Recent years have seen an apparent rise in the integration of renewable power generation, such as wind and solar, into the electrical grid (Zhang et al., 2021). The traditional power system has been changed and influenced by power electronic equipment. The stability problems are preventing a greater utilization of renewable energy. In terms of PV systems, due to installation space restrictions, large PV stations are typically placed in rural locations where power grid strength is weak, and large disturbances are common. System operation is in danger due to the effect of grid impedance and system nonlinear couplings on inverter control (Liu et al., 2022a; Hafiullah et al., 2022; Wang et al., 2017a; Zhou et al., 2022).

Inverter control stability and system voltage stability are the key topics of research on PV system stability (Zheng et al., 2018; Wei et al., 2020; Liu et al., 2022b). Typical control loops like current, frequency, and voltage control are referred to as control stability. The initial designs of these control loops typically meet the stability criteria, but when coupled to one another and to a weak power grid, the interactions between various control loops in and between different devices lead to system instability (Sun, 2011). A PV system’s voltage and frequency are generally managed by a voltage control loop and a phase-locked loop (PLL). Methods for regulating system voltage, such as power optimization control and reactive power compensation, will interact with inverter control, influencing control stability. It has been reported that series capacitor compensation causes sub-synchronization resonance in wind farms. The interactions of sub-synchronous control between wind turbines and series capacitors have been discovered (Wang et al., 2018). However, the instability is due to the unique circuit structure of doubly fed converters, which is not common in other types of converters (Huang et al., 2016; Zhang et al., 2020). For the stability issues in PV systems, Yang et al. (2019) analyzed the impact of parallel compensation on the control stability of inverters and discovered that parallel compensation decreases the phase margin of inverter current control. The lead compensation was then suggested as a solution to the issue. However, only the stability of the current control was taken into account. There has not been any discussion of the impact on system frequency control.

The frequency stability in the inverter system is generally analyzed based on a PLL (Wang et al., 2017b; Du et al., 2020; Sonawane and Umarikar, 2022). It has been proved that factors such as PI controller parameters, grid impedance, inverter current, and power factor angle significantly affect the stability of the PLL. Different stability improvement methods have been deployed, including increasing system damping, changing control parameters and structure, and intelligent optimization (Lasseter et al., 2020; He et al., 2022; Qi et al., 2022).

However, weak power grids are the focus of the majority of the work. The impact of reactive power compensation has not been taken into account. Zhang et al. (2022) explored the frequency stability problems caused by series capacitors but did not address the influence of parallel compensation. To the best of the authors’ knowledge, no comprehensive analysis of the impact of voltage regulation approaches on frequency control stability has been provided. How reactive power compensation affects frequency control stability and how to deal with the instability issue must be known.

This paper investigates the voltage and frequency instability in large PV systems. The interaction between reactive power compensation and inverter control is investigated. The main contributions of this article are as follows:

• The restriction of parallel compensation is revealed.

The following contents are organized as follows: Section 2 illustrates the voltage instability and regulation methods in PV systems. Section 3 investigates the frequency instability caused by voltage regulation. Section 4 puts forwards the stability improvement methods. Section 5 presents the simulation and experimental results and is followed by the conclusion in Section 6.

The DC bus and the AC bus are the two power buses for a typical grid-connected PV system. The voltages on these two buses are kept constant to meet the needs of the system’s normal operation and the supply of loads (Zhou et al., 2015; Reshikeshan et al., 2021). However, due to the existence of grid impedance in weak power grids, system voltage is determined by voltage control techniques and inverter control. Energy storage and reactive power compensation, in general, are required to adjust system voltage (Liu et al., 2015; Ai et al., 2021). Energy storage devices only operate on active power and are typically installed on DC buses to regulate DC voltage. The reactive power devices, on the other hand, operate on AC buses and have the ability to modify DC and AC voltage. This section analyzes the voltage problems and the voltage regulation methods in PV systems. The restriction of parallel compensation is revealed.

Reactive power compensation is an effective way of ensuring the voltage stability of the PV system and improving system power quality and reliability. However, reactive power compensation is coupled to the inverters’ control by working on inverter voltage (Sridhar et al., 2016; Sudharshan et al., 2022). When the power grid is extremely weak, and the required reactive power compensation is large, reactive power compensation can easily lead to system frequency control instability.

The traditional frequency control part in inverters is a PLL. The input signal of a PLL is inverter voltage. For a weak power grid, the stability of the PLL is affected by grid voltage, grid impedance, grid current, reactive power compensation, etc. By the superposition principle, inverter voltage can be derived as follows: V p v = T v s s V g + T i s s I p v r e f , (7) where T _vs and T _is are, respectively, the transfer function from V _g and I _pvref to V _pv, and T v s s = 1 1 + Y p v s Z s g s , T i s s = T i s Z s g s 1 + Y p v s Z s g s . (8)

In (8), Z _sg(s) is the equivalent grid impedance and Z s g s = s L g   g r i d   i m p e d a n c e   o n l y , s n L g + 1 s C s   w i t h   s e r i e s   c o m p e n s a t i o n , n L g s n L g C p s 2 + 1   w i t h   p a r a l l e l   c o m p e n s a t i o n , (9) where C _s and C _p are, respectively, the series and parallel compensation capacitors.

For simplification, (7) can be expressed in its exponential form: V p v = T v s V g e j θ g + φ v + T i s I p v r e f e j θ + φ i . (10)

The component V _pv in the q axis can be obtained from (10) after the dq transformation as follows: v p v q = V g T v s ω 0 sin θ g + φ v ω 0 − θ + T i s ω I p v r e f ⁡ sin φ i ω , (11) where || represents amplitude operation, θ _g and θ are, respectively, the phases of grid voltage and the phase detected by the PLL, and ω ₀ and ω are, respectively, the frequency of the grid and the PLL. The PV system frequency is determined by ω.

The equivalent control diagram of the PLL is shown in Figure 8. Compared with the ideal condition without grid impedance, the existence of grid impedance and reactive power compensation has introduced a current effect loop to disturb system control stability. The PI controller is able to attain the static operation state only if its input signal is zero. As a result, the voltage effect loop must be able to cancel out the current effect loop, that is: I p v r e f ≤ V g T v s ω 0 T i s ω I p v r e f ⁡ sin φ i ω (12)

Figure 9 shows the maximum current required by the stability condition in (12). When the current in a real system exceeds the curve, frequency control loses its stability. It can be seen that the series compensation can ensure the existence of an equilibrium point at the fundamental frequency by eliminating the maximum current limitation, while the parallel compensation cannot. In addition, the maximum current curves decrease as the system short circuit ratio (SCR) and related reactive power compensation increase, which means that system probably becomes unstable when system frequency deviation caused by some large disturbance results in inverter current exceeding the maximum limitation at some frequency points.

The analysis in Section II and Section III indicates that a weak power grid can cause PV system DC and AC voltage instability. Series and parallel compensation are able to solve the voltage instability problem. However, when grid strength is ultra-weak, that is, a large amount of reactive power is required, reactive power compensation will induce frequency control instability problems. As the frequency instability caused by reactive power compensation depends on the system frequency deviation range and compensation forms, this paper proposes stability improvement methods from the perspective of frequency damping and reactive power compensation collaboration. Compared with the existing methods, the methods proposed in this paper rely little on detailed system modeling and will not influence the system’s original control requirements.

For the constant grid impedance, Figure 10A shows the maximum current curves with different reactive power compensation. It can be seen that the collaboration of series and parallel compensation can improve the maximum current curve compared with parallel compensation. However, the stability region in the higher frequency range is reduced compared with series compensation. Curves with different reactive power allocations are shown in Figure 10B to investigate the influence of the allocation of reactive power among series and parallel compensation on the maximum current curve. This figure shows that for a constant grid impedance, increasing parallel compensation moves the maximum current curve toward a lower frequency range, which reduces the stability range above the fundamental frequency but enlarges the range less than the fundamental frequency. Therefore, the allocation of reactive power compensation should be made according to the system frequency deviation range. More parallel compensation allows more frequency deviation in the lower frequency range. By the same token, more series compensation is beneficial for the system with large higher frequency disturbance.

Even though the proper allocation of series and parallel compensation can improve frequency stability for different frequency disturbance directions, the maximum range is restricted. Therefore, some methods to restrict system frequency deviation must be proposed.

The methods to restrict system frequency deviation can be realized by reducing PI parameters inside the PLL control. However, the reduction of PI parameters usually leads to slow system response time, which will further influence inner current control (Hamed et al., 2017). The function of reducing PI parameters on frequency control can be equivalently transformed into an AC circuit. As the main purpose of reducing PI parameters is to limit the frequency deviation range by filtering out the undesired frequency components, the same function can also be realized outside the PLL, such as a band-pass filter in series in front of the PLL. In addition to the traditional methods, intelligent control, such as fuzzy control, can also effectively restrict system frequency deviation because of its better performance in regulating control error and the time ratio of error. The band-pass filter and fuzzy control in improving system stability are shown in Figure 11.

The band-pass filter can be expressed by T f s = 2 ξ ω n s s 2 + 2 ξ ω n s + ω n 2 , (13) where ω _n is the fundamental frequency. ξ represents the damping ability of non-fundamental frequencies, and a small ξ has a better filtering ability. Therefore, systems with a large frequency deviation need smaller ξ to improve frequency control stability.

The input signal of fuzzy control is V _pv,q and the time ratio of V _pv,q. Taking the fuzzy linguistic variables as [NB NM NS Z PS PM PB], the Gaussian function is adopted as the membership function. The fuzzy decision on K _p and K _i is given by the center of gravity (COG) method, which is shown in (14). In (14), r is the number of fuzzy rules; x _k and y _k are, respectively, the state and input variables; K _p,i and K _i,i are the discrete elements of the output fuzzy set; F _j is the membership function of the jth rule. With the aforementioned definition, the detailed design can be conveniently realized with the help of the fuzzy toolbox in MATLAB. K p x k , y k = ∑ i K p , i ∑ j = 1 r F j x k , y k , K p , i ∑ i ∑ j = 1 r F j x k , y k , K p , i , K i x k , y k = ∑ i K i , i ∑ j = 1 r F j x k , y k , K i , i ∑ i ∑ j = 1 r F j x k , y k , K i , i . (14)

The work in this paper reveals and solves the frequency stability problems caused by reactive power compensation, which can help improve system voltage and frequency stability in large PV systems. Voltage in large PV systems is influenced by grid strength. Small SCR reduces PV voltage and probably causes voltage instability. Reactive power compensation is an effective way to ensure that system voltage operates in the normal range. Series compensation is necessary for an ultra-weak grid because of the limitation to parallel compensation. However, reactive power compensation, whether it is parallel or series compensation, threatens system frequency stability. A system that needs large reactive power compensation usually has the risk of frequency control instability. A band-pass filter and fuzzy control have been proposed to solve the frequency control instability. Simulations and experiments have verified the correctness of the proposed solution.