Analytical Calculation of the RMS Value and the Spectrum of the DC-Link Current of a Dual-Inverter

Abstract

This paper is focused on the analytic definition of the DC-link current of a dual-inverter. Therefore, a two-level dualinverter for driving two independent three-phase electrical motors is considered. Space-vector modulation is taken into account as the modulation method of the inverter. Based on that, an analytic description is derived for the frequency spectrum as well as for the RMS value of the DC-link current of a dual-inverter. Contrary to the current definitions known from previous publications, the expressions presented below are defined in solved form. Therefore, the use of integral or differential equation expressions is not necessary. In this way, a basis is created for calculating the DClink current without computationally intensive numerical integration processes or SPICE simulations. Furthermore, this paper includes the metrological verification of the novel expressions. The results discussed in this publication provide the basis for stabilizing the HV-DC system and for minimizing the DClink capacitor load. Thus, they enable the DC-link capacitor of a dual-inverter to be downsized. Based on the presented definition of the DC-link current in solved form, the possibility of real-time optimization is created. Furthermore, the results outlined in this paper form the foundation to derive the control optimization for a multi-phase inverter. Index Terms-Dual inverter, Voltage Source Inverter (VSI), phase shift, DC-link current, Newton-Cotes I. INTRODUCTIONHE need of regulating the flow of energy between two or more electrical motors or comparable AC-impedances and a DC-grid is given in many applications. Thereby, the use of a dual-inverter instead of two individual inverters often makes sense due to many reasons. An example of such an application can be found in the field of electrified vehicles. As explained in [1,2], drive concepts of HEVs (hybrid electric vehicles), BEVs (battery electric vehicles) and FCEVs (fuel cell electric vehicles) are often operated with at least two electric motors. This can be explained by the advantages of performance scalability, the potential of cost savings, driving dynamics advantages (4-wheel drive, torque vectoring), and the increase in efficiency in partial load operation. The use of dual-

Calculation of RMS Current Load on DC-Link Capacitors for Multiphase Machine Drives under Carrier-Phase Shift Control

“…Terefore, the time signal i inv,upper,rms can be expressed by spectrum amplitude i inv,up (f). As explained in [20], the upper-inverter spectrum i inv,up (f) results from the sum of the spectra of the three phase currents according to…”

“…Terefore, the proposed Cotes method is more simplifed. In order to verify the efectiveness of the proposed method, the results of two approximate methods are compared, considering the carrier index m. Equations ( 11)-( 12) defne the original function, which are applied to the Newton 3/8 method proposed in literature [20] and the Cotes method proposed in this paper. Ten, the standard integral calculation method in [17], the approximate results of the Cotes method, and Newton 3/8 method are compared.…”

“…Figure 8 shows the RMS value of the dc-link capacitor current I c,rms as a function of M for diferent 1-6 times the switching frequency (after CPST). Te black line represents the calculation results of the method proposed in [17], the red line represents the calculation results of the method proposed in [20], and the blue line represents the calculation results of the method proposed in this paper. Te high precision of the Cotes method is proved by the graphic results.…”

“…In frequency domain, the capacitor RMS current is calculated according to the harmonic frequency analysis, in which the harmonic components are obtained with a double Fourier integration [17,19,20]. Tis method is clearly simple and easy to accomplish [19].…”

“…Besides, the efects on the RMS current under diferent modulation methods are analyzed in detail, and its analysis results were verifed [17]. A polynomial interpolation integral method was used to calculate the RMS current, which could eliminate the external integral term and thus simplify the analytical modeling [20,21]. Te calculation methods have low accuracy and complicated processes in the existing literature, and there is still no paper to calculate the RMS current considering the CPST efect.…”