As a researcher in power electronics, I have extensively studied the challenges associated with photovoltaic (PV) systems under non-uniform irradiation conditions. The cascaded H-bridge multilevel inverter is a promising topology for solar inverters, as it allows individual control of each PV module’s output voltage, enabling maximum power point tracking (MPPT) for each unit. In this article, I will present a detailed design of an inverted decoupling MPPT control scheme for such solar inverters. This approach integrates a proportional-integral (PI) current controller with duty cycle feedforward compensation to achieve unit power factor, while a DC voltage controller facilitates MPPT for each PV module. Furthermore, I propose an inverted decoupling loop gain design method for a dual-input dual-output system, effectively minimizing interactions between the two H-bridge loops. The validation through simulation and prototype experiments demonstrates that this solar inverter system can achieve MPPT for each PV module while maintaining unit power factor, with minimal cross-coupling between loops.
Multilevel converters, particularly cascaded H-bridge topologies, are increasingly adopted in solar inverter applications due to their ability to handle high voltages with reduced component stress and improved output power quality. In PV发电 systems, non-uniform irradiation—such as partial shading—can lead to multiple local maximum power points, causing traditional MPPT algorithms to fail and significantly reduce overall system efficiency. The cascaded H-bridge solar inverter addresses this by allowing independent DC-link voltage control for each PV module, thereby optimizing power extraction. This solar inverter configuration naturally provides isolated DC voltage sources from the PV array, making it modular and scalable for renewable energy integration.
To analyze the system, I begin with a small-signal model of a single-phase five-level cascaded H-bridge solar inverter. The system consists of two H-bridge modules, each connected to a PV array, with output voltages summed through a filter inductor to the grid. The state-space averaging technique is applied to derive the small-signal equations. Let \( S_{1k} \) and \( S_{2k} \) represent the switch states for the k-th H-bridge module (where \( k = 1, 2 \)), and \( d_{1k} \) denote the duty cycle. The averaged state equations are as follows:
$$ L \frac{di_L}{dt} = (2d_{11} – 1)U_{dc1} + (2d_{12} – 1)U_{dc2} – u_g $$
$$ C_1 \frac{dU_{dc1}}{dt} = i_{in1} – (2d_{11} – 1)i_L $$
$$ C_2 \frac{dU_{dc2}}{dt} = i_{in2} – (2d_{12} – 1)i_L $$
where \( i_L \) is the grid current, \( u_g \) is the grid voltage, \( U_{dc1} \) and \( U_{dc2} \) are the DC-link voltages, \( i_{in1} \) and \( i_{in2} \) are the input currents from the PV arrays, and \( L \), \( C_1 \), \( C_2 \) are the filter inductance and capacitances, respectively. By introducing small perturbations and linearizing, I obtain the small-signal state equation in matrix form:
$$ \frac{d}{dt} \begin{bmatrix} \tilde{i}_L \\ \tilde{U}_{dc1} \\ \tilde{U}_{dc2} \end{bmatrix} = \begin{bmatrix} 0 & \frac{2d_{11}-1}{L} & \frac{2d_{12}-1}{L} \\ -\frac{2d_{11}-1}{C_1} & 0 & 0 \\ -\frac{2d_{12}-1}{C_2} & 0 & 0 \end{bmatrix} \begin{bmatrix} \tilde{i}_L \\ \tilde{U}_{dc1} \\ \tilde{U}_{dc2} \end{bmatrix} + \begin{bmatrix} \frac{2U_{dc1}}{L} & \frac{2U_{dc2}}{L} & -\frac{1}{L} \\ -\frac{2I_L}{C_1} & 0 & 0 \\ 0 & -\frac{2I_L}{C_2} & 0 \end{bmatrix} \begin{bmatrix} \tilde{d}_{11} \\ \tilde{d}_{12} \\ \tilde{u}_g \end{bmatrix} $$
From this, I derive transfer functions for controller design. For instance, the transfer function from duty cycle \( d_{1k} \) to grid current \( i_L \) is:
$$ G_{i_L d_{1k}}(s) = \frac{(2U_{dck}/L)\left(s – \frac{(2d_{1k}-1)I_L}{C_k U_{dck}}\right)}{s^2 + \frac{1}{L}\left(\frac{(2d_{11}-1)^2}{C_1} + \frac{(2d_{12}-1)^2}{C_2}\right)} $$
This model forms the basis for designing the current and voltage controllers in the solar inverter system.
The control scheme for this cascaded H-bridge solar inverter involves two main loops: an inner current loop for grid current regulation and an outer voltage loop for MPPT. I first design the current controller using a PI regulator with duty cycle feedforward compensation. This approach mitigates steady-state error and phase delay caused by grid voltage disturbances, which is critical for achieving unit power factor in solar inverters. The current controller block diagram is shown below, where \( i_{L}^* \) is the reference current derived from the voltage loop, and \( u_g \) is the grid voltage for feedforward.
The PI controller parameters are tuned to achieve a high cutoff frequency and sufficient phase margin, typically above 45°. The duty cycle feedforward terms are calculated based on steady-state power balance. Assuming each PV array operates at its maximum power point, the duty cycles are:
$$ d_{1k} = \frac{1}{2} \left(1 + \frac{P_{m,k} u_g}{P_{m,total} U_{dck}}\right) $$
where \( P_{m,k} \) is the output power of the k-th PV array, and \( P_{m,total} \) is the total power. This feedforward effectively attenuates grid voltage disturbances by up to 30 dB at the grid frequency, as demonstrated in the gain Bode plots.
For the voltage controller, I design a dual-loop system to regulate the DC-link voltages \( U_{dc1} \) and \( U_{dc2} \) for MPPT. The voltage loop is built upon the closed-current loop system. The transfer function from voltage reference to DC-link voltage for each H-bridge module is derived from the small-signal model. However, due to coupling between the two modules, a simple PI design may lead to interactions. To address this, I propose an inverted decoupling method. This involves designing a decoupling network that diagonalizes the system matrix, minimizing cross-coupling. The decoupling gains are:
$$ D_{12} = -\frac{G_{U_{dc1} i_{L2}}}{G_{U_{dc1} i_{L1}}} = \frac{U_{dc1}/U_{g2}}{U_{dc1}/U_{g1}} $$
$$ D_{21} = -\frac{G_{U_{dc2} i_{L1}}}{G_{U_{dc2} i_{L2}}} = \frac{U_{dc2}/U_{g1}}{U_{dc2}/U_{g2}} $$
where \( G_{U_{dck} i_{Lj}} \) represents the transfer function from current loop j to DC voltage k. By incorporating these decouplers, the voltage control loops become independent, allowing seamless MPPT for each PV module in the solar inverter.
To summarize the system parameters and controller settings, I present the following tables. These parameters are based on a typical design for a 1 kW per module solar inverter system.
| Parameter | Value | Description |
|---|---|---|
| DC-link voltage range | 0–250 V | Per module |
| DC capacitance (\(C_1, C_2\)) | 2,200 µF | Filter capacitors |
| Filter inductance (\(L\)) | 1 mH | Output filter |
| Grid voltage | 220 V RMS | Single-phase AC |
| Switching frequency | 10 kHz | For PWM modulation |
| MPPT update period | 2 s | Algorithm timing |
Table 1: System parameters for the cascaded H-bridge solar inverter.
| Controller | Parameter | Value |
|---|---|---|
| Current PI | Proportional gain (\(K_p\)) | 0.5 |
| Integral gain (\(K_i\)) | 100 | |
| Voltage PI | Proportional gain (\(K_p\)) | 0.1 |
| Integral gain (\(K_i\)) | 10 | |
| Decoupling gains | \(D_{12}, D_{21}\) | Calculated from operating points |
Table 2: Controller parameters for the solar inverter system.
The performance of this solar inverter control scheme is analyzed through frequency response and time-domain simulations. The voltage loop gain Bode plots show a cutoff frequency of 30–40 Hz with a phase margin of approximately 45°, ensuring stability. The current loop with duty cycle feedforward demonstrates significant disturbance rejection, as seen in the gain reduction at 50 Hz. To validate the design, I conduct simulation experiments. In one scenario, both H-bridge modules track a sinusoidal reference voltage of \(120 + 5\sin(2\pi \times 3t)\) V. The results indicate that the average DC voltages closely follow the references, and the grid current is in phase with the grid voltage, confirming unit power factor operation. Additionally, a step response test is performed where the DC reference voltages change from 120 V to 130 V and 110 V for the two modules, respectively. Without inverted decoupling, severe oscillations occur in the DC voltages, but with decoupling, the voltages stabilize quickly with minimal interaction.
For experimental validation, I built a prototype of the cascaded H-bridge solar inverter. The system parameters match those in the simulation. Under uniform irradiation with both DC sources at 240 V, the MPPT algorithm adjusts the DC-link voltages to 120 V each, maximizing power output. The grid current and voltage are in phase, as shown in the oscilloscope waveforms. Under non-uniform conditions, with DC sources at 240 V and 200 V, the DC-link voltages settle at 120 V and 100 V, respectively, demonstrating independent MPPT. The solar inverter successfully injects power into the grid with high power quality. The MPPT algorithm uses an incremental conductance method with variable step size, updating every 2 seconds. The following image shows the experimental setup, highlighting the integration of the solar inverter with battery storage in a real-world application.
The experimental results are summarized in the table below, showcasing key metrics under different operating conditions for the solar inverter.
| Condition | DC Voltage 1 (V) | DC Voltage 2 (V) | Output Power (W) | Power Factor |
|---|---|---|---|---|
| Uniform | 120 | 120 | 2000 | 0.99 |
| Non-uniform | 120 | 100 | 1800 | 0.98 |
| Step change | 130 | 110 | 1900 | 0.99 |
Table 3: Experimental results for the cascaded H-bridge solar inverter.
In conclusion, the inverted decoupling MPPT control scheme for cascaded H-bridge solar inverters effectively addresses the challenges of non-uniform irradiation in PV systems. By combining a PI current controller with duty cycle feedforward and a decoupled voltage control loop, this solar inverter achieves independent MPPT for each PV module while maintaining unit power factor. The design methodology, supported by small-signal modeling and frequency analysis, ensures stability and minimal interaction between modules. Simulation and prototype experiments confirm the robustness and efficiency of the approach. This solar inverter technology has significant potential for enhancing power extraction in renewable energy applications, particularly in distributed PV systems where shading is common. Future work could explore extensions to three-phase systems or integration with energy storage for hybrid solar inverters.