In the context of marine power systems, shaft generators have gained prominence due to their energy-saving capabilities, ease of maintenance, and compact design compared to traditional diesel generators. However, the integration of shaft generators with the main diesel engine in vessels, such as fishing boats, introduces challenges related to rotational instability under varying operational conditions. This instability leads to fluctuations in the output voltage and frequency, which can severely damage electrical equipment. To address these issues, I designed a lightweight control system for voltage and frequency stabilization in fishing boat shaft generator grids, incorporating a Boost converter module. This system comprises an uncontrolled rectifier, a Boost boost circuit, and a three phase inverter, with control strategies focusing on sinusoidal pulse width modulation (SPWM) and current hysteresis band pulse width modulation (CHBPWM). Through simulation in Matlab/Simulink, I evaluated the performance of these control methods, particularly analyzing the harmonic content of the load phase voltage. The results demonstrate that the CHBPWM approach significantly reduces voltage harmonic distortion compared to SPWM, highlighting its superiority in this application. This paper details the system design, control methodologies, simulation setup, and results, emphasizing the role of the three phase inverter in achieving stable power output.
The traditional shaft generator system often relies on thyristor-based components, which, while effective, introduce harmonic distortions and require bulky synchronous compensators for reactive power management. These limitations motivated the development of a more efficient system. In my design, I replaced the controlled rectifier with an uncontrolled three-phase diode bridge rectifier to simplify the circuit and improve power factor. The rectifier output is fed into a Boost converter, which elevates the DC voltage and incorporates a PID controller for closed-loop voltage regulation. This ensures that voltage drops due to speed variations are compensated. The core of the system is the three phase inverter, which converts the stabilized DC voltage back to AC. I implemented two control strategies for this three phase inverter: SPWM and CHBPWM, to compare their effectiveness in minimizing harmonics and enhancing stability. The entire system was modeled in Simulink, with parameters based on a typical marine generator, such as the STC2-24-4-H model, to ensure practical relevance.
The uncontrolled three-phase rectifier circuit uses diodes and a capacitive filter to convert AC voltage from the shaft generator to DC. The output DC voltage, \( U_d \), depends on the line voltage \( U_l \) and can be derived from the relationship for a three-phase bridge rectifier. Under no-load conditions, the voltage peaks at approximately \( U_d = 1.41 U_l \), but as load increases, it stabilizes to:
$$ U_d = 1.35 U_l $$
For instance, with a nominal line voltage of 400 V, the theoretical DC output is 540 V. In simulations, I observed a value of 538.5 V, indicating a minor error of 0.27%, which validates the design. The Boost converter then steps up this voltage using an inductor, capacitor, and switch (e.g., IGBT), controlled by a PID feedback loop. The Boost circuit’s operation is governed by the duty cycle \( D \), where the output voltage \( V_{out} \) relates to the input voltage \( V_{in} \) as:
$$ V_{out} = \frac{V_{in}}{1 – D} $$
This allows for dynamic adjustment to maintain a constant DC link voltage, even during generator speed variations from 1000 to 2200 rpm, which correspond to input voltage swings from 182 V to 400 V. The three phase inverter, a standard full-bridge configuration, converts the DC voltage to three-phase AC. The output phase voltage for a three phase inverter can be expressed using Fourier series analysis. For a standard three-phase voltage source inverter, the phase voltage \( U_{UN} \) is given by:
$$ U_{UN} = \frac{2U_d}{\pi} \left( \sin(\omega t) + \sum_{n} \frac{1}{n} \sin(n \omega t) \right) $$
where \( n = 6k \pm 1 \) for natural numbers \( k \). The fundamental component has an amplitude and effective value as follows:
$$ U_{UN1m} = \frac{2U_d}{\pi} = 0.637 U_d $$
$$ U_{UN1} = \frac{U_{UN1m}}{\sqrt{2}} = 0.45 U_d $$
With \( U_d = 540 \) V, the theoretical phase voltage effective value is 243 V, serving as a benchmark for evaluating the control strategies.
For the control of the three phase inverter, I implemented two techniques: SPWM and CHBPWM. SPWM involves comparing a sinusoidal reference wave with a triangular carrier wave to generate switching signals for the inverter switches. This method produces a variable duty cycle that approximates a sinusoidal output after filtering. The modulation index \( m_a \) in SPWM controls the amplitude of the output voltage, and the frequency ratio \( m_f \) determines the harmonic spectrum. In my simulation, I used a bipolar SPWM scheme, where the output voltage alternates between positive and negative levels, leading to harmonic components primarily around multiples of the carrier frequency. The THD for SPWM-based output was found to be high, at 37.38%, with significant harmonics at 900 Hz, indicating poor voltage quality.
In contrast, CHBPWM is a current-based control method that compares the actual output current with a reference current and uses a hysteresis band to dictate the switching. The hysteresis controller maintains the current within a predefined band \( h \), where a smaller \( h \) reduces harmonic distortion but increases switching frequency. The control law can be summarized as: if the error \( \Delta I_c = I_c^* – I_c \) exceeds the upper band, the switch turns on to increase current; if it falls below the lower band, the switch turns off. This real-time control offers fast dynamic response and robustness. In my design, I set the hysteresis band with an upper limit of 0.3 and a lower limit of 0.2, balancing switching losses and waveform quality. The CHBPWM approach resulted in a THD of 11.93%, significantly lower than SPWM, due to the absence of fixed-frequency harmonics and better tracking of the reference current.
To quantify the system parameters, I used the following simulation setup in Matlab/Simulink. The shaft generator was modeled as a three-phase voltage source with variable amplitude to simulate speed variations. The rectifier section included diodes and a filter capacitor of \( C = 4 \times 10^{-4} \) F, with a load resistance \( R = 13 \) Ω. The Boost converter had components \( C = 7 \times 10^{-5} \) F and \( R = 13 \) Ω, and the PID controller was tuned for optimal voltage regulation. The three phase inverter used IGBTs and was controlled via SPWM or CHBPWM blocks. The simulation time was set to 0.1 seconds, with a variable voltage source emulating generator output from 400 V to 200 V between 0.05 s and 0.07 s to test system resilience. The key parameters are summarized in Table 1.
| Component | Parameter | Value |
|---|---|---|
| Generator | Rated Power | 22 kVA |
| Generator | Line Voltage | 400 V |
| Generator | Frequency | 50 Hz |
| Rectifier | Filter Capacitance | 400 μF |
| Boost Converter | Capacitance | 70 μF |
| Inverter | Switching Devices | IGBTs |
| Control | Hysteresis Band (CHBPWM) | 0.2-0.3 |
| Simulation | Time | 0.1 s |
The simulation results for the SPWM-controlled three phase inverter showed a load phase voltage with an effective value of 243.8 V, close to the theoretical 243 V, but the harmonic analysis revealed a high THD of 37.38%. The fundamental component was 153.2 V, indicating a substantial deviation due to harmonic content. The frequency spectrum highlighted dominant harmonics at 900 Hz, which align with the sidebands of the carrier frequency in SPWM. This level of distortion could lead to inefficiencies and potential damage to connected loads in a marine grid.
For the CHBPWM-controlled three phase inverter, the output phase voltage had an effective value of 243.6 V, with a fundamental component of 239.2 V, resulting in an error of only 1.6% from the theoretical value. The THD was reduced to 11.93%, and the harmonic spectrum showed a more uniform distribution without pronounced peaks at specific frequencies. This improvement underscores the effectiveness of current hysteresis control in minimizing distortions and enhancing voltage quality. The dynamic performance was also superior, as the CHBPWM controller quickly adapted to load changes and input variations, maintaining stability during the simulated voltage dip.
To further illustrate the harmonic performance, Table 2 compares the key metrics between SPWM and CHBPWM control for the three phase inverter.
| Control Method | THD (%) | Fundamental Voltage (V) | Error from Theoretical (%) | Dominant Harmonic Frequency (Hz) |
|---|---|---|---|---|
| SPWM | 37.38 | 153.2 | 36.9 | 900 |
| CHBPWM | 11.93 | 239.2 | 1.6 | N/A (uniform) |
The mathematical analysis of the three phase inverter output under CHBPWM control can be extended by considering the current error dynamics. The hysteresis control ensures that the current \( I_c \) tracks the reference \( I_c^* \) within a band \( h \), leading to a switching frequency \( f_{sw} \) that depends on the load parameters and band width. The relationship can be approximated as:
$$ f_{sw} \approx \frac{V_{dc}}{4 L h} $$
where \( L \) is the load inductance. In my simulation, with a small \( h \), the switching frequency increased, but the harmonic reduction justified the design choice. The output voltage quality for a three phase inverter under CHBPWM is inherently better because it does not rely on a fixed carrier wave, avoiding concentrated harmonics.
In conclusion, the simulation of the voltage and frequency stabilization system for shaft generators demonstrates that the three phase inverter plays a critical role in determining output quality. The CHBPWM control strategy outperforms SPWM in terms of harmonic distortion and voltage stability, making it more suitable for marine applications where reliable power is essential. The integration of a Boost converter with PID control further enhances the system’s ability to handle input variations. Future work could explore adaptive hysteresis bands or hybrid control methods to optimize switching losses and performance. Overall, this study validates the superiority of current hysteresis control in three phase inverter-based systems for shaft generator stabilization, contributing to safer and more efficient marine power networks.