cigreonhalfcyclesat.pdf

8/14/2019 CigreonhalfCycleSat.pdf

1/11

(*) [email protected]

Behaviour of transformers under DC/GIC excitation: Phenomenon, Impact on

design/design evaluation process and Modelling aspects in support of Design

T. NGNEGUEU*, F. MARKETOS, F.

DEVAUX

Alstom Grid

France

T. XU, R. BARDSLEY, S. BARKERAlstom Grid

UK

J. BALDAUF, J. OLIVEIRA

Alstom Grid

Brazil

SUMMARY

Power transformers are one of the most strategic equipment in the power system. Though theyare generally designed for operation under sinusoidal waves (including the harmonics), in reality, they

may be subjected to superimposed DC currents excitation with varying levels which may reach up to

few hundreds amps. These DC currents may be of external origin as GIC or HVDC ground returnmode stray currents. They may also have an internal origin, being directly linked to the use of power

electronic convertors under certain non-ideal conditions (eg. SVC transformers, HVDC transformers).

Depending on their magnitude, the DC bias currents may have a detrimental effect on theintegrity of the power transformers or their long term performance, meaning to affect the powersystem reliability. With this respect, users specifications relating to concern with superimposed DC

excitations are generally clear enough regarding expected levels and possible durations. On the otherside, a good understanding of the behaviour of power transformers or shunt reactors under combined

AC and DC excitations as well as comprehensive modelling tools are essential to enable the design of

power transformers which fit these requirements.In this paper, further to explaining the half cycle saturation effect resulting from combined AC

and DC excitations of magnetic cores, measurements on model transformers are used to illustrate this

effect. Then different aspects of numerical modelling of the phenomenon are presented withapplication to the design and design verification of a 550 MVA autotransformer prone to GIC, with

analysis performed for the no load and for the on load conditions, taking into account the load power

factor and varying levels of the DC current as appearing in the specifications. Additionally, more

specific aspects of behaviours of convertors and HVDC transformers, relating to DC bias current andrelated numerical models are addressed.

KEYWORDS

Power Transformers, DC Bias Current, DC Current Excitation, GIC, Convertor Transformers, HVDC

Transformers, Design Review, Numerical Modelling.

21, rue dArtois, F-75008 PARIS A2-303 CIGRE 2012http : //www.cigre.org


2/11

1

1) INTRODUCTION

It is common practice to design Power transformers to operate under sinusoidal conditions.

However, in reality, some power transformers need to be able to maintain normal operation under

increasingly complex excitation waveforms with the most common case being that of DC currentsbeing superimposed on the normal AC excitation. Shunt reactors operating in the electric network

might be subjected to DC currents in their windings during AC excitation. Moreover, in thyristorconverter applications such as rectifier transformers for electrolysis as well as the transformersassociated with Static Var Compensators (SVC), the transformer windings may experience a DC load

current as a result of an imbalance in the thyristor valves switching. More commonly HVDC converter

transformers are subjected to DC currents in their windings. Most importantly power transformersoperating in auroral regions such as Canada, North America as well as Scandinavia, are prone toGeomagnetically Induced Currents (GIC) flowing in the ground due to magnetic disturbances in the

upper atmosphere [1], [2], [3].Users located in areas where GIC may occur, often specify that the transformers or shunts

reactors shall be able to withstand the DC currents, superimposed to the rated AC current, in thewindings without damage or excessive hot spot temperature rise. The currents are specified in absolutenumerical values by the user and may be as high as 100A having a duration that varies from a few

seconds to several minutes.

The capability of the transformers or shunt reactors to withstand the DC currents is normallydemonstrated in the Design Review. This contribution paper employs measurements on modeltransformers in order to illustrate aspects of the behaviour of power transformers or shunt reactors

cores under combined AC and DC excitation.In the case of HVDC converter transformers, a DC current in the line neutral is often referred

to, especially in Ground Return Mode (GRM). However DC current can also exist in the valvewindings and the sources of this DC current are discussed together with an example of a simulationstudy.

Moreover, main requests in user specifications, related to transformers/shunt reactors prone to

combined DC/AC excitation are presented and the impact on design/design verification process isdiscussed.Numerical modelling techniques are shown, supporting the design verification process, inorder to mitigate the problems caused by the combined AC and DC excitations.

2) PHENOMENON

Geomagnetic storms are associated with solar coronal mass injections, or solar flares. They are

caused by increased solar activity or solar wind shock waves which interact with and createdisturbances to the Earths magnetic field. These magnetic disturbances culminate during solar storm

cycles, which tend to peak at 11 year intervals; the next peak is expected sometime during 2012-2013.The magnetic disturbances create large variations in the electric currents in the Earths magnetosphereand ionosphere which in turn induce currents, GIC, in conductors on the surface of the Earth. The

GICs flow in the east-west direction and can give rise to quasi-DC winding currents, through the

transformer grounding points, with recorded values in the order of 100 A in the neutral winding withsometime devastating results.

Superimposed DC excitation can affect the normal operation of power transformers in morethan one way. The transformer can experience very high values of magnetising current during the half-

cycle saturation leading to overheating of the windings, high winding losses and possible damage towinding insulation. Experiments carried out in an Epstein frame demonstrated this half-cycle

saturation phenomenon, Fig. 2-1, [4].There is a significant increase of the leakage flux during the half cycle saturation with more

flux leaking onto other parts of the transformer such as the windings, leads, clamps and tank, causing

more local eddy currents with possible result as localised hot spots that could affect the oilproperties over the long term, thus accelerating ageing and reducing its normal life expectancy.

Moreover the transformer will draw large amounts of reactive power causing high stress onthe already overloaded network. Superimposed DC excitation will also cause the transformer to inject


3/11

2

larger amounts of odd and even harmonics into the system thus affecting the normal operation ofprotective relays [5].

3) MEASUREMENTS ON MODEL TO ILLUSTRATE MEAN ASPECTS OF COMBINED ACAND DC MAGNETISATION OF POWER TRANSFORMERS

Experimental results are presented to illustrate the behaviour of power transformers or shuntreactors under combined AC and DC excitations [2],[6]. These results are based on a model 3 phase,three limbs distribution transformer(Fig. 3-1) with nameplate as: 30kVA, 230V/230V, Dyn. The ynconnected side of the model transformer is used for the injection of the DC currents whereas the Dconnected side is used for the AC supply. For varying levels of DC current, the RMS values of theexcitation currents from the AC source are compared for the single phase supply and the three phasesupply (Fig. 3-2).

Fig 3-1: View of a model 3 phase, 3 limbs distributiontransformer 30kVA, 230V/230V, Dyn used in the tests

Fig 3-2: RMS values of AC excitation currents for varyingDC current levels for single phase and three phase AC supply

Sensitivity to GIC currents or to significant stray DC currents that may inter the transformerfrom the grounding points (Yn connected winding) is strongly dependant on the core type. The singlephase core structures are very sensitive, requiring few DC amps to be driven into saturation.Regarding the three phase transformers, the core structures in which the zero phase sequence flux caneasily flow are more sensitive (shell type cores, core type five limbs cores) as compared to the threephase three limbs core type transformers which are less sensitive.

When the DC current is entering the three phase transformer from a line phase (eg. SVCconnected transformers), previous classification of core structures regarding sensitivity to DCexcitation may have to be revised. This is so as, compared to GIC or to GRM currents, the DCexcitation current is not evenly shared by the transformer three phases. With this respect, all thetransformer core structures will tend to be very sensitive to the DC current excitation. Behaviour of

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 0.004 0.008 0.012 0.016 0.02

time (s)

Fluxdensity

(T)

AC

AC+DC

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

-100 0 100 200 300

Magnetic field (A/m)

Fluxdensity

(T)

AC

AC+DC

Fig.2-1: Effect of superimposed DC excitation and

AC excitation on the flux density and magnetic

field of electrical steel. Top left: flux density under

pure AC excitation (red curve) and under AC+DCexcitation (black curve). Top right: BH-loop of the

steel magnetized under pure AC excitation (redcurve) and under AC+DC excitation (black curve).Bottom right: Magnetic field under pure AC

excitation (red curve) and under AC+DC excitation

(black curve).

0

0.004

0.008

0.012

0.016

0.02

-100 0 100 200 300

Magnetic field (A/m)

time(s)

AC+DC

AC


4/11

3

convertor transformers relating to DC current excitation is also more specifically dealt with in Section6 of this contribution paper.

Concluding, Fig 3-3 and Fig 3-4 display the wave shapes and harmonic content of theexcitation currents obtained for the single phase test as reported in Fig 3-2. Whereas the normal ACexcitation current is weak and its spectrum containing only the odd harmonics, depending on the levelof the injected DC current, the magnitude of the excitation current driven from the AC source is up to30 time the previous (Fig 3-3), with the spectrum containing a large amount of both the even and theodd harmonics (Fig 3-4).

Single Phase AC/DC Excitation of a Model 3 phase Distribution Transformer 30kVA, 230V/230V, Dyn (Ref. Fig.3-1)

Fig 3-3: Waves of excitation currents from the AC source(single phase supply) for varying levels of DC excitation

Fig 3-4: Spectrum of excitation currents from the AC source(single phase supply) for varying levels of DC excitation

4) SPECIFICATIONS AND IMPACT ON DESIGN/DESIGN EVALUATION PROCESS

Susceptibility to geomagnetically induced currents or significant stray DC currents as groundreturn mode (GRM) DC currents may impact the substation design. Some utilities have experimented

use of Neutral DC Current Blocking Devices to limit the harmful effect of these currents [7].

More generally, users located in areas where geomagnetically induced currents (GIC) mayoccur often specify that the transformer or shunt reactor shall be able to withstand those DC currents,

superimposed to the rated AC current in the windings, without damage or excessive hot spot

temperature rises. The DC currents are usually specified with levels which may be as high as 100 Aand duration that varies from seconds to several minutes.

This capability of the transformers or shunt reactors to withstand the DC currents needs to be

demonstrated in the Design Review, often with the aid of numerical modelling tools. One example,

shown in this paper, is the project of the two three phase, five limbs, autotransformers of 550 MVArating each, magnetised at 60 Hz, installed in substations near the city of New York.

The customer specification document indicated that geomagnetically induced currents had

previously impacted various transformers in their system and as a result they requested that: Thetransformer manufacturer shall review the design of the autotransformers and demonstrate an

understanding of the GIC effects, including appropriate modelling to simulate their impact on thetransformer operation. The capability of the autotransformers to withstand stray DC currents and/orgeomagnetically induced currents without damage or excessive hot spot temperature rise shall be

analysed by the manufacturer and demonstrated through the appropriate use of finite element or othernumerical calculation techniques. In addition, the customer requested curves showing DC current

versus time for two different hot spot values to be included in the analysis.The same concerns are also valid for shunt reactors operating in auroral regions and one

specification indicated that: The manufacturer shall present information regarding the capability ofthe shunt reactor to withstand GICs. The information shall include estimated flux, time constants and

resulting temperatures at critical locations in the magnetic circuit and other structural components at

DC current levels of 50, 100 and 200 A , for a five minutes duration in the wye-connected windings.To demonstrate the capability of the autotransformer to withstand GIC and define the

maximum allowed DC current as a function of temperature, an EMTP as well as 2D and 3D finite

element analysis software were used to check and calculate the following parameters:- Variation in the transformer core excitation current- Evaluation of the transformer core saturation- Variation of the transformer no load losses


5/11

4

- Assessment of the on load condition, taking into account the specified load power factor- Estimation of stray losses in the transformer windings- Estimation of stray losses in the leads- Estimation of stray losses in the clamping plates and in the flitch plates of the core- Estimation of stray losses in the tank

The above investigations resulted in some particularities in the transformer design in order to

avoid potential hot spots developing as a result of GICs or significant magnitude of stray DC currents.

These particularities in the design were as:- The use of continuously transposed cable (CTC) in order to cope with potentially high

circulating currents that might result as consequence of core half-cycle saturation, whilemaintaining low eddy current losses and thus suppressing the potential generation of hot spots

- Tank magnetic shunts with increased thickness to channel the leakage flux in excess in orderto minimize the tank losses and the potential for significant hot spot. Also, special materialwas used in some structural parts of the core to enhance thermal performance.

To mention that, though the mechanism of DC current flowing into convertor transformers

may be different and the magnitudes of the DC currents resulting from thyristors firing anglesunbalance usually specified with lower levels (some tens of Amps), the evaluation methodology of the

impact on the transformers can use similar numerical processes as applied for transformers and shuntreactors prone to GIC or significant stray DC currents (GRM DC currents). Convertors and HVDC

transformers are more specifically and complementarily addressed in section 6 of this paper.

5) NUMERICAL MODELS TO SUPPORT DESIGN/ DESIGN REVIEWS

The levels of the DC currents originating from different causes as discussed in the previoussections can be many times larger than the normal excitation current. Experience suggests that, when a

DC source is superimposed, the AC magnetic flux will oscillate around a value much lower than

would be expected by considering the DC current alone; the magnetic flux adjusting itself such that,the magnetizing current has a DC component equal to the DC current considered [8]. Hence, theexcitation current driven from the AC supply is not easily derived from the principle diagram as

illustrated in Fig. 2-1.In order to support the design choices, different approaches can be applied to estimate the

excitation current driven from the AC supply when a DC source is superimposed. Subsequently, thecurrents under load conditions can be derived. It is thus possible to evaluate the harmonic content of

the currents; the core, the windings, the connection leads and the structural parts losses for varying DCcurrent levels under no load condition and on load condition. These mean for each load condition, thetemperature rise of each transformer component as function of the DC current level and over all, the

transformer withstand duration as function of DC current level.For the determination of the excitation current driven from the AC source and impact on

design, it is usually resorted to approaches as empirical, electric network analysis based, FEA based orcombination (of these approaches).

- Empirical estimation of the no load excitation current

Experience as illustrated by Fig. 3-2 suggests that, under combined AC and DC

magnetization, the RMS value of the excitation current driven from the AC source could be linked tothe DC current level by a linear relationship based on available experimental data. This could give

initial calculations basis, though information on harmonics magnitudes and phases would be missingto further assess a transformer design.

- No load excitation current estimate based on electric network analysis

The no load excitation current driven from the AC source and subsequently, the currents forthe load condition can be determined based on the classical single phase T equivalent electric circuit of

the transformer as in Fig.5-1 where, referring to the primary winding, N p is the number of turns, Rpisthe winding resistance, Lp is the inductance component due to the flux path out of the core (the leakage


6/11

5

inductance in no load condition). Rm is the resistance representing the core losses and Lm is the coremagnetizing inductance (due to the flux path in the core). The core magnetizing inductance Lm seen

from the primary winding is associated with the core flux saturation characteristic as in Fig.5-2. Forthe no load condition seen from the primary side, the electric parameters of the secondary side are notused.

Fig.5-1: T Equivalent circuit for the no load

condition

Fig.5-2: Core saturation

characteristic

Fig.5-3: Core simplified

saturation characteristic

- Analytical solution of the transformer equivalent electric network

With simplifications, the transformer equivalent electric circuit in Fig.5-1 can be solvedanalytically. Such a solution was developed in [8] [9]. In particular, if the core saturation characteristic

(Fig.5-2) is approximated by the asymptotical one (Fig.5-3) where the core permeability is infinite

before saturation, meaning that, the excitation current is approximated to zero if the core is notsaturated, the solution is made even easier. With the AC voltage defined by equation (1) in Table 5-1,

one has (2) and (3) where wis the radian frequency, is the total flux seen from the primary winding,

integrating the number of turns (as is also the case in the saturation characteristics in Fig.5-2 and

Fig.5-3). With reference to the flux wave, the core is saturated during an angle 2 defined by

+ wt

and (4), giving equation (5). The total flux seen from the primary winding is also linked

to the excitation current from the AC source by equation (6) according to Fig.5-1 and Fig.5-3. With (2)

and (6), the excitation current is then identified as (7) with (8). As the average of the excitation currentover a time period is also the DC current, one has (9).

Table 5-1: Simplified Analytical Model Of The AC Excitation Current Under DC Magnetization

Equation N Equation N Equation N

dt

dwtVtv

AC

== )sin(.2)(

(1)DCMaxAC wtt += )cos()( _ (2)

w

VMaxAC

2_ =

(3)

Sat =+= )()(

(4)DCMaxACSat += )cos(_

(5) )().()( tiLLt SatPSat ++=

(6)

)]cos()cos(.[)( += wtAti

+ wt

(7)

wLL

VA

SatP )(

2

+=

(8) )]cos(.).[sin(

=A

IDC (9)

)(tvAC

Fig

10

)(t

Fig

11

)(ti Fig

12

Total inductance Lp+Lsat can be associated to the excited winding air core inductance Lair.

From the levels of the AC and DC sources, the saturation angle 2value can be determined by

solving (9) and subsequently the excitation current wave can be determined. Expression (5) suggests

that the flux DC component adjusts depending both on the source voltage and the DC current levels.The simplified analytical development as presented has limitation that, it is not accounted for the

lower magnitudes of combined AC and DC flux not resulting in full core saturation, without moretedious algebra. Resorting to network analysis packages can offer more flexibility.

- Computer solution of the transformer electric network for no load condition

The transformer equivalent circuit in Fig.5-1, can more completely and flexibly be solvedusing the EMTP (Electro Magnetic Transient Program) like electric network analysis tools which have


7/11

6

gained popularity in the academic institutions and in the industries. In that case, the core saturationcharacteristic (Fig.5-2) which could comprise hysteresis but is not needed here, can be assigned.

Fig.5-4 and Fig.5-5 show an example of application on a 3 phase, 5 limbs autotransformerrating 550 MVA, 230kV/138kV, 60 Hz. The ATP/EMTP program is used to determine the excitationcurrent driven from the AC source when the autotransformer is submitted to a GIC current of

magnitude 50A (16.66 A x 3). It is thus possible to characterize the transformer windings and

structural parts losses, meaning the heating for the no load condition. With allowance for the core

losses, withstand duration vs DC current level can be plot.

550MVA, 230kV/138kV, 60 Hz, 3 Phase AT. Excitation Current From The AC Source Under GIC 50A (16.66 A x 3)

Fig.5-4: Excitation current from the AC Source

Fig.5-5: Spectrum of excitation current from the AC source

- Currents in on load condition, taking into account the load power factor [cos(); sin()]

The EMTPs can be used to derive the excitation and the load currents waves for varying loadpower factors. An analytical approach can also be resorted to. The transformer equivalent electric

circuit is adapted for the on load condition as in Fig.5-6 where, im is the magnetizing excitation currentas determined in previous sections, ipis the total current from the AC source, Rscand Lscare the short-

circuit parameters referred to the load side, iLoadis the current in the load. Hence, taking into accountthe load power factor and the transformer short-circuit parameters, primary and load sides current

waves can easily be constituted. Fig.5-7 shows example of current waves obtained for the previous

autotransformer, under the nominal voltage, a GIC magnitude 100A(3x33.7A) and an inductive loadwith power factor 0.8, which is the most usual load characteristic specified for network transformers.

Fig.5-6: T Equivalent circuit for on load condition Fig.5-7: On load currents with PF 0.8, under GIC 100A

Single phase representation has not accounted for the core technology. However, regarding

impact of DC excitation, single phase representation of the core results is the most pessimistic effects.For the representation of the core structure/technology, a Hopkinson like approach could be

used whereby, the magnetic flux paths are represented by their reluctances with saturation and,expressing analogy between electric and magnetic elements, the whole system is solved in electric

network analysis software.

As alternative, finite element analysis (FEA) tools could be used combining magnetic fieldand electric field solutions, to directly determine current waves under DC excitation as well as their


8/11

7

effects as losses in the transformers parts. Such an approach appears computationally expensive,particularly when taking into account the core saturation characteristic.

It is usual industrial practice to proceed sequentially. After determining the currents waves,these are injected into the FEA model for the sizing of the shields and to determine the effects oftheses currents on the transformer as the stray losses in the windings (eddy currents, circulating

currents), the leads, the metallic structures (core clamps and flitch plates) and the tank.

Using the currents waves obtained as in Fig.5-7, Fig.5-8 and Fig.5-9 compare the leakage flux

patterns in the bottom tank side of the previous autotransformer, with and without GIC. Also, thelosses/loss densities in the transformer parts for varying levels of GIC can be assessed, resulting in

temperature rises (with the impact of the core losses taken into account) and transformer withstanddurations at full load.

Fig.5-10 shows plot of withstand duration at full load vs GIC levels established for the

referenced autotransformer.

550MVA, 230kV/138kV, 60 Hz, 3 Phase Auto Transformer At Full Load With Power Factor 0.8

Fig.5-8: Leakage flux plot in tank

bottom side. GIC = 0A .

Fig.5-9: Leakage flux plot in tank

bottom side. GIC= 50A (3x16.7A)

Fig.5-10: Withstand time at full load vs GIC

magnitude and ambient temperature 40C.

6) MORE SPECIFIC CONSIDERATIONS RELATING TO DC BIAS CURRENTS IN HVDC

CONVERTOR TRANSFORMERS

As discussed in the previous sections, there are generally two major types of DC bias currentin HVDC converter transformers [10]. These are the leakage currents of the ground electrodes of a DC

transmission system operated under the monopolar mode using ground return mode (GRM) and thegeomagnetically induced current (GIC) due to the magnetic disturbances in the upper atmosphere thathappen more specifically in the auroral regions such as Canada, North America as well as

Scandinavia. The DC bias current caused by these reasons is essentially direct current found to enter

and leave the directly earthed neutrals of the high voltage star-connected line windings.

There is another possible DC bias current which has an impact on converter transformers residual long-term direct current in the valve windings. The causes of this DC bias current have

been investigated by carrying out simulations using Matlab/Simulink.The DC bias current in the valve windings of converter transformers may be caused by one or

more of the following non-ideal conditions [11]:

- Firing angle asymmetry, which occurs if one of the valves in the 6-pulse (or 12-pulse) bridgesis delayed when it is meant to fire. The firing angle asymmetry is typically 0.01

o[12].

- Unbalance of the converter transformer commutation reactance, causing an overlapping timeduring which one valve is commutated to another one. The unbalance in commutationreactance is usually less than 2.5%.

- Asymmetrical AC voltages (negative sequence 3rdharmonics). Voltage unbalance can produceharmonics by its influence on the firing angle and overlap in the different phases resulting in

harmonics of the order 3= pkn where ktakes the integer values 0, 1, 2., and pis the

pulse number of the converter. Within these harmonics, the 3rd

harmonic is the lowest one andthe most probable cause of DC bias on the valve-side of the converter transformer due to its

sideband influence. The percentage of the negative sequence voltage is normally less than orequal to 0.5% in normal operating condition and 2% in extreme condition.

At : t = 0.65 E-2 sec


9/11

8

- Positive-sequence 2ndharmonics on AC side. If a small level of positive 2 ndharmonic voltageVacpexists on the AC side of the converter, a fundamental voltage Vdchwill appear on the DC

side of the converter due to the converter switching action. A fundamental frequency current

will flow through the DC side impedance, resulting in a positive sequence 2nd

harmoniccurrent and a negative sequence DC flowing on the AC side. The negative sequence DC will

begin to saturate the converter transformer core, resulting in a multitude of harmonic currents

being generated including a positive-sequence 2nd

harmonic current. Associated with this

current will be an additional contribution to the positive-sequence 2nd harmonic voltagedistortion [13]. The whole feedback loop is illustrated in Fig. 6-1.

Due to the dynamics of the instability, the DC distortion is never exactly at the fundamentalfrequency [14]. The negative-sequence DC current Iacn is not true DC but is varying slowly. Thevariation is so slow that the phrase negative-sequence DC current is used. Since this slow varying

DC current can saturate the transformer core, the positive-sequence harmonic voltage on the AC sidebecomes another cause of the valve-side DC bias.

Figure 6-1: Mechanism of core-saturation instability [13], [14]

Fig. 6-2a shows the inverter valve-side (secondary wye-connected transformer) currentwaveform from phase A C after the Discrete Butterworth Filter without considering the positive-

sequence 2ndharmonics from the inverter-connected AC network. It can be noticed that there is a DCcomponent within the phase B current though not that obvious. Figure 6-2b is the FFT (Fast Fourier

Transform) of the phase B current and it can be seen that the DC bias is around 7A.

Fig. 6-3a shows the inverter valve-side (secondary wye-connected transformer) currentwaveform from phase A C after the Discrete Butterworth Filter when taking the positive-sequence

2ndharmonics from the inverter-connected AC network into account. It can be seen that there is a very

obvious DC bias current existing in all the phases of the transformer, especially phase A which hasaround 20A DC bias. This is further verified by the FFT analysis as shown in Fig. 6-3b where, the

amplitude of the DC bias current in phase A is around 21A.

Fig.6-2a: Low-frequency wye-connected valve-side currentwaveform

Fig.6-2b: Associated FFT withouteffect of the positive-sequence 2ndharmonics


10/11


11/11

10

BIBLIOGRAPHY

[1] G .B Walker, H. Bonshek, R.C. Adams Back to back testing of svc transformers to determine

the effect of dc excitation , 8th CEPSI Singapore.[2] Olivier Maret, Triomphant Ngnegueu, Sbastien Louise, Jan Prins Etude de linfluence des

courants continus sur le comportement en service des Transformateurs, Matpost, Paper N 10,

France 2007.

[3] Jacques Aubin (Discussion Leader, Report presented at Colloquium of study committee 12) Effect of Geomagnetically induced currents on power transformers , Electra N 141 April

1992.[4] Philip Marketos, Anthony J. Moses, Jeremy P. Hall, "Effect of DC voltage on AC magnetisation

of transformer core steel", Journal of Electrical Engineering, Vol. 61, No. 7/s, 2010, 123-125

[5] John G. Kappenman and Vernon D. Albertson, Bracing for the geomagnetic storms, IEEESpectrum, March 1990, pp. 27-33

[6] Nobuo Takasu, Testsuo Oshi, et al An experimental analysis of DC excitation of transformersby geomagnetically induced currents IEEE Trans Power Delivery, Vol.9, N 2, April 1994

[7] Bolduc, L. Granger, et al Development of a DC current-blocking device for transformer

neutrals IEEE Trans Power Delivery, Vol.20, N 1, pp. 163 168, Jan. 2005

[8] J. Aubin, L. Bolduc Behaviour of power transformers submitted to solar induced currents

Proceedings of Canadian Electrical Association, 1978[9] J. Aubin, L. Bolduc Effect of direct currents in power transformers: Part I, A general theorical

approach and Part II, Simplified calculations for large transformers, Electric Power Systems

Research , 1, 291-304 (1977/1978)[10] H Li, X Cui, T Lu, Z Cheng, D Liu, An improved magnetic circuit model of power

transformers under DC bias excitation, Asia-Pacific International Symposium onElectromagnetic Compatibility, April 12-16, 2010, Bejing, China.

[11] I Norheim, Suggested methods for preventing core saturation instability in HVDC transmission

systems, Norwegian University of Science and Technology, Faculty of Information

Technology, Mathematics, and Electrical Engineering, February 18, 2002.[12] HVDC Connecting to the future, Alstom Grid, 2010

[13] J. Arrillaga et al. High voltage direct current transmission (IEE Power and Energy Series 29),

2nd Edition, The Institution of Electrical Engineers, London, United Kingdom, 1998.

[14] J. Arrillaga et al. Power system harmonic analysis, John Wiley & Sons, 1997.

cigreonhalfcyclesat.pdf

Documents