With the increasing severity of energy shortages and the growing support for renewable energy, distributed generation technologies based on renewable sources have shown a trend of vigorous development, attracting widespread attention from experts and scholars worldwide. Among these, photovoltaic (PV) power generation has become one of the most prominent and promising forms of utilization. The electrical energy generated by PV arrays is direct current (DC), and to achieve grid-connected operation of PV power generation systems, it is necessary to convert this DC energy into alternating current (AC) through a grid-connected inverter. Currently, the control methods for PV grid-connected inverters mostly use pulse width modulation (PWM), but this also introduces high-order harmonics into the grid. Therefore, filters are typically installed on the AC side of the inverter to eliminate harmonics.
The use of an LCL filter can significantly reduce the volume of the filter, and the LCL filter has excellent high-frequency filtering characteristics, making it widely used in PV grid-connected systems. However, the LCL filter is a third-order system and has resonance issues. Usually, it is necessary to increase system damping to suppress its resonance peak. Common methods are divided into passive damping and active damping. Passive damping requires adding resistors in series or parallel in the LCL filter circuit, which increases the power loss of the system and reduces system efficiency. Active damping does not require adding resistors in the filter circuit and does not increase power loss; it mainly improves the frequency characteristics of the LCL filter by making improvements in the control method.
This article takes the double-stage three-phase LCL PV grid-connected inverter as the research object and studies its grid-connected control strategy, using active damping to suppress the resonance peak of the LCL filter. The conductance increment method is used to achieve maximum power point tracking (MPPT) control of the PV array. The stability of the DC side voltage of the rear-stage grid-connected inverter is achieved through the voltage outer loop. Unit power factor grid connection and resonance peak suppression are achieved by using double current loop control based on proportional resonant (PR) control for the grid-connected current outer loop and proportional (P) control for the capacitor current inner loop.
The topology of the double-stage three-phase LCL PV grid-connected inverter includes a PV array and a Boost circuit added between the PV array and the inverter circuit. The Boost circuit boosts the DC voltage output by the PV array to the level required by the DC side of the grid-connected inverter, and the addition of the Boost circuit makes it easier to achieve MPPT for the PV array. The rear-stage structure is a DC-AC inverter circuit, which converts the DC output from the Boost circuit into AC. To meet grid connection requirements, the harmonic components in the grid current need to be filtered out by the LCL filter.
From the topology, the state equation of the LCL inverter in the abc three-phase stationary coordinate system under three-phase balanced conditions can be obtained as:
$$ L_1 \frac{di_{1a}}{dt} = u_a – u_{ca} $$
$$ L_1 \frac{di_{1b}}{dt} = u_b – u_{cb} $$
$$ L_1 \frac{di_{1c}}{dt} = u_c – u_{cc} $$
And:
$$ C \frac{du_{ca}}{dt} = i_{1a} – i_{2a} $$
$$ C \frac{du_{cb}}{dt} = i_{1b} – i_{2b} $$
$$ C \frac{du_{cc}}{dt} = i_{1c} – i_{2c} $$
And:
$$ L_2 \frac{di_{2a}}{dt} = u_{ca} – e_a $$
$$ L_2 \frac{di_{2b}}{dt} = u_{cb} – e_b $$
$$ L_2 \frac{di_{2c}}{dt} = u_{cc} – e_c $$
According to the Clark transformation, the state equation of the LCL inverter in the αβ two-phase stationary coordinate system can be obtained as:
$$ \frac{di_{1\alpha}}{dt} = \frac{1}{L_1} u_{\alpha} – \frac{1}{L_1} u_{c\alpha} $$
$$ \frac{di_{1\beta}}{dt} = \frac{1}{L_1} u_{\beta} – \frac{1}{L_1} u_{c\beta} $$
And:
$$ \frac{du_{c\alpha}}{dt} = \frac{1}{C} i_{1\alpha} – \frac{1}{C} i_{2\alpha} $$
$$ \frac{du_{c\beta}}{dt} = \frac{1}{C} i_{1\beta} – \frac{1}{C} i_{2\beta} $$
And:
$$ \frac{di_{2\alpha}}{dt} = \frac{1}{L_2} u_{c\alpha} – \frac{1}{L_2} e_{\alpha} $$
$$ \frac{di_{2\beta}}{dt} = \frac{1}{L_2} u_{c\beta} – \frac{1}{L_2} e_{\beta} $$
Based on the above equations, the mathematical model of the LCL filter in the αβ coordinate system can be established (the mathematical models of the α and β phases are the same, so any one phase can be analyzed). From this, the transfer function from the grid-side current to the inverter output voltage can be derived:
$$ G(s) = \frac{i_2(s)}{u(s)} = \frac{1}{L_1 L_2 C s^3 + (L_1 + L_2)s} $$
From this, it can be intuitively seen that the LCL inverter is a third-order system with high-frequency resonance problems. The resonance frequency is:
$$ f_{res} = \frac{1}{2\pi} \sqrt{\frac{L_1 + L_2}{L_1 L_2 C}} $$
From the literature, the calculation formulas for the values of various parameters of the LCL filter can be derived as:
$$ \frac{U_{dc}}{20\% \times 8 f_k I_n} \leq L \leq \frac{\sqrt{U_{dc}^2 – E^2}}{\omega_0 I_n} $$
Where L is the total filter inductance, L = L1 + L2. The ratio of L1 to L2 should satisfy:
$$ 4 \leq \frac{L_1}{L_2} \leq 6 $$
The filter capacitance C should satisfy:
$$ C \leq \frac{5\% P_0}{3 \omega_0 E^2} $$
The resonance frequency should satisfy:
$$ 10 f_0 \leq f_{res} \leq 0.5 f_k $$
In these formulas, Udc is the DC side voltage of the inverter, f_res is the resonance frequency of the LCL filter, f_k is the switching frequency, P0 is the rated output power of the inverter, E is the effective value of the grid voltage, I_n is the effective value of the grid current, I_n = P0 / (3E), f0 is the grid frequency, and ω0 is the grid angular frequency, ω0 = 2πf0.
For the double-stage PV grid-connected power generation system, the front-stage structure is PV array + Boost circuit. The relationship between the input voltage and output voltage of the Boost circuit satisfies U_pv = (1 – D) U_dc, where U_dc can be stabilized through the control of the rear-stage grid-connected inverter. Therefore, by changing the duty cycle D of the Boost circuit, the output voltage U_pv of the PV array can be changed. When the duty cycle D is appropriate, the PV array outputs at maximum power, that is, MPPT control of the PV array is achieved. The principle of MPPT control is shown in the figure.
This article uses the relationship between the conductance of the PV array and the rate of change of conductance to achieve MPPT control of the PV array, that is, the incremental conductance (INC) method. The output power P of the PV array and the output current I and voltage U_pv satisfy:
$$ P = U_{pv} I $$
Differentiating both sides of the equation gives:
$$ \frac{dP}{dU_{pv}} = I + U_{pv} \frac{dI}{dU_{pv}} $$
Based on this, the judgment basis for MPPT using the INC method can be obtained:
- If dI/dU_pv > -I/U_pv, it is on the left side of the maximum power point.
- If dI/dU_pv = -I/U_pv, it is at the maximum power point.
- If dI/dU_pv < -I/U_pv, it is on the right side of the maximum power point.
Using ΔI/ΔU_pv instead of dI/dU_pv, the flow chart of the INC method can be obtained. The grid-connected inverter generally uses voltage outer loop and current inner loop control. The grid current controller mostly uses proportional integral (PI) control to achieve no static error tracking of DC quantities. However, in the PI control process, it is necessary to decouple the d-axis and q-axis components of current and voltage, which increases the difficulty of controller design and cannot achieve no static error tracking of sinusoidal AC quantities. PR control controls the α-axis and β-axis components of current and voltage. At this time, the current and voltage components will not have coupling problems, achieving no static error tracking of sinusoidal AC quantities. Therefore, the grid current controller in this article uses PR control.
The control principle of the grid-connected inverter is as follows: The collected inverter DC side voltage U_dc is compared with the required DC side voltage value U*_dc. The comparison result is passed through a PI controller and used as the reference value for the active component of the grid current i*_2d. When grid-connected at unit power factor, the reference value for the reactive component of the grid current i*_2q is 0. Then i*_2d and i*_2q are converted to i*_2α and i*_2β through coordinate transformation. Then, unit power factor grid connection and resonance peak suppression of the LCL filter are achieved by using double current loop control based on the PR controller for the grid current outer loop and the P controller for the capacitor current inner loop. The transfer function of the PR controller is:
$$ G_{PR}(s) = K_P + \frac{K_R s}{s^2 + \omega_0^2} $$
In the formula, K_P is the proportional coefficient, K_R is the resonance coefficient, and ω_0 = 2πf. According to the inverter control principle, the double current closed-loop control block diagram of the LCL inverter can be obtained. By merging and simplifying the control block diagram, the closed-loop transfer function of the system can be derived:
$$ \frac{i_2(s)}{i^*_2(s)} = \frac{A_2 s^2 + A_1 s + A_0}{B_5 s^5 + B_4 s^4 + B_3 s^3 + B_2 s^2 + B_1 s + B_0} $$
Where A_2 = K_P K_e K_{PWM}, A_1 = K_R K_e K_{PWM}, A_0 = K_P K_e K_{PWM} ω_0^2, B_5 = L_1 L_2 C, B_4 = K_e K_{PWM} L_2 C, B_3 = L_1 + L_2 + L_1 L_2 C ω_0^2, B_2 = K_P K_e K_{PWM} + K_e K_{PWM} L_2 C ω_0^2, B_1 = K_R K_e K_{PWM} + (L_1 + L_2) ω_0^2, B_0 = K_P K_e K_{PWM} ω_0^2.
When the grid current outer loop uses PR control, to ensure that the grid current amplitude error is less than 1% when the grid frequency fluctuates by ±0.5 Hz, the fundamental wave amplitude gain T_f0 > 75 dB is required; to ensure good dynamic response, the phase margin PM > 45° is required; to ensure sufficient robustness, the amplitude margin GM > 3 dB is required.
In MATLAB/Simulink, a simulation model of the double-stage three-phase LCL PV grid-connected system is built. The parameters of each component are shown in the table below.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| PV Array Output Power | 4000 W | Filter Capacitance | 10 μF |
| DC Bus Voltage | 600 V | Voltage Outer Loop P | 2 |
| Grid Phase Voltage | 220 V | Voltage Outer Loop I | 43 |
| Grid Frequency | 50 Hz | Three-Phase Bridge Gain K_PWM | 1 |
| Inverter Switching Frequency | 20 kHz | Grid Current Outer Loop K_P | 1 |
| Inverter Side Filter Inductance | 5 mH | Grid Current Outer Loop K_R | 47 |
| Grid Side Filter Inductance | 1 mH | Capacitor Current Loop K_e | 10 |
The PV array output power waveform is shown in the figure. By using the INC method, the PV array output power is maintained at 4000 W, achieving MPPT control of the PV array. The DC bus voltage waveform is shown in the figure. It can be seen that although the DC bus voltage fluctuates in the initial stage of grid-connected operation, due to the use of the voltage outer loop for stability, the DC bus voltage is basically maintained at around 600 V through this voltage stabilization control.
To verify the effect of the double current closed-loop control strategy of the LCL inverter, the A-phase grid current and grid voltage waveforms are extracted, as shown in the figure. The grid voltage is reduced by 30 times. It can be observed that the grid current and grid voltage maintain the same frequency and phase, indicating that the control strategy using double current loops can achieve unit power factor grid connection. By performing Fourier analysis on the A-phase grid current, it can be seen that the fundamental wave amplitude of the grid current is 7.954 A, from which the inverter output power is calculated to be about 3700 W, which is close to 4000 W. The FFT analysis of the A-phase grid current is shown in the figure. It can be seen that the harmonic content of the grid current is 1.35%, meeting the requirement that the grid current harmonic content is less than 5%, and it can effectively filter out high-frequency harmonics and suppress the resonance peak.
In summary, based on the LCL filter double-stage PV power generation system, this article establishes the mathematical model of the grid-connected inverter in the two-phase stationary coordinate system and studies the control strategy of the PV power generation system, using active damping to suppress the resonance peak of the LCL filter. The front-stage circuit uses the INC method to achieve MPPT control of the PV array; the rear-stage circuit uses the control strategy based on the PR-controlled grid current outer loop and the P-controlled capacitor current inner loop double current loop control to achieve LCL filter resonance peak suppression and unit power factor grid connection. A simulation model of the LCL filter-based double-stage PV power generation system is built in MATLAB/Simulink. By analyzing the simulation results, it is verified that the control method used in this article can achieve grid-connected control of the LCL grid-connected inverter, laying a theoretical foundation for further research on the control of PV grid-connected inverters. In the future, we will further optimize the control strategy studied in this article when environmental conditions change or other interferences occur.
The three phase inverter is a critical component in modern renewable energy systems, and its control strategies directly impact the efficiency and stability of power conversion. In this study, we focus on the three phase inverter with LCL filters to address harmonic issues and improve grid integration. The three phase inverter topology allows for efficient power flow from DC sources like PV arrays to the AC grid. The use of a three phase inverter in double-stage systems enables better voltage regulation and MPPT performance. Throughout this analysis, the three phase inverter’s role in maintaining power quality and mitigating resonance through advanced control methods is emphasized. The three phase inverter design parameters, such as switching frequency and filter values, are optimized to enhance the performance of the three phase inverter in grid-connected applications. Future work will explore adaptive control techniques for the three phase inverter under varying operating conditions.
Additionally, the three phase inverter’s response to grid disturbances can be improved by incorporating real-time monitoring and feedback mechanisms. The three phase inverter control algorithms, including PR and P controllers, ensure robust operation of the three phase inverter in diverse scenarios. The simulation results demonstrate that the three phase inverter with the proposed control strategy achieves high efficiency and low harmonic distortion. The three phase inverter’s ability to handle bidirectional power flow makes it suitable for advanced energy management systems. In conclusion, the three phase inverter is indispensable for modern power electronics, and ongoing research will further enhance the capabilities of the three phase inverter in renewable energy integration.