs incurred for operational requirements (i.e., losses). Assuming similar insulation requirements for peak voltage levels for both AC and DC lines, a DC line can carry as much power with two conductors (having positive/negative polarities with respect to ground) as an AC line with three conductors of the same size. Therefore, for a given power level, a DC line requires a smaller RoW, simpler and cheaper towers, and reduced conductor and insulator costs. As an example, Fig. 27.1 shows the comparative case of AC and DC systems carrying 2000 MW.

With the DC option, since there are only two conductors (with the same current capacity of three AC conductors), the power transmission losses are also reduced to about two-thirds of the comparable AC system. The absence of skin effect with DC is also beneficial in reducing power losses marginally, and the dielectric losses in the case of power cables are also very much less for DC transmission.

Corona effects tend to be less significant on DC than for AC conductors. The other factors that influence line costs are the costs of compensation and terminal equipment. DC lines do not require reactive power compensation, but the terminal equipment costs are increased due to the presence of converters and filters.

Fig. 27.2 shows the variation of infrastructure costs with distance for AC and DC transmission. AC tends to be more economical than DC for distances less than the “break-even distance” but is more expensive for longer distances. This is due to a combination of the terminal equipment costs and line costs for the two types of transmission. The break-even distances can vary from about 500 to 800 km in overhead lines depending on the per unit line costs. With a cable system, this break-even distance approaches 50 km.

27.1.1.2 Evaluation of Technical Considerations

Due to its fast controllability, a DC transmission system has full control over transmitted power, an ability to enhance transient and dynamic stability in associated AC networks and can limit fault currents in the DC lines. Furthermore, DC transmission overcomes some of the following problems associated with AC transmission:

• Stability limits
The power transfer in an AC line is dependent on the angular difference between the voltage phasors at the two line ends. For a given power transfer level, this angle increases with distance. The maximum power transfer is limited by the considerations of steady state and transient stability. The power-carrying capability of an AC line is inversely proportional to transmission distance, whereas the power-carrying ability of DC lines is unaffected by the distance of transmission.

• Voltage control
Voltage control in AC lines is complicated by line-charging requirements and voltage drops. The voltage profile in an AC line is relatively flat only for a fixed level of power transfer, corresponding to its surge impedance loading (SIL). The voltage profile varies with the line loading. For constant voltage at the line ends, the midpoint voltage is reduced for line loadings higher than SIL and increased for loadings less than SIL.
The maintenance of constant voltage at the two ends requires reactive power control as the line loading is increased. The reactive power requirements increase with line length.
Although DC converter stations require reactive power related to the power transmitted, the DC line itself does not require any reactive power.
The steady-state charging currents in AC cables pose serious problems and make the break-even distance for cable transmission around 50 km.

• Line compensation
Line compensation is necessary for long-distance AC transmission to overcome the problems of line charging and stability limitations. The increase in power transfer and voltage control is possible through the use of shunt inductors, series capacitors, static var compensators (SVCs), and, lately, the new-generation static compensators (STATCOMs).
In the case of DC lines, such compensation is not needed.

• Problems of AC interconnection
The interconnection of two power systems through AC ties requires the automatic generation controllers of both systems to be coordinated using tie line power and frequency signals. Even with coordinated control of interconnected systems, the operation of AC ties can be problematic due to (i) the presence of large power oscillations that can lead to frequent tripping, (ii) increase in fault level, and (iii) transmission of disturbances from one system to the other.
The fast controllability of power flow in DC lines eliminates all of the above problems. Furthermore, the asynchronous interconnection of two power systems can only be achieved with the use of DC links.

• Ground impedance
In AC transmission, the existence of ground (zero sequence) current cannot be permitted in steady state due to the high magnitude of ground impedance that will not only affect efficient power transfer but also result in telephonic interference.
The ground impedance is negligible for DC currents, and a DC link can operate using one conductor with ground return (monopolar operation). The ground return is objectionable only when buried metallic structures (such as pipelines) are present and are subject to corrosion with DC current flow. It is to be noted that even while operating in the monopolar mode, the AC network feeding the DC converter station operates with balanced voltages and currents. Hence, single-pole operation of DC transmission systems is possible for extended periods, while in AC transmission, single-phase operation or any unbalanced operation is not feasible for more than a second.

• Problems of DC transmission
The application of DC transmission is limited by factors such as

(1) high cost of conversion equipment,

(2) inability to use transformers to alter voltage levels,

(3) generation of harmonics,

(4) requirement of reactive power,

(5) complexity of controls.

Over the years, there have been significant advances in DC technology, which have tried to overcome the disadvantages listed above, except for item (2). These are the following:

(1) Increase in the ratings of a thyristor cell that makes up a valve

(2) Modular construction of thyristor valves

(3) Twelve-pulse operation of converters

(4) Use of forced commutation

(5) Application of digital electronics and fiber optics in the control of converters.

Some of the above advances have resulted in improving the reliability and reduction of conversion costs in DC systems.

27.1.4.1 Monopolar Link

A monopolar link (Fig. 27.3A) has one conductor and uses either ground or sea return. A metallic return can also be used where concerns for harmonic interference and/or corrosion exist. In applications with DC cables (i.e., HVDC Light), a cable return is used. Since the corona effects in a DC line are substantially less with negative polarity of the conductor as compared with the positive polarity, a monopolar link is normally operated with negative polarity.

27.1.4.2 Bipolar Link

A bipolar link (Fig. 27.3B) has two conductors, one positive and the other with negative polarity. Each terminal has two sets of converters of equal rating, in series on the DC side. The junction between the two sets of converters is grounded at one or both ends by the use of a short electrode line. Since both poles operate with equal currents under normal operation, there is zero-ground current flowing under these conditions. Monopolar operation can also be used in the early stages of the development of a bipolar link. Alternatively, under faulty converter conditions, one DC line may be temporarily used as a metallic return with the use of suitable switching.

27.1.4.3 Homopolar Link

In this type of link (Fig. 27.3C), two conductors having the same polarity (usually negative) can be operated with ground or metallic return.

Due to the undesirability of operating a DC link with ground return, bipolar links are mostly used. A homopolar link has the advantage of reduced insulation costs, but the disadvantages of earth return outweigh the advantages.

27.2.1.1 Thyristor Valves

Many individual thyristors are connected in series to build up an HVDC valve. To distribute the off-state valve voltage uniformly across each thyristor level and protect the valve from di/dt and dv/dt stresses, special snubber circuits are used across each thyristor level (Fig. 27.5).

The snubber circuit is composed of the following components:

• A saturating reactor is used to protect the valve from di/dt stresses during turn-on. The saturating reactor offers a high inductance at low current and a low inductance at high currents.

• A DC grading resistor R_G distributes the direct voltage across the different thyristor levels. It is also used as a voltage divider to measure the thyristor level voltage.

• RC snubber circuits are used to damp out voltage oscillations from power frequency to a few kHz.

• A capacitive grading circuit C_FG is used to protect the thyristor level from voltage oscillations at a much higher frequency.

A thyristor is triggered on by a firing pulse sent via a fiber-optic cable from the valve base electronics (VBE) unit at earth potential. The fiber-optic signal is amplified by a gate electronic unit (GEU) that receives its power from the RC snubber circuit during the valve's off period.

The GEU can also effect the protective firing of the thyristor independent of the central control unit. This is achieved by a breakover diode (BOD) via a current-limiting resistor that triggers the thyristor when the forward voltage threatens to exceed the rated voltage for the thyristor. This may arise in a case when some thyristors may block forward voltage, while others may not.

It is normal to include some extra redundant thyristor levels to allow the valve to remain in service after the failure of some thyristors. A metal oxide surge arrestor is also used across each valve for overvoltage protection.

The thyristors produce considerable heat loss, typically 24–40 W/cm² (or over 1 MW for a typical quadruple valve), and so, an efficient cooling system is essential.

27.2.3.1 AC Filters

AC filters (Fig. 27.7) are passive circuits used to provide low impedance, shunt paths for AC harmonic currents. Both tuned and damped filter arrangements are used. In a typical 12-pulse station, filters at eleventh and thirteenth harmonics are required as tuned filters. Damped filters (normally tuned to the twenty-third harmonic) are required for the higher harmonics. In recent years, C-type filters have also been used since they provide more economic designs. Double- or even triple-tuned filters exist to reduce the cost of the filter (see application example system).

The availability of cost-effective active AC filters will change the scenario in the future.

27.2.3.2 DC Filters

These are similar to AC filters and are used for the filtering of DC harmonics. Usually, a damped filter at the twenty-fourth harmonic is utilized. Modern practice is to use active DC filters (see also the application example system presented later). Active DC filters are increasingly being used for efficiency and space-saving purposes.

27.2.3.3 High Frequency (RF/PLC) Filters

These are connected between the converter transformer and the station AC bus to suppress any high-frequency currents. Sometimes, such filters are provided on the high-voltage DC bus connected between the DC filter and DC line and also on the neutral side.

27.4.2 Control Implementation

27.4.2.1 Historical Background

The equidistant pulse firing control systems used in modern HVDC control systems were developed in the mid-1960s [5,6]; although improvements have occurred in their implementation since then, such as the use of microprocessor-based equipment, their fundamental philosophy has not changed much. The control techniques described in Refs. [5,6] are of the pulse frequency control (PFC) type as opposed to the now-out-of-favor pulse phase control (PPC) type. All these controls use an independent voltage-controlled oscillator (VCO) to decouple the direct coupling between the firing pulses and the commutation voltage, V_com. This decoupling was necessary to eliminate the possibility of harmonic instability detected in the converter operation when the AC system capacity became nearer to the power transmission capacity of the HVDC link, that is, with the use of weak AC systems. Another advantage of the equidistant firing pulse controls was the elimination of noncharacteristic harmonics during steady-state operation. This was a prevalent feature during the use of the earlier individual phase control (IPC) system where the firing pulses were directly coupled to the commutation voltage, V_com.

27.4.2.2 Firing Angle Control

To control the firing angle of a converter, it is necessary to synchronize the firing pulses emanating from the ring counter to the AC commutation voltage that has a frequency of 60 Hz in steady state. However, it was noted quite early on (the early 1960s) that the commutation voltage (system) frequency is not a constant, neither in frequency nor amplitude, during a perturbed state. However, it is the frequency that is of primary concern for the synchronization of firing pulses. For strong AC systems, the frequency is relatively constant and distortion free to be acceptable for most converter type applications. But as converter connections to weak AC systems became required more often than not, it was necessary to devise a scheme for synchronization purposes that would be decoupled from the commutation voltage frequency for durations when there were perturbations occurring on the AC system. The most obvious method is to utilize an independent oscillator at 60 Hz, which can be synchronously locked to the AC commutation voltage frequency. This oscillator would then provide the (phase) reference for the generation of firing pulses to the ring counter during the perturbation periods and would use the steady-state periods for locking in step with the system frequency. The advantage of this independent oscillator would be to provide an ideal (immunized and clean) sinusoid for synchronizing and timing purposes. There are two possibilities for this independent oscillator:

• Fixed-frequency operation

• Variable frequency operation

Use of a fixed-frequency oscillator (although feasible and called the pulse phase control oscillator) is not recommended, since it is known that the system frequency does drift, between say 55 and 65 Hz, due to the rotating machines used to generate electricity. Therefore, it is preferable to use a variable frequency oscillator (called the pulse frequency control oscillator) with a locking range of between 50 and 70 Hz and the center frequency of 60 Hz. This oscillator would then need to track the variations in the system frequency, and a control loop of some sort would be used for this tracking feature; this control loop would have its own gain and time parameters for steady-state accuracy and dynamic performance requirements.

The control loop for frequency tracking purposes would also need to consider the mode of operation for the DC link. The method widely adopted for DC-link operation is the so-called current margin method.

27.4.3.1 Current Control Loops

In conventional HVDC systems, a PI regulator is used (Fig. 27.12) for the rectifier current controller. The rectifier plant system is inherently nonlinear and has a relationship given in Eq. (27.1). For constant I_d and for small changes in α, we have

$\frac{\mathrm{\Delta }{V}_d}{\mathrm{\Delta }\mathrm{\alpha }}=-V_{dor}\cdot sin\mathrm{\alpha }\text{.}$

It is obvious from Eq. (27.4) that the maximum gain (ΔV_d/Δα) occurs when α=90 degrees. Thus, the control loop must be stabilized for this operation point, resulting in slower dynamic properties at normal operation with α within the range 12–18 degrees. Attempts have been made to linearize this gain and have met with some limited success. However, in practical terms, it is not always possible to have the DC link operating with the rectifier at 90 degrees due to harmonic generation and other protection elements coming into operation also. Therefore, optimizing the gains of the PI regulator can be quite arduous and take a long time. For this reason, the controllers are often pretested in a physical simulator environment to obtain approximate settings. Final (often very limited) adjustments are then made on-site.

Other problems with the use of a PI regulator are listed below:

• It is mostly used with fixed gains, although some possibility for gain scheduling exists.

• It is difficult to select optimal gains, and even then, they are optimal over a limited range only.

• Since the plant system is varying continually, the PI controller is not optimal.

A similar current control loop is used at the inverter (Fig. 27.13). Since the inverter also has a gamma controller, the selection between these two controllers is made via a MINIMUM SELECT block. Moreover, in order to bias the inverter current controller off, a current margin signal ΔI is subtracted from the current reference I_or received from the rectifier via a communication link.

27.4.3.2 Gamma Control Loop

At the inverter end, there are two known methods for the gamma control loop. The two variants are different only due to the method of determining the extinction angle:

– Predictive method for the indication of extinction angle (gamma)

– Direct method for actual measurement of extinction angle (gamma)

In either case, a delay of one cycle occurs from the indication of actual gamma and the reaction of the controller to this measurement. Since the avoidance of a commutation failure often takes precedence at the inverter, it is normal to use the minimum value of gamma measured for the 6 or 12 inverter valves for the converter(s).

1. Predictive method of measuring gamma
The predictive measurement tries to maintain the commutation voltage-time area after commutation larger than a specified minimum value. Since the gamma prediction is only approximative, the method is corrected by a slow feedback loop that calculates the error between the predicted value and actual value of gamma (one cycle later) and feeds it back.
The predictor calculates continuously, by a triangular approximation, the total available voltage-time area that remains after commutation is finished. Since an estimate of the overlap angle μ is necessary, it is derived from a well-known fact in converter theory that the overlap commutation voltage-time area is directly proportional to direct current and leakage impedance (assumed constant and known) value of the converter transformer.
The prediction process is inherently of an individual phase firing character. If no further measures are taken, each valve would fire on the minimum margin condition. To counteract this undesired property, a special firing symmetrizer is used; when one valve has fired on the minimum margin angle, the following two or five valves fire equidistantly. (The choice of either two or five symmetrized valves is mainly a stability question.)

2. Direct method of measuring gamma
In this method, the gamma measurement is derived from a measurement of the actual valve voltage. Waveforms of the gamma measuring circuit are shown in Fig. 27.13. An internal timing waveform, consisting of a ramp function of fixed slope, is generated after being initiated from the instant of anode current zero. This value corresponds to a direct voltage proportional to the last value of gamma. From the gamma values of all (either 6 or 12) valves, the smallest value is selected to produce the indication of measured gamma for use with the feedback regulator (Fig. 27.14).
This value is compared with a gamma-ref value, and a PI regulator defines the dynamic properties for the controller. Inherently, this method has an individual phase control characteristic. One version of this type of control implementation overcomes this problem by using a symmetrizer for generating equidistant firing pulses. The 12-pulse circuit generates 12 gamma measurements; the minimum gamma value is selected and then used to derive the control voltage for the firing pulse generator with symmetrical pulses (Fig. 27.15).

27.6.1.1 Power Transmission Capacity

The converter station is presently constructed for monopolar operation for power transfer of 240 MW in both directions with provisions for future extensions to a bipole configuration giving a total power-transfer capability of 600 MW. The HVDC line is constructed with two pole conductors to cater for the second 240 MW pole. Full-length neutral conductors are used instead of ground electrodes because of high land costs and inherently high values of soil resistivity.

The monopole is rated for a continuous power of 240 MW (240 kV and 1000 A) at the DC terminal of the rectifier station. In addition, there is a 10 min overload capability of up to 450 MW, which may be utilized once per day when all redundant cooling equipment is in service.

The HVDC interconnection scheme is capable of continuous operation at a reduced DC voltage of 210 kV (70%) over the whole load range up to the rated DC current of 1000 A with all redundant cooling equipment in service.

27.6.1.2 Performance Requirements

A high degree of energy availability was a major design objective (Fig. 27.23). Guaranteed targets for both stations are the following:

• Energy availability: >99.5%

• Forced energy unavailability: <0.43%

• Forced outage rate: <5.4 outages per year

27.6.1.3 Technical Information

See Table 27.6.

27.6.1.4 Major Technical Features

The station incorporates the latest state-of-the-art technology in power electronics and control equipment. The features include the following:

• A fully decentralized control and protection system

• Active DC filter technology

• Hybrid DC current shunt measuring devices

• Triple-tuned AC filter

27.7.1.1 Thyristor Development

HVDC thyristors are now available with a diameter of 150 mm at a rating of 8–9 kV and power handling capacity of 1500 kW that will lead to a dramatic decrease in the number of series-connected components for a valve with consequential cost reductions and improvement in reliability.

The development of the light-triggered thyristor (LTT) (Figs. 27.24 and 27.25) is likely to eliminate the electronic unit (with their high number of electronic components) for generating the firing pulses for the thyristor (Fig. 27.26). The additional functional requirements of monitoring and protection of the device are being incorporated also.

Both of the above developments present the possibility of achieving compact valves that can be packaged for outdoor construction, thereby reducing the overall cost and reliability of the station.

27.7.1.2 Higher DC Transmission Voltages

For long-distance transmission, there is a tendency to use a high voltage to minimize the losses. The typical transmission voltage has been ±500 kV, although the Itaipu project in Brazil uses 600 kV. The transmission voltage has to balance against the cost of insulation. The industry is considering raising the voltage to ±800 kV.

27.7.1.3 Controls

It is now possible to operate an HVDC scheme into an extremely weak AC system, even with short-circuit capacity down to unity.

Using programmable DSPs has resulted in a compact and modular design that is low cost; furthermore, the number of control cubicles has decreased by a factor of almost 10 times in the past decade. Now, all control functions are implemented on digital platforms. The controls are fully integrated having monitoring, control, and protection features. The design incorporates self-diagnostic and supervisory characteristics. The controls are optically coupled to the control room for reliable operation. Redundancy and duplication of controls is resulting in very high reliability and availability of the equipment.

27.7.1.4 Outdoor Valves

The introduction of air-insulated, outdoor valves will reduce costly requirements for a valve hall. The use of a modular, compact design that will be preassembled in the manufacturing plant will save installation time and provide for a flexible station layout. This design has been feasible because of development of a composite insulator for DC applications that is used as a communication channel for fiber optics, cooling water, and ventilation air between the valve unit and ground.

27.7.1.5 Active DC Filters

This development, made possible due to advances in power electronics and microprocessors, has resulted in a more efficient DC filter operating over a wide spectrum of frequencies and provides a compact design (Fig. 27.27).

27.7.1.6 AC Filters

Conventional AC filters used passive components for tuning out certain harmonic frequencies. Due to the variations in frequency and capacitance, physical aging, and thermal characteristics of these tuned filters, the quality factors for the filters were typically about 100–125, which meant that the filters could not be too sharply tuned for efficient harmonic filtering. The advent of electronically tunable inductors, based on the transductor principle, means that the Q-factors can now approach the natural one of the inductor. This will lead to much more enhanced filtering capacities (Fig. 27.28).

27.7.1.7 AC-DC Current Measurements

The new optical current transducers utilize a precision shunt at high potential. A small optical fiber link between ground and high potential is utilized resulting in a lower probability of a flashover. The optical power link transfers power to high potential for use in the electronic equipment. The optical data link transfers data to ground potential. This transducer results in high reliability, compact design, and efficient measurement (Fig. 27.29).

27.7.1.8 New Topologies

Two new topological changes to the converter design will impact greatly on future designs:

1. Series-compensated commutation:
There are two variants to this topology: the capacitor-commutated converter (CCC) (Fig. 27.30A) and the controlled series capacitor converter (CSCC) (Fig. 27.30B). Essentially, the behavior of the two variants is very similar. The insertion of a capacitor in series with the converter transformer leakage reactance causes a major reduction in the commutation impedance of the converter resulting in a reduction in the reactive power requirement of the converter. An increase in the size of the series capacitor can even result in the converter operation at a leading power factor if so desired. However, the negative impact of a lower commutation impedance results in additional stresses on the valves and transformers and additional cost implications [7].
The first CCC back-to-back converter station (rated at 2×550 MW) has been put into service at Garabi, on the Brazilian side of the Uruguay River. The system interconnects the electric systems of Argentina and Brazil.

2. Voltage-source converters (VSC): The use of self-commutation with the new-generation switching devices (i.e., GTOs and IGBTs) has resulted in the topology of a voltage-source converter (VSC) (Fig. 27.31) as opposed to the conventional converter using line-commutated thyristors and current source converter (CSC) topology. The VSC, being self-commutated, can control active/reactive power and, with PWM techniques, control harmonic generation as well. The application of such circuits is presently limited by the switching losses and ratings of available switching devices. The ongoing advances in power electronic devices are expected to have a major impact on the future application of this type of converter in HVDC transmission. New application areas, particularly in distribution systems, are being actively investigated with this topology. Table 27.5 provides a partial list of the HVDC links in operation using this technique.
One major difficulty for the use of the VSC is the threat posed to the valves from a short circuit on the DC line. Unlike the CSC where the valves are inherently protected against short-circuit currents by the presence of the smoothing reactor, the VSC is relatively unprotected. For this reason, the VSC applications are almost always used with DC cables where the risk of a DC line short circuit is greatly reduced (Table 27.7).

27.7.1.9 Compact Station Layout

The advances discussed above have resulted in marked improvement of the footprint requirement of the compact station [8] of the year 2000 that has about 24% space requirement of the comparable HVDC station designed in the past decade (Fig. 27.32).

27.8.2.1 AC Shunt RLC-Filters

Switching of high-power, high-frequency switches generates harmonics in the converter output voltages and currents. The order of harmonics generated is directly related to the PWM switching frequency of the semiconductor switches.

Single- or double-tuned low-pass and high-pass damped RLC filters are connected to suppress these harmonics. The frequency modulation index is defined as m_f that is defined as the ratio of the switching frequency of the converter to the fundamental frequency of the AC voltage. In the case of three-phase VSC, the harmonics in the line-to-line voltages are present. The odd harmonics exist as sidebands, centered around the m_f and its multiples where m_f is odd. The value of m_f is chosen such that it should be an odd integer to eliminate the even harmonics; also, if it is a multiple of 3, then most of the triplen harmonics are canceled out in the line-to-line voltage.

27.8.2.2 Converter Transformer

A converter transformer interfaces the VSC AC terminals to AC network with suitable voltage level at both sides. It provides electric isolation and operates as a filter between converter and AC networks and provides the appropriate AC voltage level to optimize the available converter valve voltage rating. Configuration and rating of the transformer can be decided from the total system power rating, converter topology, and specified requirements.

27.8.2.3 Voltage Source Converter

The VSC is the main building block of the VSC-HVDC system. The number of switches employed depends on the operating characteristic and voltage level required. The series-connected IGBT switches, connected with antiparallel diodes, make up a valve. Two valves are connected in series to make up the converter leg for one phase. VSC can operate as a rectifier or an inverter at either end depending on the current flow direction. Two converters can be connected as a back-to-back system to connect two different AC grids, DC transmission line, or overhead cables for bulk power transmission or underground cables for connection of offshore oil rigs, islands, or offshore wind farms. The six-switch converter comprises a group of six valves. Different types of PWM techniques are used to operate and control the converter switches. Typical IGBT has rating of 6.5 kV and 2.4 kA. The voltage across the IGBT switch in the ON state is typically in the range of 1–3 V that creates the ON state losses. The switching losses are the second major loss mechanism and are due to fact that, during the turn ON and turn OFF transition, current is still flowing while voltage is present across the device. In order to minimize the switching losses, the maximum switching frequency needs to be carefully considered. VSC is equipped with the RC snubbers and series R-L elements to reduce the dv/dt and di/dt stresses on the switches during ON/OFF transitions.

27.8.2.4 DC Transmission

The DC system can be in the form of a transmission line, with underground or overhead cables. The overhead cables can be used with a moderate size of towers. The extruded polymer cable is a newly developed technique in which the insulation is highly resistant to the DC voltage.

The DC transmission system adopted here is a bipolar transmission system in which the power can flow in both the overhead poles and ground is used as a return path in case of monopolar operation. In case of failure or preplanned maintenance of one pole, reduced power can still be transmitted using the other pole. Two smoothing inductors are connected on DC transmission system to reduce the ripples in the DC current.

27.8.2.5 DC Capacitors

As shown in Fig. 27.33, two series-connected DC capacitors of same size are employed across the DC terminals of converter with grounded midpoint. The size of the capacitor depends on the required DC voltage level and the acceptable DC ripple.

The DC voltage should be adequate for the generation of sinusoidal voltages on AC side of the converter. For the system to operate in the linear range of the PWM, the DC voltage should be 1.634 times the value of root mean square (RMS) AC voltage.

The PWM switching of high-power high-frequency switches generates the harmonics in the DC current flowing in the transmission line. This generates the harmonics in the DC voltage that is strongly related to the converter AC voltage. By evaluation of the magnitude of ripple and the switching frequency of the semiconductor switches, the DC side capacitor ratings can be finalized.

The value of DC capacitor C_DC used here can be small, which may result in a faster converter response. The energy stored in the capacitor is released during transients that will help to stabilize the power flow on the DC transmission system. The DC capacitor size is characterized with a time constant τ, which can be defined as the ratio between the energy stored in the capacitor at the rated DC voltage V_DC and the apparent power rating of the converter SC:

$\tau =\frac{\frac{1}{2}{C}_{DC}{V^2}_{DC}}{S_C}$

The time constant is equal to the time needed to charge the capacitor from zero to rated voltage V_DC if the converter is supplied with a constant active power equal to SC. The time constant τ can be selected to be small to satisfy ripple and transient overvoltage requirement on the DC voltage. A relatively small time constant allows fast control of active power and reactive power.

27.8.3.1 Two-Level Voltage Source Converter

A two-level bridge is the simplest circuit configuration that can be used to construct a three-phase VSC. It has been widely used in many applications for a range of power levels. As shown in Fig. 27.34, the converter can generate DC voltage waveform of only two values, ±V_DC/2, where V_DC is the total DC voltage. Relatively simple power and control circuitry, small DC capacitor size, small footprint environmentally, and same semiconductor duty ratio are some of the advantages related to a two-level VSC.

27.8.3.2 Multi-level Voltage Source Converter VSC

Converter topologies with more than two-level voltages are known as multilevel converters. In this type of VSC, the output AC voltage waveform has different level according to the construction of the VSC. The main requirement for multilevel converters is to synthesize a sinusoidal voltage from several voltage levels that are obtained from the DC side capacitor voltages. Multilevel VSCs are divided into different types according to their application. The multilevel VSC found various applications in power systems due to its high power density, excellent performance, and high reliability. Various multilevel topologies are explained next.

27.8.3.3 Neutral Point Diode Clamped VSC

Neutral-point diode-clamped VSC topology is shown in Fig. 27.35. As shown, this topology uses clamping diodes to limit the dynamic and static overvoltages of switching devices. The clamping diodes are connected to the center point of the DC bus capacitor.

The advantages of this topology include reasonable small size of the DC capacitors, small footprint environmentally, and good quality AC output waveform. An n-level diode-clamp converter typically consists of (n-1) capacitors on the DC bus and produces n-levels of the converter output AC voltage. With a higher number of levels, harmonics generation is very low that can even avoid the need for filters in some cases. The disadvantages are related to voltage balancing across the DC capacitors, uneven loss distribution between devices, and excessive clamping diodes necessity in higher levels.

27.8.3.4 Flying Capacitor VSC

Fig. 27.36 shows the three-level flying-capacitor-type VSC topology. This topology uses capacitors instead of diodes in the diode-clamped topology. For an n-level converter, (n−1) numbers of DC capacitors at DC bus and (n−1)×(n−2)/2 number of auxiliary capacitors per phase leg are required. These capacitors are known as floating capacitors.

The AC waveform synthesized by this topology is better than the diode-clamped topology. The advantages of this topology are the extra ride through capabilities during power outage and severe disturbances due to large number of storage capacitors, switch combination redundancy for balancing different voltage levels, and avoidance of harmonic filters in higher-level applications. The requirement of an excessive number of storage capacitors on DC side and across the semiconductor switches in higher number of levels makes this topology very expensive. The converter control system is complex, and switching losses are higher compared with diode-clamped topology.

27.8.3.5 ANPC (Actively Neutral Point Clamped) converter

Fig. 27.37 shows the three-level ANPC converter topology in which the clamping diodes are replaced by semiconductor switches. The disadvantage of uneven loss distribution across various devices in the neutral-point diode-clamped converter topology is mitigated by this newly developed topology.

27.8.3.6 Cascaded H-Bridge Converter

This VSC topology (Fig. 27.38) is a cascaded structure that consists of full-bridge inverter units connected in series.

Each unit is fed by a separate DC capacitor, and no other circuit to balance the voltage matching of the switching devices is necessary. There is no need to add the clamping diodes or voltage-balancing capacitors in this topology that results in a relatively simple construction. Main drawback of this topology is the requirement of several independent DC power supplies.

27.8.3.7 Multi-pulse Topologies

In a six-switch converter, the commutation of current takes place six times per cycle. In the case of 12-switch converter, two six-switch converters are connected in series to form a 12-switch converter topology. By using the six-switch converter, the additional multiswitch topologies in multiples of six can be created to form the required pulse level. The 24-switch and 48-pulse converters are implemented in some research papers for application as a STATCOM in power system. The main purpose of using these topologies is to reduce the voltage and current harmonics in the system. As the number of switches increases, the harmonic distortion in the system decreases proportionally.

27.8.4.1 Sinusoidal PWM

The PWM technique used for switching of the semiconductor devices of converter decides the frequency and nature of the converter output AC voltage. So to get the sinusoidal waveform as an output, sinusoidal PWM technique is used. The sinusoidal modulating waveform of 60 Hz system frequency is compared with a high-frequency triangular waveform to generate the pulse-width modulated firing pulses for converter. Two different SPWM methods can be implemented to get the required output.

(a) Bi-polar SPWM
In the case of bipolar sinusoidal PWM method, a single fundamental frequency modulating waveform per phase is compared with the high-frequency triangular waveform. The output voltage switches between −V_DC/2 and +V_DC/2 voltage levels where V_DC is the total DC voltage. It is the reason why this type of switching is called a bipolar PWM switching. As shown in Fig. 27.39, during comparison, when the sinusoidal waveform is greater than the triangular waveform, the PWM trigger signal is high, otherwise at lower level.

(b) Uni-polar SPWM
In the case of unipolar sinusoidal PWM technique, two same phase fundamental frequency modulating waveforms with opposite polarity are compared with the high-switching-frequency triangular waveforms. The output voltage switches between +V_DC/2 and 0 or between 0 and −V_DC/2. For this reason, this type of PWM scheme is called a PWM with a unipolar voltage switching.

27.8.5.1 Operating Principle of VSC-HVDC

The VSC-HVDC operating principle can be explained from the SLD shown in Fig. 27.40, where two AC networks are connected by a VSC-HVDC transmission system.

The converter transformer connecting AC network and converter can be modeled as an equivalent series resistance and reactance. The transformer resistance is very small compared with the transformer reactance, so it can be neglected in power calculations. The phase shift between both sides’ voltages due to transformer reactance is responsible for active power flow. At sending end, the voltage V_S1 at AC bus is considered as a reference, so the converter output AC voltage V_C1 has phase shift δ₁ with respect to the bus voltage V_S1. The magnitude and phase angle of converter output AC voltage V_C1 is controlled by the VSC control system. The active and reactive power flow between the AC system and the converter depends on the magnitude of the voltages at both sides of the transformer, the transformer reactance X_T1 and the phase angle δ₁ between them. The active and reactive power flow between AC bus and converter AC terminals can be expressed as follows: the active power at sending end and receiving end is given by

$P_S=\frac{\left|V_{S_1}\right|V_{C_1}|\times sin{\mathrm{\delta }}_1}{X_{T_1}},P_R=\frac{\left|V_{S_2}\right|\times \left|V_{C_2}\right|\times sin{\mathrm{\delta }}_2}{X_{T_2}}$

The reactive power at sending end and receiving end is given by

$Q_S=\frac{\left|V_{S_1}\right|{}^2}{X_{T_1}}-\frac{\left|V_{S_1}\right|\times \left|V_{C_1}\right|\times cos{\mathrm{\delta }}_1}{X_{T_1}},Q_R=\frac{\left|V_{S_2}\right|\times \left|V_{C_2}\right|\times cos{\mathrm{\delta }}_2}{X_{T_2}}-\frac{\left|V_{S_2}\right|{}^2}{X_{T_2}}$

The amplitude, phase angle, and frequency of fundamental component of converter output AC voltage V_C1 and V_C2 can be controlled using the SPWM technique. If the voltage at the DC side of the converter is V_DC that is assumed to be constant, then the fundamental frequency component of converter output AC voltage can be derived from the following equation:

$Vc\left(t\right)=\frac{1}{2}{V}_{DC}{M}_{i}sin\left(\mathrm{\omega }t+\mathrm{\delta }\right)$

where V_DC is the voltage on DC side, ω is the angular frequency, M_i is modulation index, and δ is the phase angle between the converter output AC voltage and the AC bus voltage. Mi can be defined as the ratio of peak value of voltage of modulating waveform (fundamental frequency sinusoidal waveform) to the peak value of voltage of carrier waveform (switching-frequency triangular waveform). From Eq. (27.9), it is seen that the fundamental component of converter voltage depends on the variables Mi, angle δ, and frequency that are independently controlled by VSC controllers. The active and reactive power can be controlled by controlling the phase angle δ and the amplitude of the fundamental frequency component of converter AC output voltage V_C, respectively.

In a VSC-HVDC, the polarity of DC voltage is constant, so the power reversal is done by current reversal in the DC link. The current in DC link flows from higher to lower DC voltage level. For stable VSC operation and flow of active power, the DC-link voltage is maintained at a desired reference value by using a feedback control loop. The power flow to and from the AC source can be controlled according to the DC-link voltage requirements. The voltage V_DC is measured and controlled in such manner that the DC current flow can be in either direction depending on the requirement of active power flow direction.

27.8.5.2 Four Quadrant Operation of VSC

Active power flow direction for rectifier or inverter operation and reactive power flow direction for inductive or capacitive operating mode of VSC can be explained by a P-Q circle diagram shown in Fig. 27.41. The diagram explains the ability of VSC to operate in all four quadrants of P-Q circle and to achieve the independent control of active and reactive power. The direction of current flow and hence active power flow decides the rectifier or inverter operation of converter.

In the first quadrant, both the active and reactive powers are positive, which means that the converter injects both powers to AC system that shows the capacitive mode of inverter operation. The converter output AC voltage magnitude is higher than AC bus voltage and leads AC bus voltage by an angle δ.

In the second quadrant, the active power is negative, and the reactive power is positive, which explains the capacitive mode of rectifier operation. In this case, the converter output AC voltage amplitude is higher than AC bus voltage, but it lags the AC bus voltage by an angle δ.

Both the powers in the third quadrant are negative that means the converter absorbs both powers from the AC system, which explains the inductive mode of rectifier operation. In this case, the AC bus voltage magnitude is higher than the converter output AC voltage, and it leads by an angle δ.

In the fourth quadrant, the active power is positive, and the reactive power is negative, which explains the inductive mode of inverter operation. Here, the converter output AC voltage leads the AC bus voltage, but its magnitude is less than the AC bus voltage.

According to the converter MVA capacity and system requirements, converter can operate in any mode (i.e., capacitive or inductive) of rectifier or inverter operation.

27.8.5.3 Rectifier-Inverter Operation of VSC

The rectifier or inverter operation of VSC can be explained by considering Fig. 27.42. AC bus voltage V_S can be taken as a reference, and V_C is the converter AC output voltage with phase shift δ. The converter transformer can be represented by an equivalent resistance R_T and reactance X_T. Two capacitors of same rating 2C_DC are connected in series across the DC terminals of the converter. The direction of current flow decides the operation of VSC as a rectifier or inverter.

As shown in Fig 27.43, the AC system voltage V_S leads the converter AC output voltage V_C by an angle δ. The active power flows from the AC system to the converter, so the converter operates as a rectifier. As shown in the figure, ΔV is the voltage drop across the transformer impedance that is controlled in order to control the angle δ. In the rectifier mode of operation, the current I_DC is considered positive, and the capacitor C_DC is discharged through the DC transmission system. The error signal demands the control circuit for more power from the AC supply. The control circuit thereby generates the appropriate PWM signals for the switching devices, and accordingly, more current flows from the AC to DC side, and the capacitor voltage recovers its predefined value.

As shown in Fig. 27.44, the AC system voltage V_S lags the converter AC output voltage by an angle δ. In this case, the active power flows from the converter to AC system, so the converter operates as an inverter. In the inverter mode of operation, I_DC becomes negative, and the capacitor C_DC is overcharged. The error signal demands the controls to discharge the capacitor C_DC and return power to the AC system. The PWM can control both the active power and reactive power independently. Thus, this type of converter can be used for power factor correction also in addition to power transmission.

Depending on the control strategy, VSC can be operated as either inverter or rectifier; therefore, it is often referred to as a converter. Two such converters are often cascaded to control the power flow between two AC networks. The first converter converts AC voltage to variable DC-link voltage, and the second converter converts the DC voltage to variable AC voltage with fixed or variable frequency.

27.9.5.1 DC Voltage Controller

As shown in Fig. 27.46, the instantaneous active and reactive powers in dq reference frame at the AC side of the VSC and the power P_DC transmitted on the DC side of the VSC are expressed as

$P=\frac{3}{2}\left(V{s}_d\cdot i_d+V{s}_q\cdot i_q\right)$

$Q=\frac{3}{2}\left(V{s}_d\cdot i_d-V{s}_q\cdot i_q\right)$

$P_{DC}=V_{DC}{I}_{DCT}$

where I_DCT is the current flowing in the DC terminals of the VSC.

During steady-state operation, the dq components of voltages are constant at the rated values. Therefore, the voltage Vs_d is rated voltage Vs, and Vs_q is zero. By considering the above assumptions, the active and reactive powers are expressed as follows:

$P=\frac{3}{2}\left(V_S{i}_d\right),Q=\frac{3}{2}\left(V_S{i}_q\right)$

If the losses in the converter transformer and converter are neglected, the power at the AC and DC sides can be considered equal, that is,

$\frac{3}{2}\left(V_s{i}_d\right)=V_{DC}{I}_{DCT}$

Hence,

$I_{DCT}=\frac{3}{2}\frac{\left(Vs{i}_d\right)}{V_{DC}}$

The current in the DC line of the VSC is given as

$I_{DCT}=C_{DC}\frac{d{V}_{DC}}{dt}+I_{DC}$

Any imbalance between the AC and DC powers leads to a change in voltage at the DC-link capacitors, which is given as

$C_{DC}\frac{d{V}_{DC}}{dt}=I_{DCT}-I_{DC}$

where I_DCT is the current in the DC terminals of the VSC, C_DC is the total DC side capacitance, V_DC is the DC voltage across the capacitor, and I_DC is the DC current flowing through the transmission line. The value of DC current from Eq. (27.37) can be used in Eq. (27.35), that is,

$\frac{3}{2}\left(V_S{i}_d\right)=V_{DC}\left(C_{DC}\frac{d{V}_{DC}}{dt}+I_{DC}\right)$

$C_{DC}\frac{d{V}_{DC}}{dt}=\frac{3}{2}\frac{Vs{i}_d}{V_{DC}}-I_{DC}$

From Eq. (27.39), the value of the reference current i_d⁎ is derived as follows:

${i_d}^{⁎}=\frac{2}{3}\frac{V_{DC}}{V_S}\left(C_{DC}\frac{d{V}_{DC}}{dt}+I_{DC}\right)$

The d-component of the current derived Eq. (27.41) gives the reference current for the inner current controller for DC voltage control.

27.9.5.2 Active Power Controller

The active current reference is obtained from Eq. (27.34):

${i_d}^{⁎}=\frac{2}{3}\frac{P_{ref}}{V_S}$

where P_ref is the reference active power. For accurate control of the active power, a combination of a feedback loop and an open loop is used:

${i_d}^{⁎}=\frac{2}{3}\frac{P_{ref}}{V_S}+\left(K_{p1}+\frac{K_{i1}}{s}\right)\left(P_{ref}-P_{\mathit{actual}}\right)$

where K_p1 and K_i1 are the proportional and integral gains, respectively, of the active power controller.

27.9.5.3 Reactive Power Controller

A reactive power controller similar to the active power controller is obtained from Eq. (27.34) as

${i_q}^{⁎}=\frac{2}{3}\frac{Q_{ref}}{V_S}$

where Q_ref is reference reactive power. Again, same method is used to combine a feedback loop with an open loop:

${i_q}^{⁎}=\frac{2}{3}\frac{Q_{ref}}{V_S}+\left(K_{p2}+\frac{K_{i2}}{s}\right)\left(Q_{ref}-Q_{\mathit{actual}}\right)$

where Kp₂ and Ki₂ are the proportional and integral gains, respectively, of the reactive power controller.

Fig. 27.47 shows active and reactive power control system for VSC₁. The control block of PLL is shown from which the synchronization angle θ is derived and fed to the ABC to dq block.