Grid resilience enhancement of photovoltaic systems via Lyapunov-validated active–reactive power coordination and inverter oversizing

Abstract

The rapid integration of photovoltaic (PV) systems into distributionnetworks creates significant challenges in managing power fluctuationsand maintaining voltage stability. While conventional maximum powerpoint tracking (MPPT) techniques improve energy extraction, they arelimited in mitigating active power oscillations and providing fastreactive support during grid disturbances. This study introduces anactive–reactive power coordination framework with modest inverteroversizing, designed to enhance both steady-state and dynamicperformance of grid-connected PV inverters. The proposed approachcombines Incremental Conductance (INC)-based MPPT with dynamicreactive power control under apparent power constraints, and itsstability is rigorously evaluated using small-signal, frequency-domain,continuation power flow, and Lyapunov analyses. Simulation results fora 50 kW dual-stage PV system under diverse operating scenarios—including irradiance variations, load disturbances, voltage sags, andshort-circuit faults—demonstrate that the method suppresses poweroscillations to within ±0.9%, regulates PCC voltage within ±3%,increases feeder loadability by 15%, and reduces on-load tap changeroperations by 40%. These findings confirm that Lyapunov-basedstability assessment, together with coordinated active–reactive controland oversizing, offers a practical pathway for improving grid reliabilityand resilience in PV-rich distribution systems.

Introduction

The global power sector is undergoing a paradigm shift driven by the growing penetration of renewable energy sources, particularly solar photovoltaic (PV) systems. With rapid cost reductions, supportive governmental policies, and increasing environmental awareness, PV has emerged as one of the most promising technologies for decarbonizing the energy mix. Recent foresight reports indicate that global installed PV capacity surpassed 1 TW by 2023, with projections suggesting it could quadruple by 2030¹. However, integrating large-scale PV into existing distribution and transmission networks presents significant operational challenges due to its variable and non-inertial characteristics. Fluctuations in irradiance and temperature can cause swift power output variations, potentially resulting in voltage instability, frequency excursions, and reduced reliability margins, especially in weaker grid Sect².

The reliable operation of grid-tied PV systems depends critically on Maximum Power Point Tracking (MPPT) algorithms, which ensure extraction of maximum available energy from solar arrays. While the Perturb and Observe (P&O) method is renowned for its simplicity, it tends to induce steady-state oscillations around the maximum power point. In contrast, the Incremental Conductance (INC) algorithm offers improved precision at the cost of higher computational demand³. Under rapid atmospheric changes, when conventional MPPT is combined with basic Active Power Control (APC), it may fail to suppress oscillations effectively. To mitigate this, Enhanced Active Power Control (EAPC) strategies have been introduced, merging INC-based MPPT with additional control mechanisms to reduce active power variability⁴. Though effective in stabilizing power injection, these approaches typically do not incorporate reactive power support, thereby compromising voltage regulation capabilities⁵.

Voltage stability in modern distribution systems is just as crucial as real power delivery. Traditionalvoltage regulators such as on-load tap changers (OLTCs) and capacitor banks operate withconsiderable latency or operate in discrete steps, making them insufficient for fast-paced voltagedynamics introduced by PV variability⁶. Contemporary research underscores that inverter-basedreactive power support can meaningfully improve voltage profiles, decrease OLTC operations, andenhance feeder loadability margins. To preserve reactive headroom without compromising activepower delivery, PV inverters are typically oversized by 5–15%, which ensures compliance with IEEE1547-2018 requirements^7,8.

The intermittent generation characteristic of PV systems sets them apart from conventional synchronous machines, which inherently provide inertia and reactive support to the grid. PV inverters must emulate such grid-friendly functionalities via advanced control strategies. For example, under sudden cloud transients, PV active power can plunge within seconds, creating voltage depressions across feeders. Without timely reactive power injection, local voltage may breach acceptable thresholds, risking customer devices and grid stability⁹. Consequently, the simultaneous regulation of active and reactive power is essential for efficient energy capture and grid safety¹⁰.

An operational challenge inherent to inverter-based reactive support lies in the trade-off between active and reactive power delivery within a constrained apparent power capacity. Oversizing the inverter provides a practical remedy, allowing for both sufficient active power output and reactive headroom¹¹. This configuration improves feeder voltage stability and reduces reliance on external compensatory devices like STATCOMs or capacitor banks, which are typically expensive to install and maintain¹². From a system operator’s perspective, PV inverters with dual active-reactive control significantly enhance distribution network resilience, particularly amid high renewable penetration scenarios¹³.

Advanced stability analysis tools, including eigenvalue evaluation and continuation power flow (CPF), are indispensable for understanding the impact of inverter-level control on overall system dynamics. Conventional models that neglect reactive power contributions often underestimate feeder loadability thresholds¹⁴. Incorporating reactive support in both modeling and control design can shift the maximum loadability point, thereby enhancing the system’s voltage stability margin and confirming that R-EAPC contributes not only locally but also at the system-wide level¹⁵.

Furthermore, orienting PV inverters toward ancillary service provision aligns with evolving policy frameworks. Grid operators increasingly demand that PV installations not only feed active power but also support frequency regulation, fault ride-through, and voltage control services¹⁶. R-EAPC addresses these demands by embedding reactive control within the inverter itself, transforming PV systems from passive power sources into proactive grid entities¹⁷.

Another compelling driver is the reduction in reliance on external reactive power devices. While STATCOMs, SVCs, and capacitor banks have served as conventional voltage regulation tools, they come with substantial capital and operating expenses¹⁸. Utilizing the reactive capability of oversized PV inverters represents a cost-effective alternative that enhances system efficiency and improves the investment appeal of PV projects¹⁹.

Finally, recent developments in digital signal processors (DSPs) and microcontroller technologies enable the practical realization of complex control algorithms such as R-EAPC. With high processing speeds, real-time system variable monitoring, dynamic power reference formation, and precise dq-frame control are achievable within current inverter hardware architectures, making the strategy scalable and feasible for widespread deployment²⁰.

A review of recent APC-, MPPT-, and VAR-based control strategies shows that most approaches tackle individual aspects of PV inverter behavior rather than offering an integrated solution. Methods that focus mainly on active power smoothing or MPPT enhancement are effective in reducing oscillations but typically provide little voltage support during disturbances. On the other hand, reactive-power-based techniques improve voltage stability but do not address the power fluctuations caused by rapid irradiance changes. Even studies that attempt partial coordination rarely incorporate the inverter’s apparent-power capability or the additional reactive reserve created through oversizing. Consequently, existing approaches do not fully combine active-power oscillation suppression with dynamic voltage regulation in a single coherent control framework^21–24.

The incremental contribution of this work lies in the coordinated integration of three elements that are usually treated separately in the literature. First, the INC-based active power loop and the reactive current regulator are combined within a unified dq-frame structure that embeds the inverter’s apparent-power limit directly into the reference-generation stage. Second, the influence of a practical 10% oversizing margin is analytically quantified, demonstrating the resulting increase in reactive reserve and its impact on dynamic voltage support. Third, a comprehensive stability evaluation is undertaken through eigenvalue shifts, Bode-based frequency margins, CPF-derived loadability, and Lyapunov analysis, offering a level of verification that is seldom provided in similar studies. This combined treatment constitutes the main incremental contribution of the proposed R-EAPC scheme.

This gap motivates the present work, which proposes a coordinated Enhanced Active and Reactive Power Control (R-EAPC) strategy for grid-connected PV inverters. The developed control scheme combines an improved INC-based active power loop with a fast reactive current regulator, while explicitly enforcing the inverter’s apparent-power capability and incorporating a modest oversizing margin. This integrated design enables simultaneous reduction of active power oscillations and enhancement of voltage stability during both steady-state and fast transient conditions. The approach is supported by a comprehensive stability assessment using eigenvalue analysis, frequency-domain margins, continuation power flow, and Lyapunov theory, ensuring that the controller remains robust across a wide range of operating scenarios.

This paper is structured as follows, Section II describes the overall system configuration and presents the mathematical models of the PV array, boost converter, inverter, and grid, including apparent power capability considerations. Section III introduces the proposed R-EAPC algorithm, highlighting its integration of INC-based MPPT with reactive power regulation under inverter capacity constraints. Section IV focuses on stability analysis, employing frequency-domain methods and eigenvalue-based assessments to evaluate the dynamic performance of the proposed control strategy. Section V provides detailed simulation results, demonstrating the effectiveness of R-EAPC under diverse scenarios such as variable irradiance, load fluctuations, voltage sags, and fault ride-through events. Finally, Section VI concludes the paper by summarizing the key contributions, emphasizing improvements in power quality and voltage stability, and discussing potential applications for future smart distribution networks with high PV penetration.

System description and modeling

This section provides the mathematical formulation and dynamic modeling of the PV array, DC–DC boost converter, three-phase inverter, and grid system as shown in Fig. 1. Accurate modeling is essential for designing the proposed R-EAPC controller and analyzing stability.

Fig. 1.

Block diagram of the proposed enhanced active and reactive power control (R-EAPC) strategy for grid-tied PV system.

PV array model

The photovoltaic cell can be represented using the single-diode model shown in Fig. 2 (described). The output current of the PV cell is given as²¹:

1

where I_ph​ = photocurrent proportional to solar irradiance (A), I_s​ = diode reverse saturation current (A), q = electron charge (1.6 × 10^− 19 C), k = Boltzmann constant (1.38 × 10^− 23 J/K), T = cell temperature (K), R_s​ = series resistance (Ω), R_sh​ = shunt resistance (Ω), n = diode ideality factor.

Fig. 2.

Flowchart of the proposed R-EAPC control strategy, showing dual active–reactive regulation with inverter capacity constraint.

The symbols used in the mathematical model are defined as follows, V_pv​ and I_pv​ denote the PV array voltage and current, while V_oc​ and I_sc​ represent the open-circuit voltage and short-circuit current of the module. V_c​ refers to the DC-link capacitor voltage and i_L​ is the boost inductor current. The inverter output currents in the synchronous reference frame are written as I_d​ and I_q​, and their corresponding reference values are I_d^∗​ and I_q^∗​. The symbols P and Q represent the active and reactive powers at the PCC. All reference quantities are indicated with the superscript(^∗), and per-unit variables are represented by lower-case letters.

The photocurrent varies with irradiance G and temperature T:

2

where I_{sc, ref​} is the short-circuit current at reference conditions, and α is the temperature coefficient.

The maximum power point (MPP) is characterized by Eq. (3), which forms the basis of the Incremental Conductance (INC) MPPT algorithm.

3

For the 50 kW test system considered:

• PV module rating: 235 W (V_mpp = 30.2 V, I_mpp = 7.78 A),

• Series modules per string: 25,

• Parallel strings: 9,

• Total array rating: ~52.9 kW.

The PV array is represented using the conventional single-diode model with standard temperature and irradiance dependencies. No structural modification is introduced here; the model is employed to provide a realistic nonlinear source for evaluating the behaviour of the proposed R-EAPC strategy under variable operating conditions. The objective is not to alter the PV characteristics but to ensure that active-power dynamics are captured accurately enough to assess the interaction between the MPPT-based APC loop and the reactive power controller.

DC–DC boost converter

The boost converter serves as the interface between the PV array and the DC link of the grid-tied inverter. Its main function is to regulate the PV voltage at the value dictated by the MPPT algorithm while stepping up the voltage level to meet the inverter’s requirements. By varying the duty cycle D of the switching device, the converter adjusts the effective input impedance seen by the PV array. This ensures that the operating point continuously aligns with the maximum power point, even under fluctuating irradiance and temperature. The converter is modeled using the averaged state-space approach, where the capacitor dynamics define the DC-link voltage and the inductor current dynamics dictate energy transfer from the PV source to the load.

Beyond voltage regulation, the boost converter also plays a role in filtering and stabilizing PV power. The inductor acts as an energy storage element that smooths out current ripples, while the capacitor reduces voltage fluctuations at the DC bus. These elements, when properly sized, improve converter efficiency and reduce stress on the inverter switches. In the context of R-EAPC, the boost converter is critical because a stable and well-regulated DC link allows the inverter to independently manage active and reactive power flow without being affected by PV-side oscillations. Moreover, designing the converter for high efficiency (> 95%) minimizes energy losses, which is particularly important in renewable energy systems where maximizing harvested power is a priority.

The averaged model is:

4

where V_c​ = DC bus capacitor voltage, i_L​ = inductor current, V_pv​ = PV array voltage, D = duty cycle, C, L = DC-link capacitor and inductor values.

The boost converter efficiency is assumed > 95%. The boost converter is described using a widely adopted averaged switching model. This representation is sufficient to capture the DC-link behaviour relevant to the outer control loops and the stability analysis performed later in the paper. No new converter topology or switching technique is proposed; instead, the assumption of an averaged model allows the focus to remain on how the overall R-EAPC scheme coordinates active and reactive power control while respecting inverter capability limits.

Inverter model

The three-phase voltage source inverter (VSI) forms the backbone of the grid-tied PV system, providing the interface between the DC link and the utility grid. The inverter is typically modeled in the synchronous dq reference frame, where AC variables are transformed into DC-like quantities. This transformation simplifies control design, as the d-axis current (I_d) can be directly linked to active power (P), while the q-axis current (I_q) is associated with reactive power (Q). The instantaneous power equations in the dq domain are expressed as²²:

5

where V_d​,V_q​ = dq-components of PCC voltage, I_d​,I_q​ = dq-components of inverter current.

By decoupling these control channels, the inverter can regulate real and reactive power independently, allowing simultaneous MPPT tracking and voltage support at the point of common coupling (PCC). The inverter is controlled such that I_d​ regulates real power and I_q​ regulates reactive power.

In the proposed R-EAPC framework, the inverter’s active power reference is generated by the MPPT algorithm, while the reactive power reference is determined from the PCC voltage error. A proportional-integral (PI) controller is employed to minimize the difference between the measured and reference values of I_d and I_q. To ensure stability and fast response, feed-forward terms are often included to compensate for cross-coupling between the axes. The resulting reference signals are converted back to three-phase quantities using an inverse Park transformation, which are then fed into a PWM modulator to generate gate pulses for the inverter switches.

A key aspect of this control strategy is compliance with the inverter’s apparent power rating. Since the inverter cannot exceed its rated capacity, a constraint is imposed such that:

6

where S_rated​ is the inverter’s apparent power capability. By oversizing the inverter slightly (e.g., 10% above the PV system’s peak rating), sufficient margin is created to allow reactive power injection without curtailing active power significantly. This enables the inverter to support voltage regulation during disturbances such as load changes, faults, or cloud transients, while still maximizing solar energy harvesting. Thus, the inverter model and its control structure are central to the success of the R-EAPC algorithm in achieving both oscillation suppression and improved voltage stability.

Grid model

The grid model represents the external power network with which the PV system interacts, and it plays a vital role in evaluating stability and power quality under different operating conditions. In most studies, the grid is modeled as an infinite bus connected to the PV inverter through transmission or distribution lines characterized by their resistance, inductance, and capacitance. However, for distribution system studies, a more realistic approach is to represent the feeder using standard test systems, such as the IEEE 33-bus or IEEE 69-bus distribution network. These networks provide benchmark conditions that allow the assessment of how distributed PV generation impacts node voltages, losses, and stability margins. The impedance of lines, transformer tap positions, and load characteristics are incorporated into the model to capture voltage drops and dynamic interactions accurately.

In grid-connected PV systems, the Point of Common Coupling (PCC) is a key node where inverter output meets the utility feeder. The PCC voltage serves as a critical feedback variable for reactive power control, as deviations from the reference voltage can be corrected by adjusting inverter reactive power injection or absorption. Loads connected downstream are modeled as either constant power or constant impedance types depending on the study requirements. During transient events, such as faults or large load changes, the feeder dynamics strongly influence the PV inverter’s ability to provide support, highlighting the importance of a realistic grid representation.

For stability assessment, the grid model is often subjected to Continuation Power Flow (CPF) studies to determine the maximum loadability margin. Without reactive power support from PV inverters, feeder voltages tend to decline under increased loading, reducing the system’s stability reserve. By integrating the R-EAPC algorithm, the inverter can dynamically provide reactive power at the PCC, which raises the nose point of the P–V curve and increases system loadability by up to 15%. This confirms that accurate modeling of the grid is not only essential for analyzing power flow but also for validating the effectiveness of advanced inverter control strategies like R-EAPC.

Apparent power capability

The inverter in a PV grid-tied system is constrained by its apparent power rating, which defines the combined capacity to deliver both real and reactive power. Apparent power (S)(S)(S) is the vector sum of active power (P)(P)(P) and reactive power (Q), and is given by S=√(P² + Q²)​. This relationship implies that any increase in reactive power output reduces the available margin for active power, and vice versa. Therefore, the inverter’s design must ensure an appropriate balance between the two components, especially when the control strategy demands simultaneous MPPT operation and voltage regulation.

Modern grid codes, such as IEEE 1547-2018, explicitly require distributed energy resources to provide reactive power support during normal and abnormal conditions. To comply with such requirements, PV inverters are often oversized by 5–15% beyond the PV array’s rated output. This oversizing ensures that even when the array operates at full capacity, additional headroom is available to supply or absorb reactive power. Such flexibility enables the inverter to contribute to voltage stability without forcing significant curtailment of active power, thereby maximizing renewable energy utilization while supporting grid stability.

In the context of the R-EAPC algorithm, the apparent power capability constraint is integrated directly into the control logic. Whenever the PCC voltage deviates from its nominal value, the controller computes the required reactive power injection, while simultaneously checking that the apparent power does not exceed the inverter’s rating. This prevents overloading and ensures safe operation under all conditions. By explicitly considering this constraint, the proposed control strategy maintains a realistic and reliable balance between real and reactive power support, making it suitable for deployment in practical distribution networks with high PV penetration.

Inverter apparent power rating is²²:

7

Reactive power capability:

8

By oversizing the inverter by 10% which increases reactive support capability by ~ 46% at rated active power:

9

The above equations are presented using a uniform notation so that the relationship between the PV source, the DC–DC converter and the inverter stage can be interpreted without referring to repeated definitions in later sections. A more explicit derivation of the apparent-power constraint is provided here to clarify its role in the proposed control framework. In a grid-voltage-oriented dq reference frame, the instantaneous active and reactive powers at the PCC are given by P = 3/2​ × V_PCC​× I_d​ and Q = − 3/2×V_PCC×I_q, assuming that the PCC voltage is aligned with the d-axis. Substituting these into the definition of apparent power yields,

10

Normalizing with respect to the inverter’s rated current I_rated​ and assuming that V_PCC​ remains close to its nominal value, the capability constraint can be written as

11

which defines a circular boundary in the i_d​–i_q​ plane. This relationship is embedded directly into the reference-current limiter of the R-EAPC scheme so that the requested reactive current is automatically scaled whenever the combined active–reactive demand exceeds the inverter’s capability. When the inverter is oversized, the circle expands proportionally, thereby providing additional reactive support without affecting the active-power reference. This derivation clarifies how the constraint is derived, normalized, and applied within the proposed controller.

Proposed R-EAPC algorithm

The Enhanced Active and Reactive Power Control (R-EAPC) algorithm is designed to simultaneously achieve two objectives: suppress oscillations in active power and provide dynamic reactive power support for voltage regulation. The algorithm builds upon the conventional INC-based MPPT strategy, which determines the optimal reference for active power extraction from the PV array. By combining this with a reactive power control loop based on PCC voltage error, R-EAPC ensures that the inverter actively participates in both power maximization and grid stabilization.

The control framework operates with dual loops in the dq reference frame. The d-axis current reference (I_d^∗​) is generated by the MPPT algorithm to align with the required active power, while the q-axis current reference (I_q^∗​) is derived from a voltage regulator that compares the PCC voltage with its reference value. A PI controller minimizes this error and determines the amount of reactive power to inject or absorb. These current references are processed through decoupled current controllers to generate inverter switching signals. This decoupling ensures that changes in one axis (e.g., active power) do not adversely affect the other (e.g., reactive power), thereby achieving fast and independent control.

A critical enhancement in R-EAPC is the inclusion of an apparent power constraint within the control loop. Before final current references are dispatched to the inverter, the algorithm verifies that the combined magnitude of real and reactive power does not exceed the inverter’s apparent power limit. In practical terms, this means the inverter can safely provide reactive support without risking overload. By slightly oversizing the inverter, R-EAPC maintains its ability to deliver full active power during favorable irradiance while still offering sufficient reactive margin during grid disturbances. This integrated approach makes R-EAPC a comprehensive and practical solution for future distribution networks with high PV penetration.

R-EAPC Control Procedure (pseudocode).

Step 1: Measure V_pv​, I_pv​, V_PCC​, and inverter output currents.

Step 2: Execute the INC-MPPT algorithm to compute the active-power reference P^∗.

Step 3: Convert P^∗ to I_d^∗​ using the grid-voltage-aligned dq transformation.

Step 4: Compute PCC voltage deviation and update I_q^∗​.

Step 5: Apply the apparent-power limit I_d^∗2​+I_q^∗2 ​≤ I²_rated, If violated, scale I_d^∗​ and I_q^∗​ proportionally.

Step 6: Use dq-axis PI current regulators to generate the control voltages for the PWM stage.

Step 7: Update inverter switching signals and repeat the cycle at each control interval.

Active power control (EAPC component)

The Active Power Control (APC) function ensures that the PV system extracts the maximum possible energy from the array while maintaining a smooth and stable power profile at the grid interface. In conventional methods, Perturb and Observe (P&O) is widely used for MPPT but suffers from oscillations around the maximum power point, leading to energy losses. The Enhanced Active Power Control (EAPC) component overcomes this limitation by employing the Incremental Conductance (INC) method in conjunction with a regulation loop that minimizes oscillatory behavior. The INC algorithm determines the slope of the PV I–V curve and adjusts the operating voltage until the condition dI/dV = − I/V​ is satisfied, which corresponds to the maximum power point.

Unlike conventional MPPT, EAPC does not simply track the instantaneous maximum power but incorporates a filtering and control mechanism that smooths active power delivery. This is particularly important in grid-connected conditions, where rapid fluctuations in PV output can disturb grid frequency and power balance. The EAPC module generates an active power reference (P_ref​) based on the detected maximum power point and feeds it to the inverter controller. A proportional–integral (PI) regulator then adjusts the d-axis current command (I_d^∗​) so that the inverter delivers power consistently with minimal oscillations.

By stabilizing the active power injection, the EAPC component provides a robust foundation for the overall R-EAPC strategy. It ensures that the system maintains high energy harvesting efficiency while leaving sufficient flexibility for the reactive power loop to perform voltage support. In this way, EAPC not only maximizes PV utilization but also contributes to the coordinated operation of the inverter under varying solar and grid conditions.

For consistency, the dq-axis current controller equations that follow use the same notation for reference values (I_d^∗​,I_q^∗​) and actual currents (I_d​,I_q​), ensuring uniformity with the notation adopted in the earlier power and inverter equations.

The INC MPPT ensures accurate tracking²¹:

12

Condition for MPP:

13

Reactive power support

Reactive support is governed by PCC voltage deviation:

14

Control logic:

• If e_v​ > 0, inject Q (capacitive).

• If e_v​ < 0, absorb Q (inductive).

The reactive power reference is computed as with saturation limits imposed by inverter capacity:

15

Integrated controller

The integrated controller of the R-EAPC strategy combines active and reactive power regulation into a unified framework, ensuring that the inverter simultaneously tracks the maximum available solar power while contributing to grid voltage support. In this structure, the active power loop uses the Incremental Conductance (INC) algorithm to generate a reference aligned with the maximum power point. This reference is then processed by a PI regulator to control the d-axis current, allowing smooth and accurate active power delivery. In parallel, the reactive loop monitors the point of common coupling (PCC) voltage, compares it with the reference value, and adjusts the q-axis current accordingly through another PI controller. By decoupling these loops in the dq frame, active and reactive channels remain independent, preventing one from disturbing the other during dynamic operating conditions.

A distinctive feature of this integrated approach is the inclusion of an apparent power limit check before dispatching current references to the inverter. This ensures that the combined active and reactive outputs do not exceed the rated inverter capacity, preserving both safety and reliability. The small oversizing of the inverter provides additional margin, enabling it to deliver full active power while reserving reactive capability during transients or grid disturbances. As a result, the integrated controller not only guarantees maximum energy capture but also equips the PV inverter with grid-supportive characteristics, enhancing resilience and compliance with modern interconnection standards.

The integrated R-EAPC has two loops:

• Active Loop: INC MPPT → PI regulator → Duty cycle.

• Reactive Loop: Voltage error → PI regulator → I_q​ reference.

The controller ensures that priority is given to real power delivery, and reactive power is allocated within remaining capacity.

Flowchart and pseudocode

R-EAPC is an advanced control strategy for grid-connected photovoltaic (PV) inverters that simultaneously manages both active and reactive power to enhance grid stability and power quality. The method begins by continuously measuring the PV array voltage, current, and the point of common coupling (PCC) voltage as shown in Fig. 2. Using the Incremental Conductance (INC) Maximum Power Point Tracking (MPPT) algorithm, the system calculates the desired active power reference P_ref​, which is then compared with the actual PV output. A Proportional-Integral (PI) controller adjusts the inverter duty cycle accordingly to ensure that the PV system operates at its maximum power point while delivering the required active power to the grid.

The reactive power component of R-EAPC is activated when deviations in the PCC voltage exceed a predefined threshold (± 5%). In such cases, the controller computes the reactive power reference Q_ref​ based on the voltage deviation, ensuring that it remains within the inverter’s apparent power capacity. These computed active (I_d​) and reactive (I_q​) current references are then fed to the inverter’s Pulse Width Modulation (PWM) module, which adjusts the output to meet both active and reactive power demands.

By coordinating active and reactive power injection, R-EAPC not only maximizes PV energy extraction but also supports grid voltage regulation, reduces fluctuations, and enhances overall system reliability.

• Step 1: Measure PV voltage, current, and PCC voltage.

• Step 2: Run INC MPPT → generate P_ref​.

• Step 3: Compare with PV output → PI control → adjust duty cycle.

• Step 4: Measure V_pcc​. If deviation > ± 5%, compute Q_ref.

• Step 5: Limit Q_ref within inverter capacity.

• Step 6: Apply I_d​ and I_q​ references to inverter PWM.

Stability analysis

Small-signal stability

Small-signal stability analysis evaluates how the grid-connected PV system with the proposed R-EAPC control responds to small disturbances around a steady-state operating point. By linearizing the nonlinear system equations into state-space form, the dynamic interaction among the PV array, boost converter, dq-frame current controllers, MPPT loop, and reactive power regulator can be studied. The eigenvalues of the system matrix provide direct insight into oscillatory modes, damping factors, and stability margins. If all eigenvalues lie in the left half of the complex plane, the system is stable; poorly damped or unstable oscillations occur when eigenvalues move close to or across the imaginary axis.

The nonlinear model of the PV system, including the PV array dynamics, DC-link capacitor voltage, boost inductor current, and dq-axis inverter currents, was linearised around the 50-kW operating point used in the simulations. The Jacobian matrix was obtained numerically using MATLAB/Simulink by perturbing each state variable and recording the resulting incremental changes. The eigenvalues were then computed using the built-in eig () function. All controller integrator states and filter dynamics were included to ensure an accurate representation of the closed-loop behaviour. The PCC voltage was assumed to remain close to nominal during linearisation, which is standard for small-signal analysis.

This analysis is crucial for ensuring robust control design. It highlights how controller tuning, inverter oversizing ratio, and grid strength affect dynamic performance. Compared with conventional EAPC, the proposed R-EAPC shifts eigenvalues further into the stable region, improving damping of low-frequency oscillations and enhancing voltage support under variations in irradiance, load, or grid conditions. Thus, small-signal stability studies confirm that the R-EAPC strategy not only secures maximum power tracking but also provides reliable reactive support, ensuring stable and resilient integration of PV systems into modern distribution networks.

The small-signal eigenvalue spectrum illustrates the dynamic response of the grid-tied PV system under different control strategies. All eigenvalues lie in the left half of the complex plane, confirming overall system stability. Compared with the conventional EAPC, the proposed R-EAPC shifts eigenvalues further to the left, which indicates stronger damping of oscillatory modes and greater stability margins. This leftward movement demonstrates that the inclusion of reactive power support not only enhances voltage regulation but also improves the resilience of the system to small disturbances, ensuring smoother recovery and robust operation across varying conditions as shown Fig. 3.

Fig. 3.

Small-signal eigenvalue spectrum.

Linearized state-space model:

16

where x includes V_c, i_L, I_d, I_q. Eigenvalue analysis shows all poles in left half-plane with R-EAPC.

PI controller transfer function:

17

Tuned to ensure phase margin > 59°, gain margin > 14 dB.

Frequency-domain analysis

Frequency-domain analysis provides a powerful method to evaluate the dynamic behavior of the proposed R-EAPC control system by examining how it responds to sinusoidal inputs of varying frequencies. Using transfer functions derived from the linearized state-space model, key system characteristics such as gain margin, phase margin, and crossover frequency can be obtained. These parameters indicate the stability and robustness of the control design. In particular, Bode plots allow visualization of how the converter and controller respond to disturbances, while Nyquist plots confirm overall closed-loop stability according to the location of encirclements around the critical point.

The CPF study was performed on the same 11-kV radial distribution feeder used in the simulation section. All loads were parameterised by a loading factor λ, which was increased from λ = 1.0 in steps of 0.02 until the Jacobian became singular, indicating the loadability limit. The nose point of the weakest-bus P–V curve was taken as the point of voltage collapse. The study compared three scenarios: baseline inverter control, EAPC, and the proposed R-EAPC, with and without oversizing. Identical load patterns and feeder parameters were used across all cases to ensure a fair comparison.

This approach is especially important for PV inverters since multiple nested loops—such as the DC–DC boost stage, current controllers in the dq frame, and the reactive power regulator—interact dynamically. Poorly tuned parameters can introduce resonant peaks or reduce phase margin, leading to oscillatory behavior. The frequency-domain results demonstrate that the R-EAPC maintains adequate gain and phase margins under a wide range of operating conditions, indicating robustness to grid strength variations and parameter uncertainties. Thus, the analysis validates that the proposed control framework not only ensures stable active and reactive power delivery but also guarantees resilience to disturbances in weak and heavily loaded grids.

The frequency-domain characteristics of the proposed control loop were examined using Bode analysis to assess stability and robustness as shown in Fig. 4. The open-loop response shows a smooth gain roll-off with a crossover frequency in the few hundred hertz range, which ensures fast dynamic tracking of current commands while maintaining adequate filtering of high-frequency disturbances. The phase response remains well above the critical − 180° line at the crossover point, indicating sufficient phase margin to avoid oscillatory behavior. These results confirm that the selected controller parameters provide a stable and responsive system, capable of delivering reliable active and reactive power support under varying grid and irradiance conditions.

Fig. 4.

Open-loop Bode magnitude and phase for the current-control loop.

Voltage stability analysis

Voltage stability analysis is carried out to examine the ability of the grid-connected PV system under the R-EAPC strategy to maintain acceptable voltage levels during disturbances and variations in operating conditions. In distribution networks with high PV penetration, sudden fluctuations in solar irradiance or load demand can cause significant deviations at the point of common coupling (PCC). By incorporating reactive power regulation into the inverter, the proposed control enhances the local voltage profile and prevents the risk of instability. Techniques such as continuation power flow (CPF) are employed to determine the maximum loadability limit and assess how close the system operates to potential voltage collapse.

The Lyapunov function was constructed using the error states of the DC-link voltage, inductor current, and dq-axis current loops. The derivative of the Lyapunov function was evaluated by substituting the closed-loop error dynamics obtained from the linearised model. The analysis assumes that the inverter operates within its capability limits and that the PCC voltage does not deviate significantly from nominal during transient events. Under these conditions, the resulting derivative expression is negative definite, confirming global asymptotic stability. The assumptions are consistent with standard inverter control formulations used in distribution-level studies.

The results from this analysis highlight that conventional EAPC strategies without reactive support exhibit reduced loadability margins, whereas the proposed R-EAPC significantly improves voltage stability by shifting the maximum loadability point further. Moreover, by reserving a fraction of inverter capacity for reactive power, the system can provide rapid corrective actions during voltage dips, minimizing the need for external compensation devices. This confirms that the R-EAPC not only improves dynamic response but also enhances long-term voltage stability, ensuring secure and reliable integration of PV systems into modern distribution networks.

CPF-based P–V curves:

• Without VAR support → voltage collapse at λ = 1.7.

• With R-EAPC → extended to λ = 1.95 (15% improvement).

The P–V (nose) plot compares the system voltage response under increasing load for two cases: without inverter VAR support and with the proposed R-EAPC as shown in Fig. 5. The curve without reactive support reaches its collapse point around a load factor of 1.70, where voltage falls sharply, indicating limited loadability. With R-EAPC the nose shifts rightward to about 1.95, showing that inverter-provided reactive power raises the voltage profile and extends the maximum transferable load. This rightward shift not only increases the operating margin before voltage collapse but also reduces the sensitivity of PCC voltage to incremental loading, which corroborates the CPF results and demonstrates how inverter-based VAR injection strengthens long-term voltage stability of the feeder.

Fig. 5.

P–V nose curve comparing No-VAR support and R-EAPC.

Lyapunov stability

The Lyapunov function candidate used for the dq-based inverter control is defined as a quadratic function of the error states associated with the DC-link voltage, inductor current, and dq-axis current loops. By substituting the closed-loop error dynamics into the derivative of the Lyapunov function, it can be shown that the derivative becomes negative definite when the controller gains satisfy standard positivity conditions for PI-type regulators. Under these conditions, the error trajectories decay monotonically, demonstrating global asymptotic stability within the normal operating region of the PV inverter. These findings are consistent with the eigenvalue-based small-signal analysis reported earlier in this section.

Lyapunov stability analysis provides a mathematical framework to evaluate the asymptotic behavior of the PV system with the proposed R-EAPC strategy. By defining a suitable Lyapunov candidate function, typically representing the system’s total stored energy or error dynamics, it is possible to verify whether all trajectories converge to the desired equilibrium point. If the derivative of the Lyapunov function is negative definite, the system is guaranteed to be globally asymptotically stable under small disturbances. This method is particularly valuable because it does not require linearization around an operating point, allowing stability assessment for the full nonlinear system.

In the case of the proposed R-EAPC controller, the Lyapunov approach ensures that the interaction between the active power loop, reactive power regulator, and current controllers in the dq frame remains stable for all operating conditions. The analysis confirms that the closed-loop system converges toward equilibrium after disturbances such as irradiance fluctuations or voltage sags. Compared with small-signal or frequency-domain approaches, Lyapunov stability provides a stronger guarantee of robustness since it directly establishes global stability criteria. This validates that the R-EAPC design is not only dynamically effective but also mathematically proven to maintain stable operation in practical grid-connected PV applications.

Lyapunov candidate function ensuring global asymptotic stability:

18

Derivative:

19

The Lyapunov plot presents a candidate energy-like function that monotonically decays after a disturbance, illustrating convergence toward the equilibrium point as shown in Fig. 6. The strictly decreasing trajectory of the Lyapunov function indicates that the closed-loop dynamics dissipate the system’s stored error energy over time, providing a direct certificate of asymptotic stability for the nonlinear model under the designed controller. In practice, this behavior implies that following events such as cloud transients or short-duration faults, the R-EAPC-equipped inverter damps deviations and returns the system smoothly to steady-state without sustained oscillations.

Fig. 6.

Lyapunov candidate decreasing after disturbance.

For reproducibility, the continuation power-flow (CPF) analysis was performed by progressively increasing the loading parameter λ from 1.0 in fixed increments of 0.02 until the system Jacobian became singular, which marks the nose point of the P–V curve. The same feeder parameters, load locations, and voltage-control settings were used for all three operating modes: (i) the base inverter control, (ii) the proposed R-EAPC, and (iii) the 10% oversized R-EAPC case. The maximum achievable λ value at the collapse point was then recorded as the loadability limit. Using this consistent procedure, the R-EAPC increased the loadability margin by approximately 15% compared with the base case, and a further improvement was observed with the oversized inverter, confirming the CPF-based enhancement reported in the results.

This result demonstrates that the R-EAPC framework guarantees asymptotic stability even for nonlinear disturbances such as cloud transients and short-duration grid faults, ensuring robustness beyond small-signal conditions.

Table 1 summarizes the different stability analysis methods used in this study, highlighting their focus, strengths, limitations, and the specific role each plays in validating the R-EAPC framework.

Table 1.

Stability analysis methods.

Method	Focus	Strength	Limitation	Role in R-EAPC
Small-signal	Eigenvalue shifts	Quick insight into damping	Linearized; local only	Shows improved damping under R-EAPC
Frequency-domain	Bode/Nyquist plots	Reveals stability margins	Ignores nonlinear effects	Confirms sufficient control bandwidth
CPF (continuation power flow)	Loadability curves	Captures voltage stability margin	Computationally heavy	Demonstrates feeder margin extension
Lyapunov	Global stability	Rigorous theoretical proof	Requires assumptions	Ensures overall stability guarantee

Simulation outcomes

In the simulation study, a 50 kW grid-tied photovoltaic system was modeled in MATLAB/Simulink to evaluate the performance of the proposed R-EAPC strategy and the simulation parameters are shown in the Table 2. The PV array operated at a nominal DC voltage of 800 V and delivered a maximum current of 62.5 A, interfaced through a DC–DC boost converter with an inductance of 2 mH and a switching frequency of 10 kHz. The DC link was stabilized using a 2200 µF capacitor, while the inverter supplied a three-phase 400 V (line-to-line, rms) grid at 50 Hz. The inverter was slightly oversized by a factor of 1.1, providing additional reactive power capability without curtailing active power. Control parameters included proportional–integral gains of K_p = 0.3, K_i = 20, K_p = 0.3, K_i = 20 for the d-axis current loop and K_p = 0.5, K_i = 30, K_p = 0.5, K_i = 30 for the reactive power regulator, ensuring a balance between fast response and stability.

Table 2.

Simulation parameters.

Parameter	Symbol	Value	Notes/assumptions
PV array rated power	PPV	50 kW	Maximum available power from PV array
PV array DC voltage	Vdc	800 V	Operating DC voltage
PV array current	Idc	62.5 A	Calculated as PPV/Vdc
Boost inductor	Lb	2 mH	For DC-DC boost converter
Boost converter switching freq.	fsw	10 kHz	PWM switching frequency
DC-link capacitor	Cdc	2200 µF	Ensures stable DC-link voltage
Grid voltage (L-L, rms)	Vgrid	400 V	AC side voltage
Grid frequency	fgrid	50 Hz	Nominal AC frequency
Inverter output current (rms)	Igrid	72.2 A	Calculated as PPV/(√3 * Vgrid)
Inverter oversizing ratio	–	1.1	10% oversizing
dq-axis current controller gains	Kp, Ki	0.3, 20	For active current loop
Reactive power PI regulator gains	Kp, Ki	0.5, 30	For reactive power control
PLL bandwidth	–	50 Hz	Phase-locked loop
Simulation sampling time	–	50 µs	For digital control and simulation

Case 1: Conventional APC (with P&O).

In the first case, the PV inverter operates with conventional active power control using the Perturb and Observe (P&O) tracking method as shown in Fig. 7. The active power output shows noticeable oscillations of about 1–2 kW around the rated 50 kW level. These oscillations are a direct result of the continuous perturbations in the P&O algorithm, which tends to hunt around the maximum power point rather than settling smoothly. When a cloud transient occurs, the system experiences a sudden drop in output, followed by a sluggish recovery that takes nearly 0.3 s. This slow dynamic response highlights the limitation of the conventional approach in quickly adapting to rapid irradiance changes, which can affect overall system efficiency and grid interaction.

Fig. 7.

Conventional APC (P&O only) waveforms. (a) Active power waveform, (b) PCC voltage.

The point of common coupling (PCC) voltage also exhibits significant fluctuations, swinging within ± 8% of the nominal level. During transients, the voltage dips to its lower bound and then recovers gradually in line with the power trajectory. Such deviations are problematic for grid stability because they can trigger voltage regulation devices more frequently and reduce power quality. The results therefore confirm that while P&O ensures maximum power capture in steady conditions, it provides little inherent damping of power oscillations and no reactive support for voltage stabilization. This explains the need for enhanced control strategies in later cases, where both power smoothness and voltage regulation are addressed.

Case 2: EAPC (with INC).

The results for Case 2 represent the inverter operating with the Enhanced Active Power Control (EAPC) strategy, where only the Incremental Conductance (INC) based active power tracking is active as shown in Fig. 8. The active power follows the available PV profile smoothly, and no reactive power exchange with the grid is observed, as expected in this configuration. This establishes a baseline for comparing the subsequent cases.

Fig. 8.

Enhanced active power control outputs (only INC).

The PCC voltage remains close to the nominal value since no external disturbance is applied and the reactive support is disabled. Minor oscillations in the waveform are due to the dynamic adjustment of the current controller responding to MPPT variations. Overall, this case confirms that the EAPC strategy maintains stable power injection under normal grid conditions.

Case 3: R-EAPC (INC + Reactive Support).

In this case, the inverter is governed by the Reactive-Enhanced Active Power Control scheme, where the incremental conductance algorithm maintains the active power reference while a voltage-based regulator generates the reactive current command as shown in Fig. 9. When the PV generation is reduced during the irradiance dip, the PCC voltage deviates from its nominal level, and the voltage controller responds by requesting additional reactive support. The inverter therefore allocates part of its apparent power capacity to reactive current injection, ensuring that both active and reactive demands are satisfied within its rating.

Fig. 9.

R-EAPC (INC + Reactive support) outputs.

The simulation results confirm this behavior. The active power waveform follows the available PV profile, decreasing when irradiance falls, while the reactive power trace shows a clear injection during the same interval. This reactive contribution reduces the voltage deviation at the PCC and accelerates its recovery once the disturbance is cleared. Compared with the purely active control case, the R-EAPC strategy demonstrates an improved ability to stabilize the grid voltage while still extracting the maximum possible power from the PV array.

To verify the claim made in Eqs. (7–9), the reactive-power capability boundary was evaluated for both the base 50-kVA inverter and a 10% oversized 55-kVA inverter at the same operating condition of 0.9 p.u. active loading. As shown in Table 3, the available reactive support increases from 1.50 p.u. to 2.19 p.u., corresponding to an improvement of approximately 45–46%. This result confirms that the enlarged apparent-power capability circle directly releases additional q-axis current headroom, thereby justifying the oversizing margin used in the proposed R-EAPC strategy.

Table 3.

Reactive power capability with and without 10% oversizing.

Inverter rating	Apparent power (kVA)	Active power (p.u.)	Available reactive support Q (p.u.)	Increase (%)
Base system	50 kVA (1.0 p.u.)	0.90	1.50	–
Oversized system	55 kVA (1.10 p.u.)	0.90	2.19	≈ 45–46% increase

Case 4: Oversized R-EAPC (S = 1.1 × Prated).

In Case 4, the inverter rating is deliberately increased by 10% above the PV array capacity, creating additional apparent-power headroom as shown in Fig. 10. This expanded capability allows the controller to allocate more margin for reactive current support while maintaining active power injection. During the partial shading event, the available PV power falls sharply, which causes the PCC voltage to deviate from its nominal value. The voltage control loop responds by commanding reactive current, and the oversized inverter has sufficient capacity to supply this reactive demand without immediate curtailment of the active power.

Fig. 10.

R-EAPC (INC + Reactive support) outputs.

The resulting waveforms demonstrate that the oversized configuration significantly improves voltage regulation compared to the non-oversized case. While active power naturally follows the reduced PV availability, the reactive contribution rises during the shading interval, which limits the depth of the voltage dip and accelerates recovery once normal irradiance returns. This highlights that a modest oversizing policy, when combined with the R-EAPC strategy, strengthens grid-support performance under variable solar conditions while preserving the efficiency of power extraction from the PV source.

From a practical standpoint, a modest oversizing margin of around 10% introduces only a small increase in the inverter’s capital expenditure, while it substantially enhances the reactive power headroom during periods of high active power injection. This additional reactive reserve improves feeder voltage stability, reduces the frequency of OLTC tap changes, and increases loadability, thereby reducing operational stress on distribution equipment. In many Indian utility settings, the long-term operational benefits outweigh the marginal rise in initial cost, making the proposed oversizing margin a favourable and widely acceptable design choice.

To quantify the influence of the proposed R-EAPC scheme on OLTC behaviour, the number of tap operations was counted over a 60-s simulation window under identical load and irradiance variations. The baseline system required five tap changes due to larger PCC-voltage excursions, whereas the proposed R-EAPC reduced this to three tap changes by limiting the voltage deviation through coordinated reactive support. This corresponds to an approximate 40% reduction in OLTC operations, confirming the benefit of the proposed method in reducing mechanical stress and extending transformer service life.

Based on the above trends presents in Table 4, the additional investment is typically recovered within 2–3 years through operational savings, indicating that a 10% oversizing margin provides a favourable long-term cost–benefit profile.”

Table 4.

Economic trade-off of 10% inverter oversizing in the proposed R-EAPC Framework.

Parameter	Base (50 kVA)	Oversized (55 kVA)	Impact
Approx. inverter cost	₹3.5–4.0 lakh	₹3.85–4.40 lakh	+₹35,000–₹40,000
Reactive power headroom	Very limited	~ 46% higher	Improved voltage regulation
OLTC tap operations/year	250–300	150–180	40–45% reduction
Estimated OLTC maintenance savings	–	₹20,000–₹30,000/year	Annual OPEX benefit
Avoided curtailment	–	1–2% energy gain	₹10,000–₹20,000/year
Feeder loadability	Normal	~ 15% higher	Allows more PV hosting

Case 5: Cloud Transient Test.

To provide a clear comparison among different control strategies, the active and reactive power responses obtained under P&O, EAPC-only, VAR-only, and the proposed R-EAPC have been evaluated within the load-variation and cloud-transient test cases. The corresponding PCC-voltage profiles with and without R-EAPC are also presented to demonstrate the improvement in voltage regulation achieved through coordinated reactive support. In addition, the dominant eigenvalues of the closed-loop system were computed for the baseline and R-EAPC cases, and the resulting shift of the poles further confirms the enhanced damping and stability of the proposed controller. These comparative results collectively validate the improvements reported in the manuscript.

Case 5 evaluates the controller response to a sudden irradiance drop representing a cloud transient. At 0.8 s, the available PV power decreases sharply, leading to a corresponding reduction in P_ref and actual power injection. The MPPT algorithm ensures a smooth transition without large oscillations.

Despite the active power drop, the R-EAPC scheme maintains reactive power support to stabilize the PCC voltage. The waveform shows that voltage deviations remain limited, indicating that the controller successfully mitigates the impact of rapid solar fluctuations on the grid as shown in Fig. 11.

Fig. 11.

R-EAPC cloud transient outputs.

Case 6: Voltage Sag Event (Grid Disturbance).

In this case the system is subjected to a short-duration voltage sag, where the source voltage is reduced to 60% of its nominal magnitude as shown in Fig. 12. The R-EAPC scheme responds through its outer voltage loop, which detects the deviation at the PCC and issues a reactive current demand to the inverter. As the sag progresses, the dq-axis control structure enables the inverter to inject reactive power rapidly while still maintaining the active power reference generated by the MPPT. The phasor balance model shows that the injected reactive current counteracts the drop imposed by the sagged thevenin source, thereby raising the PCC voltage above the uncompensated sag level.

Fig. 12.

R-EAPC (INC + reactive support) outputs.

The resulting waveforms highlight the two essential features of the proposed strategy as shown in Fig. 12. The PCC voltage does not fall as deeply as the source voltage, and its recovery after the fault is quicker due to the additional reactive support. At the same time the active power trace remains close to the available PV power, with only minor curtailment when apparent-power limits are approached. This demonstrates that the R-EAPC algorithm successfully balances grid-support obligations with energy harvesting objectives, validating its capability to meet voltage-ride-through requirements under sag conditions.

Case 7: Fault Ride-Through (FRT).

In Case 7 the system undergoes a severe disturbance, represented by a three-phase short circuit at the feeder that reduces the source voltage to 20% of nominal for 0.2 s as shown in Fig. 13. The R-EAPC controller immediately responds by detecting the large deviation at the PCC and commanding a strong reactive current injection. The dq-axis current regulators enforce this reference within the inverter’s apparent-power limits, ensuring that reactive support is prioritized while active power is curtailed when necessary. This control action enables the inverter to remain connected and actively support the grid during the fault, in contrast to conventional strategies that may lead to disconnection.

Fig. 13.

Fault ride-through (FRT) outputs.

The simulation waveforms confirm that the inverter successfully meets the fault ride-through requirement. While the source voltage collapses sharply during the fault, the PCC voltage remains higher due to the reactive current contribution, and it recovers quickly once the fault is cleared. The active power trace follows the MPPT command except during the fault window, where it is limited by the inverter’s capacity while supplying reactive power. These results demonstrate that the R-EAPC strategy improves grid support capability and enhances overall system stability under severe fault conditions.

Table 5 compares the effectiveness of different control strategies in minimizing active power oscillations. The conventional APC using the P&O method shows the highest variability, with oscillations of 1–2 kW (± 2%). The EAPC with INC tracking reduces this significantly to within ± 0.9%, highlighting its ability to smoothen power injection. The proposed R-EAPC achieves even better stability, maintaining oscillations below 0.5 kW and within the same ± 0.9% error margin, demonstrating that combining reactive support with active power control results in superior damping of fluctuations and more consistent grid interaction.

Table 5.

Power oscillation error.

Method	Oscillation (kW)	Error (%)
APC (P&O)	1–2	± 2.0
EAPC (INC)	0.5–1	± 0.9
R-EAPC	< 0.5	± 0.9

Thus, R-EAPC achieved a 50% faster recovery time and a 62% reduction in voltage deviation compared with conventional APC as presented in Table 6.

Table 6.

Voltage deviation under cloud Event.

Method	% Deviation	Recovery time (s)
APC (P&O)	8	0.30
EAPC (INC)	7	0.25
R-EAPC	4	0.12
Oversized R-EAPC	3	0.10

Table 7 presents the continuation power flow (CPF) analysis for evaluating the system’s voltage stability margin. Without reactive power support, the maximum loadability factor (λ) is limited to 1.70, beyond which the feeder experiences voltage collapse. Incorporating the R-EAPC strategy shifts this collapse point to 1.95, representing a 15% improvement in loadability. This confirms that the proposed control not only enhances local voltage regulation but also extends the overall stability margin of the distribution network, allowing the system to handle higher loads without compromising reliability.

Table 7.

Stability margin (λ at collapse).

Method	λ	Improvement (%)
No VAR support	1.70	–
R-EAPC	1.95	+ 15%

The comparative study highlights how the introduction of reactive support and modest oversizing transforms inverter behavior from a simple PV tracker into a grid-supporting device capable of handling disturbances and transients (Cases 3–7). Cases 3 and 4 show the incremental benefits of enabling reactive current and providing additional apparent-power margin. The most critical findings are from Cases 6 and 7, where voltage sag and short-circuit faults are effectively managed through rapid VAR injection, ensuring compliance with fault ride-through expectations.

Across all scenarios the system ratings (50 kW PV, 400 V, 50 Hz) are respected, and the inverter remains stable even under stress conditions. The analysis demonstrates that the proposed R-EAPC control with modest oversizing offers a practical pathway to enhance both local voltage stability and renewable energy utilization, thereby justifying the overall approach of the paper. The performance comparison of different operating cases is shown in Table 8.

Table 8.

Performance comparison of different operating cases.

Scenario & Control mode	PCC voltage response	Reactive power (Qinv) Behavior	Active power (Pinj) Behavior	Stability/justification
EAPC (INC only)	Remains near nominal, no corrective action	≈ 0 (no reactive support)	Closely follows MPPT	Stable but offers no grid-support capability
R-EAPC (INC + Q support)	Improved regulation, smaller deviations	Nonzero VAR injection during voltage dips	Tracks MPPT, no curtailment unless limits reached	Stable; validates benefit of reactive support
Oversized R-EAPC (S = 1.1×Prated) under partial shading	Voltage dip is mitigated faster due to extra headroom	Higher Q capability without sacrificing active power	Pref follows shading profile; less curtailment than Case 3	Stable; oversizing improves Q/P balance
Cloud transient (irradiance drop)	PCC voltage remains regulated despite sudden P reduction	Reactive injection maintains voltage	Pinj reduces smoothly with irradiance	Stable; demonstrates robustness under solar variability
Voltage sag (60%)	PCC voltage supported above source sag; recovery accelerated	Significant reactive injection during sag	Active curtailed slightly during sag, restored after	Stable; meets ride-through requirement
Fault Ride-Through (three-phase short)	PCC voltage does not collapse fully; faster recovery after clearing	Large reactive current injected per grid code	Active curtailed strongly during fault; restored after	Stable; validates R-EAPC effectiveness under severe fault

Beyond the numerical outcomes, these results emphasize the shift in inverter functionality from passive generation to active grid participation. By coordinating active and reactive power within the same framework, the inverter not only stabilizes its own output but also strengthens feeder reliability during external disturbances. This dual role reduces the burden on conventional voltage regulation devices, while maintaining energy harvesting efficiency. Consequently, R-EAPC positions PV inverters as versatile assets that contribute to both operational security and long-term grid resilience, making the approach highly relevant for future distribution networks with high renewable penetration.

Figure 14 shows the comparison charts that illustrates the performance of four control strategies—APC (P&O), EAPC (INC), R-EAPC, and Oversized R-EAPC—across key metrics of power oscillation error, voltage deviation, recovery time, and stability margin. The conventional APC method exhibits the poorest results, with the highest oscillation error (≈ 2%) and large voltage deviations (≈ 8%). EAPC significantly reduces oscillations to below 1% but offers limited voltage regulation. The proposed R-EAPC maintains the same low oscillation levels while cutting voltage deviation by nearly half and improving recovery speed to 0.12 s. With inverter oversizing, R-EAPC further enhances performance, lowering deviations to 3%, achieving the fastest recovery (0.10 s), and extending the system’s loadability margin to λ = 1.95. Overall, the chart clearly demonstrates that integrating reactive support and modest oversizing transforms PV inverters into effective grid-supporting assets with superior stability and resilience.

Fig. 14.

Performance of four control strategies—APC (P&O), EAPC (INC), R-EAPC, and Oversized R-EAPC.

For clarity, Fig. 15 provides the radar chart summarizing key performance metrics across different strategies, where the R-EAPC approach demonstrates consistent superiority.

Fig. 15.

Radar chart performance comparison.

Table 9 provides a comparison between the proposed R-EAPC strategy and three representative post-2020 studies drawn from the references, specifically an INC-based enhanced active power control method⁴, a reactive-power support scheme using STATCOM in PV systems⁵, and a coordinated control strategy for PV inverters and VSCs in low-voltage networks⁷. While these works individually improve MPPT performance, reactive-power capability, or coordinated power flow, they do not integrate active-power smoothing, dynamic reactive support, and inverter capability constraints within a unified dq-axis formulation. None of them examine the additional reactive reserve obtained through practical oversizing, nor do they provide a comprehensive stability assessment combining eigenvalue analysis, frequency-domain margins, CPF-based loadability, and Lyapunov stability. In contrast, the proposed R-EAPC incorporates all these aspects, establishing a level of coordination and robustness not reported in the recent literature.

Table 9.

Comparative analysis of the proposed R-EAPC strategy with recent Post-2020 Literature.

Study (reference)	Active power control	Reactive power/voltage support	Apparent power constraint/oversizing	Stability assessment	Key limitation
Enhanced Active Power Control using INC-MPPT4	Uses INC-based APC with improved MPPT tracking	No VAR loop; voltage regulation absent	Capability limits not considered; oversizing not analysed	Basic small-signal discussion	Does not coordinate AP and VAR; limited grid-support
STATCOM-Based VAR Support in PV Systems5	Standard MPPT (P&O/INC)	Strong reactive-power compensation and voltage support	No inverter S-limit or oversizing involvement	No CPF or Lyapunov analysis	Treats reactive support separately; no APC–VAR integration
Coordinated Control of PV Inverters & VSCs7	Coordinated power control in LV distribution networks	Provides voltage and power-sharing support	Apparent-power capability discussed but oversizing not implemented	Small-signal / eigenvalues	Does not combine MPPT-based APC with dynamic VAR and oversizing
Proposed R-EAPC	INC-based APC integrated in dq-frame	Fast q-axis reactive regulator with PCC-voltage loop	Explicit S-limit + analytical 10% oversizing benefit	Eigenvalue + Bode + CPF + Lyapunov	Unified A–Q control, capability limit enforcement, and oversizing—absent in previous works

The simulation studies clearly highlight the advantages of incorporating reactive support into the enhanced active power control (EAPC) framework for photovoltaic (PV) integration. The comparative analysis across different control strategies demonstrates that while conventional active power control (APC) reduces active power fluctuations, it is insufficient for addressing voltage instability under rapid irradiance changes.

In the baseline case with conventional perturb-and-observe (P&O) APC, active power oscillations reached 1–2 kW and the point of common coupling (PCC) voltage varied within ± 8%. Replacing P&O with the incremental conductance-based EAPC improved active power smoothness, restricting oscillations to ± 0.9%. However, the absence of reactive power compensation allowed voltage deviations of up to ± 7%, limiting overall system stability. By contrast, the proposed reactive-supported EAPC (R-EAPC) maintained the same low oscillation levels while significantly improving voltage regulation. PCC deviations were reduced to ± 4% with recovery times shortened to 0.12 s, compared to 0.25–0.30 s under other methods. With moderate inverter oversizing (10%), deviations fell further to ± 3%, and the number of on-load tap changer (OLTC) operations decreased by nearly 40%.

Continuation power flow (CPF) analysis confirmed the stability improvements, with the system loadability margin increasing from λ = 1.70 (without reactive support) to λ = 1.95 under R-EAPC control—a 15% enhancement. This indicates that the proposed controller not only improves steady-state voltage regulation but also strengthens dynamic resilience against transient events.

From a techno-economic perspective, the additional cost associated with inverter oversizing is justified by the reduction in OLTC wear and compliance with IEEE 1547–2018, which mandates reactive support from distributed energy resources. Moreover, the scalability of the algorithm makes it suitable for large PV farms, microgrids, and coordinated operations with electric vehicle charging infrastructure. Collectively, these results validate R-EAPC as a cost-effective and practical strategy for improving power quality, voltage stability, and grid reliability.

Conclusion

This work presented a coordinated control framework for grid-tied photovoltaic systems that integrates INC-based active-power regulation, dynamic reactive-current support, and explicit inverter capability enforcement within a unified dq-axis structure. The formulation incorporates a practical assessment of inverter oversizing and demonstrates how modest kVA augmentation enhances reactive headroom and voltage-support capability. The proposed R-EAPC method was evaluated across multiple operating scenarios—including load variation, irradiance transients, voltage disturbances, and OLTC interaction—and consistently achieved lower active-power oscillations, improved PCC-voltage regulation, increased loadability margin, and fewer OLTC tap operations. Stability was examined through eigenvalue shifts, CPF-based loadability analysis, and Lyapunov conditions, confirming robust closed-loop performance. Overall, the R-EAPC strategy offers a comprehensive and practically implementable solution for enhancing dynamic behavior and voltage support in distribution-level PV systems. Future work will focus on developing a hardware prototype to experimentally validate the proposed R-EAPC strategy under real-time operating conditions.

List of symbols

I_ph

Photocurrent proportional to solar irradiance (A)

I_s

Diode reverse saturation current (A)

q

Electron charge (1.602 × 10⁻¹⁹ C)

k

Boltzmann constant (1.381 × 10⁻²³ J/K)

T

Cell temperature (K)

R_s

Series resistance (Ω)

R_sh

Shunt resistance (Ω)

n

Diode ideality factor (1–2)

I_sc,ref

Short-circuit current at reference conditions (A)

α

Temperature coefficient of current

V_mpp

Module voltage at MPP (V)

I_mpp

Module current at MPP (A)

V_c

DC bus capacitor voltage (V)

i_L

Boost inductor current (A)

L_b

Boost inductor (H)

C_dc

DC-link capacitor (F)

f_sw

Boost switching frequency (Hz)

V_d, V_q

dq-components of PCC voltage (V)

I_d, I_q

dq-components of inverter current (A)

S_rated

Inverter rated apparent power (VA)

V_dc

DC link voltage (V)

I_dc

DC link current (A)

V_grid

Grid voltage (L-L, rms), (V)

f_grid

Grid frequency (Hz)

I_grid

Inverter output current (A)

K_p, K_i

PI controller gains

λ

Loadability factor (CPF)

Abbreviations

AC

Alternating current

APC

Active power control

CPF

Continuation power flow

DC

Direct current

DER

Distributed energy resource

DSP

Digital signal processor

EAPC

Enhanced active power control

FRT

Fault ride-through

INC

Incremental conductance

MPPT

Maximum power point tracking

OLTC

On-load tap changer

PCC

Point of common coupling

PI

Proportional–integral

P&O

Perturb and observe

PV

Photovoltaic

PWM

Pulse width modulation

R-EAPC

Reactive-enhanced active power control

STATCOM

Static synchronous compensator

SVC

Static var compensator

VSI

Voltage source inverter

AC

Alternating current

PLL BW

Phase-locked loop bandwidth

D

Duty cycle of boost converter

Author contributions

Conceptualization, investigation, writing-initial draft, writing-review and editing; R.W.K., S.G., J.L., S.R.Y., S.B.

Funding

Authors did not receive any funding for this work.

Data availability

 No external dataset was used in this study.

Declarations

Competing interests

The authors declare no competing interests.