The proliferation of distributed photovoltaic (PV) generation systems has placed significant emphasis on the development of efficient and feature-rich power electronic interfaces. Among these, single-phase solar inverters are a critical component for integrating residential and commercial-scale PV arrays with the utility grid. Traditionally, the primary function of these solar inverters has been to inject active power at unity power factor. However, evolving grid codes, such as Germany’s VDE-AR-N4105, now mandate that distributed generators, including smaller-scale solar inverters, provide reactive power support to enhance grid stability and power quality. This necessitates a fundamental re-evaluation of both the hardware topologies and control strategies employed in existing and future solar inverters.
A prominent challenge in transformerless solar inverters is the mitigation of ground leakage current, which arises due to the parasitic capacitance between the PV array and earth. The H6 bridge topology has emerged as an effective solution for single-phase, transformerless solar inverters, effectively decoupling the DC and AC sides during freewheeling intervals to suppress common-mode voltage variations and thus leakage current. However, its conventional modulation scheme is intrinsically designed for unity power factor operation. When reactive power flow is required, the inherent switching sequence breaks down, leading to severe waveform distortion in the grid current. This paper delves into the operational challenges of the non-isolated H6 bridge topology under reactive power conditions, proposes a novel modulation strategy to enable reactive power compensation while maintaining low leakage current, analyzes the root causes of current distortion, and introduces an advanced control scheme to significantly improve the grid current waveform quality.
Topology and Operational Principles of the H6 Bridge Solar Inverter
The circuit configuration of a single-phase H6 bridge solar inverter is shown conceptually in Figure 1 (though not displayed, the topology consists of switches S1-S4 forming the main H-bridge, with two additional switches S5 and S6 creating dedicated freewheeling paths). The key innovation lies in the addition of switches S5 and S6, which are typically operated at grid frequency, along with diodes D1 and D2. During the freewheeling periods in unity power factor mode, these paths disconnect the PV array from the grid, clamping the common-mode voltage and minimizing leakage current, \( i_{leak} \), which is driven by the derivative of the common-mode voltage, \( u_{cm} \), across the PV parasitic capacitance, \( C_p \):
$$ i_{leak} = C_p \frac{du_{cm}}{dt} $$
In traditional operation, the bridge output voltage \( u_{ab} \) is forced to be in phase with the grid voltage \( u_g \). To enable reactive power flow, where the grid current \( i_g \) leads or lags \( u_g \) by a phase angle \( \phi \), the modulation strategy must be fundamentally revised. The key insight is to utilize the freewheeling switches S5 and S6 for active modulation during intervals when the grid current and voltage are in opposition, rather than simply keeping one of them continuously on.
The modulation cycle is divided into four sectors based on the polarity of grid voltage and reference current, as summarized in Table 1.
| Current Direction / Voltage Direction | Positive | Negative |
|---|---|---|
| Positive | Sector II | Sector I |
| Negative | Sector III | Sector IV |
In Sectors II and IV, where current and voltage are in the same direction, conventional H6 modulation applies (e.g., high-frequency switching of S1 & S4 with S6 on in Sector II). Crucially, in Sectors I and III, where current opposes voltage, the main bridge switches (S1-S4) are turned off. Instead, switch S5 (in Sector III) or S6 (in Sector I) is pulse-width modulated. During this reactive power modulation, the voltage \( u_{ab} \) is effectively synthesized by the back-electromotive force (back-EMF) generated across the filter inductors L1 and L2 as the current freewheels through the dedicated paths. This back-EMF, which can be either 0 or \( \pm U_{dc} \) due to clamping diodes, acts as the controlled voltage source. The dynamic equation governing this process is:
$$ u_{ab} – u_g = L \frac{di_g}{dt} $$
where \( L = L_1 + L_2 \). The duty cycle for, say, S6 in Sector I can be derived from the steady-state relationship, relating the required back-EMF to the DC link voltage \( U_{dc} \). This approach allows the H6 bridge solar inverter to control both the magnitude and phase of the output current, thereby enabling reactive power injection or absorption.
Low Leakage Current and DC-Link Voltage Considerations in Reactive Mode
A critical advantage of the proposed modulation is that it preserves the low leakage current characteristic of the H6 topology even during reactive power operation. Analysis of the common-mode voltage \( u_{cm} = (u_{an} + u_{bn})/2 \) during both the active switching and freewheeling states within the reactive modulation sectors reveals that \( u_{cm} \) remains constant at \( U_{dc}/2 \). According to the leakage current equation \( i_{leak} = C_p du_{cm}/dt \), a constant \( u_{cm} \) results in negligible leakage current. This makes the H6 bridge a compelling candidate for transformerless solar inverters requiring reactive power capability.
However, operating a single-phase solar inverter with reactive power introduces a significant challenge: increased low-frequency ripple on the DC-link voltage. The instantaneous AC output power \( p_{ac} \) contains a double-line-frequency component:
$$ p_{ac} = u_g i_g = \frac{U_g I_g}{2} \cos \phi – \frac{U_g I_g}{2} \cos(2\omega t – \phi) = P_c + P_r $$
where \( P_c \) is the constant power drawn from the DC source and \( P_r \) is the oscillating power. This oscillating power must be buffered by the DC-link capacitor \( C \), leading to a voltage ripple \( u_r \). Integrating the power balance equation yields:
$$ u_r = \frac{U_g I_g}{4 \omega C U_{dc}} \sin(2\omega t – \phi) $$
Notably, for the same delivered active power \( P_m \), the apparent power \( S_o \) and consequently the current amplitude \( I_g \) are larger when \( \cos \phi < 1 \): \( I_{g2} (reactive) > I_{g1} (unity) \). Therefore, the DC-link voltage ripple amplitude is inherently larger in reactive power mode. System designers must account for this by appropriately sizing the DC-link capacitor or implementing active power decoupling techniques in such advanced solar inverters.
Space Vector PWM Implementation for Reactive Power Modulation
To facilitate digital implementation, a Space Vector PWM (SVPWM) scheme is adapted for this single-phase H6 bridge. The sector (I-IV) is determined by the polarities of grid voltage and reference current. A normalized reference variable \( X \) is defined based on the required converter output voltage:
$$ X = \frac{u_{ref}}{U_{dc}} = \frac{L \frac{di_{ref}}{dt} + u_g}{U_{dc}} $$
For the main bridge switches in active sectors (II, IV), the modulation reference is \( X \). For the freewheeling switches (S5, S6) in reactive sectors (I, III), the complementary duty cycle \( Y = 1 – X \) is used because the switch conduction state corresponds to \( u_{ab} = 0 \), opposite to the main bridge’s state mapping. The switching time instants \( T_A, T_B, T_5, T_6 \) for the bridge legs and auxiliary switches are calculated per sector based on \( X \) and \( Y \), and a symmetrical PWM pattern is generated within each control period \( T_c \). This structured SVPWM approach ensures seamless digital control of the proposed modulation strategy for the H6 bridge solar inverter.
Analysis of Grid Current Distortion in Reactive Power Mode
When the H6 bridge solar inverter operates with reactive power, the zero-crossing points of the bridge output voltage \( u_{ab} \) and the grid current \( i_g \) no longer coincide. This misalignment, coupled with the topology’s switching characteristics, leads to distinct distortion phenomena.
1. Distortion at the Output Voltage Zero-Crossing: During the dead time \( t_d \) when the bridge output transitions between positive and negative half-cycles ( \( u_{ab} = 0 \) ), the grid current freewheels uncontrolled under the sole influence of the grid voltage. In this interval, the current deviates from its reference sine wave. The distortion is more pronounced at lower power factors because the current magnitude at the voltage zero-crossing instant is \( I_g \sin \phi \), which is larger for greater \( \phi \). The current trajectory during the dead time \( [t_a, t_b] \) can be expressed as:
$$ i_g(t) = i_g(t_a) – \frac{U_g}{L\omega} (\cos \omega t – \cos \omega t_a) $$
for \( t \in [t_a, t_b] \), where \( \omega t_a = \pi – \theta/2 \), \( \omega t_b = \pi + \theta/2 \), and \( \theta = \omega t_d \).
2. Distortion at the Grid Current Zero-Crossing: This distortion occurs during the transition between reactive modulation sectors (e.g., Sector III to IV) and active modulation sectors. Two mechanisms contribute:
a) Inability to Force Current Reversal: Near the end of a reactive sector (e.g., Sector III), only a freewheeling switch (S6) is active. The voltage \( u_{ab} \) can only be 0 or \( -U_{dc} \), which may be insufficient to force the decaying inductor current to reverse direction and follow the reference current through zero promptly.
b) Non-Ideal Sector Transition: The ideal modulation reference \( u_{ref}^* \) has a discontinuity at the sector boundary. In practice, due to control loop delays and sampling effects, the actual generated reference \( u_{ref} \) cannot achieve this step change, leading to a sluggish or incorrect voltage command during the critical transition, causing current error and distortion.
These distortions increase the total harmonic distortion (THD) and can introduce a DC offset in the grid current from the solar inverter, degrading power quality and potentially causing stability issues in multi-inverter systems.
Proposed Current Waveform Improvement Control Strategy
To address the aforementioned distortions and DC offset, a multi-faceted control strategy is proposed, combining a specialized current controller with a global sliding mode scheme.
Proportional-Integral-Resonant (PIR) Current Controller
A standard Proportional-Resonant (PR) controller offers high gain at the grid frequency but provides no attenuation for DC components. The proposed PIR controller adds an integral term to actively suppress DC offset in the grid current from the solar inverter. Its transfer function is:
$$ G_{PIR}(s) = K_p + \frac{K_i}{s} + \frac{K_R \omega_c s}{s^2 + 2\omega_c s + \omega_0^2} $$
where \( K_p, K_i, K_R \) are the proportional, integral, and resonant gains, \( \omega_0 \) is the grid angular frequency, and \( \omega_c \) is the cutoff bandwidth of the resonant term. The integral action \( K_i/s \) provides very high gain at DC (\( s=0 \)), effectively eliminating steady-state DC current.
Fixed-Frequency Global Sliding Mode Control (SMC) with PIR Surface
To improve dynamic response, robustness, and specifically to smooth the transition between modulation sectors, a fixed-frequency sliding mode controller is designed. A novel sliding surface \( S \) is constructed based on the PIR controller’s error processing:
$$ S = K_p e + K_i \int e \, dt + \mathcal{L}^{-1}\left[\frac{K_R \omega_c s}{s^2 + 2\omega_c s + \omega_0^2} E(s)\right] $$
where \( e = i_{ref} – i_g \). In a more compact Laplace domain form defining the surface \( S_{PIR}(s) \):
$$ S_{PIR}(s) = \left( K_p + \frac{K_i}{s} + \frac{K_R \omega_c s}{s^2 + 2\omega_c s + \omega_0^2} \right) E(s) $$
The system state equation is \( \dot{i_g} = (u_{ab} – u_g)/L \). The control law is derived to force the system trajectory onto the sliding surface and maintain it there. Using a constant switching frequency approach with a saturation function \( \text{sat}(S/\Phi) \) to reduce chattering, the control law for the reference voltage \( u_{ref} \) (which generates \( u_{ab} \)) becomes:
$$ u_{ref} = u_g + L \left( \dot{i_{ref}} + \eta \, \text{sat}(S/\Phi) \right) $$
where \( \eta \) is a positive gain controlling the convergence rate. This SMC law offers fast disturbance rejection inherent to sliding mode control.
Global Sliding Mode for Zero-Crossing Distortion Compensation
To specifically tackle the current zero-crossing distortion caused by abrupt sector transitions, a global sliding mode design is incorporated. The standard sliding surface is modified as:
$$ S_g = S_{PIR} – f(t) $$
The function \( f(t) \) is designed such that \( f(0) = S_{PIR}(0) \) at the instant of a sector transition, and \( f(t) \to 0 \) exponentially, e.g., \( f(t) = S_{PIR}(0^+) e^{-\lambda t} \). This ensures that at the transition moment, the system starts already on the sliding surface \( S_g = 0 \), eliminating the reaching phase. The surface then smoothly evolves back to the standard \( S_{PIR} \) as \( f(t) \) decays. This global approach provides a smooth, bumpless transfer of control during the critical modulation mode switch at current zero-crossing, effectively compensating for the distortion. The stability of the overall sliding mode system is guaranteed by Lyapunov analysis, showing \( \dot{V} = S \dot{S} \leq 0 \).
Experimental Verification and Results
A 5 kVA prototype of the single-phase H6 bridge solar inverter was built to validate the proposed concepts. Key parameters are listed in Table 2.
| Parameter | Value |
|---|---|
| Rated Power | 5 kVA |
| DC Link Voltage (\(U_{dc}\)) | 400 V |
| Grid Voltage (\(U_g\)) & Frequency | 220 Vrms, 50 Hz |
| Filter Inductance (\(L_1, L_2\)) | 0.8 mH each |
| DC-Link Capacitance (\(C\)) | 3 mF |
| Switching Frequency (\(f_s\)) | 20 kHz |
Reactive Power Operation: The inverter successfully operated at a power factor of 0.95, both lagging and leading, at 4.5 kVA. The grid current accurately followed its sinusoidal reference, phase-shifted from the grid voltage, confirming the functionality of the proposed reactive power modulation strategy for the H6 solar inverter.
Leakage Current Performance: Measurements showed that the RMS leakage current remained below 15 mA during full-power operation at unity, 0.95 lagging, and 0.95 leading power factor. This verifies that the low leakage current characteristic of the H6 topology is preserved under reactive power modulation, a crucial safety feature for transformerless solar inverters.
Waveform Improvement: The effectiveness of the PIR-based global sliding mode control was clearly demonstrated. At 2 kVA output with 0.95 lagging power factor, the grid current THD was reduced from 4.3% using a conventional controller to 3.7% with the proposed waveform-improving controller. More importantly, visual inspection of the current waveform showed a significant reduction in distortion around the zero-crossing points. The FFT analysis further confirmed a reduction in lower-order harmonic content and DC offset. The improvement was consistent across the power range, being particularly effective at lighter loads where distortion issues are typically more severe.
Conclusion
This work has comprehensively addressed the challenge of enabling reactive power capability in non-isolated H6 bridge single-phase solar inverters. A novel modulation strategy was developed that actively utilizes the freewheeling switches during intervals of opposing voltage and current, allowing for full four-quadrant operation while maintaining the essential low leakage current feature. The inherent sources of grid current distortion in this mode—at both voltage and current zero-crossings—were rigorously analyzed. To counteract these issues, an advanced control strategy was proposed, combining a PIR controller for DC offset suppression with a fixed-frequency global sliding mode controller. The global sliding mode approach, featuring a dynamically constructed sliding surface, proved highly effective in smoothing the transitions between the inverter’s distinct modulation modes, thereby mitigating zero-crossing distortion and improving overall waveform quality. Experimental results from a 5 kVA prototype validated the theoretical analysis and demonstrated the practical feasibility and superior performance of the proposed solutions. This work provides a viable pathway for upgrading existing H6-based solar inverters via software/firmware updates to comply with modern grid codes requiring reactive power support, enhancing their value and functionality in future smart grids.