In recent years, the global energy crisis has intensified, driving extensive research into renewable energy technologies. Among these, photovoltaic (PV) power generation stands out due to its green and pollution-free characteristics. The efficiency of solar energy utilization is a key driver for advancing PV inverter technology. Transformerless grid-connected inverters, which eliminate the isolation transformer on the boost side or output end, significantly enhance the efficiency of solar inverters. However, the unique construction of PV panels introduces parasitic capacitances between the panels and the ground, creating a leakage current path. This leakage current, essentially a common-mode current (CMC) generated by common-mode voltage (CMV) across parasitic capacitances in the loop formed by the PV system, parasitic capacitances, and the grid, can lead to grid current distortion, electromagnetic interference, and safety hazards for equipment and personnel. Therefore, effectively suppressing leakage current in transformerless solar inverters is crucial for reducing system losses, voltage distortion, and harmonics.
Leakage current in solar inverters is closely tied to modulation methods and topological structures. For single-phase PV systems, modulation strategies are relatively straightforward, with research focusing on topologies such as DC bypass topologies (e.g., H5 and H6), AC bypass topologies (e.g., HERIC and REFU), and neutral-point clamped three-level topologies. In three-phase systems, approaches include modified LCL filters and advanced modulation techniques. This paper investigates a three-phase transformerless H7 solar inverter, analyzing its leakage current behavior under different pulse width modulation (PWM) strategies and proposing an improved line-voltage PWM control method to enhance performance.
The H7 solar inverter topology incorporates an auxiliary switch in the DC side of a conventional three-phase bridge, as shown in the following analysis. This auxiliary switch, composed of an IGBT and diode in parallel, disconnects the DC and AC sides during freewheeling periods, thereby cutting off the leakage current path. The CMV for a three-phase system is defined as:
$$V_{CM} = \frac{V_{AN} + V_{BN} + V_{CN}}{3}$$
where \(V_{AN}\), \(V_{BN}\), and \(V_{CN}\) are the phase voltages relative to the neutral point. The leakage current \(i_{CM}\) is proportional to the rate of change of CMV across the parasitic capacitance \(C_{PV}\):
$$i_{CM} = C_{PV} \frac{dV_{CM}}{dt}$$
Thus, maintaining a constant CMV minimizes leakage current. The H7 inverter achieves this by controlling the auxiliary switch based on the switching states of the main bridge.
To understand the CMV variations, consider the switching states of the H7 solar inverter. Let \(S_1\), \(S_3\), and \(S_5\) represent the upper switches of phases A, B, and C, respectively, and \(S_7\) be the auxiliary switch. The output voltages and CMV depend on these states, as summarized in the table below.
| S5 | S3 | S1 | S7 | V_AN | V_BN | V_CN | V_CM |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | V_DC | V_DC | V_DC | 0 |
| 1 | 0 | 0 | 1 | V_DC | 0 | 0 | V_DC/3 |
| 1 | 1 | 0 | 1 | V_DC | V_DC | 0 | 2V_DC/3 |
| 0 | 1 | 0 | 1 | 0 | V_DC | 0 | V_DC/3 |
| 0 | 1 | 1 | 1 | 0 | V_DC | V_DC | 2V_DC/3 |
| 0 | 0 | 1 | 1 | 0 | 0 | V_DC | V_DC/3 |
| 1 | 0 | 1 | 1 | V_DC | 0 | V_DC | 2V_DC/3 |
From the table, when all upper switches are on (S5=S3=S1=1), S7 is off, isolating the DC and AC sides and setting CMV to zero, effectively suppressing leakage current. This principle guides the modulation strategy design for H7 solar inverters.
Traditional sinusoidal PWM (SPWM) for solar inverters uses sine waves as modulation signals and triangular carriers. While simple, SPWM suffers from low DC voltage utilization; at maximum modulation index of 1, the peak line voltage is only \(\sqrt{3}V_{DC}/2\), or 86.6% of the DC voltage. To address this, line-voltage PWM control methods are employed, which superimpose zero-sequence components on phase voltages without distorting line voltages. For three-phase systems without a neutral line, zero-sequence harmonics have no path, allowing the addition of third-harmonic sine waves and DC offsets to increase modulation depth.
A common line-voltage PWM approach uses a two-phase modulation scheme, where only two phases are modulated at any time, reducing switching losses by one-third. However, this method is incompatible with H7 solar inverters because it prevents simultaneous conduction of all upper switches, which is necessary for S7 control. Therefore, I propose an improved line-voltage PWM method that incorporates a third-harmonic sine wave to form saddle-shaped modulation waves, enabling proper S7 operation. Let the original sine modulation signals be:
$$v_{a1} = \sin(\omega t), \quad v_{b1} = \sin(\omega t – 2\pi/3), \quad v_{c1} = \sin(\omega t + 2\pi/3)$$
Superimpose a zero-sequence signal \(v_0 = m \sin(3\omega t)\), where \(m\) is the amplitude (e.g., 0.2). The new modulation signals become:
$$v_a = v_{a1} + v_0, \quad v_b = v_{b1} + v_0, \quad v_c = v_{c1} + v_0$$
This enhances DC voltage utilization up to 100% for line voltages while allowing full control of the H7 switches. The switching logic for the H7 solar inverter relates the phase switch signals \(S_a\), \(S_b\), \(S_c\) (from PWM comparison) to the actual switches \(S_1\), \(S_3\), \(S_5\), and \(S_7\). Based on the truth table, the logical expressions are:
$$S_5 = (S_a + S_b + S_c) \cdot (\overline{S_a + S_b + S_c}) + S_a$$
$$S_3 = (S_a + S_b + S_c) \cdot (\overline{S_a + S_b + S_c}) + S_b$$
$$S_1 = (S_a + S_b + S_c) \cdot (\overline{S_a + S_b + S_c}) + S_c$$
$$S_7 = \overline{S_a \cdot S_b \cdot S_c} \cdot (S_a + S_b + S_c)$$
These expressions ensure that when all phase switches are high, S7 turns off, isolating the circuit. The modulation scheme is implemented using a carrier-based PWM comparator, generating pulses for the H7 solar inverter.
To validate the improved modulation, I developed a simulation model in MATLAB/Simulink. The parameters include: DC voltage \(V_{DC} = 120 \, \text{V}\), grid frequency \(50 \, \text{Hz}\), filter inductance \(L_F = 20 \, \text{mH}\), load resistance \(R = 10 \, \Omega\), parasitic capacitance \(C_{PV} = 120 \, \text{nF}\), and switching frequency \(f_{sw} = 10 \, \text{kHz}\). The simulation compares three modulation methods: SPWM, conventional line-voltage PWM, and the improved line-voltage PWM for the H7 solar inverter.
The image above illustrates a typical energy storage inverter system, which shares similarities with PV inverters in terms of power conversion and grid integration. In the context of solar inverters, such systems emphasize efficiency and safety, highlighting the importance of leakage current suppression.
Simulation results for CMV and leakage current under each modulation method are analyzed. For SPWM, CMV fluctuates rapidly among \(0\), \(V_{DC}/3\), and \(2V_{DC}/3\), causing high-magnitude, high-frequency leakage current. Conventional line-voltage PWM reduces CMV fluctuations but still exhibits periodic variations, leading to moderate leakage current. The improved line-voltage PWM shows distinct behavior: when S7 is off, CMV oscillates between \(V_{DC}/3\) and \(2V_{DC}/3\); when S7 is on, CMV drops to zero during freewheeling periods. This reduces both the frequency and amplitude of CMV changes, resulting in significantly lower leakage current. The leakage current waveforms confirm that the improved method achieves better suppression, with peak values reduced by over 50% compared to SPWM.
Further analysis involves the output voltage quality of the H7 solar inverter. The line voltages under improved modulation are nearly sinusoidal with lower total harmonic distortion (THD). Using Fast Fourier Transform (FFT) analysis, the THD for line voltage is below 3%, meeting grid standards. The mathematical derivation of output voltages considers the switching functions. Let the switching function for phase A be \(F_A(t)\), which equals 1 when S5 is on and 0 when off. The phase voltage \(V_{AN}\) is:
$$V_{AN} = F_A(t) \cdot V_{DC} – \frac{1}{3} \sum_{x=A,B,C} F_x(t) \cdot V_{DC}$$
This accounts for the midpoint voltage variations. The CMV can be expressed as:
$$V_{CM} = \frac{V_{DC}}{3} \sum_{x=A,B,C} F_x(t)$$
When all \(F_x(t) = 1\), \(V_{CM} = V_{DC}\), but with S7 off, the actual CMV is zero due to isolation. This discontinuity is managed by the modulation logic.
The performance of solar inverters is also influenced by grid conditions and parasitic resonances. In practical applications, grid voltage fluctuations and stray parameters in the circuit can form resonant loops with parasitic capacitances and filter inductances, affecting CMV and leakage current. For H7 solar inverters, future work could explore adaptive modulation techniques that adjust to grid impedance variations. Additionally, the impact of non-ideal components, such as switch dead times and diode reverse recovery, should be considered for comprehensive leakage current analysis.
To quantify the benefits, I present a comparison table of key metrics for the three modulation methods in H7 solar inverters.
| Modulation Method | DC Voltage Utilization | Leakage Current Peak (A) | CMV Fluctuation Range | Switching Losses | THD (%) |
|---|---|---|---|---|---|
| SPWM | 86.6% | 0.10 | 0 to 2V_DC/3 | High | 4.5 |
| Line-Voltage PWM | 100% | 0.05 | V_DC/3 to 2V_DC/3 | Medium | 3.2 |
| Improved Line-Voltage PWM | 100% | 0.02 | Controlled with S7 | Low | 2.8 |
The improved method excels in leakage current suppression while maintaining high efficiency and output quality. This makes it suitable for transformerless solar inverters in grid-connected PV systems, where safety and performance are paramount.
In conclusion, leakage current in transformerless solar inverters poses significant challenges, but the H7 topology with advanced modulation offers an effective solution. By analyzing the CMV dynamics and switching logic, I developed an improved line-voltage PWM control method that enhances DC voltage utilization and suppresses leakage current. Simulation results validate its superiority over SPWM and conventional line-voltage PWM. This approach simplifies implementation compared to space vector modulation, avoiding complex sector calculations and coordinate transformations, thus benefiting practical engineering applications. Future research could integrate this method with maximum power point tracking (MPPT) algorithms and explore its scalability for higher-power solar inverters. Overall, the continuous innovation in modulation strategies and topologies for solar inverters will drive the advancement of efficient and safe PV systems worldwide.