Design Modification of Rogowski Coil for Current Measurement in Low Frequency

Transcription

1 Design Modifiation of Rogowski Coil for Current Measurement in Low Frequeny M. Rezaee* and H. Heydari* Abstrat: The priniple objet of this paper is to offer a modified design of Rogowski oil based on its frequeny response. The improvement of the integrator iruit to nullify the phase differene between the waveforms of the measured-urrent and the orresponding terminal voltage is a further objet of this investigation. This paper addresses an aurate, yet more effiient measuring and proteting devie for low frequeny appliations. This requires verifiation for the simulations by physial desriptions and experimental results. These validate the superior performane of Rogowski oils over onventional urrent transformers. Keywords: Current Transformer, Frequeny Response, Integrator Ciruit, Mutual Indutane, Rogowski Coil, Terminal Resistor. 1 Introdution1 The Rogowski oil s tehnique possesses many features whih offer an advantage over iron-ored urrent measuring devies and these are well illustrated by making some hanges to its parameters for more preise measurements. A wide range of industrial appliations requires AC urrent transduers able to math both metrologial requirements, suh as auray, linearity, bandwidth, et., and appliation-oriented requirements, suh as high-level galvani insulation, ruggedness, lightweight, et. Unfortunately, none of the ommerially available AC urrent transduers is able to omply with the above requirement. Resistive shunts are haraterized by a wide bandwidth and linearity, but they do not assure galvani insulation. Hall Effet based on urrent transduers feature wide bandwidth, ompat size and galvani insulation, but are still limited in their auray and linearity and in the thermal drift. Classial eletromagneti urrent transformers assure a good ompromise between auray, long-term stability and galvani insulation, but beome inadequate when wide band, ompat size and lightweight requirements are neessary. However, any hoie of available AC urrent transduers represents a ompromise between different possibilities, depending on the partiular field of appliation [1, ]. Iranian Journal of Eletrial & Eletroni Engineering, 010. Paper first reeived 10 Apr. 010 and in revised form Ot * The Authors are with the Center of Exellene for Power System Automation and Operation, Department of Eletrial Engineering, Iran University of Siene and Tehnology, Tehran, Iran. s: mrezaee@iust.a.ir, heydari@iust.a.ir. Emerging modern protetive relays onstruted by miroproessor equipments inreases the appliations of Rogowski oil for measuring-urrent in power systems. Due to non-ferromagneti material existed in the ore of Rogowski oil, this oil is not driven into saturation and it operates as well as a linear devie, against urrent transformer (CT). Contrary to CT, Rogowski oil does not need any onverter for adapting to miroproessor's input signal of modern relays. D. Ward and J. Exton showed that Rogowski oils have better performane in a vast majority appliations; sudden short iruit test, lightning test and partial disharge monitoring, as ompared to the other urrentmeasuring devies [3]. Ramboz introdued a new onstrution of Rogowski oil, Mahinable Rogowski Coil made of a rigid nonmagneti oil and a single-layer winding [4]. Kojovi [5] and Karrer and Hofer-Noser [6] proposed a new onfiguration of Rogowski oil based on printed iruit board (PCB) being useful in transient urrent measurement. In that study, the amplitude of the oil's output signal is inreased without dereasing its bandwidth, by inreasing the number of PCB oils. In the other prior researh, for low-frequeny appliations a CT model, analyzing hysteresis phenomenon and remnant flux on its performane in fault onditions is presented [7]. it is reported that in low frequenies (5 Hz to 400 Hz), the output of the CT in fault state is less aurate and requires more orretion fators. Kojovi ompares performane harateristis of onventional CTs and Rogowski oils used for protetive relaying purposes [8]. Rogowski oils do not 3 Iranian Journal of Eletrial & Eletroni Engineering, Vol. 6, No. 4, De. 010

2 reate hazard for personnel with open seondary like onventional CTs and their output is a voltage proportional to the rate of hange of measured urrent, requiring appropriately designed relays to aept these types of signals, he believed that these oils an replae CTs for both measurement and protetion appliations in power systems [8]. This paper mainly desribes the mathematial analysis of design modifiation, based on frequeny response of Rogowski oil for 50Hz urrent measurements ranging from tenths to several thousands of amperes in eletrial power industry. The mathematial analysis and simulation results are verified by physial desriptions and experimental results. For omparative purpose, the results prove the superiority of Rogowski Coils over urrent transformers. Constrution and Transformer Funtion of Rogowski Coil Figure 1 shows that Rogowski oil being formed with helial winding loated on a toroidal rigid oil made of a non-magneti material. It is shown that the ompensating return loop (inremental pith advanement) of the helial winding sums over its irumferential length to reate an undesirable one-turn loop normal to the axis of the oil [4], [9]. The orresponding equivalent iruit onsisted of a oil's equivalent resistane R, self indutane L, mutual indutane M, self apaitane C, terminal resistane Rt, and voltage soure eind, whih is ating as a oupling iruit, is shown in Fig.. Aording to Faraday's law e ind di/dt, for the ompatibility of the urrent and indued voltage signals, the oil terminals are onneted to an integrator iruit.it is reported that the passive integrator iruit is more ompetent than the ative one [10]. Thus, by onneting the passive integrator iruit, the equivalent iruit is replaed by Fig. 3, in whih the self apaitane of Rogowski oil is omitted for low frequeny appliations. The orresponding passive integrator iruit shown in Fig. 3 onsisted of an integrator s equivalent resistane R i and apaitane C i. 3 Frequeny Response Analysis of Rogowski Coil By Laplae transform, the transfer funtion of the equivalent iruit (Fig. 3) an be written as: V M R s o t (1) I As + Bs+ C where, A, B and C are: A L C (R + R ) i i t B [L + R C (R + R ) + R R C ] i i t i t i () C (R + R ) t By onverting s to jω in (1), the phase and amplitude funtion of the equivalent iruit an be obtained: tω H(j ω) (3) (C A ω ) + ω B 1 C Aω H(j ω) tan (4) ωb Figure 4 shows the Bode diagram of the oil s transfer funtion with orresponding typial parameters of Rogowski oil and its integrator iruit listed in Table 1. The parameters shown in Table 1 an be divided as: a) Dependent parameters: R, L and M influened by strutural variations. b) Independent parameters: R t, C i and R i. Initially, prior to the design modifiation, the values of the dependent parameters (Table 1) were taken from Ramboz design values [4] while the independent values are seleted arbitrarily. Fig. Equivalent iruit of Rogowski oil. Fig. 1 Constrution of Rogowski oil. Fig. 3 Extended Equivalent iruit of Rogowski oil with integrator iruit. Rezaee & Heydari: Design Modifiation of Rogowski Coil for Current Measurement in Low Frequeny 33

3 Table 1 Typial Parameters of Rogowski Coil and its Integrator Ciruit. Parameter Speifiation R 06.7mΩ L 34.50μH M 0.654μH R t Ω C i 1μF 100Ω R i Figure 4 shows the variations of amplitude and phase funtion with frequeny for Rogowski oil. It is learly evident that the phase angle between output voltage and input urrent is very inonsistent. Basially, in time domain this differene is regarded as a time delay that is, the output voltage does not trak the input urrent exatly. This inonsisteny an lead to a ouple of undesirable effets in the system onneted to the oil: a) reating a time delay in the protetion proess during fault onditions. b) unreognizing the phase differene between voltage obtained from the potential transformer (PT) and urrent reeived from Rogowski oil. This may lead to error in measuring ative or reative power. To overome these undesirable effets, the independent parameters of the phase funtion of the oil in (5) must be hanged to suit the modified design. Hene: (R + R) ω LC(R+ R) 0 t i i t (R + R ) t (R + R ) i t ω LC i (5) However, any hange in the struture of the oil ould lead to undesirable effet in all the dependent parameters in (5). Thus, keeping the values of R, R t, L and ω in (5) unhanged, it an be rewritten as: C (R + ) 0 i i C(R + ) i i (6) Based on (6) and keeping R t onstant, the variations of resistane with apaitane is shown in Fig. 5 from whih optimal parameters for the integrator iruit an be obtained so as to nullify the time delay of the oil. Fig. 6 shows the same but with three different values of the terminal resistor, R t. It is evident from (5) that by dereasing R t, C i R i urve is delined. For example, if C i 40 μf, for R t 1 Ω, Ω and 5 Ω, the orresponding values of R i will be kω, 16. kω and 38. kω, respetively. This implies that for an optimal design, the independent parameters should be seleted suh that nullifying the phase funtion while the amplitude funtion is maximum. Hene, the amplitude funtion is: Fig. 4 Bode diagram of whole system. Fig. 5 Drawn urve based on (6). Fig. 6 Variation of the C i R i urve in R t 1Ω, Ω and 5 Ω. t H(j ω ) B t L + R C (R + R ) + R R C i i t i t i (7) 34 Iranian Journal of Eletrial & Eletroni Engineering, Vol. 6, No. 4, De. 010

4 Substituting (5) into (7), will yield to: t H(j ω) (R + R ) t (8) L + R C t i L ω By using (8), there are three options for inreasing the output of the oil. a) inreasing the mutual indutane, M of the oil as desribed in [11]. However, the hange of the oil's struture is the drawbak of this option. b) inreasing the apaitane C i of the integrator iruit, thereby inreasing the amplitude funtion to some extent. The best option is to find an optimum value of terminal resistor (R t ) thereby inreasing the oil's output to maximum extent, as shown in Fig. 7. That is: H(j ω) L ω + R 0 R t (9) R 1 L Cω t i Aording to (9), the optimal value of R t depends on C i as shown in Fig. 7. For making optimal deision on the independent parameters, initially, the highest permissible apaitane should be seleted so as to obtain an optimal value of terminal resistor, onsidering operating frequeny. This will lead to alulate the value of R i from (5). It stands to reason that the output voltage of the oil an trae the input urrent in an exat manner with the maximum amplitude. An experimental data using Rogowski oil for measuring partial disharge is shown in Fig. 8. Although it shows the Rogowski oil behavior for high frequeny measurement, it reveals information onerning the idea upon whih the variation in termination elements (for R0.5 ohms and R 10 ohms) ould hange the time delay of oil output. As a result, the proposed optimal termination element provides an exellent auray for the urrent measurement partiularly, for the phase funtion. 4 Performane Evaluation of Rogowski Coil and Current Transformer in Fundamental Frequeny It is now an arguable question for the superiority of Rogowski oil over CT for power frequeny. In power system, Rogowski oil is used for measurement and protetion appliations as the urrent transformer. So, in the performane evaluation, these appliations should be onsidered. Equipment used for measurement and protetion purposes must possess the following features: Traking the atual value in normal and fault onditions. Free from eletromagneti interferene (EMI) noises. Compatible with system requirement. Proteting the monitoring devies in fault onditions. Fig. 7 Variation of amplitude funtion in terms of R t with three different C. Fig. 8 Measured partial disharge using Rogowski oil [1]. Fig. 9 Equivalent iruit of CT. Compat in weight and size and easy installation. Very low energy onsumption. Undoubtedly, the superiority of Rogowski oil in the last two features is onspiuous. However, for the other features, CT s equivalent iruit, based on IEEE and IEC standard [8], shown in Fig. 9 should be analyzed where, Z s is nonlinear impedane desribing the behavior of CT s ore and R eqs and X eqs are the series equivalent resistane and indutane respetively. Also, Z B represents the impedane of CT s load (burden). Based on eletromagneti theory, the magneti branh of a transformer onsists of a resistane and an Rezaee & Heydari: Design Modifiation of Rogowski Coil for Current Measurement in Low Frequeny 35

5 indutane with no-load loss and no-load magneti VA, respetively. Beause of large air gap in CT and L 1/R, the indutane, L is very low. Thus, the resistane of magneti branh (R ore ) an be negleted. The leakage indutane of CT an also be ignored beause; the seondary winding is very lose to the ore. Thus, the CT equivalent iruit beomes as shown in Fig. 10 where, X s is a nonlinear indutane. The vetor diagram of simplified equivalent iruit of CT is shown in Fig. 11. Figure 11 shows that there is a differene, in both amplitude and phase values, between the measured urrent I B with the intended measured urrent I s. This differene is aused not only by variation of the CT's burden, but mainly by hanging the magnetizing urrent I e. Sine we have: E E E s s s I e X πfl μμna (10) m m 0 r πf l where f, μ 0, μ r, N, A and l are the operating frequeny, air permeability, relative permeability, number of seondary winding, the ross-setional area of CT s ore and the mean length of the ore respetively. Beause of magneti property of the ore material, the relative permeability is onsiderably hanged by the saturation effet. In addition, the output of CT is affeted by another property of magneti material; the remnant flux. Moreover, these phenomena ause many distortions on CT s output during fault onditions [8]. As suh, Rogowski oils are far better than CTs in traking the atual value in normal and fault onditions. The Influene of EMI on Rogowski oil is a drawbak, if an operational amplifier is onneted to its output. In this study, this has been overome by using the passive integrator iruit. Sine modern proteting or monitoring devies needs voltage signal input thus, Rogowski oils an be Fig. 10 Equivalent Simplified equivalent iruit of CT. Fig. 11 Vetor diagram of simplified equivalent iruit of CT. diretly onneted to them. While, CTs output urrent signal needs a onverter with no negative effets on its burden. Although, saturation effet of CT's ore is benefiial feature for proteting the monitoring devie, this leads to error in the measuring proess. However, proteting the monitoring devie using Rogowski oil an be performed by introduing a zener diode with no error reation. 5 Conlusion The analysis of the oil s transfer funtion in frequeny domain shows that the output voltage is either lagging or leading the measured urrent. The proposed method improves this undesirable phenomenon. In addition, in zero phase differene for obtaining the maximum voltage output, the terminal resistor effets were onsidered. Consequently, to nullify the phase differene and to maximize the oil s output, the suitable R t, R i and C i were seleted for preise urrent measurement. It an therefore be onluded that Rogowski oils are yet more effiient measuring and proteting devie whih an provide omparable performane with onventional CTs, for low frequeny appliations. Referenes [1] Sinapius I. G., Hoornaert W. and Middelhoek S., Measuring Current, Voltage and Power, Handbook of Sensors and Atuators, Vol. 7, Elseiver, [] Shateri H. and Jamali S., Effets of CT and VT Connetion Point on Distane Protetion of Transmission Lines with FACTS Devies, Iranian Journal of Eletrial & Eletroni Engineering, Vol., Nos. 3 & 4, pp , July 006. [3] Ward D. A., Exon J. and La T., Using Rogowski oils for transient urrent measurements, Eng. Si. Edu. J., Vol., No. 3, pp , Jun [4] Ramboz J. D., Mahinable Rogowski oil, design and alibration, IEEE Trans. Instrum. Meas., Vol. 45, No., pp , Apr [5] Kojovi L., PCB Rogowski oils benefit relay protetion, IEEE Comput. Appl. Power, Vol. 15, No. 3, pp , Jul. 00. [6] Karrer N. and Hofer-Noser P., PCB Rogowski oils for high di/dt urrent transformer, in Pro. IEEE PESC, pp , Galway, Ireland, Jun [7] das Chagas Fernandes G. F., Santos Mota W., Current Transformer Model, IEEE Transation on Power Delivery, Vol., No. 1, January 007. [8] Kojovi L. A., Comparative Performane Charateristis of Current Transformers and Rogowski Coils used for Protetive Relaying 36 Iranian Journal of Eletrial & Eletroni Engineering, Vol. 6, No. 4, De. 010

6 Purposes, IEEE Power Engineering Soiety General Meeting, pp. 1-6, June 007. [9] Cooper J., On the high frequeny response of a Rogowski oil, Journal of Nulear Energy, Part C, Vol. 5, pp , [10] Tumanski S., Indution Coil Sensors-a Review, Measurement Siene & Tehnology, Vol. 18, No. 3, pp. R31-R46, Marh 007. [11] Rezaee M. and Heydari H., Mutual Indutanes Comparison in Rogowski Coil with Cirular and Retangular Cross-Setions and Its Improvement, 3rd IEEE Conferene on Industrial Eletronis and Appliations, pp , June 008. [1] Argüeso M., Robles G. and Sanz J., Implementation of a Rogowski oil for the measurement of partial disharges, Review of Sientifi Instruments, Vol. 76, No. 6, pp , June 005. Morteza Rezaee reeived the B.S. and M.S degree in eletrial power engineering from Nooshiravani University of Babol and Iran University of Siene and Tehnology (IUST), in 005 and 008, respetively, and is pursuing the Ph.D. degree in IUST. His researh interests inlude Eletromagneti Compatibility (EMC), Current Measurement, Eletrial Mahine and Renewable Energy Conversion Systems issues. Hossein Heydari reeived the B.S. degree in eletrial engineering and the M.S. degree in power eletronis from Loughborough University, U.K., in 1985 and 1987, respetively, and the Ph.D. degree in transformer ore losses from the University of Wales, Cardiff, U.K., in Following graduation, he joined Iran University of Siene and Tehnology (IUST), Tehran, Iran, as an Aademi Member (Leturer) of the Eletrial Power Group, and was also appointed Diretor of the High Voltage and Magneti Materials Researh Center. His leture duties are eletrial mahines, eletrial measurement and instrumentations, and eletromagneti ompatibility (EMC) appliations in eletrial power systems. He is urrently with the Center of Exellene for Power System Automation and Operation, Iran University of Siene and Tehnology. His researh interests are EMC onsiderations in eletrial power systems, fault urrent limiters, superondutors, and ore losses in eletrial mahines. Rezaee & Heydari: Design Modifiation of Rogowski Coil for Current Measurement in Low Frequeny 37