In modern renewable energy systems, the grid tied inverter plays a crucial role in converting DC power from sources like solar panels into AC power for grid integration. Traditional inverters often use L or LC filters, but these can occupy significant volume, increasing costs and reducing efficiency. To address this, I explore a two-stage grid tied inverter based on an LCL filter with a time-sharing composite control strategy. This approach not only reduces the inverter’s size but also ensures high-quality grid current output. In this article, I will detail the control methodology, analyze the system under different operating modes, and validate the strategy through simulations.
The time-sharing composite control divides the inverter operation into two modes: Buck and Boost. When the input voltage is higher than the grid voltage, the system operates in Buck mode, where the front-stage chopper circuit is inactive, and the rear-stage inverter works at high frequency. Conversely, when the input voltage is lower, the system switches to Boost mode, with the front-stage circuit operating at high frequency to boost the voltage. This method reduces switching losses and allows for a smaller bus capacitor, enhancing overall efficiency. The LCL filter is employed to mitigate current harmonics, and its parameters are optimized to meet grid standards while minimizing footprint.
In the Buck mode, the control loop uses the grid current as feedback with a PI controller. However, the LCL filter introduces resonance peaks that can destabilize the system. To suppress these, I implement an active equivalent damping method, which emulates a resistor in parallel with the filter capacitor without power loss. The transfer function of the main circuit in this mode is derived as follows. Let \(V_{inv}(s)\) be the inverter bridge voltage, \(I_2(s)\) the grid current, and \(V_g(s)\) the grid voltage. The LCL filter components are \(L_1\), \(C_f\), and \(L_2\). From Kirchhoff’s laws, the relationship is:
$$ \frac{I_2(s)}{V_{inv}(s)} = \frac{1}{L_1 L_2 C_f s^3 + (L_1 + L_2)s} $$
This transfer function has a resonance peak that can cause instability. By adding active damping, the modified control block diagram includes a feedback term from the capacitor current. The damping coefficient is chosen to stabilize the system. The PI controller parameters are designed using root locus and Bode plot analysis. For instance, the proportional gain \(k_p\) is set to 10, and the integral gain \(k_i\) to 2000, ensuring a phase margin of 68.5 degrees and a gain margin of 7.61 dB. This ensures robust performance in the Buck mode for the grid tied inverter.
In the Boost mode, the front-stage inductor current is used as feedback to indirectly control the grid current. This is based on instantaneous power balance: \(V_{in} i_{Lb} = V_g i_2\), where \(V_{in}\) is the input voltage, \(i_{Lb}\) the inductor current, and \(i_2\) the grid current. The transfer function from the duty cycle \(D(s)\) to the inductor current \(I_{Lb}(s)\) is complex due to the LCL filter. It can be expressed as:
$$ \frac{I_{Lb}(s)}{D(s)} = \frac{z_5 s^5 + z_4 s^4 + z_3 s^3 + z_2 s^2 + z_1 s + z_0}{p_3 s^3 + p_2 s^2 + p_1 s} $$
where coefficients \(z_i\) and \(p_i\) depend on circuit parameters. To handle resonance, I employ a notch filter combined with a compensation network. A low-pass filter with a cutoff frequency of 4.41 kHz is used, along with an all-pass filter to improve phase margin. The compensated system achieves a phase margin of 45.4 degrees and a gain margin of 9.21 dB, as verified by Nyquist plots. This control strategy ensures stable operation of the grid tied inverter in Boost mode, effectively suppressing harmonics.
To validate the design, I conducted simulations using MATLAB/Simulink. The main circuit parameters are summarized in the table below, which are critical for the grid tied inverter performance.
| Parameter | Symbol | Value |
|---|---|---|
| DC Source | \(V_{in}\) | 110 V |
| Front-stage Inductor | \(L_b\) | 500 μH |
| LCL Filter Inductors | \(L_1\), \(L_2\) | 0.8 mH, 0.2 mH |
| LCL Filter Capacitor | \(C_f\) | 5 μF |
| Bus Capacitor | \(C_{bus}\) | 10 μF |
| Grid Voltage (RMS) | \(V_g\) | 220 V |
| Grid Power | \(P_g\) | 2000 W |
| Front-stage Switching Frequency | \(f_{Qb}\) | 40 kHz |
| Rear-stage Switching Frequency | \(f_Q\) | 20 kHz |
The LCL filter parameters are designed to meet harmonic standards. For example, \(L_1\) is calculated based on current ripple: \(L_1 \geq \frac{V_{L1} \Delta t}{\Delta I_{L1max}}\), where \(\Delta I_{L1max}\) is 20% of the inductor current. The capacitor \(C_f\) is limited to 5% of the rated power to minimize reactive power: \(C_f \leq \frac{0.05 I_g}{\omega V_g}\), with \(\omega = 314 \, \text{rad/s}\). The inductor \(L_2\) is sized to attenuate specific harmonics: \(L_2 \geq \frac{1}{\lambda} \left( \frac{V_{inv}(j\omega_h)}{\omega_h I_{g,h}} – L_1 \right)\), where \(\lambda\) is the harmonic limit per grid codes. These calculations ensure the grid tied inverter complies with regulations like GB/T 14549-1993.
Simulation results show that the time-sharing composite control effectively manages mode transitions. In Buck mode, the rear-stage inverter produces a high-frequency bridge voltage, while in Boost mode, the front-stage inductor current follows a sinusoidal half-wave. The grid current \(i_2\) tracks the grid voltage \(V_g\) with minimal phase error, as seen in the waveforms. The total harmonic distortion (THD) analysis indicates that the LCL filter significantly reduces harmonics compared to an LC filter. For instance, the THD for the LCL-based grid tied inverter is below 0.3% for harmonics above 35th order, meeting international standards. The FFT analysis reveals harmonic concentrations at low frequencies, with a slight rise around 6 kHz due to bus voltage fluctuations, but overall performance is satisfactory.
The active damping method in Buck mode proves effective in resonance suppression. The Bode plot of the open-loop system shows a resonance peak near 1 kHz, which is mitigated by the damping feedback. The compensated system has a stable phase margin, ensuring robustness. In Boost mode, the notch filter targets resonance at 3.5 kHz, as derived from the transfer function poles. The compensation network includes a PR controller to enhance tracking at the fundamental frequency. The Nyquist plot confirms stability, with no encirclements of the -1 point. These control techniques are essential for reliable operation of the grid tied inverter in varying grid conditions.
Furthermore, the time-sharing approach reduces switching losses. In traditional two-stage grid tied inverters, both stages operate at high frequency, increasing losses. Here, only one stage is active at a time, improving efficiency. The bus capacitor voltage \(V_{Cbus}\) shows some ripple during mode transitions, but this does not significantly affect the grid current quality. Future work could focus on optimizing this voltage stability through advanced control schemes. Overall, the proposed strategy offers a cost-effective solution for grid tied inverters, balancing performance and size.
In conclusion, the grid tied inverter based on LCL filter with time-sharing composite control demonstrates superior harmonic suppression and efficiency. The Buck mode uses PI control with active damping, while the Boost mode employs indirect current control with notch filters. Simulations validate that the grid current meets harmonic standards, with THD within limits. The LCL filter reduces component size by 10% compared to LC filters, aiding in compact inverter design. This makes the grid tied inverter suitable for residential and commercial solar applications. Future enhancements could include digital implementation and real-time adaptation to grid disturbances, further solidifying the role of grid tied inverters in smart grids.