basic concept operation and control of hvdc transmission system

Basic Concept, Operation and Control of HVDC Transmission System

13.00-16.00 hrs. July 29, 2008Room 2003, T.102, EGAT Head Office

Nitus Voraphonpiput, Ph.D.Engineer Level 8

Technical Analysis – Foreign Power purchase Agreement BranchPower Purchase Agreement Division

Electricity Generating Authority of Thailand

2

Objective

Introducing operation, and control of the High Voltage Direct Current Transmission System.

Note: This presentation continues from the morning session. Basic mathematics and electrical engineering knowledge will be useful for attendee.

3

Contents

1. HVAC vs. HVDC2. HVDC PrincipleQ&A for 15 minutesCoffee break 10 minutes

3. Control of DC TransmissionQ&A for 15 minutes

4

1. HVAC vs. HVDCWhy use DC transmission?

This question is often asked. One response is that losses are lower, but is it true?

Reference [2] has been explained using Insulation ratio and Power capacity in order to proof this statement.

5

1. HVAC vs. HVDC

Insulation ratio of HVAC and HVDC (Ref. 1-2)A given insulation length for an overhead line, the

ratio of continuous working withstand voltage factor (k) is expressed as, (note )

0.1 voltage withstandAC

voltagewithstandDC

(rms)

==k

A line has to be insulated for over-voltages expected during faults, switching operations, etc. Normally AC transmission line is insulated against over-voltages of more than 4 times the normal effective (rms) voltage.

21 ≤≤ k

6

1. HVAC vs. HVDC

5.2 ground)-(phase Voltage AC Rated

levelInsulationAC

(rms)1 ==k

This insulation requirement can be met by insulation corresponding to an AC voltage of 2.5-3.0 times the normal rated voltage.

For suitable converter control the corresponding HVDC transmission ratio is expressed as

7.1 ground)-(pole Voltage DC Rated

levelInsulationDC2 ==k

7

1. HVAC vs. HVDC

d

P

VV

kkk

K

2

1(rms)

voltagewithstandDClevel insulation DC

voltagewithstandAClevel insulation AC

Pole DCeach for requiredlength insulationphase ACeach for requiredlength insulation)(ratioinsulation

==

=

Insulation ratio for a DC pole-ground voltage (Vd) and AC phase-ground (Vp) is expressed as

It can be seen that the actual ratio of insulation levels is a function of AC/DC voltage. Next, determine AC/DC voltage.

8

1. HVAC vs. HVDC

Determine AC/DC voltageAssumed resistances (R) of the lines are equal in both cases (HVDC and HVAC).

AC Loss = 3 x R x IL2 and DC Loss = 2 x R x Id2

Let losses in both cases are equal, so that,

The power of a HVAC system and a bipolar HVDC system are as:

Ld II23

=

φcos3 LP IVPowerAC = dd IVPowerDC 2=

9

1. HVAC vs. HVDC

dp VVφcos

132

=

At the same power transfer,

So that,

1cos23

2cos3

===d

P

dd

LP

VV

IVIV

PowerDCPowerAC φφ

It can be seen that HVDC requires insulation ratio at least 20% less that the HVAC which essentially reflects the cost.

Thus, insulation ratio (K) can be written as

φφ cos2.1

cos1

32

2

1 ≈=kkkK

10

1. HVAC vs. HVDC

Power CapacityCompared a double circuit HVAC line (6 lines) and double circuit DC line of Bipolar HVDC.

Power transmitted by HVAC (Pac) and HVDC (Pdc) are

acac

LPdc PPkkkIV

kkkP

φφ cos47.1

cos6

2

1

2

1 ==⎟⎟⎠

⎞⎜⎜⎝

⎛=

φcos6 LPac IVP = dddc IVP 6=

On the basic of equal current and insulation, Id = IL, K=1:

11

1. HVAC vs. HVDC

For the same values of k, k1 and k2 as above and pf is assumed to 1.0, the power transmitted by overhead lines can be increased to 147%. The percentage line losses, which is inversion of the power transmit, are reduced to 68%.

In addition, for underground or submarine cables, power transmitted by HVAC cable can be increase 294 % and line loss reduced to 34%.Note: for cable k equals at least two.

12

1. HVAC vs. HVDCFrom reference [3], losses are lower is not correct.“The level of losses is designed into a transmission system and is regulated by the size of conductor selected. DC and ACconductors, either as overhead transmission lines or submarine cables can have lower losses but at higher expense since the larger cross-sectional area will generally result in lower losses but cost more.”

The reasons that HVDC have been used are:1. An overhead d.c. transmission line with its towers can be designed to be less costly per unit of length.2. It is not practical to consider AC cable systems exceeding 50km (due to VAR charging of the cable).3. Some a.c. electric power systems are not synchronized to neighboring networks even though their physical distances between them is quite small.

13

2. HVDC Principle

The HVDC valve comprises the thyristors acting as controlled switch. In the ‘OFF’ state, the thyristor blocks the current to flow, as long as the reverse or forward breakdown voltages is not exceeded.

It changes to ‘ON’ state if it is forward biased (VAK > 0) and has small positive ‘Gate’ voltage applied between the Gate and the Cathode.

Anode (A)

Cathode (K)

Gate (G)

14

2. HVDC Principle

Thyristor switches between conducting state (ON) and non-conducting (OFF) state in response to control signal (firing) as its characteristic.The Gate voltage need not to be present when the thyristor is already in ON state.

15

2. HVDC Principle

Rd

VT

Rd = ∆VAK/ ∆IA

VT

Anode (A)

Cathode (K)Anode (A)

Cathode (K)

RrRr = ∆VAK/ ∆IA Ploss-ON state = VT.IA(avg.) + Rd.IA2

(rms)

Ploss-OFF state = Rr.Ir2(rms)

iA

ir

16

2. HVDC Principle

ON-OFF state- ON state continues until current drops to zero, even reverse bias

appears across the thyristor.- The critical time to clear charge carriers in the semi-conductor

is referred as the turn-off time toff . If forward bias appears to soon, t < toff, thyristor can not OFF.

ON

OFF

OFF

VAK > 0 and VG >0

IA < 0 VAK > 0 and t < toff

t > toff

17

2. HVDC Principle

ON State OFF State

18

2. HVDC Principle

Rd = 10Ω

Th1

Ld

Th3

Th4 Th2

o30V220US == α

Vd

Id

IsVs

Single Phase Bridge Rectifier

19

2. HVDC PrincipleVs

Id

Is

Vd

α = 30°

Th3

Th4

Th1

Th2

Th3

Th4

Voltage waveform of inductor (Ld), VLd = Vd – Rd Id

Voltage waveform of resistor (Rd), VRd = Rd Id

20

2. HVDC Principle

Is

Vd

Id

50 Hz

100 Hz

150 Hz

200 Hz

250 Hz 350 Hz

300 Hz

100 Hz

Harmonics in the voltage and current waveform.

DC

DC

21

2. HVDC Principle

Even DC side does not have reactive power (Q), the reactive power still presents on the AC side. The reactive power occurrence is caused by the delay angle (α) (or called firing angle) of the current waveform.

30°

VS

IS

Vs Is

α = 30°

P = |VS| |IS| cos α

Q = |VS| |IS| sin α

time360°20 ms

Phasor of fundamental component

22

2. HVDC Principle

Is

Vd

Id

50 Hz

100 Hz

150 Hz

200 Hz

250 Hz 350 Hz

300 Hz

100 Hz

Product of Vd and Idis (active) power (P).

Product of phasor VS and phasor IS is not the apparent power (S) . It represents the active power (P) and reactive power (Q).

There are harmonic distortion power, which is a new term caused by the higher harmonics (more than 50 Hz). It is represented by D (distortion power).

Finally, S2 = P2 + Q2 becamesS2 = P2 + Q2 + D2.

23

2. HVDC Principle

Lk

Rd

Ld

Ith2

Ith1

commutation

µ is overlap angle

Ith2

Ith1

µ

Vd

Id

IsVs

It can be seen that if current is high, overlap angel is increased. In addition, if inductance is high, overlap angle is also increased.

The inductance Lk represents reactance on AC side (called commutating reactance). Due to nature of an inductor, The inductor current can not change suddenly. Thus, during turn-off of the Th1 (and Th2) and turn-on of the Th3 (and Th4), both are in conducting state for a short time (overlap time). This phenomena occurs during commutation of the thyristors.

Increasing Lk

Increasing Id

24

2. HVDC PrincipleIs

Vd

Id

Vsα = 30°µ

Th3

Th4

Th1

Th2

Th3

Th4

Inductor current can not suddenly be changed, thus there is a slope.

2)cos(coscos µααφ ++

≈

25

2. HVDC PrincipleThe impact of the overlap angle (µ) is the reduction of the average dc voltage (Vd).It decreases the harmonic content of the ac current (Is) and power factor of the AC side.

Vd

Id

Ideal case Vdo

dKdod IXVVπ2

−=

KK LfX π2=

Vd

IdVoltage drop due to

commutating reactance is represented as DX

XK

RdId

DX

DR

VT

VT and DR are very less compared to DX. Thus, there are usually neglected.

Overall voltage drop

Vd

26

2. HVDC Principle

Rd

IL

Th1

Ld

VA

Th2

Th3

Vdα

VB

VC

IL

t

o60=α o90=α o120=αo0=α

Vdα

αα coscos17.1 0dPd VVV ==

Natural commutation

VA = √ 2 VP sin ωt

VB = √ 2 VP sin ωt-120°

VC = √ 2 VP sin ωt+120°

∞→d

d

RL

3-pulse converter

27

2. HVDC Principle

1.0

-1.0

0.5

-0.5

Rectifier

Inverter

α

o60=α

o45 o180o135o90

0d

d

VV

αcos0

=d

d

VV

Positive average voltage

Negative average voltage

Inverter mode can be performed when firing angle is more than 90 degrees.

Rectifier mode can be performed when firing angle is less than 90 degrees.

Average voltage is zero when the firing angle is 90 degrees.

28

2. HVDC Principle

α=60° α=30°

Vd

Id

29

2. HVDC Principle

VA, IA

Id

VB, IB

VC, IC

Th1 Th2 Th3 Th1 Th2 Th3

120°

30

2. HVDC Principle

VA, IA

Id

Vd

α=30°α=120°

Inverter mode can be performed as long as the DC current continues flow.

Positive voltage

Negative voltage

Reversing phase sequence

31

2. HVDC Principle

t

IB ICIA

t

µ

α

αdVVA

VB

Lk

Id

Lk

Vk

IC

dkX

Xdd

ILD

DVV

ωπ

α

23

cos0

=

−=

IBIA

µ

α

Vk

VA

VB

DX

32

2. HVDC Principle

γ

γ

t

µα

dV

Vk

µ

DX

α

The commutating reactance (Xk) results in decreasing of DC voltage, but it increases DC voltage in inverter mode.

It can also be seen that the overlap time will increase when DC current is high and this can cause commutation failure in inverter mode.

Note: α + µ < 180°The extinction angle (γ) = 180 - α - µ

IBIAIBIA

180°180°

dkX

Xdd

ILD

DVV

ωπ

α

23

cos0

=

+=

33

2. HVDC Principle6-pulse converter

Vd+

Vd-

Vd+

Vd-

Vd

Vd= Vd+ - Vd-

α=0°

α=0°

-Vd-Vd+

The 6-pulse bridge consists of two 3-pulse bridges (positive and negative) connected in parallel.

34

2. HVDC Principle6-pulse bridge HVDC

Vdr Vdi

Id

Id

The HVDC comprises two converters connected in anti-parallel through smoothing reactors and DC lines. One converter is operated in rectifier mode to transmit power from the AC network to the other side whereas the other side converter is operated in inverter mode to receive power into the (other side) AC network.

Smoothing reactor

Smoothing reactor

DC line

DC line

power

power power

Reactive power

Reactive power

35

2. HVDC Principle

30°

VI.cosφ

II.sinφ

o

ooo

30

866.02

)2515cos(15cos2

)cos(coscos

≈

=++

≈

++≈

φ

µααφ

Rectifier Operation of the 6-pulse bridge converter

Assume α = 15° and µ = 25°

The converter operates in rectifier mode. It transmits active power while consumes reactive power.

36

2. HVDC Principle

145°

VI.cosφ

II.sinφ

o

ooo

145

823.02

)25135cos(135cos2

)cos(coscos

≈

=++

≈

++≈

φ

µααφ

Inverter operation of the 6-pulse bridge converter

Assume α = 135° and µ = 25°

The converter operates in inverter mode. It receives active power while consumes reactive power.

37

2. HVDC Principle

For convenience, the converter operated in inverter mode is often referred to extinction angle (γ). Thus direct voltage in inverter mode (Vdi) are expressed as

dkX

Xdd

ILD

DVV

ωπ

αα

23

90,cos0

=

>+= o

Actually, inverter is commonly controlled at constant extinction angle to prevent commutation failure. Therefore, it is not only for convenience, but also for converter control purpose. It is important to note that voltage drop caused by commutating reactance (Dx) is now negative.

µαπγγ

−−=−= Xdd DVV cos0

38

α is the control variable for rectifier and γ is the control variable for inverter.

2. HVDC PrincipleVoltage vs. current (VI) characteristics at steady state

dN

d

II

0d

d

VV

dN

d

II

0d

d

VV

α = 0°

αmax < 180 °

1.0

-1.0

1.0

1.0

-1.0

1.0

α = 0°

γ = 0°

Slope is DX

Rectifier

Inverter

Rectifier

Inverter

Incr

easi

ng α

Incr

easi

ng α

Incr

easi

ng γ

39

2. HVDC Principle12-pulse bridge HVDC

Vdr∆Vdi∆

Id

VdrY VdiY

∆ ∆

Y Y

Y

Y

Y

YId

The 12-pulse converter is required to improve harmonic current on AC sides. It comprises two 6-pulse converters connected in series. Harmonic current on AC sides are odd orders starting from 11th, 13th …. whereas even orders present on the DC side (12th, 14th…). To achieve 12-pulse, phase displacement of 30° generated by Star (Y) and Delta (∆) connection of the transformers are employed.

40

2. HVDC Principle

Y Y

Y ∆

IA

IA∆

IAY

IA

IA∆IAY

Vd∆

VdY

Vd∆VdYVd

Vd

Rectifier operation of the 12-pulse bridge converter

Assume α = 15°

and µ = 25°

41

2. HVDC Principle

Y Y

Y ∆

current

VdiVdrY Y

∆ YId

Vdi

Vdr

Id

voltageαmin < α

αmin = 5° - 7°

γmin < γ

γ min = 15° - 17°

½ Rd

½ Rd

To ensure all thyristor valves are enough forward bias to turn on.

To keep reactive power requirement on inverter side as low as possible.

Voltage drop caused by line resistance (Rd) is taken into account and the VI characteristic presents operating point of the HVDC system.

decreasing α

power

power power

Reactive power Reactive power

42

2. HVDC Principle

Detail Configuration of the HVDC

43

2. HVDC Principle

Alternatives for the implementation of a HVDC powertransmission system

i) Mono-polar Configuration

ii) Bipolar Configurationa) Earth Return

b) Metallic Return

iii) Homo-polar Configuration

44

2. HVDC Principle

Alternatives for the implementation of a HVDC powertransmission system (continued)

45

Can we use manual control for the rectifier (vary α) and the inverter (vary γ)?If we can not do that, which side should be controlled (rectifier or inverter) or control them both?What is/are the control purpose(s)?

3. Control of the DC Transmission

46


Typical control strategies used in a HVDC system consists of:

Firing ControlRectifier Current Control (CC)Inverter Constant Extinction Angle (CEA) Control Inverter Current Margin Control (CM)Inverter Voltage Control (VC)Voltage Dependent Current Limit (VDCL)Tap change Controls (TCC)Power Reversal

47


Firing ControlFunction of the firing control is to convert the firing angle

order (α*) demanded fed into the valve group control system. There might be voltage distortions due to non-characteristic harmonics, faults and other transient disturbances such as frequency variation. Thus, phase-locked loop (PLL) based firing system is generally applied.

Phase Detector

vA

vB

vC

PI Controller Voltage Controlled Oscillator

sin(.)

sin(.)

sin(.)

comparator

α*

comparator

comparator

……

⅔ π

θvo

-

verror

…

uA

uB

uC Gate firing

TsTsK )1( +

48


verror

uA vA

time

time

Firing Control (Continued)

2π

θ

timeFiring pulse of phase A

α*

α0

0

0

49


Current Control (CC)The firing angle is controlled with a feedback control

system as shown in figure. The dc voltage of the converter increases (by decrease α*) or decreases (by increase α*) to adjust the dc current to its set-point (Id*).

α*αmax

αmin

PIid*

id

-

+

Y Y

Y ∆

Vdr

Current measurement

Firing Control

vA, vB , vC

6

6

IdTsTsK )1( +

50


Constant Extinction Angle Control (CEA)The firing angle of the inverter is controlled at minimum

angle (γmin) to reduce reactive power requirement. This can be achieved by using Gamma control (γ-control).

α*αmax

αmin

PIγ*

γ

-

+

Current measurement

Firing Control

vA, vB , vC

6

6

VdiY Y

∆ Y

γ measurement

Valve voltage

51

3. Control of the DC TransmissionVI Characteristic of the CC and the CEA

current

Vdi

Vdr

Id

voltage

γ* = γmin

α*

VI Characteristic

current

VdiVdr

Id

voltage

γ* = γminα*=α min

If AC voltage on rectifier side decreases, CC decreases α* down to αmin to increase DC current (Id), but there is no operating point (X). This problem can be solved using CMC.

X

AC voltage decreasing

The intersection (X) is the operating point of the DC transmission line.

52


Current Margin Control (CMC)A better way is to use the inverter to control current less

than of the rectifier by an amount of current margin (∆Id) when the rectifier can not perform CC.

α*αmax

αmin

PI

γ*

-+Current

measurement

Firing Control

vA, vB , vC

6

VdiY Y

∆ Y

id*

id

∆id = 0.1 to 0.15

+

γ - Control

Min

imum

se

lect

ion

53

3. Control of the DC TransmissionVI Characteristic of CC, CEA and CMC

current

Vdi

Vdr

Id

voltage

γ* = γmin

α*

Combined characteristics of CC, CEA and CMC

α*=α min

If AC voltage on rectifier side decreases, CC decreases α* down to αmin to increase DC current (Id), but there is no operating point (X). This problem can be solved by CMC.

X

AC voltage decreasing

current

VdiVdr

Id

voltage

γ* = γminX

∆Id ∆IdCMC

CEA

CC

This method can maintain stable operation when AC voltage of both sides are fluctuated.

54

3. Control of the DC TransmissionWhat will happen if AC network of the inverter side is too weak!

current

Vdi

Vdr

Id

voltage

γ* = γmin

α*

In this range the intersection is poorly to define and both current controllers will hunt between the operating points.

This problem can be solved by adjust VI characteristic of the inverter to voltage control (VC) in order to avoid hunting between two controllers.

X

∆IdCMCCEA

Weak AC

current

Vdi

Vdr

Id

voltage

γ* = γminα*

∆IdCMC

CEA

VCγ* > γmin

X

More Weak

55


Voltage Control (VC)it is very effective when the inverter is connected to a weak

AC network. The normal operating point X corresponds to a value of γ higher than the minimum. Thus, the inverter (rectifier as well) consumes more reactive power compared to inverter with CEA.

α*

αmax

αmin

PI

γ*

-+

Firing Control

vA, vB , vC

6

6

VdiY Y

∆ Y

vdi*

vdi

γ - Control

Min

imum

se

lect

ion

Voltage measurement

CMC

Max

imum

se

lect

ion

56

3. Control of the DC TransmissionVoltage Dependent Current Limit (VDCL)

Commutation failures can occur during an AC fault on the inverter side. It results in continue conduction of a valve beyond its 120° conduction interval. The CC will regulate the DC current to its rated value, but in the worst case, two inverter valves may form DC short circuit and continue conducting for a long time, which can cause valve damage. To prevent this problem, DC current must be reduced. One possible to detect the AC side fault is thelowering of the DC voltage. This voltage is typically chosen at 40% of the rated voltage.

Id

57

3. Control of the DC TransmissionVoltage Dependent Current Limit (VDCL)

The VDCL is a limitation imposed by the ability of the AC system to sustain the DC power flow when the AC voltage at the rectifier bus is reduced due to some disturbance as well. The VDCL characteristics is presented below.

current

Vdi

Vdr

Idmax

voltage

α*

∆IdCMC

VC

X

Id-min

≈ 0.4

VDCL∆Idcurrent

Vdi

Vdr

Id

voltage

α*

∆IdCMC

VC

X

Id-min

≈ 0.4

VDCL∆IdIdmax

VDCL VDCLVDCL

58


Voltage Dependent Current Limit (VDCL)

id*

vd

v

Vd

Ts+11

Voltage measurement

i

Minim

um

selectionvd

CC

VDCL

iv

59


Tap Change Control (TCC)When voltage of the AC system of the rectifier and/or of the

inverter is fluctuated, transformer taps (both side) can adjust to keep the DC voltage within desired limits or suitable operating point. Generally, the tap will be changed when the firing angle of the rectifier/inverter still reach its more than 10-15 minutes to avoid interaction of other controls.

Example: if the firing angle (α) of the rectifier reaches minimum limit (αmin) for long time. It means that the AC voltage of the converter is not appropriate. Thus, AC voltage of the converter must be reduced by tap changing of the converter transformer to free the firing angle of the rectifier.

60

3. Control of the DC TransmissionPower Reversal

The VI characteristic of power reversion is presented below (VDCL and VC are not included). The station 1 (rectifier) increases firing angle (α) into the inverter region and the station 2 (inverter) decreases its firing angle (α) into rectifier region. This can be performed without altering the direction of current flow.

current

V2di

V1dr

Id

voltage

γ* = γminα* X

current

V2dr

V1di

Id

voltage

γ* = γminα* X

61


VdiY Y

∆ Y

Y Y

Y ∆ Id

Firing C

ontrol Min

.Min.

Max. M

ax.

p*/vdCAE

CC

VC

VDCL

Power order

γmin

Vd*

Firin

g C

ontr

ol

CAE

CC

VC

VDCL

γmin

Vd*

∆id

Modulation Signal

id*

p*

Vdr

TCC TCC

Master Control

∆p

α*α*

po

Vd, Id,α, γ

62

3. Control of the DC TransmissionCIGRE’s HVDC benchmark was simulated on ATP-EMTP with the typical HVDC control schemes, which the CC mode was employed at rectifier and VC mode was applied at inverter. All simulation results are presented in normalized values.

Start Up HVDC

Rectifier Current Control Inverter Voltage Control

63


Start Up HVDC

Firing Angle (α) of Rectifier Firing Angle (α) of Inverter Extinction angle (γ) is also shown

The HVDC started at 0.1 sec. The firing angle of rectifier started at 90° while the extinction angle of inverter started at 90°.

64


Power Reversal

Firing Angle (α) of Rectifier and Inverter

DC Current

The HVDC started to reverse power flow direction at 0.5 sec. Firing angle of the rectifier increased (with a ramp rate) into inverter zone while firing angle of the inverter decreased (with a ramp rate) into rectifier zone.

65


Power Reversal

The power flow direction of the HVDC reversed at 0.9 sec.

66

3. Control of the DC TransmissionVDCL performance during 1-phase fault at AC network of the rectifier station.

1 –phase Fault at AC network of the rectifier station

cba V VV

67


Fault at AC network of rectifier station

REFIdI

diV

didREF VI I.u.p Degree )( Alpha_i )( r_Alpha ir αα

rα

iα

68

3. Control of the DC TransmissionVDCL performance during 1-phase fault at AC network of the inverter station.

1-phase Fault at AC network of the inverter station

cba V VV

69


Fault at AC network of inverter station

REFIdIdiV

didREF VI I.u.p )( Alpha_i )( r_Alpha ir αα

iα

rα

Degree

70

3. Control of the DC TransmissionModulation signal is employed when a power system has a special requirement such as frequency control, power oscillation damping, etc. For example, the addition frequency control loop is included into HVDC control system to stabilize frequency of the AC system.

71


Modulation Function of EGAT-TNB HVDC

72


Power Swing Damping (PSD) Function of EGAT-TNB HVDC

Thank you very much for your attention

74

References1. Ani Gole, “HVDC Transmission Lecture Note”, University of Manitoba, 2000.2. Jos Arrilaga, “High Voltage Direct Current Transmission”, 2nd , IEE-Press, 1998. 3. Dennis A. Woodford, “HVDC Transmission”, Manitoba HVDC Research Center,

Canada, 1998.4. Erich Uhlmann, “Power Transmission by Direct Current”, Springer Verlag, 1975.5. Vijay K. Sood, “HVDC and FACTS Controllers”, Kluwer. 2004.6. Edward Wilson Kimbark, “Direct Current Transmission” vol.1, Wiley-

Interscience, 1971.7. IEEE Transmission and Distribution Committee, “IEEE guide for planning DC

links terminating at AC locations having low short-circuit capacities”, IEEE, 1997.

8. กฤตยา สมสย, นทศน วรพนพพฒน, วทวส ผองญาต, “การจาลองระบบสงไฟฟาแรงสงกระแสตรงโดย ATP-EMTP”, สมมนาวชาการระบบสง กฟผ. 2548.

basic concept operation and control of hvdc transmission system

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