## 1 Introduction
### Decoupling of Active and Reactive Powers  
Knowing that the DC-linked voltage control of grid-connected inverters is performed via the active current control channel, and reactive power injection is achieved by the reactive current control channel, the decoupling of the active and reactive current channels is a necessary demand to improve the system's overall performance and independent control of the active and the reactive powers [25]. In an inverter with an L filter, the decoupling between active and reactive power in a synchronous dq frame is achieved by feed-forward signals into the current control loop. In inverters with an LCL filter, the control system is a multi-input-multi-output (MIMO) system (2 input-2 output) with tight coupling between channels; a simple feed-forward scheme cannot provide sufficient decoupling for the system [29]. Further to the above-mentioned importance of decoupling, the potential instability issue is another aspect which necessitates the channels decoupling for MIMO systems [29]. In other words, the strong coupling between channels in MIMO systems may cause instability of the system and should be avoided. To tackle this issue, a pre-controller based on the multivariable control theory is used to decrease coupling,which makes the system column or row dominant. However, the pre-controller cannot guarantee complete decoupling [29]. To compare the different existing approaches, Table 1 is provided. In this table, the available methods in the literature are compared considering different aspects, including (i) decoupled control of active and reactive currents, (ii) stability margin and resonance damping capability, (iii) the number of needed sensors, and (iv) complexity and order of controller. Also, the proposed method is included in this table, and the results of comparison show the superiority of the proposed method compared to existing methods. It should be mentioned that all characteristics of the proposed method, indicated in Table 1, are demonstrated in theory and simulation throughout the rest of the paper. As a conclusion for the above propositions, to the best of the authors knowledge, there is a lack of a suitable control scheme which simultaneously considers both demands of (i) damping the resonant modes and (ii) the decoupling of active and reactive powers for inverters with an LCL filter. Keeping the number of sensors at minimum is another required criterion. This paper proposes a non-linear control method for a grid-connected inverter with an LCL filter that satisfies both requirements. In the proposed scheme, the minimum number of sensors is used since only grid-side currents are measured directly, and inverter-side currents and capacitor voltages are estimated using a reduced-order Luenberger observer. Having less sensors, in addition to cost reduction, can improve system reliability. Furthermore, a new scheme is presented to determine the phase margin (PM) of current control loop. The computational and PWM delays are included in the in tuning of current control loops. Based on the above explanations, the objectives of the paper are as follows:  
* the decoupling of active and reactive current channels and corresponding independent control of active and reactive powers;
* effective damping of resonant modes caused by an LCL-filter;
* using the minimum number of sensors, leading to cost reduction and improved system reliability;
* developing a parameter-tuning approach for the studied MIMO system using well-known criteria of phase and gain margin;
* consideration of computational and PWM delays in the control loop and controller parameters tuning.