## 1 Introduction  
The automotive industry has witnessed remarkable growth, marked by a recent surge in the development of downsized electrical machines with the aim of improving the energy efficiency of electric vehicles (EVs) [1; 2; 3]. Nonetheless, one of the foremost challenges confronting this pursuit is the inevitable tradeoff that arises when reducing the physical dimensions of these machines, leading to a reduction in both output torque and power. To address this issue and sustain a commendable power density, a compelling approach entails raising the operational speed of the machine. This strategy, while promising, comes with the drawback of a higher operating frequency, resulting in a concomitant increase in AC losses within the machine windings [4]. In response to this sizing dilemma, permanent magnet (PM) electrical machines have emerged as a promising solution. These machines do not possess rotor windings and are well suited for high-speed operation, exhibiting exceptional efficiency and reliability across a broad speed range. Moreover, they offer a cost-effective solution for EVs while maintaining high power density [5; 6]. Additionally, the PM-assisted synchronous reluctance machine (PMa-SynRM) has been introduced for similar applications, providing the advantage of fixed power operation and improved performance in high-speed scenarios [7; 8]. The AC losses of machine windings experience a significant increase due to the skin and proximity effects at high-frequency operation [9; 10; 11; 12]. Various methods have been documented in the literature to assess AC losses within these high-frequency machines, as listed in Table 1[11; 12; 13; 14; 15; 16; 17; 18; 19]. In a study described in [20], AC losses were computed for a PMa-SynRM employing stranded wire conductors. In [21], a group of researchers conducted a detailed analytical examination of the eddy current losses occurring in the stator windings of an interior permanent magnet (PM) machine. Their study specifically focused on a multi-strand coil configuration. Another approach outlined in [22] proposed the use of rectangular conductors to reduce AC resistance in an EV traction motor. Additionally, in [23; 24], investigations were conducted using the finite element method (FEM) to calculate high-frequency copper losses in flat hairpin windings. It is worth noting that all of the aforementioned methods assumed a pure sinusoidal current excitation when using the FEM to analyze the machine windings. However, in practical PMa-SynRMs, the machine is powered by an inverter with pulse-width modulated (PWM) current, leading to the introduction of additional AC losses due to generated harmonics. This paper presents a comprehensive investigation into winding losses under non-sinusoidal current excitation, with a specific focus on various winding topologies, all analyzed using finite element method (FEM) simulations at the strand level for inverter-fed motors. The studied topologies encompass rectangular flat conductors and stranded wires. Furthermore, the study involves the prototyping of various coil samples. The primary objective is to minimize AC losses, and through rigorous analysis, we identify the winding configuration that exhibits the best electromagnetic performance across different frequency domains. In conclusion, this research explores innovative hybrid coil configurations to effectively mitigate the adverse effects of high-frequency AC losses. By incorporating different wire materials within the same slot, this approach demonstrates significant reductions in losses and offers substantial weight savings, making it a promising advancement for electric vehicle and motor drive technologies. This paper investigates AC copper losses in inverter-fed electrical machines, focusing on various winding topologies and magnet wire materials. Key findings and innovations include:  
* Evaluating different wire topologies: This study explores flat conductor, stranded, and lift wire topologies to assess their impact on AC losses in electrical machine windings.