**ABSTRACT:**

The Proportional Resonant (PR) current controller provides gains at a certain frequency (resonant frequency) and eliminates steady state errors. Therefore, the PR controller can be successfully applied to single grid-connected PV inverter current control. On the contrary, a PI controller has steady-state errors and limited disturbance rejection capability. Compared with the L- and LC filters, the LCL filter has excellent harmonic suppression capability, but the inherent resonant peak of the LCL filter may introduce instability in the whole system. Therefore, damping must be introduced to improve the control of the system.

**PV INVERTER**

Considering the controller and the LCL filter active damping as a whole system makes the controller design method more complex. In fact, their frequency responses may affect each other. The traditional trial-and-error procedure is too time-consuming and the design process is inefficient. This paper provides a detailed analysis of the frequency response influence between the PR controller and the LCL filter regarded as a whole system.

**LCL FILTER**

In addition, the paper presents a systematic method for designing controller parameters and the capacitor current feedback coefficient factor of LCL filter active-damping. The new method relies on meeting the stable margins of the system. Moreover, the paper also clarifies the impact of the grid on the inverter output current. Numerical simulation and a 3 kW laboratory setup assessed the feasibility and effectiveness of the proposed method.

** ****KEYWORDS:**

- Single phase
- Grid-connected
- LCL filter
- Active damping
- Proportional resonant (PR) controller

**SOFTWARE:** MATLAB/SIMULINK

**CIRCUIT DIAGRAM:**

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** **Figure 1. Two-stage single-phase PV system with LCL-filter control scheme.

**EXPECTED SIMULATION RESULTS: **

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Figure 2. Grid voltage and injected current at full load with nominal parameters: simulation results. (a) Grid voltage sag; (b) grid voltage swell.

Figure 3. Grid voltage and injected current at full load with inductor *L*1 variation: simulation results. (a) Inductor *L*1 increased by 20%: grid voltage sag; (b) Inductor *L*1 increased by 20%: grid voltage swell; (c) Inductor *L*1 decreased by 20%: grid voltage sag; (b) Inductor *L*1 decreased by 20%: grid voltage swell.

Figure 4. Grid voltage and injected current at full load with inductor *L*2 variation: simulation results. (a) Inductor *L*2 increased by 150%: grid voltage sag; (b) inductor *L*2 increased by 150%: grid voltage swell; (c) inductor *L*2 decreased by 20%: grid voltage sag; (b) inductor *L*2 decreased by 20%: grid voltage swell.

Figure 5. Grid voltage and injected current at full load with capacitor *C *variation: simulation results. (a) Capacitor *C *increased by 20%: grid voltage sag; (b) capacitor *C *increased by 20%: grid voltage swell; (c) capacitor *C *decreased by 20%: grid voltage sag; (b) capacitor *C *decreased by 20%: grid voltage swell.

**CONCLUSION:**

The stability analysis of the system composed by a PR controller and an LCL filter together is not easy: the frequency responses may affect each other and the PR controller design becomes complex. The traditional method based on trial-and-error procedures, is too time-consuming, and the design process is inefficient. This paper provides a detailed analysis of the frequency response influence between the PR controller and the LCL filter.

**PR CONTROLLER**

In addition, the paper presents a systematic design method for the PR controller parameters and the capacitor current feedback coefficient, used in the active damping of the LCL filter. Using the new parameters, a numerical simulation shows that the system meets the requirements of stable margins and current tracking steady-state error. The robustness of the current controller is verified through several experimental tests carried out on a 3 kW platform varying the system parameters.

**INDUCTOR**

The Bode diagrams of the system varying inductor, capacitor, and grid impedance values confirmed that the controller parameters enhance robustness against the system parameters variation. Moreover, the system remains stable even in case of grid voltage fluctuation. Both the simulation and the experimental results assess the validity of the proposed design method.

**REFERENCES:**

- Carrasco, J.M.; Franquelo, L.G.; Bialasiewicz, J.T.; Galvan, E.; Guisado, R.C.P.; Prats, A.M.; Leon, J.I.; Moreno-Alfonso, N. Power-electronic systems for the grid integration of renewable energy sources: A survey.
*IEEE Trans. Ind. Electron.***2006**,*53*, 1002–1016. - Wessels, C.; Dannehl, J.; Fuchs, F.W. Active Damping of LCL-Filter Resonance based on Virtual Resistor for PWM Rectifiers—Stability Analysis with Different Filter Parameters. In Proceedings of the 2008 IEEE Power Electronics Specialists Conference, Rhodes, Greece, 15–19 June 2008; pp. 3532–3538.
- Castilla, M.; Miret, J.; Matas, J.; de Vicuna, L.G.; Guerrero, J.M. Control design guidelines for single-phase grid-connected photovoltaic inverters with damped resonant harmonic compensators.
*IEEE Trans. Ind. Electron.***2009**,*56*, 4492–4501. - Yi, L.; Zhengming, Z.; Fanbo, H.; Sizhao, L.; Lu, Y. An Improved Virtual Resistance Damping Method for Grid-Connected Inverters with LCL Filters. In Proceedings of the 2011 IEEE Energy Conversion Congress and Exposition (ECCE 2011), Phoenix, AZ, USA, 17–22 September 2011; pp. 3816–3822.
- Parker, S.G.; McGrath, B.P.; Holmes, D.G. Regions of Active Damping Control for LCL Filters. In Proceedings of the Energy Conversion Congress and Exposition (ECCE), Raleigh, NC, USA, 15–20 September 2012; pp. 53–60.