## 1 Introduction  
Due to their advantages over three-phase machines, multiphase induction machines have recently gained much attention for medium voltage and high-power applications [1]. These systems have high reliability, fault tolerance capability, higher power density, and reduced switch ratings in the power converters. Thus, they are well suited for many applications that are principally associated with electric vehicles (EVs), ship propulsion, electric aircraft, and remote high-power wind power generation systems [1; 2; 3]. The nine-phase drive, shown in Figure 1, has specific merits among the various possible numbers of phases, such as [4]:  
1. The stator of the standard three-phase machine can be rewound to obtain the nine-phase stator, and the rotor is still the same. 2. The nine-phase VSI can be realized as a combination of standard three-phase inverters. 3. In terms of control and fault-tolerant operation, it has additional degrees of freedom. These merits make the nine-phase machines attractive in different applications. Several contributions have been made to embody the nine-phase systems in ultrahigh-speed elevators [5], onboard chargers of electric vehicles [6; 7; 8], aerospace [9], ship propulsion, wind energy generation systems, and high-power industrial applications [1; 2; 10]. Although nine-phase machines are distinguished by their lower \(dv/dt\) value; they still have the same peak common mode voltage (CMV) as the three-phase machine, which equals \(V_{dc}\)[11; 12]. Regardless of the number of phases, the CMV seems a common problem in drive systems. Hence, it represents one of the leading research topics to be investigated in the drive systems, where it leads to multiple unwanted effects such as [11; 12; 13; 14]:  
1. Electromagnetic Interference (EMI),
2. Winding insulation failure, and
3. Damage to motor bearings due to leakage currents. The traditional solutions to mitigate CMV's effects on the drive systems are based on hardware solutions, such as using a passive output filter or grounded brushes for the bearings [13]. However, all these solutions are costly and need significant maintenance. Consequently, research has been directed to find more affordable and straightforward methods to apply. Therefore, some modifications have been adopted to the conventional Sinusoidal PWM and Space Vector Modulation (SVM) techniques to effectively reduce the CMV, beginning with three-phase drive systems [15]. These solutions were extended after that to multiphase machines. In particular, the problem of CMV reduction in five-phase machines has received substantial interest [11; 13; 16; 17; 18; 19]. Moreover, few studies have focused on the CMV reduction methods in six- and seven-phase machines such as [20; 21]. In particular, the CMV problems in the nine-phase machines have rarely been studied directly. As an example of an odd-phase multiphase machine, it has only been mentioned in [12; 22; 23]. Additionally, simulation and experimental results in these works are based on RL loads. These studies ignore the inductances and mutual inductances inside the machine subspaces, which are significant, resulting in inaccurate results. There has been no research to the authors' knowledge that has comprehensively explored this topic. This paper aims to fill this gap by proposing CMV reduction PWM schemes for symmetrical nine-phase IM drives fed from two-level VSI with optimal performance and without extra hardware components. This paper describes the nine-phase VSI modeling and introduces the basic outlines to reduce CMV in the nine-phase motor drives. Aiming to solve the CMV problem of symmetrical nine-phase machines, two unique SVM schemes to reduce the CMV are proposed. The first scheme extends the concept of CMV in the three-phase system to the nine-phase case by replacing the true zero vectors with two opposite active vectors. This approach reduces the CMV's peak by 22.2% compared with the conventional scheme.