Current transformers are very popular in the industrial
electrical appliance market today. This article has
nvestigated the effect of currents containing high
harmonic components on the accuracy of the 50/5
nductive current transformer. Modeling results show that
error of the current transformer with distorted waveform
primary current is higher than the allowed standard (greater
han 0.5%). It also demonstrates that mixing different
frequencies with different percentages is also possible
within the modeling software. Hence, various
configurations could be carried out to take into account the
most significant configuration of the inductive current
ransformer.
The results of this study suggest that current distortion
evaluation of inductive current transformer error is
necessary. In the coming time, studies related to the level
of waveform distortion and different ratios of involvement
of high-level harmonics components that affect the
accuracy of the current transformer will be made.
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ISSN 1859-1531 - TẠP CHÍ KHOA HỌC VÀ CÔNG NGHỆ ĐẠI HỌC ĐÀ NẴNG, SỐ 3(124).2018 49
ERROR ANALYSIS FOR INDUCTIVE CURRENT TRANSFORMERS UNDER
NON-SINUSOIDAL WAVEFORM CURRENT
ĐÁNH GIÁ SAI SỐ CỦA BIẾN DÒNG ĐIỆN KIỂU CẢM ỨNG TRONG
ĐIỀU KIỆN DÒNG ĐIỆN BỊ MÉO DẠNG HÌNH SIN
Anh-Tuan Phung1,3, Hoang-Phuong Vu1, Trinh-Tuan Nguyen1, Dang-Hai Nguyen1,2
1Hanoi University of Science and Technology; tuan.phunganh1@hust.edu.vn
2Hanoi University of Industry; dhai.haui@gmail.com
3International Research Institute for Computational Science and Engineering; icse@hust.edu.vn
Abstract - Instrument transformer is a popular electric device
which is used in measurement of load current. While dealing with
pure sine-wave primary current, these instrument transformers
work well with no significant problem. A primary load current which
includes high frequency components, the relative error of this
device must be reconsidered. This paper presents a research
result of the effect of high harmonic ratio primary current on the
relative error of instrument transformers. The increasing relative
error could be explained by using a first order timed delay element
of the current transformer versus the fast-changing load current.
The result can be used in either selecting the right instrument
transformer for a specific load or defining the requirements for other
electric loads to permit a correct measurement.
Tóm tắt - Máy biến dòng đo lường là thiết bị điện phổ thông được
dùng để đo dòng điện của các phụ tải. Khi dòng điện của các phụ tải
này thuần sin, độ chính xác của biến dòng điện này sẽ vẫn được
đảm bảo. Khi dòng điện của các phụ tải này không còn dạng thuần
sin và chứa các thành phần sóng hài bậc cao, độ chính xác của biến
dòng điện đo lường sẽ cần phải được xem xét. Bài báo này nghiên
cứu về tác động của dòng điện chứa sóng hài bậc cao lên độ chính
xác của biến dòng điện đo lường. Sự gia tăng về sai số của biến
dòng điện này đến từ việc lõi sắt từ của biến dòng điện phản ứng
như một khâu quán tính bậc nhất có trễ đối với các biến đổi nhanh
của dòng điện. Kết quả nghiên cứu này có thể được dùng để tham
khảo trong lựa chọn loại máy biến dòng điện hoặc yêu cầu đối với
phụ tải điện nhằm đảm bảo độ chính xác của phép đo.
Key words - current transformer, electrical steel; magnetic core;
total harmonic distortion; high frequency harmonic; relative error.
Từ khóa - biến dòng điện; thép kỹ thuật điện; lõi thép; méo dạng
sóng tổng hợp; sóng hài bậc cao; sai số tương đối.
1. Introduction
Current transformer is widely used in current
measurement and protection of power system. Its working
principle is based on the induced electromagnetic
phenomena. Its quality is judged on the relative error of
current and angle error between primary current and
secondary current. Current transformer construction
includes magnetic core, coils and insulating media [1]. The
magnetic core is manufactured with high grade silicon steel
to ensure low measuring error.
In modern power system, there are more and more
power electronic devices which participate in power
transformation and delivery process. Hence, instrument
transformer must be reviewed to respond to this change.
Large power electronic devices require a non-sinusoidal
current from the grid whose frequency is different from
50Hz (National grid frequency). These currents compose
high order frequency which are called harmonics [2]. The
main current in that case will be distorted.
To characterize this distortion, the total harmonic
distortion [3] is used:
𝑇𝐻𝐷𝑖 = √
∑ 𝐼𝑘
2∞
𝑘=2
𝐼1
2 (1)
which: 𝐼𝑘
2 – squared of the RMS value of the current
which oscillates kth time the fundamental frequency 50 Hz;
𝐼1
2 – squared of the RMS value of the fundamental
current.
High harmonic-content current will cause some
negative effects including divergence on error of current
transformer.
In the literature, effect of current and voltage harmonics
on distribution transformer losses and motors were
investigated in many publications [3], [4], [5], [6], [7].
They were mainly interested in monitoring the efficiency
degradation of the device. Others tried to compensate the
harmonics effect by using various technical solutions much
as passive filter or active harmonics filter. A very good
reference related to the current transformer model was
presented in [8], [9]. This Jiles-Atherton model was widely
used to study the current transformer in electrical
engineering software because of its demonstrated
accuracy. However, implementation of this model is not
straightforward while dealing with high harmonics current
in finite element modeling software [10], [11]. Hence,
direct experiment data handling with simple manipulation
will be favored.
In this paper, individual measured data of the silicon
steel under different frequency will be merged at different
ingredient percentage to study their mixed effect on the
current transformer. Simple data filtering technique will
be used to extract valuable information from experiment
without ignoring the main trend. Authors will evaluate the
current transformer by using a dedicated software to
figure out changes in terms of relative error and angle
error while dealing with high harmonics content primary
current.
This paper will be organized as follows: the second
section will describe the construction data of the current
transformer; current with high harmonics content will be
simulated in the third section; recommendations and future
work will be presented in the final section.
50 Anh-Tuan Phung, Hoang-Phuong Vu, Trinh-Tuan Nguyen, Dang-Hai Nguyen
2. Construction data for current transformer modeling
The device under test (DUT) is a generic current
transformer. Declared relative error of the DUT is 0.5%.
The current ratio is 50/5 – which means at 50 amps primary
current, the secondary current will be 5 amps ± 0.5% [12].
The rated voltage of this DUT is 600 VAC.
2.1. Construction data of the current transformer
2.1.1. Magnetic core
Inner diameter: 40 mm
Outer diameter: 70 mm
Core height: 55 mm
2.1.2. Windings of the current transformer
Primary winding: single turn or multiple turns (external
conductive bar or wire);
Secondary windings: 10 turns
Figure 1. The real current transformer under test
2.2. Modeling tool
Maxwell 3D software is used for the modeling of the
current transformer. This is a part of ANSYS software
package. This software is based on the finite element
method (FEM). It is widely used in the modeling of
continuous media such as Mechanical – Electrical – Heat
transfer – Fluid dynamics – Vibration and Structural
analysis. This Maxwell 3D software allows a reliable
modeling of magneto-static simulation, electric
conduction, magneto-transient and multi-physic couplings
with other tools [13].
Figure 2. Geometry of the current transformer under test
2.3. Electrical and magnetic properties of the current
transformer
The core of the current transformer is made of high
grade silicon steel with code name 30P120 from POSCO –
South Korea with a thickness of 0.3 mm; the specific loss
at 1 Tesla for a unit weight is 1.2 W/kg. Its magnetic
properties are shown on Fig. 3 Tab. 1.
Figure 3. Loss characteristics of 30P120 at 50 Hz [14], [15]
Table 1. Magnetic properties of 30P120-POSCO
STT Name Value
1 Volumic conductivity 769,230 Siemens/m
2 Core loss type Electrical steel
3 Hyteresis loss factor 0.00295106 W/m3
4 Mass density 7,650 kg/m3
The measured data will be used to properly predict
reaction of the current transformer under high harmonic
excitation.
Various frequencies have been tested and loss curves
have been recorded. They are presented on Fig. 4. One
could remark that at a higher frequency, higher loss can be
observed.
Figure 4. Measured loss curves at different frequencies [15]
Figure 5. Regression curves of simulated loss characteristics of
silicon steel at different frequencies [15]
ISSN 1859-1531 - TẠP CHÍ KHOA HỌC VÀ CÔNG NGHỆ ĐẠI HỌC ĐÀ NẴNG, SỐ 3(124).2018 51
Experimentation data contains lots of measurement
errors due to uncertainty. Porting these data into simulation
software needs care in order to filter out all the variation
When frequency increases, higher power losses due to
friction and hysteresis area increase. Magnetic domains
and domain walls in oriented silicon steel or non-oriented
steel move against each other to react to the external field.
Hence with a quick time-variant applied field, these
movements generate heat which induces higher losses.
However, in order to quantify these losses in the current
transformer, one should place the magnetic materials into real
form of the magnetic core of the concrete current transformer
and excites it with a distorted primary current [5].
3. Distorted primary current and its effects one the
magnetic core of current transformers
3.1. Fourier analysis of a periodic waveform
Input current of a generic load is considered as a
periodic waveform. An arbitrary periodic function i(t) can
be broken up into a set of simple complete orthogonal
terms [2] on an interval [−𝜋, 𝜋]:
𝑖(𝑡) =
1
2
𝑖0 + ∑ 𝑎𝑛 . cos(𝑛𝑡)
∞
𝑛=1 +∑ 𝑏𝑛 . sin(𝑛𝑡)
∞
𝑛=1 (2)
where
𝑖0 =
1
𝜋
∫ 𝑖(𝑡). 𝑑𝑡
𝜋
−𝜋
𝑎𝑛 =
1
𝜋
∫ 𝑖(𝑡). cos(𝑛𝑡) . 𝑑𝑡
𝜋
−𝜋
𝑏𝑛 =
1
𝜋
∫ 𝑖(𝑡). sin(𝑛𝑡) . 𝑑𝑡
𝜋
−𝜋
n = 1, 2, 3
Figure 6. Fourier analysis of an arbitrary periodic waveform.
Images courtesy from Wolfram Inc
Hence, a generic load current could be decomposed into
fundamental component and higher frequency
components. These higher frequency components are
called harmonics for ease of use. The total harmonic
distortion (THD) is the measurement of the harmonic
distortion present in a signal. This is defined as the ratio of
the RMS amplitude of a set of higher harmonic frequencies
to the RMS amplitude of the first harmonic, or
fundamental, frequency. The higher the percentage, the
more distortion that is present on the mains current.
3.2. Regulations on the THD of load current
International standards have a strict regulation on the
current distortion. IEC 61000-3-2 and IEEE 519 are the
most cited regulations on this area. In these standards, the
percentage of the harmonic components or absolute value
of harmonic contents is defined with respect of the
fundamental component. In Vietnam, IEC 61000-3-2 is
widely accepted as a standard for harmonic regulation. On
the other hand, circular number 39 TT/BCT-2015 [16]
issued by Ministry of Industry and Trade mentioned the
interface between sources and loads (which is described as
the point of common coupling – PCC) with strict
regulation.
Practical application of these standards and regulations
is not the subject of this paper. However, it is meaningful
to remark that harmonic pollution in Vietnam in recent
years is a matter of concern.
3.3. Effect of distorted current on relative error of current
transformer
Primary current will be simulated to be distorted at a
certain level to evaluate its effect on the current
transformer.
3.3.1. Pure sinusoidal primary current
On Figure 7, magnetic flux density on the magnetic
core of the current transformer is presented. The excitation
primary current is pure sinusoidal at fundamental
frequency – 50Hz. Maximum flux density is recorded at
3mT, average flux density is about 1mT. These values
correspond to a normal operation of the said current
transformer. The maximum flux density is located at the
proximity of secondary windings.
Figure 7. Induction distribution on the magnetic core 30P120
with pure sine excitation
Relative error between scaled secondary current to the
primary current is presented on Figure 8. When observing
the error of the current ratio and phase error for the pure
primary sinusoidal current, it is possible to see that angular
error and relative error are within the allowable range of
the precision (under 0.5%, see Figure 8). The secondary
current which is converted into primary level almost
coincides with that of the primary current. Average current
error is below 0.4%.
Thus, for current transformers using this type of
30P120 material, the standards for error rate and current
deviation of primary and secondary currents are in line
with the actual test standards. This accuracy allows the use
of this model in further studies of the effect of current
distortion on the inductive current transformer.
52 Anh-Tuan Phung, Hoang-Phuong Vu, Trinh-Tuan Nguyen, Dang-Hai Nguyen
Figure 8. Current superposition of primary and secondary
current (pure sine wave). Angular error (stepped curve) and
relative error (green curve)
Error curve tends to decrease versus time toward a
regular manner. The step representation is used to visualize
more easily the trend of the error evolution. The maximum
recorded value of the relative error is around the moment
when the current cancels out. This is coherent with the
experiment data.
3.3.2. Distorted primary current, the higher harmonic
components involved in the primary current
For the same current transformer, the primary current
flowing into the study is described below:
𝑖(𝑡) = 50√2. sin(2𝜋50𝑡) + 15√2. sin(2𝜋150𝑡)(3)
This is an electric current containing the third order
component whose effective value is 15 Ampere. The
fundamental component of the 50 Hz frequency has an
effective value of 50 Ampere. Hence corresponding
distortion value is THDi = 30%. The overlapping primary
current pattern is shown on Figure 9.
3.3.3. Error analysis with high THD percentage of primary
current
Figure 9. Synthetic primary current contains 30% of the third
harmonic. Effective value and mean value of the error
Observing the value of the current error, it can be seen
that high harmonics current affects the accuracy of the
ferromagnetic core current transformer. Here, compared to
the error of 0.4% for the pure primary sinusoidal current,
the error has increased. The mean error value here is
0.75%, which is higher than the permitted level for the
current transformer for measurement [12].
The variation of the error over time is also recorded at
a higher level than in the case of pure sinusoidal currents.
The occurrence of large errors for high harmonic
currents can be explained by considering the inductive
current transformer as a delayed inertia. As the rate of time
variation of the current increases (with high harmonics),
the frequency response of the current transformer will not
react fast enough to keep up with that variable speed.
Figure 10. Magnetic field intensity with non-sinusoidal primary
current. Mesh density on magnetic core
Figure 10 shows the distribution of the magnetic field
intensity on the secondary winding and the mesh density
on the magnetic core. Mesh density is sufficiently fine (0.2
mm grid) to accurately consider eddy current effect or the
delayed loss that may occur in the steel core of the current
transformer. The implementation of a finer mesh has
yielded comparable results, but the computational time
increases drastically, which is not suitable for evaluating
more configurations or higher frequencies.
4. Conclusions
Current transformers are very popular in the industrial
electrical appliance market today. This article has
investigated the effect of currents containing high
harmonic components on the accuracy of the 50/5
inductive current transformer. Modeling results show that
error of the current transformer with distorted waveform
primary current is higher than the allowed standard (greater
than 0.5%). It also demonstrates that mixing different
frequencies with different percentages is also possible
within the modeling software. Hence, various
configurations could be carried out to take into account the
most significant configuration of the inductive current
transformer.
The results of this study suggest that current distortion
evaluation of inductive current transformer error is
necessary. In the coming time, studies related to the level
of waveform distortion and different ratios of involvement
of high-level harmonics components that affect the
accuracy of the current transformer will be made.
Acknowledgement
The authors would like to thank Hanoi University of
Science and Technology for their financial contribution to
this group through the T2016-PC-106 project. The authors
also would like to thank the International Institute for
Computational Science and Technology (ICSE) - Hanoi
University of Science and Technology for supporting the
Maxwell 3D calculation tool used in this paper.
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(The Board of Editors received the paper on 06/12/2017, its review was completed on 08/02/2018)
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