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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 1 Hanoi University of Science and Technology; tuan.phunganh1@hust.edu.vn 2 Hanoi University of Industry; dhai.haui@gmail.com 3 International 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: 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. 2 ∑∞ 𝑘=2 𝐼𝑘 𝑇𝐻𝐷𝑖 = √ 𝐼12 (1) which: 𝐼𝑘2 – squared of the RMS value of the current which oscillates kth time the fundamental frequency 50 Hz; 𝐼12 – 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. 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 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 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 4. Measured loss curves at different frequencies [15] 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 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 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]: 1 ∞ 𝑖(𝑡) = 𝑖0 + ∑∞ 𝑛=1 𝑎𝑛 . cos⁡(𝑛𝑡)+∑𝑛=1 𝑏𝑛 . sin⁡(𝑛𝑡) (2) 2 where 𝑖0 = 1 𝜋 ∫ 𝑖(𝑡). 𝑑𝑡 𝜋 −𝜋 1 𝜋 ∫ 𝑖(𝑡). cos(𝑛𝑡) . 𝑑𝑡 𝜋 −𝜋 1 𝜋 𝑏𝑛 = ∫ 𝑖(𝑡). sin(𝑛𝑡) . 𝑑𝑡 𝜋 −𝜋 𝑎𝑛 = 51 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. n = 1, 2, 3… Figure 7. Induction distribution on the magnetic core 30P120 with pure sine excitation 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. 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 the frequency response of the current transformer will not react fast enough to keep up with that variable speed. 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), 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. REFERENCES [1] F. das Guerra Fernandes Guerra and W. Santos Mota, “Current transformer model”, IEEE Trans. Power Deliv., Vol. 22, No. 1, ISSN 1859-1531 - TẠP CHÍ KHOA HỌC VÀ CÔNG NGHỆ ĐẠI HỌC ĐÀ NẴNG, SỐ 3(124).2018 [2] [3] [4] [5] [6] [7] [8] 2007, pp. 187–194. J.-M. 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