Introduction In recent years, a no. of developments have taken place in the power systems field. The basic function of a transmission system is to transfer electrical power from one area to another area or from one network to another network.

The present trend is to transmit larger amounts of power at very high voltages.The voltages above 300KV are termed as Extra High Voltage, (EHV). The voltage exceed 750 KV are termed as Ultra High Voltages (UHV). Now-a-days larger amount of power are transmitted over long distances from

generating stations to load centers.Alternating current power is used as a power source as well as for

transmission purposes because it can be conveniently generated and also converted from one voltage to another voltage.

Why we go for EHV/UHV range for transmission purposes isi) Reduction of electrical losses and hence transmission efficiency increasesii) It improves voltage regulation because of reduction of line drop.iii) Because of high voltage, the size of conductor is less because size of the conductor is inversely proportional to the square of transmission voltage.iv) The installation cost of the transmission line per km decreases by increasing in voltage level.v) It is possible to interconnecting of power systems.vi) Less right-of-way is required.Vii) Load carrying capacitor is expressed in terms of Surge Impedance Loading(SIL) for transmission line, The surge impedance is given by Zc = where L is the series inductance and C is the shunt capacitance per unit length of the time.

/L C

Surge Impedance loading (SIL) for a transmission line is given by SIL = Where V is line to neutral voltage.From the above equation SIL varies as the square of the operating voltage. That means for increase in transmission voltage level SIL increases, thus power transfer capability of the line increases.In view of above advantages many technical problems involved in EHV transmission. The major problems arei)Corona loss and Radio interference The EHV transmission corona loss and radio interference is high because line voltage level being a governing factor in the corona loss.

Corona loss can be minimized either by increasing the conductor size or by increasing the spacing between the conductors. But the spacing between the conductors cannot be increased to a large extent because if the spacing is increased, the cost of the supports generally becomes very high. Large diameter conductors have been used to bring down the corona loss and radio interference.

But for increasing the diameter hollow and ACSR conductor are used. But the cost of manufacturing for such conductor is high and their handling is both difficult and expensive. Therefore bundled conductor after an economical solution for minimizing corona loss and radio interference for EHV.

23 / cV Z

ii) EHV line needs heavy supporting structures because of use of bundled conductors.iii) Erection is difficulty.iv) It requires high level of insulation

In view of these problems with ac, the dc transmission has staged a come back in the form of high voltage dc transmission to supplement the AC transmission system.

The first DC link was setup in 1954 between Swedish mainland and the island of Gotland. This was a monopolar, 100KV, 20 MW, cable system making use of sea return.

In 1961 an underwater dc link was setup between England and France. This was bipolar + 100KV, 160 MW cable system over a distance of about 65 KM.

HVDC transmission has also been introduced in India. +500 KV has been selected as the voltages for HVDC transmission.

A +500 KV, 1500 MW, 810 KM bipolar HVDC line has already been set up between Rihand and Delhi.

At present the world has over 50 HVDC schemes in operation for a total capacity of more than 50,000 MW and the capacity is increased by about 2000MW every year.

filter filterInverter

Station (I)Generating

StationRectifier

Station (R)

Receiving end

Step-up transformer

Step-down transformer

HVDC Transmission

Block diagram or single line diagram of HVDC is shown in fig. Generating station will generate the three phase, 50 Hz AC supply, that three

phase AC supply is given to the step up transformer. This transforms the low ac voltage to a higher ac voltage and then given to the

rectifier station(R).The rectifier converts ac voltage to a dc voltage by the thyristor valve for

transmission.By using filter we can reduce the harmonics and ripple content and transmit

the power through transmission lines. In the receiving end inverting station converts DC voltage to AC by the

thyristor valves and then stepped down by the stepdown transformer.The power received at the inverter station or receiving side Pr is less than the

power generating station Ps ie., (Ps-Pr) represents the power losses due to transmission and conversion stations. The DC power flow control is possible by varying the firing angles of the both controllers ie., rectifier station and inverting station. In rectifier station, the firing angle is varying from 0 to 90 degrees while inverting station is varies from 90 to 180 degrees. As the DC output voltage is function of cosine of the delay angle. Hence the converting stations output voltage is negative for firing angle is greater than 90 degrees. This makes the converter to operate as a line commutated inverter. In general HVDC conversions are three phase six pulse converters are used in both rectifier station and inversion station. In this bidirectional power flow is possible by changing the firing angles of the converters.

Advantages of HVDC transmission: HVDC Transmission have many advantages over ac transmission. Some of

technical and economical advantages are given below:i)For transmitting bulk power over long distance say above 500km these systems are economical.ii)During bad weather conditions, the corona loss and radio interference are lower for a HVDC line as compared to that in an ac line of the same voltage and same conductor size.iii)Compare to ac transmission, HVDC transmission is cheaper in cost because ac system required three conductors to carry power where as HVDC transmission lines require two conductors.iv)Right-of-way for a DC line is about 20-40 percent lesser than that for an ac line of the same power transmission capability.v)Unlike ac transmission, HVDC transmission system does not requires any intermediate substations for compensation.vi)The transmission losses in a HVDC transmission are lower than the ac transmission of the same power transmission capability.vii)The towers of HVDC lines are simpler, cheaper than ac lines.viii) No skin effect in HVDC lines, so uniform distribution of current over the section of the conductor. There is a skin effect in ac lines.ix)Voltage regulation is better in case of DC transmission.x)Power flow control is easy in HVDC link.xi)High reliability.

Disadvantages of HVDC transmission:HVDC transmission have few limitations as

i)Initial cost is high because it requires additional requirement of converters (rectifier and inverter stations), filters, reactive power compensators.ii)Overhead capacity is low as compared to ac transmission.iii)HVDC converter need cooling systems.iv)HVDC converters produce harmonics both ac and dc sides which may cause interference with the audio frequency communication lines.v)Reducing ripples from the dc output, filters requirement is more.vi)Maintenance of insulators is more.vii)HVDC circuit breakers is expensive.viii) Voltage transformation is not possible in DC side and hence it is to be provided on the ac side only.

I

I

HVDC link

Rectifier Inverter

AC Supply AC Grid

Converter StationConverter station consists the following equipments and as shown in fig

i.Converter unitii.Converter transformeriii.Filtersiv.Reactive powerv.Smoothing reactorvi.Switch gear

i.Converter Station: ii.Converter transformer: The converter transformer can have the different configurations, they area)Three phase, two winding transformerb)Single phase, three winding transformerc)Single phase, two winding transformer

The above of (a) and (b) type of transformer can be installed at the valve side & winding are stator and delta with neutral point ungrounded.

The configuration (c) can be used on the AC side and the transformer are connected in parallel with neutral grounded.Note: The leakage reactance of the transformer is chosen to limit the short circuit currents through any value.

The converter transformers are designed to withstand DC voltage stresses and increased eddy current losses due to harmonic currents.

iii.Filters:Three types of filters can be used in the converter station, they are

a)AC filterb)DC filtersc)High frequency (RF/PLC) filtersiv. Reactive power source:

Converter stations require reactive power supply that is dependent on the activePower loading [about to 60% of the active power]. Fortunately, part of this reactive power requirement is provided by AC filters. For addition of above the shunt (switched) capacitor, synchronous condensers and static Var systems are used. On the dependency of speed of control is desired.v. Smoothing reactor:

Generally a sufficiently large series reactor is used on DC side to get the smooth DC current and also for the protection. The reactor is designed as a linear reactor and is connected on the line side, neutral side or at intermediate location.vi. DC switch gear:

The DC switch gear is usually a modified AC equipment used to interrupt small DC currents [employed as disconnecting switches]. DC breakers or metallic return transfer breakers (MRTB) are used, if required for interruption on rated load currents.

In addition to the equipment described above, AC switch gear and associated equipment for protection and measurement are also part of the converter station.

Applications of HVDC Transmission: On the basis of applications, HVDC transmission systems are scheduled as an alternative to extra high voltage AC transmission system for the following reasons:i)Long distance high power transmission by overhead linesii)Under water transmissioniii)Transmission by underground cableiv)Asynchronous interconnection of AC systems operating at different frequencies.v)HVDC back to back systemvi)Multi terminal HVDC system for interconnecting them or more three phase AC system.

i)Long distance high power transmission:Compare to ac transmission HVDC transmission is cheaper

because 3-phase ac requires three conductors. For long distance high power transmission , HVDC systems are preferred due to their fast and easy control of power flow from sending end to the load centre. And also HVDC is economic advantages over ac system.

HVDC line losses are low because it require two conductors. EHV-AC line requires intermediate substation is required over a distance of 300 km oor compensation whereas for HVDC lines does not required intermediate substation. The per km cost of HVDC line is lesser than that of an AC line.

Under water transmission and under ground transmission:For long distances HVDC under water transmission is only the solution

because ac transmission under water cable length is limited upto 25-40km only due to problem of charging current. The submarine cables are necessary to transfer power across oceans, lakes etc.

In congested areas the power transmission is done through under ground cable. If distance is exceeding 45km, dc transmission is only feasible solution. In HVDC transmission extra cost of the converters is compensated by saving in cable costs at distants from 45km to 100 km.iii) Interconnection of the systems:

Due to its technical superiority HVDC interconnection is superior to AC interconnection.

For interconnection between two ac systems. HVDC links are preferred. HVDC links form an asynchronous tie i.e., the two ac systems interconnected by HVDC line link not in synchronous with each other, HVDC interconnection power flow can controlled fast and easy, the frequency distribution are not transferred.iv) HVDC back to back system:

Back to Back system provides interconnection between two adjacent ac systems through converter station without any transmission line. This type of schemes is employed for different frequencies in AC systems. HVDC inverter and rectifier are installed in the same station. The back to back coupling stations are installed at where two networks meet geographically.

v) Multi-terminal HVDC interconnection:More than two AC network can be interconnected asynchronously by

means of a multi-terminal HVDC system. This is new HVDC interconnection power flow from each connecter ac network can be controlled suitably. By means of this large power can be transferred. It requires large dc circuit breakage compared to other connections. The stability of multi-terminal HVDC interconnection is high.

Converter Station Equipment:The HVDC transmission system, ac is converted into DC by means of

thyristor valves. This process is called rectification. This DC is transmitted to the receiving end of the HVDC transmission line, dc is converted back to ac by means of thyristor valves. This conversion is called the inversion.

Fig shows the HVDC transmission line with the following main parts: Two 12 pulse converter unit pre-pole, thyristor valves, converter transformer, smoothing reactors, harmonic filtering equipment, control equipment and reactive power compensation equipment. Varies components of a HVDC link are discussed below.i)Thyristor valve:

Before 1970’s HVDC converters use mercury arc valves for conversion and inversion purposes. After 1970’s thyristor valves are used all HVDC schemes because of a better operating life and higher performance than those of a mercury arc valve. The use of thyristors has resulted in a considerable simplification in the design of conversion station. The ratings of thyristors have increased remarkably during the last one decade. The available current ratings of the thyristors are sufficient to meet the requirement of line current of transmission.

However, the voltage rating of individual thyristor is small as compared to line voltage. Thus a large number of thyristors are connected in series to obtain required voltage rating.

The valves are of indoor design, air insulated and air (or) water-cooled. Generally the thyristor always fail to an internal short circuit, a thyristor valve is always equipped with a number of extra thyristors in series so that even if any one of thyristor fails, the operation of the valve is not effected. As thyristor produce heat of 30-40 W/cm2 hence effective cooling system is required in practical installation. Water cooling in recommended for high power applications. Thyristors are protected from dv/dt, dI/dt, forward over voltage firing, over temperature and forward recovery protection.iii) Converter transformers:

The modern HVDC scheme six pulse or twelve pulse converters are used. Generally 12-pulse converters are more preferred as it contains high ripple frequency. There are two 3 phase transformers connecting each 12-pulse converter to the ac bus bars. One of the 3 phase transformer is star/star (Y-Y) connected and the other is star/delta (Y-Δ) connected so as to give a phase shift of 30 degrees between the two 6-pulse bridge of the converter. Converter transformer serves the following fuctions:• Short circuit currents are controlled by suitable impedance value of these transformer.• Converter transformer reactance will suppress the harmonics.• Reactive power is supplied to the converter through tap changing.

A converter transformer has a some what different design than that of normal power transformer because in the converter transformer the currents have high harmonic content so that special care has to be taken with regard to eddy current losses. To reduce the reactive power demand in steady state operation on load tap changing is normally used. Proper quality control of tap change is needed in HVDC systems because the number of tap changer operation are high in HVDC system.iii) Converter Unit:

The 12-pulse converter is formed by connecting two 3-ph 6-pulse converters connected in series. A 12-pulse converter unit is shown in fig. The use of four valve units per phase of a 12-phase converter configuration is common. A typical quadrivalve comprises from valves placed vertically one above the other to form on limb of the converter. Such an arrangement provides the most compact and economical layout of the valves and the valve housing. Three quadrivalve consists of 12-pulse converter. Valve firing signals are generated in the converter control at ground potential and are transmitted to each thyristor in the valves through a fiber optic light guide system. Snubber circuit, gapless surge arresters are used to protection of valves.iv) Smoothing reactors:

A smoothing reactor is connected in series with each pole of a converter station. The valve of inductance is between the 0.4H to 1.0H. The DC reactor is usually of air core and oil-cooled type and has the non linear magnetic characteristics. By increasing the value of inductance the current waveform on the DC side improves but control response slows down and the resonance frequency reduces making the stabilization of current control more difficult.

The smoothing reactor serves the following function mainly:• It prevents consonant commutation failures in the inverter• It decreases the incidence of commutation failures in the inverter during voltage drop in AC voltage• It reduces the harmonic voltages and currents in the dc line.• Any short circuit occurs in the line it limits the current in the rectifier. v) Control Equipment:

The firing angle control is very important in HVDC systems. This control is done by using optic fibre based hardware circuitry. In AC transmission power flow control is difficult where as in HVDC system power flow control is simple by vary the firing angle of the converters. Practical HVDC system the valve of the two converter stations are controlled in such a way that the rectifier end controls the current while the inverter end controls the voltage. These controls allow the link to maintain constant power.vi) Reactive Power compensation equipment:

Only real power is transferred through DC line, no reactive power is transmitted. However, both converters rectifier and inverter draw reactive power from the ac systems. So reactive power must balance to maintain at the two ends to ensure that ac voltage is held within specified limits. This require reactive power compensation equipments in the HVDC stations. Compensation equipment consists of AC filter capacitors which also reduces AC harmonics, shunt capacitors, synchronous condensors or static VAR systems. Sometimes combination of these equipment is also is used. Rectifier reactive power varies as the sinα, whereas the reactive power requirement of the inverter varies as the sinƔ (where Ɣ is the inversion angle of the inverter).

Both rectifier and inverter, the reactive power is also proportional to 50 to 60 percent of the active power.vii) Harmonic filtering equipment:

The 3-ph bridge converter converts pure AC supply to pure variable DC supply. But in practice the operation of converter generates harmonic currents and harmonic voltage on AC and DC side. These harmonics flows through ac and dc lines and produces harmful effects such as overheating of capacitors and generators, over voltages at points in the networks, interference with protective gear-interference with nearby communication systems, radio interference and television interference.

An ‘n’ pulse converter produce the harmonics of the order of nh+1 on ac side and nh on dc side, where h is the order of harmonics, n is the 6 pulse or 12 pulse converters. In 12 pulse converter the order of main harmonics are 12th and 24th on the dc side and 11th , 13th , 23rd and 25th on the AC side. We know that the amplitude of harmonics decrease by increasing order of harmonics. Therefore, it is required to use filters on both ac and dc side to reduce the harmonics.AC filter-design: The function of AC filter is to eliminate all the detrimental effects caused by waveform distortion and telephone interference. In the design of AC filter we have to consider mainly two basic concepts, one is size of the filter and the other is quality of filter.

The size of the filter represents the reactive power that the filter supplies at fundamental frequency and the quality of the filter represents the sharpness of tuning which increases with the ratio of its resonance inductance or capacitance to its resistance for resonant filters.

In case of high pass filter, the sharpness increases is inversely propotional to that ratio. AC filters used in HVDC systems are tuned filter which is sharply tuned to a harmmic frequency, damped filter which, is shunt connected, offer low impedance over a broad band of frequencies. Now in 12-pulse valve group operation only two damped filters are used. Damped filters are simple to design and have lower rate of the resonant over voltage and currents are compared to tunned filter.DC filter:

DC side of HVDC converter converter the voltage harmmics generation harmmic currents, whose amplitude depend on the belong inversion angle and the impedance of the DC circuit itself. The harmmics on the DC side must also be limited before entering the line. The dc reactor or smoothing reactor is sufficient to limit the magnitude of the harmmics on the dc side.

Comparision of AC and DC Transmission:The relative merits of the AC and DC transmission based on the following

factors:1.Economics of transmission2.Technical performance3.Reliability

While design the transmission we have to consider above factors. In most practical cases the technical limitations are not reached and economic limitations decides the final choice of design.1.Economics of Power Transmission:

Total cost of a transmission line is the sum of the investment and operational costs. The investment includes cost of

i) Right of way(ROW)ii) Transmission towersiii) Conductorsiv) insulatorsv) Terminal equipments

The operational costs include mainly the cost of losses and maintenance.

A DC line can carry more power with only two conductors and an AC line with the conductors of the same size. This shows that for a given power level HVDC transmission requires less ROW, simple transmission towers, less conductor-material, less insulation cost compare to AC line. HVDC line in less transmission power losses because DC lines only two conductors and also no skin effect with DC.

The dielectric losses are also less in HVDC line. Less corona effect in DC line than for AC and this also leads to selection of conductor size.

DC line terminal equipments cost in high because it requires two converters, one is rectifier station and other is inverter station, filter requirements also more in case of DC line.

Fig shows the variation of cost of transmission with respect to the line length for AC and DC transmission. DC tends to be more economical than AC for distance more than break even distance. The distance varies from 500km-800km in over head lines.

The converter used with DC line produce harmonics of voltage and current, on both ac and dc sides. These harmonics especially in the extensive ac network may cause interference with audio-frequency telephone lines. Filters are required on the ac side of each converter for reducing the magnitude of harmonics in the ac networks. These increase the cost of the converter stations. Fortunately the capacitor used in the filters also supply part of the reactive power required by the converters. The cost of the filter and of additional reactive power supply should be regarded as a part of the cost of a dc line terminal.2.Technical Performance:

Compare to AC transmission HVDC transmission has positive advantages are full control over transmitted power, improves transient and dynamic stability and also it limits the fault currents in DC lines. In addition to above advantages DC line over comes some of the problems of AC transmission. These are

i) Voltage limitii) Current limitiii) Reactive power and voltage regulationiv) Line compensationv) Stability

i) Voltage limits: The normal working voltage and the over voltages caused by switching surges and

lightning must be limited to values that will not cause puncture on flashover of the insulation. AC line voltage control is complex by the line charging and inductive voltage drops. On EHV overhead lines switching surges have become the more serious transient overvoltages, and on ac lines attempts and made to limit them to peak value of two or three times normal crest voltage. Whereas in case of DC transmission switching surges are lower than this, say 1.7 times normal voltages.

Due to corona maximum working voltage or the minimum conductor size is limited on over head lines. In cables, normal working voltage is usually the limiting factor. Insulation will withstand a DC voltage higher than the crest of the alternates voltage( times R.M.S. voltage)

ii) Current limit:The temperature of a conductor must be limits in order to avoid damage

to the conductor itself permanently increased sag on in the case of a cable to the installation in contact with it. Hence current in the conductor must be limited in accordance with its duration and the ambient temperature.

iii) Reactive Power and Voltage Regulation: On long distance ac over head lines and shorter distance ac cables, the

generation and absorption of reactive power by the line itself a serious problem.

2

The lines produce reactive power/unit lengthThe line consumes reactive power/unit lengthWhere V is operating voltageI is currentC and L are shunt capacitance and series induction/unit length Reactive power produced by the line is equal to consumer by it

In this case the load impedance has the value Zn known as the natural impedance or surge impedance of the line. The single conductor overhead line surge impedance is about 400 ohm and bundled conductors about 300 ohms, and cable is only about 40 ohms.

The power carried by the line so loaded is and is called the surge impedance loading(SIL). It depends only on voltage

and independent of distance.On a line carrying its natural load, the magnitude of voltage is the same

everywhere as shown in curve 1 in fig. Load demand is not constant always it varies with time. In over head line most economical load is greater than the natural load, P>Pn this is shown in curve 3 in fig. In this case net reactive power is consumed by the line and must be supplied from either of the end or both ends. If same voltage is maintains at both sending end and receiving end side equal amount of reactive power supplied from both ends.

If load on the line is less than the natural load, (P>Pn) net reactive power is produced by the line and is delivered to one or both ends with equal voltage at both ends, equal amounts of reactive power are delivered to both ends shown in curve 2.

Thus the voltage control in AC lines is complicated by the line charging and inductive voltage drops.

iv) Line compensation:From the above discussion AC lines require shunt end series compensation in

long distant transmission mainly to overcome the problem of line charging and stability limitations. For this purpose series capacitor and shunt inductor are used. By using static VAR systems or static VAR compensators increasing power transfer and voltage control is also possible.v) Stability:

In two machine lossless system power transmitted from one machine to other is given byWhere sending end voltageReceiving end voltagePower angle between and phasorsSeries reactance

Thus power flow in AC lines is controlled by controlling the abgle for a given power level, this angle increases with distance. The power carrying capacity of ac lines as a function of distance is shown in fig. Fig also shows the power carrying capacity of DC lines which is unaffected by the distance of transmission. AC power flow control is complex because angle cannot be changed easily/quickly.

Power flow through HVDC link is given byby varies by means of thyristor converter control and tap change control.

The power flow can be controlled quickly, easily and accurately.In HVDC line does not have series reactance and shunt reactance, reactance

power flow. Hence there is no voltage regulation and stability problem. Transmission losses are low due to absent of reactive power flow is HVDC systems.

vi). Problems of AC interconnection:Two AC power systems ae interconnected through AC ties (synchronous

inter connection). The AGC (automatic generation control) of both systems have to be co-ordinated using tie-line power and frequency signals. The operation of ac lies can problematic due to i)Presence of large power oscillation which can lead to frequent tripping. ii)Fault level increasesiii)Disturbances occurs from one system to other.

It is not possible to inter connect two different nominal frequency system. It requires the DC link to interconnect such systems. By using HVDC link, it is possible to interconnect two individually controlled AC systems which operate different frequency.

vii). Ground Impedance:In AC transmission, the flow of ground current cannot be permitted in the steady state due to high ground impedance, which will effect the power transfer and interference of telephone lines. For DC currents ground impedance is negligible. In DC transmission in operating only one conductor with return conductor act as ground for monopolar operation. If conductor is buried metallic structures, ground return is objectionable because DC current flows through that conductor leads corrosion.

viii) Short circuit level:In AC transmission additional parallel lines always results in higher fault level at

receiving end due to reduction of the overall system impedance. And hence short circuit livel increases. When an existing AC system is interconnected with another AC system by DC transmission, the fault level of each system remains unchanged. Since the DC line contributes no current to an ac short circuit beyond its rated current.ix) Power per conductor and per circuit:

Let us assume that same conductor is used ac and dc transmission and each case the current is limited by temperature rise.

and that the insulators withstand the same crest voltage to ground in each caseIe.,

AC power/conductorDC power/conductor

Now compare ac three phase, three conductors line with dc bipolar line thenBoth lines carry the same power. The dc line as simple and cheaper, having

two conductors instead of three. Consequently an overhead line requires only 2/3 as many insulators and the towers are simple, cheaper and narrow.

Choice of voltage levels:In view of bulk power transmission over long distance, proper voltage level is

to be choosen to minimise the total costs for a given power level (P).The total cost of power transmission includes investment cost C1 and cost of

losses C2.The investment cost per unit length of line can be written as,

Where n = number of conductorsA = total cross section of each conductorV = Voltage level with respect to ground

are constantsThe cost of losses per unit length is given by,

Where p= specific resistance (or) resistivity of conductorT = Total operation time during a yearL = Loss load factorP = cost per unit energy

1 0 1 2C K K nV K nA

0 1 2, ,K K K2

2

pn pTLpnVC

A

where K3 = TLpBy minimising the sum of ‘C2’ and third term in ‘C1’ we have

2

2

p pTLpVC

nA

2

3p pKV

nA

2

3

2

pK pV

K nAnA

2

23 3

pK nA K pV

2

3

K pnA pK V

Current density J is given by,

Now, total cost can be written as,

2 3

3 2

1.

P V P VJ K K

nA pK K p P V

1 2C C C 2

3

0 1 2

pK pV

K K nV K nAnA

23

0 1 2 32

3

2

. .

.

K p pK K nA K p K pK A V

K ppK A

0 1 2 3 2 3p pK K nA K K p K K pA A

0 1 2 32 pK K nA K K pA

The voltage is to be chosen to minimize the overall cost function is obtained from the above equation above. Fig shows the selection of optimum system voltage to minimize the sum of overall investment of converter, line cost and cost of losses.

In case of back to back HVDC system, there will be no DC transmission line costs. So that only the cost need to consider is the cost of converter station to improve the reliability and performance of the system.

Modern trends in DC transmission:

Recent trends or developments in the technological aspects of power electronics, power semiconductor devices, digital electronics, DC protection equipment have been increased in the applications of DC transmission.

The main objective of these developments is to reduce the cost of converter stations to improve the reliability and performance.

Power Semiconductor and Valves:The cost of converter depends upon no. of devices used in it. If no of devices connected in series or in parallel decreases then total cost of converters also decreased.

Overload capacity of device at reasonable cost will be high if its current rating increases, moreover it leads to the reduction of transformer leakage impedance, there by improving the power factor.

The cost of valves is reduced by using zincoxide gapless arresters and protective firing methods.

Most of the power semiconductors devices uses silicon the cost of silicon may be decreased by using magnetic CZ(czochralsli) method, rather than the conventional FZ(float zone) method.

Usually, it is uneconomical to use forced commutated converters operating at high voltages, which leads to the development of devices which can be turned off by the application of gate signal.

Gate turn off devices (GTO) operating at 2500V and 2000A have a drawback of large gate current to turned off.

But technology was developed for a metal oxide semiconductor (MOS) controlled thyristor for which a very small gate current is sufficient to interrupt a very large line current.

Converter Control: The development in converter control equipment is micro-computer based converter control.

With the use of such converter control it is easier to design systems with automatic transfer between systems during false operating.

This micro computer based control has the flexibility to use adaptive control algorithms for fault identification and protection.

DC Circuit Breaker: Recent developments in DC circuit breakers are useful in tapping of existing DC link parallel operation of converters is allowed rather than series operation shows some flexibility in the system growth.

In order to limit the fault current the dc breaker current should not to exceed the full load ratings.

Conversion of Existing AC Lines:o In certain cases such as to increase the power transfer limits it is necessary to convert existing AC circuits to DC.

oIn India there is an experimental project of converting single circuit (or) double circuit 220kV line is currently under commissioning stage.

Operation with weak AC systems:The strength of AC systems connected to the terminals of DC link is

measured in terms of short circuit ratio (SCR)SCR = short circuit level at the converter bus / Rated DC powerIf SCR<3, then it is weak AC system. For a weak AC system, conventional

constant extinction angle control may not be satisfactory.

In order to overcome the problems of weak AC systems constant reactive current control (or) AC voltage control have been suggested. By using static VAR systems at the converter bus fast reactive power control can be achieved.It is necessary to limit the dynamic over voltages during load rejections through converter control.The dynamic stability of power systems can be improved by power modulation techniques in the presence of weak AC systems.Co-ordinated real and reactive power control must be necessary inorder to overcome the problems of voltage variations which can limit the power modulation.

HVDC Systems in India:There are two HVDC systems in Indiai)Vindhyachal HVDC back to back systems This link is for exchange of power between northern and western regions. Each block consists of 250 MW capacitors, it can operate bidirectional and can transfer power in the range of 250 MW to 250 MW depending on systems conditions. This system is provided air insulated water cooled Thyristor valves designed for 12-pulse operation, star extended delta, two winding transformer, AC filters, capacitors ( for reactive power compensation), smoothing reactance etc.ii)Rihand-Delhi Systems

This is setup between Rihand and delhi to transmit bulk power from Rihand to Delhi. The capacity of system is +500kv, 1500MW, 810KM bipolar.

It is designed to operate bipolar, monopolar with ground return, monopolar with metallic return. The system is operates bipolar mode under normal conditions, under contingencies when one pole goes out of operation. The system automatically transfer to monopolar mode with ground at return path.

In addition to above two HVDC systems, chandrapur back to back project, chandrapur-padghu bipolar system, Jeypore back to back project and man back to back project are also proposed.

Unit-II----Analysis of HVDC Converters

Introduction:

• HVDC converters converts AC to DC and transfer the DC power, then DC is again converted to AC by using inverter station.

• HVDC system mainly consists of two stations, one in rectifier station which transfers from AC to DC network and other is inverter station which transfers from DC to AC network.

• For all HVDC converters twelve pulse bridge converters are used. Same converter can act as both rectifier as well as an inverter depending on the firing angle ‘α’.

• If firing angle α is less than 90 degrees the converter acts in rectifier mode and if the firing angle α is greater than 90 degrees the converter acts in inverter mode.

Choice of Converter configuration

• For a given pulse number select the configuration such a way that both the valve and transformer utilization are minimized. • In general converter configuration can be selected by the basic commutation group and the no. of such groups connected in series and parallel.• Commutation group means set of valves in which only one valve conducts at a time.• Let ‘q’ be the no of valves in a commutation group, ‘r’ be the no of parallel connections, ‘s’ be the no of series connections, then

the total no of valves will be = qrs

Valve Voltage Rating:Valve voltage rating is specified in terms of peak inverse voltage (PIV) it

can withstand.

The valve utilization is the ratio of PIV to average dc voltage.

Converter average DC voltage is

.sindo msqV V

q

i) Peak inverse voltage(PIV):If q is even:

then the maximum inverse voltage occurs when the valve with a phase displacement of π radian in conducting and this is given by

PIV = 2VmIf q is odd:

the maximum inverse voltage occurs when the valve with a phase shift of π+π/q in conducting and this is given by

PIV = 2Vm Cosπ/2q

. .2

2

.2.2

q

do m

q

qm q

m

qV s V Cos t d t

sq V Sin t

sq V Sinq

ii) Utilization factor:

Utilization factor = for q is even

for q is odd

2 ,.sindo

PIVV sq

q

,.sin

2sq

q

Analysis of Graetz circuit (6-pulse converter bridge):

The schematic diagram of a six-pulse Graetz circuit is shown in the fig.

This Graetz circuit utilizes the transformer and the converter unit to atmost level and it maintains low voltage across the valve when not in conduction.Due to this quality present in Graetz circuit, it dominates all other alternative circuits from being implemented in HVDC converter.The low voltage across the valves is nothing but the peak inverse voltage which the valve should withstand.

The six-pulse Graetz circuit consists of 6 valves arranged in bridge type and the converter transformer having tappings on the AC side for voltage control.

AC supply is given for the three winding of the converter transformer connected in star with grounded neutral.

The windings on the valve side are either connected in star or delta with ungrounded neutral.

The six valves of the circuit are fired in a definite and fixed order and the DC output obtained contains six DC pulses per one cycle of AC voltage wave.

a)Operation without overlap:

The six pulse converter without over lapping valve construction sequence are 1-2, 2-3, 3-4, 4-5, 5-6, 6-1.

At any instant two valves are conducting in the bridge. One from the upper group and other from the lower group.

Each valve arm conducts for a period of one third of half cycle i.e., 60 degrees.

In one full cycle of AC supply there are six pulses in the DC waveform. Hence the bridge is called as six pulse converter.

For simple analysis following assumptions are much:

i)AC voltage at the converter input is sinusoidal and constantii)DC current is constantiii)Valves are assumed as ideal switches with zero impedance when on(conducting) and with infinite impedance when off(not conducting)

In one full cycle of AC supply we will get 6-pulses in the output. Each pair of the devices will conduct 60 degrees. The dc output voltage waveform repeats every 60 degrees interval.

Therefore for calculation of average output voltages only consider one pulse and multiply with six for one full cycle. In this case each device will fire for 120 deg.

Firing angle delay:

Delay angle is the time required for firing the pulses in a converter for its conduction.It is generally expressed in electrical degrees.In otherwords, it is the time between zero crossing of commutation voltage and starting point of forward current conduction.The mean value of DC voltage can be reduced by decreasing the conduction duration, which can be achieved by delaying the pulses ie., by increasing the delay angle we can reduce the DC voltage and also the power transmission form one valve to another valve can also be reduced.

when α = 0, the commutation takes place naturally and the converter acts as a rectifier. when α > 60 deg, the voltage with negative spikes appears and the direction of power flow is from AC to DC system without change in magnitude of current. when α = 90 deg, the negative and positive portions of the voltage are equal and because of above fact, the DC voltage per cycle is zero. Hence the energy transferred is zero. when α > 90 deg, the converter acts as an inverter and the flow of power is from DC system to AC system.

Let valve 3 is fired at an angle of α. the DC output voltage is given by

Vdc = Vdo Cos α

0

0

0

60

600

0 0

2 60

6 .2

3 2 60 .

3 2 60 120

3 2

1.35

d b c bc

bc LL

dc bc

dc LL

LL

LL

LL

V e e e

e V Sin t

V e d t

V V Sin t d t

V Cos Cos

V Cos

V Cos

From above equation we can say that if firing angle varies, the DC output voltage varies.

DC Voltage waveform:The dc voltage waveform contains a ripple whose frequency is six times

the supply frequency.This can be analysed in Fourier series and contains harmonics of the

order h=npWhere p is the pulse number and n is an integer.

The rms value of the hth order harmonic in dc voltage is given by

Although α can vary from 0 to 180 degrees, the full range cannot be utilized. In order to ensure the firing of all the series connected thyristors, it is necessary to provide a minimum limit of α greater than zero, say 5 deg.Also in order to allow for the turn off time of a valve, it is necessary to provide an upper limit less than 180 deg. The delay angle α is not allowed to go beyond 180-γ where γ is called the extinction angle (sometimes also called the marginal angle).The minimum value of the extinction angle is typically 10 deg, although in normal operation as an inverter, it is not allowed to go below 15deg or 18deg.

1/22 22

2 1 1 sin1h doV V h

h

AC current waveform:It is assumed that the direct current has no ripple (or harmonics) because of

the smoothing reactor provided in series with the bridge circuit. The AC currents flowing through the valve (secondary) and primary windings

of the converter transformer contain harmonics.The waveform of the current in a valve winding is shown in fig.

/3

/3

/3

/3

/3

/3

2 .cos .

2 . cos .

2 sin

2 sin sin / 33

2 3 3 sin sin2 2

2 2 32

2 3 .

p d

p d

dp

dp

dp

dp

p d

I I d

I I d

II

II

II

II

I I

By Fourier analysis, the peak value of a line current of fundamental frequency component is given by,

Now the rms value of line current of fundamental frequency component is given by

22 3 .

22 3.2

6 .

pRMS

d

RMS

dRMS

RMS d

II

II

II

I I

Generally, the RMS value of nth harmonic is given by,

where I = Fundamental current n = nth order harmonic.

nIIn

The harmonics contained in the current waveform are of the order given by h = np + 1 where n is an integer, p is the pulse number.For a 6 pulse bridge converter, the order of AC harmonics are 5, 7, 11, 13 and higher order. They are filtered out by using tuned filters for each one of the first four harmonics and a high pass filter for the rest.

The Power Factor:The AC power supplied to the converter is given by

where cosФ is the power factor.The DC power must match the AC power ignoring the losses in the

converter. Thus, we get

Substituting for Vdc = Vdo Cos α, and I1= , we obtaincos Ф = cos α

The reactive power requirements are increased as α is increased from 0 When α = 90 deg, the power factor is zero and only reactive power is consumed.

13 cosAC LLP E I

13 cosAC DC do d LLP P V I E I 6

dI

ii) With overlap:

In fig Lc indicates leakage inductance of transfromerVd, Id = DC voltage and current flowing in the lineLd = DC side reactanceV1 = voltage across the thyristorsp,n = positive and negative pole on the line

Due to the leakage inductance of the converter transformers and the impedance in the supply network, the current in a valve cannot change suddenly and thus commutation from one valve to the next cannot be instantaneous.

For example, when valve 3 is fired, the current transformer 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 overlap (commutation) angle ‘μ’.

Commutation delay:

The process of transfer of current from one path to another path with both paths carrying current simultaneously is known overlap.

The time required for commutation or overlapping which is expressed in electrical degrees is done with commutation angle, denoted by μ.

During normal operating conditions the overlap angle is in the range of 0 to 60 degrees, in which two (or) three valves are conducting.

However, if the overlap angle is the range of 60 to 120 degrees, then three to four valves are in conducting state which is known as abnormal operation mode.

During commutation period, the current increases from 0 to Id in the incoming valve and reduces to zero from Id in the outgoing valve.

The commutation process begins with delay angle and ends with extinction angle ie., it starts when ωt = α and ends when ωt = α+μ = δ, where δ is known as an extinction angle.

There are three modes of the converter as follows:1.Mode-1----Two and three valve conduction (μ<60 deg)2.Mode-2----Three valve conduction (μ=60 deg)3.Mode-3---- Three and four valve conduction (μ>60 deg)

Depending upon the delay angle α, the mode 2 must be just a point on the boundary of modes 1 and 3.

i)Analysis of Two and Three valve conduction mode: Generally overlap angle will be less than 60 deg, so let us analyse this mode.

Timing diagram

In this mode each interval of the period of supply can be divided into two subintervals.

In the first subinterval, three valves are conducting and in the second subinterval, two valves are conducting.

Let us assume the input voltages0

0

0

cos | 60 |

cos | 60 |

cos | 180 |

a m

b m

c m

e E t

e E t

e E t

Corresponding line voltages are eac , eba, ecb

0 0

0 0

0

0

cos( 60 ) cos( 180 )

(cos( 60 ) cos( 180 ))

1 3| cos . sin . cos |2 2

3 3cos sin2 2

3 13 | cos sin |2 2

13 cos30 cos sin2

3 cos( 30 )

ac a c

m m

m

m

m

m

m

ac m

e e e

E t E t

E t t

E t t t

E t t

E t t

E t t

e E t

0 0

0 0 0 0

cos( 60 ) cos( 60 )

((cos cos60 sin sin 60 ) (cos cos60 sin sin 60 ))

1 3 1 3cos . sin . cos . sin . 3 (sin )2 2 2 2

3 sin

ba m m

m

m m

ba m

e E t E t

E t t t t

E t t t t E t

e E t

0

0 0 0 0

0

(cos( 180) cos( 60 ))

(cos .cos180 sin sin180 cos cos60 sin sin 60 )

3 3cos sin2 2

3 13 cos sin2 2

3 cos( 150 )

cb m

m

m

m

cb m

e E t t

E t t t t

E t t

E t t

e E t

Each valve will conduct for 120 degrees and each pair will conduct for 60 degrees, if there is no overlap.Let us consider non-overlap of only valve 1,2 conducting followed by overlap of 3 with 1.Ie., 1,2 and 3 conducting.

When only valve 1 and 2 conducting

1 2

3 4 5 6

0

0

0

0

0

cos( 60 )

cos( 60 )

cos( 180 )

3 cos( 30 )

a c d

b

a p a m

b b m

c n c m

d p n a c ac m

i i I I Ii I I I I

V V e E t

V e E t

V V e E t

V V V e e e E t

1 2

3

4

5

06

0

3 sin

3 cos( 150 )

ba m

n p d

n p d

c b cb m

V V

V e E tV V V V

V V V V

V e e e E t

When valve 3 is fired then 3 will overlap with 1 and it will be 3 valve conduction periods ie., 1, 2 and 3.

For this period the emanation for the voltage and current are different and thus can be obtained as follows:

Consider that valve 3 is ignited at angle ‘α’ and for overlap angle both 1 and 3 conduct together.The duration of overlap 1 and 3 will conduct top with 2 at the bottom as shown in the fig.

Just at the beginning, ωt = αAt ωt = α

When the overlap ends at an angle (α+μ)At ωt = (α+μ)

The angle (α+μ) is called extinction angleDuring overlap a loop is formed as N-3-1-NFor this loop,

1

3 0di I

i

1

3

0

d

ii I

3 1b a c c

di die e L Ldt dt

3 13 sinm c cdi diE t L Ldt dt

Assuming the dc current either i1 alone conduct, i3 alone when 3 alone conducts should be equal to IdSo both 1 and 3 conduct overlap

So

Integrating both sides

1 3

1 3

d

d

i i Ii I i

33

3

3

3

3

3 1

3 sin ( )

3 sin 2

3 sin . 2

3 sin . 2

3 cos2 .

3cos cos

2 .

m c c d

m c

m c

t t

m c

tm

c

md

c

di diE t L L i idt dtdi

E t Ldt

E t dt L di

E t dt L di

E t iL

Ei t I i

L

At ωt = (α+μ);

(or)

where

During overlap the line-line voltage of the short circuited phase is zero and two line to neutral voltage Va and Vb during which overlapping period. Half sum of Va and Vb,

3 di I

2

3 1

2

3 cos cos( )2

cos cos( )

3 cos cos2

32

md

c

d s

md

c

ms

c

EIL

I I

Ei I i tL

EIL

2a b

a be eV V

0 0

0 0 0 0

0

(cos 60 ) cos( 60 )2

(cos .cos60 sin .sin 60 cos .cos60 sin .sin 60 )2

.2cos .cos602

cos2

m

m

m

m

E t t

E t t t t

E t

E t

2c

a beV V

During this overlap period various voltages and currents are

, bring conducting devices

Similarly sets of equations apply for other overlap period such as between 3 and 5 (or) 4 and 6 (or) between 6 and 2 etc. with only appropriate change in time.

1 3 2

3 2

2

4 5 6

1

1 2 3

4

5

6

(cos cos )(cos cos )

0cos

2 2cos ( ) cos( 180)

0

23 cos2

a d d s

b s

c d

a b p m

c n c m m

d

d

d

d p n

cc

m

i i I i I I ti i I ti i Ii i I

e tV V V E

V V e E t or E tV V VV VV VV V

V V V

ee

E t

i) Expression for average DC voltageDuring one cycle there will be six pulse of DC voltage each pulse having

one non-overlap duration and one overlap duration.For example between α and (α+μ) devices 1,2 and 3 will conduct, (α+μ) to α+π/3 when only 3 and 2 will conduct. Total duration for the pulse being π/3.

1, 2, 3 conduct 3 & 2 conduct

301 3 cos 3 cos 150

23

d m mV E t E t d t

0 0

0 0 0 0

33 sin( ) sin 3 sin 210 sin 1502

3 3 33 . (sin sin ) sin 210 cos cos210 sin sin .cos150 cos sin1502

3.3. 3 3 1 3 3 1sin sin cos sin sin cos2 2 2 2 2

3 3 3 sin sin2

mm

m m

m m

m

E E

E E

E E

E

cos 3 sin 3 sin cos

3 33 sin 3 sin cos 3 sin 3 sin cos

2mE

3 3 cos cos23 3 cos cos2

cos cos2

d

d

dod

EV

EV

VV

When E = rms phase voltageIf α = 0; μ = 0

If μ = 0, no overlap

cosd doV V

3 3 223 3

d

d do

EV

EV V

ii) Voltage drop due to overlapΔVd = output voltage with out overlap – output voltage with overlap

Voltage drop due to overlap, We know

Substituting the above expression in ΔVd, we get

cos cos cos2

cos cos cos2 2

cos cos2 2

dodo

do dodo

do do

VV

V VV

V V

cos cos2do

dVV

2 cos cosd sI I

2

cos cos d

s

II

2

2

2

321.

2 3 32

do dd

s

ms

do cd

m mdo

c

V IV

I

EQI

V LIE E

VL

2.

2 33

3

do cd

m

d d c

c d

d c d

V LI

E

V I L

L I

V R I

where

= Equivalent commutation resistance

3 2

6

c c

c c

R fL

R fL

cR

DC voltage and valve voltage waveforms for rectifier when α=15 deg, µ = 15 deg, δ = 30 deg

Inversion:In HVDC converters thyristor is used, it is a unidirectional device.The current in a converter cannot be reversed.Therefore power reversal can be obtained only by reversal of the average DC voltage.Converter will operate as a rectifier for firing angle α < 90 deg, and power flows from AC to DC side.When firing angle α > 90 deg, the average output power Pd becomes negative and power flows form DC to AC.

For an inverter, it is usal to define an advance angle β = π-α, also δ= π – γ

Therefore

Also

or

cos cos2

cos cos2

cos cos2

doidi

doi

doi

VV

V

V

2 cos cosdi sI I

coscos

di doi ci d

di doi ci d

V V R IV V R I

Inverter voltage and Valve voltage γ = 15 deg µ = 15 deg β = 30 deg

Comparision of waveforms of Rectifiers and Inverters:

i)Rectifier average voltage across valve is negative, average voltage across inverter valve is positive.

ii)Both rectifier and inverter modes of operation, the voltage across the valve is negative immediately after extinction of the arc, but in case of inverter valve voltage in negative much shorter duration than in the rectifier.

iii)In both modes of operation, voltage across valve is positive just before conduction begins, but in the rectifier it is positive for short duration than in the inverter

iv)Four minor voltage jumps per cycle, two of which are half as at ignition and other half of that at extinction.

ACAC

Vdo1 Vdo2Vdo

1 co

s a

Vdo

2 co

s B

Vd1

Vd2

Rc1 Rc2RL

Rectifier

Control Concept in HVDC:

Equivalent circuit of a HVDC transmission link

One of the major advantages of a HVDC link is the rapid controllability of transmitted power through the control of firing angle of the converters.Modern converter control are not only fast but also very reliable and they are use for protection against line and converter faults.

The current in a dc link operating in steady state is given by ohm’s law

Where RL= link resistanceRc1 and Rc2 = rectifier and inverter resistance

In above equation cos β is used with +Rc2 in the inverter, operates constant ignition angle, (or) cos γ and –Rc2 if extinction angle γ is constant.

If the line is uniform and if Rc1=Rc2 the voltage at the midpoint of the line as well as the current can be controlled by controlling the internal voltages.

Each internal voltage can be controlled by either1.Firing angle control2. Control of alternating voltage usually by tap changes of converter transformer. Firing angle control is rapid but tap – changing is slow both thus means of control are applied co-operatively at each terminal.

Firing angle control is used initially for rapid action and in followed tap-changing for restore is α for the rectified or voltage in the inverter.

1 2

1 2

do dod

c L c

V Cos V Cos or CosI

R R R

AC current and DC voltage Harmonics:The current waveform of the valve is distorted. The actual expression for the

current can be derived from fourier analyses.

The fundamental current, where

where Ф is the power factor angle

1/22 21 11 12I I I

11 1

11 1

cos cos6cos2

6 2 sin 2 sin 2sin4 cos cos

d

d

I I I

I I I

From the equations, the power factor angle is

where

Harmonic component with no overlap

1/22 2

2 sin 2 sin 2tancos 2 cos 21 2 cos 22

sin 1 sin 12 2,

1 11 cos cos2

h

ho

I A B ABI n

h hA B

h h

n

6 dho

II

h

From the fig all the harmonics especially of higher order, decreases sharply with increases of μ and the reduction factor lies in the range 0.1 to 0.2

Variation of AC current harmonics with overlap-----------------------------

The DC voltage harmonics are altered due to overlap is

where

122 21 2 cos 2

2

cos 12

1

cos 12

1

h

do

V C D CDV

hC

h

hD

h

ii) Overlap Angle greater than 60 degrees:

Overlap angle is in greater than 60 deg is abnormal, this will occur only at low alternating voltage. In this case minimum no. of valves conducting are 3, and there are intervals when four valves are conducting.This is because when commutation process started, the previous valves are not yet completed.When four valves are conducting they constitute a three-phase short circuit on the ac source and a pole-to-pole short circuit on the dc terminals.

Equivalent circuit for four valve conduction

Average Direct voltage

0 02 cos 30 cos 303

sd

II

02

33 cos 302

dd do

s

IV V

I

Combined Characteristics of Rectifier and Inverter:The relation between Vd, Id is called a characteristic of the converter

We know that

where Vdo no load direct voltageVd Direct voltage on load with delay angle ‘α’ and overlap angle μ.

Similarly

where

cos cos cos2

cos cos21 cos cos2

dod do

dod

d

do

VV V

VV

VV

cos cos22

1 cos cos cos cos2 2 21 cos cos sin sin

2 2 2 2

dd

l

l c c

dd

do

dd

s

VIX

X fL LVVVIII

For fixed value of delay angle α, different values of Vd/Vdo can be found for various values of overlap angle μ.The curves are plotted with Vd/Vdo on y-axis and Id/2Is on X-axis.It is possible to change operating point on Vd/Id characteristic by changing α

Inverter:

The Inverter characteristics are similar to the rectifier characteristics.Inverter operation 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.

Coice of Best Circuit for HVDC Converters:Different HVDC converter circuits are discussed as follows:

1-φ Full-Wave RectifiersIn this circuit contains two valve, and centre tap transformers.

In fig shown the line-to-neutral secondary voltage e1 and e2, having a phase difference of one half period 180 deg.

During positive half cycle valve-1 conducts and during negative half cycle valve-2 conducts.

The average DC voltage is shown in fig.When valve-2 in conducting, the total secondary voltage appears across

valve-1, similarly when valve-1 is conducting e2-e1 appears across valve-2.The primary mmf must oppose the secondary mmf.

0

0

1 .

2

21.57

d m

m

md

m d

m d

V E Sin t d t

E Cos t

EV

E V

E V

Voltage:i)Average voltage is Voltage

ii) Peak inverse voltage:

2 2.2

3.142

m d

d

d

PIV E V

VV

Currents:

For half of secondary winding

V A rating:

VA rating of valve

For 1-φ full wave converter

VA rating

1/22

0.52

0.7072 2

ddavg d

d ddRMS d

II I

I II I

avgPIV I

2

22

.

.

avg

dd

d d

d

PIV I

IV

V IP

3.142 dP

Transformer rating:

Transformer secondary rating

Transformer primary rating

Q Primary voltage has crest value Tem and RMS value

2

22 2 2

21.571

rms rms

dd

d d

d

I EI V

I V

P

1.111 1.111d

d dITV PT

0.7071.111

m

d

TETV

Bridge Rectifiers:

During positive half cycle of AC supply valve 1 and 2 are conduct , load side voltage is same as source.

During negative half cycle valve 3 and 4 are conducting the load voltage and valve voltage are shown in fig.

Although the bridge circuit may appear more complicated then the full wave circuit because it has four valves instead of two, the secondary winding is used more effectively and the PIV of each valve has been halved for a given DC output voltage.

Therefore Peak Inverse Voltage, PIV = Em

Voltage

i)Average voltage,

ii)

0

1 .

2

21.57

1.57

d m

md

m d

m d

m d

V E Sin t d t

EV

E V

E VPIV E V

Currents:

VA rating:

VA rating of valve

For bridge rectifier

VA rating of all valves

1/22

0.52

0.7072

ddavg d

ddrms d

II I

II I

davgPIV I

4

42

3.14

davg

d davg

d d

d

PIV I

V I

I VP

Transformer rating:

VA rating of secondary winding = primary winding = 1.111Pd

Three-Phase Rectifier:For large amount of power is required we go for three-phase rectifier.In this rectifier ripple is smalls in magnitude and higher in frequency than in 1-φ

Converters.In this circuit direct current in the secondary winding saturates the transformer

cores. To avoid saturation Y-connection is replaced by the zig-zag connection, in which the DC mmf’s of the two secondary winding on the same core canal out.

i)Average voltage,

ii)PIV = max voltage appeared across SCR when it is not conducting

0

0

0

0

150

30

150

30

1 .23323 3 32 3 0.8262 2 2

0.8261.209

m

m

m mm

d m

m d

E Sin t d t

E Cos t

E VE

V EE V

3

3 1.2092.094

m

d

d

PIV E

VV

iii) Average current,

iv) RMS current,

v) Volt-Amp rating of all valves = No. of valves x PIV x Avg. current/valve

0

0

0

0

150

30

150

30

1 .2

12

0.3333

davg d

d

ddavg d

I i d t

i

II I

0

0

1/2150

2

30

12

30.5773

dRMS d

d

d

I I d t

I

I

3 33

3 3 1.2093

2.0940

dm

dd

d

IE

IV

P

vi) VA rating of transformer secondary winding 3

33 2

23

1.481

rms rms

d m

d

d

I EI E

P

P

3-φ Bridge Rectifier:In the 3-φ mid point rectifier load voltage is equal to line to neutral voltage and it

is line to line voltage.The circuit is shown in fig. is a 3- φ full wave bridge rectifier (or) 3- φ six-pulse

bridge rectifier .In this circuit upper group device will conduct when supply voltage is most

positive where as lower group devices will conduct when supply voltage is most negative.

0

0

0

0

0

0

0

0

90

30

900

30

900

30

0

150

30

2

/6

62

3 3 sin 30

3 3cos 30

3 3

0.6043 33 3 0.604 1.046

(1 cos30 ) 3 0.134 1.047 0.140

1 0.3332 3

12

d AB

m

m

md

m d d

m d d

m d d

davg d d

rms d

V V d t

E t d t

Et

EV

E V V

PIV E V V

E V V

II I d t I

I I t

25 /6 11 /6

2

7 /6

230.816

33

9

d

d

d

avg

dm

d d

I d t

I

IPIV I

IE

V I

i) Average voltage:

ii) Peak inverse voltage,iii) Peak-Peak ripple =

iv) Average current,

v) RMS current,

vi) VA rating of valves