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A2-303
CIGRE 2012
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
J. BALDAUF, J. OLIVEIRA
Alstom Grid
Brazil
T. XU, R. BARDSLEY, S. BARKER
Alstom Grid
UK
SUMMARY
Power transformers are one of the most strategic equipment in the power system. Though they
are 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 return
mode 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 the
integrity of the power transformers or their long term performance, meaning to affect the power
system 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 other
side, 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 with
application 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 and
related numerical models are addressed.
KEYWORDS
Power Transformers, DC Bias Current, DC Current Excitation, GIC, Convertor Transformers, HVDC
Transformers, Design Review, Numerical Modelling.
(*) triomphant.ngnegueu@alstom.com
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 currents
being 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 thyristor
converter applications such as rectifier transformers for electrolysis as well as the transformers
associated 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 transformers
operating in auroral regions such as Canada, North America as well as Scandinavia, are prone to
Geomagnetically 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 the
windings without damage or excessive hot spot temperature rise. The currents are specified in absolute
numerical 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 normally
demonstrated in the “Design Review”. This contribution paper employs measurements on model
transformers 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 valve
windings and the sources of this DC current are discussed together with an example of a simulation
study.
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 is
discussed. Numerical modelling techniques are shown, supporting the design verification process, in
order 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 create
disturbances to the Earth’s 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 Earth’s magnetosphere
and 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 with
sometime devastating results.
Superimposed DC excitation can affect the normal operation of power transformers in more
than one way. The transformer can experience very high values of magnetising current during the halfcycle saturation leading to overheating of the windings, high winding losses and possible damage to
winding 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 oil
properties 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 on
the already overloaded network. Superimposed DC excitation will also cause the transformer to inject
1
larger amounts of odd and even harmonics into the system thus affecting the normal operation of
protective relays [5].
2.0
2.0
1.5
1.5
AC+DC
0.5
0.0
-0.5
-1.0
0
0.004
0.008
0.012
0.016
AC+DC
1.0
0.02
AC
Flux density (T)
Flux density (T)
1.0
0.5
0.0
-100
-0.5
0
100
200
300
200
300
AC
-1.0
-1.5
-1.5
-2.0
-2.0
time (s)
Magnetic field (A/m)
Magnetic field (A/m)
-100
0
100
0
0.004
0.008
time (s)
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+DC
excitation (black curve). Top right: BH-loop of the
steel magnetized under pure AC excitation (red
curve) and under AC+DC excitation (black curve).
Bottom right: Magnetic field under pure AC
excitation (red curve) and under AC+DC excitation
(black curve).
AC+DC
0.012
0.016
AC
0.02
3) MEASUREMENTS ON MODEL TO ILLUSTRATE MEAN ASPECTS OF COMBINED AC
AND DC MAGNETISATION OF POWER TRANSFORMERS
Experimental results are presented to illustrate the behaviour of power transformers or shunt
reactors 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 yn
connected side of the model transformer is used for the injection of the DC currents whereas the D
connected side is used for the AC supply. For varying levels of DC current, the RMS values of the
excitation currents from the AC source are compared for the single phase supply and the three phase
supply (Fig. 3-2).
Fig 3-1: View of a model 3 phase, 3 limbs distribution
transformer 30kVA, 230V/230V, Dyn used in the tests
Fig 3-2: RMS values of AC excitation currents for varying
DC current levels for single phase and three phase AC supply
Sensitivity to GIC currents or to significant stray DC currents that may inter the transformer
from the grounding points (Yn connected winding) is strongly dependant on the core type. The single
phase 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 can
easily flow are more sensitive (shell type cores, core type five limbs cores) as compared to the three
phase three limbs core type transformers which are less sensitive.
When the DC current is entering the three phase transformer from a line phase (eg. SVC
connected transformers), previous classification of core structures regarding sensitivity to DC
excitation may have to be revised. This is so as, compared to GIC or to GRM currents, the DC
excitation current is not evenly shared by the transformer three phases. With this respect, all the
transformer core structures will tend to be very sensitive to the DC current excitation. Behaviour of
2
convertor transformers relating to DC current excitation is also more specifically dealt with in Section
6 of this contribution paper.
Concluding, Fig 3-3 and Fig 3-4 display the wave shapes and harmonic content of the
excitation currents obtained for the single phase test as reported in Fig 3-2. Whereas the normal AC
excitation current is weak and its spectrum containing only the odd harmonics, depending on the level
of the injected DC current, the magnitude of the excitation current driven from the AC source is up to
30 time the previous (Fig 3-3), with the spectrum containing a large amount of both the even and the
odd 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 ground
return 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) may
occur 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 A
and 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 MVA
rating 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: “The
transformer manufacturer shall review the design of the autotransformers and demonstrate an
understanding of the GIC effects, including appropriate modelling to simulate their impact on the
transformer operation. The capability of the autotransformers to withstand stray DC currents and/or
geomagnetically 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 other
numerical 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 of
the 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
3
-
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, while
maintaining 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 order
to minimize the tank losses and the potential for significant hot spot. Also, special material
was 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 angles
unbalance 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 shunt
reactors 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 previous
sections 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, the
excitation 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, the
currents 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 DC
current levels under no load condition and on load condition. These mean for each load condition, the
temperature 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 or
combination (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 to
the 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 missing
to 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 for
the 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, Np is the number of turns, Rp is
the winding resistance, Lp is the inductance component due to the flux path out of the core (the leakage
4
inductance in no load condition). Rm is the resistance representing the core losses and Lm is the core
magnetizing 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. For
the no load condition seen from the primary side, the electric parameters of the secondary side are not
used.
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 solved
analytically. 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 not
saturated, the solution is made even easier. With the AC voltage defined by equation (1) in Table 5-1,
one has (2) and (3) where w is the radian frequency, φ 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 2α defined by
π − α ≤ wt ≤ π + α 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 current
over 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
(1)
(2)
dφ
φ
(t ) = −φ AC _ Max cos( wt ) + φ DC
V
φ AC _ Max = 2 w
v AC (t ) = V 2 . sin( wt ) = −
dt
(4)
(5)
φ Sat = φ AC _ Max cos(α ) + φ DC
φ (π − α ) = φ (π + α ) = φSat
φ (t ) = φSat + ( LP + LSat ).i(t )
i (t ) = − A.[cos(wt) + cos(α )]
(7)
A=
π − α ≤ wt ≤ π + α
v AC (t )
V 2
( L P + L Sat ) w
(8)
φ (t )
Fig
10
A
I DC = π .[sin(α ) − α . cos(α )]
N°
(3)
(6)
(9)
i (t )
Fig
Fig
11
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 2α value 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 more
tedious 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 solved
using the EMTP (Electro Magnetic Transient Program) like electric network analysis tools which have
5
gained popularity in the academic institutions and in the industries. In that case, the core saturation
characteristic (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 autotransformer
rating 550 MVA, 230kV/138kV, 60 Hz. The ATP/EMTP program is used to determine the excitation
current 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.5-5: Spectrum of excitation current from the AC source
Fig.5-4: Excitation current from the AC Source
-
Currents in on load condition, taking into account the load power factor [cos(ϕ
ϕ); sin(ϕ
ϕ)]
The EMTPs can be used to derive the excitation and the load currents waves for varying load
power 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 current
as determined in previous sections, ip is the total current from the AC source, Rsc and Lsc are the shortcircuit parameters referred to the load side, iLoad is the current in the load. Hence, taking into account
the 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 load
with 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 field
and electric field solutions, to directly determine current waves under DC excitation as well as their
6
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 of
theses 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, the
losses/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 withstand
durations 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
At : t = 0.65 E-2 sec
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 40°C.
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 current
in 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 the
geomagnetically induced current (GIC) due to the magnetic disturbances in the upper atmosphere that
happen 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) bridges
is delayed when it is meant to fire. The firing angle asymmetry is typically 0.01o [12].
- Unbalance of the converter transformer commutation reactance, causing an overlapping time
during which one valve is commutated to another one. The unbalance in commutation
reactance is usually less than 2.5%.
- Asymmetrical AC voltages (negative sequence 3rd harmonics). Voltage unbalance can produce
harmonics by its influence on the firing angle and overlap in the different phases resulting in
harmonics of the order n = k ⋅ p ± 3 where k takes the integer values 0, 1, 2…., and p is the
pulse number of the converter. Within these harmonics, the 3rd harmonic is the lowest one and
the 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 or
equal to 0.5% in normal operating condition and 2% in extreme condition.
7
Positive-sequence 2nd harmonics on AC side. If a small level of positive 2nd harmonic voltage
Vacp exists on the AC side of the converter, a fundamental voltage Vdch will 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 harmonic
current 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 voltage
distortion [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 fundamental
frequency [14]. The “negative-sequence DC current” Iacn is not true DC but is varying slowly. The
variation 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 side
becomes 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) current
waveform from phase A – C after the Discrete Butterworth Filter without considering the positivesequence 2nd harmonics from the inverter-connected AC network. It can be noticed that there is a DC
component 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) current
waveform from phase A – C after the Discrete Butterworth Filter when taking the positive-sequence
2nd harmonics 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 has
around 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 current
waveform
Fig.6-2b: Associated FFT without effect of the positivesequence 2nd harmonics
8
Fig.6-3a: Low-frequency wye-connected valve-side current
waveform
Fig.6-3b: Associated FFT with effect of the positivesequence 2nd harmonics
It can be seen from the above simulation results that the positive-sequence 2nd harmonic
existing in AC network is the main reason of the valve-side DC bias current compared with the other
three potential reasons. Therefore, the positive-sequence 2nd harmonic in the AC network may need to
be reduced or filtered out, if practical for the system, so as to reduce the valve-side DC bias current.
7) CONCLUSION
Power transformers are one of the most strategic equipment in the power system. Though they
are 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. Depending on their magnitude, the DC bias currents may have a detrimental
effect on the integrity of the power transformers or their long term performance, meaning to affect the
power system 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
other side, 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 the requirements.
In this contribution paper, further to explaining the half cycle saturation effect resulting from
combined AC and DC excitations of magnetic cores, measurements on model transformers have been
used to illustrate this effect. Then different aspects of the numerical modelling of the phenomenon
have been presented with application to the design and design verification of a 550 MVA
autotransformer prone to GIC. The analysis has considered the no load as well as the on load
conditions, taking into account the load power factor and varying levels of the DC current as
appearing in the specifications. More specific aspects of the behaviour of convertors and HVDC
transformers relating to DC bias currents, and related numerical models have also been addressed.
Overall, it has been illustrated that, the problematic of DC current excitation is a mature topic,
reasonably well understood by power transformers manufacturers and also that, this problematic can
be taken into account in the power transformers designs when specified by the users.
9
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