7

2. LITERATURE SURVEY

2.1 HVDC Technologies in Recent Days

Two basic converter technologies are used in modern HVDC transmission systems.

These are conventional line-commutated current source converters (CSCs) and self-

commutated voltage source converters (VSCs). Figure 2.1 shows a conventional HVDC

converter station with CSCs.

Figure 2.1: Conventional HVDC with Current Source Converters

2.1.1 Line-commutated current source converter

Conventional HVDC transmission employs line-commutated CSCs with thyristor

valves. Such converters require a synchronous voltage source in order to operate. The basic

building block used for HVDC conversion is the three phase, full-wave bridge referred to as

a six-pulse or Graetz bridge. The term six-pulse is due to six commutations or switching

operations per period resulting in a characteristic harmonic ripple of six times the

fundamental frequency in the DC output voltage. Each six-pulse bridge is comprised of six

controlled switching elements or thyristor valves. Each valve is comprised of a suitable

number of series-connected thyristors to achieve the desired DC voltage rating. The DC

terminals of two six-pulse bridges with AC voltage sources phase displaced by 300 can be

connected in series to increase the DC voltage and eliminate some of the characteristic AC

current and DC voltage harmonics. Operation in this manner is referred to as 12-pulse

8

operation. In 12-pulse operation, the characteristic AC current and DC voltage harmonics

have frequencies of 12n+1 and 12n, respectively.

The 300 phase displacement is achieved by feeding one bridge through a transformer

with a wye-connected secondary and the other bridge through a transformer with a delta-

connected secondary. Most modern HVDC transmission schemes utilize 12-pulse converters

to reduce the harmonic filtering requirements required for six-pulse operation; e.g. , fifth and

seventh on the AC side and sixth on the DC side.

This is because, although these harmonic currents still flow through the valves and

the transformer windings, they are 1800 out of phase and cancel out on the primary side of

the converter transformer.

2.1.2 Self-commutated voltage source converter

HVDC transmission using VSCs with pulse-width modulation (PWM), commercially

known as HVDC Light, was introduced in the late 1990s. Since then the progression to

higher voltage and power ratings for these converters has roughly paralleled that for thyristor

valve converters in the 1970s. These VSC-based systems are self commutated with insulated-

gate bipolar transistor (IGBT) valves and solid-dielectric extruded HVDC cables. Figure

illustrates solid-state converter development for the two different types of converter

technologies using thyristor valves and IGBT valves.

HVDC transmission with VSCs can be beneficial to overall system performance.

VSC technology can rapidly control both active and reactive power independently of one

another. Reactive power can also be controlled at each terminal independent of the DC

transmission voltage level.

This control capability gives total flexibility to place converters anywhere in the AC

network since there is no restriction on minimum network short-circuits capacity. Self-

commutation with VSC even permits black start; i.e., the converter can be used to synthesize

a balanced set of three phase voltages like a virtual synchronous generator.

The dynamic support of the AC voltage at each converter terminal improves the

voltage stability and can increase the transfer capability of the sending- and receiving-end

AC systems, thereby leveraging the transfer capability of the DC link.

9

Figure 2.2: HVDC IGBT Valve Converter Arrangement

HVDC transmission, the VSC converters themselves have no reactive power demand and can

actually control their reactive power to regulate AC system voltage just like a generator

[4-5].

2.2 HVDC Applications

HVDC transmission applications can be broken down into different basic categories.

Although the rationale for selection of HVDC is often economic, there may be other reasons

for its selection. HVDC may be the only feasible way to interconnect two asynchronous

networks, reduce fault currents, utilize long underground cable circuits, bypass network

congestion, share utility rights of- way without degradation of reliability, and to mitigate

environmental concerns. In all of these applications, HVDC nicely complements the AC

transmission system.

2.2.1 Long-distance bulk power transmission

HVDC transmission systems often provide a more economical alternative to AC transmission

for long-distance bulk power delivery from remote resources. Higher power transfers are

possible over longer distances using fewer lines with HVDC transmission than with AC

transmission. Typical HVDC lines utilize a bipolar configuration. Bipolar HVDC lines are

comparable to a double circuit AC line since they can operate at half power with one pole out

of service but require only one-third the numbers of insulated sets of conductors as a double

circuit AC line. Automatic restarts from temporary DC line fault clearing sequences are

10

routine even for generator outlet transmission. No synchro-checking is required as for

automatic reclosures following AC line faults since the DC restarts do not expose turbine

generator units to high risk of transient torque amplification from closing into faults or across

high phase angles. The controllability of HVDC links offer firm transmission capacity

without limitation due to network congestion or loop flow on parallel paths. Controllability

allows the HVDC to “leap-frog” multiple “choke-points” or bypass sequential path limits in

the AC network. Therefore, the utilization of HVDC links is usually higher than that for extra

high voltage AC transmission, lowering the transmission cost per MWh. This controllability

can also be very beneficial for the parallel transmission since, by eliminating loop flow, it

frees up this transmission capacity for its intended purpose of serving intermediate load and

providing an outlet for local generation.

Whenever long-distance transmission is discussed, the concept of “break-even

distance” frequently arises. This is where the savings in line costs offset the higher converter

station costs. A bipolar HVDC line uses only two insulated sets of conductors rather than

three. This results in narrower rights-of-way, smaller transmission towers, and lower line

losses than with AC lines of comparable capacity. A rough approximation of the savings in

line construction is 30%. Although break-even distance is influenced by the costs of right-of-

way and line construction with a typical value of 500 km, the concept itself is misleading

because in many cases more AC lines are needed to deliver the same power over the same

distance due to system stability limitations. Furthermore, the long-distance AC lines usually

require intermediate switching stations and reactive power compensation. This can increase

the substation costs for AC transmission to the point where it is comparable to that for

HVDC transmission.

For example, the generator outlet transmission alternative for the ±250-kV, 500- MW

Square Butte Project was two 345-kV series-compensated AC transmission lines. The first

6,000-MW stage of the transmission for the Three Gorges Project in China would have

required 5×500-kV AC lines as opposed to 2 ×±500-kV, 3,000-MW bipolar HVDC lines.

2.2.2 Underground and submarine cable transmission

Unlike the case for AC cables, there is no physical restriction limiting the distance or

power level for HVDC underground or submarine cables. Underground cables can be used

on shared rights-of way with other utilities without impacting reliability concerns over use of

11

common corridors. For underground or submarine cable systems there is considerable

savings in installed cable costs and cost of losses when using HVDC transmission.

Depending on the power level to be transmitted, these savings can offset the higher

converter station costs at distances of 40 km or more. Furthermore, there is a drop-off in

cable capacity with AC transmission over distance due to its reactive component of charging

current since cables have higher capacitances and lower inductances than AC overhead lines.

Although this can be compensated by intermediate shunt compensation for underground

cables at increased expense, it is not practical to do so for submarine cables. For a given

cable conductor area, the line losses with HVDC cables can be about half those of AC cables.

This is due to AC cables requiring more conductors (three phases), carrying the reactive

component of current, skin-effect, and induced currents in the cable sheath and armor. With a

cable system, the need to balance unequal loadings or the risk of postcontingency overloads

often necessitates use of a series-connected reactors or phase shifting transformers. These

potential problems do not exist with a controlled HVDC cable system. Extruded HVDC

cables with prefabricated joints used with VSC-based transmission are lighter, more flexible,

and easier to splice than the mass-impregnated oil-paper cables (MINDs) used for

conventional HVDC transmission, thus making them more conducive for land cable

applications where transport limitations and extra splicing costs can drive up installation

costs. The lower-cost cable installations made possible by the extruded HVDC cables and

prefabricated joints makes long-distance underground transmission economically feasible for

use in areas with rights-of-way constraints or subject to permitting difficulties or delays with

overhead lines.

2.2.3 Asynchronous ties

With HVDC transmission systems, interconnections can be made between

asynchronous networks for more economic or reliable system operation. The asynchronous

interconnection allows interconnections of mutual benefit while providing a buffer between

the two systems. Often these interconnections use back-to-back converters with no

transmission line. Asynchronous HVDC links act as an effective “firewall” against

propagation of cascading outages in one network from passing to another network.

Asynchronous ties can eliminate market “electrical seams” while retaining natural

points of separation. Interconnections between asynchronous networks are often at the

12

periphery of the respective systems where the networks tend to be weak relative to the

desired power transfer. Higher power transfers can be achieved with improved voltage

stability in weak system applications using CCCs. The dynamic voltage support and

improved voltage stability offered by VSC-based converters permits even higher power

transfers without as much need for AC system reinforcement. VSCs do not suffer

commutation failures, allowing fast recoveries from nearby AC faults. Economic power

schedules that reverse power direction can be made without any restrictions since there is no

minimum power or current restrictions.

2.2.4 Multiterminal systems

Most HVDC systems are for point-to-point transmission with a converter station at

each end. The use of intermediate taps is rare. Conventional HVDC transmission uses

voltage polarity reversal to reverse the power direction. Polarity reversal requires no special

switching arrangement for a two terminal system where both terminals reverse polarity by

control action with no switching to reverse power direction. Special DC-side switching

arrangements are needed for polarity reversal in a multiterminal system, however, where it

may be desired to reverse the power direction at a tap while maintaining the same power

direction on the remaining terminals. For a bipolar system this can be done by connecting the

converter to the opposite pole. VSC HVDC transmission, however, reverses power through

reversal of the current direction rather than voltage polarity. Thus, power can be reversed at

an intermediate tap independently of the main power flow direction without switching to

reverse voltage polarity.

2.2.5 Power delivery to large urban areas

Power supply for large cities depends on local generation and power import

capability. Local generation is often older and less efficient than newer units located

remotely. Often, however, the older, less-efficient units located near the city center must be

dispatched out-of merit because they must be run for voltage support or reliability due to

inadequate transmission. Air quality regulations may limit the availability of these units. New

transmission into large cities is difficult to site due to right-of-way and land-use constraints.

Compact VSC-based underground transmission circuits can be placed on existing dual-use

rights-of-way to bring in power as well as to provide voltage support, allowing a more

economical power supply without compromising reliability. The receiving terminal acts like

13

a virtual generator delivering power and supplying voltage regulation and dynamic reactive

power reserve. Stations are compact and housed mainly indoors, making sitting in urban

areas somewhat easier. Furthermore, the dynamic voltage support offered by the VSC can

often increase the capability of the adjacent AC transmission.

2.3 System Configurations and Operating Modes

Figure 2.3 shows the different common system configurations and operating modes

used for HVDC transmission. Monopolar systems are the simplest and least expensive

systems for moderate power transfers since only two converters and one high-voltage

insulated cable or line conductor are required. Such systems have been used with low-voltage

electrode lines and sea electrodes to carry the return current in submarine cable crossings.

In some areas conditions are not conducive to monopolar earth or sea return. This

could be the case in heavily congested areas, fresh water cable crossings, or areas with high

earth resistivity. In such cases a metallic neutral- or low-voltage cable is used for the return

path and the DC circuit uses a simple local ground connection for potential reference only.

Back-to back stations are used for interconnection of asynchronous networks and use AC

lines to connect on either side. In such systems power transfer is limited by the relative

capacities of the adjacent AC systems at the point of connection. As an economic alternative

to a monopolar system with metallic return, the midpoint of a 12-pulse converter can be

connected to earth directly or through an impedance and two half-voltage cables or line

conductors can be used. The converter is only operated in 12-pulse mode so there is never

any stray earth current.

VSC-based HVDC transmission is usually arranged with a single converter connected

pole-to-pole rather than pole to- ground. The center point of the converter is connected to

ground through a high impedance to provide a reference for the DC voltage. Thus, half the

converter DC voltage appears across the insulation on each of the two DC cables, one

positive the other negative.

14

Figure 2.3: HVDC Configurations and Operating Modes

The most common configuration for modern overhead HVDC transmission lines is

bipolar with a single 12-pulse converter for each pole at each terminal. This gives two

independent DC circuits each capable of half capacity. For normal balanced operation there

is no earth current. Monopolar earth return operation, often with overload capacity, can be

used during outages of the opposite pole. Earth return operation can be minimized during

monopolar outages by using the opposite pole line for metallic return via pole/converter

bypass switches at each end. This requires a metallic-return transfer breaker in the ground

electrode line at one of the DC terminals to commutate the current from the relatively low

resistance of the earth into that of the DC line conductor. Metallic return operation capability

is provided for most DC transmission systems. This not only is effective during converter

outages but also during line insulation failures where the remaining insulation strength is

adequate to withstand the low resistive voltage drop in the metallic return path. For very-

high-power HVDC transmission, especially at DC voltages above ±500 kV (i.e., ±600 kV or

±800 kV), series connected converters can be used to reduce the energy unavailability for

15

individual converter outages or partial line insulation failure. By using two series-connected

converters per pole in a bipolar system, only one quarter of the transmission capacity is lost

for a converter outage or if the line insulation for the affected pole is degraded to where it can

only support half the rated DC line voltage. Operating in this mode also avoids the need to

transfer to monopolar metallic return to limit the duration of emergency earth return.

2.4 Economic Considerations

A study for Oak Ridge National Laboratory reported on a survey to 3 suppliers of

HVDC equipment for quotations of turnkey costs to supply two bipolar substations for four

representative systems. Each substation requires one DC electrode and interfaces to an AC

system with a short circuit capacity four times the rating of the HVDC system. The four

representative systems are summarized in Table 1. Table 2 provides a major component

breakdown based on average values derived from the responses of the suppliers. The turnkey

costs are in 1995/96 US dollars and are for one terminal only with the assumption that both

terminals would be provided by the same supplier. The back-to-back DC link cost is for the

complete installation. Transmission line costs cannot be so readily defined. Variations

depend on the cost of use of the land, the width of the right-of-way required, labor rates for

construction, and the difficulty of the terrain to be crossed. A simple rule of thumb may be

applied in that the cost of a DC transmission line may be 80% to 100% of the cost of an AC

line whose rated line voltage is the same as the rated pole-to-ground voltage of the DC line.

The cost advantage of DC transmission for traversing long distances is that it may be rated at

twice the power flow capacity of an AC line of the same voltage.

Table 2.1: Four Representative HVDC Systems for Substation Cost Analysis

System no. D.C. voltage Capacity A.C. Voltage

1. +250 kV 500 MW 230 kV

2. +350 kV 1000 MW 345 kV

3. +500 kV 3000 MW 500 kV

4. Back – to – back 200 MW 230 kV

16

Table 2.2: Average Breakdown of HVDC Turnkey Costs from three HVDC Suppliers

Item Project component Back-to-back

200 MW

+250 kV

500 MW

+350 kV

1000 MW

+500 kV

3000 MW

1 Converter valves 19.0% 21.0% 21.3% 21.7%

2 Conv. Transformers 22.7% 21.3% 21.7% 22.0%

3 D.C. Switchyard 3.0% 6.0% 6.0% 6.0%

4 A.C. Switchyard 10.7% 9.7% 9.7% 9.3%

5. Control Protection 8.7% 8.0% 8.0% 7.7%

And Communication

6. Civil Works 13.0% 13.7% 13.7% 13.7%

7. Auxiliary power 2.0% 2.3% 2.3% 2.3%

8. Project admin 21.0% 18.0% 17.3% 17.3%

Total Estimated cost M Rs. 2165/- 7250/- 10,685/- 22585/-

Cost – Rs./kW/Station 10850/- 7250/- 5350/- 3750/-

When electricity must be transmitted by underground or undersea cables, AC cables

become impractical due to their capacitive charging current if longer than a critical length

which for undersea applications is less than 50 kM for distances longer than this critical

length with today’s technology requires DC cables. The choice is system specific, and

economic considerations will prevail [6-10].

2.5 Environmental Considerations

The electrical environmental effects from HVDC transmission lines can be

characterized by field and ion effects as well as corona effects. The electric field arises from

both the electrical charge on the conductors and for a HVDC overhead transmission line,

from charges on air ions and aerosols surrounding the conductor. These give rise to DC

electric fields due to the ion current density flowing through the air from or to the conductors

as well as due to the ion density in the air. A DC magnetic field is produced by DC current

flowing through the conductors. Air ions produced by HVDC lines form clouds which drift

away from the line when blown by the wind and may come in contact with humans, animals

17

and plants outside the transmission line right-of -way or corridor. The corona effects may

produce low levels of radio interference, audible noise and ozone generation.

2.5.1 Field and corona effects

The field and corona effects of transmission lines largely favor DC transmission over AC

transmission. The significant considerations are as follows:

1. For a given power transfer requiring extra high voltage transmission, the DC transmission

line will have a smaller tower profile than the equivalent AC tower carrying the same

level of power. This can also lead to less width of right-of-way for the DC transmission

option.

2. The steady and direct magnetic field of a DC transmission line near or at the edge of the

transmission right-of-way will be about the same value in magnitude as the earth’s

naturally occurring magnetic field. For this reason alone, it seems unlikely that this small

contribution by HVDC transmission lines to the background geomagnetic field would be

a basis for concern.

3. The static and steady electric field from DC transmission at the levels experienced

beneath lines or at the edge of the right-of-way have no known adverse biological effects.

There is no theory or mechanism to explain how a static electric field at the levels

produced by DC transmission lines could effect human health. The electric field level

beneath a HVDC transmission line is of similar magnitude as the naturally occurring

static field which exists beneath thunder clouds. Electric fields from AC transmission

lines have been under more intense scrutiny than fields generated from DC transmission

lines.

4. The ion and corona effects of DC transmission lines lead to a small contribution of ozone

production to higher naturally occurring background concentrations. Exacting long term

measurements are required to detect such concentrations. The measurements taken at

cross-sections across the Nelson River DC lines in Canada failed to distinguish

background from downwind levels. While solar radiation influences the production of

ozone even in a rural environment, thereby maintaining its level, any incremental

contribution from a DC line source is subject to breakdown, leading to a resumption of

background levels downwind from the line. Investigations of ozone for indoor conditions

18

indicate that in well mixed air, the half-life of ozone is 1.5 minutes to 7.9 minutes.

Increases in temperature and humidity increase the rate of decay.

5. If ground return is used with monopolar operation, the resulting DC magnetic field can

cause error in magnetic compass readings taken in the vicinity of the DC line or cable.

This impact is minimized by providing a conductor or cable return path (known as

metallic return) in close proximity to the main conductor or cable for magnetic field

cancellation. Another concern with continuous ground current is that some of the return

current may flow in metallic structures such as pipelines and intensify corrosion if

cathodic protection is not provided. When pipelines or other continuous metallic

grounded structures are in the vicinity of a DC link, metallic return may be necessary

[11-19].

2.6 Station Design and Layout

The converter station layout depends on a number of factors such as the DC system

configuration (i.e., monopolar, bipolar, or back-to-back), AC filtering, and reactive power

compensation requirements. The thyristor valves are air-insulated, water-cooled, and

enclosed in a converter building often referred to as a valve hall. For back-to-back ties with

their characteristically low DC voltage, thyristor valves can be housed in prefabricated

electrical enclosures, in which case a valve hall is not required. To obtain a more compact

station design and reduce the number of insulated high-voltage wall bushings, converter

transformers are often placed adjacent to the valve hall with valve winding bushings

protruding through the building walls for connection to the valves. Double or quadruple

valve structures housing valve modules are used within the valve hall. Valve arresters are

located immediately adjacent to the valves. Indoor motor-operated grounding switches are

used for personnel safety during maintenance. Closed-loop valve cooling systems are used to

circulate the cooling medium, deionized water or water-glycol mix, through the indoor

thyristor valves with heat transfer to dry coolers located outdoors. Area requirements for

conventional HVDC converter stations are influenced by the AC system voltage and reactive

power compensation requirements where each individual bank rating may be limited by such

system requirements as reactive power exchange and maximum voltage step on bank

19

switching. The AC yard with filters and shunt compensation can take up as much as three

quarters of the total area requirements of the converter station.

The central equipment of a DC substation is the thyristor converters which are usually

housed inside a valve hall. Outdoor valves have been applied such as in the Cahora Bassa DC

transmission line between Mozambique and South Africa. In this example, two poles are

represented which is the usual case and is known as the “bipole” configuration. Some DC

cable systems only have one pole or “monopole” configuration and may either use the

ground as a return path when permitted or use an additional cable to avoid earth currents.

Figure 2.4 indicates a bipole HVDC configuration. Essential equipment in a DC

substation in addition to the valve groups includes the converter transformers. Their purpose

is to transform the AC system voltage to which the DC system is connected so that the

correct DC voltage is derived by the converter bridges. For higher rated DC substations,

converter transformers for 12 pulse operation are usually comprised of single phase units

which are a cost effective way to provide spare units for increased reliability. The secondary

or DC side windings of the converter transformers are connected to the converter bridges.

The converter transformer is located in the switchyard, and if the converter bridges are

located in the valve hall, the connection has to be made through its wall. This is

accomplished in either of two ways. Firstly, with phase isolated busbars where the bus

conductors are housed within insulated bus ducts with oil or SF6 as the insulating medium or

secondly, with wall bushings. When applied at DC voltages at 400 kV or greater, wall

bushings require considerable design and care to avoid external or internal insulation

breakdown.

Harmonic filters are required on the AC side and usually on the DC side. The

characteristic AC side current harmonics generated by 6 pulse converters are 6n + 1 and 12n

+1 for 12 pulse converters where n equals all positive integers. AC filters are typically tuned

to 11th, 13th, 23rd and 25th harmonics for 12 pulse converters. Tuning to the 5th and 7th

harmonics is required if the converters can be configured into 6 pulse operation. AC side

harmonic filters may be switched with circuit breakers or circuit switches to accommodate

reactive power requirement strategies since these filters generate reactive power at

fundamental frequency. A parallel resonance is naturally created between the capacitance of

the AC filters and the inductive impedance of the AC system. For the special case where

20

such a resonance is lightly damped and tuned to a frequency between the 2nd and 4th

harmonic, then a low order harmonic filter at the 2nd or 3rd harmonic may be required, even

for 12 pulse converter operation.

Figure 2.4: Bipole HVDC Configuration

Characteristic DC side voltage harmonics generated by a 6 pulse converter are of the

order 6n and when generated by a 12 pulse converter, are of the order 12n. DC side filters

reduce harmonic current flow on DC transmission lines to minimize coupling and

interference to adjacent voice frequency communication circuits. Where there is no DC line

such as in the back-to-back configuration, DC side filters may not be required. DC reactors

are usually included in each pole of a converter station. They assist the DC filters in filtering

harmonic currents and smooth the DC side current so that a discontinuous current mode is

not reached at low load current operation. Because rate of change of DC side current is

limited by the DC reactor, the commutation process of the DC converter is made more

robust.

Surge arresters across each valve in the converter bridge, across each converter bridge

and in the DC and AC switchyard are coordinated to protect the equipment from all over

voltages regardless of their source. They may be used in non-standard applications such as

21

filter protection. Modern HVDC substations use metal-oxide arresters and their rating and

selection is made with careful insulation coordination design [5,20].

2.7 Series Capacitors with DC Converter Substations

HVDC transmission systems with long DC cables are prone to commutation failure

when there is a drop in DC voltage Ud at the inverter. The DC cable has very large

capacitance which will discharge current towards the voltage drop at the inverter. The

discharge current is limited by the DC voltage derived from the AC voltage of the

commutating bus as well as the DC smoothing reactor and the commutating reactance. If the

discharge current of the cable increases too quickly, commutation failure will occur causing

complete discharge of the cable. To recharge the cable back to its normal operating voltage

will delay recovery.

The converter bridge firing controls can be designed to increase the delay angle α

when an increase in DC current is detected. This may be effective until the limit of the

minimum allowable extinction angle γ is reached.

Another way to limit the cable discharge current is to operate the inverter bridge with

a three phase series capacitor located in the AC system on either side of the converter

transformer. Any discharge current from the DC cable will pass into the AC system through

the normally functioning converter bridge and in doing so, will pass through the series

capacitor and add charge to it. As a consequence, the voltage of the series capacitor will

increase to oppose the cable discharge and be reflected through the converter bridge as an

increase in DC voltage Ud. This will act as a back emf and limit the discharge current of the

cable, thereby avoiding the commutation failure.

The proposed locations of the series capacitor are shown in figure 2.5 and figure 2.6

in single line diagram form. With the capacitor located between the converter transformer

and the valve group, it is known as a capacitor commutated converter (CCC). With the

capacitor located on the AC system side of the converter transformer, it is known as a

controlled series capacitor converter (CSCC). Each configuration will improve commutation

performance of the inverter but the CSCC requires design features to eliminate

ferroresonance between the series capacitor and the converter transformer if it should be

instigated [21-26].

22

Figure 2.5: Capacitor Commutated Converter Configuration

Figure 2.6: Controlled Series Capacitors Converter

2.8 Basic System Model

2.8.1 System model for time domain analysis

For the stability analysis of AC-DC systems with the inclusion of AC network

transients, it is adequate to model the converter in a simplified fashion neglecting the AC and

DC harmonics. The switching action in the converters is ignored in analysis.

2.9 Converter Model

Two types of models are available.

23

2.9.1 Simplified continuous time model

Figure 2.7: Simplified Continuous Time Equivalent Circuit of a Bridge

2.9.2 Detailed model of the converter

For detailed dynamic simulation of HVDC systems, it is necessary to represent the

switching action in the valves, assuming that the valves can be modeled as ideal switches.

The switch is turned on at the instant of firing which in turn is determined by the converter

control system including gate pulse firing control. The switch turns off when the current in

the valve goes to zero. The turn-off time required can be simulated by closing the switch if a

forward voltage appears within the turn-off time.

Figure 2.8: The Equivalent Circuit for the Transient Simulation of a Bridge

The converter bridge has been modeled by the equivalent circuit shown in figure 2.8.

This is a variable voltage source behind a variable inductance. This applies for the case when

transformer winding resistances are neglected and the leakage reactances in all the phases are

assumed to be identical.

24

The transition from two valves to three valve conduction occurs at the firing of a

valve, it is assumed that there is a forward voltage across the incoming valve. α is delay

angle. The angle of advance β is related in degrees to the angle of delay a by:

β = 180.0 - α …2.1

Extinction angle γ depends on the angle of advance β and the angle of overlap µ and

is determined by the relation:

γ = β - µ …2.2

The transition from three to two valve conduction can be estimated from

( )LL

dd

E

iiXct

2coscos 21 +=− ωα

…2.3

Where, id1 is the DC current at the firing of the incoming valve and id2 is the current at the

transition. ELL is the rms value of the commutation voltage of the incoming valve. It is

assumed that at the instant t = 0, the commutation voltage becomes positive. Equation 2.3 is

based on the assumption of sinusoidal commutation voltages [27-29].

2.9.3 Modeling of DC network

The DC network is assumed to consist of smoothing reactor, DC filters and the

transmission line. The smoothing reactor and DC filters can be represented by lumped

parameter linear elements. The DC line can also be modeled as a T or π equivalent if the

higher frequency behavior is not of interest.

As an example, consider a one pole with ground return. A single six pulse bridge in

each station is modeled. Neglecting DC filters, the DC network is shown in figure 2.9 which

also shows the simplified converter models (continuous time) as components.

Figure 2.9: Equivalent Circuit of a 2TDC System – Positive Pole with Ground Return

The smoothing reactors at the two ends are designated as Ldr and Ldi. The subscripts r

and i refer to the rectifier and inverter terminal respectively. The series resistance of the

25

smoothing reactor is not shown in the diagram but can be accounted quite easily. The state

equations for the network shown in figure 2.9 are

−+

−=

−+

−=

ti

dicdi

ti

tidi

tr

cdrdr

tr

trdr

L

Evi

L

R

dt

di

L

vEi

L

R

dt

di

( )didrc ii

Cdt

dv −= 1

where,

2

LLLL drcrtr ++=

2

LLLL diciti ++=

2

RRRR drcrtr ++=

2

RRRR diciti ++=

In general, the state equations for any DC network can be written as

DCDCDCDC BuXAY += …2.7

DCDC CXy = …2.8

Where,

[ ]didrTDC EEu =

[ ]didrTDC iiy =

2.9.4 Modeling of AC networks

General

For long term stability analysis the AC network can be assumed to be in steady state.

In this case,three phase representation is used for analysis of unsymmetrical networks.

In the case of transient analysis of symmetrical three phase networks, it is adequate to

consider only two phase representation using α , β components or D, Q components

(defined on the synchronously/rotating reference frame). The latter has the advantage of

…2.4

…2.5

…2.6

26

eliminating the time-varying coupling between AC and DC system, and, hence, is convenient

for analytical studies. It also has the advantage that, in steady state D, Q components is

constants and is related to the phasors in load flow analysis.

Formulation of State Equations

Figure 2.10: Positive Sequence AC Network

Consider the positive sequence network shown in figure 2.10. This network is excited

by voltage and current sources at specific nodes. The contribution at the converter bus from

the DC system is a current source dependent on the converter DC current. In general, the

state equations for the network shown in figure 2.10 can be written as

[ ] [ ] [ ] pppp ISESxRx 21

.

++= …2.9

Where, px.

is the vector of state variables corresponding to inductor currents in links and

capacitor voltages in the tree branches pE and

pI are the injected voltage and current vectors.

[R], [S1] and [S2] are constant matrices, functions of the network parameters. It is assumed

that the network equations are linear. The negative sequence network is also identical to the

network shown in figure 2.10, except for the replacement of the sources pE and

pI by nE and

nI . Hence, the state equations for the negative sequence network are

[ ] [ ] [ ] nnnn ISESxRx 21

.

++= …2.10

2.9.5 Transformation to D-Q components

The transformation from p, n variables to D-Q variables is defined by the following

equations:

−=

Q

D

n

p

x

x

U

U

U

U

x

x

0

0

0

0

cos

sin

sin

cos

θθ

θθ …2.11

27

Where, U is the identity matrix of dimension equal to the order of pX or nX . 0θ is the

angle by which the D axis leads a stationary axis. It is to be noted that

00 ωθ =

dt

d …2.12

is assumed to be constant.

Substituting equation 2.11 in equation 2.9 and 2.10 leads to the following equations

[ ] [ ] [ ] DDQDD ISESxxRx 210

.

++−= ω …2.13

[ ] [ ] [ ] QQDQQ ISESxxRx 210

.

+++= ω …2.14

Where, ED, EQ and ID, IQ are the D, Q components of the voltage and current sources

respectively.

2.9.6 Interface with DC system

The current injected into the AC network at the converter bus is proportional to the

average DC current that flows in the link. If harmonics are neglected, then the fundamental

component of the current IA is given by

dbA inI

±=

π6 …2.15

Where, id is the DC current flowing in the converter, nb is the number of bridges connected in

series at a station (including both poles). The positive sign is to be taken for the inverter and

the negative sign applies to the rectifier station.

Figure 2.11: Phasor Diagram of Quantities at the Converter Bus

28

The injected current IA in steady state leads the converter bus voltage by an angle φ . The

phasor diagram shown in figure 2.11 gives the relative position of the current and voltage

phasors in D-Q reference frame. From this, the following equations can be derived.

( )vAAD II δφ+= sin …2.16

( )vAAQ II δφ+= cos …2.17

The angle vδ by which the converter bus voltage phasor V leads the Q axis, is given by

Q

Dv V

V=δtan …2.18

The angle φ is defined by

= −

aV

vd1cosφ …2.19

for the inverter, and by

πφ +

−= −

aV

vd1cos …2.20

For the rectifier, Vd is the average DC voltage across a converter bridge. It is to be

noted that equations 2.16 to 2.20 are nonlinear and have to be linearized for the analysis of

stability of the equilibrium (operating) state of the AC/DC system. In equidistant pulse firing

scheme, the delay angle is not only determined by the current controller but is also affected

by the angle vδ . As the angle vδ increases, the delay angle increases (as the voltage phasor

has increased lead), even if the change in delay angle demanded by the current controller is

zero.

2.9.7 Modeling of a synchronous generator

The state equations of a synchronous machine are written in terms of the phase

variables (three phase currents or flux linkages). However, these equations are nonlinear and

time-varying due to the dependence of inductance coefficients on the rotor angle. The time-

varying system equations can be transformed into the time-invariant form by Park's

transformation. However, the direct use of equations in Park's variables (in d-q components)

is not feasible in multi-machine systems due to the existence of multiple Park's reference

29

frames corresponding to individual machine rotors. The interface between the machine and

network equations is defined by the following transformation which relates d-q (rotor

reference frame) variables to D-Q (synchronously rotating reference frame) variables.

Figure 2.12: Circuit Model for the Stator of a Synchronous Machine

−=

q

d

Q

D

f

f

f

f

δδ

δδ

cos

sin

sin

cos …2.21

Where, δ is the rotor angle defined by

0θθδ −= r …2.22

Where, rθ is the rotor angle with respect to a stationary axis f is any variable- voltage,

current or flux linkage.

The introduction of multiple transformations in multimachine systems is

cumbersome. A hybrid machine model where the time-varying coupling between the stator

and the rotor is transformed to the dependent current sources in the stator is used, where the

stator is represented by the equivalent circuit shown in figure 2.12. The current source is

defined by

qds SICII += …2.23

where,

+

−=3

2cos

3

2coscos

3

2 πθπθθ rrrtC …2.24

30

+

−=3

2sin

3

2sinsin

3

2 πθπθθ rrrtS …2.25

( )cbats IIII =

dI and qI are defined by

rtdd kI ψ= , ccr

tqq kkI ψψ += …2.26

Where, rψ is the vector of rotor flux linkages described by

[ ] qdfdrr iBiBEBAp 321 +++= ψψ …2.27

st

d iCI = , st

q iSI = …2.28

where,

( )cbats IIII = ,

dt

dp =

The vectors dkBBB ,,, 321 and qk are constants depending only on the machine parameters. The

flux linkage cψ is associated with a fictitious dummy coil, which is introduced to eliminate

dynamic saliency (X"d ≠ X"q). cψ is defined by the equation

( )[ ]qdqcc

c ixxT

""1.

−+−= ψψ …2.29

dc x

k"

1= …2.30

Tc is the time constant of the dummy coil and is arbitrarily chosen. The per unit inductances

aaL" and abL" appearing in the equivalent circuit of figure 2.12 are given by

"""" xxLL dbbaa ==− …2.31

0"2" xLL abaa =+ …2.32

0x is the zero sequence reactance of the machine.

31

The advantage of this hybrid model is that the stator is represented by an equivalent circuit

with constant parameters. The phase variables can now be transformed into 0αβ variables as

follows

[ ] 01 pns iCi = …2.33

where,

( )00' iiii nppn β=

[ ]

−−=1

1

1

2

32

30

2

12

12

3

11C …2.34

Figure 2.13: The Stator Circuit Model in P Variable

The transformed equivalent circuit in p component is shown in figure 2.13. The current

sources pI and nI are defined as

rqrdp III θθ sincos += …2.35

rqrdn III θθ cossin +−= …2.36

The equivalent circuit shown in figure 2.13 is attached to the p sequence network of the rest

of the AC system.

The relationship between D-Q components of the generator current sources and dI , qI are

given below.

δδ sincos qdD III += …2.37

32

δδ cossin qdQ III +−= …2.38

the electrical torque eT on the generator rotor is given by the following expression

( ) ( )QDDQqddqe IiIixIiIixT −=−= "" …2.39

The variablesaI , qI are related to the d-q components of stator flux linkages by the

following equations

( )ddd Iix += "ψ , ( )qqq Iix += "ψ …2.40

The hybrid model is used for stability analysis or transient analysis directly.

2.10 Basic System Model for Frequency Domain Analysis

The configuration of the HVDC transmission system model is as shown in figure

2.14. The linearized model is formed in a three-step process. The division of the system into

a number of smaller subsystems, the description of each sub system using a linearized model,

and, finally, the interconnection of the subsystems. This approach relies on the principle of

superposition for linear or linearized systems, and is a simpler approach than linearizing the

nonlinear equations which describe the system directly.

Figure 2.14 Model used for frequency Domain Analysis

The HVDC system is modeled using nine subsystems, which are the rectifier and

inverter AC systems, the rectifier and inverter AC filters and shunts capacitors, the DC

system, the rectifier and inverter HVDC converters, and the rectifier and inverter PLLs. The

firing angle-control inputs are left uncontrolled in the system. This model is used for the

representation of the general dynamics of an HVDC system in the frequency range between 2

and 200 Hz on the DC side.

33

2.10.1 State model formation

In order for the HVDC system to be represented in state model form, it is necessary

that a linear state model of each subsystem is available. A linear time-invariant state model

dynamically relates the subsystem inputs, outputs, and states using a state equation 2.41 and

an output equation 2.42, which are specified by the constant matrices. In the situation where

a state model is obtained by linearizing a system around an operating point, the input, output

and state variables represent the deviation of the system variables from their operating point

values.

BuAxx += …2.41

DuCxy += …2.42

The inputs and outputs of the state model are either signal or electrical variables.

Signal variables are associated with the measurement of electrical variables and control

subsystems, while electrical variables occur as voltage–current pairs, and are associated with

the electrical terminals of the subsystems. When connecting electrical subsystems together at

a busbar, only one subsystem can be represented in current-input voltage-output (impedance)

form, while all others must be represented in voltage-input current-output (admittance) form.

The subsystem in impedance form provides the voltage input for all of the subsystems in

admittance form, while the addition of the current outputs of the subsystems in admittance

form provides the current input to the subsystem in impedance form. A convention is adopted

where the flow of current into an electrical terminal is assumed to be of positive sign. It is

important to correctly choose the inputs and outputs of electrical subsystems such that firstly,

the inputs and outputs, which are to be connected together, are compatible, and secondly the

subsystems are proper. Only those systems which are proper, meaning the transfer functions

between the inputs and outputs of the system have at least as many poles as zeros, are able to

be described in the above state model form. If it is not possible to accommodate an improper

electrical subsystem (more zeros than poles) by interchanging inputs and outputs, then a

proper subsystem can be formed by adding extra poles above the frequency range of interest

to the system. Since standard methods are available to convert between proper–domain

transfer functions and state model representations, with respect to the input and output

relationships of the system, these two representations are equivalent. In cases where

subsystems are defined in terms of frequency response data, it is necessary to fit an s-domain

34

transfer function to the frequency response data. For simple frequency responses, an s-

domain representation can be obtained by inspection, while for more complicated frequency

responses, transfer-function fitting algorithms are available.

When forming system models, it is likely that a particular type of component, such as

the PLL and HVDC converter subsystems in the case described, will occur in multiplicity. In

this situation, it is of significant advantage to adopt a modular approach where the state

model of the component is specified as the output of a function. The subsystem state model

functions collectively form a library of components which may be called repeatedly during

the formation of system models. After proper defining the subsystems, they are connected

together to form a state model of the overall system.

2.10.2 Converter frequency-conversion process model

The conversion of electrical energy between AC and DC frequency is achieved by the

periodic firing of the HVDC converter thyristor valves. The switching action is the direct

cause of HVDC system nonlinearity, and the linearized representation of this process is of

significant importance to the system model. The converter is a complex single-frequency

input multiple frequency output modulators. A number of interactions, due to the frequency-

conversion process, occur between different frequencies on the AC and DC sides. An

arbitrary frequency on the DC side of the converter is related to two frequencies on the AC

side, separated by twice the fundamental frequency, positive sequence frequency, and

negative sequence frequency. A model which considers only these interactions is referred to

as a three-port model and is essentially of the describing function type. The zero-sequence

component of the AC system waveforms are omitted from the system models as they are

neither generated by nor affect the operation of three-phase power-electronic devices, such as

the HVDC converter.

Frequency conversion exhibits time-variance and cannot be directly represented in the

required state model form. In order to model the system in a time-invariant manner, it is

necessary to decouple the frequency-conversion process from the model of the converter.

The effect of the frequency-conversion process is accounted for by frequency shifting the

equations which describe the dynamics of the subsystems on the AC side of the converter.

Even though frequency conversion does not appear explicitly in the analysis, the interactions

are correctly represented through the altered subsystem dynamics. The dynamics of the

35

subsystems on the AC side of the converter can be frequency shifted using Park’s

transformation, or the transfer function zero-pole shifting approach.

2.10.3 AC system variable representation

As usual, three distinct representations of three-phase AC system voltage and current

variables are useful for the purposes of system modeling and control. The representations are

positive and negative sequence ( )pn components, direct and quadrature ( )DQ components,

and magnitude and angle ( )ma components. The transformations between the three AC

variable representations are described. The DQ and ma representations are with respect to a

synchronously rotating frame of reference, while sequence components may be at their actual

frequency or referred to their equivalent DC side frequency, depending on the context in

which they are used.

2.10.4 AC system variable transformations

The transform between DQ and PN components in equation 2.43 is obtained by

applying Park’s transformation to positive and negative sequence distortions. In this case, the

direct axis is referenced to a phase angle of zero, and the quadrature axis has been chosen to

lead the direct axis. If the frequency conversions involved with the transform are assumed to

be implicit, then the transform is considered linear

−=

n

p

Q

D

X

Xii

X

X

11 …2.43

The linearization of the transform between ma and DQ components in the synchronous

reference frame is given in equation 2.44

Where, XmD and XaD are the operating point magnitude and angle of the AC variable.

( ) ( )( ) ( )

∆∆

−=

∆∆

a

m

amoa

amoa

Q

D

X

X

XXX

XXX

X

X

0cos0sin

0sin0cos …2.44

2.10.5 Algorithm for the interconnection of the subsystems

The first step of the algorithm requires that the state models be diagonally appended.

The appended system, represented using capital letters for the inputs, outputs, and states, is

then rearranged so that all inputs/outputs, which are to be left unconnected, are grouped

together (indicated by the subscript 1), and all inputs/outputs which are to be connected are

grouped together (indicated by the subscript 2)

36

Using the matrix , which specifies the connections between the outputs and the inputs,

[ ]

=

2

121 U

UBBAXX …2.45

=

2

1

2221

1211

2

1

2

1 U

U

DD

DD

C

C

Y

Y …2.46

22 YHU =

the variables U2 and Y2 are eliminated from 2.49 and 2.50, resulting in a state model of the

form

( )[ ] ( )[ ] 1211

222121

222 11 UDHDHBBXCHDHBAX −− −++−+= …2.47

( )[ ] ( )[ ] 12122121121

221211 111 UDHDHDDXCHDHDCY −−++−+= − …2.48

Where, ‘I’ is the identity matrix.

2.10.6 AC system and filters

The rectifier and inverter AC systems and filters are represented using frequency

dependent equivalents which describe their electrical characteristics as seen from the AC

terminals of the converters. The HVDC converter uses AC voltage as an input, while the

nature of the AC system (series inductance) and the AC filters (shunt capacitance) means that

these subsystems are most appropriately represented in admittance and impedance forms,

respectively. To enable the connection of the subsystems at the AC terminals of the

converters without the need for variable transformations, a common sequence component is

chosen to represent the AC variables. The relationships between the inputs and outputs of the

AC system model are described by 2.48. It is assumed that the positive and negative

sequence admittances of the AC system acY are equal, and that there is no coupling between

the sequences

=

acn

acp

ac

ac

acn

acp

V

V

Y

Y

I

I …2.49

The frequency-conversion process of the converter is accounted for by frequency

shifting the AC system equations. This is achieved by representing the admittance acY in

zero-pole transfer function form, and then adding oj ω± to the values of the zeros and poles,

as described by equation 2.49 and 2.50. As the transfer-function zeros and poles have been

37

shifted in opposite directions, the poles of the subsystem still form complex conjugate pairs.

The AC filters are modeled in impedance form using the same process described

( )0)( ωjsYsY acacp += …2.50

( )0)( ωjsYsY acacn −= …2.51

2.10.7 DC system

The DC system has two electrical terminals which are connected to the DC terminals

of the rectifier and inverter. The series inductive nature of the DC system (smoothing reactor

and DC transmission line) means that the system is best described in admittance form as

described by equation 2.53. This representation is directly compatible with the converter DC

terminal current input and voltage-output variables.

=

2

1

2221

1211

2

1

V

V

YY

YY

I

I …2.52

2.10.8 HVDC converter

The state model of the HVDC converter used is obtained from the frequency-domain

model derived by Van Ness and Anderson.The frequency-domain model is more accurate

than that required for the analysis of HVDC system dynamics, its availability has allowed the

effect of converter model accuracy on the dynamics of the system model to be assessed. The

small-signal-linearized relationships between the converter input and output variables are

described by equation 2.54.

∆

∆∆

=

∆∆∆

cc

Idc

Vncn

Van

lkji

hgfe

dcba

Vdc

Ian

Iag

…2.53

The quantities a to l are referred to as the transfers, and are described as analytic functions of

the converter operating point.

2.10.9 HVDC converter model

The six-pulse HVDC converter is described by the transfers where the AC side

variables are written in terms of their equivalent DC side frequencies. To model higher pulse

converters, it is necessary to scale the transfers in accordance with the series and parallel

38

connections on the AC and DC sides. All AC side variables are referred to the valve side of

the converter transformer. The transfers depend on the operating point of the converter which

is specified by the parameters V1 and φ. These are the peak magnitude and angle of the

fundamental frequency positive sequence component of the AC phase voltages, and are the

firing and commutation angles, and is the commutation reactance in ohms. In this form, the

transfers describe the operation of a positive pole rectifier where the current flow into the

converter has been assigned a positive value. In order to model a positive pole inverter, it is

necessary to change the signs of the transfers c, g, i, j, l.

−∠

Π−

Π−=

22sin1

23 000 µµµ

cX

jaL

+∠

Π−

Π+=

22sin1

2

3 000 µµµc

Xjf

L

( )

−−−∠

Π= 00

02 22

sin3 µϕαµ

LXb

( )

+−+∠

Π= 00

02 22

sin3 µϕαµ

LXe

( )

−∠

−−−−∠Π

−=22

sin23 00

0

µµϕα jc

( )

+∠

−+−+∠Π

−=22

sin23 00

0

µµϕα jg

( ) ( )

−−−∠

Π−

Π−=

22sinsin

3 00

00

1 µϕαµαLX

Vd

( ) ( )

+−+∠

Π−

Π−=

22sinsin

3 00

00

1 µϕαµαLX

Vh

( )ϕα −+∠Π

+= 0

33ji

( )ϕα −−∠Π

−= 0

33jj

Π−+

Π=

23

23 0

0

µω

ω XLj

Xk L

39

( )01 sin

33 αΠ

−= Vl

The change in the HVDC system dynamics resulting from the use of converter

models, which take into account varying degrees of frequency dependence in the transfers,

indicates that a model where the transfers are approximated as constants is of sufficient

accuracy. The constants are naturally chosen to be the value of the frequency-domain

transfers at zero frequency on the DC side, and are consistent with the differentiation of the

standard steady-state converter equations. Transfer �, ���� � �� � as the form of a

zero and is the only case where a constant approximation is inappropriate. The constant

component of this transfer is the value which is obtained by differentiating the converter

steady-state equations, while the frequency-dependent component is the time-averaged value

of the commutation reactance seen from the DC side.

Figure 2.15: Small Signal Model of the PLL

The frequency-domain HVDC converter model is derived assuming an ideal

equidistant firing angle control system where the firing angle ramp references are fixed in

time. This is not the case in reality as the ramp references are made to track the changes in

the converter terminal AC voltage angle using a PLL system. The firing angle required by the

converter model is the angle where the correct firing instants are obtained using ramp

references which are fixed in time. This is given by the firing angle desired by the controller

less the PLL-output reference angle.

� = ��� − �� …2.55

2.10.10 Phase locked loop

The Phase locked loop (PLL) is a negative feedback-control system which tracks the

changes in the phase angle of the positive sequence fundamental frequency component of the

converter AC bus voltage. The Phase locked loop generates a ramp reference function which

40

is synchronized to the AC voltage. This output is used to define the ramp reference

associated with each of the converter thyristors and ensures that the firing instants are

synchronized to the AC voltage.

The PLL system modeled is of the DQZ type, the three major components of which

are an error signal calculator, PI controller, and voltage-controlled oscillator (VCO). The

error signal is calculated as the component of the AC voltage with respect to a sinusoidal

representation of the PLL-output ramp reference. This signal, which in the small-signal case

is proportional to the phase difference between the AC voltage and output reference, is used

to slow down or speed up the VCO so that the component and, hence, phase difference

between the AC voltage and PLL output become zero. The small-signal dynamics of the PLL

system are represented by the block diagram of figure 2.15.

The input to the model is the angle component of the AC bus voltage in the

synchronous reference frame, which is obtained from a sequence or component

representation of the AC voltage using the transforms described above. The open-loop

transfer function consists of the series combination of a gain, which is the operating point

magnitude component of the AC voltage, a PI controller, and an integrator which represents

the operation of the VCO. Controller integral action is required so that the PLL is able to

track changes in the frequency of the AC bus voltage with zero steady-state error. The

parameters of the PI controller are normally chosen such that the output reference angle is

only able to follow changes in the AC voltage angle which are slower than approximately

5Hz. Since the modes of oscillation resulting from the interconnection of the electrical

subsystems are usually at significantly higher frequencies than 5 Hz, the inclusion of the PLL

has only a very limited effect on the these modes. Despite this, the representation of the PLL

is still of importance, particularly at the inverter where a low-frequency instability arises

when the inverter AC system has a very low SCR [30-32].

2.11 System Stability

The stability of an interconnected power system is its ability to return to normal or

stable operation after having been subjected to some form of disturbance. Conversely,

instability means a condition denoting loss of synchronism or falling out of step. Stability

considerations have been recognized as an essential part of power system planning for a long

41

time. With interconnected systems continually growing in size and extending over vast

geographical regions, it is becoming increasingly more difficult to maintain synchronism

between various parts of a power system.

The dynamics of a power system are characterized by its basic features given below:

1. Synchronous tie exhibits the typical behavior that as power transfer is gradually increased

a maximum limit is reached beyond which the system cannot stay in synchronism, i.e., it

falls out of step.

2. The system is basically a spring-inertia oscillatory system with inertia on the mechanical

side and spring action provided by the synchronous tie wherein power transfer is

proportional to sin δ or δ (for small δ; δ being the relative internal angle of machines).

3. Because of power transfer being proportional to sin δ, the equation determining system

dynamics is nonlinear for disturbances causing large variations in angle δ. Stability

phenomenon peculiar to non-linear systems as distinguished from linear systems is

therefore exhibited by power systems (stable upto a certain magnitude of disturbance and

unstable for larger disturbances).

Stability Improvement

PSS and HVDC stabilizers are both the powerful control methodologies for power

swings in power system. Being the traditional damping controllers, Power System Stabilizers

(PSS) have also been proved to be the effective means to suppress electromechanical power

swings in power system. The HVDC system is assumed to have infinitely fast dynamics with

respect to the AC system. The fast power modulation capability of an HVDC link has been

utilized to improve the damping of electromechanical mode oscillations in a parallel AC-DC

power system for a long time. By modulating the transmitted power on the DC line, the

damping of electromechanical swings between systems interconnected by parallel AC and

DC interties are greatly improved.

Power system stability problems are classified into three basic types

� Steady state stability

� Transient stability

� Dynamic stability

42

2.12 Stability Analysis

The transient stability analysis is used to investigate the stability of a power system

under sudden and large disturbances such as faults followed by their clearing under the action

of protective relays. A methodology for the solution of system equations involves differential

equations for the dynamic system including generator and controllers and algebraic equations

describing the network. A major assumption in the transient stability analysis is to neglect

line transients and consider only the fundamental frequency behavior of the AC network.

This assumption is valid for the simulation of low frequency (below 5Hz) transients,

although not applicable for the simulation of subsynchronous frequency transients.

2.12.1 Stability analysis using simplified converter model

Transient stability analysis is conducted with the help of simplified model. The valve

switching is neglected and the converter is represented by the average DC voltage equation

dcd IRaUU −= θcos

Where, θ is either delay angle (α) for a rectifier or extinction angle (γ) for the inverter. The

coefficient 'α' includes the effect of on-load tap changer. U is the converter bus AC voltage.

This model is similar to that used in power flow analysis. However, there are some

differences. The transformer tap is assumed to be constant (at the value prior to the initiation

of the disturbance) as the tap changer dynamics is very slow.

The power or reactive power is not specified as the power controller is not fast acting.

-Instead, the dynamics of power (and auxiliary) controller including VDCOL, are

represented. The current order (reference value) is obtained as the output of the power

controller.

During a transient, it is possible to reverse the power flow under the action of an

emergency controller. The converter may be blocked following fault and unblocked after a

time delay.

2.12.2 Response type converter controller

Controller is represented with detailed or response type model. In case of response

type model of converter controller, the dynamics of the current/extinction angle and firing

controllers are neglected and only the steady-state controller (Ud -Id) characteristics are

represented.

43

2.12.3 DC network

The DC network is represented as a resistive network, a single resistance ignoring energy

storage elements.

Figure 2.16: DC Network Represented as Resistive Network

2.12.4 Dynamic representation using equivalent circuits

For dynamic analysis, DC network is represented by the simple equivalent circuits of the

type shown in figure 2.17. Even here, the shunt branches may be neglected. This type of

network representation is used when detailed controller representation is employed.

Figure 2.17: DC Network Represented as a ‘T’ Network

2.12.5 Solution methodology

There are various options that are available in the modeling of converters, controllers

and the DC network. Actually these are not altogether independent choices. For example, the

resistive network or transfer function representation of the DC network can only be used with

the response type controller models. The combinations of the various types of component

models used for analysis are illustrated in following table 2.3.

44

Table 2.3: Combinations of Various Models Used for Analysis

Sr. No. Converter Model Control Model DC Network

1 Simplified Response Type Resistive Network

2 Simplified Detailed Equivalent Circuit

2.12.6 Direct methods for stability evaluation

The basic procedure in applying energy functions for direct stability evaluation is outlined

below:

The post full system defined by,

( )yxfx ,.

=

( )yxgo ,=

has an associated energy function W(x, y, t) such that

0...

=∂

∂+∂∂+

∂∂=

t

Wy

y

Wx

x

WW

Some components of W may be path dependent. This is the case when the

transmission line losses, non-constant power loads and excitation controllers are considered.

The system is said to be stable if ( ) cc WtW <1 Where, 1ct is the clearing time (of the fault) and

Wc is the critical energy. Evaluation of Wc, is a bit difficult, which is obtained from

( )** , uuc yxWW =

( )** , uu yxgO=

Where, x*u is termed as the controlling unstable equilibrium point (UEP) which is closest to

the fault trajectory. In equation for Wc, the path dependent terms in W are ignored. The

determination of UEP can be complex as there are several of them in large systems. An

alternate approach is to employ potential energy boundary surface (PEBS) method where,

cW is determined from

( )ffpc yxWW ,max=

45

Where, Wp is the potential energy (the sum of the components of W which do not depend on

the rotor velocities) and the subscript ‘f’ indicates the maximum of W to be found along the

fault trajectory. Actually, this is an easy computational method for finding value of Wc,. The

contribution of the DC link to the energy function is the terms given below

( )∑ ∫=

+−=

N

kk

v

v k

dkkokdkdc dV

V

QPW

k

ko1

δδ

Where, dkP , dkQ are the power and reactive power at converter bus k, kV , kδ are the bus

voltage magnitude and angle respectively. It is assumed that there are N converter buses. The

integral may have to be determined approximately.

2.12.7 Transient stability

Assume that a small rotor oscillation of frequency ‘h’ is exhibited in a synchronous

machine, which can be represented by ∆δ, additional electrical complex torque ∆Te and

mechanical complex torque ∆Tm are induced. In complex torque coefficient method, these

increments of the electromagnetic torque and mechanical torque of a machine under a h Hz

(h < f , and f, is the base system frequency) disturbance can be represented by following

equations

( ) ( )...

ωδ ∆+∆=∆ hDhKT eee ….2.56

( ) ( )...

ωδ ∆+∆=∆ hDhKT mmm ….2.57

Ke and De are called as the electrical spring coefficient and electrical damping coefficient

respectively and Km, and Dm are called as the mechanical spring coefficient and mechanical

damping coefficient respectively.

For torsional modes of turbine-generator oscillation, the value of Ke, is relatively

small in comparison to that of Km. Hence, the electrical spring coefficient has little effect on

rotor torsional oscillations. However, the inherent damping of the turbine-generator torsional

modes is extremely low, and the damping contribution of the electrical system can be a

significant factor. Hence, the emphasis is to examine the damping contribution of the power

system.

The electrical damping coefficient can be represented as:

46

∆

∆= .

.

ω

e

ee

TRD …2.58

Where ∆ T�� , ∆ω� are the increment of the electrical torque and electrical speed respectively,

introducing the definition of the electrical complex torque coefficient.

( ) eee

e jhDKT

jhK +=∆∆=

δ

We obtain the electrical spring constant Ke and damping constant De. Similarly, we define

the complex torque coefficient

( ) mmm

m jhDKT

jhK +=∆∆=

δ

Where, Km is called mechanical spring constant and Dm, the damping constant. To indicate

the interaction effect between electrical and mechanical system, the following equation is

given

( ) ( ) ( ) ( )mememe DDjhKKjhKjhK +++=+

The basic criterion of the torsional mode of oscillation at h Hz to consider unstable or

unstable interaction between electrical and mechanical system is

( ) ( ) 0≥+ hKhK em

and

( ) ( ) 0<+ hDhD em

The torque equation under such disturbance is written as

ema TTT −=

Where ma TT , and eT are the accelerating, mechanical and electrical torque respectively.

In terms of power the equation can be written as

ema PPP −=

aP , the accelerating power, is taken as the difference between the mechanical power input

and the electric power output.

2.13 Harmonics in HVDC

47

Harmonics are defined as periodic signals with frequencies which are multiple of

fundamental frequency.

a) Characteristic Harmonics:

The characteristic harmonics are harmonics of that order which are always present

even under ideal operation – balanced AC voltages, symmetric three phase network and

equidistant pulses. In the converter analysis, the DC current is assumed to the constant. In

this case, there are harmonics in AC current of the order.

1±= nph

Where, p is the pulse number, n is any integer. The harmonics in the converter DC voltage

are of the order.

nph =

b) Non – characteristic harmonics:

The harmonics of the order other than the characteristic harmonics are termed as non

characteristic. These are due to (i) imbalance in the operation of two bridges forming a 12

pulse converter (ii) firing angle errors (iii) unbalance and distortion in AC voltages and (iv)

unequal transformer leakage impedances.

2.13.1 Filters in HVDC terminal station

Following types of filters are provided for harmonic elimination

� AC filters

� DC filters

� Active filters

A] AC Filters

The following are various types of AC filters that can be used

1. Single tuned filter

2. Double tuned filter

3. High pass filter

• Second order filter

• C type filter

The single tuned filters are designed to filter out harmonics of single frequency. The

double tuned filters are used to filter out two discrete frequencies. The double tuned filters

48

are used to filer out two discrete frequencies, instead of using two single tuned filters. Their

main advantages are (i) only one inductor is subject to full line impulse voltage and

(ii) power loss at the fundamental frequency is considerably reduced.

The second order high pass filters are designed to filter out the higher harmonics.

The tuning of these filters is not critical. The losses at the fundamental frequency can be

reduced by using a C type filter where the capacitor C in series with L, provides a low

impedance path to the fundamental component of current.

A typical converter system with 12 pulse converters has double tuned (or two single

tuned) filter banks to filter out 11th and 13th harmonics and a high pass filter bank to filter out

the rest of harmonics. A third harmonics filter is included to filter out the non- characteristic

harmonic of the third order (particular with weak AC systems where some voltage unbalance

is expected).

All the filter branches appear capacitive at fundamental frequency and supply reactive

power.

B] DC filters

The harmonics in the DC voltage across the converter contain both characteristic and

non-characteristic orders. These harmonics result in current harmonics in DC lines and cause

noise in telephone circuits.

The harmonic current generated in the line can be computed from the knowledge of

harmonic voltage sources at the conveners, smoothing reactor, DC filter and line parameters.

The harmonic current varies with the distance (from the converter station) along the line.

The DC filters are also of single or double tuned type. The choice of DC filters

affect over voltages due to DC line resonances and line faults. The smoothing reactor and

the surge capacitor play a role in the first and the second case respectively, It is found that

DC filters help in limiting the over voltage at the DC terminals caused by monopolar DC line

faults. The DC filters are stressed by direct voltages in addition to harmonic voltages.

C] Active Filter

The principle of the active DC filter is to inject a current generated by a power

amplifier into the DC circuit with such amplitude and phase that it cancels the DC side

harmonics coming from the converter. The amplifier is controlled by a high speed signal

49

processor controller, taking its input from the measured harmonic current entering the DC

line.

The current entering the DC line is measured by the harmonic current transducer. The

PWM amplifier is protected against transient over voltages and over currents by the thyristor

protection.

2.14 Design of AC Filter

2.14.1 Criteria of design of filter

The AC harmonic filters constitute a significant proportion in the capital cost of the

HVDC terminal substation. A large area in converter substation in covered by AC filters.

The criterion of choice of filter size depends on

• Harmonic elimination

• Reactive power requirement.

• Permissible deviation in sinusoidal waveform

• Permissible telephone interference

• Cost of AC filters

2.14.2 Performance parameters

The major design objective of AC filters is to reduce the telephone interference. This

can be measured by the following performance indices.

Harmonics Distortion

This can be measured in different distortion

D = 1002 xE

ZI

I

m

nnn∑

=

In percentage where In, Zn and E1 are the harmonics current injected, the harmonics

impedance of the system and the fundamental component of the line to neutral voltage

respectively, m is the highest harmonics considered.

Total Effective Distortion

Deff = ( )

100

2

1

2

2

xE

ZI

I

m

nnn

∑

=

50

Individual Harmonics Distortion

In some cases, the harmonics distortion can be defined individually for a single harmonics as

Dn =

1E

InZn x 100

Telephone Influence Factor

This is an index of possible telephone interference and is defined as

TIF =

( )

I

m

nnnn

E

FZI2

1

2

2

∑

=

Where, Fn = 5nf1Pn

Pn is the C message weighting used by Bell Telephone System (BTS) and Edison Electric

Institute (EEI) in USA. This weighting reflects the frequency dependent sensitivity of the

human ear and has a maximum value at the frequency of 1000 Hz.

Telephone Harmonics Form Factor (THFF)

This is analogous to TIF except that

Fn = 800

1nfWn

Where Wn is the psophometric weight at the harmonics order n, as defined by the

Consultative Commission on Telephone and Telegraph System (CCITT).

IT product

In BTS-EEI system, there is another index called IT product and is defined by

IT = ( ) 2

1

2

2

∑

=

m

nnnFI

KIT product is defined as: KIT = 1000

IT

Although there are no specific standards on the performance requirements, the

suggested values of the above mentioned indices are given in table [33-35].

51

Table 2.4: Performance Indices

Index Range Suggested Value

TIF 25-50 30

D 2-10 4%

Deff 2-5 3%

Dn - 1%

2.15 Control System

The functions of the control system can be stated as

1. Maintaining DC power, DC voltage and DC current as desired by the operating personel.

2. Ensuring that normal control is within the design limits of the HVDC system and to avoid

unwanted shutdowns due to protection actions.

3. Switching of AC filter to control the harmonic distortion and reactive power flow.

4. Control of the converter transformer taps changers.

5. Safe switching of AC and DC switches, breakers, dis-connectors and grounding switches.

6. HVDC transmission systems must transport very large amounts of electric power which

can only be accomplished under tightly controlled conditions. DC current and voltage is

precisely controlled to affect the desired power transfer. It is necessary therefore to

continuously and precisely measure system quantities which include at each converter

bridge, the DC current, its DC side voltage, and delay angle α and for an inverter, its

extinction angle γ.

7. Two terminal DC transmission systems are the more usual and they have in common a

preferred mode of control during normal operation. Under steady state conditions, the

inverter is assigned the task of controlling the DC voltage. This it may do by maintaining

a constant extinction angle γ. which causes the DC voltage Ud to droop with increasing

DC current Id as shown in the minimum constant extinction angle γ characteristic A-B-

CD in figure 2.18. The weaker the AC system at the inverter, the steeper the droop.

Alternatively, the inverter may normally operate in a DC voltage controlling mode which

52

is the constant Ud characteristic B-H-E in figure 2.18. This means that the extinction

angle γ must increase beyond its minimum setting depicted in figure 2.18 as 180.

Figure 2.18: Steady State Ud-Id Characteristics for a Two Terminal HVDC

System

8. If the inverter is operating in a minimum constant γ or constant Ud characteristic, than the

rectifier must control the DC current Id. This it can do so long as the delay angle α is not

at its minimum limit (usually 50). The steady state constant current characteristic of the

rectifier is shown in figure 2.18 as the vertical section Q-C-H-R. Where the rectifier and

inverter characteristic intersect, either at points C or H, is the operating point of the

HVDC system.

53

9. The operating point is reached by action of the on-line tap changers of the converter

transformers. The inverter must establish the DC voltage Ud by adjusting its on-line tap

changer to achieve the desired operating level if it is in constant minimum γ control. If in

constant Ud control, the on-line tap changer must adjust its tap to allow the controlled

level of Ud be achieved with an extinction angle equal to or slightly larger than its

minimum setting of 180 in this case.

10. The on-line tap changers on the converter transformers of the rectifier are controlled to

adjust their tap settings so that the delay angle α has a working range at a level between

approximately 100 and 150 for maintaining the constant current setting Iorder (see figure

2.18). If the inverter is operating in constant DC voltage control at the operating point H,

and if the DC current order Iorder is increased so that the operating point H moves

towards and beyond point B, the inverter mode of control will revert to constant

extinction angle γ control and operate on characteristic A-B. DC voltage Ud will be less

than the desired value, and so the converter transformer on-line tap changer at the

inverter will boost its DC side voltage until DC voltage control is resumed.

11. Not all HVDC transmission system controls have a constant DC voltage control such as

is depicted by the horizontal characteristic B-H-E in figure 2.18. Instead, the constant

extinction angle γ control of characteristic A-B-C-D and the tap changer will provide the

DC voltage control.

2.15.1 Current margin

The DC current order Iorder is sent to both the rectifier and inverter. It is usual to

subtract a small value of current order from the Iorder sent to the inverter. This is known as

the current margin Imargin and is depicted in figure 2.18.

The inverter also has a current controller and it attempts to control the DC current Id

to the value Iorder - Imargin but the current controller at the rectifier normally overrides it to

maintain the DC current at Iorder. This discrepancy is resolved at the inverter in normal steady

state operation as its current controller is not able to keep the DC current to the desired value

of Iorder - Imargin and is forced out of action. The current control at the inverter becomes active

only when the current control at the rectifier ceases when its delay angle α is pegged against

its minimum delay angle limit. This is readily observed in the operating characteristics of

figure 2.18, where the minimum delay angle limit at the rectifier is characteristic P-Q. If for

54

some reason or other such as a low AC commutating voltage at the rectifier end, the P-Q

characteristic falls below points D or E, the operating point will shift from point H to

somewhere on the vertical characteristic D-E-F where it is intersected by the lowered P-Q

characteristic.

The inverter reverts to current control, controlling the DC current Id to the value Iorder

- Imargin and the rectifier is effectively controlling DC voltage so long as it is operating at its

minimum delay angle characteristic P-Q. The controls can be designed such that the

transition from the rectifier controlling current to the inverter controlling current is automatic

and smooth.

2.15.2 Converter control

For the sake of convenience, the overall control can be divided into three categories:

1. Power control, auxiliary control and voltage dependent current order limiter (VDCOL).

The output of this block is the current order.

2. Constant Current (CC) and Constant Extinction Angle (CEA) controls. These are usually

of feedback type but the extinction angle control can also be of predictive (open loop) type.

The output of these controllers is a control voltage that determines the instant of gate pulse

generation. The input is taken as the current order (generated locally or at the remote station)

or the extinction angle reference (generated locally). The communication delay in

transmitting the current order may have to be represented.

3. Gate pulse generator which has input from the CC or CEA controller and determines the

instant of gate pulse generation for each valve. There are basically two types of firing control

schemes.

i) Individual phase control (IPC)

ii) Equidistant Pulse Control (EPC)

a)Pulse Frequency Control (PFC)

b)Pulse Phase Control (PPC)

55

Figure 2.19: Power and Auxiliary Controller Block Diagram

Figure 2.20: Rectifier and Inverter Controller Block Diagram

The effect of IPC / EPC can be included in the controller model in conjunction with

the simplified converter model. The basic difference in the two schemes is that the change in

the phase of the converter bus AC voltage will affect the delay angle in case of EPC, while it

does not in the case of IPC. The converter control is usually represented by block diagrams

and specifying the transfer function of each block. A typical controller block diagram is

shown in figure 2.19 and 2.20.

56

The time delay Td is introduced if continuous time model of the converter is used and is

given by

od pf

T2

1=

Where,

p = pulse number, Π

=2

oof

ω

This delay is to be ignored if the discrete model of the converter is used, in which

case, the delay angle is obtained by sampling the output of the controller at intervals

corresponding to dT2 .

The limiters in the control system are to be represented carefully. The limiters can be

of wind up type or non-wind up type. In the wind up type, the limiter is treated as a separate

block with the input variable unrestricted while the output variable is limited within a

specified range. In the case of a non-wind up limiter, (which is normally applicable at the

output of an integrator) the output variable of the block directly preceding the limiter is

restricted. There is no need for a separate block to represent the limiter, in this case.

The major difference between the two types of limiters is that there is a time lag

introduced in the case of the wind up limiter, when the output variable is at its limits. For

example, if a wind up limiter is applied at the output of an integrator, the output of the limiter

will change only after some time has elapsed following the reversal of the input to the

integrator.

The control system for one pole is illustrated in figure 2.21. The primary objective of

the control system is to send out firing pulses to the thyristor valves in order to keep the

transmitted DC power or DC current at the ordered level disregarding AC and DC

disturbances. The power order is set by the operating engineer with possible contributions

from various power modulation functions.

The power order goes through the Pole power Control (PPC), which calculates a

current order and coordinates the two stations through the telecommunication system

(TCOM) system. The current order is then sent to the converter.

57

Figure 2.21.docx

58

Figure 2.22.docx

59

firing control (CFC), which calculates the corresponding alpha and sends out firing pulses.

The CFC also ensures that the firing is done within the limits of the thyristor valves.

Alpha (α), Gamma (γ) and Ud are also superevised and controlled to be within their

respective design limits. This is achieved in the voltage and reactive control (VARC)

function which as outputs gives a Gamma reference to the CFC and Ud, Alpha, and Gamma

references to the tap changer control (TCC). The TCC controls the tap changers on the

converter transformers in order to, within the limits of the design, follow the Ud, Alpha and

Gamma references.

The reactive power balance of the HVDC converter stations is controlled by the

Reactive Power Control (RPC), which switches AC filters in order to keep the reactive power

balance, as well as harmonics generated by the HVDC stations, within design limits.

The tasks of the pole sequences (FSQ) are primarily to assist the operating engineers

for changing control modes, ensure safe switching of DC disconnectors and DC breakers at

connection and disconnection of a pole, changes of modes of operation e.g. Monopolar

earth return/metallic return. Coordination between the stations is done by the PSQ through

the TCOM.

2.16 Functions in HVDC Control System

2.16.1 Pole power control system

The main purpose of the Pole Power Control system is to calculate a current order

and thereby keep the transmitted DC power or DC current constant at the ordered level

disregarded AC and DC disturbances, while still maintaining the stability of the DC system.

Two different modes exist, either power or current control mode.

2.16.2 Power control mode

The power control mode keeps the DC power transmitted equal to the power order

given by the operating engineer. The power order and the power ramp are given to a stepping

logic function, which ramps the power order. In order to keep the power constant, variations

in the DC voltage are compensated for, by adjusting the current order accordingly. To the

60

power order obtained in this way, different additional contributions can be added from

various power modulation functions. The current order is obtained by dividing the total

power order by the direct voltage response measured at the DC high voltage divider. This is

the main mode of operation.

2.16.3 Power modulations

The inherent high speed power control capability of the HVDC transmission system

can be utilized for stabilization and/or frequency control of the surrounding AC systems. The

contribution from power modulation control functions is therefore, superimposed on the

normal operating engineer set power order. The PPC handles four different types of power

order modulations. The contribution from various power modulation functions could either

be seen as a strict additional power order or as an additional power order with an update of

the Stepping Logic Function. The former is useful for power frequency modulations which

do not normally give a permanent contribution. The latter is useful for modulation functions

that do give a permanent contribution or when the contribution is intended to be permanent.

Activation and deactivation of power modulation may cause smooth power change if the

scenario is such that the modulation function is active while being turned on or off. If the

modulation function updates the Stepping Logic Function there will not be a power change

when turned off.

Damping Control

The Damping control will normally always be activated. The Damping Control

receives the AC frequency from both stations, and gives a power contribution to the PPC in

order to damp oscillations in the AC network. Damping control will be available in power

control, normal power direction but not in islanded operation.

Frequency Control

The Frequency control is active while in islanded operation. The frequency control

receives the AC frequency from both stations, and gives a power contribution to the PPC in

order to maintain the frequencies in both stations at islanded operation. Frequency control

will be available in power control, normal power direction and in islanded operation.

61

2.16.4 Current Margin Regulator

The CMR compensates for the loss in DC current when the rectifier looses current control

(i.e. alpha is limited to alpha min). The CMR will be available in joint control.

2.16.5 Fast Stop

The Fast stop function will, when manually activated, stop the HVDC transmission

fast and in a safe way. If the pole is in joint control then, the DC power will first be ramped

down with a fast ramp rate. Then the PSQ will coordinate the blocking of both converters. If

the pole is not in joint control then Fast stop will ramp down power with the fast rate and

block the respective pole. In case of emergency there is also an "Emergency Stop" provided.

It trips the converter breaker.

2.16.6 Reactive Power Control

The purpose of the RPC is to control properties in the AC network connected to the

convener station. The quantity to be controlled is either AC bus voltage or reactive power

exchange with the AC system the system should also make sure that enough filters of

different types are connected to prevent excessive harmonics to enter into the AC system.

The means used to perform these tasks are switching of the different AC filters.

2.16.7 Voltage and angle reference calculation

The objective of the VARC is to ensure that the DC voltage, extinction angle gamma,

or firing angle alpha, will be within design limitations during steady state conditions. This is

done by calculating target values in DC voltage, gamma and alpha reference which are then

sent to the TCC. The DC voltage, alpha and gamma reference target values will also be sent

to the CFC.

Ud, UdiO and angles are coordinated between the two stations for various operation

modes and power levels. The DC voltage, common in both stations with the exception of DC

line resistance, is controlled by the VARC. Telecommunication is used to calculate, on line,

the resistance. Since the DC voltage is controlled in one station the resistance is used to

62

ensure proper voltage control. During telecommunication outages the resistance value is

frozen.

Figure 2.23: Overview of VARC

2.16.8 Tap Changer Control

The TCC system is designed to control the Load Tap Changers of the converter

transformers. The objective of the TCC is to keep ordered alpha, gamma and DC voltage to

the target values determined by the VARC.

2.16.9 Converter Firing Control

The CFC receives a current order from the PPC and sends out firing pulses in such a

way that the ordered current is maintained. The dynamics of the HVDC transmission system

is determined primarily through the settings of the Voltage Dependent Current Order Limiter,

VDCOL and the Current Control Amplifier CCA.

To assist the AC system in recovering from faults, the reactive power consumed by

the converters must often be limited. The Voltage Dependent Current Order Limiter,

VDCOL, accomplishes this by reducing the transmitted current at low DC voltage. The

Current Control Amplifier, CCA, is principally a P-I regulator, where the proportional part

executes instantaneous changes, while the integrator part maintains the value of current

63

during steady state conditions. The current control amplifier will have a high enough gain

and suitable dynamics to reach the demands regarding speed and stability. The output signal

from the current control amplifier is a reference for the firing angle and used as an input

order to the firing control system.

Figure 2.24: Overview of CFC

Firing Control

The objective of the firing control is to convert the ordered alpha into corresponding

firing pulses. The allowed changes of the firing angle are dependent upon the operation

mode. An alpha rate of change limiter is therefore included in order to avoid too fast changes.

Especially in regions where the commutations may become unsuccessful, i.e. low gamma.

One important task of the Firing Control is to secure that the firing instant does occur

within the time limitations which are set with regard to design limitations of the converter

bridge and thyristor valves. This is accomplished through the following features. The voltage

has to reach a certain level (UMIN, corresponding to. approximately 50 at normal voltages)

across the thyristor valve to enable firing. For inverter operation the value (ALPHA MIN) is

set to around 1000 in order to prevent reversed voltage, and thereby reversed power.

Predictive commutation margin (AMIN) control ensures that the extinction angle, is kept

above the minimum value, normally 170, in order to minimize the risk for commutation

failures.

64

Figure 2.25: Overview of the firing control

Control Pulse Generator

Control Pulse Generator distributes the control pulses to the correct thyristor valves.

One control pulse per valve is sent, i.e. 12 for a twelve pulse bridge per cycle. furthermore,

block, block with bypass pair, deblock and selection of bypass pair are performed in this

system. The orders are received from either the pole sequences or from protections.

Sub Synchronous Damping Controller

Torsional modes of oscillation of nearby generators will modulate the frequency of

the AC system. The SSDC will ensure that the HVDC provides positive damping for these

oscillations

The SSDC is integrated in the convener firing control. The controller modulates the

firing angle (α) directly inside the firing control system.

Figure 2.26: Sub Synchronous Damping Controller

65

2.16.10 Pole Sequences Control System

The pole sequences control system contains control functions for control of switching

at operation mode changes, start and stop of the transmission and control mode changes such

as joint and separate. The sequence control functions are divided into two parts, the

interlocking part and the coordination part.

2.16.11 Valve Control

The valve control receives electrical pulses (CP) from the pole control and converts

them to optical firing pulses (FP) which are sent to each thyristor in the valves. The status of

the thyristors are monitored and sent via bitbus to the Thyristor Monitoring (THM) in the

pole control system.

2.16.12 Pole Control Communication System

The pole control communicates between the stations through the telecommunication

system. The pole control communicates within each station between different control

cubicles through bitbus systems. This can also be done through high speed links.

2.17 Voltage Control

The voltage control function consists of three functions named:

• Open Line Test Control.

• Overvoltage Limiter (only in rectifier operation).

• Voltage Regulator

2.17.1 Open Line Test Control (OLTC)

Open Line Test is a test function, which is used manually by the operators to energize

the DC side with direct voltage. The test function is used for testing the isolation on the DC

side after a longer period of deenergization. Open Line Test is activated manually. The DC

voltage can be set by the operator to a desired level. The rectifier terminal generates a DC

voltage with normal polarity, while the inverter generates a voltage of reversed polarity. The

direct voltage from a 12-pulsc bridge at peak rectification can be written as:

( )60cos**3

*3

4 −= απUdiOUd

66

This equation indicates that the direct voltage starts to increase at alpha 150 degrees

and will reach a maximum level at alpha 60 degrees. The above mentioned equation is valid

only if the current is zero, which is approximately correct if only the DC switchyard is

included in the test. If the DC line is included in the test, corona losses and other losses will

reduce the DC voltage, but since a closed loop control is used this will be compensated by a

reduction in alpha. A diagram for OLTC is shown in figure 2.27.

Figure 2.27: Open Line Test Control

The input to the OLTC is the reference voltage UD REF OLT which is set by the

operator. This input is then fed through a rate-of-change limiter. The difference between the

voltage reference and the actual DC voltage UD POL is the input to the PI-controller. The

parameters of the PI-controller must be set to values that are suitable. The output from the

integrator is limited between zero and 95 degrees. In steady state, the output from the OLTC

can be written as:

( ) ( )( )dssUT

tU ∆−−∆= 1*K-155DOLTALPHAOR

Where, ∆U is UD REF OLT - UD POL. OLTALPHAORD is expressed in electrical degrees.

Since the controller is limited to 950, the minimum value of the firing angle which

gives the highest possible DC voltage is 600.

2.17.2 Overvoltage Limiter (OVL)

If for some reason the rectifier is started against an open DC line, an overvoltage

occurs due to the earlier mentioned relation between alpha and UD at operation with zero

current. Reflections at open line ends also contribute to the overvoltage.

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At deblock the control amplifier will lower alpha in order to establish minimum

current. This will normally stop when alpha reaches the UMIN-criterion (5 ele. deg.). As can

be seen from the equation for Ud the maximum voltage is reached for alpha lower than 600.

This means that during start against an open line the firing angle must be increased to values

about 800 - 900 to prevent high overvoltages.

A start against an open DC line can occur when:

• The rectifier is started without telecommunication and the inverter has not been started

(human error).

• The inverter is blocked without By Pass Pair (BPP) during operation without

telecommunication, or if a low speed telecommunications link is used (in case telecom

delay greater than 0-100 ms). This gives the worst case since the current order is high,

giving the fastest increase of DC voltage.

A start against an open DC line can be detected as a combination of high DC voltage

and low DC current. However, normal charging current of the DC side can be rather high,

especially if DC cables are connected.

In many cases the overvoltage limiter is not sufficient to prevent high DC voltage,

depending on the high rate of change of the DC voltage.

2.17.3 Voltage Regulator (VCAREG)

A voltage controller is implemented in both rectifier and inverter operation. The main

function of this controller is for reduced voltage operation, but it is also advantageous for

normal voltage operation. The voltage controller is a PI-regulator that is acting on the

minimum and maximum limits of the current controller. In inverter operation it will decrease

the maximum alpha limit of the CCA, whereas in rectifier operation it increases the

minimum alpha limit. The output from the voltage controller in turn is min/max limited from

external sources. Figure 2.28 indicates the control action of the voltage controller.

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Figure 2.28: The Control Action of the Voltage Controller

In normal voltage operation the reference voltage to the voltage controller is set

slightly above the operating voltage, so as not to interfere with normal tap changer control.

Normally this level is set approximately one tap changer step above (approx. 1-1.25%

above). By keeping the reference close to the operating voltage, there is an advantage that if

the AC voltage increases rapidly, the controller will act and keep the DC voltage at the

reference.

At reduced voltage operation the reference voltage is lowered to the desired value,

and the controller will consequently lower the DC voltage.

The reference voltage is normally higher in the rectifier end, to keep the voltage

control in the inverter. If inverter current control is desired, the reference to the rectifier

needs to be lower than that of the inverter (here disregarding the influence of the DC line

voltage drop for simplicity).

2.18 Bipole Control

The bipole control will ensure that the total power of the DC bipolar transmission

remain at the ordered value and that the current is equally distributed between the two poles,

thereby the earth current can be kept low. The bipole control also ensures that the ordered

bipole power will be kept during faults in one of the poles, by utilization of power

compensation in the other pole. Bipole functions consist of pole power transfer functions,

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pole order distribution functions and current balance functions. The bipolar transmission can,

by using pole assigned control functions, be operating in synchronous and backup

synchronous.

2.18.1 Bipolar power control

In bipolar power control, BPC, both poles are selected in bipole control and power

control. Maintaining of ordered bipolar power with current balance between the poles is the

primary task in BPC. Compensation between the poles is achieved in BPC if power loss

occurs in one pole. If bipolar power is operating in synchronous control, the transmission is

running in synchronous bipolar power control. This mode is the normal operating mode of

the HVDC bipolar transmission. In case, the telecommunication links are out of service in

one or both poles, Backup Synchronous Control, BSC, will automatically be selected to one

or both poles, with the transmission still running in bipolar power control.

In synchronous bipolar control the operator initiated bipole start order is sent to the

pole sequences which take care of the coordination with the other station. Both poles are

started simultaneously. The bipole stoorder can be given at minimum power, a STOP order is

automatically given to the respective pole sequence and both poles will be blocked

simultaneously.

Figure 2.29: Pole Order Distributor

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Pole Order Distributor

In BPC the Bipole Power Order, BPO, is scaled in each pole by its own DC pole

voltage divided by the bipole voltage, to obtain pole orders, which ensures a current balance

between the poles, independent of DC voltage fluctuations, and thereby a low earth current

shown in figure 2.29.

Pole Power Transfer Scheme

When one pole is in bipole control, it has the possibility to compensate for power

fluctuations, due to limitation, start/stop or fault in the other pole that may occur.

Figure 2.30: Pole Power Transfer Scheme

The compensation is carried out as fast as possible up to pole limit with maintained

bipole power. The compensation is performed by adding an order contribution from the other

pole, to the pole order. The order contribution is the difference between the pole order and

limited pole order. To ensure fast compensation, the measured power of the faulty pole used

in the pole power transfer scheme, is set to zero at fault show in figure 2.30.

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Fine Current Balancer

To minimize the earth current of the bipole in BPC further, a PI-regulator, fed by the

earth current, is giving a current balance contribution to the pole current order, in each pole.

The earth current is measured on the electrode line with high accuracy.

2.19 Views of Other Researchers

Many researchers have contributed in the field of HVDC transmission systems. The

contribution which seems to be the mile stones is described in preceding paragraphs.

Narain G. Hingorani in his paper, ‘HIGH-VOLTAGE DC TRANSMISSION: A

power electronics workhorse’ has discussed about the roll and scope of HVDC technology in

the context of power electronics in transmission systems and the state of the art and new

developments within the technology are reviewed. He mentions the applications,

configurations etc. Further he has discussed international business and reliability of the

systems and reasons for failures. He states, ‘Work is under way to raise the voltage capability

of the 100-mm wafer from the 8-kV thyristor to 1@-12-kV. Then, too, thyristors based on

120- to 150-mm silicon wafers are in development’. He further narrates the achievements of

ABB, Siemens and others suppliers in continuous development of the HVDC technology [2].

Dr. B.K.Anderson has published many papers related to various aspects of HVDC

technology. In one of his paper he states, ‘During the B4 session at the 2004 CIGRE meeting

a new method for the conversion of AC lines to HVDC operation was outlined. The idea is to

use all three conductors of the AC line, with three converters. This has the advantage of

utilisation of the full current capacity of the three existing conductors, and does not require a

metallic earth return [4].

Hirofumi Akagi narrates the major developments in large static converters and its

utility/industry applications in the past years upto 2000 [7].

Madhu Chinthavali et.al has published their article regarding 4H-SiC GTO Thyristor

models for HVDC converters [9-10].

R.A.Valiquette has written a paper about Life Extension of the New Zealand HVDC

Link .The New Zealand HVDC link is one of the two oldest HVDC links that is still running

with original installed equipment from 1965. The New Zealand HVDC link was upgraded

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and modernized in 1992 when a new thyristor pole was added, the line voltage was raised,

new cables added and the original mercury arc poles were equipped with new control

equipment and rearranged to operate in parallel on one pole. Their report describes briefly

the original link, the upgrade in1992, the life-extension initiatives that have been completed

to date, and some future options etc.[39].

Douglas A. Halamay et al. have highlighted the technical aspects and feasibility study

etc. of HVDC transmission links [40-43].

R. Billinton, S. Aboreshaid, M. Fotuhi-Firuzabad presented a probability analysis

technique to evaluate the degree of reliability well-being of bulk generation and HVDC

transmission systems. The system well-being is categorized in terms of system health and

margin in addition to the conventional risk index. Such a technique enables power system

designers, planners and engineers to analyze the generating system and the HVDC

transmission system independently by obtaining the wellbeing area diagrams for each

system. The technique is illustrated by application to a simple hypothetical configuration and

a practical HVDC system [44-53].

C.T. Wu et.al. and Masahiro Hirose et. al. have given their operational experiences

of respective HVDC projects [54-57].

C. B. Modolo et.al. have contributed regarding telecommunication in HVDC systems

[58-60] . Farouk A.M. Rizk et.al. are discussed about their research regarding components in

HVDC like bushings , transformer etc.[61-63]

M. R. Aghaebrahimi et.al. have contributed to power tapping from HVDC systems [64-67]

Gerhard Schmidt, Bernd Fiegand and Stephan Callbeck have discussed about

Environmental aspects of HVDC transmission System. They have discussed, ‘”Electrical and

magnetic fields are linked inseparably to their sources and are not carried into residential

areas by wind are other meteorological factors. Above certain frequencies, the energy present

in electromagnetic fields can lead to electrons being ejected from atoms, which could be the

cause of hereditary damage or even cancer in animals and human beings. This invasive

interference cannot be produced by electrical or magnetic fields up to 30 kHz because the

energy content is too low”. They also have discussed about corona effects and materials and

concluded that “Corona effects on the surface of high voltage overhead power transmission

lines are the principal source of radiated noise. Appropriate design measures can minimise

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these effects. When choosing the materials for the thyristor valve towers, it is important to

ensure that only self-extinguishing or noncombustible, non-flammable and non-drip

substances defined by the most stringent fire behaviour classification UL 94 V-0 are used.

This practice can almost eliminates the risk of fire”[ 68].

Figure 2.31: Electric Field of Monopolar and Bipolar 450 kV HVDC

Overhead line

Stephen A. Sebo and others have worked for the environmental aspects. Field

measurements, corona discharge are the issues of interest [69-77].

Denis Lee et. al. have mentioned the probabilities of exploring added advantages

with the use of Multi-Terminal HVDC [78].

K. R. Padiyar, Nagesh Prabhu have provided a model for analysis and control of

VSC based HVDC system which uses twelve pulse three level converter topology. The

modelling of the VSC system including network transients is discussed in details and is

expressed in D-Q variables. A systematic approach for parameter optimization in selecting

the controller gains is discussed in detail [79].

F. Schettler et. al. has contributed for modeling, control design and analysis of VSC

based HVDC transmission systems as well as CSC technology [80-86].

A. M. Gole et. al. has published their article regarding hybrid HVDC converters and

their impact on dynamic performance [87].

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Guo-Jie Li et.al. has discussed means for Nonlinear Control for Stability

Improvement [88-90].

J. Arrillaga et.al. has discussed modeling in harmonic domain and small signal

modeling and EMTP and other simulation software etc.[91-93].

A.K. David et. al. have developed the ‘Robust Co-ordinated Control Scheme for

HVDC Transmission with Parallel AC Systems’ and various such alternatives are suggested

by many researchers to enhance the control of HVDC systems [94].

Zhu Yi-ying et.al. have conducted research related to ‘Measures of Restraining DC

Current through Transformer Neutrals’. It is mentioned that, monopole ground return mode

may cause DC current through the transformer neutrals which are connected to the ground

and make the transformers DC biases. With the increase of HVDC transmission power, some

transformers through which there will be more DC current going may be saturated, which

brings some problems such as acutely shaking, increased noises and overheating when power

system is in the normal operation. Not only the safety of transformer but also the normal

operation of power system may be impacted in this case. There are various measures to

restrain DC current through transformer neutrals and one of them is putting a capacitor in

series between transformer neutral and ground.

Figure 2.32: The Sketch Map of the Capacitor and Corresponding Protection Equipment

It has been proved to be the optimal measure. A capacitor with very big capability

will be needed to endure big fault current. It is also stressed that bypass equipment is

needed to connect in parallel with the capacitor [95].

Haifeng Liu, Zheng Xu have put forward a new method to tune the parameters of an

HVDC small signal modulation controller. Small signal stability of an AC/DC power

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system is analyzed using the test signal method. The frequency of the test signal is scanned

at the HVDC rectifier current set point, and the oscillated active power flow in the parallel

AC tie line is obtained. The open-loop transfer function between the current reference signal

of the HVDC constant current regulator and the active power flow in the parallel AC inter-tie

is identified by Fourier decomposition and curve fitting with time domain simulations using

electromechanical transient programs. Parameters of the HVDC small signal modulator are

tuned based on the root locus method of the classical control theory [96].

Edmundo Barrera-Cardiel has presented a paper which includes the design of the

hardware and software of the ACDC converter controllers for an HVDC transmission

system. The structure of the converter controllers is based on a 16-bit microcontroller. The

microcontroller includes the facilities needed to support fast real-time control in a single

chip. The main functions included in the terminal controllers are the control of the firing

instants of the bridge valves, the control of the transformer tap changer, and the monitoring

of the signals needed for the control and study of the HVDC transmission system. One of the

special features of the controller is that, with the use of the high-speed input /output system

of the microcontroller, the precision to detect input pulses and to output thyristor firing

signals is not affected by the corresponding latency in the response of the CPU to the

interrupts.

Figure 2.33: Block Diagram of the DC Current Transducer

Their paper contains the details of the design of the AC and DC voltage and current

transducers, the thyristor conducting state detectors, the thyristor gating circuits, the

microcontroller expansion interface, and the software of the terminal controllers [97]. K.G.

Narendra et. al. have investigated about other aspects of control and protection [98-100].