Magnetically Controlled ElectricalReactors

Collection of ArticlesEd. Prof. A.M. Bryantsev, Dr. Sc. (Eng)

Moscow

Znack

2012

Magnetically Controlled Electrical Reactors. Collection of

Articles. 2nd enlarged edition. Ed. Prof. A.M. Bryantsev,

Dr. Sc. (Eng). M.: Znack, 2011, pp. Ill.

Magnetically controlled reactors (CR) have become widely used

in the power generation industry in recent years. Dozens of

three-phase shunt CRs with capacities of 25, 100 and 180 MVA are

now operated in 110, 220, 330 and 500 kV networks. A stable market

for arc-extinguishing reactors for 6-10 kV networks has been formed.

The book contains articles on the CR theory and calculation

methods and on the experience of their development, manufacture,

tests, implementation and operation. The performance data of CRs,

their curcuit diagrams, factory and network test data, and photos are

provided as well as information materials of a company engaged in

R&D, manufacture and commissioning of CRs.

The book is meant for specialists in the field of electricity and

power engineering, engineers and researchers, and for university

professors, post-graduates and students.

ISBN 978-5-87789-060-2 , 2011

ontents

Foreword to the Second Edition . . . . . . . . . . . . . . . . . . . . . . . 3

A.M. Bryantsev. Electric Reactors Controlled by BIAS Magnetizationin Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

A.M. Bryantsev. Magnetically Controlled Ferromagnetic Devices withExtreme Saturation of Parts of the Magnetic System . . . . . . . . . . . 10

A.M. Bryantsev. Principal Equations and Characteristicsof MagneticRectifier Controlled Reactorswith Strong Saturation of the Magnetic Circuit . . . . . . . . . . . . . . 22

M.A. Biki, E.N. Brodovoi, A.M. Bryantsev, L.V. Leites,A.I. Lurie, Yu.L. Chizhevsky. Electromagnetic Processesin HighPower Controlled Reactors . . . . . . . . . . . . . . . . . . . . . 33

A.M. Bryantsev, E.E. Makletsova, A.G. Dolgopolov, A.I. Lurie,G.A. Evdokunin, Yu. A. Lipatov. Shunting Reactors Controlledby BIAS Magnetization for (35500)kV Grids . . . . . . . . . . . . . . . 56

V.G. Pekelis, S.Yu. Chashkina. Effectiveness of HighPowerControllable Shunting Reactors . . . . . . . . . . . . . . . . . . . . . . . . 71

S.V. Zhakutova. Controllable Shunting Reactorsfor ReactivePower Compensation and Voltage Regulationin Kazakhstan Power Grids . . . . . . . . . . . . . . . . . . . . . . . . . . 81

A.M. Bryantsev, A.G. Dolgopolov, A.I. Lurie, S.M. Zilberman,M.A. Biki and S.V. Ukolov. ThreePhase Controllable ShuntingReactor (100 MVA, 220 kV) at the Siberian Chita Substation . . . . . . 89

A.G. Dolgopolov, S.G. Dolgopolov, A.I. Zaitsev,V.P. Shipitsin. Industrial Operation of a ControllableThreePhase Shunting Reactor (110 kV, 25,000 kVA)

at the Permenergo Kudymkar Substation . . . . . . . . . . . . . . . . . . 105

A.M. Bryantsev, A.G. Dolgopolov, O.M. Dubrovina. Power Control ofThreePhase Controllable Shunting Reactor . . . . . . . . . . . . . . . . . 116

B.I. Bazylev, M.A. Bryantsev, Yu.P. Spiridonov. Design of ControllableArcquenching Reactors for 6 and 10kV Grids . . . . . . . . . . . . . . 127

A.I. Lurie, A.N. Panibratets, V.P. Zenova,V.N. Elagin, B.I.Bazylev. FMZO Neutralizersfor Ruom Controllable Arcquenching Reactorsin Grid with Isolated Neutral Line . . . . . . . . . . . . . . . . . . . . . 137

A.I. Lurie, A.N. Panibratets, and V.P. Zenova. Electrodynamic Strengthin ShortCircuiting of Ruom Controllable Arcquenching Reactors. . . . 149

247

A.M. Bryantsev, A.I. Lurie, A.G. Dolgopolov,G.A. Evdokunin, B.I. Bazylev. ArcQuenching MagneticBiasControlledReactors with Automatic of Ground Fault Capacitive CurrentCompensation for 6 to 35 kV Networks . . . . . . . . . . . . . . . . . . . 165

A.M. Bryantsev, A.G. Dolgopolov, A.I. Lurie. A Unique 330kV180 MVA Magnetically Controlled Shunt Reactor is Putinto Operation at the Baranovichi Substation . . . . . . . . . . . . . . . . 185

A.M. Bryantsev, A.G. Dolgopolov, A. I. Lurie, B.I. Bazylev,S.V. Ukolov, A.I. Zaitsev, Y.V. Sokolov, N.G. Akhmetzhanov.A New 180MVA Magnetically Controlled Shunt Reactor WasCommissioned For the First Time in a 500kV Network . . . . . . . . . 196

A. Bryantsev, M. Bryantsev, B. Bazylev, S. Dyagileva, R. Karymov,A. Lurie, A. Negryshev, E. Makletsova, S. Smolovik. PowerCompensators Based on Magnetically Controlled Shunt Reactorsin Electric Networks with a Voltage between 110 kV and 500 kV. . . . 204

A. Bryantsev, S. Smolovik, A. Dorofeev, M. Zilberman, A. Smirnov.Magnetically Controlled Shunt Reactor Applicationfor AC HV and EHV Transmission Lines. . . . . . . . . . . . . . . . . . 215

A.M. Bryantsev, A.G. Dolgopolov, G.A. Evdokunin,Y.A. Lipatov A.I. Lurie, E.E. Makletsova. MagneticallyControlled Shunt Reactors to meet of Russias Power Industrythe Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

Technical Expertise on project Magnetically Controlled ShuntReactors for 35500 kV Electric Networks . . . . . . . . . . . . . . . . . 237

Foreword to the Second Edition

The decision to reprint the book has been taken due to amarket increase in controllable shunt reactor (CSR) purchases for110500 kV networks by power facilities in the Russian Federationand other countries. While at the time of the first publication in2004 only a few prototype models and pilot batches were produced,the CSR deliveries exceeded US$100 million between 2006 and2009. By now, CSR of 25, 32, 63, 100 and 180 MVA for all voltagelevels from 110 to 500 kV have been, are being or are about to beinstalled. The use of CSR reduces power losses, stabilizes voltage ,and increases the transfer capability and reliability of highvoltageelectrical grids. The experience of the CSR operation (the firstCSR of 25 MVA has been working successfully in a 110 kV networkfor more than 10 years) proved their high reliability. For thisreason, the introduction of CSR is regarded as one of the most promising areas in the modernization of electrical grids of the RussianFederation in the technical policy of the Federal Grid Company ofUnified Energy System (JSC FGC UES).

The success of the CSR is based on the fact that it possesses fullfunctionality of a thyristorreactor group (TRG) with a stepuptransformer but is much less expensive and basically no differentfrom a conventional generalpurpose power transformer in design,manufacturing and maintenance. In combination with a capacitorbank (CB), a CSR can perform all functions of a highvoltage reversible reactive power compensator (reactive power source), i.e.,the same functions as a static var compensator (SVC) and a synchronous compensator. There are more than twenty reactive powersources with CSRs in operation today. Since a CSRbased reactivepower source is connected directly to the point of the grid wherevoltage is to be maintained, it has a lower installed capacity of equipment and provides more accurate voltage support.

The reasons for the interest attracted by CSRbased andCBbased reactive power sources are not only their much lower

3

costs than SVC or synchronous compensators but also significantlylower installation and operation costs. The CSR is placed on anoutdoor site of a substation and does not require a separate heatedbuilding and special maintenance.

In addition,the CSR has some important functional featuresdistinct from other reactive power compensation devices. Afterfaults and voltage sags in the grid, a large portion of load is disconnected after reclosure, so restoring voltage can increase greatly. Inthis situation, however, the CSR builds up practically full power instantly, which compensates the voltage increase and prevents loadreconnection failures.

It should be noted that good experience in operation of allCSRs, including those used as part of reactive power sources, didnot reveal any shortcomings in the design parameters of the reactors, particularly, their response speed under normal operating conditions.

This edition of the Collection includes additional articles devoted to highvoltage 110500 kV reactive power sources based oncontrollable shunt reactors and capacitor banks. The potentialdemand for reactive power sources is much higher than that forcontrollable shunt reactors as such.

A.M. Brayntsev, October 2011

4

Electric Reactors Controlled by BIASMagnetization in Power Systems

A.M. Bryantsev

This issue is devoted to electrical reactors controlled by biasmagnetization. The first special issue on this topic (in February1991) focused on the theory of their creation, their performance,their applications, and experience in manufacturing and testing thefirst prototypes.

Since then, the situation has significantly changed. Today, various types of such reactors are produced, in the power range from190 kV A to 180 MV A, in all voltage classes from 6 to 500 kV;dozens are already in operation. Such rapid commercial introduction of a new electricalengineering product cannot be attributedsolely to the enthusiasm of the developers and the skill of marketing specialists, but indicates certain fundamental benefits of thenew design.

A simplified analysis of these benefits may be based on Fig. 1.The structure and phase configuration of all controllable reactorscorresponds to Fig. la. In phase terms, the controllable reactor isessentially a twowinding transformer with a split rod. One winding(the grid winding) is connected to the grid (U g

); the other (the

control winding) is connected to a controllable dc voltage source( )Uc

. Sections of the grid and control windings are in an opposing

parallel configuration, with no direct electromagnetic coupling.Each phase winding creates its own magnetic fluxes: an industrialfrequency ac flux for the grid winding; and a controllable dc biasflux for the control winding. The dc bias flux shifts the ac fluxtoward the saturation region of the magnetization curve of thesteel, thereby modifying the inductive resistance of the device.

The voltage and current variation corresponding to this processmay be seen in Fig. 2. When the terminals of the grid winding areconnected to the grid and there is no energy in the control circuit

5

( , )U ic c

0 0 , alternating fluxes of the same magnitude and directi

on appear in the split rod. They do not exceed the saturation fluxesin any cross section of the magnetic system, while the current inthe grid winding is practically zero ( )ig 0 . This is the idling mode.The current and voltage variation for this case is shown in Fig. 2for the time intervals from to to t1 and beyond t8. When energy issupplied to ( )U ic c

0 or removed from ( )U ic c

0 the control circuit,

there is a transient increase or decrease in the grid current ig and

control current ic (time intervals t t1 2 , t t3 4 , t t5 6 , t t7 8 ). For

example, transition from one steady mode to another within twoperiods of the grid voltage calls for a mean controlcircuit power ofaround 5% of the rated controllablereactor power, but only duringthe transient process. In any steady mode for example, semi periodic (rated) or fully periodic (maximum) the power consumedby the control circuit is sharply reduced, since it is only required

6

Fig. 1. Circuit diagram of one phase of a controllable electrical reactor (a) and apossible equivalent functional circuit (b).

for compensation of the ohmic losses in the control winding and isno more than tenths of a percent of the rated power.

The graphs in Fig. 2 are obtained by calculation using specialprograms on the basis of Fig. la. However, these graphs may be reproduced with high accuracy using the equivalent functional circuitin Fig. lb, where the phase element of the controllable reactor is represented as an opposing parallel thyristor pair with linear inductiveresistances in series. In the equivalent circuit, inductances Lgw , Lcware the inductances of the grid and control windings with a completely saturated magneticsystem rod; is the thyristor controlangle, corresponding to the duration of the saturated rod statewithin the half period of the grid voltage, expressed in electrical degrees. The range of from 0 to corresponds to the whole possiblerange of operating conditions. For example, the thyristor control

7

Fig. 2. Characteristic voltage and current curves for controllable reactor: U g , i g

,grid voltage and current; U c

, ic , control voltage and current; , thyristor control

angle.

angle corresponds to reactor idling. The angle /2 corresponds to semiperiodic saturation or rated operation. Finally, corresponds to maximumcurrent consumption or fully periodic saturation.

The equivalent functional circuit in Fig. 1b not only permits thecombination of familiar devices so as to describe the characteristicsof a controllable reactor in a power system. It also clearly reflectsthe economic potential of controllable reactors. We see that the reactor consists structurally of a transformer that is very similar, interms of losses and consumption of materials, to the analogoustwowinding transformer of comparable power and vo At the sametime, in functional capabilities, the reactor corresponds to thewidely used thyristorreactor connected to a highvoltage gridthrough a coupling transformer. Thus, in contrast to the traditionaldesigi coupling transformer plus a reactor and a thyristor in series we only need a specific transformer unit, in which the windinginductance acts as the reactor, while the saturated rod acts as theopposing parallel thyristor pair. Instead of three components, wemay use only one component, of power consumption comparablewith any of the three.

The concept of a reactor controlled by bias magnetization as atransformer unit that serves the function a semiconductor deviceunderlies all the developments of the last decade and permits optimal use of current disigns both in the transformer industry and inpower electronics.

In 19951996, the production of controllable arcquenching reactors for (635)kV distribution grids was organized at EnergiyaRamensk electricengineering plant. Operational experience completely confirms their high performance; in particular, their usehalves the incidence of grid emergencies. Note that this effect isgreatest in grids with aging equipment. Judging from the orders received, we may look forward to the systematic replacement of several thousand electromechanical devices by arcquenching reactors.

8

Since 1998, the Russian ElectricalEngineering Institute,Elektricheskie Upravlyaemye Reaktory Joint Stock Company, Zaporozhtransformator Joint Stock Company, and Ramenskii Elektrotekhnicheskii Zavod Energiya Joint Stock Company (EnergiyaRamensk electricengineering plant) have been preparing for theproduction of controllable shunting reactors for (110500)kV grids.Projects include the following:

in 19981999, the installation of a controllable reactor(25 MVA, 110 kV) at the Permenergo Kudymkar substation;

in 20012002, the manufacture and installation of a controllable reactor (100 MVA, 220 kV) at the Siberian Chita substation;

in 2002, the manufacture of a controllable reactor (180 MVA,500 kV) for the Belenergo Baranovichi substation.

Expert evaluation of the results suggests that the largescaleintroduction of shunting reactors controlled by bias magnetizationshould be a priority in the reequipment of highvoltage(110500 kV) grids. The total effect for the grid as a whole is 34 %reduction in power losses, 3050 % increase in the throughput ofintersystem links, and restoration of the quality of the electricpower to meet international standards.

The development, production, and operation of reactors controlled by bias magnetization will be considered in more detail inthe remainder of this issue.

First published: Electrical Engineering, vol. 1, 2003. pp. 24.

9

Magnetically Controlled Ferromagnetic Deviceswith Extreme Saturation of Parts

of the Magnetic System

A.M. Bryantsev

The development of highcapacity controllable inductive devices for shunt reactive power compensation in electrical grids playsan important part in the enhancement of electrical energy quality[1, 2]. The most widespread design in this area is regulation ofinput current using a reactor connected inseries with a thyristorswitch [3]. Along with that, attempts are still made to develop magnetically controlled reactors. Their advantage is a relatively lowcontrol power, which is especially important for highcapacity installations.

A general analysis of controllable reactor designs existing nowallows to conclude that their main technical disadvantages are considerable distortion of current waveforms and increased loss in themagnetic core during biasing magnetization. The need to suppressnonlinear distortions by adjusting the circuit complicates thedesign and worsens the performance. In particular, the experienceof manufacturing production prototypes has shown that the totalloss was 7 or 8 times higher than control power due to increasedloss in steel [4]. This is caused in large measure by the conventionalapproach to the design of magnetic systems when the field intensityof the fundamental frequency does not exceed 20 or 30 kA/m evenin highcapacity devices under rated operating conditions. The regulation capabilities of magnetized electric steel are used there to alimited extent and nonlinear distortions are high (solid lines inFig. 1). With such a relatively low intensity of the biasing magnetization field, the active zone of induction is located mainly in thehysteresis area of the magnetization curve, which increases loss inthe steel.

10

These disadvantages can be largely avoided by maximizing theuse of the control range of electric steel induction. Since nonlineardistortions during the biasing magnetization of electric steel decrease in the area of technical saturation, it makes sense to put thewhole induction variation range within this area. The distortions ofthe intensity curve disappear in this case (dotted lines in Fig. 1).Further growth of the biasing magnetization field will not increaseany more the alternating component of the field intensity. If induction varies in the fashion:

b M tm cos (1)

the field intensity can be represented as:

h B ctg t h B Bm m

(cos cos ) * , (2)

where h* is a relative value of the field intensity for basic Bs , o1:

hb B

t b Bs

s*

cos cos

Oif

if

B Bm m* is a relative value of the first harmonic component of in

duction; arccos( )/B B Bs so corresponds to the moment of in

11

Fig. 1. The basis of determining the control ranges of electric steels (for piecewiselinear approximation of the average magnetization curve [8])

duction transition to the area of technical saturation (in radians); is the slope angle of the linear part of the magnetization curve(Fig. 1); and tg o.

The expansion of the function h* in the Fourier series yields thefollowing expressions for the amplitudes of the harmonic components:

Ho* (sin cos ); 1

(3)

H11 2

2* sin ;

(4)

Hi

ii

iii

* sin( ) sin( )

1 11

11

, (5)

where i 2,3,4,5 are serial numbers of higher harmonic components.

The degree of steel saturation is characterized by the angle inthis set of equations. The extreme saturation is achieved when . In this case HI

*1, Ho

*1, Hi

*0. A numerical harmonic ana

lysis using more accurate approximating expressions that take intoaccount the smoothness of the transition of the magnetization

12

Fig. 2. The variation of the nonlinear distortion coefficient of a threephase devicefor piecewiselinear approximation of the magnetization curve (the solid line) andfor the approximation in accordance with [5] (the dotted line).

curve to the technical saturation area [5] shows that the us of equations (3), (4), and (5) results in a significant error only for a weakbiasing magnetization. The error in the main harmonic component,the constant component and integral nonlinearity indices coefficients of harmonics discussed below is reduced starting withH* . ( / ) 005 6 (Fig. 2).

The above expressions allow to estimate graphically basic regulating characteristics and specific features of the nonlinear distortions that determine the electromagnetic state of a device for different degrees of steel saturation. For example, the following aspectsare of interest for finding a desirable biasing magnetization mode:the ratios of the first harmonic component of the magnetic field intensity to the effective intensity value (which determines the degreeof current density increase in windings during biasing magnetization, k

) and to the effective values of even harmonics and of theconstant component (which defines the relative value of the controlcurrent, ky), and the odd harmonic coefficients kh and the coefficients of odd harmonics of positive and negative sequence, kh3ph(which define the distortions of current consumed by a onephaseand a threephase controllable ferromagnetic device, respectively).The results of the calculations of these quantities and the ratios H 2H1 o/ used as a criterion of biasing magnetization efficiency

[6] are given below:

,degrees

H1* k

ky kh kh ph3

36.87 0.052 1.787 1.263 0.772 0.302 1.357

46.57 0.094 1.644 1.163 0.593 0.141 1.328

53.13 0.141 1.560 1.103 0.465 0.077 1.298

60 0.196 1.504 1.064 0.363 0.076 1.268

72.54 0.312 1.442 1.019 0.198 0.080 1.207

84.26 0.436 1.417 1.002 0.062 0.036 1.143

13

90 0.5 1.414 1 0 0 1.111

101.5 0.626 1.424 1.012 0.076 0.042 1.043

113.5 0.748 1.455 1.052 0.093 0.031 0.972

126.8 0.858 1.507 1.175 0.062 0.015 0.854

143.1 0.948 1.590 1.235 0.042 0.016 0.811

161.8 0.993 1.686 1.357 0.009 0.006 0.737

180 1.0 1.732 1.414 0 0 0.707

It can be seen from the calculation results that if the coefficientof biasing magnetization efficiency is used as a criterion for selecting the normal rating of a device, the saturation of the magneticcircuit should be as low as possible. In fact, however, the increasein the consumption of active materials due to biasing magnetizationdepends on the coefficient of loss increase in the winding, k

,which takes its minimum value for H1

* 0.5. To minimize nonline

ar distortions of the input current in normal operation the degree ofthe magnetic system saturation should be even higher (H1

* 1). The

higher harmonic components vary within the control range, in accordance with (5),by the law described by the sum of two harmonicoscillations with frequencies of i1 and i1 [7]. The number of extremums of the ith harmonic component is less than its serialnumber by one (Fig. 3). The absolute maximum is the extremumclosest to the point /2:

H i

ii

ii(max)*

( )sin

2

11

22

. (6)

The maximum values of odd harmonics 3, 5, and 7 are equal to0.06892, 0.02523, and 0.01293, respectively.

Higher harmonic components are absent in the extreme saturation mode ( , HI

*1). There are nonlinear distortionsat the

point /2, only for even harmonic components that cannotflow out to the electrical grid both in onephase and in threephasedevices. If extreme saturation is provided under the rated operating

14

conditions, the coefficient of the distortion of current consumed bya onephase device becomes zero at two points ( / ,2 ) andits value does not exceed 0.095 starting with 80. This valuedoes not exceed 0.08 in a threephase device starting with an angleof 50. When / ,2 the coefficient of harmonics in thecurrent of a threephase device is less than 0.05. So, the optimum operation mode in terms of minimum nonlinear distortions and additional

consumption of winding metal lies in the range of hI* .005 to 1.

The values of field intensity corresponding to extreme saturation depend on the amplitude of the induction of the alternatingmagnetic flux and the size of nonmagnetic channels between thewinding and the saturated part of the magnetic circuit. In extremecase , the amplitudes of the main component field intensity andspecific magnetizing power for B Hm I

* * are:

H Bs1 o

1.6 MA/m;

15

Fig. 3. The variation curve of magnetic field intensity harmonics in the function ofthe angle of induction transition to the technical saturation area of the magnetization curve.

q Bg

s1

2

2

!

65 kWA/kg ,

where B Ts 2 [8]; g 7650 kg/m3 is the density of electric steel;

and is angular frequency.The specific parameters being so high, the saturated parts make

only a part of the magnetic system volume. For this reason, onepossible design of a controllable ferromagnetic device with biasingmagnetization close to the extreme is making active parts of themagnetic conductor in the form of segments of limited length withreduced crosssections (Fig. 4), [9]. To reduce additional loss fromleakage fluxes, these parts should be distributed along the magneticconductor, for example, using the method described in [8]. The reduced crosssections of the parts Sy and their total length l shouldbe chosen so that the required degree of their saturation( . *0 5 11" "h H ) is achieved in the rated magnetization mode while the

rest of the magnetic conductor remains unsaturated (the maximuminduction value does not exceed the saturation induction ofsteel Bs ):

B S B B Ss y" ( )oH , (7)

16

Fig. 4. The conceptual design of the magnetic conductor of a magnetically controlled ferromagnetic device with extreme saturation of the magnetic circuit parts.

where BoH is the rated value of the constant component of induction in the parts with reduced crosssections.

The transformation of relationship (7) including the previousexpressions yields:

# $

k S S Bs y m i

1 11 1* ( cos ) , (8)

where ks is the coefficient of reduction of the active parts of themagnetic conductor; i is the angle of the transition of inductionto the technical saturation area of the curve under the rated conditions.

The presence of a channal parallel to the part of reducedcrosssection influences the field intensity value with which the setvalue of H H1

* can be achieved since the slope of the weberampere

characteristic increases. In this case, in accordance with (2), thefield intensity under the rated conditions is

H H B B ctgH B B k k

H H m sH m s s

1 11

2

* ** *

p

o

, (9)

where kp is a coefficient to allow for the bulging of the field fromparts of reduced crosssection and the leakage flux of the winding.

The required total length of parts of reduced section can befound from the equality of the first harmonic component of themagnetizing force and the magnetomotive force of the winding [9]:

k lL A

H B B k kH m s s p1

1

1

o* *

, (10)

where A is the rated amplitude of the linear density of the first harmonic component of the magnetizing force and L is the height ofthe winding (Fig. 4).

The only constraint for selecting the induction of the alternating flux in the parts of reduced crosssection is noload magneti

17

zing force that determines the depth of current regulation of thedevice. Calculations have shown that even for B Bm s the portion ofnoload magnetizing force is not greater than 3% to 5% of themagnetizing force that can be achieved under extreme saturationfor modern electric steels.

In general, considering relations (8) and (10), the winding dataand the electromagnetic parameters of a ferromagnetic device containing the proposed magnetic system can be found conventionallyusing wellknown methods based on the minimization of the calculated costs of the active part.

The controllable ferromagnetic devices where a mode close toextreme saturation is applied should have a relatively low level ofloss in steel under the rated conditions because the main part of theinduction range is shifted to the anhysteretic area in the parts of reduced crosssection. The rest of the magnetic conductor remainsunsaturated up to the rated conditions, which also causes a relatively small increase in loss due to the shift of the minor hysteresiscycle. The table below shows the data of testing a threephasemodel of a 15 kvar controllable reactor assembled as shown in

18

Fig. 5. The schematic of loss measurement from the side of the power winding of a15 kV%A threephase controllable reactor.

Fig. 5 with a sixleg magnetic conductor. The magnetic conductorwas made at first with equal crosssections of all parts. Then, partsof reduced crosssection with ks 0.5 and k1 0.045 correspondingto H H1

* 0.5 were obtained by separating partially the yokes and by

appropriate displacement of the sheets of the cores in the areas ofyokecore joints. The mass of these parts (about 2 kg) was 1.13 %of that of the magnetic conductor.

As can be seen from the table, the noload current and loss ofthe device increased in the second case by factors of 1.66 and 1.08,respectively. The loss dropped, however, in the rated mode of biasing magnetization, by about 40 %, mainly due to lower loss in thesteel1.

Comparison characteristics of a 220 kV 15 kVA threephase

controllable reactor

Parameter

Magnetic conductor design

With equalcrosssections of allparts

With extremesaturation of activeparts with reducedcrosssections

Noload current, A 1.63 2.7

Rated current, A 39.5 39.5

Noload losses, W 140 152

Rated loss, W 715 430

The coefficient ofcurrent harmonicsunder rated conditions

0.19 0.035

The induction of noload alternating flux was 1.1 T for both designs in the bulk of the magnetic conductor. The calculated noload induction grew up to 2.2 T in the parts of the magnetic conduc

19

1 The experiments were conducted and data processed by Engineers S.A. Gordeevand V.N. Mozherin.

tor with reduced crosssections and the field intensity in the ratedoperation mode reached 163 kA/m with the linear density of themagneto motive forces of the windings being 7.4 kA/m. The distortion of rated current kh ph3 was caused by a relatively large length ofthe unsaturated parts of the magnetic conductor (the impact of theunsaturated parts will be less in reactors of higher capacity becauseof a relatively larger mass of the active parts of the magnetic conductor). To provide the same level of nonlinear current distortionsin a model with the conventional biasing magnetization system, anadditional reactor (referred to as a compensating throttle in [6])is required, whose mass is about 30 % of that of the active part ofthe device. Hence, the extreme saturation of the active parts of themagnetic system has a beneficial effect both by weight characteristics and by loss.

The disadvantage of the extreme biasing magnetization is a relatively inefficient use of electric steel in unsaturated parts of themagnetic conductor. According to (4) and (7), the values of ksfrom 0.5 to 0.33 correspond to values of h H1

* 0.5 to 1.0 for Bm

* 1.

So, the induction of the alternating flux in the unsaturated part ofthe magnetic conductor is within 0.67 T to 1 T despite the fact thatit is equal to the saturation induction Bs in the active parts. An analysis of the form and dimensions of the magnetic system over awide range of rated power values has shown that the relative size ofactive parts is small for rated powers below tens of kvar and theaverage alternating flux induction depends on the induction in theunsaturated part of the magnetic system. As the rated power increases, the relative size of active parts in the magnetic conductorgrows. The total length of the parts of reduced crosssections becomes comparable to the height of the winding starting with capacities of 3040 MVA mainly due to higher linear density of magnetomotive force and leakage paths between the winding and activeparts. As the result of this, The average amplitude of alternatingflux induction in the whole magnetic system increases to between1.3 T and 1.5 T as a result and the beneficial effect of the extreme

20

saturation of the active parts in the magnetic circuit can be felt tothe highest extent.

References (in Russian)

1. A.G. Kraiz and L.V. Leites. On Inductive Devices for Static Var Compensators. Elektrichestvo, No. 10, 1979.

2. Electric Equipment to Assure High Quality of Electric Power // I.M.Bortnik, V.V. Khudyakov, V.N. Ivakin, at al. Elektrotekhnika, No. 3, 1981.

3. V.V. Khudyakov and V.A. Chvanov. A Static Controllable ReactivePower Source. Elektrichestvo, No. 1, 1969.

4. A CoreType Controllable Reactor with a Spatial Magnetic Conductorin 35110 kV Electrical Grid// A.M. Bryantsev, S.E. Sokolov, Sh.Sh. Biktashev, at al. Power Plants. Elektrostantsii, No. 5, 1982.

5. A.M. Bryantsev and E.N. Brodovoi. The Approximation of the MainMagnetization Curve of Highly Saturated Ferromagnetic Devices. PowerIndustry. Proceedings of Higher Education Institutes, No. 4, 1985.

6. A.M. Bryantsev. A Magnetic Thyristor Reactive Power Regulator.Elektrotekhnika, No. 10, 1984.

7. A.A. Bulgakov. Electronic Devices of Automatic Control. Moscow:Gosenergoizdat, 1951.

8. L.V. Leites. Electromagnetic Calculations of Transformers and Reactors. Moscow: Energy, 1981

9. A.s. 1164795 (USSR) An Electroinduction Device/ A.M. Bryantsev.Published in BI, No. 24, 1985.

First published: Electricity, 1986, 2, pp. 2330.

21

Principal Equations and Characteristicsof MagneticRectifier Controlled Reactors

with Strong Saturation of the Magnetic Circuit

A.M. Bryantsev

The magneticrectifier controlled reactors were developed basedon the principle of formation and control of the biasing magnetization flux using successive cyclic shunting of a part of the windingsby the switch elements of the converter and on the idea of achieving strong saturation of the active parts of the magnetic circuit inthe rated duty when the operating point of the magnetic flux ismostly situated in the technical saturation area of the magnetization curve [1, 2]. Quite a large number of circuit versions of thesecircuits is known today (Fig. 1).

We consider below the action, basic regularities and the qualitative pattern of magneticrectifier controlled reactors using a simplified analytical model as an example to avoid particulars (Fig. 2)and making the following assumptions:

The voltage of the source connected to the reactor is sinusoidal:

u U tm sin ,

The weberampere curve of the magnetic cores is piecewise:

FRs

0 when

when s

o s

;

( ) ,

where is the current flux value in a core; s is the saturationflux; R

o is the magnetic core resistance in complete saturation. No loss. The magnetic field is insignificant outside the steel of the

magnetic conductor .

22

The rectifier switches of the converter are ideal. The duration of switching transients is shorter than the ne

twork frequency period.Two or more switches can close at the same time in the reac

tors electrical circuit only at the moment of their commutation.We consider therefore only three basic conditions that determinethe operation of the device (Fig. 2 b, c, d). An analysis of eachcondition and generalization of the findings imply the followingequations that determin the variations of magnetic fluxes (MF)and phase currents:

dd t

K t UW

tm1 11

( ) sin ;p

(1)

23

a) b) c)

d)

Fig. 1 Schematic examples of rectifier magneticrectifier controlled onephase (a,b) and threephase (c, d) reactors.

dd t

K t UW

tm2 11

( ) sin ;p

(2)

i F FW

K t F FWp

1 2 1 21

p p( )

; (3)

i i i i F FW

K t F FWc k k k

o 1 2c c

1 2 1 21

( )

, (4)

where Um is the amplitude of the voltage applied to the windingends; is the angular frequency of the network; Wp is the numberof turns in the phase winding; Wc is the number of turns in thecontrol winding loop; 1 2, are instantaneous values of magneticcore fluxes; F F1 2, are instantaneous values of MF; is the relativenumber of turns in the winding sections shunted by a converterswitch; i p is an instantaneous value of the phase current; and i c isan instantaneous value of biasing magnetization current shortedthrough the switch elements of the converter.

The right side of equations (1) and (2) along with the sinusoidalnetwork voltage contains an expression for control voltage:

u K U tc t m

( ) sin

1. (5)

The specific form of the Uc graph depends on the operationmode of the converters switches , which is indirectly assigned bythe switching function in the form:

KKKK

t( )

;

;

1 10

1 2

is closed;0; is closed;

is closed.

So, the shunting of some winding turns is equivalent in itsimpact to an increase in the instantaneous value of voltage appliedto the switching sections of a halfphase by a value proportional to ( )1 1 with simultaneous reduction of the voltage in nonswitc

24

hing sections by the same value. By synchronizing the converterwith the network frequency and changing accordingly the firingangle of its switches we can change the value and the sign of theconstant component in the Uc graph. As a result, bias magnetization fluxes appear in the active part of the magnetic conductor alongwith the main harmonic component of the flux despite the harmonicity of the applied voltage. Their rate and direction of incrementdepend on the constant component of the control voltage . Ip phasecurrent and Ic control current contain two components each, thefirst ones of which agree with classical equations describing currentsin saturable reactors. Their value and form depend on the saturation of the magnetic circuit and are magnetization currents in thephysical sense. The main components of the phase current, therefore, is purely inductive. The components of the current proportio

25

p

c

p

c

c

a)

b)

c)

d)

c

Fig. 2 Phase analytical model (a) and its main conditions (b, c, d).

nal to ( )1 1 depend on the operation of the converter . The

control current steps are caused by a discrete change in the numberof turns of the control winding because some of these turns areshunted by the converters switches. The additional component ofthe phase current is nothing but the input current of the converterreduced to voltage of the power winding. The nature of the converters input current depends on the specific form of the function K t( )and it can contain in principle both active and reactive componentsof any sign. The active components appear when the magnetic fieldenergy changes in the reactor. The biasing magnetization currentincreases when the sign of the active component is positive anddecreases when it is negative. The typical curves of the variations ofthe control voltage and biasing magnetization currents of the reactor combined with the curve of the power winding voltage areshown in Fig. 3. Thus, rectifier the magneticrectifier controlled reactors are selfmagnetized inductive resistors. Their active partcombines the functions of a magnetized ferromagnetic coil and of atransformer to supply power to the converter. The converter ensures an energy exchange regulated in intensity and direction between the magnetization loop and electrical grid. This conclusion istrue for any version of rectifier the magneticrectifier controlled reactor. The difference between the electric circuits (Fig. 1) liesmainly in different distribution of the harmonic components of biasing magnetization currents and of the converter current in windingsections [3]. And the more individual non coincident loops arethere in a reactor, the more materials are needed to build it. Fromthis point of view, the most practical circuit is one shown inFig. 1a, which has only one AC/DC winding.

One of the most important characteristics of a controllabledevice is its response time. To estimate the response time of themagneticvalve controllable reactor, let us integrate (1), (2). Weobtain that the fluxes in halfphases contain timevariable constantcomponents equal in absolute value but opposite in directions alongwith the main harmonic components, the same in amplitude anddirection in both halfphases, which can be found from thewellknown expression

26

p

1mmU

W

. (6)

For the circuit (Fig. 2) under review, the maximum incrementof this component during the network frequency period is

omax ( ) ( )

0 0 1 141n n m

. (7)

If we consider known the biasing magnetization flux 0r atwhich the reactor operates in the rated duty cycle, then, based on(7), we can represent the minimum time needed for its transitionfrom idling to rated power, expressed by the number of the networkfrequency periods in the form:

n WW

UU

m

1 12 0

0r

1r

c

p

0r

1rmax,

27

c

p

p

Fig. 3. The time charts of variation of the switching function, voltages and currentsof the reactor.

where U0max is the peak value of the constant component of control voltage (5) .

A simple quantitative analysis of (8) shows that when the network frequency f is 50 Hz, the time of the transition of the reactorfrom idling to its rated duty can be 0.33 sec for 0.015 to 0.03 inthe technically practical range of 1m and 0r. If the response timeis increased to 0.1 sec, does not exceed 0.1 (Fig. 4). It is possiblein principle to make a reactor with a response time about equal tothe network frequency period; but it is hardly practical because, as grows, the capacity of the converter increases to that of the reactor itself.

The currents of the reactor are functions of the MF, of the saturable parts of the magnetic circuit (3), (4). Accurate determination of interrelationships between values of halfphase currents and

the MF of the windings in the active part of the reactor is a separate problem of calculating the magnetic circuit depending on its specific design features. At the same time, the generalized results of research into different types of controllable reactors have shown thatthe relative time of finding the operating point of the flux in the saturation area of the magnetization curve during a network frequency period can be used as a general measure of the saturation extentof the magnetic circuit to characterize the qualitative pattern of theelectromagnetic condition of a magnetized ferromagnetic device.Numerically, this time is equal to the value of the MF cut off angleof a part of the magnetic circuit. The basic regularities of the elect

28

cp

Fig. 4. For the estimation of the response time of a controllable reactor.

romagnetic condition of magnetized steel as a function of the angle are discussed in [4]. The efficiency of biasing magnetization thenature of nonlinear distortions, and the consumption of materialsfor the active part was shown to depend unequivocally on theextent of saturation of the active parts of the reactors magnetic circuit in the rated duty r. And the least consumption of active materials corresponds to r 90 (halfcycle saturation). When r 180 (fullcycle saturation), the nonlinear distortions in thereactors currents are minimal.

In some cases, however, even the fullcycle saturation in therated duty is insufficient to meet the requirements for the harmonica of the operating current, for instance, when this device is used asan arcextinguishing reactor. The waveform the MF of the magnetic circuit can be improved by saturating two subsequent parts instead of one part.

The higher harmonic components in the MF waveform are reduced most efficiently if the magnetic resistance of two saturatedparts is twice as much as that of saturation of one of them, thesecond part to be saturated when the first part is in the condition ofsemicycle saturation. The graphic explanation of the above can beseen in Fig. 5. The harmonic spectrum of MF in such twostep saturation is characterized by the following expressions:

F F F F tt m imi

( ) sin

0 12

, (9)

FR m

i jj

00 1

1

2

(sin cos ); (10)

FR

mm

ij

i1

0 1

1

2 2

2

sin; (11)

FR i

i

i

ijmm j j

i

0 1

1

2 1

1

1

1

sin( ) sin( )

, (12)

where 1, 2 are the switching angles of the twostep magnetization curve (Fig. 5).

29

The results of calculating the MF of the third harmonic component for the cases of magnetizing one and two subsequent partsof the magnetic circuit are shown in Fig. 6a. It can be seen that inthe second case the third harmonic components of the two partscompensate each other to a great extent starting from the halfcyclesaturation of the first part and further on. The range of low distortions (less than 5 %) in the waveform of the MF of the phase extendsto twothirds of the variation range of the main harmonic component of the phase (Fig. 6b). The maximum effective value of oddhigher harmonics of the MF does not exceed 5 % of the maximumvalue of the MF of the main harmonic component.

The distortions of the phase current of the reactor are composed of the distortions of the saturation current the first componentin equation (3) and of the converter current, which is the secondcomponent of (3). The harmonic composition of the saturationcurrent repeats completely the odd harmonic series of the MF ofthe magnetized part.

The distortions induced by the converter current depend to alesser extent on the saturation of the magnetic system and occureven under full linearization of the latter. Their pattern depends onthe specific design and the operation mode of the converter switches, which is described in sufficient detail in numerous publicationsdedicated to the analysis of the converter devices supplying inductive load. However, due to its relatively small quantity, the influenceof this component on the resultant waveform of the phase current

30

Fig. 5. For the explanation of the principle of twostep biasing magnetization oftwo subsequent parts.

will be noticeable only in the reactors with high response time (lessthan 0.1 sec).

The results described in this article were obtained after substantial simplifications in the design model of the magneticrectifiercontrolled reactor. At the same time, they do not only clarify theprinciple of operation and key regularities of the devices but alsodefine rather accurately some quantitative parameters and characteristics. For example, the expression for the estimation of responsetime (8) by an unlimited surge of transient was derived withoutregard to any loss in the device, and the results of calculation usinga more accurate model and experiment yield practically the samevalues. This is because the time constant of the natural damping oftransients caused by the loss is equal to dozens of seconds, which isabout two orders of magnitude higher than the time constant of dynamic processes in the super excitation mode. The use of improvedapproximating expressions instead of piecewiselinear approximationvirtually has no effect on the qualitative and quantitative results of

31

a) b)

Fig. 6. The variations of the third harmonic component of the MF(a) and of thecoefficients of odd harmonics and of the first harmonic component (b) when one(curve 1) and two subsequent parts with interconnected geometry (curve 2) are saturated.

the calculations of the harmonic composition of the current sand regulating characteristics. The results and conclusions of the integratedanalysis of the electromagnetic condition of a ferromagnetic deviceaccording to the switching angle of the magnetization curve remaincompletely valid in the case of more rigorous equivalent circuits ofthe active part taking into account the relationship of the geometrical dimensions of the magnetic conductor and the windings.

However, the assumptions thus made restrict the scope of theseexpressions. For example, it is impossible to calculate the firing delayangles of the converter without regard to loss for the steadystateconditions of different current capacities of the reactor. One cannotcalculate the MF of the weakly saturated parts of the magnetic circuit and noload currents of the reactor without improved approximation. The answers to these and other questions are separate problemsof further research, whose formulation and solution methods are largely dependent on specific design features, capacity, and applicationof rectifier magneticrectifier controlled reactors.

References (in Russian)

1. Authors Certificate No. 989597 (USSR). The An Electric Reactorwith Magnetization/ A.M. Bryantsev// Otkrytiya. Izobreteniya. , 1983, No. 2.

2. Authors Certificate No. 1061180 (USSR). An Electrical Inductor/A.M. Bryantsev// Otkrytiya. Izobreteniya. . , 1985. No. 24

3. A.M. Bryantsev, E.N. Brodovoy, I.I. Leonov, and S.A. Gordeev. AMethod of Adjusting the Current Waveform of ThreePhase ControllableFerromagnetic Devices. University Proceedings. Electrical Engineeringseries, 1986, No. 6

4. A.A. Bryantsev. Magnetized Ferromagnetic Devices with Extreme Saturation of the Magnetic System Parts. Elektrichestvo, 1986, No. 2.

First published: Electrical engineering, 1991, 2, p. 2428.

32

Electromagnetic Processesin HighPower Controlled Reactors

M.A. Biki, E.N. Brodovoi, A.M. Bryantsev, L.V. Leites,A.I. Lurie, Yu.L. Chizhevsky

Theoretical and experimental studies to develop magneticallycontrolled reactors (CR) have been carried out in Russia and otherseveral decades. The results of these efforts are described in publications by M.S. Libkind, A.M. Bamdas, H. Becker, E.D. Friedlander and others. The interest in shunt CRs has increased dramatically, however, in the last few years for a variety of reasons. Firstly, ascompared with static VAR compensators (SVC) of reactive power,the CRs are less costly per unit of reactive power, their operation issimpler and their production can be quickly mastered by transformer manufacturers. Secondly, new design solutions were proposedincluding those that increased sharply effective inductance, improved winding connections, etc. Finally, there was an increased needfor controllable shunt reactors for the power transmission lines thatare frequently under loaded.

The Moscow Electrical Plant and the Zaporozhye TransformerWorks (ZTZ) started recently to develop 180MVA CRs in thethreephase bank to meet the needs of the electrical power industry. These manufactures adopted the connection circuit of the reactor described in [1]. ZTR separated the operating (power) winding(PW) and control winding (CW)for a 525 kV reactor for a variety ofreasons (high voltage of the power winding, etc.). All the designsmake use of biasing magnetization with strong saturation of parts ofthe magnetic circuit[2].

The publications dedicated to magnetic amplifiers (saturablecore reactors and transducers), for instance [3, 4] described a greatnumber of complicated circuits and conditions had been consideredbut the approach and results set forth below were not found there.The wellknown theory of magnetic amplifiers took into account

33

first of all the electrical of circuit elements, immaterial for ahighpower shunt reactor, and ignored leakage fluxes between thewindings, quite important in this case. An objective of this article isto take the latter factor into account.

A simple and graphic design method [5] is needed for engineering a commercial reactor along with the machine computationthat takes into account not only the primary but also the secondarycircuit and design features. This method should explain the electromagnetic processes in the reactor and help to apply efficiently thedesign methods and software developed for power transformers anduncontrolled reactors.

A piecewiselinear representation of the electric steel responsecan provide sufficiently accurate results for strong saturation. Itallows to estimate quantitatively the extent of biasing magnetizationas a portion of a period of the network frequency, within which theinstantaneous value of the flux exceeds the saturation flux of amagnetized part [6].

The idealized schematic circuit of connection between the windings of two cores of a singlephase CR coincides with one of thecommon circuits of magnetic amplifiers (Fig. 1). There are two

34

Fig. 1. The schematic circuit of a CR with the series connection of PW and CWparts.

PW

CWy

c

cc c

c

c

y yy

y

y

y

closed magnetic conductors each of which is enveloped by a part(half) of each winding and CW. The respective parts are connected in series, one accordant and the other opposite. For example,Fig. 1 demonstrates the accordant connection of the PW parts(which is equivalent in essence to one winding enveloping twocores at once) and the opposite connection of the CW parts. Theelectrical resistances of the windings are very small compared to inductive resistances and the supply voltage of the CW required in thesteadystate mode is low.

Assumptions. 1. There is no loss, i.e., there is no CW voltage inthe steadystate mode (uy 0).

2. The induction curve of the magnetic core steel is piecewiselinear (Fig. 2):

H when B B

H B B when B Bs

s s

0

0( )/(1)

where |H| is the magnetic field strength modulus, 074 10

Henry/m is the magnetic constant; |B| is the magnetic flux densitymodulus in steel; and Bs is the saturation induction of steel; Bs = 2.0 T or 2.1 T.

35

Fig. 2. The adopted approximation of the flux density curve of steel.

3. The yokes of the magnetic conductor are not saturated andtheir magnetic conductivity is infinite in all modes reviewed here( ) .

4. The magnetic induction at all the points of the core steel is thesame prior tosaturation, i.e., the whole core is saturated simultaneously. This assumption is close to reality because the height of thetransformer core and winding is usually much larger than the radius(confirmed by studies of the transformer resistance to short circuits).

5. The flat surfaces of wide unsaturated yokes adjoin the ends ofthe cores and of the concentric equidistant windings of equal heights. It is this assumption including assumptions 3 and 4 that reduces the field problem to the circuit calculation. Certainly, the designed heights of the aperture and windings can differ here from theactual winding heights just like it happens in designing equivalentcircuits of multiwinding transformers [7]. The length of a core assumed in calculating its magnetic resistance can differ from theactual height of the aperture. The intervals between the windingends and yokes and the unevenness of the windings can be takeninto account for calculating the magnetic field in the aperture usingREST [8] or other software. The assumptions 3, 4, and 5 are notrequired for toroidal design with windings evenly distributed overthe circumference.

6. All the parameters of the windings of the two cores pairs andof cores A and X themselves are equal. The cores are magneticallyindependent (there are unsaturated lateral yokes in the case of acommon magnetic system ).

7. The windings are slim. The same area enveloped by the equivalent middle turn of the core winding is included in the calculations of magnetic fluxes and flux linkages. The influence of the finitethickness of the windings is insignificant as a rule. This influencecan be accounted by using the method, given in [9].

The following conditions are introduced below to simplify thedesignations and formulas, to make the narrative and perceptioneasier, and to avoid ambiguity in the description:

36

8. CW is the internal winding and PW is external (Fig. 3). Thearea enveloped by a PW turn (SC ) is equal to the sum of the leakagepath area (Sp) and the area enveloped by a CW turn (Sy ), that isSC y pS S . Refs. [1, 2] consider only a special case when the samewindings are used as PW and CW, i.e., the windings are combined.The combination allows reducing the consumption of materials andloss in comparison with the separate windings but the converterturns out to be under the potential of the power winding middlepoint. In this special case, there is no leakage path between thewindings (Sp 0), the areas enveloped by the PW and CW turns areequal (SC yS ) and the expressions for reactor parameters are simpler than the general formulas derived below. When the PW is located inside near the core and the CW is external, which impossiblein lowpower reactors, the relations can be found in a similarmanner. Some of them are given below but without derivation.

9. The numbers of turns are the same ( )w w wPW CW . The leakage inductance Lp of the winding pair of the core (PW and CW)and the dynamic inductances (L d di / see Section 126 ofGOST 1988074) of the power winding LC and of the controlwinding Ly of the core have the same type of expressions for thesaturated core , which correspond to the absence of the core under

37

Fig. 3. The adopted layout of windings on the CR core.

y

CW PW

p

st

L w S hp p02 / , L w S hc c0

2 / , L w S hy y02 / , (2)

10. assumption 2:And assumption 7 and condition 8 imply that:

L L Lc y p . (3)

When the numbers of the turns are not the same, the currentsand voltages derived below should be reduced to the real number ofturns for the given winding. For example, if it is designated thatw wCW , then current of the CW should be multiplied and the CWvoltage divided by the ratio w wPW CW .

10. The network voltage curve u (on PW terminals) is sinusoidal:

u U tm cos .

Equations. The following relations for the voltages u, currents i,magnetic flux densities B and fluxes can be written using the circuit and designations in Figs. 1 and 3, A and X subscripts for theleft core and right core, respectively, l for the leakage path, p forthe PW and c for the CW:

u u ucA cX c ; i i icA cX c ; u u uyA yX y ; i i iyA yX y ; (4)

B i w h B i w h

B B B i w hA A

A X

p c pX cX

p p p c

0 0

0

/ ; / ;

/ ;(5)

p p p p

c y p cX yX p

A A p p p X

A A

B S B S

;

; ;(6)

u =

u =u +

c c p

c c p

A A yA yA

A X

w ddt

w ddt

u w ddt

w ddt

;

, (7)

which implies for uy 0 (assumption 1):

38

u uyA yX ; u u ucA cX c /2 , (8)

that is the network voltage is divided equally between the powerwindings of the two cores.

The main feature of this paper is the representation of eachmode as an alternation of the following possible conditions of the Aand X cores as follows:

Both cores are unsaturated (B BstA s and B BstX s ) and wedenote this condition below by the subscript 0.

One of the cores is unsaturated while the other is saturated(B BstA s and B BstX s or B BstA s and B BstX s ), that is the relativenumber of saturated cores is 0.5 hence the subscript 0.5.

Both cores are saturated (B BstA s and B BstX s ), which condition is denoted by the subscript 1.0.

If one of these conditions occurs during the whole period of themode under review, such mode is called the characteristic modeand is designated by an appropriate subscript.

Consider these conditions.It follows from the Amperes circuital law for the unsaturated

core A (B BstA s ) under assumption 2 that i w i wC y 0, whence

i ic y , (9)

and for the unsaturated core X (B BstX s ) we have i w i wC y 0, thatis

i ic y . (10)

If both A and X cores are unsaturated, then the only possibilityto comply with equations (9) and (10) is the absence of both currents, that is ic 0 and iy 0. Hence, the currents in the windingscan exist only when at least one of the cores is saturated. The absence of the PW current is associated with the infinite inductanceof this winding, L0 .This condition corresponds to the noloadoperation of the transformer.

39

If one of the cores is saturated and the other is not, the magnetic induction By in the channel between the core and the controlwinding of the unsaturated core is zero and is doubled in the saturated core in the leakage path of this core

Bi w i w

hBy.sat

c yp

0 2 . (11)

The magnetic induction in the steel of the saturated core is greater than By. sat by the steel saturation induction Bs:

B B B B Bs yst. sat . sat s p 2 . (12)

When one of the two cores of the reactor is saturated (subscript0.5), the dynamic inductance of PW ( ).L05 can be determined, forinstance, from the magnetic field energy W for the current ic:

LW

i i

B hS S S

w S Sp y

0 505

2 2

2

02

2 2 4

2 4

,.

( )

c c

p

0p p y2

/ ( ).h L L L L 2 4 2p y c y

(13)

In terms of the magnetic field outside the steel, this conditioncorresponds to a transformer whose secondary winding (CW) isunder inductive load and to a yoke reactor with a subdivided winding two windings with series accordant connection (CW andPW) and ferromagnetic yokes adjoining their ends for the windingsof the saturated core.

When both cores are saturated, a change in the iPC current provokes the same change in the the induction and magnetic fluxes inthe sections of the two coresand, therefore, induced electromotiveforce in the CW circuit is zero, because the CWs of the A and Xcores are opposite. Consequently, the dynamic inductance of thePW provided that all the cores of the reactor are saturated (subscript 1.0) is:

L Ll c, .0 2 (14)

40

Here the ac component of the magnetic field outside the steelcorresponds to a yoke reactor with one winding (PW). The CWcurrent does not change under this condition, i y const. The characteristics of all abovedescribed possible conditions of a reactorare listed in Table 1 below.

Table 1

Possible conditions of the reactor

Relativenumber ofsaturated

cores

r of coresRatio

of currentsDynamicinductanceA X

0 i iC y 0

0.5 1

1i iC yi iC y

2(L LC y )

1.0 1 1 iy const 2LC

Characteristic steadystate modes. If none of the reactor coresare saturated during the whole period , the currents of both windings are zero. This mode can be called the noload mode(NLM) or zero mode (subscript 0). The magnetic induction is zerooutside the steel and sinusoidal inside the steel:

B B t Bm st sin 0, (15)

where B B t Bst m sin 0; B is an arbitrary (based on historydata) value of the average induction during the period within ( )B Bs m besides, the values of the induction B0 in the A and Xcores may differ; and Sst is the steel crosssection in one core.

If each core is saturated during a halfperiod (we denote thismode with the subscript 0.5 calling it the mode of halfperiod saturation), the dynamic inductance of the reactor PW is constantduring the whole period and is equal to L05. . Under these conditi

41

ons, the PW current and induction in the leakage path Bp are sinusoidal. According to (9) and (10) the CW current is equal to thePW current sinusoid modulus i iy PW . According to (11), the induction By in the channel between a core and CW is equal todouble induction in the leakage path ( )B By 2 p during one halfperiod and is zero (By 0) during the other halfperiod. The inductioncurve in the steel of a core is the sinusoid halfwave during onehalfperiod when this core is saturated. It is equal to doubled induction in the leakage path and is shifted from the time line by thesteel saturation induction Bs . The induction is also the sinusoidhalfwave during the other halfperiod. The amplitude of the sinusoid is equal to doubled induction in the leakage path multiplied bythe ratio of the area Sy (enveloped by the middlle turn of the CW)and the area Sst (steel crosssection). This halfwave is shifted fromthe Xaxis by the same saturation induction Bs .

The voltage of each CW of the cores uyA and u yX is sinusoidaland according to (6) with regard to (2), (3) and (13) is equal to

ud

dtddt

u wSdB

dtu wS di

dyAyA

cA A A ( )p c pp c

pc

2 0

tu L u

Lu

L L L

L Lu

L

L L

cp

cc

c y p

c yc

y

c y2 205. ( ). (16)

If both cores are saturated during the whole period, the minimum induction modulus in the steel being equal to the saturationinduction (this mode is denoted by 1.0 and is called as the fullperiod, extreme saturation mode), the dynamic inductance of the PWis equal to L10. during the whole period. Under these conditions, thePW current and leakage path induction are sinusoidal and the CWcurrent is constant and equal to the amplitude of the PW current.The curves of the induction in the channel near a core and of theinduction in core steel are sinusoidal, one of them lying on thetime line and the other being shifted from this line by the saturati

42

on induction value. The voltage of each CW of the core is similar to(16) and is equal to

u u L uL

uL L

Lu

L

LyA

cp

cc

c p

cc

y

2 2 210.. (17)

The amplitude of the PW current I U Lm m10 2. /( ) c is used further as the basis for calculating the currents and for their harmonicanalysis in other modes.

The expressions for currents, inductions in all the paths and inboth cores and for the voltages of the CW parts in the three characteristic modes described above are given in Table 2. Their curvesfor L Ly c/ .0 4, B Bm s/ 0.85, B Bpm m/ 0.125, S Sst y/ 0.5 areshown in Fig. 4 with solid lines. The voltages of the PW parts in allof the modes according to (8) are equal to the voltages of the CWparts in the noload mode as follows:

Table 2

The formulas for the currents, inductions and voltages of the CW partsfor all the characteristic modes of CRs

Parametr Mode

Noloadoperation

(subscript 0)

Halfperiod saturation(subscript)

Fullperiodsaturation

(subscript 1)0 t t 2

Im 0 IUL Lm

m

y0 5 2, [ ( )]

cI

uLmm

1 0 2, ( )

c

ic 0 I tm0 5, sin I tm1 0, sin

iy 0 I tm0 5, sin I tm0 5, sin Im1 0,

B mp 0 B I w hm mp 0 5 0 0 5, , /B

I w hm

m

p 1 0

0 1 0

,

, /

Bp 0 B tmp 0 5, sin B tmp 1 0, sin

B Ay 0 2B tmp 0 5, sin 0 B tmp 1 0 1, (sin )

43

B Xy 0 0 2B tmp 0 5, sin B tmp 1 0 1, (sin )

B AstB tBm

cpA

sin

2B t Bm sp 0 5, sin 2 0 5B

S

S

t B

my

s

p

,

sin

B t

Bm

s

p 1 0

1, (sin

)

B XstB tBm

cpX

sin

2 0 5BS

S

t B

my

s

p ,

sinst

2B t Bm sp 0 5, sin B t

Bm

s

p 1 01

, (sin

)

u uA Xy y U tm cos / 2 U tL L Lm ccos / ( ) y yU tL

Lm cos y

c2

Apparently, the reactor does not generate higher harmoniccomponents of the current (strictly under the above assumptionsand almost ideally in actual reactors) in both halfperiod saturationand fullperiod saturation modes. It was confirmed by modelbasedanalysis and by tests of the highpower reactor described below.

It is advisable, therefore, to choose one of these modes as therated duty. Where the halfperiod saturation mode is selected thesteel is used slightly worse but the loss in the control winding ismuch lower than in fullperiod saturation. This can be seen quitewell in Fig. 4 where the halfperiod saturation mode is marked witha cross. If a power system has several banks of reactors at adjacentsubstations, the control is possible such that all the banks exceptone operate in the noload or rated mode, i.e., they do not generate any harmonics [10]. Under this control, the currents of the harmonic getting into a network are substantially lower than for thecase when all the reactors have the same loads but the overall loss isslightly higher.

A further increase in the CW current of the reactor above Im1(extreme saturation) does not affect the PW current and the accomponents of inductions and voltages. As the CW current grows,the loss in the CW increases as do the forces of the network frequency, which cause noise and vibration (usual forces have doublenetwork frequency).

44

Intermediate steadystate modes. It is convenient to characterizethe modes by the K

/ factor, where, according to [6], is halfthe duration of the saturated state of the core in radians within oneperiod, that is K

is the relative portion of the period, during whicheach core is saturated. The value of K

0 corresponds to thenoload mode, K

0 5. to the halfperiod saturation mode andK

10. to the fullperiod saturation mode.If each core is saturated less than for half the period (K

0 5. ),the process goes on according to the noload curves in Fig. 4during the portion of the period ( )1 2 K

. If 1 is the moment of saturation of the A core with

1 0 5 ( . )K , these are parts of tfrom 0 to 1, from ( ) 1 to ( ) 1 , from ( )2 1 to ( )2 1 andso on. The process follows the halfperiod saturation curves in

45

Fig. 4. The curves of the currents, magnetic inductions and voltages of the CWparts under the noload (0), halfperiod (0.5) and fullperiod (1) saturation (solidlines) and when the A core is saturated at the moments 1 (dash line) and 2 2 (dashanddot line).

Fig. 4 in the parts from 1 to ( ) 1 and from ( ) 1 to ( )2 1 (during the 2K

period portion), , the curves of currents and inductions beingshifted vertically so that there are no steps at the moments 1, ( ) 1 and so on (dash lines in Fig. 4). The angles 1and are related through the formula ( . )0 5 1 . For thehalfperiod saturation 1 0 and in the noload mode 1 2 / .

When each core is saturated longer than half the period( . )K

0 5 , the process follows the maximum (fullperiod) saturationcurves in Fig. 4 during the portion of the period ( )2 1K

. These arethe parts from 0 to 2, from ( ) 2 to ( ) 2 and from ( )2 2 to2, where 2 is the moment of withdrawal of the X core from thesaturated state and of the transition from saturation of both cores tothe saturation of only A core, where

2 ( )K . The processfollows the curves of halfperiod saturation in Fig. 4 during the restof the period (the parts from 2 to ( ) 2 and from ( ) 2 to( )2 2 , the current and induction curves being shifted verticallyso that there are no steps at the moments 2, ( ) 2 and so on(dashanddot lines in Fig. 4). The angles 2 and are relatedthrough the formula ( . )0 5 2 . For the halfperiod saturation2 0 and in the noload mode 2 2 / .

The expressions for voltages, currents and inductions derivedabove in the form of piecewise sinusoidal curves allow to determinethe parameters of the modes in the range from noload to fullperiod saturation.

In particular, the following expressions were obtained in [10]for the amplitudes of harmonic components of the winding currents:

I I K Hnm m L n 10 1.*( ) ( ) when / ,2 K

/ . ;0 5 (18)

I I H K Hnm m n L n 10.* *( ) ( ) when / ,2 K

0 5. , (19)

where n 0, 1, 2, is the number of the current harmonic component, n 0 is a constant component, n 1 is the main component;

46

Im1.0 is the amplitude of the PW current in the fullperiod saturation; KL is a factor that characterizes the position of the windings

and their spacing; K L L L LL c y c y ( )/( ) ; Hn*( ) and H * ( )

is the relative harmonic current when the windings are combined(Lp 0 and KL 0) for the argument ! equal to and ( ) , , respectively, according to [2], the relative currents (magnetic fieldstrengths) being defined as:

H0* (sin cos )/ ; ! ! ! (20)

H1 2* ( sin )/ ; ! ! (21)

Hpn

n jn

n jnn2 3

1 11

11, ,...,

* sin( ) sin( )

"

#

$

%

&

'

. (22)

The examples of the dependence of the current harmonic components on K

and KL are given in Fig. 5 and the dependence of I1on I0 is shown in Fig. 6.

Formulas (18) to (22) and the curves in Fig. 5 pertain to the netcurrents (by MMF and by ampere turns) of all core windings (PW,CW and an additional winding if any). The odd harmonic components of the current flow in the PW and even and null harmonicsflow in the CW. If the internal CW is connected into the delta in athreephase reactor or in a threephase bank of reactors, the currents of odd harmonics with the numbers multiple of three will flowin this winding instead of the PW.

When the CW is internal and the PW is external, we haveL Ly c and 0 1 KL and when the windings are opposite, L Ly cand 1 0KL . For halfperiod saturation (K 0.5) and when thewindings are combined (L Ly c , KL 0), the PW current is exactlyhalf the current in the fullperiod saturation and is greater then thehalf when the PW is external and is less than the half, when it is internal.

47

The K

factor was chosen in Fig. 5 and the average CW current(constant component) in Fig. 6 as the mode characterizing arguments. These relationships are universal for all the CR types underreview. It can be seen in Fig. 6 that the current consumed by a reactor from the network is almost exactly proportional to the constant component of the current in the range from noload operationto the halfperiod saturation mode while further the relationship isnonlinear.

The input impedance and loss of the reactor. The input impedance of the reactor for the fundamental harmonic is:

z U I U I I Im m m m m m1 1 10 1 10 ( / )/( / ),, ,

where I Im m1 10/ , is the parameter from Fig. 5 or 6. In particular, inthe of halfperiod and fullperiod saturation modes:

48

Fig. 5. The examples of the relationship of the constant component of the currentI0 and of the amplitudes of the 1st, 2nd, 3d, and 5th harmonic components andK

/ for combined windings (L Ly c , KL 0 shown by solid lines),for the external PW (L Ly c04. , KL 0,43 shown by dash lines) and for the internal PW(L Ly c2 , KL 0,33 shown by dashanddot lines).

z x L Lc y1 0 5 0 5 2, , , ( ) (

and

z x Lc110 10 2, , , . (

The noload current specified in Table 2 is shown to be zero,which corresponds to the idealized characteristic of the steel(Fig. 2). The actual noload current and loss of the reactor can befound using the calculation method for the noload mode of ordinary highpower transformers because fluxes in the reactor coresare sinusoidal in this mode. In other modes, the iron loss has thesame order of magnitude as in the noload mode.

The iron loss in the mode of fullperiod saturation are invariably less than that in the noload mode because the ac componentof the magnetic induction in the cores is several times less than innoload mode (Fig. 4).

The reactor loss caused by winding currents (load loss) can becalculated by the methods used in the transformer industry. In

49

Fig. 6. The examples of the relationships of I m1 and of the distortion current Idist5(beginning from the 5th harmonic component) and I0 (see the designations inFig. 5).

particular, major losses in halfperiod and fullperiod saturationare, respectively:

I r r w wm CO OY CO OY0 52 2 2 2

,( / )/

and

I r r w wm CO OY CO OY102 2 22 2

,( / )/ ,

where r rPW CO( ) and r rCW OY( ) are the dc resistances of the PW andCW of the reactor phase and w wPW CO( ) and w wCW OY( ) are thenumbers of turns of the PW and CW.

An additional loss in the halfperiod saturation mode is equal tothe halfsum of the losses from two calculations including the casewhen the MMFs of the PW and CW are accordant (the half periodin the saturated core) and opposite (the core is unsaturated). Additional loss in the fullperiod saturation mode are caused by theMMF of the PW only because there is no ac component in theCW. The loss in intermediate modes can be determined approximately using quadratic interpolation of the losses in the characteristicmodes.

The total loss in a highpower reactor is below its rated capacityby two or three orders of magnitude. Therefore, it practically doesnot affect the input impedance of the reactor.

Transients. The transients in the CR can be calculated approximately using the above relationships based on the listed assumptions . The most interesting and practically important is powerpickup and shedding by the reactor.

Suppose constant voltage is applied stepwise to the control winding in the power pickup mode (forcing). If the reactor operatedin the minimum power mode before that (null or noload mode),the transient consists in the winding currents appearing and increasing, and in the successive transition of the reactor into the halfperiod saturation (0.5) and fullperiod saturation mode (1.0). Thetime needed to achieve the modes 0.5 and 1.0 can be estimated byformulas:

50

t TUw

U wBB

T BB

Q

KQy

y c

s

m

s

m0 5 444 444, , ,

p

; (23)

t t BB

S

Sm

s

y

c10 0 5 1, , ( (

. (24)

The times t0 5, and t10, include a nocurrent pause

t t B BB

s m

s10 0 5, ,

,

where T f1/ is the voltage period of frequencyf f Hz T( , . sec) 50 0 02 ; Uy is the constant CW voltage; U is the

rms network voltage, U Um / 2; Qp is the power of the reactor;

Qnp is the capacity of the control system converter; and K is the relative factor whose value depends on how the capacity of the converter is defined.

The first version of formula (23) can be usedto calculate theresponse speed of the reactors and the second version to compareapproximately the reactors response speed with the relative capacity of the control system (for instance, ifKQ Q t p )003 01505. . sec. ).

Formulas (23) and (24) are convenient for estimating the CRresponse speed because the 0.5 mode is usually close to the ratedduty, and the 1.0 mode to the extreme load mode. They can be alsoused to estimate power shedding time (unforcing). In addition,quite simple estimates can be obtained for the case of intermittentCW voltage (i.e., taking into account voltage drop in the converternetwork).

Pilot reactor. The abovedescribed approach makes it possible toapply methods and design programs intended for ordinary powertransformers and reactors operating with sinusoidal currents andvoltages to designing a highpower CR for which halfperiod saturation is the rated duty. In particular, additional loss caused by

51

eddy currents in magnetically transparent parts winding wiresand small structural elements (also approximately in the massive structural elements) is equal to the halfsum of loss caused bythe magnetic field of the sinusoidal currents of the winding on thesaturated core (opposite MMFs, transformer mode), and by thefield of the windings on the saturated core (accordant MMFs, reactor mode). It increases significantly the reliability of the calculations and allows to build highpower reactors without largescalephysical modelling. The manufacturing process of the CR differslittle from that for generalpurpose power transformers by process.

In 1991, ZTZ made a model (actually a pilot) of a singlephase500kV shunt CR designated RODTsU60000/500U1 for operationin a threephase 180 MV(A bank. Its rated parameters were as fol

lows: (1) voltage: 525/ 3 kV, (2) power: 60 MVA, (3) frequency:50 Hz, (4) regulation range at the rated voltage: 1 % to 140 % ofrated power (maximum power being proportional to square voltagefor different voltage rating ), (5) power rate of change: 180 MV(A/sper phase, (6) total weight: 153 tons, (7) copper weight: 13 tons, (8)steel weight: 70 tons, (9) rated loss: 440 kW, (10) noload loss:60 kW, (11) threephase power winding connection: Y, and (12)control winding connection: *.

The power winding of the reactor has the middle input in the Hconnection, i.e., it has four parallel branches. To avoid high voltages between adjacent parallel branches in case of accidental closureof all valves, these branches are transposed several times. A thyristor converter is used for regulating the dc component of the CW. Itis supplied through an auxiliary transformer from the same CW.The converter operates like a rectifier when the reactor picks uppower or when its power remains constant, and like an inverterwhen the reactor power is shedded. The capacity of the converterin a continuous duty equals only the loss in the control winding,i.e., it amounts to several tenths of percent of the CR rated power.The capacity of the converter is 2 % or 3 % for forcing that ensurea response speed of 0.3 to 0.5 sec. When the branches are provided

52

from 2 % or 3 % of the CW turns, the auxiliary transformer is notrequired. The magnetic conductor of the CR is shellcore with twocores and two lateral yokes.

As opposed to ordinary shellcore transformers, the direction ofthe ac magnetic fluxes of the two cores was chosen to be accordantto reduce the crosssection of the lateral yokes and to make possible closure of the dc component of the flux constant by relativelyshort end yokes. The magnetic leakage flux is closed by magneticshunts at the ends of the windings, which are made in the form ofwound split rings. According to calculations, the rated duty practically coincides with the halfperiod saturation mode.

The loss, weight, and dimensions of the CR are approximatelythe same as those of a doublewound transformer of respective capacity and voltage with an OLTC device.

Tests carried out by the manufacturer and at the Belyi RastSubstation have confirmed the operability of the reactor and haveproved the acceptable accuracy of the abovedescribed method forthe analysis of electromagnetic processes and of expressions derivedfor calculations of the key characteristics of the reactor. Standardtests (GOST 348488, GOST 1167785, and GOST 1946974),noise measurements in noload and shortcircuit tests, thermal testsin the nearrated duty, an analysis of the PW current harmoniccomposition, and power pickup and shedding time measurementswere carried out. The results of the measurements given below werecompared with the data obtained by calculation using the aboveformulas and computer methods, which take into account more accurately, among others, the nonlinearity of the steel magnetizationcurve [11, 12].

The halfperiod saturation current of the reactor calculated byformulas (3) and (13) was 203 A for the rated dimensions of themagnetic conductor and windings. The PW current was sinusoidalin this mode under the assumptions used in the article. Accordingto a more accurate calculation on a computer allowing for asmooth inflection of the steel magnetization curve [13], the third

53

harmonic component of the singlephase reactor current was 1.1 %of the first harmonic component, the fifth harmonic componentwas 0.28 %, the seventh harmonic component was 0.22 %, theninth harmonic component was 0.11 % and the eleventh harmoniccomponent was 0.07 %. The calculated distortion current

I I Idist ( ...) . %.

32

52 05 12 . The test results have shown, that

halfperiod saturation occurs when the current is 213 A (which is5 % higher than the calculated current and 7 % higher than therated current). The currents of these harmonics measured with anonlinear distortion meter were 0.6, 0.26, 0.22, 0.18, and 0.08 %,respectively, and the distortion current was 0.75 %, which is substantially less than that calculated according to [1113].

The measured time of transition from noload to the rated dutywas 0.28 sec, the calculations by the method of [11] yielded0.29 sec and the estimate by approximate formula (24) 0.3 sec. Theresults seem to be very encouraging for the introduction of controlled shunt reactors of this type.

Tentative calculations have demonstrated the possibility of developing 750kV and 1150kV controlled shunt reactors.

References

1. A.M. Bryantsev. A Magnetic Thyristor Reactive Power Regulator. Elektrotekhnika, 1984, No. 10. Elektrotekhnika (In Russian).2. A.M. Bryantsev. Magnetized Ferromagnetic Devices with Extreme saturationof Parts of the Magnetic System. Elektrichestvo, 1986, No. 2.(In Russian).3. H. Storm. Magnetic Amplifiers. M.: Foreign Literature Publishers, 1957.(In Russian).4. M.A. Rosenblat. Magnetic Amplifiers, 3d ed. M.: Sov. Radio, 1960.5. Electromagnetic Process in HighPower Controlled Reactors / M.A. Biki,E.N. Brodovoi, A.M. Bryantsev et all. ISEF91. International Symposium onElectromagnetic Fields in Electrical Engineering. Sept. 1820, 1991, Southampton University, England. Warszawa: Instytut Elektrotechniki, 1991.6. H. Becker, D. Brandes, . . ThreePhase Shunt Reactors with Continuously Controlled Reactive Current CIGRE. Pap. 3113. Paris. 1972.

54

7. L.V. Leites. Electromagnetic Calculations of Tranformers and Reactors. M.: Energiya, 1981. (In Russian).8. M.P. Saveliev, A.N. Panibratets. Calculations of the Electrodynamic Resistance of Transformers on a Minsk32 Computer. Elektrotekhnika, 1978, No. 4.9. N.A. Blavatskaya, L.V. Leites. Use of MagnaticCircuit Diagrams to Calculatethe WeberAmpere Characteristics of Reactors. Elektrotekhnika, 1985, No. 5.(In Russian).10. A.M. Bryantsev. MagneticRectifier Controlled Reactors with Extreme Saturation of the Magnetic Circuit (Theory fundamentals, Implementation Principles,studies, Examples of Manufacture). Doctoral Thesis. AlmaAta, 1992. (In Russian).11. G.A. Evdokunin, E.V. Korshunov, E.A. Sepping, Y.Y. Yarvik. A ComputerAided Calculation Method for Electromagnetic Transients in FerromagneticDevices with an Arbitrary Structure of the Magnetic and Electrical Circuit. Elektrotekhnika, 1991, No. 2.12. E.V. Korshunov, V.A. Krasnopivtsev. Static and Dynamic Characteristics of a500kV Controlled Reactor. Elektrotekhnika, 1991, No. 2.13. A.M. Bryantsev, E.N. Brodovoi. Approximation of the Main MagnetizationCurve of Strongly Saturated Ferromagnetic Devices. University Proceedings. Energetika, 1985, No. 4.

First published: Electricity, 1991, 6, p. 110.

55

Shunting Reactors Controlled by BIASMagnetization for (35500)kV Grids

A.M. Bryantsev, E.E. Makletsova, A. G. Dolgopolov,A.I. Lurie, G. A. Evdokunin, Yu. A. Lipatov

A group consisting of the Zaporozhtransformator Joint StockCompany, the Ramenskii Elektrotekhnicheskii Zavod EnergiyaJoint Stock Company, the Elektricheskie Upravlyaemye ReaktoryJoint Stock Company, and the V.I. Lenin AllRussian ElectricalEngineering Institute has developed a series of highvoltagecontrollable reactors for (35500)kV grids. Analysis of the characteristics and functional capabilities of these reactors by Russian,Mexican, Chinese, Brazilian, Indian, and other specialists showsthat shunting reactors controlled by bias magnetization provide aunique combination of voltage stabilization, reduced losses, and increased operational reliability in extended transmission lines andgrids. Such reactors cost practically half as much as units with analogous capabilities and earn back their costs in 1.52 years.

The use of such controllable reactors in place of reactors thatare uncontrollable or stepwise controllable is especially expedient ingrids with a variable load graph. Together with capacitor batteries,control