Analysis of radiation patterns in a three-phase motor with a stator winding as a circular array of antennas. The thesis presents a method of evaluating radiated emissions (RE) that occur in the stator winding of a three-phase motor drive system. The stator winding of a given motor reference model is assumed to be a circular array of radiating antennas.
Radiation patterns can be obtained by calculating the magnetic vector potential of a balanced three-phase current source distribution. Radiation patterns can be evaluated by 3D full-wave electromagnetic simulation using the Finite Element Method (FEM). Meaningful radiation patterns can be analyzed with three-phase current excitation properly engaged.
The stator winding coils are now positioned, mutual coupling effect between the coils cannot be neglected. The multiport RLC network path model is proposed to compensate to calculate proper radiation patterns. Design of winding structure and estimation of radiated emission in reference motor model 2.1 Modeling of stator winding in three-phase motor.
The error percentage of the radiation gives a pattern of the far field radiation and measured at a distance of 1 meter Figure 8.
Introduction
Before measuring radiated emissions from AC motors, estimating the radiation pattern through 3D simulation is an essential advance. The winding structure of a three-phase AC motor can be thought of as a series of circular radiators. Each spatial current distribution component can derive any magnetic vector potential to analyze the radiation pattern.
The comparison of the measured radiation pattern to the realistic coil model and the evaluation of the calculation through the array antenna method at the resonant frequency is the ultimate goal. The modified approach is expected to compensate for the radiation pattern mismatch due to unbalanced coupling. Excited cases according to harmonic numbers must be classified to analyze the radiation pattern in the three-phase system.
Electromagnetic analysis remains unaffected by the order of phase excitation due to the symmetry of the winding structure. The reference model is supposed to predict the radiation pattern before measuring the radiated emission of the existing winding structure.
Design of winding structure and estimation of radiated emission in reference motor model
Modeling of stator winding in three-phase motor
Winding sequence and direction of current excited in one terminal. The winding structure must meet two symmetrical conditions [10]. a) The number of coils per phase winding must be a whole number. The angle between the phase windings (𝛼𝑝ℎ ) must be an integer multiple of the phasor angle of the angle (𝛼𝑧), where t means the greatest common divisor of Q and p. The basic voltage phasor diagram for the winding and the calculation of the voltage in one phase are shown in Figure 4.
The winding factor (𝑘𝑤1) based on the winding distribution for the base can be calculated as a ratio of the geometric sum and the sum of the absolute values. As discussed in the first paragraph, the simulation model consists of single stator windings without stator and rotor cores.
Radiation region boundary classification
The far-field condition at the approach of an antenna also varies with its electrical magnitude, whether it is electrically small or electrically large. The electrical size of the antenna is classified into three areas, including the fuzzy area, according to the ratio of the wavelength to the range. Under the conditions of the stator winding parameters, the loop circumference of one winding can be calculated as C = 0.704 m.
With this value, we can classify its electrical magnitude as different frequency ranges. Classification of electrical quantity including its frequency range is arranged in Table 2 [12]. To define the radiation type in unclear cases, the error rates between the measured 1000 mm radiation and far-field radiation patterns are taken into account.
Estimation of radiation pattern with 3D full-wave electromagnetic simulation
To compare the result from the case of k = 1 and k = 2, the result indicates the same pattern due to only changes in the phase sequence. Comparing radiation patterns from (r𝐸𝜙) and (r𝐸𝜃), 𝜙 directional, which is end-winding component of stator winding, has dominant radiation. Ideally, the radiation pattern should be in a non-value result due to its balanced current distribution of three-phase coils.
However, the result shows almost zero volts for each component compared to the case where k = 1 or 2.
Array antenna approach to analyze radiation in ac motor
- Theoretical approach to estimate radiation pattern
- Mutual coupling effect among excitation of looped winding
- Analysis of radiation pattern between simulation results and array antenna method
- Additional winding model analysis
Since the winding of the stator winding has two different vector components, the total magnetic vector potential can be calculated independently from the sum of its axial component and the end-turn component [12]. To calculate the magnetic vector potential of the proposed method, the derivation of the current source distribution is the initial process. However, the far-field radiation pattern can be obtained due to the relatively small error between the near-field radiation and the far-field radiation.
To analyze the radiation pattern from the stator winding structure model, the mutual coupling effect between the coil loop cannot be neglected since the coils are tightly wound. To compensate for the deterioration of the coupling effect, a multi-port RLC network circuit model can be proposed. Using the circuit model, the modified current source element is alternatively included in the calculation of the corresponding radiation pattern.
With the calculated impedance value for each port network, the compensated current source for each port is redistributed. The radiation pattern field can be scaled in volts by multiplying the measured electric field and the emitter-receiver distance. Thus, the radiation pattern measured from the simulation model and the calculated far-field radiation pattern must be the same.
The calculated electric field can be represented in two directions theta direction and pi direction. In the radiation pattern in the 𝜃 direction at 𝜃 = 90°, the simulation result has existed value, but the array antenna calculation results in empty pattern. Ideally, the magnitude of the far-field radiation is 0 due to the suppression of the overall current distribution by each other.
In the same way as the previous model, the resonance point can be found by plotting the reflection coefficient of the bundled gate excitation. Compared with simulation results, the calculation results show a more refined relationship, but more difference in the magnitude of the radiation. Compare with the integral slot winding model, the gate excitation level is matched by controlling the input current source.
Nevertheless, the magnitude of the total radiation shows a larger value due to the adjacent state of the coil winding. Thus, the antenna array approach is an important method for measuring radiation patterns from the stator winding of an AC motor.
Measurement setup
To design three-phase power-divided circuit, the designed circuit must divide equivalent power level into each differential phase tuning 120 degrees while maintaining matched impedance. To design the phase difference of 120° staggered line, the equation for the transmission line is derived below:. First, the target phase difference in radians should be fixed to obtain electrical line difference. stands for target phase difference, ∆𝑙 stands for target length difference of the microstrip transmission line.
Before designing layout, simulation using Q3D simulation should be continued to double the result of phase shift. It is designed to have all three phases in case each port excitation suppresses each other. Before measuring an electric field from a realistic winding model, simulation results and realistic model must coincide with resonance point.
CONCLUSION
Acknowledgement
