FEM Based Parametric Analysis of AC Line Reactors

Transcription

1 FEM Based Parametric Analysis of AC Line Reactors S. Balci 1, N. Altin, S. Ozdemir 3 and I. Sefa 4 1 Department of Electric, Institute of Science and Technology, Gazi University, Ankara, Turkey, selamibalci@gazi.edu.tr Department of E&E Eng., Faculty of Technology, Gazi University, Ankara, Turkey, naltin@gazi.edu.tr 3 Ataturk Vocational School, Gazi University, Ankara, Turkey, sabanozdemir@gazi.edu.tr 4 Department of E&E Eng., Faculty of Technology, Gazi University, Ankara, Turkey, isefa@gazi.edu.tr Abstract-- Single or three phase AC line reactors are used for harmonic elimination at the input stage of controlled or uncontrolled rectifiers. Design parameters of these reactors mainly related to current level, cost, size, losses, core structure etc. Although they carry nonlinear currents, they usually considered as carry linear currents in the first design stage. In case of nonlinear current, peak value of current is higher than linear condition. Consequently, saturation effect may occur on the core and harmonic elimination tasks cannot be achieved accurately. In this study, AC line reactor is designed and modeled by using single phase standard EI metric laminations to simplify the understanding of nonlinear effects. The parametric analysis of the reactors for linear and nonlinear conditions are carried out and compared. Inductance variation of reactor is analyzed according to current, number of turns and air-gap length parameters by parametric analysis. The reactor is modeled and simulated with the co-simulation of Maxwell and Simplorer. During the simulation, the nonlinear current waveform, which is the most important design parameter of an AC reactor, is also considered. Simulation results such as saturation, core losses and flux distributions are visualized and compared for both linear and nonlinear conditions. Keywords AC reactor, FEM, magnetic modeling, parametric analysis, core losses, inductance variation, co-simulation. I. INTRODUCTION In general, front ends of the static power converters include AC-DC and AC-AC converters. AC and DC motor drives, cycloconverters, uninterruptible power supplies, battery charging systems and electroplating rectifiers are some application areas of these types of systems. In order to meet the international standards and to obtain the reliable operation, the input current harmonic levels should be reduced by using AC line reactors. Generally, calculation methods and lamination types used in reactor design procedure is similar to conventional transformers. Because the reactor has a winding while a transformer has two windings, mutual coupling effect cannot be used as the criterion like in transformer [1]. Silicon steel stacks are used in line frequency applications and amorphous, ferrite or sendust (Kool Mμ) materials used in C, E and I forms for high frequency applications such as PWM inverters. It is known that, systems with line frequency diode/thyristor rectifier front ends generate current source harmonics. Thus, AC inputs of these systems should be filtered to prevent the negative effects of harmonics []. L, LC or LCL filters are commonly used in passive or active harmonic filtering systems [3]. Value of the flux and the inductance value of the reactor are depended on core cross section area A c, number of turns N and permeability of magnetic material μ r. A controllable reactor with multi-stage winding is used to decrease current harmonic level [4]. Reluctance of the magnetic circuit of the reactor is increased via air gaps located in core for steel laminations or ferrite cores. So, inductance value and harmonic elimination level of AC input current can be controlled. It is reported that locating air-gaps in reactor cores of uninterruptible power supplies (UPS) has some advantages such as reduce input current THD and less ripple DC [5]. Airgaps on the core decrease the inductance value, thus inductor size is getting bigger [6]. On the other hand, air-gaps which are located on the reactor and the transformer cores increase the leakage flux and affect the power conversion [7]. Also, airgaps located on the core of filter reactors affect the flux distribution and eddy current losses [8]. Core loss of the AC reactors used in high frequency systems such as PWM inverters is hard to calculate with conventional methods. Loss mapping method is used to calculate the core losses in these applications [9]. Finite Element Method (FEM) based software can be used to calculate nonlinear core losses and visualize the saturation effects. Usage of FEM software has also some advantages. For example working with the simulation can help students to get acquainted the design process and to teach the limitations of simulation. The simulation is just a step on the road to the actual design [1]. In the design process, inductance value, core and winding losses can be easily calculated by using FEM-based software to obtain the optimal design parameters before producing a prototype model. Estimation of the flux distribution and losses This work is supported by Gazi University Academic Research Projects Units, under grant 7/1-1 project number /13/$ IEEE 138

2 requires complex calculations especially in nonlinear load conditions by using conventional mathematical methods. Flux distribution and saturation effects can be visualized via this type of software which provides useful information to the designers. Another advantage of Finite Element Analysis (FEA) is that taking a reactor as a reference and its equivalent electric circuit, the procedure allows us to obtain the equivalent electric circuits for every situation, changing different parameters, such as the number of turns, size of the core, air-gap length, etc., which makes it a method for general application [11]. In this study, an AC reactor built up with EI-1 size laminations, has been modeled and simulated with Maxwell 3D and Simplorer co-simulations which were performed simultaneously. The parametric analysis of the proposed model according to current values, number of turns and airgap length has been carried out. The waveforms of induced voltage on the reactor and variation of the inductance value were interpreted. So, optimal values of number of turns and air-gap length were determined for the reactor which was built up with EI1 laminations with standard sizes. Also, core losses were investigated and flux distribution was visualized for both linear and nonlinear current conditions. In order to investigate the losses of harmonic components, which are resulting under these conditions by FFT, spectrum graphs have been obtained. II. THEORETICAL ANALYZING OF DESIGN PARAMETERS Unlike the air-cored reactors, iron cored reactors have their own saturation characteristics. The inductance value of reactor decreases with increasing level of current. The saturation characteristics of a reactor can be influenced by the type of core material, core geometry (cross section area), the number of turns and the air-gap length. Due to reasons given below, there is a difference between the calculated inductance value and the measured inductance: The reactor's core causes an inhomogeneous flux distribution The core's lamination stacking factor Production tolerances Thermal effects [1]. Air-gaps on the core increase the equivalent reluctance, consequently the inductance is reduced. The inductance value L of any reactor can be calculated with Eq. 1. μn Ac N L = = (1) l R c Where μ is magnetic permeability of core material, N is number of turns, A c is cross section area of magnetic core and l c is the length of magnetic circuit. The inductance value can be adjusted by changing magnetic permeability while other parameters are constant. However, magnetic permeability value is related with saturation of core material. Saturation of magnetic circuit can be prevented by operating at the linear region of B-H magnetization curve. Air-gaps should be located at the magnetic circuit to prevent the saturation. Because the air-gaps increase the reluctance, inductance is decreased and thus saturation is prevented. The leakage flux should be increased in reactors to obtain this situation unlike transformers which operate at the regions near the saturation point. A larger air-gap makes a larger reluctance and therefore a lower inductance value. If the air-gap gets too large (approaching 1% of the core plan), then fringing becomes excessive, and multiple air-gaps are needed []. If an air-gap placed in the core, total core reluctance value is given as Eq.: R t = Rc + Rg. () Reluctance values of core (R c ) and air-gap (R g ) are given with Eq. 3-4 respectively: lc R c = (3) μ A c c lg R g = (4) A μ g Relation between the magnetic permeability of silicon steel stack and air-gap is given below: 3 c (5) μ = 1 μ So, when an air gap is located at the core, reluctance of the magnetic core can be neglected and reluctance of the air-gap can be assumed as total reluctance (Rt Rg). If Eq. is rewritten according to this assumption, Eq. 6 and 7 can be written for inductance value of a reactor with air-gap: N L = R L g N μ Ac = 7) lg As seen from Eq. 7, inductance value of a magnetic circuit is; directly proportional with the square of number of turns (N ), directly proportional with core cross section area (A c ), Inversely correlated with the air-gap length (l g ). As a result, it is seen that, these three parameters must be changed to adjust inductance value. Magnetic energy stored at air-gap can be calculated by using Eq. 8: 1 B μ (6) W m = (8) 139

3 Thus electrical energy stored at the reactor can be found by Eq. 9: 1 We = Li By using Eq. 8 and 9, size of the air gap which should be located at the core can be found by Eq. 14: lg LImax 4 1 BmaxAc (9) μ = (m) (1) Where, cross section area is given in cm unit. By neglecting fringing flux and the other non-ideal conditions, length of the air-gap which should be located at the core can be found by Eq. 1 in unit of m [13]. III. MODELING AND ANALYSIS OF AC REACTOR Three dimensional (3D) model of single phase AC reactor which is produced by using plotting editor of Maxwell for core sizes of EI1 is given in Fig. 1. In this model, M33-5A silicon steel which has 1.7 T saturation flux density and 3.3 W/kg specific core losses for 1.5 T is used as core material. Maxwell 3D software calculates and plots the core losses according to the specific core losses value under the operation frequency Fig. 1. Three dimensional model of AC reactor built up with EI1. This base model is used for parametric analysis of the single phase AC reactor with parametric solution setup. The effects of these parameters on inductance value are plotted as a graph. Achievement of the desired inductance value of the design of the reactor using only mathematical calculations is rather difficult matter. This is because the core material exhibits nonlinear behavior and its exposure to the saturation effect. The most useful method against saturation is air gapped core placement. Thus, core material's magnetization curve becomes approximately linearly and the inductance value is stable to changes in the current. Harmonic components of nonlinear loads impacts constitute the core of the reactor is an issue should be investigated more. Parametric inductance graph is formed by the data obtained from parametric solver. Optimum reactor value can be selected by using 3D graphics to meet the standards. So there is no need to complicated mathematical calculations. From this graphic, design parameters, such as desired inductance value, the optimal number of turns and air-gap length can be selected easily. On the other hand, according to change of the current level can be seen change in the value of inductance. IV. SIMULATION RESULTS Firstly parametric analysis of the reactor has been carried out by using Maxwell s parametric solution for values given in Table I. Data and graphs are obtained from the parametric analysis of software. TABLE I. PARAMETRIC SOLUTION SETUP Reactor Parameters Range Step Size N (turns) turns l g (mm) -4.5 mm I rms (A) -8 1 A Cross-section area of the reactor core is kept at a fixed value, the winding number of turns and air-gap length are changed parameters and parametric analysis of the reactor according to the reports, such as 3D parametric inductance graph can be plotted in Fig.. According to this graph, as the current increases, the inductance value increases, however, as the air-gap length increases, the inductance value decreases. While there was no air gap, the magnetic saturation due to increased ratio the current through the impact of inductance value decreases too much. However, very little variation is obtained with increases in the level of the current while there is an air gap on the core. Designs for the desired air-gap length, using the data obtained from these graphs are determined by the inductance and current values. The induced voltage on reactor for selected values (for 5 turns and 3 mm air-gap length) can be seen in Fig. 3. In linear load condition, the induced voltage value is equal to 4.5% of supply voltage. In this case, the reactor inductance value is.488mh. L (H) Current (A) Fig.. Parametric 3D graph of the inductance variation Air Gap (mm) 133

4 InducedVoltage(Winding1) [V] Fig. 3. Induced voltage waveform for linear load condition. Single or three-phase bridge rectifiers draw non-sinusoidal currents from the grid. Because these currents consist of harmonic components such as 3rd, 5th and 7th harmonic, voltage induced on the reactor is non-sinusoidal as seen in Fig. 4. Because this situation is effective on the reactor core losses and saturation effects, it must be taken into consideration in the design stage of the reactor. 5 3 VM4.V [V] mag(vm4.v) [V] Fig. 4..Induced voltage waveform for nonlinear load condition.induced voltage FFT spectrum for nonlinear load condition The modeled AC reactor is also tested with three phase linear and nonlinear load conditions. Maxwell 3D model of the reactor is loaded to Simplorer for co-simulation analysis. Simulation is carried out for 5 ms and with the.1 ms time steps. Resistive load with 5 Amp/phase rated value is used as linear load, and three phase capacitive loaded rectifier is used as nonlinear load. Simplorer model of the system is seen in Fig.5. Load power is 34.5 kw as equal for both linear and nonlinear load conditions. Filter capacitor 94μf is used to reduce output voltage ripple at the DC link. Line frequency rectifiers draw non-sinusoidal currents from the grid because of their nonlinear nature. On the other hand, linear system draws sinusoidal currents from the supply. The flux distributions and calculated core losses are seen in Fig. 6 and Fig.7 for both cases, respectively. Flux distributions are scaled Fig. 6. Flux distribution for nonlinear operation, Flux distribution for linear operation. and colored with maximum value of 1.6 Tesla. Saturation effect in nonlinear condition is clearly seen in these figures. Core losses and flux distributions for nonlinear and linear load conditions are substantially different from each other. Core losses for each phase reactor are calculated as 5.41 W for linear operation mode and 17.8 W for nonlinear operation mode. These values are found by calculating the average of the data shown in Fig. 7. It is seen that total core losses are 3.9 times higher than linear mode in nonlinear mode and this power loss heats the reactor. As can be seen in Fig. 8, harmonic spectrum of core loss graphs, due to the effects of high frequency, current flow of nonlinear loads consist of more losses. Greater values than the magnitude of the harmonic components cause the core to heat up more. Also, peak value of the flux is 1.46 times higher than linear load condition in nonlinear load condition because of the crest factor of current. Higher flux density causes higher heat on the reactor core. Output voltage waveform of simulated rectifier with modeled AC reactor is seen in Fig. 9. As seen from figure, ripple of output DC voltage is lower than 1% and this means that DC filter capacitor values is sufficiently big. In addition, the amplitudes of the harmonic components are very small. 1331

5 THREE_PHASE1 3PHAS A * sin ( * pi * f * t + PHI + phi_u) ~ ~ PHI = PHI = -1 AC reactor T1 T4 T T5 T3 T6 RL B6U B6U1 D1 D3 D5 C Rload ~ PHI = -4 D D4 D6 linear load nonlinear load Fig. 5. Simulation circuit of AC reactor in Simplorer. FEA1.CORELOSS Vo [V] Name Y m m m1 Name Delta(Y) d(m1,m.4159 m FEA1.CORELOSS Fig. 7. Core losses waveform for nonlinear operation, Core losses waveform for linear operation. mag(fea1.coreloss) mag(fea1.coreloss) Fig. 8. Core losses FFT spectrum graph for nonlinear operation, Core losses FFT spectrum graph for linear operation. mag(r4.v) [V] Fig. 9. Rectifier output voltage waveform. Rectifier output voltage FFT spectrum graph. V. CONCLUSIONS AC reactors are generally used in rectifiers to decrease the harmonic levels and to prevent the voltage notches. Because of the AC reactors operated under nonlinear current conditions, conventional calculation techniques are insufficient in the designing of reactor. In this study, parametric analysis of the AC reactor is carried out by using Maxwell 3D software to obtain desired design parameters. EI laminations are used in modeled AC reactor and both sinusoidal and non-sinusoidal current conditions are investigated, and results of these two conditions are reported and compared. The parameters of the parametric analysis are determined as number of turns, current value and length of the air-gap. As a result of parametric analysis, inductance variation is obtained as three-dimensional graphics. Design parameters according to the rated current and the desired inductance value can be easily determined by these graphs. Thus, the production process is rather shorter. 133

6 The modeled reactor is simulated for three phase constant voltage type rectifier load. Although power levels and root mean square values of the currents are the same, in non-sinusoidal current condition, peak value of the AC input current is 5% higher than linear current condition because of the crest factor effect. This situation is very important for determining the core cross section area and it must be considered. Otherwise, saturation may occur while actual current value is lower than the rated current value. Also, total core loses are 3.9 times higher in nonlinear load condition than linear condition. REFERENCES [1] A.Donuk, M.Rotaru and J. K. Sykulsk, Defining and Computing Equivalent Inductances of Gapped Iron Core Reactors, ISEF 11-XV International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering, Funchal, Madeira, September 1-3, 11. [] F.Z.Peng, Gui-Jia Su and G.Farquharson, A Series LC Filter for Harmonic Compensation of AC Drives, IEEE Power Electronics Specialists Conference, PESC 99, pp , August [3] K.H. Ahmed, S.J.Finney and B.W.Williams, Passive Filter Design for Three-Phase Inverter Interfacing in Distributed Generation, IEEE Compatibility in Power Electronics, CPE '7, Electrical Power Quality and Utilisation, Journal Vol. XIII, No., pp. 1-9, June 7. [4] K. Bao-quan, T. Hong-jiang and L.Liyi, Research on DC Magnetic Flux Controllable Reactor, IEEE International Conference on Electrical Machines and Systems, ICEMS 8, pp , October 8. [5] B.M. Wells, Magnetic Components in UPS, IEE UPS Colloquium, pp. 4/1-4/7, February [6] P.D. Evans and B.M. Saied, Calculation of Effective Inductance of Gapped Core Assemblies, IEEE Proceedings-Electric Power Applications, Vol. 133, Pt. B, No. 1, pp , January [7] Y.Lu, K.W.E.Cheng and S.L.Ho, Investigation of the leakage inductances and the energy conversion in air-gap transformers, IEEE Proceedings of Sixth International Conference on Advances in Power System Control, pp. 7-75, November 3. [8] S. Nogawa, M.Kuwata, T.Nakau, D.Miyagi and N.Takahashi, Study of Modeling Method of Lamination of Reactor Core, IEEE Trans.on Magnetics, Vol. 4, No. 4, pp , April 6. [9] T.Shimizu and S.Iyasu, A Practical Iron Loss Calculation for AC Filter Inductors Used in PWM Inverters, IEEE Transactions on Industrial Electronics, Vol. 56, No. 7, pp. 6-69, July 9. [1] A.F.L.Nogueiraand R. M. L. Boudec, Computer-Aided Analysis of Gapped-Core Inductors Operating under A Wide Range of Excitations, CEE'7 nd International Conference on Electrical Engineering, ISEC-Coimbra Portugal, pp , 6-8 November 7. [11] R.A.Salas and J.Pleite, Simulation of The Saturation and Air-Gap Effects in A Pot Ferrite Core with A -D Finite Element Model, IEEE Transactions on Magnetics, Vol. 47, No. 1, pp , October 11. [1] H.Kreis, Measuring Inductance in Power Inductors, measurement_instrument_dpg1-series_16.pdf. [13] R.W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, nd ed., New York: Kluwer Academic Publishers, 1, pp