Simulation and Analysis of Electromagnetic Transient Characteristics of Controllable Reactor of Transformer Type

Transcription

1 Siulation and Analysis of Electroagnetic Transient Characteristics of Controllable eactor of Transforer Type TIAN MINGXING, ZHAO QIANU, YIN JIANNING, LIU YIBIN Autoation and Electrical Engineering Lanzhou Jiaotong University Lanzhou Gansu CHINA Abstract: This paper analyzed the winng construction of Controllable eactor of Transforer Type (CT), based on the duality theory a new transient odel of CT is proposed. It can reflect the electric circuit coupled with agnetic circuit correctly. Fitting the agnetization curve with the function fitting ethod and the siulation results prove the accuracy of the odel. Proposing vide CT s working process into operating process and grade-changing process. And analyze and research the transient processes of the two processes respectively. Accorng to the transient odel build CT no-load switching-in atheatical odel, do siulation research with ATP-EMTP, analyze the phenoena of agnetizing inrush current in operating process. And analyze current of each winng in grade-changing process, the siulation results verify the correctness of the odel and analyze the transient characteristic of CT. Key-Words: Controllable eactor of Transforer Type; Transient odel; ATP-EMTP; Magnetizing inrush current; Transient characteristic 1 Introduction With the increasing level of power line voltage, the EHV power and high surge ipedance loang copact transission line is developing very fast. But this leads to a critical proble -- Ferranti effect. In order to guarantee the security, reliability, stability of the power grid, reactive power copensation device ust be used to achieve the purpose of reactive power balance and voltage control [1]. In recent years, CT (Controllable eactor of Transforer Type) has been stued as a new type of controllable reactor. It has the characteristics as fast and sooth adjustent and sall haronic current. CT is not only able to provide real-tie solution to the proble of Ferranti effect but also independent fro an over reliance on power electronic technology. To study the transient process of CT, the establishent of an accurate equivalent odel is necessary The reference [1] analyzed the working characteristics of the CT by establishing the polygon equivalent circuit odel, this odel can reaction coupling between the winngs, but ignored the core saturation characteristic, which ake the results of transient process is not accurate, and the odel is not only coplex, also bring fficulties for the design of CT. The reference [2] analyzed the operation ode of CT by establishing the equivalent circuit odel of any parallel branches, but it ignored the leakage resistance and resistance between the winngs. So it ake the calculation results of control winng current is erroneous. And this odel d not consider the core saturation characteristic, thus it is not suitable for transient study. The reference [3] analyzed the equivalent circuit odel of ulti-winng transforer. And the ray for equivalent circuit odel is proposed. But this odel ignored the coupling effect and core saturation characteristic. So this odel not only does not apply to transient study but also reduce the accuracy of the calculation result of current. The reference [4] established trapezoidal equivalent circuit odel by using duality principle. The odel considered the electroagnetic coupling E-ISSN: X 15 Volue 14, 215

2 between the winngs and the alternating agnetic flux leakage, but ignored the core saturation characteristic. Therefore, this paper based on the structure of CT, a new equivalent circuit odel for the practical application is proposed. In this odel, agnetic leakage flux and the core saturation are considered. Besides, the coupling relation between electric circuit and agnetic circuit is reflected. The reference [5] analyzed the transition process of the CT, and cae to a conclusion that there is zero transient in CT on the preise of ignoring the excitation branch. This paper study on the transient process of CT under the sae contion but couldn't get sae conclusion. In adtion, this paper conducts a detailed study of the transient process of CT. And obtain the transient current of each winng. 2 CT basic operation principle CT is ainly coposed of high voltage work winng, low voltage control winng and thyristors, the basic operation principle is shown in figure u1 W1 i2 W2 in i3 W3 Wn CL2 CL3. CLn Fig.1 Basic circuit agra of CT In figure1, W 1 is work winng, W 2 W 3 W n are control winngs, Th 2 Th 3 Th n are anti-parallel thyristors, CL 2 CL 3 CL n are current liiting inductors, u 1 is work voltage. When put the voltage on work side, we can adjust reactive power capacity by control the size of conduction angle of the anti-parallel thyristors. As the figure 1 shows, CT is ulti-winng transforer whose control winngs are work in the state of short-circuit in sequence. The core winng structure of CT is shown in figure 2. The outerost layer W 1 is Th2 Th3 Thn work winng, W 2 W 3 W 4 which close to the core are control winngs. The core structure is syetrical. So analyze the right half of core. W 1 W 2 W 3 W 4 Φ W 4 Φ 13 W 3 Φ 12 Φ 11 Φ 14 Φ 1 Fig.2 Core winng structure of CT In figure 2, Φ is half of ain agnetic flux of core, Φ is agnetic flux of core yoke, Φ 11 Φ 12 Φ 13 Φ 14 Φ 15 are leakage agnetic flux between winngs. 3 The transient odel of CT 3.1 Magnetic circuit odel Accorng to the figure 2 can get the agnetic circuit odel of CT which is shown in figure 3. i4 i Φ Φ 14 Φ 13 Φ 12 Φ 11 Φ 1 Φ i2 Φ W4 Φ W3 Φ W2 Φ W1 F 4 F 3 F 2 F 1 Fig.3 Magnetic circuit odel of CT In figure3, F 1 F 2 F 3 F 4 are agnetootive force of each winng respectively, are resistance of core and core yoke respectively, are resistances of leakage agnetic flux between the winngs, i2 i3 i4 are resistances of core between the leakage agnetic circuit. Accorng to Gauss theore in agnetic field and Apere cycle theore, a agnetic circuit equation is built as follows (Because the resistance of core between the leakage agnetic circuit is far less than excitation reluctance, so here is ignored): W 2 W 1 Φ E-ISSN: X 151 Volue 14, 215

3 F1 + F2 + F3 + F4 φ + φ + φ11 + φ φ φ φ1414 = N1 + N 2i2 + N 3i3 + N 4i4 = F1 + F2 + F3 + F4 φ = φ + φ1 + φ11 + φ12 + φ13 + φ14 (1) piecewise fitting and does tests with MATLAB which is shown in figure 6. The siulation result proves that the fitting ethod adopted in this paper is able to describe the characteristic of nonlinearity of core odel. B / T Measured curve Calculated curve 3.2 Circuit odel Accorng to the forula (1) as well as the duality principle of circuit and agnetic circuit, the trapezoidal equivalent circuit odel of CT which is shown in figure 4 is built. u 1 1:1 L 1 L 11 L 12 L 13 L 14 N 1:N 2 N 1:N 3 N 1:N 4 N CL 2 1 N CL 3 u 1 N 1 CL 4 2 u2 u 3 u L u 4 3 u 4 N 3 N 4 Th 2 Th 3 Th 4 L N H / A/ Fig.6 The agnetization curve of Measured and calculated And the atheatical odel of core is shown in forula (2): B = 1.21/ H H H / H B = e H < H H ax (2) Fig.4 Circuit odel of CT In figure 4, the nonlinear inductance L L are the inductance of core and core yoke respectively, the linear inductance L 1 L 11 L 12 L 13 L 14 are the leakage inductance of each winng respectively. 3.3 The core odel The agnetization curve of 3Q13 type grain-oriented agnetic steel sheet which is published by Wuhan Iron and Steel Mining Copany is shown in figure 5. B / T H / A/ Fig.5 Magnetization curve of grain-oriented agnetic steel sheet For the convenience of calculation and high precision, function fitting ethod is adopted to build the core odel of CT. By contrasting the fitting results of soe coon functions, the paper, describes the nonlinearity of core in the ethod of 4 The transient process of CT The working process of CT can be subvided into operating process and grade-changing process. The operating process is no-load input the power grid. The grade-changing process is working side put into the power grid and control winngs work as progressive single branch ode [1]. 4.1 The operating process The research of operating process, ainly consider the no-load closing process. The voltage equation for CT is shown as below: 1 dψ u1 = L1 + 1i 1 + N1 ψ = f ( i ) (3) = i And: dψ dψ db = = k = kµ dh So: ( L1 + kµ N1) = u1( t) (4) Set L = L1 + kµ N1, = 1, and E-ISSN: X 152 Volue 14, 215

4 u 1( t) = U cos( ω t + α). The forula (4) can be siplified into: U 1 + = cos( ω t + ) L L α Set the switch for closing oent t=, i 1 (t) should eet the initial contion: i 1 t = = Get i 1 (t) solution consists of two parts: one is steady state coponent part,the other is transient state coponent, as follows: U ( t) = [ cos( ωt + α) + ω L + ωlsin( ωt + α) e t L (5) ( cosα + ωlsinα)] We can get to know fro the forula (5), steady current is a cosine function, the transient current decreases gradually and tends to zero eventually. In order to get the further reduction, we ake: cosφ = / + ω L sinφ = ωl / + ω L And put into forula (5), so U ( t) = [cos( ωt + + ω L (6) t L α φ) cos( α φ)e ] And φ = arctan( ωl / ). i 1 (t) and u 1 (t) have the sae cycle, but the phase angle fall behind φ 9, so we can further reduction the forula (6) as follows: U ( t) = [sin( ωt + α) + ω L (7) t L e sinα] Thus, the forula (7) is the atheatical odel of CT in no-load input power grid. As we can see fro the forula, working current is ainly coposed of two parts, one is the ac power sinusoidal coponent the other one is the dc coponent which is decreasing in the for of index. Besides, the value of working current is influenced by initial angle α at input oent. It s not hard to see fro the forula, the aplitude of the dc coponent is axiu when π / 2. As the agnetization curve is nonlinear, inrush current is 4~6 ties of rating. In this paper, a 5 kv CT for no-load switching-in siulation research is shown in figure 7. i / KA Fig.7 Excitation current of CT It is can be seen fro the siulation results of figure 7, the transient process lasted 24 cycles, and inrush current attenuation in the for of index, the attenuation constant is associated with the degree of saturation of core, the reactance of the feature of CT akes its attenuation slower. And the inrush current reached 4.92 ties of rated current. The spire of the wave shows that there is higher haronic coponent in working current. 4.2 The grade-changing process Take advantage of electroagnetic transient progra ATP-EMTP to set up CT siulation odel. The basic idea of ethod to deal with various circuit coponents is use the fferential equation to describe voltage and current relationships of various circuit coponents in the process of transition [7]. Based on the equivalent circuit odel of CT in figure 4, the siulation odel is built. The grade-changing process of CT is control the thyristors action of each branch. Stipulated that put the control winng into work at the ode of progressive single branch. And use the trigger pulse to control each thyristors. Using the electroagnetic transient siulation software ATP-EMTP to siulate the grade-changing process and adapting the birectional thyristors Type-12 instead of reverse parallel thyristors. Select the TACS type 24 of the transient control syste for each thyristors trigger pulse sequence. Factor which influencing the grade-changing process of transient response is the action oent for each branch of thyristors. Different actions E-ISSN: X 153 Volue 14, 215

5 oent can lead to fferent initial voltage and fferent transient process. Accorng to the above analysis, the current of each winng at zero oent and peak oent is siulated respectively as follows: (1) The oents of thyristors switch-in are.55s,.515s,.525s,.535s (naely source voltage is zero points) respectively. The current siulation results are shown in figure figure 9. / A (a) The siulation wavefor of i 1 / A i / A i2 i3 i4 i5 i / A (a) The siulation wavefor of i 1 i2 i3 i4 i (b) The siulation wavefor of each control winng current Fig.8 The wavefors of current in zero tie As the figure 8(a) shows, the aplitude of i 1 will increase when input each control winng. This is because CT is controlled by the access of control winng to achieve the purpose of the reactive power balance and voltage control. As figure 8(b) shows, the control winngs which have accessed to circuit will be affected by the access of subsequent control winngs. And the aplitude of control current which have accessed to circuit is decreasing after the access of each subsequent control winng. This is because the existence of utual leakage resistance between the control winngs. When put all the control winngs into circuit, each branch current also can reach steady state. But, at this point the transition period of grade-changing process is.23s. (2) The oents of thyristors switch-in are 5s, 5.1s, 5.2s, 5.3s (naely source voltage is peak points) respectively. The current siulation results are shown in (b) The siulation wavefor of each control winng current Fig.9 The wavefors of current in peak tie As figure 9 shows, the rule of current wavefors is siilar to the figure8. But the highest transient current is four ties in zero tie. And at this point the transition period of grade-changing process is.21s. Coparing figure 8(a) and figure 9(a), the transition process of the CT is not affected by oent of thyristors switch-in and there is a transition process inevitably. Coparing figure 8(b) and figure 9(b), transient current in peak tie is bigger than it in zero tie. And it can affect the reliability and life of the CT. Accorng to the characteristic of birectional thyristors, if reove the control signals, the thyristors will switch-off only when the current through the zero oent. So the tie of switch-off is at the source voltage peak oent and there is no transient process. 5 Conclusions There are any factors that influence the CT transient response, fferent processes have fferent factors. This paper propose to vide CT s working process into two independent but interactional processes: operating process and grade-changing process. And the transient processes of the two processes are analyzed E-ISSN: X 154 Volue 14, 215

6 and researched respectively. (1) The factors causing transient response in the operating process are the initial phase angle of supply voltage at the oent of access and the nonlinearity characteristic of the core. No atter which initial phase angle we adopt, the transient process ust inevitably exist. But, when the initial phase angle is π / 2, the instantaneous value of inrush current reaches axiu. (2) The factor causing transient response in the grade-changing process is the conduction angle of thyristors. The forer control winngs accessed could be affected by the latter control winngs accessed, which ake the decrease of branch current aplitude with the accesses of each latter control winng but intensive instantaneous current with each input. And, whatever the conduction angle of thyristors is, the transition process always exists. (3) The exit process of CT is controlled by anti-parallel thyristors in series at control winngs. Therefore, if the control signal is reoved, the CT will not be turned off unless zero-cross current appears. And there is no transient process. eferences: [1] TIAN Mingxing. Basic Theoretical esearch on Controllable eactors of Transforer Type, Xi an Jiaotong University, 25. [2] TIAN Mingxing. Operation Mode of a Controllable eactor with Multiple Parallel Branches, Transactions of China Electro Technical Society, Vol.12, No.21, 26, pp [3] TIAN Mingxing, Li Qingfu. Polygon Type Equivalent Circuit Model of Multi-Winng Transforers, Journal of Xi an Jiaotong University, Vol.6, No.38, 24, pp [4] Jian Wang, Arthur F. Witulski. Derivation Calculation and Measureent of Paraeters for a Multi-winng Transforer Electrical Model, IEEE, APEC, Dallas, TX USA, No.1, 1999, pp [5] TIAN Mingxing, LI Qingfu. Calculation and Siulation of a Controllable eactor of Transforer Type, Journal of Xi an Jiaotong University, Vol.8, No.38, 24, pp [6] ZHENG Weijie, ZHOU Xiaoxin. Equivalent Electro-agnetic Transient Model Based on Dynaic eluctance for Magnetically Controlled Shunt eactor, Proceeng of the CSEE, Vol.4, No.32, 211, pp.1-6. [7] LI Xuan, YE Guoxiong, WANG Xiaoqi, et al. Transient Characteristics of 1kV Capacitor Voltage Transforer Based on ATP-EMTP, High Voltage Engineering, Vol.9, No.34, 28, pp [8] TANG Xiaoling, LI Minzu, LIU Jingyuan, et al. Siulation and Analysis of Transient Characteristics of Capacitor eactive Power Copensation by Adjusting Voltage with Thyristors, High Voltage Apparatus, Vol.1, No.45, 29, pp [9] DUAN Liyong, WANG Chengin, ALEXANDOV G. N.. esearch on the Birectional Control Principle of eactive Power Based on a Transforer Type Controllable Shunting eaction, Power Syste and Clean Energy, Vol.1, No.29, 213, pp [1] A. Nawikavatan, C. Thaart, T. Niyosat. The Current Transforer Model with ATP-EMTP for Transient esponse Characteristic and Its Effect on Differential elays Perforance, IEEE, Advances in Power Syste Control, Operation and Manageent (APSCOM 29), Hong Kong, China, 29, pp.1-6. E-ISSN: X 155 Volue 14, 215