In the evolving landscape of automotive electrification, the development of efficient and compact range extender systems represents a critical technological pathway. While the battery electric vehicle offers the ultimate goal of zero tailpipe emissions, challenges related to charging infrastructure, initial cost, and range anxiety persist. Hybrid solutions, particularly series configurations utilizing a range extender, present a pragmatic and transitional technology. This approach mitigates the immediate infrastructure demands of the pure battery electric vehicle while significantly reducing emissions and fuel consumption compared to conventional vehicles. The core of a series range extender is a dedicated generator set, comprising an internal combustion engine operating at a fixed, high-efficiency point and a generator that converts mechanical energy into electrical power to charge the traction battery. The design of this generator is paramount, as it directly influences the system’s overall efficiency, power density, packaging, and NVH characteristics. Unlike traction motors for a pure battery electric vehicle, the range extender generator operates within a relatively narrow and steady speed band, allowing for optimization focused on specific operational points rather than a wide speed-torque envelope.
This article details the comprehensive electromagnetic and thermal design process for a high-power-density, hairpin-wound permanent magnet synchronous generator (PMSG) intended for a range extender application in a compact passenger vehicle. The work begins with a derivation of key performance requirements based on vehicle-level energy management strategy. Subsequently, the electromagnetic design is executed, culminating in a detailed multi-physics analysis using advanced simulation tools to validate performance and thermal management under steady-state operating conditions.
1. Requirements Analysis and Electromagnetic Design Philosophy
The target application is an A0-segment vehicle. The generator must integrate seamlessly with a specifically downsized internal combustion engine. The primary design objective is to achieve high efficiency and power density within strict spatial and cost constraints. The key performance parameters are summarized in Table 1.
| Parameter | Value |
|---|---|
| DC Link Voltage | 336 V |
| Rated Power (Prated) | 28 kW |
| Rated Speed (nrated) | 3600 rpm |
| Maximum Speed (nmax) | 6000 rpm |
| Maximum Phase Current (Imax) | 95 Arms |
| Target Peak Efficiency | > 95% |
1.1 Fundamental Sizing Equations and Electromagnetic Loading
The initial sizing of any electrical machine is governed by its output power equation, which relates key electromagnetic and geometric parameters. For a PMSG, the apparent power can be expressed as:
$$ S = m E I $$
where $m$ is the number of phases, $E$ is the phase back-EMF, and $I$ is the phase current. A more practical form for initial sizing, linking the machine’s main dimensions to its output, is derived from the fundamental theory. The required internal volume of the stator is given by:
$$ D_{i1}^2 L_{ef} = \frac{60 P’}{ \pi^2 \alpha_p K_{Nm} K_{dp} B_{\delta} A n} $$
where:
$D_{i1}$ = Stator bore diameter (m)
$L_{ef}$ = Effective stack length (m)
$P’$ = Rated output power (W)
$\alpha_p$ = Pole arc coefficient
$K_{Nm}$ = Air-gap flux density waveform factor (≈1.11 for sinusoidal)
$K_{dp}$ = Winding distribution factor
$B_{\delta}$ = Specific magnetic loading or air-gap flux density (T)
$A$ = Specific electric loading or linear current density (A/m)
$n$ = Rotational speed (rps)
The product $D_{i1}^2 L_{ef}$ is the core volume determining the torque-producing capability. The electromagnetic torque $T_{em}$ is directly related to these loadings:
$$ T_{em} = \frac{\pi}{2\sqrt{2}} B_{\delta 1} A D_{i1}^2 L_{ef} $$
where $B_{\delta 1}$ is the fundamental component of the air-gap flux density. The selection of $A$ and $B_{\delta}$ is a critical trade-off. A high $A$ increases copper losses and thermal stress but allows for a smaller machine diameter. A high $B_{\delta}$ reduces the required amount of permanent magnet material but increases iron losses and risk of saturation. For a range extender generator targeting high power density and operating at a relatively constant speed, we can push these loadings to the upper limits dictated by thermal and material constraints. Initial values were chosen as $B_{\delta}$ = 0.75 T and $A$ = 20 kA/m.
The aspect ratio $\lambda = L_{ef} / D_{i1}$ influences dynamic performance, mechanical rigidity, and thermal behavior. A common range for PM machines is 0.6 to 1.5. A smaller $\lambda$ (shorter, wider machine) generally offers better heat dissipation from the end-windings and higher maximum speed capability, which is relevant for the over-speed condition of 6000 rpm. The aspect ratio is linked to the rotor’s mechanical limits by:
$$ \lambda \approx \frac{\rho \cdot t_b \cdot \omega_b}{2 \rho_{Fe}} $$
where $\rho$ is the number of pole pairs, $t_b$ is the acceleration time constant, $\omega_b$ is the base speed, and $\rho_{Fe}$ is the density of the rotor core material. Considering the stable operating nature of a range extender, dynamic acceleration is less critical than thermal and efficiency performance. An initial aspect ratio of approximately 0.6 was selected to favor a compact diameter and enhance cooling.
1.2 Initial Design Parameters and Topology Selection
Based on the sizing equations and application constraints, an initial set of design parameters was established. An interior permanent magnet (IPM) rotor topology with a “V” shaped magnet arrangement was chosen. This configuration provides significant reluctance torque, improving overall torque density and efficiency, and offers robust mechanical integrity for the magnets at high speeds. To maximize power density and slot fill factor, a hairpin (rectangular wire) winding was specified for the stator. This technology, increasingly common in traction drives for battery electric vehicles, offers significantly higher copper slot fill (often >70%) compared to traditional round wire windings, reducing DC copper losses and improving thermal conductivity from the winding to the stator core. The initial key design parameters are summarized in Table 2.
| Parameter | Value |
|---|---|
| Topology | IPM, Internal Rotor |
| Pole / Slot Number | 8 Poles / 48 Slots |
| Winding Type | Hairpin (4 layers) |
| Stator Bore Diameter, $D_{i1}$ | 200 mm |
| Stack Length, $L_{ef}$ | 120 mm |
| Aspect Ratio, $\lambda$ | 0.6 |
| Air-gap Length | 1.0 mm |
| Target Air-gap Flux Density, $B_{\delta}$ | 0.75 T |
| Target Electric Loading, $A$ | 20 kA/m |
| Permanent Magnet Material | NdFeB N42EH |
| Magnet Radial Thickness | 5 mm |
2. Electromagnetic Simulation and Performance Analysis Using Motor-CAD
To validate and refine the initial design, a detailed electromagnetic model was built using Motor-CAD software. This environment allows for integrated electromagnetic, thermal, and lab analysis. The 2D cross-section of the FEA model reflects the geometry defined in Table 2.
2.1 Modeling and Material Definitions
The stator and rotor cores were modeled using NO18-1160 non-oriented silicon steel laminations. The hairpin winding was configured as a 4-layer, single-parallel path design with a coil pitch of 6 slots (full pitch for an 8-pole, 48-slot machine). The winding factor analysis confirmed a fundamental winding factor $K_{dp}$ of approximately 0.925. The rotor was axially segmented into 5 sections to minimize eddy current losses in the magnets. The mass of key active materials was extracted from the model, as shown in Table 3, providing a basis for power density calculation and thermal mass estimation.
| Component | Material | Mass (kg) |
|---|---|---|
| Stator Core & Yoke | NO18-1160 Steel | 9.9 |
| Rotor Core & Yoke | NO18-1160 Steel | 7.3 |
| Windings | Copper | 2.92 |
| Permanent Magnets | NdFeB N42EH | 1.016 |
The total active mass is approximately 21.1 kg, leading to an active power density of about 1.33 kW/kg for the rated operating point, a significant value indicative of the high-density design.
2.2 Electromagnetic Field Analysis
A magnetostatic analysis at no-load condition reveals the flux density distribution. The results show a high level of magnetic utilization. The average flux density in the stator teeth is around 1.2 T, with localized saturation peaks near the magnet bridges reaching up to 2.14 T. This level of saturation is acceptable for the selected silicon steel grade and is a deliberate trade-off to maximize torque production per unit volume. The air-gap flux density waveform, extracted along a circumferential path, shows a rich harmonic content due to the slotting and IPM topology, which will influence the back-EMF waveform.
The no-load phase back-EMF at the rated speed of 3600 rpm was simulated. The fundamental relationship is:
$$ E_0 = 4.44 \cdot f \cdot K_{dp} \cdot N \cdot \phi_{10} $$
where $f$ is the electrical frequency, $N$ is the series turns per phase, and $\phi_{10}$ is the fundamental flux per pole. The simulated back-EMF waveform had a fundamental RMS value of approximately 100 V at 3500 rpm, aligning well with the target voltage for the 336 V DC link after rectification. The total harmonic distortion (THD) of the back-EMF was analyzed. While the hairpin full-pitch winding suppresses some sub-harmonics, the IPM topology and slot harmonics contribute to a non-sinusoidal waveform. This has implications for control strategy and potentially introduces torque ripple, a factor considered during the rating analysis.
2.3 Torque Performance Analysis
The cogging torque, generated by the interaction between the permanent magnet MMF and the variable reluctance of the slotted stator, was evaluated. For the 8-pole/48-slot combination (a slot per pole per phase, q=2), the least common multiple (LCM) of poles and slots is 48, resulting in a cogging torque period of 7.5 mechanical degrees. The peak-to-peak cogging torque was simulated to be below ±1.5 Nm.
The rated torque output at 3600 rpm and 95 Arms was simulated under loaded conditions. The average electromagnetic torque reached the target value of approximately 74 Nm (derived from $T = P_{rated} / \omega_{rated}$). However, the instantaneous torque exhibited a ripple of about ±5 Nm peak-to-peak. This ripple is attributed to the combined effects of cogging torque and the interaction of current harmonics with the non-sinusoidal back-EMF. While acceptable for the steady-state generation duty of a range extender, minimizing this ripple would be a focus for NVH refinement, especially as the standards for refinement in hybrid vehicles approach those expected in a premium battery electric vehicle.
3. Coupled Electromagnetic-Thermal Analysis
The high power density of this design inherently leads to significant loss generation. Effective thermal management is not an afterthought but a co-equal design driver alongside electromagnetic performance. For a range extender application, the generator is typically packaged in close proximity to the internal combustion engine, exposing it to a harsh under-hood thermal environment. Therefore, a liquid cooling jacket is the standard and necessary solution.
3.1 Thermal Model Setup
A coupled electromagnetic-thermal analysis was performed in Motor-CAD. The thermal model incorporates a spiral water jacket surrounding the stator lamination stack. The coolant (a 50/50 water-glycol mix) inlet temperature was set to 80°C, reflecting the integrated cooling circuit often shared with the engine. A high flow rate of 12 liters per minute was specified to ensure effective heat extraction. The main heat sources are the winding Joule losses (DC and AC) and the iron losses in the stator and rotor cores, which are calculated by the electromagnetic solver based on the operating point.
The most challenging thermal path is from the interior of the hairpin winding bundles to the coolant. The thermal conductivity of the impregnation resin and the insulation system is critical. The model uses standard thermal conductivity values for copper, laminated steel, and a Class H insulation system.
3.2 Steady-State Thermal Performance
The simulation was run for the worst-case continuous operating condition: rated power (28 kW) at 3600 rpm for a duration sufficient to reach thermal steady-state (simulated for 30 minutes). The resulting temperature distribution is shown conceptually below, with key hotspot temperatures extracted in Table 4.
The highest temperature occurs within the hairpin winding end-turns, reaching a steady-state peak of approximately 151°C. The average winding temperature is around 140°C. Given a coolant inlet of 80°C, this corresponds to a maximum winding hot-spot temperature rise of about 71°C. This is within the allowable temperature limit for a Class H (180°C) insulation system, providing a sufficient margin for reliability under continuous operation. The stator teeth and yoke temperatures are lower, typically between 110°C and 130°C, as they are in direct contact with the cooling jacket. The rotor temperature is higher due to its isolation from the primary coolant path, reaching levels around 135°C at the magnet locations, which is still safe for the N42EH grade magnets.
| Component | Average Temperature (°C) | Hotspot Temperature (°C) |
|---|---|---|
| Stator Windings (Slot) | 135 | – |
| Stator Windings (End-Turn) | 145 | 151 |
| Stator Teeth | 125 | – |
| Stator Yoke | 110 | – |
| Rotor Core / Magnets | 130 | 135 |
| Coolant (Outlet) | 85 | – |
This thermal analysis confirms that the proposed electromagnetic design, when paired with the specified spiral water jacket cooling, is thermally feasible. It underscores the necessity of integrated thermal design from the outset. A less effective cooling system would force a derating of the electromagnetic loadings, directly reducing the achievable power density—a key differentiator for compact range extender systems competing for space in vehicle platforms that may also be designed for a pure battery electric vehicle variant.
4. Conclusion and Future Perspectives
This study has successfully detailed the electromagnetic and thermal design process for a high-power-density hairpin-wound IPM generator for a series hybrid electric vehicle range extender. Starting from vehicle-level requirements, fundamental sizing equations were applied to establish key parameters such as stator bore diameter, stack length, and electromagnetic loadings ($A$ and $B_{\delta}$). The choice of an 8-pole/48-slot IPM topology with hairpin windings was driven by the imperative for high torque density, efficiency, and effective thermal management.
Finite element analysis validated the electromagnetic performance, confirming the achievement of the target 28 kW output at 3600 rpm with an acceptable level of torque ripple. The design exhibits a high active power density exceeding 1.3 kW/kg. Crucially, the subsequent coupled electromagnetic-thermal analysis demonstrated that with a conventional spiral water jacket cooling system, the machine can operate continuously at its rated point without exceeding the thermal limits of its Class H insulation system or demagnetizing the permanent magnets.
The results indicate that the designed generator is a viable and competitive solution for next-generation range extender applications. It provides a blueprint for achieving the compactness and efficiency required to make series hybrids a compelling alternative, both as a transitional technology and as a potential long-range complement to the core architecture of a battery electric vehicle.
Future work will focus on several advanced areas. First, multi-objective optimization algorithms could be employed to further refine the Pareto front between efficiency, power density, torque ripple, and cost. Second, a more detailed transient thermal analysis, including thermal cycles and overload conditions, would enhance the reliability assessment. Third, exploring advanced cooling techniques, such as direct oil cooling of the hairpin end-winds or integrated stator cooling channels, could push the continuous power rating even higher. Finally, system-level integration studies, including the acoustic signature of the generator and its control interaction with the engine and the power electronics, are essential for ensuring the refinement expected by consumers, whether they are driving a hybrid or a pure battery electric vehicle.