PWM inverter-excited iron loss characteristics of a reactor core

In this paper, we focus on an evaluation of iron losses in a reactor core under pulse width modulation (PWM) inverter excitation. We examine the inverter- and sinusoidal-fed iron losses of the reactor core through both experiments and numerical simulations. The proposed measurement includes operation at a higher frequency than is used commercially. We discuss the building factor (BF) of reactor losses under PWM inverter and sinusoidal excitations based on material iron losses measured in a ring specimen. The BF calculation based on inverter-fed tests is an almost constant value because the magnetic flux density distributions related to the carrier frequency mostly do not depend on the reactor gaps.


I. INTRODUCTION
Reactors are made mostly of silicon steel and are widely used as filters in pulse width modulation (PWM) inverter circuits to reduce the harmonic component or in boost converters to store the electrical energy instantaneously.2][3][4] Therefore, in order to estimate the iron losses of an iron core under the PWM inverter excitation with sufficient accuracy, it is necessary to correctly understand the influence of carrier frequency.
Recently, reactor and inductor losses have been evaluated under sinusoidal excitation, 5,6 squareformed excitation, 7 and an AC filter. 8,9It is important to evaluate the impact of reactor core losses.In this study, the iron loss characteristics of an inverter-excited reactor are evaluated and compared to the case of sinusoidal-fed operation.
The building factor (BF) of any magnetic core is defined as the ratio between the losses of the iron core and the iron losses of the material.The evaluation of BF allows us to understand the iron losses caused by factors such as the manufacturing process, the core geometrical configuration, or any effects of the operating conditions not related to the material itself.Some studies have focused on the building factors evaluated in transformers, 10 reactors under sinusoidal excitation, 6 and motors. 11,12The next step is to understand the iron losses under PWM inverter excitation using the BF.
This paper addresses the evaluation of iron losses of a reactor core under PWM inverter excitation.We examine inverter-and sinusoidal-fed iron losses of a reactor core through both experiments and numerical simulations.The proposed measurement includes higher frequency operation than the commercial one.Furthermore, we discuss the BF of reactor losses under PWM inverter and sinusoidal excitations based on material iron losses measured in a ring specimen.a Electronic mail: yao@toyota-ti.ac.jp 2158-3226/2017/7(5)/056618/7 7, 056618-1 © Author(s) 2017

A. Experimental setup of reactor and ring tests
Figure 1 illustrates the configuration of the experimental setup used to measure the iron loss characteristics of the reactor core (CS-125) 6,13 made of non-oriented (NO) electrical steel sheets (35H300).An air gap of the reactor core is set at 2 mm, the core mass M rea is 1.4 kg, and the number of turns of the reactor coil is 320.
Here, we perform two kinds of reactor iron loss tests.The first reactor test consists of exciting the core with a sinusoidal voltage using a function generator and a linear amplifier.The second test is to measure the iron loss of the reactor core excited by a single-phase PWM inverter.In this manner, the iron losses of the reactor core are affected by the PWM carrier frequency, unlike the first test.The PWM inverter output has a fundamental frequency f 0 and a carrier frequency f c .In the following experiments, the modulation index m is set to 0.5 and the switching dead time is set to 3500 ns.
We now discuss the estimation method for obtaining the reactor iron losses under inverter and sinusoidal excitations.The reactor input active electrical power P in is measured by an analog-todigital (A/D) converter (PXI-5122, National Instruments).The measurement sampling frequency is 10 MHz and the resolution is 14 bit.In order to calculate the copper losses, the rms current I 1 is calculated from the obtained current waveform.The reactor iron loss can be obtained as where R(= 0.56 Ω) denotes the resistance of four coils in series.
In our experiments, the magnetic flux density B rea is measured using a B-coil wound around the reactor core and is given by B rea = ∫ V rea dt/(N rea S rea ), where V rea denotes the B-coil voltage, N rea (=5) is the number of turns of B-coils, and S rea (= 665 mm 2 ) is the cross-sectional area of the reactor core.The peak magnetic flux density in the reactor is adjusted by tuning the applied voltage.
In this paper, in order to obtain the BF, we also perform measurements of the iron losses of the ring specimen under inverter and sinusoidal excitations as shown in Fig. 1.The ring specimen is made of NO electrical steel sheets using a wire-cut technique to reduce the deterioration of magnetic properties by mechanical stress.In our study, the iron loss of the ring specimen is regarded as the material loss.The iron loss based on the ring core can be described by where φ(= 7650 kg/m 3 ) is the density of the magnetic sheet, H = N 1 I/L is the magnetic field intensity, and We discuss the method of evaluating the BF of the reactor core.To do this, we proposed a comparison of the iron loss of the ring core W ring with the iron loss of the reactor core W rea .That is, the BF is described by Note that, for the calculation, W ring can be either W ringsin or W ringinv depending on whether the sinusoidal-fed ring test or the inverter-fed ring test is being considered.

B. Numerical method
Figure 2 shows an analysis model for the finite-element method (FEM) with A − φ method.The laminating structure is homogenized as a bulk structure in the model.The total iron losses of the reactor and ring specimen correspond to the hysteresis and eddy current losses.The experimental trials give the total reactor iron losses but not the loss repartition between the hysteresis loss and eddy-current loss in the laminating, rolling, and transverse directions.To discuss the loss repartition and characteristics, we perform a finite element analysis.Based on the experimental parameters, ideal voltage waveforms are used as the input of the numerical analysis, which is a time-stepped simulation.
In our numerical simulation, the iron losses of the reactor core W reanum are described by where W hys denotes the hysteresis loss, W eddylami is the eddy current loss in the laminating direction, and W eddytranandrol is the eddy current loss in the transverse and rolling directions.Here, α is the coefficient of hysteresis loss, κ (= 2) is the anomaly factor, β is the coefficient of eddy current loss, B is the magnetic flux density, f is the frequency, T is the period, σ is the conductivity, is the volume, and ne (= 215, 200) is the number of elements.Finally, ie represents the element number.Here, the conductivities in the laminating, rolling, and transverse directions are set at 0 S/m, 1.923 × 10 6 S/m, and 1.923 × 10 6 S/m, respectively.

A. Experimental results and discussion
Figure 3 (a) shows the reactor loss characteristics with respect to the carrier frequency at (f 0 = 50 Hz; B = 0.6 T) and (f 0 = 500 Hz; B = 0.1 T).The iron losses of reactor core for these two parameters have the same tendency.The iron losses under inverter excitation decrease with increasing carrier frequency.The figure also shows the reactor iron loss under sinusoidal excitation for comparison purposes.The reactor core losses increase compared with the sinusoidal-fed operation because of B H curve minor loops 2 and increasing eddy currents.
Figure 3 (b) shows the ring loss characteristic as a function of the carrier frequency.The experimental ring tests are done in the same manner as the reactor tests.The iron losses in the inverter-fed ring show the same tendency as in the reactor core under inverter excitation, as shown in Fig. 3 (a).The reactor losses are larger than those of the material due to the increasing eddy current losses caused by the leakage magnetic flux density near the reactor gaps.
Figure 3 (c) shows the BF calculation results for each of the tested carrier frequencies at (f 0 = 50 Hz; B = 0.6 T) and (f 0 = 500 Hz; B = 0.1 T).As mentioned above, the BF differs with the type of ring test, which corresponds to iron losses under inverter and sinusoidal excitations (W ringinv and W ringsin ).Because the iron losses in the inverter-fed ring test are larger than those in the sine-fed ring test, the BF calculated based on the sine-fed test is larger.The iron losses of the reactor under inverter excitation are logically higher than the intrinsic material iron loss.
The BF calculated based on the inverter-fed test is almost a constant value as shown by the red lines in Fig. 3 (c) at (f 0 = 50 Hz; B = 0.6 T) and (f 0 = 500 Hz; B = 0.1 T).Note that the eddy currents at the end of the reactor core increase locally due to fringing flux caused by the air gap.However, for material and reactor iron losses under inverter excitation, the rate of decrease of iron losses as a function of the carrier frequency is almost the same value.In the next section, the reason for having the almost constant value is discussed using numerical simulations.

B. Numerical results and discussion
Here, we investigate the iron loss repartition and characteristics using 3D-FEM.Due to the high frequency of the carrier signal, it is necessary to have a high sampling frequency for the data input in the numerical simulations.This means a small time step and then a long calculation time.To reduce the calculation time, only the cases at f c = 1 and 4 kHz under inverter excitation are simulated at f 0 = 50 Hz.
Figure 4 (a) shows the reactor iron losses under sinusoidal excitation and inverter excitation at f c = 1 and 4 kHz.Here, the calculated total iron losses are about 0.85 W lower than the measurement at f c = 1 kHz in Fig. 3 (a).However, the numerically obtained results in Fig. 4 (a) are qualitatively in agreement with the experimental results in Fig. 3 (a).Thus, based on the numerical and experimental results, we can qualitatively discuss the iron loss with respect to the carrier frequency.
As shown in Fig. 4 (a), W eddylami accounts for about 30% and 21% of the total iron losses at f c = 1 and 4 kHz, respectively.W eddylami decreases with increasing carrier frequency.However, when f c is changed, W eddytranandrol and W hys are almost the same.The rate of decrease of total iron losses as a function of the carrier frequency is caused by the eddy current loss in the laminating direction.
Figures 4 (b) and (c) show the magnetic flux density distributions for calculating W eddylami on the area indicated by the square in Fig. 2.These figures show the distributions normalized by each maximum value of magnetic flux densities at 1.95 and 7.95 kHz, which correspond to about twice the respective carrier frequencies (f c = 1 and 4 kHz).Here, the eddy current losses at 1.95 and 7.95 kHz correspond to each maximum value in harmonic components with the carrier frequency.When f c is set at 1 kHz as shown in Fig. 4 (b), the strong region of the magnetic flux density (green region) expands compared to f c = 4 kHz in Fig. 4 (c).Thus, W eddylami increases with decreasing carrier frequency.Note also that, in the magnetic flux density distributions, the region close to the reactor gap and other regions of the reactor show almost the same characteristics.It is believed that the rate of decrease as a function of the carrier frequency has the same tendency between the reactor and ring tests.Therefore, the BF calculated based on the inverter-fed test is an almost constant value and it is expected that we can estimate the iron losses of the reactor based on those of the ring test.Further numerical and experimental studies are necessary to realize a loss estimation method based on the BF.4), ( 5), ( 6) and ( 7

IV. CONCLUSION
We focused on the impact of reactor core losses under PWM inverter and sinusoidal excitations.We experimentally and numerically confirmed that the iron losses of the reactor core decrease with increasing carrier frequency.To discuss the iron loss characteristics of the reactor core and BF, a comparison with the material iron loss was also performed under inverter and sinusoidal excitations.The inverter-fed ring showed the same tendency as the reactor core under inverter excitation at fundamental frequencies of 50 and 500 Hz.The BF calculated based on the inverter-fed test was an almost constant value because the magnetic flux density distributions related to the carrier frequency mostly did not depend on the reactor gaps.It is expected that we can estimate the iron losses of the reactor based on those of the ring test.The evaluation of the BF of reactor iron losses excited by an inverter using commercial and higher frequencies will be keys to designing the reactor core.
FIG.1.Schematic of reactor and ring tests to experimentally measure the iron losses.We considered two excitation methods: PWM inverter and sinusoidal excitations.

FIG. 2 .
FIG. 2. Schematic of numerical model (1/8-region model).The working conditions based on the experimental results are simulated by three-dimensional (3D) FEM using the JMAG software.See Ref.5 for the details of the 3D FEM model.

FIG. 4 .
FIG. 4. Numerically obtained iron loss repartition and magnetic flux density distributions at f 0 = 50 Hz; (a) Iron loss repartition obtained from Eqs. (4), (5), (6) and (7); (b) Magnetic flux density distribution for calculating W eddylami with Eq. (7) at 1.95 kHz and f c = 1 kHz in the square area of Fig. 2. The magnetic flux density distribution is normalized by its maximum value.At 1.95 kHz, W eddylami depending on f c = 1 kHz becomes the maximum value; (c) Magnetic flux density distribution at 7.95 kHz and f c = 4 kHz using the same method as shown in (b).
FIG. 4. Numerically obtained iron loss repartition and magnetic flux density distributions at f 0 = 50 Hz; (a) Iron loss repartition obtained from Eqs. (4), (5), (6) and (7); (b) Magnetic flux density distribution for calculating W eddylami with Eq. (7) at 1.95 kHz and f c = 1 kHz in the square area of Fig. 2. The magnetic flux density distribution is normalized by its maximum value.At 1.95 kHz, W eddylami depending on f c = 1 kHz becomes the maximum value; (c) Magnetic flux density distribution at 7.95 kHz and f c = 4 kHz using the same method as shown in (b).