**1. Introduction**

The rapid penetration of renewable energy sources (RESs) connected to the grid and distribution systems with power electronic converter topologies has changed the expected grid requirements to guarantee an appropriate performance under grid faults. In addition to the performance and reliability of the system under power electronic circuits in normal conditions, stability and grid support under grid faults are crucial due to restrictive grid code requirements [1,2]. Moreover, stability and reliability of the grid-connected inverter (GCI) under grid voltage faults must be considered for microgrid applications [3–8] with battery storage systems [9,10].

In particular, the most common fault type in electrical networks is unbalanced voltage conditions, which can easily occur in any voltage sags, and cause double-frequency power oscillations. In addition to requiring a positive sequence of active power (P) and reactive power (Q) injection by RESs through the GCI, these oscillations must be compensated for by injecting appropriate negative-sequence current sets. However, this aim cannot be realized by using conventional methods.

Proportional-integral (PI) controller-based vector control methods for GCI structures considering balanced voltage conditions are given in [11–13]. These methods decouple grid currents into P and Q generating components, and the PI current controllers achieve stable operation. However, this popular structure is fragile under voltage problems due to a low bandwidth of the PI controllers.

One of the first contributions related to the control of GCIs under unbalanced voltages is given in [14,15], by using decoupled PI control of positive- and negative-sequence dq frames. This structure is also known as the double synchronous reference frame (DSRF) method, and is used by many researchers [16,17]. Proportional-resonant (PR) [18,19] controllers are also extensively used for GCIs, which feed forward a resonant controller tuned at double the grid frequency. Direct power control methods [20,21] control the required power without additional inner current loops. The method given in [22] gives an enhanced operation of decoupled DSRF (DDSRF) operation by using feed-forwarded resonant controllers. Model-based predictive control [23,24] methods minimize the cost function by predicting the future current and power components of the GCI under an unbalanced voltage operation.

The decoupled control of synchronously rotating positive- and negative-sequence dq currents, as given in [14,15], is an effective method for the control of GCIs. However, this method suffers from simultaneously dissipating active and reactive power oscillating components. An instantaneous power theory calculations-based independent P and Q control strategy is given in [25], by proposing different current reference calculations depending on the power requirements. A robust power flow algorithm, which is based on the disturbance rejection control algorithm, is given in [26]. These methods given in [23–26] can independently dissipate P and Q double-frequency oscillations. However, the shape and magnitude of non-sinusoidal injected currents highly increase current harmonics in the system, which limits the effectiveness of these methods.

Three-phase four-leg inverters can generate sinusoidal voltage waveforms in a wide range of nonlinear operating conditions for more sensitive loads, such as for data transfer and military purposes, as they can also issue power quality requirements [27,28]. However, an additional phase-leg and inductance complicates the circuit and reduces the overall efficiency.

Grid synchronization is of great importance for robust control of GCIs; fast and accurate estimation of grid voltage parameters is essential to operate under grid faults. Different Phase Locked Loop (PLL) algorithms are available in the literature, aiming to operate under grid voltage problems [29–32]. It was assumed in this study that symmetrical positive- and negative-sequence component decomposition of the grid voltage was properly realized, such as is given in [33] under grid faults.

A disturbance observer (DOb)-based controller is a simple and robust structure that estimates external disturbances and uncertainties; thus the effect of disturbances and uncertainties are suppressed [34]. Estimated disturbances and system uncertainties are fed forward to the inner control loop; thus the robustness of the system is obtained. An additional external controller could be cascaded to achieve the desired performance goals, such as power and/or speed in electrical systems, as the DOb controls uncertain plant and removes the effect of external disturbances in the inner control loop.

Doubly fed induction generator (DFIG)-based wind turbines are also very fragile under grid voltage problems [7,8,35–38], and it can be considered that problem solution techniques applied to DFIG applications can be utilized in GCI applications. DOb-based current controllers are applied to DFIGs and GCIs in [39,40] by considering robustness against parameter variations under balanced voltage sets. However, this method must be carefully tuned to suppress double-frequency oscillations. This study modeled the grid dynamic model in synchronously rotating, symmetrical positive- and negative-sequence dq frames. Therefore, decoupled positive- and negative-sequence dq current components were independently controlled by achieving robust control under grid voltage faults. In addition to the availability of simultaneous positive- and negative-sequence current injection, the proposed method was not affected by other external disturbances and uncertainties, such as grid impedance variations.

Integral terms in conventional PI controllers must be carefully tuned to prevent unwanted overshoots for a wide range of operations. In addition, windup effects of the integrator must be considered for real-time systems. Instead of conventional PI controllers and fed-forwarded parameter-dependent cross-coupling terms, proposed proportional controllers with a low-pass filter DOb are sufficient for robust operation, as the DOb accurately estimates and feeds forward uncertain terms. The control structure is simple and can be applied in real-time systems.

The main contribution of this study is a proportional decoupled current controller with a fed-forwarded low-pass filter DOb, which satisfies positive-sequence power requirements by independently controlling negative-sequence currents. The main advantage of this P + DOb current controller is to bring freedom from the sensitivity of the controllers with regard to variations in the grid parameters during operation for various reasons. Other methods outlined in [23–26] simultaneously control P and Q oscillations, as well as robustly satisfy positive-sequence power requirements. However, these methods inject non-sinusoidal currents to the grid at the instant of unbalanced voltage conditions. Conventional PI controllers are sensitive to parameter variations and anti-windup effects. This is the first reported study for a decoupled dq current control structure by using symmetrical component decomposition and estimating the disturbances with the DOb concept. The study was implemented on a Matlab/Simulink (2014B, MathWorks, Natick, MA, USA) simulation platform.
