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Scientific Reports volume 15, Article number: 24697 (2025) Cite this article
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Solar energy is environmentally friendly and one of the most significant renewable energy sources. This energy is a leading renewable energy source, contributing significantly to sustainable development goals. In grid-connected photovoltaic (PV) systems, reactive power management is essential for maintaining voltage stability and ensuring reliable operation. However, the influence of fluctuating solar irradiation (G) on reactive power (Q) behavior is often underrepresented in conventional inverter control strategies. This research addresses this gap by modeling the dependence of reactive power on solar irradiance using a data-driven curve-fitting approach. The methodology involves the acquisition of real-world operational data, preprocessing, selection of an appropriate analytical model, and validation of its performance. The findings indicate that reactive power increases under low irradiance conditions, primarily due to inverter behavior and grid voltage support requirements. The resulting analytical expression offers a practical framework for integrating irradiance-dependent reactive power control into inverter firmware or grid management software. The model performed with high accuracy with an R² of 0.9955. This contribution enhances the ability of PV systems to respond dynamically to environmental changes, improving grid compatibility, operational efficiency, and voltage regulation in modern distributed energy networks.
The increasing global demand for clean, sustainable energy has accelerated the integration of renewable energy sources into power systems, with PV solar technology playing a pivotal role due to its scalability, declining costs, and minimal environmental impact. The global shift toward sustainable and renewable energy has accelerated the deployment of PV systems, which now play a critical role in modern power networks. As the share of solar energy in the electricity mix increases, maintaining stable grid operation becomes increasingly complex. One of the most pressing technical challenges associated with large-scale PV integration is the management of reactive power, essential for voltage regulation and overall system stability^1,2,3. In grid-connected PV systems, inverters are responsible for both converting direct current (DC) output from PV modules into AC power and for supplying or absorbing reactive power as needed by the grid. However, most inverter control strategies focus on active power optimization and voltage-based reactive power response, without accounting for how variations in solar irradiance influence reactive power requirements^2,3,4. This oversight becomes especially critical during periods of low or rapidly changing irradiance, where voltage regulation needs are highest. The novel contribution of this research lies in offering an irradiance-dependent analytical model for reactive power behavior, derived from real-world PV system data. Unlike previous studies that rely on complex simulations or assume static reactive power behavior, this model is lightweight, accurate.
Most research focuses on power factor control or active power generation, but and developing a sustainable analytical expression solely based on solar irradiance for reactive power might be less explored. The objective of the work would be to develop a practical, reliable model that grid operators or engineers can use to predict and manage the reactive power output of grid-connected PV systems as a function of solar irradiance, thus improving grid performance and stability^5,6. By accurately predicting reactive power based on solar irradiance, the model can help improve the dynamic operation of PV inverters, which is crucial for reducing energy losses and optimizing grid integration strategies. The developing a sustainable analytical expression between solar irradiation and reactive power was found by the curve fitting method. Solar PV systems can be categorized based on their connection type, functionality, and application⁷.
Grid-Connected PV Systems, these systems are directly connected to the utility grid and can export excess electricity, operates independently of the grid, relying on battery storage to supply electricity when solar generation is insufficient⁹. A grid-connected PV system and an off-grid solar PV system serve different purposes and have distinct operational characteristics^8,9,10. Below is a comparison based on key factors:
Connection to the Grid
Grid-Connected PV System: Remains connected to the utility grid and can export excess power.
Off-Grid PV System: Operates independently without any connection to the grid.
Power Supply Reliability
Grid-Connected: Reliable since the grid serves as a backup when solar generation is insufficient.
Off-Grid: Requires batteries or backup generators to provide power when solar output is low (e.g., at night or during cloudy days).
Energy Storage Requirement
Grid-Connected: Typically does not need batteries, as excess power is fed into the grid¹¹.
Off-Grid: Requires battery storage to ensure continuous power supply.
System Components
Grid-Connected: Solar panels, inverters, and grid connection equipment.
Off-Grid: Solar panels, charge controllers, batteries, and inverters.
Cost Consideration
Grid-Connected: Lower initial cost as there is no need for batteries.
Off-Grid: Higher cost due to the need for battery storage and additional infrastructure.
Energy Independence
Grid-Connected: Dependent on the grid; power outages may still affect users.
Off-Grid: Provides complete energy independence but requires careful system design to meet energy demands.
Efficiency
Grid-Connected: Higher efficiency as energy can be directly used or exported^12,13.
Off-Grid: Lower efficiency due to energy losses in battery storage and conversion.
Suitability
Grid-Connected: Ideal for urban areas with stable grid supply.
Off-Grid: Suitable for remote locations where grid access is unavailable or unreliable.
The developing a sustainable analytical expression between solar irradiation and reactive power was found by the curve fitting method. Reactive power is crucial in grid-connected PV solar systems because it helps maintain grid stability, ensures voltage control, improves power quality and enables compliance with grid regulations, ultimately optimizing the efficiency and reliability of solar power integration into the electrical grid. In¹⁴, a comparative study of reactive power control methods for photovoltaic inverters in low-voltage networks was analyzed. Reactive power management also plays a role in minimizing transmission losses. By optimizing the power factor and voltage levels, the efficiency of energy transmission from the solar PV system to the grid can be improved, reducing energy waste. Additionally, reactive power compensation helps improve the power factor of the system^15,16.
The connection point between the PV system and the grid plays a vital role in determining the overall performance, security and stability of both the PV system and the wider power grid. This interface governs the flow of active and reactive power, facilitates synchronization with grid parameters, and serves as the location where control, protection, and monitoring systems operate. Any disturbances or abnormalities occurring at this point—such as harmonic injection, voltage deviations, or improper protection coordination can propagate throughout the distribution network, affecting power quality and potentially compromising grid reliability. As such, a thorough understanding and careful design of the interconnection point are essential to ensure seamless integration of PV systems while maintaining compliance with grid codes and operational standards.
Power factor is a measure of how efficiently electrical power is being used. A poor power factor (often caused by insufficient reactive power) can lead to increased energy losses and inefficiencies in the grid infrastructure.
By optimizing the power factor and voltage levels, the efficiency of energy transmission from the solar PV system to the grid can be improved and reducing energy waste¹⁷.
Grid stability depends on maintaining a balance between reactive power and active power. Solar PV systems typically produce active power that can cause voltage variations if not balanced with reactive power. Proper management of reactive power ensures stable grid operation and reduces the likelihood of voltage sags or surges. Reactive power helps regulate voltage levels within acceptable limits. In^18,19, the reactive power control and regulation of the three-phase inverter is investigated, while in²⁰, the performance of the 8.2 kWp grid-connected photovoltaic system is investigated.
Solar PV systems can inject active power into the grid which affects voltage PV systems has been studied. On partially cloudy days solar irradiation can vary quickly as clouds move across the sky. This causes rapid fluctuations in active power generation. The ability to supply reactive power and control voltage levels in grid-connected PV systems is increasingly important as PV penetration in the grid grows. A grid-connected PV solar system and an off-grid PV solar system differ significantly in terms of design, functionality, and application. A grid-connected PV system is directly linked to the utility grid, allowing it to draw or supply electricity as needed.
This system primarily relies on solar power but can access grid electricity when solar generation is insufficient. Excess energy generated by the solar panels can be fed back into the grid, often through net metering or feed-in tariff programs, reducing electricity costs. Since grid-connected systems do not require battery storage, they have lower initial costs and maintenance requirements²¹. However, they are dependent on grid availability and backup. In contrast, an off-grid PV system operates independently of the grid and requires battery storage to supply electricity during periods of low solar generation, such as nighttime or cloudy days²².
Several studies have examined the relationship between PV generation and environmental conditions, focusing mainly on active power fluctuations due to irradiance and temperature changes²³. Fewer works have MPPT and active power control^24,25. However, as PV penetration increases, reactive power control has emerged as a critical capability for supporting voltage stability and grid compliance²⁶. Modern grid codes, such as IEEE 1547 and EN 50549, mandate that inverters in distributed generation systems provide reactive power support under varying voltage and frequency conditions²⁷. In response, research has explored various inverter-based reactive power control strategies, including fixed power factor control, Volt-VAR control, and dynamic VAR support based on local grid conditions^28,29,30.
In a grid-connected photovoltaic PV system, the point of interconnection with the utility grid is critical, as various dynamic events may occur at this interface, potentially impacting power quality, system stability, and the bidirectional flow of energy. where various dynamic phenomena such as harmonic distortion, voltage fluctuations, and coordination challenges in protection schemes can arise, potentially compromising power quality and system reliability. The increasing integration of PV systems into distribution networks has introduced new challenges to power system operation and reliability.
While grid-connected PV systems offer significant environmental and economic benefits, their interconnection with the utility grid can give rise to a range of technical issues. Specifically, at the point of common coupling (PCC), dynamic events such as harmonic distortion, voltage fluctuations, and complications in protection coordination are frequently observed. These phenomena can degrade power quality, disrupt voltage regulation, and impair the effectiveness of conventional protection schemes. As the penetration of distributed generation continues to rise, understanding and mitigating these impacts is essential for ensuring stable and reliable grid operation.
In a grid-connected PV system, the solar inverter serves as a critical component at the point of interconnection with the utility grid. Its primary function is to convert the DC generated by the PV modules into alternating current (AC) compatible with grid standards in terms of voltage, frequency, and waveform. Beyond basic power conversion, the inverter is responsible for synchronizing the output with the grid, ensuring proper phase alignment and stable frequency. It also plays a key role in power quality management by minimizing harmonic distortion and maintaining voltage stability.
Modern grid-tied inverters incorporate advanced functionalities such as maximum power point tracking (MPPT), anti-islanding protection, reactive power support, and real-time monitoring. Additionally, the inverter contributes to protection coordination by interfacing with grid protection devices and complying with grid codes to ensure safe and efficient operation under normal and fault conditions. As the gateway between the PV array and the utility grid, the inverter’s performance directly impacts the reliability and efficiency of the entire system.
The principle diagram of a grid-connected PV solar energy system plays a crucial role in understanding, designing, and analyzing the system’s functionality. This diagram serves not only as a blueprint for system installation but also as a foundational tool for troubleshooting, performance assessment, and compliance with safety and grid standards²⁹. By illustrating power flow and control mechanisms, it supports efficient system optimization and helps ensure that the PV system operates reliably, sustainably, and in coordination with the larger electrical infrastructure. The principle diagram of the grid-connected PV solar system is given in Fig. 1.
Principle diagram of grid connected PV solar system.
The principle diagram of a grid-connected PV solar system, showing key components like solar panels, a boost converter, an inverter, a meter and the grid connection. Solar irradiation exhibits a clear variation throughout the day, primarily due to the position of the sun relative to the earth’s surface¹⁶. As the sun rises, solar irradiance gradually increases from zero.
As it climbs higher in the sky, the irradiance continues to increase, reaching its peak around midday. After the peak irradiation around noon, solar irradiation begins to decrease as the sun starts its descent. The sun’s angle becomes less direct, increasing the atmosphere’s impact in reducing the energy reaching the surface. During low solar irradiation periods (early morning, late afternoon, cloudy days), PV generation decreases significantly^31,32. As the sun approaches the horizon, the solar irradiation continues to drop until it reaches zero at sunset. The sunlight passes through more atmospheric layers, scattering much of the energy before it reaches the surface. The reactive power in a grid-connected solar PV system can exhibit variations throughout the day, much like solar irradiation.
Many grid codes and regulations require that grid-connected generators, including solar PV systems contribute to maintaining grid stability through reactive power support. Compliance with these regulations ensures that the grid can handle the variable and distributed nature of renewable energy sources like solar power. Inverters are responsible for converting the DC electricity generated by the PV modules into AC electricity that is compatible with the electrical grid or the loads in a home or building. This conversion is critical because most electrical grids operate on AC power.
Increasing the efficiency of energy transmission from a solar PV system to the grid and minimizing losses is crucial for maximizing energy yield and improving system performance. Advanced MPPT algorithms ensure the PV system operates at its optimal power output under varying irradiance conditions^33,34,35. Additionally, Using high-efficiency transformers with low iron and copper losses improves energy transfer. High-performance circuit breakers and protection devices reduce power dissipation. That sounds like an interesting and complex topic! You’re delving into how reactive power varies with changes in irradiance in PV systems, especially focusing on inverter control mechanisms in grid-connected settings. In a grid-connected PV system, the inverter plays a crucial role in converting the DC from the solar panels to alternating current (AC) that can be fed into the grid. Inverters often have control mechanisms to manage various system parameters, including reactive power, which is crucial for grid stability³⁴. The relationship between Irradiance and reactive power is as given below.
Reactive power is essential for maintaining voltage levels in the grid, even though it doesn’t directly contribute to active power generation.
Reactive power can vary with changing irradiance levels because the output of the PV system depends on the incident solar radiation.
As irradiance increases, the active power produced by the PV system rises, but the inverter may adjust the amount of reactive power to maintain grid stability, voltage regulation, and minimize harmonic distortion
In grid-connected PV systems, inverter control mechanisms play a crucial role in ensuring the efficient operation and integration of solar power into the electricity grid.
These mechanisms enable the inverter to convert DC power from the solar panels into AC power, while also managing the interaction between the system and the grid to meet technical, regulatory, and safety requirements. Some key control mechanisms involved are:
Power Factor Control: Inverters often operate at a predefined power factor, but they can also dynamically adjust it based on grid conditions.
Volt-VAR Control: Many modern inverters use volt-ampere reactive control, which adjusts reactive power in response to voltage fluctuations, helping stabilize grid voltage.
Constant Reactive Power: Some inverters are set to provide constant reactive power (independent of active power) or adjust reactive power based on voltage measurements. Inverters are often required to either provide or absorb reactive power in certain grid conditions. By doing so, they help manage voltage levels and improve grid stability, especially in regions with high penetration of renewable energy.
Solar inverter control mechanisms in grid-connected photovoltaic systems are essential for ensuring that the solar power system operates efficiently, safely, and in compliance with grid standards. These mechanisms allow the system to dynamically adjust to varying conditions, support grid stability, and ensure high-quality power delivery. Inverters also play a critical role in maintaining the voltage and frequency of the AC power. They ensure that the power output matches the voltage and frequency of the electrical grid to avoid disruptions. This is particularly important when the PV system is connected to the grid, as the inverter must synchronize the generated AC power with the grid’s existing voltage and frequency.
A static synchronous compensator (STATCOM) is a type of flexible AC transmission system (FACTS) device used for reactive power compensation in power systems. In a grid-connected solar system, incorporating a STATCOM can significantly enhance the system’s performance and reliability. STATCOM-based reactive power compensation has a wide range of applications in grid-connected solar systems. Solar energy systems, especially large-scale installations, can produce or consume reactive power. STATCOMs can provide reactive power support when the solar system produces excess real power or absorb reactive power when needed. This helps maintain the power factor close to unity and improves the overall power quality. Reactive power compensation is essential for the smooth and efficient operation of grid-connected solar PV systems. It helps maintain voltage stability, improves power quality, enhances system reliability, optimizes efficiency, meets regulatory requirements, and provides economic benefits^14,16. By addressing the challenges associated with reactive power, solar PV systems can operate more effectively and contribute positively to the overall power grid.
The change in reactive power in a grid-connected PV system is influenced by various factors such as including solar irradiance, the control strategies of the inverters and the grid’s reactive power requirements. Reactive power is essential for voltage regulation, and its availability from the PV system depends on the system’s operating conditions. Inverters are equipped with MPPT algorithms that ensure the system is always operating at the maximum power point of the PV modules. This maximizes energy generation by adjusting the load to match the optimal power point given the current irradiance and temperature conditions. MPPT is particularly important because solar power generation is nonlinear and sensitive to environmental changes.
In grid-connected PV systems, the requirement for reactive power control arises from the need to maintain voltage stability and power quality within the electrical grid. As solar irradiance varies due to changes in weather conditions and time of day, the active power output of PV systems fluctuates significantly. These fluctuations can cause voltage deviations and instability at the point of common coupling (PCC) if not properly managed. To mitigate these issues, modern grid codes and utility standards often mandate that PV inverters not only supply active power but also participate in voltage regulation by providing or absorbing reactive power. This becomes especially critical in distribution networks with a high penetration of renewable sources, where voltage rise and reverse power flow can occur during periods of low load and high generation. Therefore, reactive power control strategies must be dynamic and responsive to real-time solar conditions, ensuring that the PV system supports the grid by modulating its reactive power contribution accordingly, thereby enhancing overall system reliability and operational efficiency. The reactive power Q_PV(t) is controlled to maintain grid voltage at the PCC. It must satisfy:
where; S_PV is apparent power rating of the inverter, Q_PV(t) is reactive power injected or absorbed and P_PV(t) is active power. Inverters have a maximum apparent power (S), so reactive power (Q) is limited by the available capacity after supplying active power. We can set a limit condition:
is found as. Although PV panels themselves generate only direct current (DC) active power, the inverter plays a crucial role in controlling and injecting reactive power based on grid needs and its control strategy. Here’s how the inverter influences reactive powe Inverter’s role in reactive power control. A solar inverter also called a grid-tied or grid-following inverter) converts DC power from the PV modules into alternating current (AC) power. Beyond this basic role, modern inverters particularly smart inverters are capable of:
Injecting reactive power (capacitive behavior)
Absorbing reactive power (inductive behavior)
Operating at different power factors (not just unity)
This is achieved through control algorithms that adjust the inverter’s output current phase angle relative to the voltage at the point of common coupling PCC. Inverter behavior is determined by its reactive power control mode, including:
Constant Power Factor Mode: Maintains a fixed ratio between P and Q.
Constant Q Mode: Delivers a fixed amount of reactive power regardless of voltage.
Volt-Var Control Mode: Dynamically adjusts Q based on local voltage levels (most common for voltage regulation).
In Volt-Var control, the inverter uses a programmed curve (defined by standards (like IEEE 1547) to inject or absorb reactive power depending on the voltage at the PCC. Solar inverters respond to:
Voltage sags/swells by adjusting Q
Grid faults (via fault ride-through settings) by injecting reactive power to support voltage recovery
Frequency deviations (in advanced inverters) with coordinated active/reactive power responses
Solar inverters do not generate reactive power inherently, but they synthesize it through power electronics and control. Their influence on reactive power in a grid-connected PV system depends on:
Inverter capacity and DC power availability
Control algorithms (e.g., Volt-Var)
Grid voltage and frequency conditions
Compliance with grid codes or utility requirements
In a grid-connected PV system, the inverter continuously monitors the voltage at its point of common coupling (PCC). Based on this measured voltage and a predefined control curve—typically a Volt-Var characteristic the inverter determines whether it needs to inject or absorb reactive power. This mechanism helps regulate grid voltage locally, supporting system stability especially in weak or heavily loaded distribution networks. The control logic embedded in the inverter performs real-time voltage measurements and uses them to compute the required reactive power.
This enables PV systems to supply reactive power when voltage is too high or absorb reactive power when voltage is too low. On partially cloudy days, solar irradiance can fluctuate rapidly causing corresponding changes in the active power output of the PV system. In response, inverters may dynamically adjust their reactive power output to stabilize voltage fluctuations caused by these changes. This study offers a mathematical approach to predict reactive power in PV systems based on solar irradiance, contributing to more efficient grid integration of renewable energy sources. Understanding how reactive power varies with solar conditions helps in the planning and optimization of grid-connected PV systems, ensuring better grid stability and reducing energy losses.
Despite the growing deployment of grid-connected PV systems, managing voltage stability and reactive power fluctuations remains a significant challenge especially under rapidly changing irradiance conditions. Traditional inverter control strategies often fail to optimally regulate reactive power in real-time, which can lead to voltage deviations and grid instability, particularly in systems with high solar penetration. This study presents a novel irradiance-dependent reactive power model integrated with inverter control logic, distinguishing itself by directly linking solar irradiance variations with dynamic reactive power behavior. Unlike existing works that either focus on steady-state conditions or assume constant inverter performance, this research models the real-time interaction between irradiance, inverter response, and grid voltage regulation. The proposed approach can be practically implemented in inverter firmware or grid management software, offering actionable insights for smart grid applications and voltage support mechanisms in high-renewable scenarios. The control strategies and system configurations for curve fitting-based reactive power control are summarized in Table 1.
Solar systems are connected to the grid through inverters, which convert DC power generated by the PV panels into AC power suitable for the grid and the aim of improving the sustainability of these types of developments. Modern inverters can also manage reactive power to help with voltage regulation and power factor correction. While the primary function of the inverter is to convert DC to AC, many inverters are designed to also manage reactive power. The capability to provide or absorb reactive power is often independent of the solar irradiation level as long as the inverter is operating within its capacity. Additionally, reactive power support can be influenced by the grid requirements and inverter settings. For instance, during periods of high solar irradiation the inverter might be programmed to absorb or supply reactive power to help stabilize the voltage on the grid. However, this control is often set by the utility or grid operator rather than being a direct function of the amount of solar irradiatio PV panels should be oriented towards the equator (south in the northern hemisphere, north in the southern hemisphere) for maximum exposure. If the system is grid-connected, it needs to comply with utility requirements for net metering to sell back excess power. The nonlinear variation of reactive power due to solar irradiation is difficult to determine, especially in the sunrise and sunset time interval. At the same time, it is quite difficult to develop an exact for such variations.
Solar irradiation (also called solar insolation) refers to the power per unit area received from the Sun in the form of electromagnetic irradiation. Standard Test Conditions (STC) play a critical role in the evaluation and comparison of photovoltaic systems by providing a consistent and controlled framework under which the performance of solar modules is measured. These conditions ensure that all manufacturers and researchers assess PV modules under the same environmental parameters, allowing for reliable benchmarking and performance predictions. Without STC, it would be challenging to distinguish whether differences in output are due to module quality or varying environmental factors. As such, STC serve as a foundational reference point for both design optimization and system sizing in real-world applications, even though actual operating conditions may differ significantly. It’s a key input that directly affects PV system performance.
Units: Typically measured in W/m² (watts per square meter)
Measurement Device: Pyranometer or reference cell
Purpose of Measurement:
Typical Values:
Clear, sunny day: ~ 1000 W/m² at STC.
Cloudy day: 100–400 W/m²
Night: ~ 0 W/m²
In a grid-connected photovoltaic solar system, the measurement of solar irradiation is carried out using devices capable of capturing the intensity of sunlight incident on the solar modules, ensuring accurate monitoring of environmental conditions affecting energy production. Reactive power is measured through instrumentation designed to monitor electrical parameters within the system, typically integrated into energy metering equipment or inverter-based monitoring systems that assess power flow characteristics between the PV array and the electrical grid.
The measurement of solar irradiation and reactive power is fundamental to the performance and stability of a grid-connected solar PV system. Accurate solar irradiation data allows for the precise estimation of energy generation potential, enabling optimal system design, forecasting, and real-time performance monitoring. It directly influences decisions regarding panel orientation, tracking systems, and expected energy yield. On the other hand, measuring reactive power is essential for maintaining power quality and voltage stability within the grid. The principal diagram for the measurement of solar irradiation and reactive power in the grid-connected solar PV system is shown in Fig. 2.
Measurement of solar irradiance and reactive power in grid-connected solar PV system.
Data acquisition in a grid-connected solar PV system involves the continuous collection and monitoring of electrical and environmental parameters to understand system behavior, particularly the relationship between solar irradiance and reactive power. This process typically includes the use of sensors to measure solar irradiance and devices that capture electrical outputs such as voltage, current, and reactive power from the inverter. The collected data is transmitted and recorded through data loggers or centralized control systems, allowing for real-time analysis and historical performance tracking. In systems where on-site measurement is not possible, data acquisition can also be achieved through online monitoring platforms provided by inverter manufacturers or through public databases that offer solar irradiance and PV performance datasets. This data is crucial for developing control strategies, validating models, and optimizing grid interaction, as it reflects how environmental variations impact power generation and reactive power behavior. Accurate data acquisition enables system operators and researchers to ensure efficient energy conversion, maintain voltage stability, and comply with grid regulations.
In a grid-connected solar PV system’s two critical parameters to measure are solar irradiance and reactive power. A solar irradiance meter is a device used to measure the amount of solar irradiance received on a specific surface over a given period. It quantifies the power per unit area, typically expressed in watts per square meter (W/m²). Solar irradiance meters are crucial for evaluating the efficiency of solar panels, monitoring solar energy systems and conducting environmental and meteorological studies. These devices typically employ sensors such as pyrometers or photodiodes to detect and measure solar energy. By providing real-time data, they offer valuable insights for researchers, engineers and solar power technicians to monitor and optimize system performance. An equivalent circuit for measuring reactive power in a grid-connected PV solar energy system based on solar irradiation is essential because it provides a simplified yet accurate representation of the system’s behavior under varying conditions.
Reactive power is a concept that arises in alternating current electrical systems. It’s typically denoted in volt-ampere-reactive (VAR). Reactive power is crucial in grid-connected systems because it affects voltage stability of analyzers can measure reactive power, active power, apparent power and power factor. These devices are usually installed at the inverter output to get an accurate reading of the power flow. Reactive power refers to the power oscillating between the source and load in an AC system due to inductive or capacitive elements.
In grid-connected photovoltaic systems, reactive power is exclusively controlled and delivered by the inverter. PV modules generate only DC active power, while the inverter converts this into AC and manages all reactive power functions required for grid stability and voltage regulation. Solar irradiation directly affects the voltage, current, and power output of a PV system.
The equivalent circuit is essential for analyzing and measuring reactive power in relation to solar irradiation in a grid-connected PV solar system. It serves as a simplified electrical model that represents the behavior of the PV array and its interaction with the power grid under varying solar conditions. By using this model, it becomes possible to simulate and predict how changes in solar irradiation affect both the generation of active power and the system’s reactive power behavior. The equivalent circuit helps in identifying how components such as inverters respond to dynamic environmental conditions, allowing for the design of control strategies that ensure compliance with grid codes. PV solar energy system is shown in Fig. 3.
Equivalent circuit for measuring reactive power according to solar irradiation in a grid-connected PV solar system.
An equivalent circuit reduces the complexity of a PV system by representing key components like PV arrays, inverters and grid connections as simple electrical elements resistors, capacitors, inductors and current/voltage sources. This makes it easier to understand and analyze the reactive power dynamics. The grid load used in the grid-connected PV solar energy system is as given below. (4 MW ohmic load, 120 kV/25 kV 47 MVA transformer, 30 MW and 2 MVAr inductive load, 120 kV 250 MVA utility load). Using an equivalent circuit to measure reactive power in a grid-connected PV solar system offers several advantages. Characteristics, which help technical staff and researchers analyze the behavior of reactive power under varying solar irradiation conditions.
Reactive power control in grid-connected PV systems is managed exclusively by the inverter. While PV modules generate active power based on the available solar irradiance, they are passive devices and have no inherent capability to produce or regulate reactive power. The inverter, as the active interface between the PV array and the electrical grid, is solely responsible for injecting or absorbing reactive power as required by grid voltage conditions. This function is critical for maintaining voltage stability, particularly in low-voltage networks with high PV penetration. The ability of inverters to provide dynamic reactive power support, independent of active power. The integration of PV systems into electrical distribution networks has prompted extensive research on their operational impacts, particularly in relation to power quality and voltage regulation. Numerous studies have addressed the role of inverters in facilitating the interface between PV modules and the grid, with a specific focus on maximum power point.
The characteristics of the SUNPOWER SPR-305-WHT solar panel are important for evaluating its suitability and performance in grid-connected PV systems. This panel is known for its high efficiency, primarily due to the use of monocrystalline back-contact solar cells, which reduce electrical losses and maximize energy conversion. Its high power output in a relatively compact size makes it ideal for installations where space is limited but high energy yield is required. Additionally, the panel exhibits strong performance under low-light and partial shading conditions, enhancing overall energy production throughout the day and across varying weather conditions. Its durability and long-term reliability, supported by robust materials and a strong warranty, contribute to lower maintenance costs and a longer service life. Understanding these characteristics is essential for accurate system design, energy yield forecasting, and achieving long-term return on investment in solar energy projects. The features of the solar panels used in the solar PV facility are given in Table 2.
In grid-tied PV systems, PV modules and inverters serve distinct but interdependent functions. PV modules are responsible for converting solar irradiance into direct current (DC) electricity through the photovoltaic effect. Their performance is governed primarily by environmental factors such as irradiance and temperature, and they operate passively without any capability to influence or respond to grid conditions. In contrast, inverters actively manage the interface between the PV array and the electrical grid. They convert the DC output of the PV modules into alternating current (AC) and are solely responsible for controlling reactive power flow. This includes supplying or absorbing reactive power to support grid voltage levels, a capability that PV modules themselves do not possess. Therefore, while the PV modules determine how much active power is available based on solar input, it is the inverter that regulates power quality and contributes to grid stability through dynamic control mechanisms.
While these approaches offer effective solutions under stable operating conditions, they often overlook the influence of solar irradiance variability on the inverter’s reactive power behavior. In a grid-connected PV system, the inverter serves as the active interface between the photovoltaic array and the utility grid, converting the direct current electricity generated by the PV modules into alternating current suitable for grid injection. While the PV modules are responsible for energy generation based on solar irradiance, they operate passively and have no role in grid interaction or power quality management. In contrast, the inverter is solely responsible for regulating both active and reactive power output. Reactive power essential for maintaining voltage stability and complying with grid codes is handled exclusively by the inverter. Modern inverters are equipped with control algorithms, such as fixed power factor, Volt-VAR, or dynamic droop-based methods, that enable them to adjust reactive power output in real time in response to voltage variations at the PCC. These functions operate independently of the active power output from the PV modules, allowing the inverter to continue supporting grid voltage even under low irradiance or curtailed generation conditions. This study focuses on modeling the behavior of reactive power as a function of solar irradiance, capturing how inverters respond to environmental changes to meet voltage regulation demands.
The observed correlation between solar irradiance and reactive power output is a direct consequence of the inverter’s embedded control mechanisms, which are designed to respond to grid voltage conditions. Under low irradiance, active power generation is reduced, and grid voltage may tend to drop especially in distribution networks with high PV penetration and limited voltage regulation infrastructure. In response, inverters activate Volt-VAR or droop control modes, supplying additional reactive power to stabilize voltage at the PCC. Conversely, at high irradiance levels, the active power output increases and local voltage typically rises, prompting the inverter to reduce or absorb reactive power to avoid overvoltage conditions.
This dynamic behavior explains the inverse relationship observed in the model: reactive power increases as irradiance decreases, not due to the PV modules themselves, but as a functional response of the inverter to maintain voltage stability. The derived analytical correlation holds significant importance in grid-connected PV solar systems, as it encapsulates both environmental inputs, such as solar irradiance, and the internal control logic of the system. This dual representation enables a more accurate and dynamic understanding of the system’s behavior under varying operating conditions. By integrating real-time environmental data with the system’s inherent control responses, the correlation becomes highly suitable for predictive control strategies and embedded system implementation.
This is particularly relevant for voltage regulation, where the inverter’s control mechanism plays a central role. The inverter must respond quickly and accurately to fluctuations in generation and load demands to maintain voltage stability within acceptable limits. Through the analytical correlation, the control system can anticipate and adapt to changes in solar input, enabling the inverter to regulate voltage more effectively and ensuring consistent power quality and reliable grid interaction.The derived analytical correlation thus reflects not only environmental input (irradiance) but also the system’s internal control logic, making it suitable for predictive control or embedded implementation. Voltage control by the inverter control mechanism is shown in Fig. 4.
Voltage control by the inverter control mechanism.
This diagram depicts a typical Volt-VAr control curve implemented in smart inverters. The curve defines the inverter’s reactive power output as a function of the local voltage at the point of common coupling. Within a specified voltage range, the inverter adjusts its reactive power injection or absorption to maintain grid voltage stability. Outside this range, the inverter either supplies maximum capacitive reactive power (when voltage is low) or absorbs maximum inductive reactive power (when voltage is high). There is a strong correlation between inverter control mechanisms and grid voltage dynamics. Advanced inverter controls (especially droop-based, VSG, and grid-forming types) actively contribute to voltage regulation, improve grid stability, and enhance resilience in weak or renewable-dominated grids.
To develop a more realistic and reliable model of an on-grid photovoltaic PV system, it is essential to incorporate voltage levels, inverter setpoints, and reactive power control modes in a unified and dynamic framework. These elements work in concert to ensure the PV system operates efficiently, supports grid stability, and meets regulatory requirements. Voltage levels define the operational context of the PV system whether it’s connected at low voltage (residential or small commercial), medium voltage (larger commercial or community systems), or high voltage (utility-scale). Each level introduces different challenges in terms of voltage regulation and fault response. For instance, systems connected to low-voltage networks are more susceptible to voltage fluctuations caused by high PV penetration and lower network impedance. Accurate modeling requires capturing these nuances, including line impedances, transformer characteristics, and short-circuit ratios. Inverter setpoints provide the reference targets that dictate how the inverter behaves under normal and abnormal conditions.
These include voltage setpoints at the point of PCC, active power limits based on solar irradiance and inverter rating, and reactive power or power factor targets. These setpoints are not static; they should be allowed to respond dynamically to grid conditions. For example, if grid voltage rises beyond nominal, the inverter should shift its operating point to absorb reactive power, helping to bring voltage back within acceptable limits. This dynamic interaction must be embedded into the control logic of the model. Such a system can simulate real-world behaviors like voltage rise in weak grids, the impact of cloud transients on power flow, and the effectiveness of inverter controls in mitigating these effects. This holistic approach is essential for designing future-ready PV systems that are both grid-friendly and reliable under dynamic operating conditions. A reliable PV grid integration model must integrate:
Accurate voltage level and network impedance profiles.
Well-defined inverter set points for voltage and power outputs.
Flexible reactive power control modes like Volt-Var.
Compliance with dynamic conditions (faults, irradiance variability).
Reactive power control modes, such as constant power factor, fixed reactive power, Volt-Var, and adaptive strategies, directly influence voltage regulation and grid support capabilities. Among these, Volt-Var control is particularly critical in realistic modeling as it allows the inverter to autonomously vary reactive power in response to voltage deviations. This mode can be defined using a piecewise-linear curve that maps inverter reactive power output to local voltage measurements, with defined deadbands and limits to prevent instability or overreaction.
By integrating all these components into a single model where voltage levels determine network behavior, inverter setpoints establish operational boundaries, and reactive power control actively maintains voltage stability the model becomes not only realistic but also robust.
Modern power electronic inverters, which interface PV systems with the electrical grid, offer the capability to mitigate voltage instability through reactive power control. Inverter-based control strategies such as Volt-Var control (reactive power as a function of terminal voltage), constant power factor mode, and adaptive voltage regulation enable these systems to contribute not only active power but also voltage support. Despite the development of these strategies, many simulation models used in system planning and analysis continue to treat inverter control behavior simplistically, often ignoring the interplay between voltage dynamics, setpoint variability, and real-time control responsiveness. This study addresses the research gap in comprehensive modeling by developing a detailed simulation framework that integrates grid voltage levels, inverter setpoints for both active and reactive power, and dynamic reactive power control strategies. By accurately modeling these interactions, the proposed framework provides a more reliable tool for evaluating the impact of PV systems on voltage regulation and grid performance.
The Sun Power SPR-305-WHT is a high-efficiency solar panel model designed for grid-connected PV systems. Its high efficiency, strong performance under a variety of conditions and long-term durability make it a top choice for residential and commercial solar installations. It also offers a good balance of power output and the panel is designed to withstand harsh environmental conditions. In addition, many companies in the photovoltaic industry have set their own targets for achieving sustainability and reducing their carbon footprint.
Data acquisition systems play a crucial role in capturing real-time irradiance levels, DC/AC power output, voltage, current, and power factor. This data is essential for analyzing how changes in irradiance affect the system’s reactive power exchange with the grid. By continuously collecting and processing this information, operators can implement adaptive inverter control strategies that ensure voltage stability, comply with grid codes, and enhance the overall efficiency of the PV system. In essence, the integration of data acquisition allows for the dynamic assessment of the irradiance–reactive power relationship, supporting both operational reliability and advanced grid-support functionalities. Solar irradiation directly affects the active power (P) generation of a PV system. Higher irradiation results in higher DC power from the PV array, which the inverter converts into AC power. Reactive Power change according to solar irradiation in Grid-connected PV Systems is given in Tables 2 and 3.
Solar energy is environmentally friendly and one of the most significant renewable energy sources, playing a vital role in sustainable energy development. In grid-connected PV systems, the relationship between solar irradiation and reactive power is critical not only for optimizing system performance but also for ensuring grid stability. However, this relationship is often overlooked in inverter control design, particularly under variable irradiance conditions. The lack of accurate models linking reactive power behavior to changing solar input limits the effectiveness of reactive power management strategies.
This study addresses this gap by investigating the dependence of reactive power on solar irradiation in grid-connected PV systems. The main objective is to develop an analytical model that captures this relationship using curve-fitting techniques applied to empirical data. The methodology involves systematic data collection, preprocessing, model selection, and performance evaluation. Results reveal that reactive power tends to increase under low irradiance conditions due to inverter response mechanisms and grid voltage regulation requirements. The proposed model can be integrated into inverter firmware or grid management tools to improve real-time reactive power control and enhance the stability and efficiency of PV-integrated power systems. This study fills these gaps by developing a simple yet accurate analytical model that directly relates solar irradiance to reactive power output, using curve-fitting techniques based on real-world data. The model is transparent, computationally lightweight, and suitable for implementation in inverter firmware or grid planning software. It enables proactive reactive power support under variable irradiance an operational advantage not addressed by most current strategies.
In conclusion, an equivalent circuit is a valuable tool that helps engineers design analyze and optimize the reactive power management of grid-connected PV systems. It simplifies the study of complex interactions between the inverter PV array and grid making it an essential approach for improving system performance and reliability. In a grid-connected PV solar system reactive power management is crucial to maintaining voltage stability and power quality in the grid. Solar irradiance plays a significant role in determining the amount of active power generated by a PV system but the relationship between reactive power and solar irradiance is managed through the inverter’s control algorithms.
Modern grid codes (e.g., IEEE 1547, EN 50549) increasingly require PV inverters to support grid voltage regulation via reactive power control, especially at high solar penetration levels. Inverters are designed to meet these requirements, whereas PV modules are not involved in any compliance or grid-interactive functionalities. During midday when irradiance exceeds 800 W/m², the model predicts minimal Q injection, shifting voltage support to capacitor banks. At dawn and dusk, the model anticipates elevated Q demands from PV inverters, enabling pre-emptive dispatch of reactive support from central sources or setting priority flags in Volt-VAR coordination schemes. By embedding the irradiance–reactive power relationship directly into inverter firmware or grid simulation platforms, the proposed model offers a practical enhancement to both real-time control and strategic planning. Its transparency and ease of implementation distinguish it from more complex, black-box approaches such as neural networks or dynamic simulations.
Solar irradiation affects the amount of active power generated by the PV system but reactive power management is more influenced by the grid requirements and inverter settings. Inverters play a crucial role in regulating reactive power to maintain stability on the solar grid, and this function is designed to complement the power generation capabilities of the solar PV system, independent of variations in solar irradiation^29,30. The increase in reactive power values at low solar irradiance is typically a result of the inverter’s response to changing operational conditions, including voltage regulation needs, power factor adjustments, and grid demands. Understanding these dynamics is important for optimizing the performance of grid-connected PV systems and ensuring effective grid support.
In a grid-connected PV system, solar irradiation and reactive power usually vary inversely. In the morning when solar irradiance is low the change in reactive power in a grid-connected PV system often exhibits nonlinear behavior. This phenomenon is primarily due to the relationship between the inverter’s operation and the characteristics of power generation under low-light. This phenomenon can often be visualized as a nonlinear curve of reactive power output against time during the morning period. The curve may appear to have small oscillations, sharp spikes, or gradual changes, reflecting the nonlinear nature of the inverter response to increasing irradiance.
The relationship between solar irradiation and reactive power in a grid-connected solar PV system is a key factor in ensuring efficient energy management and grid stability. As solar irradiation directly influences the amount of active power generated by the PV panels, it also affects the inverter’s capacity to manage reactive power. Under high irradiance conditions, the inverter may prioritize active power output, potentially limiting its ability to supply or absorb reactive power. Conversely, during low irradiance periods, more inverter capacity may be available to support reactive power compensation. Understanding this dynamic relationship is crucial for designing control strategies that balance energy production with power quality requirements. It also aids in voltage regulation, power factor correction, and compliance with grid codes. Ultimately, this interplay determines how effectively the PV system can support grid demands while maximizing energy harvest, making it a critical area of focus for both system designers and grid operators. The graph given in Fig. 5 was drawn using the values in Table 1.
Relationship between solar irradiation and reactive power in grid- connected solar PV system.
The variation of solar irradiation significantly influences reactive power in grid-connected PV systems. During high solar irradiation periods, inverters prioritize active power and leading to reduced reactive power capacity. In contrast, during low solar radiation inverters can provide more reactive power support, helping stabilize grid voltage. The proper management of these variations through advanced inverter control, grid code compliance, and system optimization is crucial for ensuring the stable and efficient operation of grid-connected PV systems. A local reactive load is incorporated into the system to evaluate the reactive power control capability of the inverter in maintaining a unity power factor at the AC busbar. By introducing this reactive load, the system’s ability to compensate for reactive power demand is tested, ensuring that the net reactive power at the point of common coupling remains close to zero. This regulation is essential for achieving a unity power factor, which minimizes power losses, improves voltage stability, and ensures efficient operation of the grid-connected photovoltaic system. The inverter dynamically adjusts its reactive power output in response to the reactive load, thereby validating its control algorithm and confirming compliance with grid support requirements.
Solar energy is one of the most prominent renewable energy sources and plays a crucial role in achieving sustainable development. In grid-connected PV systems, maintaining voltage stability requires effective control of reactive power, which is influenced by variable solar irradiation throughout the day. However, conventional inverter control strategies often do not account for the dynamic relationship between irradiation and reactive power demand, limiting system performance and grid compatibility. This study aims to model the dependence of reactive power on solar irradiation in PV systems by deriving an analytical equation using curve-fitting techniques.
The methodology involves data collection under real operating conditions, preprocessing, model selection, and performance validation. The results demonstrate that reactive power tends to increase under low solar irradiance, a behavior primarily attributed to inverter operation and the need to maintain voltage levels in compliance with grid requirements. The proposed model provides a practical tool for improving inverter control algorithms and can be integrated into inverter firmware or grid management software. By capturing the irradiance-dependent behavior of reactive power, this work contributes to enhancing the efficiency, reliability, and voltage support capabilities of PV systems in modern smart grids.
The influence of the solar inverter on reactive power in a grid-connected PV system is critically important for maintaining voltage stability, enhancing grid reliability, and ensuring compliance with grid codes. As PV generation increases across distribution networks, the conventional centralized approach to voltage regulation becomes less effective. In this context, the inverter serves as the primary tool through which reactive power is managed locally. Reactive power is essential for controlling voltage levels within acceptable limits. Unlike traditional rotating machines, solar PV panels do not inherently produce reactive power. It is the inverter, through its electronic control capabilities, that enables the injection or absorption of reactive power as needed by the grid. This is typically achieved through algorithms that respond to real-time voltage measurements at the point of common coupling, allowing the inverter to adjust its output in accordance with control strategies such as Volt-Var or constant power factor regulation.
The dynamic nature of solar generation further amplifies the inverter’s role. Since PV output fluctuates with irradiance, the inverter must manage its limited apparent power capacity between delivering active power and supplying reactive support. This trade-off becomes especially important during peak solar output, when the inverter may prioritize active power and limit reactive contribution, or during low-generation periods, when more capacity is available for voltage support. Moreover, as inverters become more advanced—integrating communication, forecasting, and coordination with utility systems they serve not just as passive converters, but as intelligent agents contributing to overall grid stability. The inverter’s ability to modulate reactive power in response to grid needs makes it indispensable in distributed generation environments, where decentralized voltage support is a prerequisite for resilient and efficient operation. In summary, the solar inverter’s influence on reactive power in a grid-connected PV system is foundational to the modern power system’s ability to accommodate high levels of renewable energy while maintaining stable, high-quality voltage profiles throughout the network.
The grid-connected PV system plays a vital role in promoting sustainable energy by enabling the direct integration of solar power into the electrical grid, thereby reducing dependency on fossil fuels and enhancing energy security. It allows for efficient utilization of solar energy at both residential and utility scales while supporting grid stability through active and reactive power management. Within this system, the three-level inverter is of particular importance due to its ability to improve power quality and conversion efficiency. Unlike conventional two-level inverters, a three-level inverter produces output waveforms that are closer to a pure sine wave, which significantly reduces harmonic distortion and electromagnetic interference.
This not only enhances the performance and lifespan of connected equipment but also lowers filtering requirements and switching losses. Furthermore, the three-level topology allows better voltage control and improved thermal performance, making it especially suitable for medium- to high-power PV applications. The combination of grid integration and advanced inverter technology ensures that solar PV systems operate more reliably, efficiently, and in accordance with modern grid standards. Figure 6 shows the grid-connected PV system and three-level inverter.
The grid connected PV system and three level inverter.
Grid-connected PV systems are critical to the transition toward sustainable energy infrastructure, enabling the direct integration of solar power into the utility grid. These systems reduce reliance on fossil fuels, lower greenhouse gas emissions, and enhance the overall energy mix with distributed generation. A key component enabling this integration is the inverter, which converts the DC output of solar panels into AC current suitable for grid use. Among various inverter topologies, the three-level inverter—typically based on the neutral-point clamped (NPC) architecture offers significant advantages in grid-connected applications.
In grid-connected PV systems utilizing three-level inverters, the choice of modulation strategy plays a critical role in determining inverter performance, output quality, and overall system efficiency. Traditional Pulse Width Modulation (PWM) techniques are widely used for controlling inverter switches to generate sinusoidal output voltages. However, for multilevel topologies such as the Neutral Point Clamped (NPC) three-level inverter, more advanced methods like Space Vector Pulse Width Modulation (SVPWM) offer substantial benefits. SVPWM maximizes the DC bus voltage utilization, reduces switching losses, and generates output voltages with significantly lower total harmonic distortion (THD) compared to conventional sinusoidal PWM.
This results in improved power quality at the grid interface and better dynamic performance, particularly under fluctuating solar irradiance conditions. Moreover, SVPWM allows more precise control of both active and reactive power, facilitating compliance with grid codes and supporting ancillary services such as voltage regulation and fault ride-through. Its efficient use of the available voltage vectors enables smoother transitions between switching states, which is particularly beneficial in high-power applications where switching losses and electromagnetic interference must be minimized. Therefore, integrating SVPWM in three-level inverters enhances the overall effectiveness of grid-connected PV systems by optimizing switching behavior and ensuring high-quality, stable power delivery to the utility grid.
The analytical model developed in this study linking solar irradiance directly to reactive power output—offers a practical and lightweight solution for integration into modern inverter control systems. Due to its low computational complexity and real-time compatibility, the model can be embedded into inverter firmware to dynamically adjust reactive power support based on current environmental conditions, enhancing voltage stability during irradiance fluctuations. Additionally, the model can be incorporated into grid management software or distribution system simulation tools to improve planning and coordination of distributed PV resources. This allows system operators to better anticipate reactive power requirements across varying solar conditions and optimize voltage profiles in low-voltage networks with high PV penetration.
A Perturb and Observe (P&O) based Maximum Power Point Tracking (MPPT) control strategy is implemented in conjunction with a boost DC-DC converter to ensure that the PV array operates continuously at or near its maximum power point (MPP). The P&O algorithm achieves this by periodically perturbing the operating voltage of the PV array and observing the resulting change in power output. If the power increases, the perturbation continues in the same direction; if it decreases, the direction of the perturbation is reversed. This iterative process enables dynamic adaptation to changing environmental conditions, such as irradiance and temperature, thereby optimizing energy extraction from the PV system. The boost converter plays a critical role by adjusting the voltage level between the PV array and the load or grid interface, allowing effective tracking of the MPP under varying operating conditions.
This study presents a fuzzy logic-based control approach for managing both active and reactive power in a grid-connected photovoltaic system that employs a three-level neutral-point-clamped (NPC) inverter. The fuzzy logic controller dynamically adjusts the inverter’s output to optimize power exchange with the grid, ensuring efficient energy utilization and compliance with grid support requirements. By using a three-level NPC inverter, the system benefits from improved voltage quality, reduced harmonic distortion, and enhanced control over power flow, contributing to the stable integration of photovoltaic generation into the electrical grid.
The variation of reactive power all day long in grid-connected PV systems is closely linked to changes in solar irradiance and the operational characteristics of inverters. Understanding this variation is crucial for effective grid integration, voltage regulation, and system performance optimization. Accurate modeling and analysis of reactive power variation can help ensure stable and efficient operation of PV systems within the grid. Cloud cover can cause sudden changes in solar irradiance which in turn affects the active power output and requires the inverter to adjust reactive power accordingly.
The relationship between solar irradiation and reactive power is vital for ensuring the stable and efficient operation of grid-connected PV systems. It affects voltage regulation, system performance, grid integration, and compliance with regulations. By effectively managing this relationship, PV systems can contribute to a more reliable and efficient power grid, optimize performance, and achieve economic benefits. Curve fitting is a statistical technique used to find the best-fitting curve or mathematical function that represents a set of data points. This method is widely used in various fields, including data analysis, modeling and forecasting. The goal of curve fitting is to create a mathematical model that approximates the underlying relationship between variables in a dataset. This model can then be used to make predictions, analyze trends, or understand the relationship between variables. Curve fitting method is a powerful technique for modeling relationships between variables and making predictions. MATLAB toolboxes and add-ons are as follows:
Curve Fitting Toolbox: This toolbox is essential for users who need advanced fitting capabilities, model validation, and graphical analysis. It provides automated fitting workflows, tools to specify custom models, and integrated diagnostics.
Optimization Toolbox: This toolbox is used in conjunction with lsqcurvefit to solve nonlinear least-squares problems. It offers optimization algorithms that can be used to minimize the residual sum of squares in curve fitting and other optimization problems.
Statistics and Machine Learning Toolbox: This toolbox provides additional functions for statistical analysis, model validation, and performance metrics. It is particularly useful for tasks such as cross-validation and goodness-of-fit measures such as R², RMSE, AIC and BIC to check the generalization of the model.
The choice of model and fitting method depends on the nature of the data and the specific goals of the analysis. By following a structured approach and using appropriate tools, you can effectively fit curves to data and gain valuable insights. Curve fitting is a powerful technique for modeling relationships between variables and making predictions. The choice of model and fitting method depends on the nature of the data and the specific goals of the analysis. By following a structured approach and using appropriate tools, one can effectively fit curves to data and gain valuable insights. MATLAB provides a comprehensive environment for curve fitting, from simple linear models to complex nonlinear and custom models, with extensive visualization and analysis tools to ensure the model selected is appropriate and effective. The integration of specialized toolboxes and external software enhances MATLAB’s capabilities in handling various curve fitting challenges.
Choose an appropriate mathematical function that best represents the relationship between solar irradiation and reactive power. Common functions used for curve fitting include linear, polynomial, exponential, logarithmic, and power functions. Solar irradiation is generally higher around solar noon when the sun is at its highest point in the sky. Early in the morning and late in the afternoon, the sun is lower and its rays are less direct, leading to lower irradiation levels. Additionally, cloud cover, atmospheric humidity and other weather conditions can significantly impact solar irradiation. Clouds can block or scatter sunlight reducing the amount of direct and diffuse irradiation reaching the ground.
In grid-connected PV systems, solar inverters are increasingly required to support reactive power management, especially under conditions of fluctuating solar irradiance caused by cloud cover. When clouds pass over a PV array, the output of active power drops rapidly due to the reduction in sunlight. However, the inverter can still operate within its apparent power limits to provide or absorb reactive power, supporting voltage regulation at the point of interconnection. This capability is critical for maintaining grid stability, especially in distribution networks with high PV penetration, where voltage fluctuations due to variable generation can be pronounced. Advanced inverters equipped with dynamic Volt-VAR control can autonomously adjust their reactive power output in response to local voltage changes, even when active power generation is reduced due to cloud transients. Furthermore, these inverters can maintain a pre-set power factor or follow a utility-specified reactive power profile, contributing to grid support functions such as voltage ride-through and stabilization. Thus, the inverter’s ability to decouple reactive power support from active power availability under cloudy conditions enhances the resilience and controllability of PV systems integrated into modern power grids.
The solar irradiation curve for all hours of a clear, cloudless day is a fundamental reference for understanding the daily energy availability from the sun. It provides a detailed profile of how solar energy varies from sunrise to sunset, typically forming a smooth, bell-shaped curve that peaks at solar noon. This curve is essential for predicting the performance of grid-connected PV systems, as it directly influences the amount of electricity that can be generated throughout the day. By analyzing this curve, system designers can optimize the sizing of PV modules, inverters, and energy storage components to match expected energy output with demand. It also serves as a baseline for comparing real-world performance under varying weather conditions and for evaluating the impact of shading or soiling. Furthermore, this consistent and predictable pattern is valuable for planning grid operations, scheduling energy dispatch, and implementing predictive control strategies that enhance the reliability and efficiency of solar energy integration into the power grid. The solar irradiation curve for all hours of a clear and cloudless day is as given in Fig. 7.
Solar irradiation curve for all hours of a clear, cloudless day.
The solar radiation curve for a clear, cloudless day typically follows a smooth, bell-shaped pattern over the course of daylight hours. This curve represents the intensity of solar energy (typically measured in watts per square meter, W/m²) reaching the Earth’s surface and is a function of the sun’s position in the sky. The data values for the change in solar irradiation throughout the day are provided below. Data values regarding the change in reactive power all day long are also provided below.
G=[38.40 42.21 46.72 51.91 55.51 59.21 66.43 71.62 77.47 83.20 95.10 104.62 108.43 117.74 130.42 144.13 157.64 163.23 170.71 175.75 186.97 195.16 209.14 219.79 228.91 234.86 239.96 242.13 247.62 254.92 263.80 275.36 278.55 287.64 294.83 307.38 319.94 327.02 335.63 347.79 359.13 367.43 380.94 393.78 401.86 413.92 417.59 427.75 435.75 444.93 453.95 461.76 467.92 475.72 483.27 489.71 498.95 515.69 520.17 527.82 540.23 556.07 570.56 581.72 597.34 611.70 623.24 639.58 648.10 657.46 665.70 680.75 695.58 704.71 715.22 729.67 748.59 760.97 771.39 783.78 796.92 802.76 904.59 817.75 828.19 836.54 841.79 853.74 860.36 871.56 880.97 889.14 906.74 918.11 929.65]
As solar irradiation changes all day long the output of the PV panels varies. Although PV systems primarily produce real power (active power), the associated inverter systems can also provide or absorb reactive power. The inverter’s ability to manage reactive power depends on the solar output and the configuration of the inverter. Data values regarding the change in reactive power throughout the day are given below.
Q=[2553.91 2373.65 2200.38 2200.39 1946.72 1863.59 1730.23 1652.26 1577.91 1516.03 1414.73 1352.18 1330.68 1284.73 1234.63 1190.81 1155.95 1143.25 1127.43 1117.47 1096.82 1082.93 1060.80 1045.13 1032.33 1024.25 1017.56 1014.69 1007.63 998.57 987.84 974.89 971.34 961.98 954.92 943.76 934.03 929.22 924.07 918.12 913.98 911.81 909.77 909.44 909.96 911.66 912.36 914.70 916.87 919.62 922.48 925.00 926.97 929.38 931.58 933.30 935.46 938.21 938.66 939.10 938.93 937.09 937.09 930.48 924.63 918.41 913.09 905.48 901.65 897.67 894.45 889.48 885.98 884.63 883.88 884.31 887.37 890.78 894.38 899.36 905.25 908.00 940.16 915.15 920.03 923.76 925.99 930.61 932.85 936.03 938.04 939.26 940.13 939.41 937.70]
The change in reactive power throughout the day in a grid-connected solar system is influenced by the interplay of solar irradiance, inverter capabilities and settings grid voltage, load demands and regulatory requirements. Effective management of reactive power is crucial for maintaining grid stability and optimizing the performance of the PV system. The curve fitting method was used to find developing a sustainable analytical expression between solar irradiation and reactive power in the grid-connected solar system.
This study addresses this gap by developing an analytical model that captures the dependence of reactive power on solar irradiance. Using curve-fitting methods applied to empirical data, the model reflects how inverters adjust reactive power output in response to changing environmental conditions. The goal is to improve reactive power management strategies and support firmware-level or grid-integrated solutions. Practical steps in model selection in MATLAB. This program provides several tools to help with model selection and fitting:
The curve fitting toolbox: includes functions like fit, which allows you to try different types of models (e.g., polynomial, Gaussian, exponential) and evaluate their fit using various statistics.
Custom models: With fittype, you can define custom models tailored to your data.
Validation: MATLAB allows you to visualize the residuals and calculate goodness-of-fit metrics like R², RMSE, etc.
Model function selection is critical because the model you choose directly affects not just the accuracy of your fit but also the interpretability of your results and the model’s ability to generalize to new data. A well-selected model should balance accuracy with simplicity, avoid overfitting or underfitting, and ideally provide clear insights into the data’s underlying process. Testing different models, using appropriate validation techniques, and analyzing the fit quality with tools available in MATLAB help ensure that your model serves both descriptive and predictive purposes. This makes the selection of a good model one of the most important steps in the curve fitting process. It sounds like you’re describing a mathematical model that captures the relationship between solar radiation and reactive power using a combination of known mathematical functions. Specifically, you’re combining:
Logarithmic functions,
Trigonometric functions,
Inverse functions.
This kind of composite function might arise in physical systems where multiple factors interact in complex ways, such as in electrical engineering, where reactive power (often related to power factor) can be influenced by varying environmental factors like solar radiation. I’ll explain how these components could fit together in such a model, and suggest a possible form for g(x). The g(x) function is a combination of known mathematical functions.
where; C1, C2, and C3 are constants that would need to be determined from empirical data, x represents the solar irradiation (or some variable associated with it), the logarithmic term log (x) models a non-linear relationship between the solar irradiation and reactive power that might arise due to saturation effects or logarithmic responses, the trigonometric term cos(x) captures oscillatory or cyclical behavior, which is often useful in modeling periodic phenomena and the inverse term 1/x might capture asymptotic behavior or diminishing returns, where the effect of solar irradiation on reactive power decreases after a certain threshold. The finding of constants C1, C2 and C3 by the curve fitting method is shown in Appendix A. In grid-tied PV systems, the availability of reactive power affects the efficiency of power transfer. By understanding the relationship between solar irradiation and reactive power, operators can optimize power flow, reduce losses, and enhance overall system efficiency. In grid-tied PV systems the availability of reactive power affects the efficiency of power transfer.
By understanding the relationship between solar irradiation and reactive power, operators can optimize power flow, reduce losses, and enhance overall system efficiency. The developed expression facilitates efficient reactive power management, optimizing grid stability while minimizing energy losses. Since solar irradiation is variable and directly impacts the active and reactive power output of PV systems, an analytical expression aids in forecasting energy contributions to the grid. This is particularly valuable for scheduling generation, integrating energy storage systems, and planning grid expansion. The analytical expression of reactive power depending on solar irradiation is expressed as follows.
We calculated how well the model matches the data using the R-squared (R²) value, which shows how much of the variation in the data is explained by the model. An R² value close to 1 means the model fits the data very well. In this case, the R² value is 0.9955, which means the model explains more than 99.5% of the variation in the data. This suggests that the model provides an excellent fit and closely represents the observed values. A analytical expression of reactive power in grid-connected PV solar systems is crucial for several reasons, particularly in the context of varying solar irradiation. Consistency was observed between the measurement data and theoretical values.
Understanding the analytical expression of reactive power in relation to solar irradiation enables better management of grid stability, improves system performance, ensures regulatory compliance, and optimizes economic benefits. It is a key aspect of modern grid-connected PV systems ensuring that they contribute effectively to both energy production and grid support. Modern PV inverters are equipped with reactive power control capabilities. The inverter can be programmed to provide or absorb reactive power based on grid requirements or voltage levels. The inverter’s reactive power output can vary depending on the real power being generated and the grid’s needs. The relationship between solar irradiance and reactive power can be inversely proportional under certain conditions. This inverse relationship is essential to understand for grid stability and efficient power management, as reactive power plays a significant role in maintaining voltage levels in the grid.
The variation between solar irradiation and reactive power in a grid-connected PV system is a critical aspect that influences both system performance and grid stability. As solar irradiation fluctuates throughout the day due to changing weather conditions, the amount of active power generated by the PV array also varies. This, in turn, affects the inverter’s capacity to manage reactive power, as the inverter has a limited apparent power capacity that must be divided between active and reactive components. During periods of high solar irradiation, most of the inverter’s capacity is used for active power generation, reducing its ability to supply or absorb reactive power. Conversely, under low irradiation conditions, the inverter may have more available capacity for reactive power support. Understanding this variation is essential for dynamic voltage regulation, maintaining power factor within acceptable limits, and ensuring compliance with grid codes. It also helps in designing intelligent control strategies that allow the PV system to adapt to real-time changes in environmental conditions while supporting the overall stability and reliability of the electrical grid. The relationship between solar irradiation and reactive power in the grid-connected solar system is shown in Fig. 8.
Variation between solar irradiation and reactive power in a grid connected PV system.
In the morning when the irradiation is low, the change in reactive power is nonlinear. During low irradiance periods, reactive power might fluctuate, leading to nonlinear variations in reactive power output. The goal is to find a closed-form expression or an algorithm that describes the reactive power as a function of irradiance and other system parameters. This expression helps predict the system’s behavior under different environmental conditions. Significant fluctuations in reactive power in a grid-connected PV system at high irradiation levels occur due to various factors related to the design of PV inverters, grid dynamics and control strategies. These fluctuations can impact the stability and performance of the grid and understanding the underlying reasons can help optimize the system for better efficiency and reliability.
Optimizing the inverter’s response time to voltage deviations ensures smoother reactive power output, even during high solar irradiation. The relationship between reactive power values and solar irradiance in a grid-connected PV system is essential to understand for optimizing system performance. By measuring and deriving analytical expressions for reactive power as it correlates with solar irradiance, we can better predict and control the reactive power output of the PV system based on real-time irradiance levels. Inverters must comply with grid codes that govern how distributed energy resources like PV systems should behave. This includes regulating voltage, providing reactive power, and disconnecting the PV system in case of grid faults.
In a grid-connected solar PV system, the reactive power values vary with solar irradiance in a non-linear fashion, particularly noticeable at sunrise and sunset. During these times, irradiance levels are low and rapidly changing, which causes non-linear fluctuations in reactive power values as the PV system transitions between lower and higher power states. Absolute error is the difference between the measured results and the analytical results. By calculating the absolute errors, you can determine how close the developed expression is to the values under varying conditions. This step is important to determine the reliability of your model in predicting reactive power based on solar radiation. Relative errors are the ratio of the absolute error to the true value and are expressed as a percentage. It highlights the performance of the developed model under different operating conditions. It helps to understand whether the deviations are significant or insignificant according to the scale of the measured values. Including these error metrics in our study not only validates the analytical model but also emphasizes the practicality and novelty of our approach in optimizing reactive power management in grid-connected PV systems.
Highlighting these findings in article will emphasize the uniqueness of our study, particularly in how the derived analytical expressions offer a novel, irradiance-based approach to managing reactive power in grid-connected PV systems. This approach could provide valuable insights for future grid-integrated renewable energy models. When PV systems are optimized to manage reactive power based on real-time conditions, like fluctuating solar irradiance, they can either supply or absorb reactive power as needed reducing dependency on other reactive power sources. This not only minimizes transmission losses but also enhances overall grid. This can result in cost savings and enhanced economic performance of the solar installations. As more PV systems are integrated into the grid, understanding and managing the interaction between solar irradiation and reactive power becomes increasingly important. Sudden changes in solar irradiation (due to clouds passing over or other weather conditions) can lead to rapid changes in PV output and, consequently, reactive power requirements.
The amount of solar irradiance directly affects the power output of PV systems. While active power primarily depends on irradiance and system efficiency, reactive power is influenced by grid voltage, power factor settings, and inverter control strategies. In grid-connected PV systems, inverters regulate reactive power to maintain grid stability, compensate for voltage fluctuations, or comply with grid codes. The reactive power output can vary non-linearly with changes in irradiance and grid conditions. Modern inverters also provide monitoring capabilities, allowing operators or users to track the performance of the PV system in real-time. They can send and receive data about system performance, including energy production, fault detection, and sometimes even provide remote control. Inverters regulate the voltage and frequency of the AC output to ensure compatibility with the grid. Measuring solar irradiance and reactive power in a grid-connected PV system is critical for understanding its performance and operational efficiency. Analytical methods or software tools like MATLAB/Simulink can be used to estimate reactive power based on known system parameters and operating conditions. Many regions require grid-tied PV systems to adhere to specific reactive power support criteria to ensure grid compatibility.
An analytical expression helps in quantifying and meeting these regulatory requirements, making PV systems more compliant and easier to integrate. Operation of equipment such as inverters, which convert DC power from PV panels into AC power for grid connection, depends on managing both active and reactive power. Variations in solar irradiation impact the load on inverters and their efficiency in maintaining grid stability. Additionally, fluctuations in reactive power can impact the overall power quality of the grid. This includes issues like voltage regulation, power factor correction and mitigation of harmonics components. Solar irradiation variations influence the reactive power demand from the grid, particularly in scenarios where the PV system is a significant portion of the generation capacity.
When irradiation levels are high, typically during peak sunlight hours, the PV panels generate more electricity. In this scenario, the power factor tends to be higher because the real power output closely matches the apparent power drawn from the grid. Whereas, when irradiation levels are low, such as during cloudy weather or nighttime, the PV panels produce less electricity. In these conditions, the power factor may decrease because the real power output diminishes compared to the apparent power drawn from the grid. This may be due to reduced efficiency or increased reactive power flow.
Reactive power is crucial for maintaining voltage stability in the grid. Solar irradiation directly affects the amount of active power (real power) generated by the PV system. The variation in solar irradiation leads to fluctuations in active power output, which in turn can affect the reactive power requirements of the grid-connected system. The relationship between solar irradiation and reactive power in grid-connected PV systems underscores the need for careful planning, monitoring, and control to ensure reliable grid operation and optimize power quality. It was observed that the graphs of Fig. 4 found as a result of the measurement and Fig. 6 found analytically changed inversely. Reactive power demand tends to increase during both morning and evening hours when solar irradiation is low, especially in systems that rely heavily on solar PV for power generation. Conventional sources or compensating devices are often required to balance this reactive power demand and maintain voltage stability of the grid.
As solar irradiation begins to increase, PV systems start generating power, but initially, their contribution is small. Many PV inverters do not supply reactive power; instead, they prioritize active power generation. In the evening, the load demand (especially residential) generally increases. Many loads like lighting and appliances introduce more reactive power demand, potentially causing voltage dips. Harmonic components in solar energy systems result in reduced energy quality and distortion of the sinusoidal waveform of voltage and current. To provide quality electrical energy, the power factor in PV solar systems must be close to unity. Grid operators and utility companies need to manage the balance between reactive and active power to ensure stable and reliable operation of the grid.
Matlab programming is widely used for modeling, simulation and analysis in engineering and scientific fields. In this case, the authors likely used Matlab programming for developing a model that simulates the behavior of a grid-connected PV system, especially its interaction with grid parameters like voltage and reactive power. Inverters can provide reactive power support to the grid, helping maintain voltage stability. Reactive power doesn’t contribute to active energy but is crucial for managing voltage levels and ensuring the efficient transmission of active power. Inverters can be programmed to either inject or absorb reactive power based on grid needs, helping avoid overvoltage or under voltage situations.
Variations in solar irradiation directly affect the dynamic behavior of the PV system, necessitating robust control strategies to manage reactive power flow and voltage levels. Continuous research and innovation are essential for addressing these concerns and advancing the environmental sustainability of solar PV technology.
Fluctuations in reactive power can indeed impact the overall power quality of grid-tied solar systems. Power quality refers to how effectively electrical power is delivered to meet the demands of the load without causing instability or inefficiency in the grid. Reactive power is a critical component in maintaining stable voltage levels, and fluctuations in reactive power can have several consequences that affect power quality. Some of the work that can be done in the future; this expression is improved by incorporating additional environmental factors such as temperature changes, shading effects and the influence of dynamic weather conditions. Furthermore, future work can focus on validating the proposed model under various grid conditions such as varying grid voltages and frequency fluctuations to increase its applicability in real-world scenarios. In addition, the integration of this analytical expression into advanced control strategies for reactive power compensation can be investigated to optimize the stability and efficiency of grid-connected PV systems.
This work has significant implications for sustainable energy solutions, as it enables enhanced grid performance with renewable sources and minimizes the dependence on fossil-fuel-based power generation. By facilitating the stable integration of solar power, this research supports the global push toward a cleaner, more resilient energy landscape. This work provides a foundation for improving the understanding and control of reactive power in PV systems, advancing the integration of renewable energy into modern power grids.
Future research should aim to implement the proposed control strategies on real-time digital simulation platforms or hardware-in-the-loop (HIL) systems to assess their performance in practical settings. Evaluating latency, responsiveness, and stability under real grid conditions would offer deeper insights into operational viability. Additionally, aligning these strategies with updated smart inverter standards, such as IEEE 1547-2018, can ensure compliance and enhance interoperability within modern power systems. There is also value in exploring adaptive or AI-based control techniques that dynamically respond to rapid fluctuations in solar irradiance and grid disturbances. Further work should examine how these strategies influence the hosting capacity of distribution networks and their contribution to overall grid stability, especially in scenarios with high PV penetration and limited reactive power support from traditional sources.
Data associated with the study can be obtained from the corresponding author upon request.
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Electric and Energy Department, OSB Vocational School, Mardin Artuklu University, Mardin, Turkey
Suleyman Adak
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S.A. wrote the main manuscript text and S.A. prepared the figures. All authors reviewed the manuscript.”
Correspondence to Suleyman Adak.
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Adak, S. Control strategy evaluation for reactive power management in grid-connected photovoltaic systems under varying solar conditions. Sci Rep 15, 24697 (2025). https://doi.org/10.1038/s41598-025-08918-y
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Received: 07 February 2025
Accepted: 24 June 2025
Published: 09 July 2025
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DOI: https://doi.org/10.1038/s41598-025-08918-y
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