As solar energy continues to gain prominence as a renewable source, photovoltaic (PV) power generation has become a key focus in modern energy systems. In high-voltage and high-power applications, the efficiency and performance of solar inverters are critical. I have been researching a novel topology known as the open-end winding dual solar inverter system, which offers advantages over traditional multilevel inverters, such as higher voltage levels and independent maximum power point tracking (MPPT) for multiple PV arrays. However, under unbalanced power conditions caused by shading or component failures, this system can experience over-modulation, leading to degraded grid current quality. In this article, I will explore the mathematical modeling, control strategies, and a reactive power compensation scheme to mitigate these issues, ensuring robust operation of solar inverters in practical scenarios.
The open-end winding dual solar inverter topology consists of two two-level inverters connected to independent PV arrays on the DC side and an open-winding transformer on the AC side, as illustrated in the following figure. This configuration allows each solar inverter to operate at its own MPPT, maximizing energy harvest from the PV arrays. The system effectively synthesizes a three-level output, reducing harmonic distortion and improving efficiency compared to conventional solar inverter designs. However, when power imbalance occurs, the inverter linked to the higher-power array may enter over-modulation, necessitating control interventions.
To understand the system dynamics, I first derived the mathematical model in the synchronous rotating dq-reference frame. The open-end winding dual solar inverter system can be described by the following equations, where the output voltages are the vector difference between the two inverters:
$$ V_d = E_d – \omega L i_q + L \frac{di_d}{dt} + i_d R = V_{d1} – V_{d2} $$
$$ V_q = E_q + \omega L i_d + L \frac{di_q}{dt} + i_q R = V_{q1} – V_{q2} $$
Here, \( V_d \) and \( V_q \) represent the synthesized d- and q-axis voltages of the overall system, while \( V_{d1}, V_{q1} \) and \( V_{d2}, V_{q2} \) correspond to the individual solar inverters. \( E_d, E_q \) are grid voltages, \( i_d, i_q \) are grid currents, \( \omega \) is the grid angular frequency, \( L \) is the filter inductance, and \( R \) is the line resistance. This model highlights that the system’s performance depends on the coordination between the two solar inverters, which is crucial for implementing effective control strategies.
For modulation, I employed a 180° decoupled space vector PWM (SVPWM) strategy. In this approach, the reference voltage vectors for the two solar inverters are phase-shifted by 180°, enabling the synthesis of a larger voltage hexagon and improving DC-link utilization. The voltage space vectors for each two-level solar inverter are shown below, and their combination yields 19 distinct vectors for the open-end winding system, offering high redundancy and low harmonic distortion.
To achieve independent MPPT for both PV arrays, I designed a dual-loop control scheme. The outer loop regulates the DC-link voltages \( V_{dc1} \) and \( V_{dc2} \) to track their MPPT references, while the inner loop controls the grid currents. The power imbalance factor \( k \) (0 ≤ k ≤ 1) is derived from the voltage errors and used to distribute active power between the solar inverters. The control equations are summarized as follows:
$$ I_d^* = G_{\Sigma}(V_{dc1}^* – V_{dc1} + V_{dc2}^* – V_{dc2}) $$
$$ k = G_{\Delta}(V_{dc1}^* – V_{dc1} – (V_{dc2}^* – V_{dc2})) $$
$$ V_d^* = G_{PI}(I_d^* – I_d) + \omega L I_q + E_d $$
$$ V_q^* = G_{PI}(I_q^* – I_q) – \omega L I_d + E_q $$
where \( G_{\Sigma} \) and \( G_{\Delta} \) are voltage regulators, and \( G_{PI} \) represents PI controllers. This control framework ensures that each solar inverter operates at its maximum power point, but under significant power imbalances, over-modulation can occur, which I addressed through reactive power compensation.
The over-modulation mechanism arises when the grid current magnitude falls below a minimum threshold, causing the higher-power solar inverter to exceed its modulation index. I analyzed the stability region by deriving the critical condition for over-modulation. For unit power factor operation, the grid current magnitude \( I_{gd} \) is given by:
$$ I_{gd} = \frac{P_1 + P_2}{3V_g / 2} $$
where \( P_1 \) and \( P_2 \) are the output powers of the two PV arrays, and \( V_g \) is the grid voltage. The minimum current \( I_{min} \) required to avoid over-modulation for each solar inverter, assuming SPWM, is:
$$ I_{min} = \max\left\{ \frac{4}{3} I_{dc1}, \frac{4}{3} I_{dc2} \right\} $$
with \( I_{dc1} \) and \( I_{dc2} \) as the DC currents. Over-modulation occurs when \( I_{gd} \leq I_{min} \), leading to distorted grid currents. To solve this, I proposed a reactive power compensation strategy that injects a controlled amount of reactive current to increase the overall grid current magnitude, thereby reducing the voltage reference for the over-modulating solar inverter.
The reactive compensation design is based on three constraints: active power balance for each solar inverter, total active power balance for the system, and reactive power balance including grid and inductor components. These constraints are expressed as:
$$ \frac{3}{2} V_1^* I_g \cos \phi_1 = P_1 $$
$$ \frac{3}{2} V_g I_g \cos \phi = P_1 + P_2 $$
$$ V_g I_g \sin \phi = \omega L I_g^2 + \frac{V_1^* I_g (P_1 + P_2) \sin \phi_1}{P_1} $$
where \( \phi \) is the angle between grid voltage and current, \( \phi_1 \) is the angle between the system voltage reference and current, and \( V_1^* \) is set to \( V_{dc1}/2 \) at the over-modulation boundary. Solving these equations yields the required grid current magnitude \( I_g \) and angle \( \phi \), from which the reactive current reference \( I_q^* \) is computed:
$$ I_q^* = I_g \sin \phi $$
This value is fed into the control loop to adjust the q-axis current, effectively compensating for the power imbalance. The compensation slightly reduces the power factor, but this can be corrected by external reactive power devices in the PV plant, ensuring unit power factor at the grid connection point. This approach enhances the operational range of the solar inverter system under unbalanced conditions.
To validate the control scheme, I conducted simulations and experiments using parameters typical for a 40 kW system. The table below summarizes the key parameters used in the study, which are essential for designing and evaluating the solar inverter performance.
| Parameter | Value |
|---|---|
| DC Source Voltage | 656 V |
| Series Resistance | 1.6 Ω |
| DC-Link Capacitance | 3.36 mF |
| Filter Inductance | 3.5 mH |
| Transformer Ratio | 364/380 |
| Switching Frequency | 5000 Hz |
| Rated Power | 40 kW |
| Grid Line Voltage (RMS) | 396 V |
Under balanced power conditions, with \( P_1 = P_2 = 15.76 \text{ kW} \), the system operated at unit power factor, and the synthesized line voltage exhibited a three-level waveform, confirming the equivalence to a traditional three-level solar inverter. The grid current THD was below 5%, demonstrating good performance. For slight power imbalance (e.g., \( P_1 = 15.76 \text{ kW}, P_2 = 12.11 \text{ kW} \)), the grid current remained sinusoidal with a THD of 4.08%, as the current magnitude satisfied the over-modulation avoidance condition. However, under severe imbalance (e.g., \( P_1 = 15.76 \text{ kW}, P_2 = 10.61 \text{ kW} \)), over-modulation occurred, increasing THD to 6.47% without compensation.
With reactive compensation applied, the grid current THD improved to 3.93%, and the modulation indices of both solar inverters stayed within limits. The table below compares the performance metrics under different scenarios, highlighting the effectiveness of the compensation strategy for solar inverter systems.
| Scenario | Power Imbalance | Grid Current THD (Without Compensation) | Grid Current THD (With Compensation) | Remarks |
|---|---|---|---|---|
| Balanced | None | 4.50% | N/A | Unit power factor operation |
| Light Imbalance | \( P_2 \) reduced by 23% | 4.08% | N/A | No over-modulation |
| Heavy Imbalance | \( P_2 \) reduced by 33% | 6.47% | 3.93% | Compensation enabled |
The experimental results aligned with simulations, using a platform with two 20 kW rectifiers emulating PV arrays and a TMS320F28335 DSP controller. Waveforms captured with oscilloscopes and current probes confirmed that the reactive compensation scheme successfully mitigated over-modulation, ensuring stable operation of the solar inverter system. The synthesized line voltage maintained a multilevel characteristic, and grid currents met harmonic standards even under unbalanced conditions.
In conclusion, the open-end winding dual solar inverter topology offers significant benefits for high-power PV applications, including independent MPPT and improved voltage quality. Through mathematical modeling and 180° decoupled SVPWM, I developed a control framework that enables efficient power management. The proposed reactive power compensation strategy addresses over-modulation during power imbalances, enhancing the robustness and efficiency of solar inverter systems. This work contributes to advancing solar inverter technology, supporting the integration of renewable energy into the grid. Future research could explore adaptive compensation methods or integration with energy storage systems to further optimize performance.
From a broader perspective, the development of such control strategies is vital for the scalability of solar power. As solar inverter designs evolve, incorporating features like reactive compensation can reduce reliance on external devices, lowering costs and improving reliability. I believe that continuous innovation in solar inverter technology will play a key role in achieving sustainable energy goals, making systems more resilient to environmental variations and grid demands. The insights from this study can be applied to other multilevel inverter topologies, fostering advancements in power electronics for renewable energy.