test

ANALYSIS OF HVDC

CONVERTERS

UNIT II

www.eeecube.com

www.eeecube.com

The pulse number of a converter is defined as the number of pulsations (cycles of
ripple)of direct voltage per cycle of alternating voltage.
The conversion from AC to DC involves switching sequentially different sinusoidal
voltages onto the DC circuit.
The output voltage of the converter consists of a DC component and a ripple whose
frequency is determined by the pulse number.

PULSE NUMBER

www.eeecube.com

www.eeecube.com

VALUE AND SWITCHES

A valve can be treated as a (controllable) switch which can be turned on at any
instant, provided the voltage across it is positive.
A diode is an uncontrolled switch which will turn on immediately after the voltage
becomes positive whereas the thyristor switching can be delayed by an angle or
(alpha).

The opening of the switch(both for diode and thyristor) occurs at the current zero
(neglecting the turn-off time).

www.eeecube.com

www.eeecube.com

CHOICE OF CONVERTER CONFIGURATION

• The configuration fora given pulse number is

selected in such a way that both the valve and
transformer (feeding the converter) utilization
are maximized.

• The configuration shown in Fig. is not the best.

In general, a converter configuration can be
defined by the basic commutation group and the
number of such groups connected in series and
parallel.

• If there are ‘q’ valves in a basic commutation

group and r of these are connected in parallel and
s of them connected to in series, then

P = q r s --------------(1)

www.eeecube.com

www.eeecube.com

• The valve voltage rating is specified in terms of peak inverse voltage (PIV) it has

to withstand.

• The ratio of PIV to the average dc voltage is an index of the valve utilization.
• The average maximum dc voltage across the converter is given by

 VALUE RATING

----------------- (2)

www.eeecube.com

www.eeecube.com

• The peak inverse voltage (PIV) across a valve can be obtained as follows :
• If ‘q’ is even. then the maximum inverse voltage occurs when the valve with a

phase displacement of  radian (l80°) is conducting and this is given by

PIV =2𝐸𝑚------------------

(3)

• If ‘q’ is odd, maximum inverse voltage occurs when the valve with a phase shift

of 𝜋 ∓

𝜋
𝑞is conducting.

• In this case, PIV =2𝐸𝑚 cos

𝜋
2𝑞−−−−−−−−−−−−−−−− − 4

• The value utilization factor is given by

𝑃𝐼𝑉
𝑉𝑑𝑜

=
2𝜋

𝑠𝑞 sin𝜋

2𝑞

for q even −−−−−−−−− −(5)

𝑃𝐼𝑉
𝑉𝑑𝑜

=
𝜋

𝑠𝑞 sin 𝜋

2𝑞

for q odd −−−−−−−−−− −(6)

www.eeecube.com

www.eeecube.com

Multiple Choice

In Monopolar system, the pole is

• positive

• negative

• positive and negative

• none

 TRANSFORMER RATING

• The current rating of a valve is given by

𝐼𝑣 =

𝐼𝑑
𝑟 𝑞----------- (7)

Where , 𝐼𝑑 is the DC current which is assumed to be constant.

• The transformer rating on the valve side is given by ,

------------ (8)

www.eeecube.com

www.eeecube.com

• The transformer utilization factor

𝑆𝑡𝑣

𝑉𝑑𝑜𝐼𝑑
is only a function of q. The optimum

value do of q which results in maximum utilization is equal to 3. It is a fortunate
coincidence that the AC power supply is 3 phase and the commutation group of 3
valves is easily arranged.

For q = 3,

𝑆𝑡𝑣

𝑉𝑑𝑜𝐼𝑑= 1.481 --------- (9)

• The transformer utilization can be improved further if two valve groups can share

a single transformer winding. In this case, the current rating of the winding can
be increased by a factor of
2 while decreasing the number of windings by a

factor of 2.

For this case,

𝑆𝑡𝑣

𝑉𝑑𝑜𝐼𝑑= 1.047 ---------- (10)

www.eeecube.com

www.eeecube.com

Multiple Choice

monopolar system has pole with

• positive

• negative

• positive and negative

• none

• For a 6 pulse converter, this can be easily arranged. The Graetz circuit

shown in Fig. is obtained when the two windings are combined into
one.

• Thus, it is shown that both from valve and transformer utilization

considerations.

Graetz circuit is the best circuit for a six pulse converter.

• In HVDC transmission, the series conduction of converter groups has

been preferred because of the ease of control and protection as well as
the requirements of high voltage rating.

• Thus a 12 pulse converter is obtained by the series connection of two

bridges. The 30° phase displacement between the two sets of source
voltages is achieved by the

transformer connections, Y/Y for feeding

one bridge and Y/A for feeding the second bridge.

• The use of 12 pulse converter is preferable over the six pulse converter

because of the reduced filtering requirements. However, increase in
pulse number beyond 12 is not

practical because the non-

characteristic harmonics are not eliminated.

www.eeecube.com

www.eeecube.com

SIMPLIFIED ANALYSIS GARETZ CIRCUIT

• Without overlap

• With overlap

www.eeecube.com

www.eeecube.com

 WITHOUT OVERLAP

www.eeecube.com

www.eeecube.com

 WITHOUT OVERLAP

• At any instant two valves are conducting in the bridge.
• The following assumption are made to simplify the analysis.

• The dc current is constant.
• The valves can be modelled as ideal switch with zero impedance, when ON ,

and with infinite impedance when OFF

• The AC voltage at the converter bus are sinusoidal and remains constant.

• One period of the AC supply voltage can be divided in to 6 intervals each

corresponding to the conduction of a pair of valves.

• The DC voltage waveform repeats for each interval.
• Thus for the calculation of the average dc voltage it is necessary to consider

only one interval

www.eeecube.com

www.eeecube.com

• Assuming the firing of 3 is delayed by an angle alpha (  ) , the

instantaneous dc voltage Vd during the interval is given by

www.eeecube.com

www.eeecube.com

𝑉𝑑 = 𝑉𝑑𝑜 cos 𝛼

www.eeecube.com

www.eeecube.com

• The range of alpha is from 0 degree to 180 degree

and correspondingly Vd can vary from +Vdo to –
Vdo .

• Thus the same converter can acts as a rectifier or

inverter depending upon whether the dc voltage is
+ve or –ve.

• AC CURRENT WAVEFORM

• It is assumed that the direct current has no ripple.
• There is normally valid because of the smoothing

reactor provided in series with the bridge circuit.

• The rms value of the fundamental components of

the current is given by,

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

 POWER FACTOR

The ac power supplied to the converter is given by

𝑃𝐴𝐶 =

3𝐸𝐿𝐿𝐼1 cos 𝜑

The DC power must match AC power, ignoring the losses in the converter , thus we get

www.eeecube.com

www.eeecube.com

• The reactive power requirements are increased as alpha is decreased from zero.

• When alpha is 90degree the power factor is zero and only reactive power consumes.

www.eeecube.com

www.eeecube.com

 WITH OVERLAP

• Due to leakage inductance if the converter transformer and the impedance in the supply

network, the current in a valve cannot change suddenly and the commutation from one
valve to next cannot be instantaneous.

• For example : When Valve 3 is Fired.
• The Current transfer from valve 1 to valve 3 takes a finite period during which both valves

are conducting.

• This is called OVERLAP and its duration is measured by the OVERLAPANGLE ()

• Three modes of the converter as follows.

MODE 1 : Two and three valve conduction ( u < 60degree )
MODE 2 : Three valve conduction ( u = 60 degree)
MODE 3 : Three and four valve conduction (u > 60 degree )
www.eeecube.com

www.eeecube.com

 ANALYSIS OF TWO AND THREE VALVE CONDUCTION MODE

• For the interval considered, the circuit can be reduced to that shown in diagram,

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

It is analogous to armature reaction in the dc machine in the sense that in only represents a voltage drop and not a
power loss
www.eeecube.com

www.eeecube.com

ANALYSIS OF THREE AND FOUR VALVE CONDUCTION MODE

www.eeecube.com

www.eeecube.com

ANALYSIS OF THREE AND FOUR VALVE CONDUCTION MODE

• When the overlap angle exceeds 60 degree , the minimum number of valves

conducting are three and there are intervals when four valves are conducting.

• This is because when a commutation process is started, the previous commutation

process is not yet completed.

• For example , when valve 3 is fired to valves 1,6 and 2 are still conducting

• The equivalent circuit for this condition is shown in fig,

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

• The above equation can be written as

𝑽𝒅 =

𝟑𝑽𝒅𝒐 𝐜𝐨𝐬 𝜶 − 𝟑𝟎° − 𝟑𝑹𝒄𝑰𝒅

• The equivalent commutating resistance for this case 3 times that for the case with

overlap angle less than 60 degree.

www.eeecube.com

www.eeecube.com

CONVERTER BRIDGE CHARACTERISTICS

1. Rectifier
2. Inverter

www.eeecube.com

www.eeecube.com

RECTIFIER

• The rectifier in general has 3 modes:
• 1stmode : 2 and 3 valve conduction mode ( u< 60 degree )

• 2ndmode : 3 valve conduction mode only for (alpha < 30 degree ) u = 60 degree
• 3rdmode : 3 and 4 valve conduction mode (alpha >= 30 degree )

• As per the current continues to increase, the converter operation changes over

from mode 1 to mode 2 and finally to mode 3.

• The DC voltage continues to decrease until reaches to zero

www.eeecube.com

www.eeecube.com

• For mode 1 :

𝑉𝑑
𝑉𝑑𝑜

= cos 𝛼 −𝐼𝑑

2𝐼𝑠

• For mode 2 :

• For u = constant , the characteristics are elliptical and the equation is given by

(

𝑉𝑑 𝑉𝑑𝑜

cos𝑢

2

)2+ (

𝐼𝑑 2𝐼𝑠
sin𝑢

2

)

2

= 1

www.eeecube.com

www.eeecube.com

• Mode 3 :
• The boundary of the rectifier

operation is shown in fig.

• The co ordinates of point A, B,

C, D and E on the boundary
give in the table

• The points E corresponding to

the maximum power O/P of the
converter

𝑉𝑑
𝑉𝑑𝑜

=
3 cos(𝛼 − 30 ) − 3𝐼𝑑

2𝐼𝑠

www.eeecube.com

www.eeecube.com

 INVERTER

• The inverter characteristics are similar to the rectifier characteristics
• However, the operation as an inverter requires a minimum commutation

margin angle during which the voltage across the valve is negative

• Hence the operating region of an inverter is different from that for a rectifier.

FIRST RANGE

SECOND RANGE

THIRD RANGE

𝛽 < 60°
𝜀 = 𝛾

60° < 𝛽 < 90°

𝜀 = 60° − 𝑢

= 𝛾 − (𝛽 − 60°)

𝛽 > 90°

𝜀 = 𝛾 − 30°

www.eeecube.com

www.eeecube.com

 FIRST RANGE

• The commutation margin angle 𝜀 is equal to the extinction angle 𝛾 only

values of 𝛽 ≤ 60°

• The voltages across the value has a positive dent because of the secondary

commutation.

 SECOND RANGE

• With increased over lap and consequently earlier ignition of the value, the

dent encroaches on the period in which the valve voltage would otherwise
be negative

 THIRD RANGE

• With Decreased commutation margin , the dent becomes entirely negative

,If any dent changes takes places.

𝜷 < 𝟔𝟎°

𝟔𝟎° < 𝜷 < 𝟗𝟎°

𝜷 > 𝟗𝟎°

www.eeecube.com

www.eeecube.com

CHARACTERISTICS OF A TWELVE PULSE

CONVERTER

• As long as AC voltage at the converter bus remains sinusoidal the operation of one

bridge is unaffected by the operation of the other bridge connected in series

• In this case, The converter characteristics are with the assumption that the AC

voltage at the converter bus remains constant.

• The region of rectifier operation can be divided in to the Five modes

www.eeecube.com

www.eeecube.com

• Mode 1 :

4 and 5 value conduction

0 degree < u < 30degree

• Mode 2 :

5 and 6 value conduction

30 degree < u < 60 degree

• Mode 3 :

6 value conduction

0 < alpha < 30 degree u=60 degree

www.eeecube.com

www.eeecube.com

• Mode 4 :

6 and 7 value conduction

60 degree < u < 90 degree

• Mode 5:

7 and 8 value conduction

90 degree < u < 120 degree

• It is noted that, the second mode is continuous of the 1stmode Similarly, 5th

mode is continuous of 7thmode

• The region of the mode 3 shrinks to a point when alpha exceeds 30 degree

www.eeecube.com

www.eeecube.com

• When no AC filters are provided and the source reactance Is not zero the operation

of either bridge is affected by the commutation process taking place in the other
bridge.

• In this case operation of the twelve pulse converter is quite complex and there

complex and there could be additional modes

• 5 value conduction
• 6-7 – 8-7 valve conduction
• Also there could be new modes of 5-6-7-6 valve conduction , depending on the

value of coupling factor K is defined by

K =

𝑋𝑠

𝑋 𝑠+𝑋𝑇

Where Xs is the source reactance

XT is the converter transformer leakage reactance

www.eeecube.com

www.eeecube.com

• It is to be noted that the interaction between adjacent bridges can be neglected if

the converter bus voltages are sinusoidal.

• However, the presence of source reactance results in the variation off the

magnitude of the bus voltage.

• This can affect the shape of the converter characteristics.

www.eeecube.com

www.eeecube.com

DETAILED ANALYSIS OF CONVERTERS

• Some of the assumptions can be made

• The system is described by sets of linear differential equations, and each set is

applicable for particular conduction pattern of the values in bridge.

• AC system is symmetrical and source voltages are balanced

• Firing pulses are generated at equal interval of time.

www.eeecube.com

www.eeecube.com

• The solution is periodic in steady state ,each period can be divided in to p

intervals where p is the pulse number of the converter.

• Each interval in general can be sub divided in to sub interval as follows

• 0 < t < t1 corresponding to the Conduction of ( m+1 ) valves.
• t1 < t < T1 corresponding to the Conduction of m valves.

www.eeecube.com

www.eeecube.com

• For Example , 6pulse converter
• Normal mode consists of 3 and 2 valve conduction.

• First computing from a non linear equation to form

𝑓(𝑡1) = 0

Once (𝑡1) is obtained initial conditions can be calculated from linear equation

www.eeecube.com

www.eeecube.com

• Some of the assumptions can be made for calculating boundary conditions.

• Magnetic fluxes and electric charges must be continuous function of time.
• The current in the outgoing valve is zero at 𝑡 = 𝑡1

DEVELOPMENT OF THE METHOD FOR STEADY STATE ANALYSIS

• It contains there are two sub intervals, it is described as equations

www.eeecube.com

www.eeecube.com

• The orders of the state vector x1 and x2 are (n+1) and n respectively.
• Since outgoing valve current becomes zero at t=t1,one state variable is eliminated

in second outgoing.

• Solutions for above equations are

• Where xs1(t) is the forced response in sub interval I

www.eeecube.com

www.eeecube.com

• From the boundary conditions, We have

• In is the identity matrix of nth order

• Where C = [0:1]

• From the consideration of symmetry, We have

www.eeecube.com

www.eeecube.com

www.eeecube.com

www.eeecube.com

SMOOTHING REACTOR

• Smoothing reactors are intended to provide a high impedance to the flow of

harmonic currents, and to reduce the rate of current rise on failures in direct
current (d.c.) systems.

• Two main application fields are defined as follows:
• * The direct current has superimposed harmonic components. This situation

occurs in d.c. systems for industrial applications. Since the system voltages are
generally not higher than 10kV, these reactors are usually designed for indoor
application.

• * The direct current has small superimposed harmonic components. This situation

occurs in HVDC transmission systems. The d.c. system voltages are generally
50kV or higher.

www.eeecube.com

www.eeecube.com