Three-phase inverters play a critical role in modern industrial and energy systems by efficiently converting direct current (DC) from sources like batteries, solar cells, or fuel cells into alternating current (AC) with adjustable frequency and amplitude. Their high efficiency and control flexibility make them indispensable in applications such as motor drives, renewable energy integration, and power distribution. However, the reliability of three-phase inverters is often compromised by failures in power semiconductor switches, such as Insulated Gate Bipolar Transistors (IGBTs) or Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs). Among these failures, open-circuit faults in switches are particularly common and can lead to severe system degradation, including distorted output currents, reduced efficiency, and even complete system shutdown. To address this issue, we propose a fault diagnosis method based on current value analysis for detecting and locating open-circuit faults in single and double switches of three-phase inverters. This method leverages the analysis of phase current waveforms under normal and faulty conditions, utilizing normalized current values and statistical sampling to achieve rapid and accurate fault detection. By focusing on the unique characteristics of current deviations during faults, our approach minimizes computational burden and enhances robustness against load variations, making it suitable for real-time applications in traction drives and industrial machinery.
The topology of a standard two-level three-phase voltage source inverter is illustrated in the figure below, which includes six semiconductor switches (T1 to T6) and six freewheeling diodes (D1 to D6). The load is typically connected in a star configuration, but for analysis purposes, it can be equivalently represented as a delta-connected load to simplify current calculations. In this structure, each switch pair (e.g., T1 and T2 for phase A) operates in a complementary manner to generate the required AC output voltages.
Under normal operating conditions, the three-phase inverter produces balanced sinusoidal output voltages with a phase difference of 120 degrees between each phase. The phase voltages can be expressed as vector quantities:
$$ \vec{U}_{An} = U_m e^{j\omega t} $$
$$ \vec{U}_{Bn} = U_m e^{j(\omega t – 2\pi/3)} $$
$$ \vec{U}_{Cn} = U_m e^{j(\omega t – 4\pi/3)} $$
where \( U_m \) is the amplitude of the phase voltage, and \( \omega \) is the angular frequency. The line voltages, which are critical for current analysis, are derived from the phase voltages and can be represented as:
$$ \vec{U}_{AB} = \sqrt{3} U_m e^{j(\omega t + \pi/6)} $$
$$ \vec{U}_{BC} = \sqrt{3} U_m e^{j(\omega t – \pi/2)} $$
$$ \vec{U}_{CA} = \sqrt{3} U_m e^{j(\omega t + 5\pi/6)} $$
For a balanced three-phase load with equivalent delta-connected impedance \( Z_{\Delta} \), the phase current in, for example, phase A can be calculated using Kirchhoff’s current law. When switch T1 is closed, the current in phase A is the sum of currents generated by the line voltages \( U_{AB} \) and \( U_{AC} \) across the respective impedances:
$$ \vec{I}_A = \frac{\vec{U}_{AB}}{Z_{\Delta}} + \frac{\vec{U}_{AC}}{Z_{\Delta}} $$
The magnitude of the normal phase current under balanced conditions is given by:
$$ |\vec{I}_A| = \frac{\sqrt{3} U_m}{|Z_{\Delta}|} $$
Open-circuit faults in the switches disrupt the normal current flow, leading to distinct patterns in the output currents. We categorize these faults into four types for comprehensive analysis:
| Fault Type | Description | Example Switches |
|---|---|---|
| Type I | Single switch open-circuit fault | T1, T2, T3, T4, T5, T6 |
| Type II | Two switches open on the same inverter leg | T1 & T2, T3 & T4, T5 & T6 |
| Type III | Two switches open on different legs and opposite sides | T1 & T4, T1 & T6, T2 & T3, T2 & T5, T3 & T6, T4 & T5 |
| Type IV | Two switches open on different legs but same side | T1 & T3, T1 & T5, T2 & T4, T2 & T6, T3 & T5, T4 & T6 |
When an open-circuit fault occurs in a switch, such as T1, the current in the affected phase during specific intervals drops significantly. For instance, if T1 fails open, the current in phase A during the positive half-cycle becomes nearly zero because the path through T1 is interrupted. The fault current magnitude under such conditions is reduced to approximately one-third of the normal value:
$$ |\vec{I}_{AF}| = \frac{U_m}{|Z_{\Delta}|} $$
Thus, the ratio of the fault current to the normal current is:
$$ R = \frac{|\vec{I}_{AF}|}{|\vec{I}_A|} = \frac{1}{\sqrt{3}} \approx 0.577 $$
However, in practical scenarios, the maximum value of the output phase current during a fault does not exceed one-third of the rated amplitude due to the redistribution of currents through alternative paths, such as freewheeling diodes. This characteristic forms the basis of our fault detection method. For each switch, we define a “fault detection waveform” as the current waveform in the phase that is most affected by that switch’s open-circuit fault. For example, the fault detection waveform for T1 is the positive half-cycle of phase A current, while for T2, it is the negative half-cycle of phase A current. Similarly, for T3 and T5, the fault detection waveforms are the positive half-cycles of phases B and C, respectively, and for T4 and T6, the negative half-cycles of phases B and C.
To implement the fault diagnosis, we first normalize the sampled phase currents using a reference value to account for variations in operating conditions. The normalization formula is:
$$ I_S = \frac{I_{\text{sample}}}{I_{\text{ref}}} $$
where \( I_{\text{sample}} \) is the instantaneous current sample, and \( I_{\text{ref}} \) is the rated current amplitude. The starting point of each fault detection waveform is identified by detecting zero-crossing points in the current signals. For a switch like T1, the zero-crossing condition is determined by three consecutive samples:
$$ i_s(k) > 0, \quad i_s(k) – i_s(k-1) > 0, \quad i_s(k-2) < 0 $$
The sample with the smallest absolute value among these three is marked as the starting point. The number of samples in one period of the current waveform is given by:
$$ N_0 = T_0 \times f_0 $$
where \( T_0 \) is the period of the inverter current, and \( f_0 \) is the sampling frequency. The fault detection waveform for each switch spans half a period, from the starting point to \( N_0/2 \) samples later. The peak value of the fault detection waveform, denoted as \( I_{Tp} \) for switch \( p \), is calculated as the average of samples at positions \( N_0/4 \) and \( N_0/4 + 1 \).
Under normal conditions, only a small fraction of samples in the fault detection waveform have normalized values below 1/3. However, when a switch experiences an open-circuit fault, almost all samples in its fault detection waveform fall below this threshold. We count the number of such samples \( N_C \) using:
$$ N_C = \begin{cases}
N_C + 1 & \text{if } I_S > 0.33 \\
N_C & \text{if } I_S \leq 0.33
\end{cases} $$
The fault detection function is then defined as:
$$ F_D = \begin{cases}
1 & \text{if } \frac{2N_C}{N_0} \geq 1 \\
0 & \text{if } \frac{2N_C}{N_0} < 1
\end{cases} $$
To enhance robustness against load variations, we introduce an imbalance factor \( K_{UN} \) to assess the load condition:
$$ K_{UN} = \frac{1}{6} \sum \left| \frac{I_{AVG} – I_{Tp}}{I_{AVG}} \right| $$
where \( I_{AVG} \) is the average of the six \( I_{Tp} \) values:
$$ I_{AVG} = \frac{1}{6} \sum_{p=1}^{6} |I_{Tp}| $$
If \( K_{UN} \) exceeds a predefined threshold, indicating significant load changes, the current samples are re-normalized using:
$$ I_R = \frac{I_{\text{sample}}}{I_{Tp}} I_{\text{ref}} $$
This ensures that the fault diagnosis remains accurate even under dynamic operating conditions. Additionally, to prevent misdiagnosis due to simultaneous faults in two switches on the same side of the inverter, we apply exclusion rules based on the fault patterns. For example, if faults are detected in T1, T4, and T6 simultaneously, we exclude T1 as it may be influenced by the combined effect of T4 and T6 faults. The table below summarizes these exclusion rules:
| Switch Under Diagnosis | Excluded Same-Side Faults |
|---|---|
| T1 | T4 & T6 |
| T2 | T3 & T5 |
| T3 | T2 & T6 |
| T4 | T1 & T5 |
| T5 | T2 & T4 |
| T6 | T1 & T3 |
Experimental validation of the proposed method was conducted using a dSPACE-based hardware-in-the-loop platform, which included a three-phase inverter cabinet, IGBT switches, current sensors, and real-time communication interfaces. The inverter was subjected to various open-circuit fault scenarios, including single and double switch faults, under both steady-state and dynamic load conditions. The current samples were processed at a sampling frequency of 10 kHz, and the fault diagnosis algorithm was implemented in the dSPACE Control Desk software.
For a single switch fault in T1, the fault detection waveform in phase A showed that all samples in the positive half-cycle dropped below the 1/3 threshold within 8 ms of fault occurrence. Similarly, for double switch faults, such as T1 and T2 open, the fault detection waveforms for both switches were identified within 18 ms, demonstrating the method’s rapid response. Under load variations, the re-normalization process effectively maintained diagnosis accuracy, as seen in tests where the load power suddenly dropped by 50%. The imbalance factor \( K_{UN} \) triggered re-normalization, and the fault detection for T1 and T3 open-circuit faults was achieved within 18 ms, confirming the method’s robustness.
The advantages of our current value-based fault diagnosis method for three-phase inverters include low computational demand, as it relies on simple arithmetic operations and statistical counting; high accuracy in locating faults, even in complex scenarios involving multiple switches; and adaptability to load changes through dynamic normalization. Compared to voltage-based methods, it eliminates the need for additional sensors, reducing cost and complexity. Furthermore, the use of fault detection waveforms and exclusion rules minimizes false alarms, enhancing reliability in practical applications such as electric vehicle drives and industrial motor controls.
In conclusion, the proposed method provides a comprehensive solution for open-circuit fault diagnosis in three-phase inverters by leveraging current value analysis. It effectively addresses the limitations of existing approaches, such as sensitivity to load variations and computational intensity, while ensuring fast and precise fault localization. Future work could explore integration with machine learning techniques for predictive maintenance and extension to multi-level inverter topologies.