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Using TACS Functions Within EMTP to Set Up Current-Transformer Model Based on the Jiles–Atherton Theory of Ferromagnetic Hysteresis Shun-Tsai Shun-Tsai Liu, Sy-Ruen Sy-Ruen Huang , Member, Hung-Wei Chen Member, IEEE , and Hung-W
Abstract—The
subject of this paper is to construct a currenttransformer (CT) model based on the Jiles–Atherton (J–A) theory of ferromagnetic hysteresis using transient analysis of control systems (TACS) functions within the Electromagnetic Transients Program (EMTP) in a closed-loop manner. The J–A theory of ferromagnetic hysteresis is presented by the nonlinear first-order ordinary differential equations and inclusive of five parameters that can be found by measurements measurements of hysteresis hysteresis characteristic. We can use TACS functions within EMTP to describe the J–A theory of ferromagnetic hysteresis. The powerful advantage of this way is the interactio interaction n between between the electric electrical al network network and TACS in EMTP. EMTP. Compared with the CT model based on the type 96 nonlinear hysteresis inductor, the simulated result of the CT model based on the J–A theory of ferromagnetic hysteresis is almost the same in steady-state situations, but apparently different in a fault transient situation. The analysis and simulation of the actual measured fault profiles in the Taiwan power system is an example of the validation of this proposed model. Therefore, this proposed CT model based on the J–A theory of ferromagnetic hysteresis has the analysis capability of the transient response. The flexibility of TACS makes the simulation of any other situation easier and is another advantage. Index
Terms—Current Current
transfor transformer mer (CT), (CT), Electro Electromagne magnetic tic Transients ransients Program Program (EMTP), (EMTP), Jiles–Athe Jiles–Atherton rton (J–A) hystere hysteresis sis model, transient analysis of control systems (TACS).
I. INTRODUCTION HE topic of this paper is to construct a current-transformer (CT) model based on the Jiles–Atherton (J–A) theory of ferromagnetic hysteresis using transient analysis of control systems (TACS) functions within the Electromagnetic Transients Progra Program m (EMTP) (EMTP).. The J–A hyster hysteresi esiss theory theory descri describes bes the magmagnetization process of ferromagnetic materials and, therefore, is regarded as a physical model of ferromagnetic hysteresis [1]. The reaction of the CT model based on the J–A theory is according to the physical characteristic of ferromagnetic materials. For the investigation of power system transient problems, it is practical to use this model. Discussions about J–A theory of ferromagnetic hysteresis [2]–[1 [2]–[10] 0] publis published hed papers papers mostly mostly descri describe be the basic basic magmagnetic characteristic characteristicss or parameters parameters influence. Knowing how
T
Manuscript received May 17, 2006; revised November 30, 2006. Paper no. TPWRD-00276-2006. The authors are with the Energy Conversion Laboratory, Laboratory, Department of Electrical Engineering, Feng Chia University, University, Taichung Taichung 40724, Taiwan, R.O.C. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2007.905809 10.1109/TPWRD.2007.905809
to use this model is rarely talked about. Compared with other methods, the J–A theory of ferromagnetic hysteresis constitutes first-order nonlinear ordinary differential equations and has five parameters that can be determined by hysteresis loop measurements. This paper is intended to set up the CT model based on the J–A theory of ferromagnetic hysteresis using TACS within EMTP. In the power system, the equipment used for ferromagnetic materi material al to perfor perform m energy energy conve conversi rsion on is popul popular ar all over. over. When When we study the transient response of the power system, the nonlinear characteristic of the CT caused by core magnetic saturation is always bothersome. When When discussing overcurrent, inrush current, and ferroresonance of CT influence on power systems, the the key key poin pointt is the the nonl nonlin inea earr char charac acte teris risti ticc of CT caus caused ed by core core magnetic saturation [11]. Knowing how to set up the CT model becomes very important. The rest of this paper is organized as follows. Section II describes describes the J–A theory of ferromagnet ferromagnetic ic hysteresi hysteresis, s, while Section III describes how to set up the J–A hysteresis model using TACS functions. Section IV states the simulated results of the proposed proposed model model compar compared ed with with anothe anotherr CT model model including including the type 96 nonlinear nonlinear hysteresis hysteresis inductor. Section V then displays the analysis and simulates the actual measured fault profile to validate this proposed model. Conclusions are finally made in Section VI. II. II. J–A J–A THEORY OF FERROMAGNETIC H YSTERESIS The The main main prop proper erty ty of the the J–A J–A theo theory ry of ferr ferrom omag agne neti ticc hyster hysteresi esiss is is the the decom decompos positi ition on of of the the magne magnetiz tizati ation on into into its rever reversib sible le compon component ent , which which corres correspon ponds ds to domain domain bending during the magnetization process, and its irreversible compon component ent , which which corres correspon ponds ds to domain domain wall wall displa displacecement against the pinning effect [2] (1) The effec effectiv tivee field field
and flux densit density y
are calcul calculate ated d by (2) (3)
where where is the magnet magnetiza izatio tion n force force in the core, core, is an interd interdoomain coupling coupling factor, factor, and is the permeabili permeability ty of free space. space. The anhyst anhystere eretic tic magnet magnetiza izatio tion n is given given by the Lange Langevin vin function
0885-8977/$25.00 © 2007 IEEE
(4)
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Fig. 2. CT model based on the J–A theory of ferromagnetic hysteresis.
Fig. 1. Interaction between the electrical network and TACS in EMTP.
where is the saturation magnetic moment of the core material and is a shape parameter. The hysteresis differential equation for irreversible susceptibility can be shown as (5) where
is a directional parameter, 1 for , and 1 for . The component of reversible magnetization reduces the difference between the prevailing irreversible magnetization and the anhysteretic magnetization at the given fi eld strength. This can be expressed as (6) where is a domain fl exing parameter. The hysteresis differential equation for reversible susceptibility can be expressed as (7) Combining (1)–(7) derives the hysteresis differential equation for magnetization (8)
III. SETUP OF C URRENT T RANSFORMER M ODEL B ASED ON J–A THEORY OF F ERROMAGNETIC H YSTERESIS The TACS is used to solve the differential and algebraic equations completed by a series of interconnecting elements, such as transfer function, gain, limiters, algebraic and logical variables, and other special components. Use of TACS is the same as the electrical circuit in EMTP [12]. These components are described by the adequate parameters, via processing, and the solution can be found. Any TACS signal can feed back to the electrical network as a voltage or current source, or as a signal controlling the operation of a switch, valve, or diode. Similarly, the voltage or current of any node of an electrical network in EMTP can be retrieved as the source signal of TACS. The interaction between EMTP and TACS is shown as Fig. 1. According to the following description of J –A theory of ferromagnetic hysteresis and TACS functions, the CT model based on J –A theory of ferromagnetic hysteresis can be established as Fig. 2. The fl owchart of the J –A hysteresis model using TACS
Fig. 3. Flowchart of the J–A hysteresis model using TACS functions.
functions is shown as Fig. 3. The procedure of this model is as follows. Step 1) Thecurrent can be captured from the power circuit by the type 91 component of TACS as magnetomotive force (MMF). Step 2) The type 98 component is an operator of algebraic and logic calculations. The type 58 component is an integrator. The type 59 component is a differentiator. Via a series of operations, the fl ux density using the J –A hysteresis model can be found in a closed-loop manner. Step 3) The induced voltage of the CT through a physical response can be found. Finally, this voltage feeds back to the power circuit from TACS using the type 61 component.
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Fig. 5. Hysteresis curve of the CT J –A hysteresis model in the steady-state situation.
Fig. 4. (a) Circuit diagram of the test system. (b) Equivalent circuit diagram of the test system including the CT model.
TABLE I CORE P ARAMETERS OF CT J–A H YSTERESIS M ODEL
IV. SIMULATION AND T EST In general, the type 96 nonlinear component is used to simulate the CT hysteresis characteristic in EMTP these days. The hysteresis information of this component can be found from an experiment or by solving ordinary differential equation using software (such as MATLAB). The combination of this component and other necessary elements can construct the CT model with a hysterersis characteristic. The circuit diagram of the test system is shown as Fig. 4(a). It is a 230-kV power system inclusive of the generator, transmission line, and load. That switch is closed to simulate the fault situation. The CT is used to detect the current of the transmission line. The equivalent circuit diagram of the test system, including the CT model, is shown in Fig. 4(b). The core parameters of the CT J –A hysteresis model are shown in Table I. is the turn ratio, is the length of the average magnetic path, is the cross area of the core, and is the coercivity of core. The simulating hysteresis curve
Fig. 6. Secondary currents of CT based on the J–A hysteresis model and type 96 nonlinear hysteresis model in the steady-state situation.
of the CT J–A hysteresis model is shown in Fig. 5. For the comparison of the transient response with a type 96 nonlinear hysteresis component, both hysteresis characteristics are the same. When the power circuit operates in the steady-state situation, the secondary currents of the CT based on the J –A hysteresis model and type 96 nonlinear hysteresis model are shown in Fig. 6. The difference between the two models is very tiny. While the fault occurs in the power circuit, the fault current is shown in Fig. 7. The CT secondary currents using the J–A hysteresis model and type 96 nonlinear hysteresis model are shown as Fig. 8. Since the dc component of faulted current drives the core magnetic material to saturation, the simulated results are explicitly different. In the fault transient situation, the fl ux will follow the alteration of the MMF according to the core physical property. The hysteresis curve of the CT J –A hysteresis model is not the same in every cycle as shown in Fig. 9. V. ACTUAL P ROFILE AND V ALIDATION The analysis and simulation of the single-phase ground fault of the power-supply system in Taiwan is an example to validate the accuracy of the CT J –A hysteresis model. A one-line diagram of the power-supply system is shown in Fig. 10. There are two generating units, two transformers, two transmission lines, two buses, and six circuit breakers (CBs) in this system. CTs are plugged on transmission lines for measuring the currents. When a transmission-line fault occurs, the dc component of the fault current makes the core magnetic field of the CT and transformers reach saturation. This saturating effect of the CT makes
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Fig. 7. Fault current on the transmission line.
Fig. 8. CT secondary currents using the J-A hysteresis model and type 96 nonlinear hysteresis model in the fault transient situation.
Fig. 9. Hysteresis curve of the CT J–A hysteresis model in the fault transient situation.
Fig. 11. Actual measuring transient profiles of three-phase voltage on line 2, when single-phase ground fault of line 2 occurs. (a) Three phase. (b) R phase. (c) S phase. (d) T phase.
Fig. 10. One-line diagram of the power-supply system.
the measuring current produce serious distortion. This phenomenon can be simulated by the J –A hysteresis model. Actual measuring transient pro files of three-phase voltage and current on line 2 are shown in Figs. 11 and 12, when the R-phase ground fault of line 2 occurs. At the #1 time point, the R phase of line 2 happens to ground fault and reduces to zero; and are lightly distorted. increases to 4 p.u. due
to fault; and produce waveform distortion due to dc components. The magnitude of diminishes to 20% for demonstration of the entire waveform. At the #2 time point (about 2.5 cycles later), the CBs open and cut off current by extinguishing arc as current reaches zero. presents the abnormal phenomenon; and produce waveform distortion due to transient recovery voltage of CB switching. At the #3 time point, the switching time of the R-phase CB lags half cycle to the other two phases; therefore, the clear time of R phase also lags half cycle to the other two phases. The core parameters of the transformer J –A hysteresis model are shown as Table II. Compared with Table I, we can find
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Fig. 12. Actual measuring transient profiles of three-phase current on line 2, when single-phase ground fault of line 2 occurs. (a) Three phase. (b) R phase. (c) S phase. (d) T phase.
TABLE II CORE P ARAMETERS OF T RANSFORMER J –A H YSTERESIS M ODEL Fig. 13. Simulating transient waveforms of three-phasevoltage on line 2, when the single-phase ground fault of line 2 occurs. (a) Three phase. (b) R phase. (c) S phase. (d) T phase.
that the core parameters of the CT and transformer are apparently different. Simulating transient waveforms of the threephase voltage and current on line 2 are shown as Figs. 13 and 14. Compared with actual measuring transient waveforms, the simulating result is very perfect. Therefore, the J–A hysteresis model of the CT and transformer can adequately describe the core magnetic characteristic.
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with the type 96 CT model, there is no difference in the steadystate situation. The simulating results are apparently different in the fault transient situation. The type 96 CT model cannot describe the saturating effect of the magnetic fi eld. This J–A hysteresis model is used to set up the CT and transformer hysteresis characteristic. The simulation of the single-phase ground fault of the power-supply system in Taiwan is completed to validate the accuracy of the J –A hysteresis model. Besides, the signal source of this model can come from any node of the power circuit. With a series of TACS calculations, the output result feeds back to the power circuit. The fl exibility of this model is another major advantage. REFERENCES [1] D. C. Jiles and D. L. Atherton, “ Theory of ferromagnetic hysteresis,” Magnet. Magn. Mater., vol. 61, pp. 48–60, 1986. [2] J. V. Leite, N. Sadowski, P. Kuo-Peng, N. J. Batistela, J. P. A. Bastos, and A. A. de Espindola, “Inverse Jiles-Atherton vector hysteresis model,” IEEE Trans. Magn. , vol. 40, no. 4, pp. 1769–1775, Jul. 2004. [3] J. V. Leite, N. Sadowski, P. Kuo-Peng, N. J. Batistela, and J. P. A. Bastos, “ The inverse Jiles-Atherton model parameters identification,” IEEE Trans. Magn. , vol. 39, no. 3, pt. 1, pp. 1397–1400, May 2003. [4] N. Sadowski, N. J. Batistela, J. P. A. Bastos, and M. Lajoie-Mazenc, “An inverse Jiles-Atherton model to take into account hysteresis in time-stepping finite-element calculations,” IEEE Trans. Magn., vol.38, no. 2, pp. 797–800, Mar. 2002. [5] P. R. Wilson, J. N. Ross, and A. D. Brown, “Magnetic material model characterization and optimization software,” IEEE Trans. Magn. , vol. 38, no. 2, pt. 1, pp. 1049–1052, Mar. 2002. [6] P. R. Wilson and J. N. Ross, “ Definition and application of magnetic material metrics in modeling and optimization,” IEEE Trans. Magn., vol. 37, no. 5, pp. 3774–3780, Sep. 2001. [7] P. R. Wilson, J. N. Ross, and A. D. Brown, “ Optimizing the JilesAtherton model of hysteresis by a genetic algorithm,” IEEE Trans. Magn., vol. 37, no. 2, pt. 2, pp. 989–993, Mar. 2001. [8] Y. Bi and D. C. Jiles, “ Measurements and modeling of hysteresis in magnetic materials under the action of an orthogonal bias field,” IEEE Trans. Magn., vol. 35, no. 5, pt. 2, pp. 3787–3789, Sep. 1999. [9] W. M. Polivka, “Subcircuit modeling of magnetic cores with hysteresis in PSPICE,” IEEE Trans. Aerosp. Electron. Syst. , vol. 38, no. 4, pp. 1425–1434, Oct. 2002. [10] D.C. Jiles, J.B. Thoelke, and M.K. Devine, “Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis,” IEEE Trans. Magn. , vol. 28, no. 1, pp. 27–35, Jan. 1992. [11] Working Group C-5 of the System Protection Subcommittee of the IEEE Power System Relaying Committee, “ Mathematical models for current, voltage, and coupling capacitor voltage transformers,” IEEE Trans. Power Del., vol. 15, no. 1, pp. 62–72, Jan. 2000. [12] Electromagnetic Transients Program (EMTP) Revised Rule Book Version 3.0 vol. 1, EPRI. [13] R.W. Wall and B. K.Johnson, “Using TACS functionswithin EMTP to teach protective relaying fundamentals,” IEEE Tans. Power Syst., vol. 12, no. 1, pp. 3–10, Feb. 1997. Fig. 14. Simulating transient waveforms of three-phase current on line 2, when the single-phase ground fault of line 2 occurs. (a) Three phase. (b) R phase. (c) S phase. (d) T phase.
Shun-Tsai Li , photograph and biography not available at the time of publication.
VI. CONCLUSION
Sy-Ruen Huang (M’93), photograph and biography not available at the time of publication.
This paper proposes a method of setting up the CT model based onthe J–A theory of ferromagnetic hysteresis using TACS functions within EMTP. This model can honestly and naturally react according to the core physical characteristic. Compared
Hung-Wei Chen, photograph and biography not available at the time of publication.
