In the context of increasing global energy demand and the depletion of fossil fuels, solar energy has emerged as a promising renewable source. Photovoltaic (PV) systems rely heavily on various types of solar inverter to convert direct current (DC) from solar panels into alternating current (AC) for grid integration. Among these, centralized inverters, string inverters, and microinverters are commonly used in large-scale and distributed installations. In high-power applications, multiple inverters are often connected in parallel to meet power requirements. However, parallel operation introduces circulating currents that degrade system efficiency and reliability. This paper focuses on the suppression of switching-frequency circulating current (SFCC) caused by carrier asynchronization between parallel-connected inverters. A novel carrier synchronization control method is proposed to dynamically compensate for carrier phase differences, thereby minimizing SFCC. The method adjusts the phase of the triangular carrier based on the measured SFCC amplitude, halting adjustment once the current falls below a predefined threshold. Mathematical analysis, simulation, and experimental results validate the effectiveness of the proposed approach for various types of solar inverter architectures.
To understand the origin of SFCC, consider a typical parallel system consisting of two three-phase voltage-source inverters sharing a common DC bus and connecting to the grid through individual filter inductors. Each inverter employs sinusoidal pulse-width modulation (SPWM) with a triangular carrier wave. When the carriers of the two inverters are not synchronized, a phase difference θ (0 ≤ θ ≤ π) arises between their switching instants. This leads to voltage differences across the filter inductors, generating a circulating current that oscillates primarily at the switching frequency. The equivalent circuit can be modeled using Kirchhoff’s voltage law, giving the following relationship for the SFCC, denoted as ih:
$$
i_h = \frac{1}{2sL} \left[ (u_{1a} – u_{2a}) + (u_{1b} – u_{2b}) + (u_{1c} – u_{2c}) \right]
$$
where L is the filter inductance (assuming L1=L2=L), u1x and u2x are the phase output voltages of inverter 1 and inverter 2 respectively, and s is the Laplace operator. This equation shows that SFCC is directly proportional to the sum of voltage differences across the three phases. Using double Fourier series expansion for the PWM output voltages, the relationship between the carrier phase difference θ and the amplitude of SFCC can be derived. For instance, the a-phase output voltage of inverter 1 and inverter 2 can be expressed as:
$$
u_{1a} = \frac{M E}{2} \sin(\omega_s t) + \frac{2E}{\pi} \sum_{m=1,3,5,\dots}^{\infty} \frac{1}{m} J_0\left(\frac{m M \pi}{2}\right) \sin\left(\frac{m \pi}{2}\right) \cos(m \omega_c t) e^{-j m 0} + \cdots
$$
$$
u_{2a} = \frac{M E}{2} \sin(\omega_s t) + \frac{2E}{\pi} \sum_{m=1,3,5,\dots}^{\infty} \frac{1}{m} J_0\left(\frac{m M \pi}{2}\right) \sin\left(\frac{m \pi}{2}\right) \cos(m \omega_c t) e^{-j m \theta} + \cdots
$$
Neglecting higher-order terms and focusing on the fundamental switching-frequency component (m=1, n=0), the SFCC can be simplified to:
$$
i_h = \frac{1.416 U_{dc}}{\pi \omega_c L} \sqrt{2(1 – \cos\theta)} \cos(\omega_c t)
$$
Thus, the peak magnitude of SFCC is a function of θ, DC-link voltage Udc, switching angular frequency ωc, and filter inductance L. When θ=0, SFCC is zero; as θ increases from 0 to π, the circulating current grows monotonically, reaching its maximum at θ=π. This mathematical model confirms that carrier phase misalignment is the root cause of SFCC in parallel inverter systems, independent of the specific types of solar inverter employed.
To suppress SFCC, two control strategies are compared: a traditional proportional-integral (PI) regulator and the proposed carrier synchronization method. Both methods extract the switching-frequency component from the zero-sequence current using a bandpass filter, then compute its amplitude via a Fourier transform. The amplitude is used as feedback to generate a phase compensation angle θcomp. In the PI control approach, the error between the measured SFCC amplitude and a reference (typically zero) is passed through a PI controller to produce θcomp. This angle is then converted into a time delay ΔT for the carrier counter of the slave inverter. The conversion is given by:
$$
\Delta T = \frac{\theta}{360^\circ} \cdot \frac{1}{f_c}
$$
where fc is the switching frequency. The PI controller can effectively reduce SFCC but may suffer from slower convergence and sensitivity to parameter variations.
The proposed carrier synchronization method adopts an adaptive stepwise adjustment. Initially, the compensation angle is set to a default value (e.g., 90°). The SFCC amplitude is monitored after each adjustment. If the amplitude decreases, the compensation angle is increased in the same direction; if it increases, the direction is reversed. This iterative process continues until the SFCC amplitude falls below a preset threshold, at which point the adjustment stops. The algorithm is simple to implement and does not require precise system modeling. Figure 1 illustrates a typical experimental setup used to validate the method; the hardware platform includes two parallel inverters with a shared DC source and grid connection, supporting various types of solar inverter configurations.
Simulations and experiments were conducted using the parameters listed in Table 1. Two initial carrier phase differences (θ = 60° and θ = 120°) were tested. The SFCC was recorded before and after activating the suppression control at t = 0.2 s. Table 2 summarizes the performance comparison between the PI control and the synchronization method.
| Parameter | Value |
|---|---|
| DC-link voltage Udc | 400 V |
| Filter inductance L1, L2 | 6 mH |
| Grid-side inductance LNET | 1 mH |
| Grid phase voltage (RMS) | 220 V / 50 Hz |
| Switching frequency fc | 5 kHz |
| Control method | Settling time (s) | Suppression ratio (%) |
|---|---|---|
| PI control | 0.05 | 97 |
| Synchronization control | 0.02 | 99 |
Results show that both methods effectively reduce SFCC. The synchronization control achieves faster convergence (0.02 s vs. 0.05 s) and slightly higher suppression (99% vs. 97%). The experimental waveforms confirm that the output current distortion is significantly reduced after compensation. These findings hold for different initial phase differences and are applicable to a wide range of types of solar inverter, including those used in residential, commercial, and utility-scale PV systems.
In conclusion, this paper presents a detailed analysis of switching-frequency circulating current in parallel inverters caused by carrier phase misalignment. A carrier synchronization control method is proposed and validated through both simulation and experimentation. The method adaptively adjusts the carrier phase until the SFCC is minimized, offering rapid suppression with minimal computational overhead. Compared to conventional PI control, the proposed technique provides faster response and superior steady-state performance. Future work will extend the method to multi-inverter clusters (more than two units) and investigate its robustness under unbalanced grid conditions and varying types of solar inverter topologies.