PCB Rogowski Coil for Electronic Current Transducer

Transcription

1 Sensors & Transducers 014 by IFSA Publishing, S. L. PCB Rogowski Coil for Electronic Current Transducer Zhigang Di, Chunrong Jia, Jingxuan Zhang College of Electrical Engineering, Hebei United University, Tangshan Hebei , China Tel.: , fax: Received: 11 May 014 /Accepted: 7 May 014 /Published: 31 May 014 Abstract: The Electronic Current Transducer has been applied in power system for measurement and relay protection. To improve the stability of transducer and increase the coefficient of mutual induction of Rogowski coil, a novel Rogowski coil, namely PCB Rogowski coil was proposed. First, the relationship between conureuration parameters and electromagnetic parameters were analyzed, and simulated their relationships. Second, the influence of thermal expansion on relative error was analyzed. Third, the Rogowski coil configuration parameters were optimized and the optimum parameters were proposed. At last, frequency character of optimum Rogowski coil was simulated. The configuration parameters were h = mm, b = 50 mm, a = 30 mm, h = 0.08 mm, w = 0.8 mm, the mutual-inductance of optimum Rogowski coil is H, L = H. The conclusion can be drawn from simulation result that the optimum PCB Rogowski coil has enough mutual-inductance so as to adapt small current measurement, and it is easy to manufacture in large quantities. Copyright 014 IFSA Publishing, S. L. Keywords: Electronic current transducer, Small current measurement, Rogowski coil, Optimum design. 1. Introduction In power system, current transducer is the most equipment for electrical energy measurement and relay protection, the precision and reliability of current transducer have crucial relationship with safe, reliable and economic working. With the unceasing expansion of power system, the transmission capability is increasing unceasingly, voltage class is higher and higher. As a result, the increasing strict claim is made for current transducer. This moment, the traditional electromagnetism current transducer exposed a series of defects, such as complicated configuration, inherent magnetic saturation, small dynamic state, and so on [1]. While with the development of photoelectric technology, electronic current transducer was invented, and it has simple configuration, small volume, light weight and so on []. So it is deemed to the ideal succedaneum for electromagnetism current transducer. With the development of science technology, electronic current transducer is developing for accuracy measurement, fiber transmission and digital output directions. But the mutual-inductance of Rogowski coil is very small because it has no iron core, and the manufacture in quantity is difficult for traditional Rogowski coil because enameled wire is brittle. According to the above mentioned, a novel high precise PCB Rogowski coil was designed in this paper. The measurement range is 0 ~ 100 A, and it has better linearity and very minor phase error, it can meet the requirement of 0. level current transducer.. Principle of Electronic Current Transducer Electronic current transformer can adopt traditional current transformer, Hall sensor, Rogowski coil or optical equipment as sensing 06

2 component, utilizes fiber as transmission medium between first converter and second converter, also equipped with signal process system to magnify and transmit, finally output the analog or digital voltage signal [3, 4]. The development of fiber current transformer is now toward to active type and passive type. The active type has the virtues such as simple configuration, steady operation, and so on. So this task designed an active fiber current transformer, and adopted Rogowski coil as sensor head, the framework of this transformer is shown in Fig. 1. Fig. 1. Diagram of electronic current transformers. The busbar current is sampled by Rogowski coil, then the voltage signal will be achieved. This signal will be disposed by high voltage signal process circuit, so as to achieve the voltage signal which is proportional to busbar current. First, this signal will be converted to digital signal by ADC. Then, it will be converted to optical signal by EOC, and be transmitted to low voltage portion by fiber. The low voltage portion receives the optical signal and disposes it properly, then exports digital signal and analog signal. 3. Design of Rogowski Coil Rogowski coil was first proposed in 191 [5], it is a kind of sensor, which is made of copper wire and nonmagnetic framework. It can be utilized to measure current by electromagnetic induction. Compared with traditional current transducers, Rogowski coil has inapproachable merits as follows [6]: 1). Good linearity. ). High measurement precision, it can be up to 0.1 %, normally is 1~3 %. 3). Wide measurement range, the same coil can measure currents from several A to thousands A. 4). Wide frequency range, it can be 0.1~1 MHz, especially it can be 00 MHz. 5). It can measure small current in restricted area which can t be measured by other technologies. Because of the virtues above, the Rogowski coil was utilized as sensor head of fiber current transducer. Because the Rogowski coil has no iron core, when it measure small currents which is smaller than 1000 A, the output voltage is so weak that it is very difficult to measure precisely because of interference signals. So the manufacture of Rogowski coil which is suit for small current measurement is the acknowledged difficulty [7]. Traditional Rogowski coil is manufactured by twining enameled wire on nonmagnetic framework, so it is difficult to make enameled wire density and cross-sectional area well distributed. As a result, traditional Rogowski coil has poor repeatability and big dispersion, then steady coefficient of mutual inductance, uniform distribution parameters and antiinterference are unlikely [8]. So although all kinds of traditional Rogowski coil were proposed, the high accuracy and batch production are hard to realize, the application and industrial development are limited [9, 10]. In order to solve this problem, the novel PCB Rogowski coil was proposed in this paper. PCB Rogowski coil can realize digital wiring and automation production, so as to overcome some disadvantageous factors of traditional Rogowski coils [11]. PCB Rogowski coil was first proposed by Koovic in 001 and was licensed patent in USA [1], the enameled wires were formed by wiring copper foil which goes through PCB guide holes. From then on, some kinds of PCB Rogowski coil emerged, they were manufactured by copper foil going through guide holes of Double-Sided Boards [13], so they have simple wiring, easy to twine tightly, more important, they can avoid the influence of disturbing current that first conductor deviate from coil center. But they still have bigger dispersion and poor antiinterference because coiling does not form real symmetrical circular structure, and the plane of single circular loop does not pass through coil axis. PCB Rogowski coil can be fabricated very accurate because of full automation, the error can be 1 mil. So PCB Rogowski coil not only overcome the shortcomings of traditional Rogowski coil, but also is superior to traditional Rogowski coil on sensitivity, measurement accuracy and steady performance Principle of Rogowski Coil The frame sketch map of Rogowski coil is shown in Fig.. In Fig., Q is framework of coil, Ri is inside radius, Ro is outside radius, h is the height of frame sketch. Supposed number of primary winding is N 1, secondary winding is N, primary winding is inside secondary winding, the current pass through is I(t), then according to the Ampere law of magnetic circuit, the induced voltage of secondary winding is dφ μ0n1n Ro di e(t) = = hln (1) dt π Ri dt 07

3 Mω H ( ω) = L C ω + R C ω Mω[ R C ω + (1 L0C 0ω )] = (1 L C + ( R C ω) ω ) 0 0 (5) According to the formula (5), the phase error is RC 0 0ω θ = arctg, 1 LCω 0 0 (6) which L, R 0, C 0 is equivalent inductance, resistance and capacitance of Rogowski coil. Fig.. The frame sketch map of Rogowski coil. di While e( t) = M, so dt μ 0N1N Ro M = hln () π Ri According to sinusoidal alternating current, the output voltage root-mean-square value is E = ωmi N (3) The equivalent circuit diagram of Rogowski coil is shown in Fig. 3 [14]. 3.. The Structure of PCB Rogowski Coil When fabricate PCB Rogowski coil, first design Protel picture utilizing drawing software, then utilize advanced numerical control technique to process according to picture parameters. So the shortcomings of artificial wiring are avoided, and the PCB Rogowski coil can meet practical requirement. The structure of PCB Rogowski coil is shown in Fig. 4. The design was utilized double sided PCB, two circles represent inside and outside boundary of PCB Rogowski coil, black full line represent top wire, dotted line represent bottom wire, black dot represent through hole via PCB, which connect top and bottom wires. Top and bottom wires are distributed radiating outward and uniformly-spaced centered-circle center. The cross section of designed PCB Rogowski coil is rectangle because of the limitation of PCB production technology, shown as Fig. 5. Fig. 3. The equivalent circuit diagram of Rogowski coil. If the input is sinusoidal alternating current, the transition function is Mω H( ω) = L0 R0 L0 C0ω + ( + R0C0 ) ω + ( + 1) R f R f (4) Fig. 4. The structure of designed PCB Rogowski coil. For the given Rogowski coil, the output voltage has differential relationship with input current, but because of the influence of coil parameters, there is certain phase error. So the output voltage has not strict differential relationship with input current. If the Rogowski coil is utilized to measure alternating current, and secondary winding is open, namely R =, the transition function is f Fig. 5. Cross section of designed PCB Rogowski coil. 08

4 4. Analysis of Rogowski Coil According to the principle of PCB Rogowski coil, the electromagnetic parameters self-inductance L 0 and internal resistance R 0 can be computed as [15] R 0 L 0 μ0n h b = ln, (7) π a 4πa( b a) Lwire 16ha = ρc +, (8) ' 3 ω h ω which μ 0 = 4π 10 7 H/m, ρ c = Ω m, N is the number of windings, a and b is the inside and outside radius, h is the height of PCB, h` is the thickness of wire, w is the width of wire, l c is the length of single side single winding, L wire is the whole length of wiring copper foil, L wire =l c *N. The error of mutual-inductance is ). For the same a, b is bigger, is quicker to 0. 3). Before decreases to 0, for the same a, will increase with the increase of b. 4). After decreases to 0, for the same a, will decrease with the increase of b. 4.. The Relationship of b and the Error of Mutual Inductance According to formula (9), taking a =, 4, 6 cm, b = 6 ~ 0 cm, the relationship of b and is shown in Fig. 7. b + a b = ln 1 (9) ( b a) a 4.1. The Relationship of a and the According to formula (9), taking b = 8, 10, 1 cm, a = ~8 cm, the relationship of a and is shown in Fig. 6. Fig. 7. Relationship of b vs.. Fig. 6. Relationship of a vs.. The conclusion can be drawn from Fig. 6 that: 1). In a certain range, the will decrease with the increase of a, until = 0, then will increase with the increase of a. But as we know, a is smaller than b, so the error is limited. The conclusion can be drawn from Fig. 7 that: 1). In a certain range, the will decrease with the increase of b, until = 0, then will increase with the increase of b. But as we know, b is limited, so is limited. ). For the same b, a is smaller, is quicker to 0. 3). Before decreases to 0, for the same b, will increase with the increase of a. 4). After = 0, for the same b, will decrease with the increase of a. In summary, in the process of design PCB Rogowski coil, lots of extrinsic factor should be considered. As for inside and outside radius, on the premise of big mutual-inductance, the sensitivity and accuracy should be considered. As a result, the suitable a and b has important signification for PCB Rogowski coil design. 09

5 4.3. The Relationship Between Height and R 0 For the copper wire, according to formula (8), taking a = 30 mm, b = 80 mm, h` = 0.08 mm, w = 0. mm, the relationship between h and R 0 is shown in Fig. 8. From Fig. 8, the conclusion is that: 1). For the given w, the influence of h on R 0 is very weak. ). For the given other extrinsic factors, R 0 is proportionate to h. Fig 8. The relationship between h and R0. of 0. ~ 1.9 mm, and this is very significance for the accuracy and sensitivity of the system. In conclusion, for the given a and b, h and w are the main influencing parameters on R 0. Fig. 8 and Fig. 9 indicate that h has a few influences on R 0, but w has serious influence. So the research on R 0 can know about the property of PCB Rogowski coil overall, and have practical guidance on fabrication. 5. Optimization on PCB Rogowski Coil The accuracy and reliability of PCB Rogowski coil must be ensured, so the optimization is very important. Matlab software was utilized to optimize PCB Rogowski coil, and the dynamic characters were analyzed for different structure parameters according to formula (5). Taking a = 30 mm, b = 50 mm, sampling resistor is 400 Ω, h and N were changed respectively, the variety law of dynamic characters under step response was researched. According to formula (5), the transmission function has real coefficient, and the roots of characteristic equation were located in left half plane of the complex plane, so the measurement system is steady. Taking h = 1 mm, N = 600 ~ 1000, the step responses for N = 600, 800, 1000 were shown in Fig The Relationship Between w and R 0 According to formula (8), taking a = 30 mm, b = 80 mm, h` = 0.08 mm, h = 1 mm, the relationship between w and R 0 is shown in Fig. 9. Fig. 10. The step response of different N. Fig. 9. The relationship between w and R0. From Fig. 9, for the given a, b, h`, h, the conclusion can be drawn that: 1). R 0 is affected by w heavily, and R 0 will decrease with w heavily in certain range. ). If w exceeds 1.9 mm, R 0 can t change with w anymore. In summary, considering big mutual-inductance and R 0, w must be in the range From Fig. 10, the conclusion can be drawn that N is bigger, the raise time of step response is longer, response velocity is slower, the setting time of system steady state is longer, and the system sensitivity is lower too. But according to formula (), for the given a and b, the bigger N will have bigger mutual-inductance, the width w must be smaller, so R 0 must increase. As a result, according to mentioned above, N = 800 is optimum, and four PCB Rogowski coil cascade together, for each coil, N =

6 Taking N = 800, h =, 3, 4 mm, the dynamic characteristics were shown in Fig. 11. magnetic field around it, so the accuracy must be affected. As a result, method and design of electromagnetic shielding for PCB Rogowski coil is very important [16]. Fig. 11. The dynamic characteristics of different h. From Fig. 11, the conclusion can be drawn that for bigger h, the raise time of induced voltage will increase, and the setting time of system steady state is longer, response velocity is slower too. While according to formula (), the bigger h will have bigger mutual-inductance, namely has stronger induced signal. In practice, it is very difficult to fabricate PCB Rogowski coil for too big or too small h, as a result, the height of PCB Rogowski coil must be chosen properly. According to mentioned above, h = mm is optimum. 6. Numeral Simulation Sum up, according to the optimization above, the practical optimum single ring PCB Rogowski coil has following structure parameters: h = mm, a = 30 mm, b = 50 mm, h` = 0.08 mm, w = 0.8 mm, N = 800. In application, four PCB Rogowski coils cascade as negative direction, and the electronic parameters are: R 0 = 8.5 Ω, M = 1.63*10-6 H, L = 1.31*10-4 H, C 0 = 345 pf. To make the measurement circuit work at the best damping mode and eliminate resonance oscillation, taking Ra = 430 Ω. In order to research the performance of PCB Rogowski coil which measure current, according to the formula (4), Matlab software was utilized to simulate the system, and the frequency characteristics curve was shown in Fig Method and Design of Electromagnetic Shielding for PCB Rogowski Coil The working environment of Rogowski coil is very special, there is strong electric field and Fig. 1. Frequency characteristics curve of designed PCB Rogowski coil Method and Design of Electric Field Shielding Rogowski coil is connected in high voltage power system, the electric field of high voltage power system will couple through distribution capacitance of power line and Rogowski coil, then affect the accuracy of Rogowski coil. Assumed that u 1 is the power line voltage, u is the induced voltage of Rogowski coil, c 1 is the distribution capacitance between power line and Rogowski coil, c is the distribution capacitance between Rogowski coil and the ground, so u c u 1 1 = (10) c1 + c According to the formula (10), the voltage of Rogowski coil has relationship with their distribution capacitance and ground capacitance. Distribution capacitance among Rogowski coils are difficult to adust because Rogowski coils are bell socketed in measured power line, so method and design of electric field shielding must be adopted. The essence of electric field shielding is to make external power line terminate on shielding layer, the inside implements can avoid the influence of power line, so the shielding layer must be made of metal conductor. For this reason, a copper foil was wrapped on Rogowski coil to protect PCB Rogowski coil from affecting of electric field. In the process of wrapping copper foil, the head cannot connect with the end to avoid producing loop current. And the shielding field of Rogowski coil must connect with shielding line of output voltage, they only have one ground point. 11

7 7.. Method and Design of Magnetism Field Shielding In complex working environment of Rogowski coil, there are lots of stray magnetism fields, which can produce voltage in Rogowski coil. The induced voltage of measured current is necessary signal, others are noises. In order to measure current accurately, stray magnetism fields must be shielded. Magnetism field shielding is more difficult than electric field shielding because low frequency magnetic field lines can penetrate metal layer and affect Rogowski coil, as a result, only the low resistance of high permeability material was utilized to shunt magnetic field lines. In this paper, the cast iron box was utilized, the Rogowski coil was placed in box, so stray magnetism field lines were shunt to cast iron box, and the Rogowski coil was protected from stray magnetism fields. In the process of design, cast iron box can shunt the magnetism field lines produced by measured current, and can produce current in box, so as to affect current measurement. So the following steps were adopted. 1). Open a main air gap groove along crosssectional of box, which is shown in Fig. 13. Fig. 13. The appearance of cast iron box. Because the magnetoconductivity of cast iron is bigger than air, air gap groove make iron box can t form loop, reluctance is very big, so the main magnetic flux will flow into the Rogowski coil inside the iron box. ). Open a crack along interior side of iron box so as to make main magnetic flux can flow into the Rogowski coil. Without this crack, there will be an induced current along iron box, so the main magnetic flux can t penetrate shielding box. 8. Conclusions The influence of structure parameters (wire width, PCB height, inside and outside radius) on electromagnetic parameters (mutual-inductance and internal resistance) was researched. Then the frequency performance and step response of different structure parameters (N and h) was researched, and carried on simulation analysis on research result. According to the result above, the optimum structure parameters were proposed. Finally the design of electromagnetic shielding for PCB Rogowski coil was proposed. From the research of this paper, the conclusion can be drawn that the designed PCB Rogowski coil has high sensitivity and accuracy, especially it has big mutual inductance. Acknowledgements This research was supported in part by the Basic Research Program of Hebei province No and A proect supported by scientific research fund of Hebei provincial education department (ZD01310); Doctor Scientific Research Foundation of Hebei United University. References [1]. Shen Zhu, Luo Chengmu, Recent progress in electronic current transformers, Automation of Electric Power System, 5,, 001, pp []. Fiber Optic Sensors Working Group, Optical Current Transducers for Power Systems: A Review, IEEE Transon Power Delivery, 9, 4, 1994, pp [3]. International Electrotechnical Commission, IEC , Electronic Voltage Transformers. [4]. International Electrotechnical Commission, IEC , Electronic Current Transducers. [5]. W. Rogowski, W. Steinhaus, Die Messung der Magnetischen Spannung, Archtrotech, 1, 1, 191, pp [6]. Ray W. F., The use of Rogowski coils for low Amplitude current waveform measurement, in Proceedings of the IEE Colloquium on Measurement Techniques for Power Electronics, University of Birmingham (UK), 199, pp [7]. Lubomir Koovic, Rogowski coils Suit Relay Protection And Measurement, IEEE Computer Applications in Power, July 1997, pp [8]. Li Hongbin, Chen Qing, Zhang Mingming, et al., Rogowski coils with high accuracy based on printed circuit boards, High Voltage Engineering, 30, 4, 004, pp [9]. Chen Qing, Li Hongbin, Zhang Mingming, et al., Analysis and design of Rogowski coils with main and assistant printed circuit boards, Automation of Electric Power Systems, 8, 16, 004, pp [10]. Wang C. Y., Chen Y. P., Zhang G., etc., Design of printed circuit board Rogowski coil for highly accurate current measurement, in Proceedings of the IEEE International Conference on Mechatronics and Automation, 007, pp [11]. Zhang Y., Li H. B., The reliable design of PCB Rogowski coil current transformer, in Proceedings of the International Conference on Power System Technology, 006, pp [1]. Koovic L. A., Skendzic V., Williams S. E., etc., High precision Rogowski coil, USA, Patent ,

8 [13]. Robles G., Argueso M., Sanz J., etc., Identification of parameters in a Rogowski coil used for the measurement of partial discharges, in Proceedings of the IEEE Instrumentation and Measurement Technology Conference, 007, pp [14]. Jin Yongtao, Liu Huiin, Xiong Lingling, Analysis on the frequency characteristics of Rogowski coil and also means to broaden the bandwidth of frequency response, Electrical Measurement & Instrumentation, 40, 9, 003, pp [15]. K. Heumamn, Magnetic Potentiometer of High Precision, IEEE Trans on IM, 15, 4, 1966, pp [16]. Qiao Hui, Research and realization of novel current transducer based on Rogowski coil, Master Thesis, WuHan University, Copyright, International Frequency Sensor Association (IFSA) Publishing, S. L. All rights reserved. ( 13