## 1 Introduction  
Over the past decade, dual motor drive systems have become prevalent in power application systems due to their advantages such as high efficiency, small size, compact design, and reliability. Dual motors are coupled to a common shaft to provide greater torque and higher speeds while reducing motor stress and increasing lifetime in electric vehicles and powertrains. In addition, two motors operate separately for the azimuth and elevation axes to provide full hemispherical coverage and precise targeting capabilities in the tank's turret/gun systems, radar and artillery control systems, and antenna pointing mechanisms. Three-phase PMSMs are commonly used in these applications due to their high efficiency, power density, reliability, precise control, and suitability. These motors are separately controlled by two parallel three-phase inverters connected to a common DC bus. PMSMs are controlled by VSIs with pulse width modulation (PWM). VSIs produce a square-wave output which introduces numerous harmonic components that create the input ripple current. This ripple current degrades battery life or fuel cell durability by feeding back through the power electronics converter, while also causing the bus voltage to fluctuate, compromising the overall reliability of the power supply. To mitigate these problems, direct current link (dc-link) capacitors are essential for motor drive systems to correct power factor, diminish ripple current and minimize electromagnetic interference, and suppress voltage spikes caused by leakage inductance and switching operations [1]. Dc-link capacitors are significantly larger and heavier than other components in three-phase inverters, occupying more than 40% of the volume of the inverter [1]. They are highly failure-prone components in power electronic systems. Their reliability is significantly affected by operating conditions such as temperature, humidity, ripple current, and voltage [2]. The research in [3] indicates that lower operating voltages and temperatures can dramatically extend the lifespan of electrolytic capacitors. Specifically, operating at 90% of the rated voltage reduces failure rates by 40%, and each 10 \({}^{\circ}\)C reduction in temperature doubles the expected lifetime [4]. The degradation also involves a nonlinear increase in equivalent series resistance (ESR) and a reduction in capacitance. Heating in dc-link capacitors arises from the current flowing through them and their ESR. In addition, the root mean square (RMS) of the ripple current in the dc-link capacitors can reach 60% of the phase currents of the PMSMs [5]. Thus, ripple current has a significant impact on the size and reliability of capacitors, leading to the development of methods for analyzing and reducing the capacitor current ripple of dual three-phase inverters driving PMSMs. The RMS value of the dc-link capacitor current can be determined using simulation, RMS analysis, and the spectral resolution method [6]. Although the time-dependent analyses performed in this study are sufficient for the RMS value of the capacitor current, only the spectral resolution method using double Fourier series analysis provides information about the harmonics of the dc-link capacitor current. Another research study in [7] presents an analysis of dc-link current harmonics using a double Fourier series for SPWM, SVPWM, and discontinuous PWM to show significant differences in the dc-link current spectra between modulation strategies. The harmonics of the input current for three-phase VSIs are analyzed by the double Fourier series method in [8]. In addition, the dc-link capacitor current and output phase current of the two- and three-level three-phase inverter are analyzed in [9]. However, these articles do not offer any recommendations for reducing the capacitor current. The proposed method in [10; 11] equalizes the rectifier output and inverter input side currents to eliminate the dc-link current ripple and use a smaller capacitance.