Advance Controller for Power Quality and Performance Improvement of Grid-Connected Single-Phase Rooftop PVS

—This article presents a robust controller for a single-phase single-stage photovoltaic systems (PVSs) converter connected to the grid. A high-efficiency single-phase single-stage converters are prone to double-frequency oscillations and dc-link voltage fluctuations when connected to a PVS. It introduces phase shift and injects harmonics in the grid current. To address this issue, a robust dc-link voltage controller is proposed. It can achieve a fast transient response with lesser overshoot under power intermittency and grid-side disturbances. A filter is employed to reduce the impact of switching frequency; however, a Lyapunov-based inner loop current controller with an active damping method minimizes the effect of resonance and achieves system stability. The proposed composite controller guarantees the system’s robustness against grid disturbances and parameter uncertainties. In addition, it eliminates the effect of phase shift and achieves zero steady-state error. Both the simulation and experimental results are presented to demonstrate the performance of the controller.

I N DISTRIBUTED generation (DG) systems, the advance- ment of renewable energy sources increases the role of small-scale photovoltaic (PV) integrated systems [1].These systems mainly focused on increasing efficiency, reliability, power density, and cost reduction [2].To achieve this, various converter topologies are discussed to improve the power density at a lesser cost [2], [3].Typically, more than one conversion stage reduces the power density and reliability of the system.Therefore, in grid-connected PV (GCPV) systems, single-stage power converters are convenient to achieve high efficacy and reliability.However, in single-stage GCPV systems, due to single-stage conversion, a rapid change in dc-link voltage dynamics may lead to stability issues.
The increased integration of PV-based systems as DG raises the concern of system dynamics and stability during grid disturbances, such as voltage sag and load change.To achieve the desired stability level, a fast dynamic response controller is inevitable.The dynamic analysis of such systems can be classified as the dynamic response of the dc-link voltage controller (typically in the range of 0.1 s) and the dynamic response of the current controller (typically within 0.01 s) [4], [5].Therefore, various control methodologies are adopted to improve the system's performance.This can be normally achieved by the development of a robust outer loop control for voltage regulation [6] and integration of an all-pass filter in the current controller [7].In a single-stage system, the GCPV system has to perform all operations related to the stable dc-link voltage, maximum power extraction from the PV source, and grid current reference generation.However, the major concerns of the single-stage GCPV system are the high power quality and stability.Moreover, the utilization of the LC L filter introduces additional poles, which causes a resonance issue and further influences the stability of the system [8].Therefore, a current controller with active damping is usually employed [9].This increases the requirement for a robust controller to address the PV-and grid-side disturbances.
Recently, nonlinear controllers have been proposed to improve the performance and suppress the disturbances [10].These nonlinear controllers enhance the system dynamics and achieve a large stability margin [11], [12], [13], [14].However, the feedback linearization approach discussed in [12] and [13] has low-power quality.In [14], an H ∞ controller is discussed for dc-link voltage regulation and µ synthesis current controller for grid-side control.It can achieve robustness against grid impedance variation with lesser number of sensors and compensates for the time delay.The focus is to improve both the transient response and disturbance rejection capability.However, it operates at a high switching frequency and has high dc-link voltage ripple and overshoot with higher controller complexity.An adaptive gain observer is used in [15] to achieve good disturbance rejection and reduce the sensitivity to noise.However, the inclusion of the nonlinear controller causes variable switching frequency and has a steady-state error in the grid current [10], [15].In [16], an active disturbance rejection controller (ADRC) is discussed to regulate the dc-link voltage of the GCPV system, which is imminent for power quality improvement.However, this method is discussed only for three-phase systems and has high complexity.In single-phase GCPV systems, the double-frequency oscillation across dc-link voltage increases the harmonics injected into the grid current and reduces the power quality of the system.Moreover, in a singlestage single-phase GCPV system, dc-link voltage fluctuation and phase shift are introduced due to the input PV power intermittency and double line frequency, respectively.Furthermore, during grid-side disturbances such as voltage sag and load change, these oscillations become more severe, which requires a fast transient response for achieving system stability.Moreover, the impact of dynamic and server load change is not discussed at the DG level.The voltage deviation across dc-link from its nominal value may damage the inverter switches or dc-link capacitor, which can further initiate the protection devices and cause an involuntary shutdown of the GCPV system [17].
To address the issues related to single-phase single-stage systems, various nonlinear current controllers and adaptive PI approaches for dc-link voltage control are discussed in [18], [19], and [20].In [18], a nonlinear PI (NPI) approach is utilized to reduce the harmonic content by scheduling the gain to the change in the error signal.However, with changes in the error signal, recalculation of the gain is required, which introduces a processing delay and necessitates advanced processors.An NPI predictive controller is proposed in [19] for a two-stage three-phase GCPV system, which gives high tracking performance.However, the utilization of the model predictive approach increases the complexity.Moreover, the grid voltage is considered balanced; thus, system uncertainties (such as inductance variation) and grid-side disturbances are not considered.An adaptive PI controller for dc-link voltage control of a single-phase grid-connected ac/dc converter is discussed in [20].It addresses the double-frequency oscillation issue and dc-link voltage fluctuation, considering a resistive load at dc-link.However, it has a slow dynamic response, high operating switching frequency, and limited grid current THD due to the utilization of the L filter.To reduce the effect of double-frequency ripple in the reference current generation, a notch filter-based approach is utilized in [21] and [22].However, it affects the transient response of the system.Moreover, an effective active decoupling method is discussed in [23] to eliminate the double-frequency ripple, which requires additional hardware for the circuit.In [24], a moving average filter (MAF) is utilized in the reference current generation loop to reduce the low-frequency current ripple.However, the utilization of the linear controller limits the dynamic performance and disturbance rejection capability.Furthermore, in a single-phase GCPV system, the perturbation and system parameter variation adversely affect the performance of the current feeding into the grid and dc-link voltage, which can jeopardize the stability under load change and grid disturbances [25], [26].
Therefore, to achieve stability in cohesion with fast transient response, an NPI controller in conjunction with the Lyapunovbased inner loop controller is proposed in this article.Moreover, an MAF is employed in the current reference generation loop to eliminate the effect of double-frequency ripples and reduce the grid current harmonics.The NPI controller in the outer loop can provide a fast transient response and good disturbance rejection by adaptively adjusting the gain based on the input error signal.Thus, it renders a high gain when the dc-link error is small and a low gain when the error is high.The proposed NPI controller counteracts the delay introduced by the MAF in the current loop and achieves unity power factor (upf) operation.Moreover, the proposed control loop introduces a switching function to eliminate phase delay and limit noise sensitivity.Furthermore, the Lyapunov-based inner loop current control helps to attain stability despite internal and external disturbances, as well as parametric uncertainties, and renders active damping by including a capacitor voltage loop.A proportional-resonant (PR) controller is also employed in the inner loop to ascertain the current from the inverter and attains zero steady-state error for the grid current.The proposed controller can address the major issues related to a single-phase single-stage GCPV system.It reduces the effect of the double-frequency oscillation in the reference current generation, thus improving the current quality.Moreover, by achieving upf operation, it eliminates the effect of phase shift caused by loop ripple [17].Furthermore, it can provide a fast transient response under both PV-side intermittency and grid-side disturbances.
The major contributions of the work are highlighted in the following.2) The proposed NPI controller with MAF can effectively reduce the harmonics in the reference grid current, achieving fast tracking of dc-link reference and robustness against system disturbances.3) A Lyapunov-based inner loop current control can assure the stability of the GCPV system against grid-side uncertainties and reduce the issue of resonance in the grid current.

II. SYSTEM MODELING
Fig. 1 depicts the schematic of a single-phase PV integrated system connected to the grid with an LC L filter.A stable dc-link voltage can be obtained utilizing a capacitor (C dc ), connected between the PV array and the voltage-source inverter (VSI) for a single-stage conversion.The operation of the single-stage GCPV system can be described by the state space model in the following equation: where τ i (= L i /r i ) and τ g (= L g /r g ) represent the inverterand grid-side inductor time constant, respectively.The inverter output voltage v i = s u .V dc , and s u is the switching function of four inverter switches, where u denotes inverter switches {1, 2, 3, 4} to control the inverter system.This can be further defined as s u = S u + s u , which includes the switching function in steady-state and perturb deviation of u in the system.The proposed controller utilizing the switching function s u can further control the state of the system to force the grid current to become sinusoidal and in phase with the grid voltage.The modeling of the system can be described as grid-side current control i g and PV-side dc-link voltage control v dc .Thus, the state variables for grid-side control and PV-side control can be defined by the following equation: where i g , i i , v c , and v dc are the measured values of the GCPV system and i gref , i iref , v cref , and v dcref are the estimated references of the proposed controller.In the steady state, assuming that references track the measured values and s u = S u , the state variable (3) can be applied in the model (1), which simplifies the model as where ẋ is the derivative of x.

III. DC-LINK CONTROL AND CURRENT QUALITY IMPROVEMENT
The proposed controller for a single-stage single-phase GCPV system is shown in Fig. 2. To operate a solar array efficiently at its maximum power point (MPP), an incremental conductance-based MPP tracking (MPPT) algorithm is employed, as shown in Fig. 3.It ensures precise and fast convergence of PV control with minimal computational burden.The MPPT control ensures a consistent dc-link voltage (v * dc ) while directing the maximum PV power to the grid [23], [27].Furthermore, the dc-link voltage regulates the magnitude of grid current, and a maximum power feedforward loop defined by ( 6) is utilized to improve MPP tracking.The feedforward is crucial to regulate the maximum power from PV to the grid, even in the presence of voltage fluctuations.To improve the dynamic response and reduce the effect of double line frequency, a combination of NPI with MAF control is proposed.The maximum reference grid current can be described as where I m is the magnitude of the maximum reference grid current, I ff is the feedforward current considering no reactive power feeding into the grid for an upf operation, P pv is PV power obtained from MPPT algorithm, V gm is the magnitude of the grid voltage, and I loss is the loss component obtained.The loss component can be regulated by the proposed outer loop controller, which helps to regulate the dc-link voltage and minimize the effect of double-frequency ripple in the generated reference grid current.Furthermore, the generated maximum reference grid current is fed to a robust Lyapunov-based inner loop current controller to achieve fast dynamic response and stability under disturbance with zero steady-state error.However, to achieve high-quality grid current, the resonance damping is essentially for an LC L filter-based system.Therefore, a capacitor voltage loop is accumulated in the proposed control approach, which improves the power quality and assures the global stability of the system.

A. Proposed DC-Link Voltage Control
In the GCPV system, the current is controlled as an inner loop with a higher bandwidth relative to the outer voltage loop.Thus, the dc-link can be modeled as a state variable, considering that it is a single integral plant, which generates the input variable to the current controller.Furthermore, considering u as input and y as an output of dc-link controller, the plant can be represented as where d i is an input disturbance of the system [28].In terms of error, the desired output for dc-link controller can be written as In the closed-loop system, with the presence of the disturbance d i , for the absolute tracking of the reference, the control logic must satisfy that x 4 (t) → 0 when t → ∞ in a closedlooped system.Thus, a standard PI controller can be usually employed as where proportional and integral gains are represented by k p and k i , respectively.Using the standard control design methods such as Bode diagram and pole placement with optimization, the voltage control loop can be tuned [17].However, due to 90 • phase lag of the integrator, it persists the saturation issues, thus affecting the stability of the system.Therefore, the integral gain should be reduced to zero during system transients to obviate overshoot, saturation, and instability.An NPI-based dc-link voltage control is proposed to accomplish a fast dynamic response.It converges the tracking error x 4 between dc-link voltage, v dc , and reference dc-link, v dcref , obtained from the MPPT algorithm to zero with lesser overshoot.In the proposed dc-link controller, a nonlinear gain function, fal(x 4 ), is introduced, which, by using a nonlinear mechanism, allows larger gains with smaller errors and smaller gains with larger errors.This leads to a reduction in steady-state error, high disturbance rejection capability, and robustness of the controller where m is the gain of a nonlinear function fal(x 4 ), sgn(x 4 ) is a signum function, and δ p can be selected to limit the gain of the function fal(x 4 ).The linear operation of the function fal(x 4 ) can be accrued with m = 1.However, to converge the dc-link error and x 4 to zero in finite duration, the value of m must be less than 1.Therefore, in order to mitigate the bounded disturbance encountered by the nonlinear function fal(x 4 ), the selection m should be restricted to a narrowed bounded range, i.e., when 0 < m < 1.Furthermore, it is also possible to achieve zero steady-state error with the function fal(x 4 ) without using the integral control, i.e., when m → 0. Therefore, to achieve faster convergence, fal(x 4 ) should operate as a nonlinear gain function by properly selecting gain m (i.e., 0 < m < 1).
In the presence of external disturbances, by eliminating the phase delay due to integral control, the function fal(x 4 ) can accomplish an enhanced stability margin and reduce the steady-state error to zero.However, It reduces the controller's sensitivity to noise [28].Hence, an integral controller is introduced to further lower the gain, during a steady state when the error is small.This can be acquired by a function gal(x 4 ) defined in the following equation: By considering the operation of functions in (10) and (11), the modified NPI controller can be deduced as where G k p = k p max fal(x 4 ) and the outer-loop voltage controller for dc-link.This accelerates the dynamic response by limiting the open-loop gain and improves the filtering capacity of double-frequency ripple.However, the output of the NPI controller contains an amount of double-frequency ripple, which can increase the harmonic content in the reference grid current due to x 4 .Therefore, an MAF filter is implied [30] to attenuate the low-frequency component in the reference current, as shown in Fig. 2, which can be expressed as where T s is the sampling time, which is considered 25 µs.
The MAF can filter the frequency harmonic component without influencing the dc component.Therefore, the total loss component across the dc bus can be described as Thus, dc-link error, x 4 , can be modified by the outer loop controller gain given as where G k is the gain of the outer loop voltage controller, which can help to regulate the dc-link voltage with the nonlinear gain corresponding to the dc-link error signal.

B. Lyapunov Function-Based Current Control
The Lyapunov function-based inner loop current control can achieve global stability around its equilibrium point.The single-stage GCPV system reaches the equilibrium point when the state variables x 1 = x 2 = x 3 = x 4 = 0 [31].Thus, the energy dissipation across the state variables converges to zero.
In a PV-based VSI system with an LC L filter, global stability can be obtained considering the energy stored in the capacitors and inductors, which can be deduced utilizing the Lyapunov stability theorem.The Lyapunov function can be expressed as As ( 16) is a positive definite scalar function, according to the Lyapunov direct method, the GCPV system is considered to achieve global stability when the derivative of ( 16) is a negative definite Substituting ( 4) into (17) gives Applying the defined state variable from (3), we can get When the estimated system parameters match the actual values, V (x) is always negatively rendered that the perturbed control input can be selected as where α i is a positive scalar gain, i.e., α i > 0 such that s u becomes a negative coefficient.However, under parametric uncertainties, the selected value of α i should be large enough to dominate (19) to V (x) become negative definite.Thus, by considering (20), the switching function s u can be obtained as where In a closed-loop single-phase GCPV system, ( 22) can assure global stability.However, to mitigate the steady-state error in the grid current due to parametric perturbations and minimize the effect of a differentiator, a PR controller G PR (s) can be implied [31] G PR (s) = K p + 2K r ω c s s 2 + 2ω c s + ω 2 (23) where ω and ω c are the natural frequency and cutoff frequency, respectively.The PR controller reduces the steady-state error to zero and generates the reference inverter current, as shown in Fig. 4 Although (21) with PR controller can achieve global stability, it is incorrigible to dampen out the effect of the resonance due to only inverter-side current compensation.Therefore, for achieving the damping in the grid current, (20) can be modified by including the capacitor voltage error (x 3 ) where α v is a capacitor voltage feedback gain.The effect of the double-frequency ripple, present in the dc-link error, x 4 , can be minimized by an NPI with MAF control, which modifies the grid current reference in (25) to obtain (26).Thus, the final switching function can be obtained as (26), and the control logic is shown in Fig. 4 s

C. Design Guideline
The proposed nonlinear controller is composed of standard PI parameters k pmax and k imax and nonlinear functions fal(x 4 ) and gal(x 4 ), which include the selection of m, δ p , and δ i .
The design approach required tuning the gain of the standard PI controller for desired dc-link voltage dynamics, which can be considered as the maximum the tuned gains k pmax and k imax .Furthermore, the design approach is done by theoretically analyzing the parameter selection depending upon the behavior of the nonlinear functions on different values within a limited range [18], [28].
The gain factor m can be selected such that 0 < m < 1 yields a high gain when the dc-link error is small and a low gain for the higher value of error.It ameliorates the dynamic performance and tends to achieve zero steady-state error in dc-link.The selection of δ p for the function fal(x 4 ) can preclude the chattering phenomenon by limiting the gain to k pmax /δ (m−1) p [32].However, to incorporate an integral control during steady state (i.e., during small error), a function gal(x 4 ) is applied by adjusting the value of δ i (selected as δ i < δ p /10), which further restrains the gain of the NPI controller.The optimum adjustment of the gain related to fal(x 4 ) and gal(x 4 ) can ameliorate the transient performance and disturbance rejection ability.The selection of k pmax = 55 and k imax = 0.001 is similar to the conventional PI control discussed in [17], considering the gain of the nonlinear function m = 1.Furthermore, to improve the performance of the dc-link voltage control, the parameters of the NPI controller are selected as m = 0.325, δ p = 0.214, and δ i = 0.01.
The outer loop dc-link controller has a similar tuning method to standard PI control dc-link voltage with improved dynamic performance and high disturbance rejection.Therefore, the proposed controller can directly replace the standard PI controller after selecting the bounded limit for m (i.e., 0 < m < 1).
The inner loop current controller design guideline depends upon the selection of α i and α v gains, as described in [31].The proper selection of the gains corresponds to a fast dynamic response and lesser harmonics response in the grid current.Thus, the optimum value of α i can achieve low current harmonics and provide global stability to the GCPV system.However, proper selection of α v can achieve resonance damping in the grid current.Therefore, by the analysis of the root locus of the dominant closed-loop poles, the optimum values of α i and α v are selected as −0.0023 and 0.287, respectively.
The design of the dc-link voltage controller also depends on the proper selection of dc-link capacitor C dc [17], [23], which regulates the dc ripple around a reference value.The dc-link capacitors can be chosen as where ω g is the grid angular frequency, δv dc is the dc-link ripple, and P g is the power injected into the grid.The capacity of the dc-link capacitor, C dc , helps to reduce ripple voltage and vice versa.When C dc is large, however, the size, weight, and cost of the converter increase.

D. Stability Analysis
The stability of the proposed controller ( 26) can be defined by the stability of the Lyapunov-based inner loop control and the NPI-based outer loop control, operating as a cascaded control structure.The stability of the outer loop control u(t) can be defined by the stability of the proportional control G k p = k pmax fal(x 4 ), which contains a nonlinear function fal(x 4 ), as described in (10).In the NPI controller plant (8), the disturbance w can be ignored for the sake of simplicity of the stability analysis.Then, the final effective nonlinear feedback control, without limiting the gain of the controller, can be written as The proposed control law in (28) can guarantee the asymptotic stability of the closed-loop system when k pmax is selected such that [28] k p max > sup considering the plant of the system unknown and f (x 4 ) as the accounts for the nonlinear dynamics of x 4 in the system.To validate the above, a Lyapunov function V (x 4 ) = x 2 4 /2 is selected.Then, the derivative of V (x 4 ) can be As per Lyapunov stability theorem, the stability of the system can be achieved when (30) satisfies the following conditions.1) If x 4 f (x 4 ) ≥ 0, and k pmax > 0, then s V (x 4 ) < 0 for x 4 ̸ = 0. 2) If x 4 f (x 4 ) < 0, and k pmax > 0 then for V (x 4 ) < 0 k p max |x 4 | m+1 > |x 4 f (x 4 )|, or equivalent to (29).Therefore, the asymptotic stability of the closed-loop control law (28) can be defined by the proper selection of the controller gains k pmax and m.
The stability of the inner loop Lyapunov-based controller can be determined by the closed-loop transfer function of the reference grid current to the actual grid current [31].Linearizing (1), (3), and ( 26) around the equilibrium point can give the characteristic in the following equation: where It is clear that all coefficients of the characteristic equation are positive constants, considering that α i < 0, α v > 0, K p > 0, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE I
PARAMETERS FOR SIMULATION AND EXPERIMENT Fig. 5. Simulation results showing performance of the proposed controller in steady state while transferring rated power into the grid at upf. and K r > 0. Therefore, all poles are positioned in the left half of the s-plane if 4 ) > 0 are satisfied.Hence, by selecting the proper gains of the controller, stability can be ensured to satisfy the above conditions.

IV. RESULTS AND DISCUSSION
Tests of the proposed controller are conducted in MATLAB and experimentally verified with the dSPACE MicroLabBox-based platform against the PV array, grid, and load disturbances.The detailed parameters related to the PV array and single-stage single-phase GCPV system with an LC L filter are presented in Table I.

A. Simulation Results
1) Performance Under Steady State and Perturbation of Solar Irradiance: Fig. 5 shows the performance of single-stage GCPV in a steady state at PV irradiance of 1000 W/m 2 at 25 • .At the point of common coupling (PCC), the grid current i g remains in phase with grid voltage v g under the upf operation.It can be observed that the inverter current, i i , has high harmonics, which is further minimized in generated grid current i gref .The proposed Lyapunov-based inner loop controller shows that the grid current i g tracks the reference grid current i gref and diminishes the steady-state error to zero.With an active power of 3 kW, a peak grid current of 18.23 A (13 A rms) is fed into the grid at a THD of 1.34%.The active damping employed can eliminate the effect of resonance.However, the effect of double line frequency on grid current, i g , can be mitigated by the proposed NPI with an MAF and proceeds with a stable dc-link voltage.
Fig. 6 shows the performance of the proposed controller under perturbation of the solar irradiance, considering a step change from 1000 to 500 W/m 2 and 500 to 1000 W/m 2 at 25 • .The proposed NPI controller shows faster dynamics with change in irradiance, which keeps the dc-link stable.The dc-link voltage shows the fast convergence on a timescale of 60 ms for both step-up and step-down changes in irradiance.The proposed dc-link controller can conveniently suppress the disturbances due to the power change on the PV side.As shown in the zoomed-in view in Fig. 7, with the fast convergence of the dc-link, the grid current i g becomes stable within one cycle to ensure the stability of the GCPV system.The sudden change in irradiance at 0.505 s reduces the grid current to 9.5 A (peak value), as shown in Fig. 7, which increases the THD to 2.43%.However, it is under  the acceptable range of IEEE standard 1547-2003.Moreover, as shown in Fig. 8, the magnitude of the reference grid current I m gref generated does not contain any second harmonic oscillation due to the presence of double-frequency ripple in the dc-link.
2) Performance Under Grid-Side Disturbances: The robustness of the proposed controller to the grid disturbances is observed, as shown in Fig. 9.A voltage sag of 50% is considered for a duration of 1 s in the grid voltage at PCC.Under severe grid disturbance, the dc-link voltage V dc is stable, and the grid current I g has a low ripple with the upf operation.An increase in the grid current is due to the decrease in voltage at PCC, which keeps the input PV voltage and output active power feeding into the grid balanced.The dc-link voltage across the inverter is stable at the maximum power generated from the PV system.However, the current across the inverter increases to achieve maximum power transfer with no reactive power, Q g compensation into the grid.Furthermore, a reduction in load current can be assumed to compensate for the power.
Moreover, with the increase in the grid current, the active power P g decreases due to higher losses across the inverter and filter resistance.It can be observed that the grid current can be increased between 2 and 3 s and has a %THD of 0.52%.The dc-link fluctuation settled within 80 ms with an overshoot of 10 V.The grid current is stable during the disturbance and restored to normal under three cycles during grid voltage fluctuation.
3) Performance Under Sudden Connection and Disconnection of Local Load: The dynamic response under sudden load connection and disconnection of 2.1-kW local load at PCC is tested.The proposed controller keeps the dc-link stable and the PV integrated system synchronized with the grid, as shown in Fig. 10.However, a step change in load causes a steep change in grid current, with an increase in the grid current THD to 3.12% from 1.34% during steady state, which is under IEEE standard 1547.The load transient gets settled instantly, and the power transfers from solar PV to the local load at PCC.Therefore, the active transfer to the grid is reduced to 900 W.Moreover, the grid current is still tracking the reference at upf without having a stability problem.It is observed that when the generated capacity is higher than the household consumption or local load, the generated excess power is considered to be exported into the grid.
4) Performance With Variation in Filter Parameters and Grid Impedance: Fig. 11(a) exhibits the steady-state performance of the grid current and voltage with +20% variation in LC L-filter parameters.The grid current is still in phase with the grid voltage, while the rated power is transferred into the grid.The proposed NPI with the Lyapunov controller shows robustness to parameter uncertainties.Moreover, in Fig. 11(b), the performance of the system with grid impedance variation at PCC is tested.The grid voltage and current are in phase with each other when the grid inductance, Z g , changes from 0.25 to 2.25 mH.

B. Experimental Results
Experimental analysis on a hardware testbed consists of Semikron inverter switches SKM100GB063D with LV25 voltage and HX 25-P current sensors.The complete setup and block representation of the connection for experimental platform is shown in Fig. 12.The controller was compiled into a dSPACE MicroLabBox for generating the switching pulses at a sampling period of 25 µs.
1) Performance Under PV-Side Disturbances: The performance of the proposed controller is validated under PV-side  disturbance, considering a sudden change in irradiance, as shown in Fig. 13.The proposed controller sustains the stability of the dc-link for a ramp change in irradiance from 1000 to 700 W/m 2 and then to 1000 W/m 2 .The proposed NPI controller with MAF shows a fast transient period of 80 ms with a lesser overshoot of 4.7%.Despite input PV power fluctuations, the fast convergence of the proposed dc-link controller ensures the stability and robustness of the system.Moreover, it mitigates the double-frequency ripple.Hence, transfer high-quality power with current THD of 1.4% and 2.03% in 1000 and 700 W/m 2 , respectively.Furthermore, it prevents phase deviation and reduces the third harmonic injection.
2) Performance Under Grid-Side Disturbances: The disturbance rejection capability of the proposed controller is tested under grid disturbance, considering a 50% voltage sag in the grid voltage at PCC.In Fig. 14, it can be seen that with the sudden voltage sag, the dc-link is kept stable at MPP by the proposed controller with a maximum overshoot of 3.5% and a transient period of 110 ms.Moreover, by eliminating the effect of phase shift due to dc-link ripple in single-stage single-phase GCPV systems, the grid current and voltage are in phase, which gives the upf operation.Moreover, to maintain grid-to-PV power balance during voltage sag periods, the grid current increases.
3) Performance With the Sudden Change in the Local Load: The dynamics of the proposed controller are tested with sudden connection and disconnection of 2.1-kW local load, as shown in Fig. 15.The load current I L , grid current I g , power feeding into the grid P g , and the dc-link voltage V dc are exhibited to present the dynamic performance.When a load transient of 2.1 kW is employed, it introduces a steep change in the grid current.However, the proposed controller maintains the stability of the system under load disturbances.During a load change of 2.1 kW, a change from 3 kW to 900 W can be detected in power feeding into the grid, which increases the grid current THD to 3.34%.However, with the proposed controller, it is under IEEE standard 1547.Moreover, due to  the proposed controller, conserving the stability of the system at MPP during load disturbance, the dc-link voltage does not show any change.
Fig. 16 shows the effect of the sudden connection of a 4.5-kW load, which is higher than the maximum available PV power of 3 kW.The controller, ensuring the stability of the GCPV system, allows a negative power of 1.5 kW to the local load.The sudden higher loading forces the grid current I g and 180 • phase difference with the grid voltage V g .

C. Comparative Performance Evaluation
A comparative performance evaluation is studied in Table II with existing state-of-the-art literature [14], [20], [21], [23], [25], [27], [33].The proposed controller for the single-phase single-stage GCPV system has a minimum current THD of 1.34%.Moreover, the grid current settled in 1.5 cycles with a lesser overshoot of 3%, which is faster than its counterpart due to the NPI-based controller in conjunction with the Lyapunov controller.It has comparably equal performance to the [23]; however, [23] utilizes a passive LC resonant circuit across dc-link as an external hardware to eliminate the double-frequency ripple.Moreover, it has two extra switches than the conventional single-phase system and has a higher switching frequency, which can increase the overall power loss across the converter.Fig. 17 shows a comparative performance of the dc-link controller under a change in irradiance from 1000 to 500 W/m 2 at 0.805 s and 500-1000 W/m 2 at 1.505 s.Both NPI and basic PI controllers maintain the dc-link voltage stability with sudden changes.However, the proposed NPI has a settling time of 60 ms, which is faster than the standard PI controller of 100 ms.Moreover, with the introduction of MAF, the dc-link ripple is 10 V, which is under the maximum limit of 10% of the rated voltage across the capacitor.It is well observed that the proposed controller can effectively address the major issues of the single-phase single-stage GCPV system.

V. CONCLUSION
A robust cascaded nonlinear controller is proposed to improve the performance of the grid current for a singlephase single-stage GCPV system with an LC L filter.In the case of both internal and external disturbances, the inner loop Lyapunov current controller can ensure global stability and robustness.Moreover, an active damping and zero steady-state error can also be accomplished.Furthermore, the proposed nonlinear controller for outer loop control has fast dynamic performance against external disturbances.The inclusion of an MAF filter eliminates the effect of double-frequency ripple and reduces the harmonics in grid current.Therefore, the combination of the proposed outer loop controller with filter and feedforward term improves the dc-link voltage regulation and compensates for the phase delay.With a high gain for lower error values and a low gain for high error values, it can ensure robustness and stability against PVside disturbances.Furthermore, a robust inner loop controller with cohesion of the proposed outer loop eliminates the effect of phase shift in the grid current and improves the power quality.A hardware testbed with the proposed controller tested the effectiveness under various PV-and grid-side disturbances.Hence, the proposed controller can be recommended for single-phase rooftop PV to the grid-integrated system.

Fig. 1 .
Fig. 1.Single-stage PV integrated grid-connected inverter system with an LC L filter.

Fig. 6 .
Fig. 6.Simulation results showing dynamic performance of GCPV system with PV-side disturbances.

Fig. 7 .
Fig. 7. Zoomed-in view showing the grid current and grid voltage under step change in irradiance.

Fig. 8 .
Fig. 8. Zoomed-in view of proposed NPI controller performance, showing reference grid current and dc-link voltage.

Fig. 9 .
Fig. 9. Simulation results showing the performance of the controller under grid-side disturbances, considering 50% voltage sag in the grid voltage.

Fig. 10 .
Fig. 10.Performance of the controller under sudden connection and disconnection of the local load at PCC.

Fig. 11 .
Fig. 11.Simulation results showing the robustness of the controller under parametric uncertainties.(a) Considering 20% change in filter parameter and (b) with high grid impedance (Z g = 0.1 , 4.25 mH).

Fig. 12 .
Fig. 12. Experimental platform for single-stage system.(a) Complete setup.(b) Block representation of the connection.

Fig.
Fig. Experimental result showing the robustness of the controller under PV intermittency of 1000-700 W/m 2 .

Fig. 15 .
Fig. 15.Experimental result exhibits the robustness of the proposed controller under sudden connection and disconnection of 2.1-kW load.

Fig. 16 .
Fig. 16.Experimental result exhibits the robustness of the proposed controller under sudden connection and disconnection of 4.5-kW load.

Fig. 17 .
Fig. 17.Performance of dc-link controller under a change in irradiance with NPI and basic PI controller.

TABLE II COMPARATIVE
ANALYSIS Fig. 14.Experimental result showing the robustness of the controller under 50% voltage sag.