In recent years, the demand for efficient and sustainable energy solutions has driven research into advanced solar power systems. Among various technologies, concentrated solar thermal power generation stands out due to its maturity and adaptability, particularly in remote areas where grid access is limited. The key component in such systems is the generator, which converts mechanical energy from a linear prime mover into electrical energy. Traditional linear generators, while simplifying the system by eliminating rotary-to-linear motion conversion, suffer from low efficiency and power density, especially under low-speed operation typical of solar-driven systems. To address these limitations, we propose a magnetic-field modulated permanent magnet linear generator (M-FMPMLG) integrated into a solar power system. This generator leverages magnetic field modulation to enhance secondary speed, thereby improving power output and overall system efficiency. In this article, we detail the design, optimization, electromagnetic analysis, and experimental validation of the M-FMPMLG, emphasizing its application in solar power systems.
The M-FMPMLG combines a magnetic gear with a linear generator, resulting in a dual-mover structure that amplifies the secondary speed through field modulation. This design is particularly suitable for solar power systems where the prime mover, such as a Stirling engine in a dish-type setup, provides low-speed linear motion. By increasing the operational speed of the generator’s secondary component, the M-FMPMLG achieves higher power density and better material utilization compared to conventional linear generators. Our work focuses on a series-coupled topology that simplifies the magnetic circuit, reduces manufacturing complexity, and allows for greater travel range of the secondary mover. This makes it ideal for integration into solar power systems, enhancing their thermoelectric conversion efficiency.
In the following sections, we discuss the structural design of the M-FMPMLG, including the selection of modulation modes and key parameters. We then present optimization techniques for thrust characteristics and output voltage quality, followed by electromagnetic analysis using finite element methods. Experimental results from a prototype are provided to validate the design. Throughout, we highlight the relevance of this technology to solar power systems, underscoring its potential to revolutionize energy harvesting in renewable applications.
The design of the M-FMPMLG begins with its structural configuration. We adopted a series-coupled topology that integrates the high-speed mover of the magnetic gear with the generator’s secondary, eliminating the need for complex three-layer air gaps. This approach not only simplifies the magnetic circuit but also enhances the practicality of the generator in solar power systems by allowing unrestricted secondary travel. The primary components include the primary windings, secondary mover, low-speed mover, and modulation blocks. To facilitate fixation and improve magnetic performance, we used longitudinal H-shaped modulation blocks instead of traditional rectangular ones. These blocks concentrate magnetic flux and reduce material usage without compromising the modulation effectiveness, which is crucial for maintaining stable operation in a solar power system.
The modulation mode selection is critical for optimizing performance in a solar power system. Based on magnetic field modulation theory, the speed relationship between movers can be expressed as:
$$v_{m,k} = \frac{m_p}{m_p + k n_s} v_d + \frac{k n_s}{m_p + k n_s} v_2$$
where \( m = 1, 3, 5, \ldots, \infty \), \( k = 0, \pm 1, \pm 2, \ldots, \infty \), \( v_{m,k} \) is the speed of the modulated harmonic field, \( p \) is the pole pair number of the secondary and low-speed movers, \( n_s \) is the number of modulation blocks in the effective length, \( v_d \) is the speed of the high- and low-speed movers, and \( v_2 \) is the speed of the modulation blocks. For maximum thrust, we set \( m = 1 \) and \( k = -1 \), yielding:
$$v_{1,-1} = \frac{p}{p – n_s} v_d – \frac{n_s}{p – n_s} v_2$$
This corresponds to Mode 1 operation, where the modulation blocks are fixed, making it suitable for low-speed drives like those in solar power systems. The gear ratio \( G \) is defined as \( G = -p_1 / p_2 \), where \( p_1 \) and \( p_2 \) are the pole pairs of the low-speed and high-speed movers, respectively. In our design, we aimed for a gear ratio of 1.5 to balance speed amplification and structural feasibility for solar power system integration.
Determining the main dimensions of the M-FMPMLG involves calculating the electromagnetic power and thrust. The generator constant \( C_A \) is given by:
$$C_A = \frac{240 p \tau^2 l_\delta f}{\pi^2 P’}$$
where \( \tau \) is the pole pitch, \( l_\delta \) is the effective transverse width of the core, \( f \) is the output frequency, and \( P’ \) is the calculated electromagnetic power. The product \( 2p \tau^2 l_\delta \) represents the key size parameter, proportional to the electromagnetic thrust \( F_e \):
$$2p \tau^2 l_\delta = \frac{9.81 \times 2 (1 – \varepsilon_L) F_e}{K_{dp} B_\delta A_L \cos \phi \eta_s}$$
Here, \( K_{dp} \) is the winding factor, \( B_\delta \) is the air-gap flux density, \( A_L \) is the electrical loading, \( \varepsilon_L \) is the voltage drop coefficient, \( \cos \phi \) is the power factor, and \( \eta_s \) is the synchronous efficiency. For a solar power system, we selected parameters to maximize power density while considering the low-speed input. The table below summarizes the main design parameters:
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Rated Voltage (V) | 0.8 | Gear Ratio \( G \) | 1.5 |
| Air Gap (mm) | 1.5 | Pole Pairs \( p_1 \) | 9 |
| Calculated Poles | 2 | Pole Pairs \( p_2 \) | 6 |
| Calculated Slots | 8 | Pole Pitch \( \tau \) (mm) | 16.8 |
| Slot Pitch (mm) | 15 | Material | NdFe35 |
| Electrical Loading \( A_L \) (A/m) | 3.5 × 10³ | Core Width \( l_\delta \) (mm) | 25 |
Parameter optimization was conducted to improve thrust characteristics and output voltage quality. For thrust, we focused on reducing fluctuations and increasing magnitude. After optimization, the low-speed mover thrust increased by 3.98 times, and thrust ripple decreased from 2.564% to 0.594%, a 76.8% reduction. For the no-load induced electromotive force (EMF), we optimized the permanent magnet structure, slot dimensions, and air gap to enhance amplitude and reduce total harmonic distortion (THD). The EMF amplitude rose from 0.69 V to 0.91 V, and THD decreased from 5.69% to 2.32%, significantly improving power quality for the solar power system.
Electromagnetic analysis was performed using 2D finite element modeling to assess magnetic field distribution, no-load EMF, and power density. The magnetic field lines show that most flux passes through the air gap and closes via the primary core, with some leakage due to the large air gap. The longitudinal H-shaped modulation blocks exhibit reasonable flux distribution, confirming their effectiveness. The air-gap flux density reaches a maximum of 0.76 T, with harmonic analysis revealing dominant third harmonics on the primary side due to structural asymmetry. On the magnetic gear side, the harmonics align with design parameters, validating the theoretical approach.
The no-load EMF is derived from Faraday’s law:
$$e_0 = -N \frac{d\psi}{dt}$$
where \( N \) is the number of turns per phase and \( \psi \) is the flux linkage. Under a low-speed mover velocity of 0.1 m/s, the secondary moves at 0.15 m/s in the opposite direction, inducing a three-phase EMF. The waveforms are symmetric, with amplitudes of 0.92 V, 0.89 V, and 0.92 V for phases A, B, and C, respectively. Harmonic analysis indicates higher low-order harmonics in phases A and C due to end effects, but overall symmetry is maintained, which is crucial for stable operation in a solar power system.
Power density comparison with a conventional linear generator highlights the advantages of the M-FMPMLG. The output power \( P_{\text{out}} \) for a star-connected symmetric load is:
$$P_{\text{out}} = \frac{3U^2}{R}$$
where \( U \) is the phase voltage and \( R \) is the load resistance. At \( R = 5 \, \Omega \) and a prime mover speed of 0.1 m/s, the M-FMPMLG achieves a 48% higher terminal voltage than a conventional generator, leading to a power density increase of 2.18 times. This demonstrates the superior performance of the M-FMPMLG in solar power systems, where space and efficiency are critical.
A prototype was built and tested to validate the design. The no-load EMF and terminal voltages were measured under various loads. The table below compares calculated and measured phase voltages at \( R = 5 \, \Omega \):
| Phase | Calculated Voltage (V) | Measured Voltage (V) |
|---|---|---|
| A | 0.84 | 0.79 |
| B | 0.89 | 0.83 |
| C | 0.84 | 0.79 |
The slight discrepancies are attributed to losses and manufacturing tolerances. The voltage regulation \( \Delta U_i \) for each phase is calculated as:
$$\Delta U_i = \frac{E_0 – U_i}{U_N} \times 100\%, \quad i = A, B, C$$
where \( E_0 \) is the no-load EMF amplitude and \( U_N \) is the rated voltage. The following table shows \( \Delta U \) for different loads, indicating good load adaptability for the solar power system:
| Load (Ω) | \( \Delta U_A \) (%) | \( \Delta U_B \) (%) | \( \Delta U_C \) (%) |
|---|---|---|---|
| 3 | 23.98 | 14.60 | 23.98 |
| 4 | 19.54 | 10.13 | 19.67 |
| 5 | 16.75 | 7.36 | 16.75 |
| 7 | 13.32 | 3.86 | 13.32 |
| 9 | 11.29 | 1.81 | 11.29 |
| 11 | 9.90 | 0.48 | 10.03 |
| 13 | 9.01 | -0.48 | 9.14 |
| 15 | 8.25 | -1.21 | 8.38 |
In conclusion, the M-FMPMLG offers a promising solution for enhancing the efficiency of solar power systems. Its field modulation capability increases secondary speed, leading to higher power density and better material utilization. The series-coupled topology simplifies construction and allows for greater flexibility in secondary travel. Experimental results confirm the design’s validity, with good voltage regulation and output characteristics. Future work will focus on improving output power quality and developing control strategies tailored for solar power system integration. This technology has the potential to significantly advance renewable energy harvesting, making solar power systems more efficient and reliable.