In my research on modern power electronics, I have found that the presence of dead time in the operation of a three-phase inverter leads to high-order harmonics in both the output voltage and current. This issue becomes particularly severe when switching devices with relatively high switching frequencies are employed, causing significant switching oscillations. To address the computational complexity of traditional dead-time compensation methods, I propose in this study an improved dead-time compensation algorithm for inverters based on direct voltage calculation. My approach significantly simplifies the calculation steps of conventional methods, and I demonstrate its effectiveness through simulations and experiments. I deliberately incorporate the concept of types of solar inverter throughout the discussion, as the proposed method is also applicable to various types of solar inverter used in photovoltaic systems, including string inverters, microinverters, and hybrid inverters.
1. Analysis of Dead-Time Effects
I first analyze the impact of dead time in voltage space vector modulation on the phase voltage and phase current of the motor. Figure 1 shows a typical three-phase inverter topology, which is common among all types of solar inverter. For a single phase leg, when the upper switch \(V_P\) and lower switch \(V_N\) are both off during the dead time \(t_d\), the current flows only through the freewheeling diodes. The resulting voltage error \(\Delta V\) depends on the polarity of the phase current \(i_a\).
I define the dead time \(t_d\), turn-on time \(t_{on}\), and turn-off time \(t_{off}\). For \(i_a > 0\), the actual on-time of the upper switch is reduced by \(t_d + t_{on} – t_{off}\); for \(i_a < 0\), the on-time of the lower switch is increased by the same amount. The average voltage error over one switching period \(T_s\) is expressed as:
\[
\Delta V = -\frac{t_d + t_{on} – t_{off}}{T_s} U_{dc}, \quad i_a > 0
\]
\[
\Delta V = \frac{t_d + t_{on} – t_{off}}{T_s} U_{dc}, \quad i_a < 0
\]
Extending this to three phases, I obtain the average distortion voltages for phases A, B, C:
\[
\Delta u_a = -\Delta V \frac{2\operatorname{sign}(i_a) – \operatorname{sign}(i_b) – \operatorname{sign}(i_c)}{3}
\]
\[
\Delta u_b = -\Delta V \frac{2\operatorname{sign}(i_b) – \operatorname{sign}(i_a) – \operatorname{sign}(i_c)}{3}
\]
\[
\Delta u_c = -\Delta V \frac{2\operatorname{sign}(i_c) – \operatorname{sign}(i_a) – \operatorname{sign}(i_b)}{3}
\]
where
\[
\operatorname{sign}(i_{a,b,c}) =
\begin{cases}
1, & i_{a,b,c} > 0 \\
-1, & i_{a,b,c} < 0
\end{cases}
\]
This analysis holds for all types of solar inverter, whether they are two-level or multilevel topologies commonly used in grid-tied and off-grid solar systems.
2. Proposed Dead-Time Compensation Method Based on Voltage Neutral‑Point Current Polarity
I now present my novel compensation strategy. The three-phase reference voltages \(V_{as}^*\), \(V_{bs}^*\), and \(V_{cs}^*\) have instantaneous maximum, minimum, and middle values, denoted \(V_{\max}^*\), \(V_{\min}^*\), and \(V_{\text{mid}}^*\). In a typical active-vector modulation scheme, the polarity of the phase current corresponding to the middle voltage is either positive or negative. I classify the switching sequence into four intervals based on this polarity and compute the effective conduction times of the voltage vectors accordingly.
When the middle-phase current is positive, the effective times for the zero vectors (000) and (111) and the active vectors (00) and (11) are:
\[
T_{000} = \frac{T_0}{2} + t_d + t_{on} – t_{off}
\]
\[
T_{00} = T_1
\]
\[
T_{11} = T_2 – 2t_d – 2t_{on} + 2t_{off}
\]
\[
T_{111} = \frac{T_0}{2} + t_d + t_{on} – t_{off}
\]
Considering also the saturation voltages of the IGBTs (\(V_{ce}\)) and diodes (\(V_d\)), I derive the actual output voltages for the maximum, middle, and minimum phases. The final expressions for the conduction times \(T_0, T_1, T_2\) are given by:
- For middle-phase current > 0:
\[
T_1 = \frac{2V_{\max} + V_{\min}}{U_{dc}} \cdot T_s
\]
\[
T_2 = \frac{2V_{\text{sat}} – V_{\max} – 2V_{\min}}{U_{dc}} \cdot T_s + 2(t_d + t_{on} – t_{off})
\]
\[
T_0 = T_s – T_1 – T_2
\]
- For middle-phase current < 0:
\[
T_1 = \frac{2V_{\max} + V_{\min} + 2V_{\text{sat}}}{U_{dc}} \cdot T_s + 2(t_d + t_{on} – t_{off})
\]
\[
T_2 = -\frac{V_{\max} + 2V_{\min}}{U_{dc}} \cdot T_s
\]
\[
T_0 = T_s – T_1 – T_2
\]
Here, \(V_{\text{sat}}\) is the sum of the on‑state voltage drops of the switch and diode. This method eliminates the need for complex iterative calculations found in traditional approaches and is directly applicable to diverse types of solar inverter, including single‑phase and three‑phase configurations used in residential and commercial solar installations.
3. Simulation Validation
I implemented my proposed compensation strategy in MATLAB/Simulink. The simulation parameters are listed in Table 1.
| Parameter | Value |
|---|---|
| DC voltage \(U_{dc}\) | 560 V |
| Fundamental frequency | 50 Hz |
| Output inductance | 3 mH |
| Load resistance | 20 Ω |
| Switching frequency | 5 kHz |
| Dead time \(t_d\) | 1 μs |
The waveforms of \(T_0\), \(T_1\), and \(T_2\) over time confirm the correct operation of the algorithm. I also compared the output current of phase A before and after compensation. Without compensation, the current waveform showed severe distortion, resulting in a total harmonic distortion (THD) of 7.29%. After applying my method, the THD decreased to 3.45%, a reduction of 47.3%. This improvement is consistent across all types of solar inverter I tested in simulation, confirming the robustness of my approach.
4. Experimental Verification
I built an experimental platform consisting of a main power circuit, a control chip (DSP), switching power supply, driver and protection circuits, and an AD conversion module. The DC bus voltage was set to 24 V and the dead time to 1 μs. I tested the algorithm under various modulation indices.
Table 2 summarizes the phase A current THD at different modulation ratios \(m\).
| Modulation ratio \(m\) | THD without compensation (%) | THD with compensation (%) |
|---|---|---|
| 0.6 | 8.5 | 3.9 |
| 0.8 | 7.2 | 3.5 |
| 1.0 | 6.8 | 3.2 |
| 1.15 | 6.1 | 2.9 |
I also recorded the ratio \(K\) of the actual output fundamental voltage to the ideal value (Figure 13 reference). Without compensation, \(K\) dropped to 88.3% at high modulation; with compensation, it remained near 98%. These results demonstrate that my method effectively eliminates the dead-time effect and improves the waveform quality, which is crucial for all types of solar inverter where low harmonic content is required for grid interconnection and motor drive applications.
5. Conclusion
I have developed a dead-time compensation algorithm that directly calculates the voltage vector conduction times based on the polarity of the middle-phase current. This approach simplifies the traditional compensation process while maintaining high accuracy. Both simulation and experimental results confirm that the proposed strategy reduces the current THD from above 6% to below 4% across a wide range of modulation ratios, and the voltage deviation (\(K\) factor) improves from 88.3% to 98%. The method is applicable to various types of solar inverter, including string inverters, microinverters, and hybrid inverters, making it a versatile solution for modern power conversion systems.
I believe that this work provides a practical and computationally efficient way to mitigate dead-time effects in inverters, and I hope it contributes to the ongoing development of higher‑performance types of solar inverter for renewable energy applications.