Comparative Evaluation of Control Strategies for A Filterless Three-level Grid-Connected Photovoltaic Inverter

The rapid expansion of photovoltaic (PV) energy conversion systems has intensified research into high-efficiency and high-power-quality grid-connected converters. As the penetration of PV systems continues to increase, ensuring efficient and low-distortion power injection into the utility grid becomes a critical challenge [1]. Among the various power converter topologies, multilevel inverters, particularly three-level Neutral Point Clamped (NPC) structures, offer significant advantages over conventional two-level inverters by reducing voltage stress on semiconductor devices and improving output waveform quality with lower total harmonic distortion (THD) [2, 3].

Traditionally, grid-connected inverters rely on output filters such as Inductor (L), Inductor-Capacitor (LC) and Inductor-Capacitor-Inductor (LCL) filters, to attenuate switching harmonics and meet grid interconnection standards. However, these filters increase system complexity, cost, and losses, and may introduce resonance issues, especially under weak grid conditions. As a result, filterless grid-connected inverter configurations have recently attracted growing attention. In such systems, the control strategy plays a crucial role, as it must compensate for the absence of passive filtering while ensuring high current quality and stable operation under dynamic conditions such as irradiance variations. In this work, the term "filterless" refers to the absence of dedicated LC or LCL output filters, while only the inherent grid inductance, including the line inductance, is considered, without adding any external filtering components.

Several control strategies have been investigated to address these challenges. Classical methods such as Hysteresis Current Control (HCC) are widely used due to their simplicity and fast dynamic response. However, they typically suffer from variable switching frequency and degraded performance under rapid irradiance changes, leading to increased current distortion [4]. Pulse Width Modulation (PWM)-based control strategies offer fixed switching frequency and improved harmonic distortion, but their performance strongly depends on controller tuning and may be limited under highly dynamic conditions.

In contrast, Model Predictive Control (MPC) has emerged as a powerful alternative in power electronics applications. MPC predicts the future behavior of the system and selects the optimal switching state by minimizing a cost function, enabling improved current tracking and reduced THD. Several studies have demonstrated the effectiveness of Finite Control Set Model Predictive Control (FCS-MPC) for grid-connected inverters, including approaches aimed at reducing common-mode voltage and enhancing power quality [5, 6]. Moreover, recent reviews highlight ongoing improvements in MPC design to reduce computational burden and enhance robustness [7].

In addition to linear and predictive approaches, nonlinear control techniques such as backstepping control have shown strong potential for handling system nonlinearities and ensuring closed-loop stability. Backstepping-based controllers have been successfully applied to grid-connected PV systems, demonstrating robust performance in power regulation and grid synchronization [8].

However, despite the extensive research in this field, several limitations remain. Most existing studies focus on a single control strategy or consider inverter configurations equipped with output filters. The performance of different control techniques under filterless conditions, particularly in the presence of rapid irradiance variations, has not been sufficiently investigated. Furthermore, a fair and systematic comparison between classical, predictive, and hybrid control strategies under identical operating conditions is still lacking. In addition, the potential benefits of combining nonlinear control techniques such as backstepping with MPC have not been fully explored for filterless grid-connected multilevel inverters.

The main novelty of this work lies in the proposed hybrid Backstepping-MPC strategy. Unlike conventional hybrid approaches where controllers were simply combined, the proposed method adopts a hierarchical structure. The backstepping controller first generates a stabilizing reference voltage based on Lyapunov stability theory, ensuring improved dynamic stability. This reference is then tracked by a FCS-MPC, which optimally selects the inverter switching states. This structure allows the simultaneous exploitation of stability guarantees and predictive optimization, resulting in improved robustness, faster transient response, and reduced current distortion under variable irradiance conditions.

In this context, this paper presents a comprehensive comparative study of several control strategies, namely HCC, PWM-based control, MPC, and hybrid Backstepping-MPC approach, applied to a filterless three-level grid-connected PV inverter operating under variable irradiance conditions. In this study, the PV source, DC/DC boost converter, Maximum Power Point Tracking (MPPT) algorithm, Phase-Locked Loop (PLL) synchronization, and load model are considered as a fixed framework. The comparison is strictly focused on the inverter current control strategies to ensure a fair and consistent evaluation.

The performance of each control technique is assessed based on key performance indicators, including PV power extraction, current tracking accuracy, grid-injected power quality, dynamic response under irradiance variations, and THD of both current and voltage.

Multilevel inverters play a key role in energy conversion, particularly for applications requiring high voltage and power. Unlike conventional structures, these inverters generate an output voltage closer to a sine wave, thereby reducing harmonic distortion and improving energy efficiency. Their advanced design offers significant advantages in terms of efficiency, reduced stress on components, and compatibility with modern electrical networks. Thanks to these features, multilevel inverters are widely adopted in various fields such as grid-connected PV systems, high-power industrial drives, electric traction, and smart grids [15-17].

Figure 4. Three-level Neutral Point Clamped (NPC) inverter

Among multilevel inverter topologies, the three-level Neutral Point Clamped (NPC) inverter shown in Figure 4 has gained significant attention due to its balanced compromise between performance, complexity, and reliability. By introducing an additional voltage level through a clamped neutral point, the NPC inverter is capable of generating three discrete output voltage levels $\left(+\frac{V_{D C}}{2}, 0,-\frac{V_{D C}}{2}\right)$, which significantly reduces harmonic distortion compared to conventional two-level inverters. Moreover, the three-level NPC structure allows for lower voltage stress across the power switches, making it particularly suitable for grid-connected PV systems operating at medium and high power levels.

3.1 Hysteresis Current Control

In this control strategy, the inverter currents are regulated directly in the three-phase abc reference frame. The reference currents are obtained from the inverse Park transformation applied to the dq-axis current references.

3.1.1 Current error definition

The current tracking errors for each phase are defined as:

$e_a=i_a^*-i_a$               (4)

$e_b=i_b^*-i_b$              (5)

$e_c=i_c^*-i_c$                (6)

where, $i_x^*$ and $i_x$ denote the reference and measured phase currents, respectively, with

$x \in\{a, b, c\}$

3.1.2 Hysteresis band

A fixed hysteresis band (h) is imposed on the current errors that:

$\left|e_x\right| \leq h$            (7)

$x \in\{a, b, c\}$

The controller aims to maintain the phase currents (i_a, i_b and i_c) within this predefined hysteresis band around their references.

3.1.3 Switching law principle

The switching decisions are made according to the following rule:

• if $\mathrm{e}_x>h$, the phase voltage is increased to force the current to decrease its error.
• if $e_x<-h$, the phase voltage is decreased to force the current to decrease its error.

For a three-level NPC inverter, the available phase voltage levels are given by:

$v_x \in\left\{+\frac{V_{d c}}{2}, 0,-\frac{V_{d c}}{2}\right\}$            (8)

The appropriate voltage level is selected in real time to ensure fast current tracking and to keep the current within the hysteresis bounds. The hysteresis bandwidth h is selected as a compromise between current ripple and switching frequency.

3.2 Pulse Width Modulation control of the three-level inverter

In the conventional PWM control strategy for the three-level NPC inverter, the reference current is first processed through a proportional-integral (PI) controller to generate the reference voltage [18, 19].

The PI controller is defined as:

$V_x^{r e f}=K p\left(i_x^*-i_x\right)+K i \int\left(i_x^*-i_x\right) d t$                (9)

The reference voltage is then compared with two triangular carrier signals, one for the upper switch (Vc+) and one for the lower switch (Vc-), to generate the switching signals:

$\begin{aligned} & S_1=1, \mathrm{~S}_2=0, \mathrm{~V}_{\text {ref}}>V c+\left(\text {output} \frac{V_{d c}}{2}\right) \\ & S_1=1, \mathrm{~S}_2=1, \mathrm{Vc}-\mathrm{V}_{\text {ref}}<V c+(\text {output} 0) \\ & S_3=1, \mathrm{~S}_4=0, \mathrm{~V}_{\text {ref}}<V c-\left(\text {output}-\frac{V_{d c}}{2}\right)\end{aligned}$                (10)

Finally, the phase voltage applied to the load is calculated as:

$\begin{aligned} & V_{\text {phase }} =\left\{\begin{array}{l}+\frac{V_{d c}}{2}, \mathrm{~S}_1=1 \text { and } \mathrm{S}_2=0 \\ 0,\left(\mathrm{~S}_1=1 \text { and } \mathrm{S}_2=1\right) \text { or }\left(\mathrm{S}_3=1 \text { and } \mathrm{S}_4=1\right) \\ -\frac{V_{d c}}{2}, \mathrm{~S}_3=1 \text { and } \mathrm{S}_4=0\end{array}\right.\end{aligned}$              (11)

This approach ensures a fixed switching frequency and improved harmonic performance compared to hysteresis control.

3.3 Model Predictive Control strategy

In the proposed MPC-PI control strategy for the three-level NPC inverter, the future grid currents are predicted using a discrete-time model of the inverter:

$i_x(k+1)=i_x(k)+\frac{T_s}{L_q}\left(V_x(k)-V_{\text {grid }}-R_g i_x(k)\right)$               (12)

where, i_x(k) is the output current at the sampling instant k, V_x(k) is the inverter output voltage, V_grid is the grid voltage, and L_g, R_g are the series inductance and resistance of the grid.

The sampling time T_s is kept identical for all control strategies to ensure a fair comparison.

The control objective is to minimize the tracking error between the predicted grid currents and the three-phase reference currents Iref, generated through the inverse Park transformation, in order to ensure unity power factor:

$J=\sum_{x=a, b, c}\left(i_x^*-i_x(k+1)\right)^2+\lambda \Delta S$               （13)

$i_x^*$: reference grid current of phase x.

$i_x(\mathrm{k}+1)$: predicted grid current of phase x at the next sampling instant.

$\lambda$: weighting factor used to penalize switching activity.

$\Delta S$: switching variation term, representing the change in inverter switching states between two consecutive sampling instants.

$\Delta S=\sum \mid S(k)-S(k-1)$              （14)

where,

S(k): inverter switching state at sampling instant k.

S(k-1): inverter switching state at the previous sampling instant.

At each sampling instant, the optimal switching state is selected from the set of all admissible inverter states U by minimizing the cost function:

$S_{o p t}(k)=\arg \min _{S(k) \in U} J$            （15)

The cost function is designed to minimize the current tracking error while limiting the switching frequency through the weighting factor λ, ensuring a trade-off between tracking performance and switching losses [20-25].

3.4 Backstepping-MPC control strategy

To further enhance the dynamic performance and robustness of the grid-connected three-level NPC inverter operating without an output filter, a hybrid Backstepping-MPC strategy is adopted. This approach combines the stability guarantees of nonlinear backstepping control with the optimal switching selection capability of MPC [26].

In contrast to conventional MPC approaches, the proposed strategy integrates a backstepping-based reference voltage within the predictive control framework. This intermediate control variable, derived from Lyapunov stability theory, ensures a stable control objective before the optimization stage. As a result, the MPC is used not only for current tracking but also for selecting the optimal switching state that best approximates the stabilizing control action, thereby improving dynamic performance and robustness.

This structure ensures that stability is guaranteed by the backstepping stage, while the MPC optimizes the switching states to accurately track the stabilizing reference.

However, the computational burden remains manageable due to the finite number of switching states in the FCS-MPC framework.

3.4.1 Phase current dynamic model

Considering the coupling inductance L_g and resistance R_g of grid, the dynamic model of each phase current can be expressed as:

$L_g \frac{d i_x}{d t}=v_x-v_{g, x}-R_g i_x$                (16)

where,

• v_x is the inverter output phase voltage
• v_g,x is the grid phase voltage
• i_x is the grid current

$x \in\{a, b, c\}$

3.4.2 Backstepping control design

The current tracking error for each phase is defined as:

$e_x=i_x-i_x^*$               (17)

A Lyapunov candidate function is chosen as:

$V=\frac{1}{2} e_x^2$               (18)

Taking the derivative of V and substituting the system dynamic yields:

$\frac{d V}{d t}=e_x\left(\frac{1}{L_g}\left(v_x-v_{g, x}-R_g i_x\right)-i_x^*\right)$           (19)

To ensure asymptotic stability $\frac{d v}{d t}$, the virtual control is defined as:

$v_x^{r e f}=v_{g, x}+R_g i_x+L_g i_x^*-k e_x$           (20)

where, k > 0 is a backstepping gain.

This reference voltage guarantees exponential convergence of the current tracking error.

3.4.3 Integration with Model Predictive Control

Since the inverter can only generate a finite number of voltage levels, the continuous reference voltage $V_x^{\text {ref}}$ cannot be applied directly. Therefore, FCS-MPC is used to select the optimal switching state.

The discrete-time prediction model is given by:

$\begin{gathered}i_x(k+1)=i_x(k)+\frac{T_s}{L_g}\left(v_x^{\text {ref }}(k)-v_{g, x}(k)\right. \left.-R_g i_x(k)\right)\end{gathered}$              (21)

For each admissible switching state of the three-level NPC inverter, the predicted current is computed and evaluated using the following cost function:

$J=\sum_{x=a, b, c}\left(i_x^*-i_x(k+1)\right)^2+\lambda \Delta S$             (22)

The switching state that minimizes the cost function while producing a voltage vector closest to $V_x^{r e f}$ is applied during the next sampling period.

The present study provides a comprehensive comparative analysis of four current control strategies applied to a filterless three-level grid-connected PV inverter operating under variable irradiance conditions. The investigated controllers include HCC, PWM-based control, MPC, and a hybrid Backstepping-MPC strategy. The analysis was carried out under identical system conditions, where the PV source, DC-DC boost converter, MPPT algorithm, and grid synchronization system were kept unchanged, ensuring a fair evaluation focused exclusively on the inverter current control stage.

The results show that HCC offers fast dynamic response but suffers from variable switching frequency and increased current ripple under rapid irradiance variations. PWM control improves switching behavior and reduces harmonic distortion; however, its performance remains sensitive to controller tuning and operating conditions. MPC demonstrates improved current tracking and reduced THD due to its optimization-based decision mechanism, although its performance may still be limited under strong nonlinearities and fast transient variations.

The proposed hybrid Backstepping-MPC strategy overcomes these limitations by combining the advantages of nonlinear stabilization and predictive optimization. The backstepping controller ensures system stability and provides a stabilizing reference based on Lyapunov theory, while the MPC ensures optimal switching state selection to accurately track this reference. This hierarchical structure significantly improves dynamic response, enhances robustness against irradiance fluctuations and achieves superior current quality with reduced THD below the IEEE limit of 5%, despite the absence of an output filter.

Future work will focus on extending the study to more complex grid conditions and improving control performance under nonlinear loads.