In recent years, solar electric vehicles have gained significant attention due to their extended driving range. As a researcher in this field, I have focused on expanding the application of onboard photovoltaic (PV) panels and reducing operational costs. Traditional PV systems require additional power electronic devices for grid connection, which increases cost and space requirements. To address this, we propose a novel six-phase electric-drive-reconstructed on-grid inverter that reuses existing hardware from the vehicle’s propulsion system. This approach eliminates the need for extra components, enabling efficient energy transfer from onboard PV panels to the grid while ensuring zero electromagnetic torque in the motor during operation. In this article, I will detail the theoretical analysis, circuit topology, control strategies, and experimental validation of this system, emphasizing the importance of the on-grid inverter in enhancing vehicle sustainability.
The core innovation lies in leveraging the multi-phase motor’s degrees of freedom to achieve zero electromagnetic torque, allowing the motor windings to be repurposed for power conversion. We analyze the conditions for zero torque in an asymmetric six-phase permanent magnet synchronous motor (ASPMSM) and derive a circuit topology that integrates seamlessly with the vehicle’s drivetrain. Key aspects include the vector space decoupling (VSD) technique, Park transformations, and a dual-stage control strategy for maximum power point tracking (MPPT) and grid current regulation. Experimental results from a 660 W prototype confirm the feasibility and performance of our on-grid inverter, demonstrating low total harmonic distortion (THD) and rapid response to changing PV conditions. Throughout this discussion, the term “on-grid inverter” will be frequently referenced to highlight its role in enabling bidirectional energy flow.
Introduction to Solar Electric Vehicles and On-Grid Inverters
Solar electric vehicles represent a promising advancement in sustainable transportation, combining photovoltaic technology with electric propulsion. However, a major challenge is the efficient utilization of onboard PV energy, particularly for grid interaction during stationary periods. Conventional systems employ separate on-grid inverters, which add cost, weight, and complexity. In our work, we aim to overcome this by reconfiguring the vehicle’s six-phase drive system into an on-grid inverter, thus creating a multifunctional platform. This not only reduces overall system cost but also optimizes space usage, making it ideal for modern electric vehicles. The on-grid inverter functionality is crucial for feeding excess solar energy into the grid, potentially reducing electricity costs and supporting grid stability.
Our approach builds upon electric-drive reconstruction concepts, where power electronic converters and motor windings are reused for ancillary functions like charging or grid-tie applications. By analyzing the ASPMSM’s electromagnetic properties, we ensure that during grid-tie mode, the motor produces no torque, preventing unintended rotation and ensuring safety. This article will systematically explore the theoretical foundations, practical implementation, and experimental validation of our six-phase on-grid inverter, underscoring its significance in the evolving landscape of solar mobility.
Theoretical Analysis of Zero Electromagnetic Torque in ASPMSM
To enable the reuse of motor windings for an on-grid inverter, it is essential to eliminate electromagnetic torque. For an ASPMSM, the torque production is primarily governed by currents in the d-q reference frame. Using vector space decoupling (VSD), the six-phase currents can be mapped into orthogonal subspaces: α-β (fundamental), x-y (secondary), and o1-o2 (zero-sequence). The VSD transformation matrix is given by:
$$ T_{vsd} = \frac{1}{\sqrt{3}} \begin{bmatrix} 1 & \frac{1}{2} & -\frac{1}{2} & -\frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{2} & 0 \\ 0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2} & \frac{1}{2} & \frac{1}{2} & -1 \\ 1 & -\frac{1}{2} & -\frac{1}{2} & \frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{2} & 0 \\ 0 & \frac{\sqrt{3}}{2} & \frac{\sqrt{3}}{2} & \frac{1}{2} & -\frac{1}{2} & 1 \\ 1 & -1 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & -1 & 1 \end{bmatrix} $$
This decomposition allows independent control of torque-producing and non-torque-producing currents. The α-β subspace is further transformed to the d-q frame using Park transformation:
$$ T_{park} = \begin{bmatrix} \cos\theta_e & \sin\theta_e \\ -\sin\theta_e & \cos\theta_e \end{bmatrix} $$
where $\theta_e$ is the electrical angle of the motor. The electromagnetic torque $T_e$ in an ASPMSM is proportional to the q-axis current $i_q$, as expressed by:
$$ T_e = \frac{3}{2} p (\lambda_m i_q + (L_d – L_q) i_d i_q) $$
where $p$ is the number of pole pairs, $\lambda_m$ is the permanent magnet flux linkage, and $L_d$, $L_q$ are d-q inductances. For zero torque, we require $i_q = 0$. Through analytical derivation, we identify three conditions that satisfy this:
- $i_\alpha = 0$ and $i_\beta = 0$
- $i_\alpha = 0$ and $\theta_e = \pm \frac{\pi}{2}$
- $i_\alpha \neq 0$ and $\theta_e = \arctan\left(\frac{i_\beta}{i_\alpha}\right)$, with $0 \leq \theta_e < \frac{\pi}{2}$
Here, $i_\alpha$ and $i_\beta$ are currents in the α-β subspace. Our on-grid inverter design utilizes condition 3, where the current vector aligns with a fixed angle, resulting in no rotating magnetic field. This is achieved by appropriately configuring the motor windings and control signals. Table 1 summarizes these conditions and their implications for torque cancellation.
| Condition | Currents in α-β Subspace | Electrical Angle $\theta_e$ | Torque Status |
|---|---|---|---|
| 1 | $i_\alpha = 0$, $i_\beta = 0$ | Any | Zero |
| 2 | $i_\alpha = 0$ | $\pm \frac{\pi}{2}$ | Zero |
| 3 | $i_\alpha \neq 0$, $i_\beta = 0$ | 0 | Zero |
In practice, condition 3 is most suitable for our on-grid inverter because it allows non-zero currents to flow for power conversion while maintaining $\theta_e = 0$. This ensures the motor remains stationary, and the windings can be used as inductors or transformers in the power circuit. The underlying principle is that the current vector is static in the α-β plane, producing no rotating flux. We can express this mathematically as:
$$ i_\alpha = I_m \cos(\omega t), \quad i_\beta = 0 $$
where $I_m$ is the current magnitude and $\omega$ is the grid frequency. Substituting into the torque equation yields $T_e = 0$, validating the feasibility of our approach for an on-grid inverter system.
System Topology of the Six-Phase Electric-Drive-Reconstructed On-Grid Inverter
Based on the zero-torque condition, we propose a circuit topology that reconfigures the ASPMSM and its associated six-phase inverter for grid-tie operation. The system comprises the motor windings, a six-phase voltage source inverter (VSI), DC-link capacitors, a battery, and mode switches (S1 to S7). During normal driving mode, all switches are set to connect the inverter to the motor windings for propulsion. In on-grid inverter mode, the switches are reconfigured to form two stages: a front-end boost converter and a rear-end grid-tie inverter. Specifically:
- Phases U, V, W of the motor are connected in parallel to the PV panel via the inverter legs, acting as inductors for the boost converter.
- Phases A, B, C are connected to the grid, with B and C in parallel and A directly linked, forming the grid-side inverter.
This configuration ensures that $i_\beta = 0$ and $\theta_e = 0$, satisfying condition 3 for zero torque. The boost converter steps up the PV voltage to a stable DC-link voltage, while the grid-tie inverter converts DC to AC synchronized with the grid. By reusing hardware, we eliminate the need for additional inductors or transformers, reducing cost and volume. The on-grid inverter thus operates efficiently, with the motor windings serving dual purposes without compromising performance.
To quantify the benefits, Table 2 compares our reconstructed on-grid inverter with a conventional separate on-grid inverter system in terms of component count and estimated cost.
| Component | Reconstructed System | Conventional System | Savings |
|---|---|---|---|
| Power Switches | 6 (reused from drive) | 6 + 4 (additional) | 4 switches |
| Inductors | Motor windings (reused) | 2-3 separate inductors | 2-3 inductors |
| Current Sensors | Reused from drive | Additional sensors | 3-4 sensors |
| Control Hardware | Shared DSP | Dedicated controller | 1 controller |
| Total Cost Estimate | Low (minimal additions) | High (extra components) | ~30% reduction |
The topology’s versatility allows seamless switching between driving and grid-tie modes, making it ideal for solar electric vehicles that require frequent energy exchange with the grid. Our on-grid inverter design not only reduces hardware but also enhances system reliability by leveraging proven drivetrain components.
Control Strategy for the On-Grid Inverter
The control of our six-phase on-grid inverter involves two primary loops: the front-end boost converter with MPPT and the rear-end grid-tie inverter with current regulation. We employ a perturbation and observation (P&O) algorithm for MPPT due to its simplicity and effectiveness. The P&O algorithm adjusts the PV voltage to track the maximum power point by comparing power increments. Mathematically, the duty cycle $D_{PV}$ for the boost converter is derived from:
$$ D_{PV} = 1 – \frac{V_{PV}}{V_{dc}} $$
where $V_{PV}$ is the PV voltage and $V_{dc}$ is the DC-link voltage. The MPPT algorithm computes a reference voltage $V_{PV}^*$ by perturbing the operating point and observing power changes. The control law can be summarized as:
$$ \Delta D = k_p (P(k) – P(k-1)) \cdot \text{sign}(\Delta V_{PV}) $$
where $k_p$ is a gain, $P(k)$ is the instantaneous power, and $\Delta V_{PV}$ is the voltage perturbation. This ensures optimal power extraction from the PV panel, feeding into the on-grid inverter efficiently.
For the grid-tie inverter, we use a cascaded control structure with an outer voltage loop and an inner current loop. The voltage loop maintains the DC-link voltage at a reference value $V_{dc}^*$ using a PI controller:
$$ I_{ref} = k_{p,v} (V_{dc}^* – V_{dc}) + k_{i,v} \int (V_{dc}^* – V_{dc}) dt $$
where $I_{ref}$ is the reference current amplitude. The inner current loop regulates the grid current $i_g$ to follow a sinusoidal reference in phase with the grid voltage $v_g$. A proportional-resonant (PR) controller is employed for zero steady-state error at grid frequency:
$$ G_{PR}(s) = k_{p,i} + \frac{2k_{r,i} \omega_c s}{s^2 + 2\omega_c s + \omega_g^2} $$
where $\omega_g$ is the grid angular frequency, and $\omega_c$ is the cutoff frequency. The reference current is generated as:
$$ i_{ref}(t) = I_{ref} \sin(\omega_g t + \phi) $$
with $\phi$ set to 0 for unity power factor. The modulation signals for the grid-side inverter are produced via pulse-width modulation (PWM). Table 3 outlines the key control parameters used in our implementation.
| Parameter | Symbol | Value | Description |
|---|---|---|---|
| DC-Link Voltage Reference | $V_{dc}^*$ | 400 V | Target voltage for boost stage |
| Grid Frequency | $f_g$ | 50 Hz | Standard grid frequency |
| Switching Frequency | $f_{sw}$ | 10 kHz | PWM frequency for both stages |
| MPPT Perturbation Step | $\Delta V_{PV}$ | 0.5 V | Voltage increment for P&O |
| PI Controller Gains (Voltage) | $k_{p,v}$, $k_{i,v}$ | 0.5, 10 | Tuned for stability |
| PR Controller Gains (Current) | $k_{p,i}$, $k_{r,i}$ | 5, 100 | Ensures current tracking |
This control strategy ensures that the on-grid inverter operates efficiently under varying PV conditions, maintaining grid synchronization and low harmonic distortion. The integration of MPPT and grid current control is crucial for maximizing energy harvest and complying with grid standards.
Experimental Validation and Results
To validate our on-grid inverter design, we built a 660 W prototype platform using an ASPMSM, a six-phase VSI, and associated sensors. The experimental setup includes a DC power supply emulating the PV panel, the motor-inverter system, isolation transformers, and measurement equipment. Key specifications are listed in Table 4.
| Component | Model/Specification | Role in On-Grid Inverter |
|---|---|---|
| DC Power Supply | 3 kW programmable | Emulates PV panel (set to 250 V) |
| ASPMSM | 2 kW, 2 mH winding inductance | Provides windings for boost and inverter |
| Six-Phase Inverter | IGBT FF300R12ME4 | Power switching for both stages |
| DSP Controller | TMS320F28335 | Implements control algorithms |
| Voltage Sensor | WHV05AS3S6 | Measures DC-link and grid voltages |
| Current Sensor | WHB25LSP3S1 | Measures PV and grid currents |
In the tests, we operated the system in on-grid inverter mode with $V_{dc}^* = 400$ V and a switching frequency of 10 kHz. The grid voltage was 220 V AC at 50 Hz. We first evaluated steady-state performance by measuring grid current and voltage waveforms. As shown in Figure 1 (represented by the inserted image), the current is sinusoidal and in phase with the voltage, indicating unity power factor operation. The total harmonic distortion (THD) of the grid current was analyzed using a power analyzer, resulting in a value of 2.81%, which meets typical grid codes (e.g., below 5%). This demonstrates that our on-grid inverter effectively minimizes harmonics, ensuring clean power injection.
To verify zero electromagnetic torque, we monitored the α-β current trajectories using the VSD transformation. The trajectory appeared as a straight line along the α-axis, confirming $i_\beta = 0$ and thus no rotating field. This aligns with condition 3 and ensures motor safety during grid-tie operation. We also tested dynamic response by simulating a change in PV maximum power—specifically, by stepping the grid current reference from 3 A to 1.7 A RMS. The system responded quickly, stabilizing within a few grid cycles, as evidenced by the current waveform settling to the new reference. This highlights the robustness of our control strategy in adapting to varying solar insolation.
Quantitative results are summarized in Table 5, which compares key performance metrics against design targets. The on-grid inverter achieves high efficiency and low distortion, validating its practicality for solar electric vehicles.
| Metric | Measured Value | Target Value | Status |
|---|---|---|---|
| Grid Current THD | 2.81% | <5% | Pass |
| DC-Link Voltage Regulation | ±2 V (398-402 V) | ±5 V | Pass |
| Response Time to Step Change | 50 ms | <100 ms | Pass |
| Efficiency (PV to Grid) | 94.5% | >90% | Pass |
| Motor Torque during Operation | 0 Nm | 0 Nm | Pass |
These experimental outcomes confirm that our six-phase electric-drive-reconstructed on-grid inverter is viable for real-world applications. The reuse of drivetrain components does not compromise performance, and the system adeptly handles both steady-state and transient conditions. This reinforces the value of integrated designs in reducing cost and complexity for solar electric vehicles.
Extended Discussion on On-Grid Inverter Applications
The concept of an on-grid inverter integrated into a vehicle’s drivetrain opens up numerous possibilities beyond mere grid-tie functionality. For instance, during peak sunlight hours, the vehicle can feed surplus energy to the grid, potentially generating revenue through net metering. Conversely, at night or during low solar availability, the same hardware could be used for vehicle-to-grid (V2G) services, supporting grid stability. Our on-grid inverter design facilitates these bidirectional flows without additional hardware, making it a versatile platform for smart grid integration.
Moreover, the multi-phase nature of the system offers redundancy. If one phase fails, the remaining phases can continue operation, albeit at reduced power, enhancing reliability. This is particularly beneficial for safety-critical applications like electric vehicles. We can extend the control strategy to include fault-tolerant modes, where the on-grid inverter adapts its modulation scheme to maintain performance. For example, in case of an open-circuit fault in one motor winding, the currents can be redistributed using the remaining phases, ensuring continuous grid connection.
From an economic perspective, the cost savings from hardware reuse are substantial. As shown in Table 2, our on-grid inverter reduces component count by approximately 30%, which translates to lower manufacturing costs and potentially lower vehicle prices. This could accelerate the adoption of solar electric vehicles, contributing to broader environmental goals. Additionally, the reduced weight and volume improve vehicle efficiency, further extending driving range—a key advantage for consumers.
Future work could explore higher power levels, integration with battery management systems, and advanced grid-support functions like reactive power control. The on-grid inverter could also be combined with wireless charging technologies, creating a comprehensive energy ecosystem for electric vehicles. Ultimately, our research underscores the importance of innovative power electronic architectures in achieving sustainable mobility.
Conclusion
In this article, we have presented a comprehensive study on a six-phase electric-drive-reconstructed on-grid inverter for solar electric vehicles. By analyzing the conditions for zero electromagnetic torque in an ASPMSM, we derived a circuit topology that reuses motor windings and inverter hardware for grid-tie operation. The control strategy incorporates MPPT for PV optimization and precise current regulation for grid synchronization. Experimental results from a 660 W prototype validate the system’s performance, showing low THD, fast dynamic response, and zero motor torque. Our on-grid inverter design offers significant cost and space savings compared to conventional systems, making it a promising solution for enhancing the viability of solar electric vehicles. As the demand for renewable energy integration grows, such multifunctional inverters will play a crucial role in shaping the future of transportation and energy systems.