Reactive Power Source

31.2.4 Reactive Power Source

Converter stations consume reactive power that is dependent AC Filters (Fig. 31.7) are passive circuits used to provide low on the active power loading (typically about 50–60% of the

31.2.3.1 AC Filters

impedance, shunt paths for ac harmonic currents. Both tuned active power). The ac filters provide a part of this reactive and damped filter arrangements are used. In a typical 12-pulse power requirement. In addition, shunt (switched) capacitors station, filters at 11th, 13th harmonics are required as tuned and static var systems are also used. filters. Damped filters (normally tuned to the 23rd harmonic) are required for the higher harmonics. In recent years, C-type filters have also been used since they provide more economic

31.2.5 DC Smoothing Reactor

designs. Double- or even triple-tuned filters exist to reduce the

A sufficiently large series reactor is used on the dc side of cost of the filter (see Fig. 31.23).

the converter to smooth the dc current and for the converter The availability of cost-effective active ac filters will change protection from line surges. The reactor (Fig. 31.8) is usually

the scenario in the future. designed as a linear reactor and may be connected on the line side, neutral side, or at an intermediate location. Typical values

31.2.3.2 DC Filters

of the smoothing reactor are in the range 240–600 mH for long distance transmission and about 24 mH for a BB connection.

These are similar to ac filters and are used for the filtering of

dc harmonics. Usually a damped filter at the 24th harmonic is utilized. Modern practice is to use active dc filters (see also

31.2.6 DC Switchgear

the application example system presented later). Active dc fil- ters are increasingly being used for efficiency and space saving This is usually a modified ac equipment and used to inter- purposes.

rupt only small dc currents (i.e. employed as disconnecting switches). DC breakers or metallic return transfer breakers (MRTB) are used, if required, for the interruption of rated

31.2.3.3 High Frequency (RF/PLC) Filters

load currents.

These are connected between the converter transformer and In addition to the equipment described above, ac switchgear the station ac bus to suppress any high-frequency currents. and associated equipment for protection and measurement are Sometimes such filters are provided on the high-voltage dc also part of the converter station.

FIGURE 31.7 Installation of an ac filter in the switchyard. FIGURE 31.8 Installation of an air-cooled smoothing reactor.

832 V. K. Sood

31.2.7 DC Cables

where

Contrary to the use of ac cables for transmission, dc cables

π · 2 ·V LL do not have a requirement for continuous charging current.

V dor =

Hence the length limit of about 50 km does not apply. More-

π · ωL over, dc voltage gives less aging and hence a longer lifetime cr

R cr =

where

for the cable. The new design of HVDC light cables from ABB

=2·π·f

are based on extruded polymeric insulating material instead

of classic paper-oil insulation that has a tendency to leak. Due

where “f ” is the power frequency.

to their rugged mechanical design, flexibility, and low weight, For an inverter:

polymer cables can be installed in underground cheaply with a There are two options possible depending on choice of the plowing technique, or in submarine applications, it can be laid delay angle or extinction angle as the control variable in very deep waters and on rough sea-bottoms. Since dc cables

are operated in bipolar mode, one cable with positive polarity −V di =V doi · cos β − R ci ·I d and one cable with negative polarity, very limited magnetic (31.2) fields result from the transmission. HVDC light cables have

−V di =V doi · cos γ − R ci ·I d (31.3) successfully achieved operation at a stress of 20 kV/mm.

where

V dr and V di – dc voltage at the rectifier and inverter

31.3 Analysis of Converter Bridge

respectively.

V dor and V doi – open circuit dc voltage at the rectifier and To consider the theoretical analysis of a conventional 6-pulse

inverter respectively.

bridge (Fig. 31.9), the following assumptions are made: R cr and R ci – equivalent commutation resistance at the • DC current I d is considered constant.

rectifier and inverter respectively. • Valves are ideal switches.

L cr and L ci – leakage inductance of converter transformer at • AC system is strong (infinite).

rectifier and inverter respectively. Due to the leakage impedance of the converter transformer,

I d – dc current.

commutation from one valve to the next is not instantaneous.

α – delay angle.

An overlap period is necessary and, depending on the leakage, β – advance angle at the inverter, (β = π − α). either two, three, or four valves may conduct at any time. In

γ – extinction angle at the inverter, γ = π − α − μ. the general case, with a typical value of converter transformer

leakage impedance of about 13–18%, either two or three valves conduct at any one time.

31.4 Controls and Protection

The analysis of the bridge gives the following dc output voltages:

In a typical two-terminal dc link connecting two ac systems (Fig. 31.10), the primary functions of the dc controls are to:

For a rectifier:

• Control the power flow between the terminals. • Protect the equipment against the current/voltage stresses

V dr =V dor · cos α − R cr ·I d (31.1)

caused by faults.

Ld

DC System

AC system 1

AC System 2

Local Controls

Master Controls

Dispatch center

FIGURE 31.9 Six-pulse bridge circuit. FIGURE 31.10 Typical HVDC system linking two ac systems.

31 HVDC Transmission 833 • Stabilize the attached ac systems against any operational

TABLE 31.2 Requirements of the dc link mode of the dc link.

Steady-state requirements

Dynamic requirements

The dc terminals each have their own local controllers.

A centralized dispatch center will communicate a power order Step changes in dc current or

Limit the generation of

non-characteristic harmonics

power flow

to one of the terminals that will act as a master controller and

Maintain the accuracy of the

Start-up and fault induced

has the responsibility to coordinate the control functions of

controlled variable, i.e. dc current

transients

the dc link. Besides the primary functions, it is desirable that

and/or constant extinction angle

the dc controls have the following features:

Cope with the normal variations in

Reversal of power flow

the ac system impedances due to

• Limit the maximum dc current: Due to a limited thermal

topology changes

inertia of the thyristor valves to sustain overcurrents, the

Variation in frequency of

maximum dc current is usually limited to less than 1.2 pu attached ac system for a limited period of time.

• Maintain a maximum dc voltage for transmission: This reduces the transmission losses, and permits optimization of the valve rating and insulation.

• Minimize reactive power consumption: This implies that

31.4.1 Basics of Control for a Two-terminal

the converters must operate at a low firing angle. A typ-

DC Link

ical converter will consume reactive power between 50 From converter theory, the relationship between the dc voltage and 60% of its MW rating. This amount of reactive V

d and dc current I d is given by Eqs. (31.1)–(31.3). These power supply can cost about 15% of the station cost, three characteristics represent straight lines on the V

d –I d plane. Notice that Eq. (31.2), i.e. beta characteristic, has a positive The desired features of the dc controls are indicated below: slope while the Eq. (31.3), i.e. gamma characteristic, has a negative slope. The choice of the control strategy for a typical

and comprise about 10% of the power loss.

1. Limit maximum dc current: Since the thermal inertia two-terminal dc link is made according to the conditions in of the converter valves is quite low, it is desirable to

the Table 31.3.

limit the dc current to prevent failure in the valves. Condition 1 implies the use of the rectifier in con-

2. Maintain maximum dc voltage for transmission pur- stant current control mode and condition 3 implies the use poses to minimize losses in the dc line and converter of the inverter in constant extinction angle (CEA) control valves. mode. Other control modes may be used to enhance the

3. Keep the ac reactive power demand low at either con- power transmission during contingency conditions depend- verter terminal: This implies that the operating angles ing upon applications. This control strategy is illustrated in at the converters must be kept low. Additional benefits

Fig. 31.11.

of doing this are to reduce the snubber losses in the The rectifier characteristic is composed of two control valves and reduce the generation of harmonics. modes: alpha-min (line AB) and constant current (line BC).

4. Prevent commutation failures at the inverter station The alpha-min mode of control at the rectifier is imposed by and hence improve the stability of power transmission. the natural characteristics of the rectifier ac system, and the

5. Other features, i.e. the control of frequency in an ability of the valves to operate when alpha is equal to zero, isolated ac system or to enhance power system stability.

i.e. in the limit the rectifier acts a diode rectifier. However,

In addition to the above desired features, the dc controls will since a minimum positive voltage is desired before firing of have to cope with the steady-state and dynamic requirements the valves to ensure conduction, an alpha-min limit of about of the dc link, as shown in Table 31.2.

2–5 ◦ is typically imposed.

TABLE 31.3 Choice of control strategy for two-terminal dc link Condition no. Desirable features

Reason

Control implementation

Use constant current control at the rectifier 2 Employ the maximum dc voltage, V d For reducing power transmission losses Use constant voltage control at the inverter 3 Reduce the incidence of commutation failures

1 Limit the maximum dc current, I d For the protection of valves

Use minimum extinction angle control at inverter 4 Reduce reactive power consumption at the

For stability purposes

Use minimum firing angles converters

For voltage regulation and economic

reasons

834 V. K. Sood I max limit = 1.2 pu

V d α-min-limit-in-rectifier

CEA

P α-min-limit-in-inverter

I min =0.2 pu

I di

I dr

(a)

(b)

FIGURE 31.11 Static V d –I d characteristic for a two-terminal link: (a) unmodified and (b) modified.

The inverter characteristic is composed of two modes: The resultant current chopping would cause high over- gamma-min (line PQ) and constant current (line QR). The

voltages to appear on the valves. The magnitude of crossover point X of the two characteristics defines the oper-

I d -min is affected by the size of the smoothing reactor ating point for the dc link. In addition, a constant current

employed.

characteristic is also used at the inverter. However, the cur-

rent demanded by the inverter I di is usually less than the At the inverter:

current demanded by the rectifier I dr by the current margin

1. Alpha-min limit at inverter

I which is typically about 0.1 pu; its magnitude is selected The inverter is usually not permitted to operate inad- to be large enough so that the rectifier and inverter constant

vertently in the rectifier region, i.e. a power reversal current modes do not interact due to any current harmonics

occurring due to an inadvertent current margin sign which may be superimposed on the dc current. This control

change. To ensure this, an alpha-min-limit in inverter strategy is termed as the current margin method.

mode of about 100–110 ◦ is imposed. The advantage of this control strategy becomes evident if

2. Current error region

there is a voltage decrease at the rectifier ac bus. The operating When the inverter operates into a weak ac system, the point then moves to point Y. In this way, the current transmit-

slope of the CEA control mode characteristic is quite ted will be reduced to 0.9 pu of its previous value and voltage

steep and may cause multiple crossover points with control will shift to the rectifier. However, the power trans-

the rectifier characteristic. To avoid this possibility, the mission will be largely maintained near to 90% of its original

inverter CEA characteristic is usually modified into value.

either a constant beta characteristic or constant voltage The control strategy usually employs the following other

characteristic within the current error region. modifications to improve the behavior during system distur- bances:

31.4.2 Control Implementation At the rectifier:

31.4.2.1 Historical Background

The equidistant pulse firing control systems used in mod- This modification is made to limit the dc current as ern HVDC control systems were developed in the mid-

1. Voltage dependent current limit, VDCL

a function of either the dc voltage or, in some cases, 1960s [5, 6]; although improvements have occurred in their the ac voltage. This modification assists the dc link to implementation since then, such as the use of microproces- recover from faults. Variants of this type of VDCL do sor based equipment, their fundamental philosophy has not exist. In one variant, the modification is a simple fixed changed much. The control techniques described in [5, 6] value instead of a sloped line.

are of the pulse frequency control (PFC) type as opposed

to the now-out-of-favor pulse phase control (PPC) type. All This limitation (typically 0.2–0.3 pu) is to ensure a these controls use an independent voltage controlled oscilla- minimum dc current to avoid the possibility of dc tor (VCO) to decouple the direct coupling between the firing current extinction caused by the valve current drop- pulses and the commutation voltage, V com . This decoupling ping below the hold-on current of the thyristors; an was necessary to eliminate the possibility of harmonic insta- eventuality that could arise transiently due to harmon- bility detected in the converter operation when the ac system ics superimposed on the low value of the dc current. capacity became nearer to the power transmission capacity

2. I d -min limit

31 HVDC Transmission 835 of the HVDC link, i.e. with the use of weak ac systems.

65 Hz, due to the rotating machines used to generate elec- Another advantage of the equidistant firing pulse control tricity. Therefore, it is preferable to use a variable frequency was the elimination of non-characteristic harmonics during oscillator (called the PFC oscillator) with a locking range of steady-state operation. This was a prevalent feature during the between 50 and 70 Hz and the center frequency of 60 Hz. This use of the earlier individual phase control (IPC) system where oscillator would then need to track the variations in the system the firing pulses were directly coupled to the commutation frequency and a control loop of some sort would be used for voltage, V com .

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 To control the firing angle of a converter, it is necessary to method widely adopted for dc link operation is the so-called

31.4.2.2 Firing Angle Control

synchronize the firing pulses emanating from the ring counter current margin method. to the ac commutation voltage that has a frequency of 60 Hz in steady state. However, it was noted quite early on (early 1960s), that the commutation voltage (system) frequency is

31.4.3 Control Loops

not a constant, neither in frequency nor in amplitude, during a Control loops are required to track the following variables: perturbed state. However, it is the frequency that is of primary concern for the synchronization of firing pulses. For strong

• Ordered current I or at the rectifier and the inverter.

ac systems, the frequency is relatively constant and distortion • Ordered extinction angle (γ o ) at the inverter. free to be acceptable for most converter type applications. But,

as converter connections to weak ac systems became required

31.4.3.1 Current Control Loops

more often than not, it was necessary to devise a scheme for In conventional HVDC systems, a proportional integral (PI) synchronization purposes which would be decoupled from the regulator is used (Fig. 31.12) for the rectifier current controller. commutation voltage frequency for durations when there were The rectifier plant system is inherently non-linear and has a

perturbations occurring on the ac system. The most obvious relationship given in Eq. (31.1). For constant I d and for small method is to utilize an independent oscillator at 60 Hz that changes in α, we have can be synchronously locked to the ac commutation voltage frequency. This oscillator would then provide the (phase) ref-

erence for the generation of firing pulses to the ring counter = −V dor · sin α (31.4)

during the perturbation periods, and would use the steady- state periods for locking in step with the system frequency.

It is obvious from Eq. (31.4) that the maximum gain The advantage of this independent oscillator would be to ( V d / α) occurs when α = 90 ◦ . Thus the control loop provide an ideal (immunized and clean) sinusoid for synchro- must be stabilized for this operation point, resulting in slower nizing and timing purposes. There are two possibilities for this dynamic properties at normal operation within the range independent oscillator:

12–18 ◦ . Attempts have been made to linearize this gain and have met with some limited success. However, in practical

• Fixed frequency operation. terms, it is not always possible to have the dc link operating • Variable frequency operation.

with the rectifier at 90 ◦ due to harmonic generation and other Use of a fixed frequency oscillator (although feasible, and protection elements coming into operation also. Therefore, called the PPC oscillator) is not recommended, since it is optimizing the gains of the PI regulator can be quite ardu- known that the system frequency does drift, between 55 and ous and take a long time. For this reason, the controllers are

I or

Ring

K/(1 + sT)

VCO

Counter

DCCT FIGURE 31.12 Control loop for the rectifier.

836 V. K. Sood

ΔI

from gamma controller

I or

K/(1 + sT)

VCO

Ring Counter

− I d MINIMUM

SELECT

DCCT

FIGURE 31.13 Current controller at the inverter.

often pre-tested in a physical simulator environment to obtain • Direct method for actual measurement of extinction approximate settings. Final (often very limited) adjustments

angle (gamma).

are then made on site. In either case, a delay of one cycle occurs from the indication Other problems with the use of a PI regulator are listed of actual gamma and the reaction of the controller to this below: measurement. Since the avoidance of a commutation failure

• It is mostly used with fixed gains, although some possi- often takes precedence at the inverter, it is normal to use the bility for gain scheduling exists.

minimum value of gamma measured for the 6- or 12-inverter • It is difficult to select optimal gains, and even then they valves for the converter(s). are optimal over a limited range only. • Since the plant system is varying continually, the PI

1. Predictive method of measuring gamma

controller is not optimal. The predictive measurement tries to maintain the commu-

A similar current control loop is used at the inverter tation voltage–time area after commutation larger than a (Fig. 31.13). Since the inverter also has a gamma controller, specified minimum value. Since the gamma prediction is only the selection between these two controllers is made via a MIN- approximate, the method is corrected by a slow feedback loop IMUM SELECT block. Moreover, in order to bias the inverter that calculates the error between the predicted value and actual current controller off, a current margin signal I is subtracted value of gamma (one cycle later) and feeds it back. from the current reference I or received from the rectifier via a

The predictor calculates continuously, by a triangular communication link.

approximation, the total available voltage–time area that remains after commutation is finished. Since an estimate of the overlap angle m is necessary, it is derived from a well-

Telecommunication requirements

known fact in converter theory that the overlap commutation As was discussed above, the rectifier and inverter current orders voltage–time area is directly proportional to direct current and must be coordinated to maintain a current margin of about the leakage impedance (assumed constant and known) value 10% between the two terminals at all times, otherwise there of the converter transformer. is a risk of loss of margin and the dc voltage could run

The prediction process is inherently of an individual phase down. Although, it is possible to use slow voice communica- firing character. If no further measures were taken, each valve tion between the two terminals, and maintain this margin, the would fire on the minimum margin condition. To counter- advantage of fast control action possible with converters may act this undesired property, a special firing symmetrizer is

be lost for protection purposes. For maintaining the margin used; when one valve has fired on the minimum margin angle, during dynamic conditions, it is prudent to raise the current the following two or five valves fire equidistantly. (The choice order at the rectifier first followed by the inverter; in terms of either two or five symmetrized valves is mainly a stability of reducing the current order, it is necessary to reduce at the question.) inverter first and then at the rectifier.