In modern power electronics, the single phase inverter plays a critical role in various applications such as renewable energy systems, uninterruptible power supplies, and motor drives. However, the performance of a single phase inverter is often compromised by the dead-time effect, which introduces undesirable low-order harmonics and reduces output voltage quality. Traditional approaches, including dead-time compensation and elimination strategies, have limitations in complexity and effectiveness. This article proposes a novel sinusoidal dead-time optimization strategy that minimizes harmonic distortion while ensuring system reliability. By varying the dead-time width sinusoidally over half the fundamental period and aligning its phase with the output current, the proposed method significantly reduces low-order harmonics. The strategy incorporates a fixed dead-time segment near zero-crossing regions to maintain safe operation. Mathematical analysis using double Fourier series establishes a unified model, and experimental results on a 1 kW single phase inverter validate the effectiveness of the approach.
The dead-time effect in a single phase inverter arises from the necessary delay inserted between switching transitions to prevent shoot-through faults in voltage-source inverters. This dead-time causes error voltages that accumulate over a fundamental period, leading to baseband harmonic distortion. For a single phase inverter employing sinusoidal pulse-width modulation (SPWM), the dead-time introduces error voltages proportional to the current direction. The output voltage deviation $\Delta u$ can be expressed as a function of the dead-time $T_d$ and DC bus voltage $E$. In a conventional single phase inverter with fixed dead-time, the error voltage contains significant low-order harmonics, such as the 3rd, 5th, and 7th, which degrade power quality. The Fourier series representation of the error voltage for a fixed dead-time $T_d$ is given by:
$$ \Delta u = \frac{E T_d}{\pi} \sum_{n=1,3,5,\ldots}^{\infty} \frac{1}{n} \sin(n \omega t) $$
where $\omega$ is the angular frequency. This results in a total harmonic distortion (THD) that can exceed 6% under typical operating conditions. To address this, the proposed sinusoidal dead-time strategy modulates $T_d$ as a function of the output current phase. Specifically, the dead-time width varies as $T_d = T_m |\sin(\theta)|$, where $T_m$ is the peak dead-time and $\theta$ is the phase angle of the output current. However, to ensure safety, a minimum fixed dead-time $T_{\text{min}}$ is inserted when the sinusoidal value approaches zero. The distribution angle $\delta$ is defined as $\delta = \arcsin(T_{\text{min}} / T_m)$, which determines the proportion of fixed to sinusoidal dead-time. The conventional fixed dead-time case corresponds to $\delta = 90^\circ$.
The unified mathematical model for the error voltage in a single phase inverter under sinusoidal dead-time is derived using double Fourier analysis. The error voltage $\Delta u$ can be represented as:
$$ \Delta u = \frac{E}{\pi} \int_{-\pi}^{\pi} \text{sign}(i) T_d d\theta $$
where $i$ is the output current. For sinusoidal dead-time with distribution angle $\delta$, the dead-time function is piecewise defined:
$$ T_d = \begin{cases}
T_{\text{min}} & \text{for } 0 \leq \theta \leq \delta \text{ or } \pi – \delta \leq \theta \leq \pi \\
T_m |\sin \theta| & \text{otherwise}
\end{cases} $$
The Fourier coefficients for the base component and low-order harmonics are computed as follows. The fundamental component $U_1$ and the nth harmonic component $U_n$ are given by:
$$ U_1 = E f_c \left[ \frac{\pi – 2\delta + \sin(2\delta)}{4 \sin \delta} + (1 – \cos \delta) \right] $$
$$ U_n = \frac{E}{4} \left( \frac{2 T_m}{\pi} \right) \left\{ \frac{\sin[(n+1)\delta]}{n+1} – \frac{\sin[(n-1)\delta]}{n-1} \right\} + \frac{E T_{\text{min}}}{\pi} \frac{1 – \cos(n\delta)}{n} $$
These equations show that as $\delta$ decreases, the low-order harmonic components reduce significantly, but the fundamental component also decreases, indicating a trade-off. For instance, when $\delta = 20^\circ$, the 3rd harmonic is reduced by over 70% compared to the fixed dead-time case, but the fundamental voltage drops by approximately 50%. This highlights the importance of selecting an optimal $\delta$ based on the application requirements of the single phase inverter.
To quantify the harmonic performance, the relative harmonic coefficient $K_n$ is defined as the ratio of the nth harmonic under sinusoidal dead-time to that under fixed dead-time. For a single phase inverter, $K_n$ is expressed as:
$$ K_n = \frac{1}{2 \sin \delta} \left[ \frac{\sin[(n+1)\delta]}{n+1} – \frac{\sin[(n-1)\delta]}{n-1} \right] + \frac{1 – \cos(n\delta)}{n} $$
The following table summarizes the THD and fundamental voltage for different distribution angles in a single phase inverter with parameters: $E = 200\,V$, switching frequency $f_c = 10\,kHz$, modulation index $m = 0.6$, and $T_{\text{min}} = 3\,\mu s$.
| Distribution Angle $\delta$ (°) | Fundamental Voltage $U_1$ (V) | THD (%) | Reduction in 3rd Harmonic (%) |
|---|---|---|---|
| 90 (Fixed) | 97.49 | 6.12 | 0 |
| 70 | 95.31 | 4.87 | 25.4 |
| 50 | 91.45 | 3.65 | 45.2 |
| 30 | 85.12 | 2.41 | 62.8 |
| 20 | 78.33 | 1.79 | 72.1 |
Experimental validation was conducted on a 1 kW single phase full-bridge inverter to verify the proposed strategy. The single phase inverter was controlled using a DSP TMS320F28335, and output voltage waveforms were analyzed for various $\delta$ values. The results demonstrate that as $\delta$ decreases from $90^\circ$ to $20^\circ$, THD improves from 6.12% to 1.79%, representing a 70.75% reduction. However, the fundamental voltage decreases from 97.49 V to 78.33 V, which must be considered in design. The harmonic spectrum analysis reveals that the 3rd harmonic drops from 5.3 V to 1.48 V, the 5th harmonic from 2.1 V to 0.87 V, and the 7th harmonic from 1.5 V to 0.89 V for $\delta = 20^\circ$.
The impact of distribution angle on harmonic content is further illustrated by the following equations for specific harmonics in a single phase inverter. The 3rd harmonic voltage $U_3$ as a function of $\delta$ is:
$$ U_3 = \frac{E}{4} \left( \frac{2 T_m}{\pi} \right) \left[ \frac{\sin(4\delta)}{4} – \frac{\sin(2\delta)}{2} \right] + \frac{E T_{\text{min}}}{\pi} \frac{1 – \cos(3\delta)}{3} $$
Similarly, the 5th harmonic $U_5$ is:
$$ U_5 = \frac{E}{4} \left( \frac{2 T_m}{\pi} \right) \left[ \frac{\sin(6\delta)}{6} – \frac{\sin(4\delta)}{4} \right] + \frac{E T_{\text{min}}}{\pi} \frac{1 – \cos(5\delta)}{5} $$
These equations show non-monotonic behavior for some harmonics; for example, $U_5$ increases slightly as $\delta$ decreases from $90^\circ$ to $50^\circ$ before decreasing. This underscores the need for careful optimization in a single phase inverter to balance harmonic reduction and fundamental voltage preservation.
In practice, the implementation of sinusoidal dead-time in a single phase inverter requires real-time calculation of the output current phase. This can be achieved using phase-locked loops (PLLs) or current observers. The computational burden is minimal compared to complex compensation algorithms, making it suitable for low-cost microcontrollers. Additionally, the strategy is robust to parameter variations and load changes, as it relies only on the fundamental current phase. For a single phase inverter with high switching frequencies, the reduction in low-order harmonics improves overall efficiency and compliance with power quality standards such as IEEE 519.
In conclusion, the sinusoidal dead-time optimization strategy offers a significant improvement over traditional methods for single phase inverters. By leveraging a variable dead-time that follows the output current phase, the method minimizes low-order harmonics without adding complexity. The distribution angle $\delta$ provides a design trade-off between harmonic reduction and fundamental voltage loss. Experimental results confirm that THD can be reduced to below 2% with proper selection of $\delta$, enhancing the performance of single phase inverters in various applications. Future work could explore adaptive $\delta$ tuning based on load conditions to further optimize single phase inverter performance.