© The Author(s), published by EDP Sciences, 2025

List of abbreviations

PV: Photovoltaic

AC: Alternating Current

RPC: Reactive Power Control

APC: Automatic Power Control

MPPT: Maximum Power Point Tracking

1 Introduction

Since the advent of industrial society, fossil fuels have been extensively exploited. As non-renewable resources, fossil fuels cause significant environmental pollution when burned. Consequently, countries around the world have been actively developing renewable energy technologies to reduce their dependence on fossil fuels [1]. According to data from the International Renewable Energy Agency (IRENA), by 2025, the global cumulative installed capacity of PV systems will reach 1860 GW, with distributed PV accounting for 32% (approximately 595 GW), becoming a core growth driver. In 2024, China’s new installed capacity was 85.22 GW, accounting for about 60% of the global increase. In the same year, the United States added 36.4 GW of utility-scale PV capacity, representing approximately 58% of national total new power generation capacity [2]. Distributed photovoltaics are primarily rooftop or small-scale building systems, connected to the power grid via low-voltage lines and not subject to centralized grid dispatch. As the installed capacity of photovoltaics continues to rise, overvoltage issues have started to emerge in the low-voltage distribution network. In the low-voltage distribution network, the R/X ratio is high, and the grid voltage is influenced not only by reactive power distribution but also by active power distribution [3, 4]. When the PV power output is high due to sufficient sunlight, power backflow may occur in the distribution network, leading to an increase in voltage at the end of the line. Excessive line voltage can reduce the stability of the power grid and may lead to malfunctions in user loads near overvoltage nodes, ultimately leading to economic losses [5–7].

Various methods of voltage regulation (RPC) using reactive power have been proposed in reference [8–11] to address the overvoltage issue in the distribution network. However, the impact of reactive power on the network voltage is limited, making the use of reactive power alone for voltage regulation less effective. A method for regulating voltage (APC) by reducing active power output has been proposed. However, reducing active power can compromise the economic benefits of PV systems. In low-voltage distribution networks, photovoltaic generation is primarily in the form of small-scale distributed systems, and a significant reduction in PV output may result in economic losses for the users of these systems [12]. Various control strategies that utilize both active and reactive power to regulate voltage are proposed. In the distribution network, overvoltage conditions often occur on lines with multiple PV power sources, with the most severe overvoltage typically occurring at the end of the line [13, 14]. The strategy is employed to ensure that the voltage at the grid connection point does not exceed the limit by reducing active power. However, the active power output of the PV system at the end of the line is reduced the most, which negatively impacts the economic interests of photovoltaic users at the line’s end [13]. The coordination of multiple PV power supplies was addressed in reference [15] and [16], where a macro-control method was proposed that leverages the reactive power capacity of other photovoltaic systems to assist in voltage regulation. However, a detailed implementation strategy for coordinating the control of multiple PV power supplies was not provided. The proposed strategy is designed only for the case of a single PV power supply being connected and is not applicable to scenarios where multiple PV power supplies are installed on a single feeder line [14].

This paper proposes an auxiliary voltage regulation control strategy for photovoltaic inverters. When the grid voltage is within the normal range, the photovoltaic system operates at the maximum power point with a unit power factor. As the grid voltage increases, the photovoltaic system begins to absorb reactive power to help suppress further voltage rise. If the grid voltage continues to exceed the preset threshold, the photovoltaic system reduces its active power output to prevent the voltage from increasing further. Once the photovoltaic system reaches its regulation limit, the system transmits a signal to the next higher-level inverter. Upon receiving the signal, the upper-level inverter adjusts the set voltage in the regulation strategy to match the current grid voltage, and the process continues until all photovoltaic systems reach their regulation limits. This control strategy enables each photovoltaic inverter to actively participate in the grid’s voltage regulation process while maximizing the economic benefits of each photovoltaic power source.

This paper focuses on addressing the issue of coordinated regulation of reactive and active power of PV sources and their participation in voltage adjustment of distribution networks. The proposed strategy can fully exploit the voltage support capability of PV sources, ensure the economic benefits of photovoltaic power generation, and achieve multi-machine coordinated control of distributed PV sources. Simulation examples verify the effectiveness of the proposed strategy.

2 Causes of overvoltage of distribution network caused by photovoltaic access

The typical structure of a low-voltage distribution network containing distributed PV power is shown in Figure 1.

Figure 1 Distribution network with photovoltaic sources.

In Figure 1, U_k represents the voltage magnitude at node k; P_k and Q_k are the active power and reactive power flowing into node k respectively; P_pv,k and Q_pv,k are respectively the active and reactive power emitted by the k photovoltaic power supply; P_load,k and Q_load,k indicate the local load at node k. The relationship between the horizontal and vertical components of voltage drops and voltage is as follows:$$\begin{array}{c}∆{ \dot{U}}_k=\frac{R_k{P}_k+X_k{Q}_k}{\left|{\dot{U}}_k\right|}\\ \delta {\dot{U}}_k=\frac{X_k{P}_k-R_k{Q}_k}{\left|{\dot{U}}_k\right|}\end{array}$$(1)

The phasor diagram showing the relationship between the node voltage and the horizontal and vertical components of the voltage drop is presented in Figure 2.

Figure 2 Voltage drop phasor diagram.

In low-voltage distribution networks, the phase angle difference between two nodes is small, and the difference in voltage amplitude is primarily influenced by the vertical component of the voltage drop, while the horizontal component can be neglected. Therefore, the voltage difference between the nodes can be expressed as:$$\left|{\dot{U}}_{k-1}\right|-\left|{\dot{U}}_k\right|\approx ∆{\dot{U}}_k=\frac{R_k{P}_k+X_k{Q}_k}{\left|{\dot{U}}_k\right|}$$(2)

In low-voltage distribution networks, R≫X the voltage amplitude is mainly affected by the active power distribution. When line losses are neglected, the active power flowing into the k node can be expressed as:$$P_k=P_{\mathrm{load},k}+P_{k+1}-P_{\mathrm{pv},k}$$(3)

When sunlight is sufficient, the power generated by the photovoltaic system significantly exceeds the local load, P_pv≫P_load the active power is transmitted from the end of the line to the grid, become:$$P_k\approx -P_{\mathrm{pv},k}+\sum _{i=k+1}^n-P_{\mathrm{pv},i}=\sum _{i=k}^n\left(-P_{\mathrm{pv},i}\right)$$(4)

After neglecting line losses, the voltage drop formula of each node can be expressed as:$$\left|{\dot{U}}_{k-1}\right|-\left|{\dot{U}}_k\right|\approx ∆{\dot{U}}_k\approx -\frac{R_k\sum _{i=k}^n{P}_{\mathrm{pv},i}+X_k\sum _{i=k}^n{Q}_{\mathrm{pv},i}}{\left|{\dot{U}}_k\right|}$$(5)

According to equation (5), under conditions of high sunlight intensity, the active power generated by the photovoltaic system significantly exceeds the local load. As a result, the voltage at the end of the distribution network becomes significantly higher than the voltage at the beginning of the line, and the end voltage will increase with the rising photovoltaic output, ultimately causing the voltage at the end of the line to exceed the limit.

3 Auxiliary voltage regulation control strategy

In low-voltage distribution networks, the R/X ratio is large, and the impact of reactive power adjustments on voltage regulation is limited. Consequently, active power regulation becomes essential for voltage control. However, reducing active power will affect the economic benefits of photovoltaic systems. According to equation (5), overvoltage at the end of the line is most severe when sunlight is abundant. If voltage control is based solely on reducing active power according to the grid voltage at the connection point, the active power output of the photovoltaic system at the end of the line will be significantly reduced, while the active power output from systems further upstream will only be slightly affected. Such a control strategy disproportionately disadvantages photovoltaic users at the line end. Therefore, photovoltaic systems need to work in coordination with each other to ensure the economic benefits of each user while maximizing the voltage regulation capabilities of each photovoltaic inverter.

The proposed strategy utilizes both reactive and active power to regulate the voltage. The strategy calculates the maximum power in real-time through maximum power estimation to ensure that each PV power source contributes 10% of the available active power to voltage regulation. Small AC signals are injected into the system to facilitate communication between the PV power sources, ensuring coordinated voltage regulation. The detailed steps are as follows.

1. When the grid voltage is within the voltage regulation dead zone, each photovoltaic power supply operates in unit power mode.

2. As the grid voltage continues to rise and exceeds the dead zone, the photovoltaic power supply initiates reactive power absorption proportional to the grid voltage.

3. When the grid voltage reaches the voltage limit, the photovoltaic power supply begins to reduce active power, unit capable of reducing up to 10% of the available active power to assist in system voltage regulation.

4. When a photovoltaic power supply reaches its adjustment limit, if the voltage continues to rise, the unit sends a signal to the previous inverter indicating that the adjustment limit has been reached. Upon receiving the signal, the last photovoltaic power supply will set the current grid voltage as the reference voltage for the voltage control strategy to participate in system voltage regulation.

3.1 Reactive power control strategy

The reactive power control strategy employs Q-U droop control, with the voltage amplitude at the grid connection point serving as the reference. The reactive power output of the photovoltaic inverter is determined by the voltage amplitude at the grid connection point. The relationship between reactive power and the voltage at the grid connection point is as follows:$$Q=\{\begin{array}{c}\begin{array}{cc}-Q_{\max },& U\ge U_{\mathrm{limit},\mathrm{up}}\end{array}\\ \begin{array}{cc}-\frac{Q_{\max }\left(U-U_{\mathrm{dz},\mathrm{up}}\right)}{U_{\mathrm{limit},\mathrm{up}}-U_{\mathrm{dz},\mathrm{up}}},& U_{\mathrm{limit},\mathrm{up}}>U>U_{\mathrm{dz},\mathrm{up}}\end{array}\\ \begin{array}{cc}0,& U_{\mathrm{dz},\mathrm{up}}\ge U\ge \end{array}{U}_{\mathrm{dz},\mathrm{low}}\\ \begin{array}{cc}\frac{Q_{\max }\left(U_{\mathrm{dz},\mathrm{low}}-U\right)}{U_{\mathrm{dz},\mathrm{low}}-U_{\mathrm{limit},\mathrm{low}}},& U_{\mathrm{dz},\mathrm{low}}>U>\end{array}{U}_{\mathrm{limit},\mathrm{low}}\\ \begin{array}{cc}{Q}_{\max },& U\le \end{array}{U}_{\mathrm{limit},\mathrm{low}}\end{array}$$(6)

Reactive power leads to increased losses, so a voltage dead zone is set in the Q-U control strategy to optimize economic benefits. When the grid voltage is within the dead zone, the photovoltaic inverter operates at unit power. Once the voltage exceeds U_limit, the inverter outputs the maximum reactive power. For this study, the dead zone voltage and U_limit are set to 1.02 and 1.05, respectively. The Q-U curve for reactive power regulation is shown in Figure 3.

Figure 3 The relationship between reactive power and voltage emitted by photovoltaic source.

The upper limit of reactive power regulation is limited by the minimum power factor of the system and the maximum capacity of the photovoltaic inverter, and 0.7 is selected as the minimum power factor in the control strategy of this paper.$$Q_{\max }=\min \left\{\left|P\tan \left(\arccos F_{\min }\right)\right|,\sqrt{S^2-P^2}\right\}$$(7)

Where F_min is the minimum power factor, P is the active power emitted by the current photovoltaic, S is the rated capacity of the photovoltaic inverter.

3.2 Active power control strategy

When the voltage at the grid connection point rises to U_set and continues to increase, the active power output must be reduced to control the voltage rise. Throughout the day, fluctuations in sunlight intensity and temperature cause corresponding variations in the power output of the photovoltaic system. At any given moment, the photovoltaic system has a maximum output power, P_max. For example, consider the active power control strategy at a specific time: the voltage at the grid connection point is monitored. If the voltage exceeds U_set, the photovoltaic system reduces the output power. When the active power is reduced to 0.9P_max, the PV inverter reaches the limit of active power adjustment, corresponding to the left boundary of the shaded area in Figure 4.

Figure 4 PV source operating range when voltage control.

The shaded area represents the operating range of the photovoltaic power supply under the control strategy described in this paper. Once the active power regulation limit is reached, if the voltage continues to rise beyond U_set, the photovoltaic system will send a signal to the next-level photovoltaic inverter. Take the 4-nodes in Figure 1 as an example:$$U_4=U_{\mathrm{set},4}$$(8) $$∆U_4=\frac{0.9R_4{P}_{\max }-X_4{Q}_{\max }}{\left|\dot{U_4}\right|}$$(9)

Once the signal from the next level is detected, the system identifies that the PV power supply at the next level has reached the active power regulation limit and the point of common coupling voltage has exceeded the permissible threshold. After detecting the signal, the PV power supply takes the current point of common coupling voltage as the new U_set:$$\begin{array}{c}{U}_3\approx U_{\mathrm{set},4}-∆U_4\\ U_{\mathrm{set},3}=U_3\end{array}$$(10)

PV cells regulate the output power through adjustments to the operating voltage. To reduce the output power of PV cells, the operating voltage needs to be increased; to increase the output power, the operating voltage of PV cells needs to be decreased. The overall process of the active power regulation strategy is shown in Figure 5.

Figure 5 Active power control process.

3.3 Maximum power estimation of photovoltaic cells

To ensure the stability of the system during normal operation, the PV power supply should work in region II. When the system voltage is normal, the PV power supply operates in the maximum power point tracking (MPPT) state, corresponding to point M in Figure 6. When the voltage exceeds Uset, the active power is continuously reduced until the active power reaches 0.9P_max, transitioning from from point M to point A in Figure 6. Upon reaching point A, the system reaches the adjustment limit.

Figure 6 Photovoltaic cell P-V curve.

The dP/dU value is larger at the operating point A. To prevent large power fluctuations, two steps can be used for power reduction and MPPT as shown in Figure 5. To make the PV cell operate at point A, it is necessary to calculate the maximum power of the PV cell in real-time. The model of the PV cell is shown in Figure 7. The model is relatively simple and has high accuracy.$$I=I_{\mathrm{ph}}-I_0\left[\exp \left(\frac{U+{\mathrm{IR}}_s}{n{U}_{\mathrm{th}}}\right)-1\right]-\frac{U+{\mathrm{IR}}_s}{R_{\mathrm{sh}}}$$(11)

Figure 7 Equivalent circuit of photovoltaic cell.

Where I and U are the output current and voltage of the PV cell, respectively; I_ph is the photo-generated current; I₀ is the reverse saturation current of the diode; n is the diode ideality factor; U_th is the temperature potential; R_s is series internal resistance; R_sh is parallel internal resistance.

Equation (11) demonstrates that the formula for calculating the maximum power is complex and computationally intensive to solve directly on a small controller. In order to simplify the calculation, the quadratic polynomial of illumination and temperature can be used to calculate the maximum power of PVs [17–19].$$P_{\max }=a_{1}T+a_2{T}^2+b_{1}G+b_2{G}^2+\mathrm{cTG}+d$$(12)

Where P_max is the maximum output power of the PV cell under the corresponding temperature and illumination conditions; T and G are temperature and intensity of illumination, respectively. The coefficients in the equation can be derived from a linear regression analysis of the P_max, G and T data of the PV cells. A PV module consists of many series and parallel units. Under the assumption that the array is unobstructed, the entire module can be estimated in the same way and the total power is equal to the sum of the power of the small units. In this paper, the PV cells of type SPR-305 E-WHTD are used, and linear regression is applied to the data to derive the parameters for their maximum power estimation as shown in Table 1.

By substituting the parameters from Table 1 into equation (12), the estimated maximum power calculated by equation (12) is compared with the actual maximum power of photovoltaic cells, and the results are shown in Table 2.

Figure 8 illustrates the surface composed of the estimated power values under different illumination and temperature, and the purple points in Figure 8 represent the data from 16 PV cells used in the regression calculation. As evident from Figure 8 and Table 2, equation (12) demonstrates high accuracy in calculating the maximum power.

Figure 8 Surface of maximum power estimate.

3.4 Communication between inverters based on small AC signal

The auxiliary voltage regulation strategy proposed in this paper uses the power line as the transmission line of communication and achieves communication between PV inverters by injecting a small AC signal into the system.

The communication process is illustrated in Figure 9. Taking the kth PV power supply as an example, when the voltage exceeds the limit after reaching the adjustment limit, the kth PV power supply injects k small AC signals within a short period of time. When a small AC signal is detected for k times in a short time, the k−1th PV power supply sets U_set,k−1 to the current point of common coupling voltage value U_k−1 according to the voltage regulation measures.

Figure 9 Information transmission process between PV sources.

The communication strategy injects a signal into the system by superimposing a small AC signal on the original modulated wave, and only one PV power supply outputs a small AC signal at the same time. As shown in Figure 10, when any of the PV power supplies outputs a small AC signal, the other power supplies can detect the signal at the point of common coupling. The amplitude of the detected signal is the amplitude obtained by the impedance voltage divider after attenuation of the small AC signal filter. Therefore, the threshold should be comprehensively considered according to the filter and network parameters.

Figure 10 System simplification diagram with a small AC signal.

To avoid misjudgment and false operation caused by insufficient accuracy of the extraction algorithm during detection, the frequency of the small AC signal must be carefully selected to avoid proximity to the system’s fundamental frequency. Since the points of common coupling of the PV power supplies are close to the load, the selected frequency should also avoid the harmonic frequency easily generated by some civil and industrial loads. In addition, since a filter is present on the AC side of the PV inverter, the selected small signal frequency cannot be too high. The signal frequency must be lower than the cut-off frequency of the filter rectifier on the AC side of the inverter to prevent the signal from being attenuated too much when passing through the filter. In this paper, the frequency of the small AC signal is selected as twice the fundamental frequency of 100 Hz, while the amplitude is determined based on the system’s total harmonic content. Generally, the total harmonic content of the inverter should not exceed 5%, and the single harmonic content should not exceed 3% [20–21]. For the simulation, the distribution network voltage amplitude is set to 311 V, and the small AC signal amplitude is selected as 5 V.

4 Simulation analysis

To validate the proposed control strategy, the topology depicted in Figure 1 is simulated on MATLAB, and the parameters used in the simulation are shown in Table 3. PV_1~4 have the same parameters, and the initial value of U_set for each PV power supply is 1.05 p.u.

As light intensity continuously increases, the active power output of the photovoltaic power supply also increases. According to equation (5), when the output power of the PV power supply increases, the voltage at each node in the Distribution network continues to increase, as shown in Figure 11. At around 11:25, the voltage at PV4 reaches the upper voltage limit of 1.05 p.u. If the PV power supply still maintains the MPPT control strategy, the voltage of each node of the distribution network will continue to rise until the node voltage exceeds the limit, and there is a voltage safety risk.

Figure 11 The voltage of grid-connection point and Uset of PV4 and PV3.

The outputs of PV₄ and PV₃ under the proposed control strategy are depicted in Figure 12 and Figure 13, respectively. The PV power supply absorbs reactive power from the grid according to equation (6) as the point of common coupling voltage U increases continuously. P_max is the maximum power value estimated by the maximum power estimation method. The PV power supply remains in the MPPT state until the system reaches its regulation limit. As shown in Figure 11 and Figure 12, when the voltage U₄ exceeds U_set,4, PV₄ starts to reduce the active power in active power reduction mode. At this time, the reactive power is also reduced by the limitation of the minimum power factor of the system. Therefore, the voltage at PV4 is effectively controlled.

Figure 12 The active and reactive power of PV4.

Figure 13 The active and reactive power of PV3.

When P_pv,4 is equal to 0.9P_max, PV₄ reaches the regulation limit, a small AC signal is injected into the system, as shown in Figure 14. When PV₃ detects the small AC signal from PV₄, U_set,3 is set to the current U₃ value of 1.046 p.u. When the voltage continues to rise, PV₃ begins to reduce the active power, and enter the next regulatory process similar to PV₄.

Figure 14 Small AC signal detected at PV3.

Each PV power supply performs real-time Fourier analysis on the point of common coupling voltage to extract the 100 Hz frequency component. As shown in Figure 14, four small AC signals are detected within a short period, indicating that PV₄ has reached its regulation limit. Upon detecting these signals, PV₃ initiates a response by setting the current voltage as the new U_set,3. The active and reactive power coordination control strategy presented in this study is compared with the traditional RPC strategy. Under identical operating conditions, the voltages of each node at different times under the control of two different strategies are shown in Figure 14.

Figure 15 illustrates that reactive power regulation can effectively regulate voltage to some extent, but the voltage will still exceed the limit quickly when the PV power is high. The voltages at each node at 12:00 noon are shown in Table 4. Taking U₄ in Table 4 as an example, the grid voltage is 1.069 without control. After adding reactive power control, the grid voltage drops to 1.059, and the node voltage drops to 1.054 after 10% active power reduction by using the control strategy of this paper. After the voltage exceeds the limit, 10% active power reduction of the PV power supply significantly impacts the regulation of grid voltage.

Figure 15 Node voltage under two control strategies.

The simulation results show that the proposed control strategy is effective in suppressing the voltage overlimit problem of high proportion PV access to the distribution network. When the photovoltaic reactive power support capacity alone cannot restrain the voltage overlimit of the distribution network nodes, other reactive power compensation measures or active power regulation means are needed at this time, and relevant research results have been obtained, which will not be described here.

5 Conclusions

To address the voltage limit violation challenges in low-voltage distribution networks with high-penetration PV integration, an innovative distributed PV auxiliary voltage regulation strategy utilizing small AC signal communication is proposed. The developed control methodology optimally leverages the reactive power support capability of PV inverters while maintaining PV generation economic efficiency. Compared with conventional RPC approaches, the proposed strategy demonstrates enhanced performance in three critical aspects: (1) Comprehensive utilization of PV reactive power regulation margin across various operational scenarios; (2) Strategic active power curtailment implementation during PV surplus conditions for effective voltage rise mitigation; (3) Coordinated multi-PV control mechanism ensuring equitable active power reduction allocation and preventing control conflicts. The small AC signal-based communication architecture enables decentralized PV systems to achieve cooperative voltage regulation without requiring centralized control, effectively addressing the challenges of disordered regulation and associated economic losses in conventional autonomous control schemes.

Acknowledgments

This paper is supported by Science and technology foundation of State Grid Hebei Energy Technology Service Co. Ltd (The principal research and testing technology of fast voltage regulating device of power grid with photovoltaic power station participation, TSS2023-07).

References

All Tables

All Figures

	Figure 1 Distribution network with photovoltaic sources.
In the text

	Figure 2 Voltage drop phasor diagram.
In the text

	Figure 3 The relationship between reactive power and voltage emitted by photovoltaic source.
In the text

	Figure 4 PV source operating range when voltage control.
In the text

	Figure 5 Active power control process.
In the text

	Figure 6 Photovoltaic cell P-V curve.
In the text

	Figure 7 Equivalent circuit of photovoltaic cell.
In the text

	Figure 8 Surface of maximum power estimate.
In the text

	Figure 9 Information transmission process between PV sources.
In the text

	Figure 10 System simplification diagram with a small AC signal.
In the text

	Figure 11 The voltage of grid-connection point and Uset of PV4 and PV3.
In the text

	Figure 12 The active and reactive power of PV4.
In the text

	Figure 13 The active and reactive power of PV3.
In the text

	Figure 14 Small AC signal detected at PV3.
In the text

	Figure 15 Node voltage under two control strategies.
In the text