Review of Small-Signal Converter-Driven Stability Issues in Power Systems

New grid devices based on power electronics technologies are increasingly emerging and introduce two new types of stability issues into power systems, which are different from traditional power system stability phenomena and not well understood from a system perspective. This paper intends to provide the state of the art on this topic with a thorough and detailed review of the converter-driven stability issues in partial or all power electronics-based grids. The underlying and fundamental mechanisms of the converter-driven stability issues are uncovered through different types of root causes, including converter controls, grid strength, loads, and converter operating points. Furthermore, a six-inverter two-area meshed system is constructed as a representative test case to demonstrate these unstable phenomena. Finally, the challenges to cope with the converter-driven stability issues in future power electronics-based grids are identiﬁed to elucidate new research trends.


I. INTRODUCTION
E LECTRIC power systems today are undergoing a transformation from large machine predominant slow electromechanical dynamics to more small or medium-sized semiconductor-induced fast electromagnetic dynamics due to the increasing penetration of power electronics converters (PECs) in the generation, transmission, distribution, and load [1]- [3]. Such an evolution will provide high flexibility, full controllability, sustainability, and improved efficiency for future power grids; however, it also imposes new challenges to power system stability. As indicated by the major results of the work of the IEEE Task Force in [4], in addition to the impacts on classic power system stability issues (rotor angle stability, voltage stability, and frequency stability) [5], two new stability classes, resonance stability and converter-driven stability, are also introduced by the PECs.
For the classical categories of power system stability, many studies have been conducted to analyze the impacts of PECs as listed in Table 1, including impacts on the rotor angle stability [6]- [15], the voltage stability [10], [16], [17], and the frequency stability [18]- [21]. The interactions between PECs and synchronous machines are also studied, such as the interactions between the synchronous machines and various grid-forming control approaches in [22]. It can be seen that the impacts of PECs on classic power system stability can be either beneficial or detrimental. The detrimental impacts are mainly due to the reduction of system inertia and improper converter control design, while the benefits are mainly due to the faster control dynamics and stronger output regulations of the converters.
For the two new categories of PECs-induced power system stability, the unstable phenomena and possible causes are briefly described in [4]. The resonance stability issues are mainly caused by the effects of flexible alternating current transmission systems or high-voltage direct current transmission systems (HVDC) on torsional aspects (i.e., torsional resonance), and the effects of doubly fed induction generator (DFIG) controls on electrical aspects (i.e., electrical resonance), which encompass the subsynchronous resonance (SSR). The causes of resonance stability have been identified and the solutions have also been proposed accordingly. For example, devices such as static var compensators can be used to damp torsional resonance, and supplemental controllers in DFIG control can help to damp the electrical resonance.
The converter-driven stability issues may exhibit in different forms from classic power system stability issues as indicated by the documented incidents of the unstable operations in power electronics-based grids (PEGs) from field tests, e.g., sub-synchronous oscillations induced between wind turbines generations (WTGs) and series compensated lines in the ERCOT region [23] or harmonic instability issues in photovoltaic (PV) farms [24], [25]. The converter-driven stability is further classified as of slow-or fast-interactions based on the frequencies of the instability [4]. The slow-interaction converter-driven stability refers to the stability issues driven by the slow dynamic interactions between the slow outer control loops of converters and other slow-response components in power systems, typically around system fundamental frequency; while the fast-interaction converter-driven stability (also referred to as harmonic stability [26]) involves the problems caused by fast dynamic interactions between the fast inner control loop of converters and other fast-response components in power systems, typically in the range of hundreds of hertz to several kilohertz. The converter-driven instability may arise due to many different reasons, such as converterinterfaced generation (CIG) controls, grid strength, converterinterfaced loads (CIL), operating conditions, power transfer limits, and other similar factors [27], [28]. For example, the fast control dynamics of the CIGs may result in rapid frequency changes or transiently distorted voltage/current waveforms, which may lead to the over-reaction of protections fitted to the inverters and cause system tripping [29]. Therefore, it is of significance to fully understand and identify the exact causes for the converter-driven instabilities such that the proper system and converter operation can be designed accordingly.
This paper aims at exploring the underlying fundamental mechanism of converter-driven stability issues in power systems. First, the state of the art on different types of instability issues caused by typical converters in power systems is summarized; and then different stability analysis approaches, such as passivity-based approach or eigenvalue analysis, are applied to systematically analyze the root causes, including the converter-control-induced issues (i.e., control delay, inner and outer control loops, and converter switching actions) and the grid-condition-induced issues (i.e., grid strength, loading conditions, and the system operating conditions). Next, simulation studies are performed using a two-area meshed  network test case. In the end, some open research issues and challenges of the converter-driven stability are discussed accordingly.

II. MECHANISMS OF CONTROL DYNAMICS-INDUCED CONVERTER-DRIVEN STABILITY ISSUES
The dynamics of the entire power grids are determined by the dynamics of each piece of equipment in the system. Therefore, the characteristics of each device in the system need to be investigated. In conventional power grids driven by physical laws, general models for SGs can be obtained in a quasi-static format since the transients of interest are within a narrowband (0.1 Hz to 5 Hz [30]) and the fundamental frequency fluctuations are negligible (due to the large inertia of the rotor [31]). However, in PEGs driven by converter controls, there has not been a generic model yet since PECs highly depend on manufactures and are effective in wide control regions. Plus, the frequency variations cannot be neglected due to the low system inertia. Hence, this section attempts to cover the most used PECs with the root cause analysis for converter-driven stability issues in a wideband control range in power systems.
The converter-interfaced generations and loads in power systems generally use voltage-sourced converters (VSCs), which can be further classified as current-type VSCs as shown in Fig. 1 and voltage-type VSCs as shown in Fig. 2.
The current-type VSCs (also termed as grid-following inverters, GFLs) have been used in many applications, such as PVs, ESSs, and Type-4 WTGs at the generation side or fast-charging stations at the load side. The output current i L is usually controlled with a proportional-integral (PI) controller in the synchronous frame or with a proportional-resonance controller in the stationery frame. Additionally, a PLL unit  is used to obtain the angle θ of the converter terminal voltage in the stationary frame or of measured signals in the synchronous frame. The voltage-type VSCs (also termed as grid-forming inverters, GFMs) are to establish system voltage and frequency autonomously [32]. A typical P-f and a Q-v droop control are adopted to realize power synchronization. The voltage control is to regulate the output voltage, and the current control is to provide damping for the LC resonance and to limit the overcurrent.
Additionally, the converter-interfaced transmissions normally have a rectifier station and an inverter station with either line commutated converter (LCC) as shown in Fig. 3 or VSC as shown in Fig. 4. The LCC-HVDC has been widely used in long-distance transmissions with two common LCC control loops, i.e., constant extinction angle control (CEAC) and constant dc voltage control (CDVC). The VSC-HVDC is also a preferred transmission solution, especially in offshore wind farms with two-or three-level VSC or modular multilevel converters. The rectifier side of VSC-HVDC is normally with PLL control, active power/dc voltage control, and reactive power/ac voltage control loops [33], and the inverter side structure is like current-type VSCs. To limit the scope of this paper, the dc-link dynamics are ignored considering only the dc/ac and ac/dc stages.
The control-induced converter-driven stability (fast-and slow-interaction) issues arising from these four kinds of converters in power systems will be discussed from the following aspects: control delay, inner/outer control, and switching actions. It should be noted that these causes are coupled and may mix to cause converter-driven instabilities.

A. CONVERTER CONTROL DELAY (FAST INTERACTION)
The PECs may cause current harmonics in power systems as shown in Fig. 5 with 830 Hz harmonics in a wind farm [40]. The unstable sources can be identified with the bus VOLUME 9, 2022 participation factors (PFs) calculated from the multi-inputmulti-output transfer function matrix model of the power system and eigenvalue sensitive analysis. Specifically, the converters with larger PFs would introduce harmonic resonances into the system.
The fundamental mechanism behind the phenomena can be further revealed by the passivity-based stability criterion, i.e., for a system described by a rational transfer func- [42]. Therefore, if a converter impedance is non-passive at some frequencies when connecting to another passive system, instability will possibly happen within these non-passive regions (NPRs). Accordingly, the output admittance of current-type VSCs with LCL filters Y o1 (s) is derived, and the converter passivity is examined to identify the root causes. The results show that there is a high frequency (HF) NPR which is caused by the interactions between LC resonance frequency f r and system control delay T d . The delay here is assumed to be k times of switching period T sw , which is typically 1.5 and can be reduced to 0.5 with more advanced digital control. The conclusions are: (1) when f r < f sw 4k , the HF-NPR in GFLs with LCL filter is (f r , f sw 4k ) as shown in Fig. 6(a); (2) when f r = f sw 4k , there is no HF-NPR, and (3) , [43]- [46]. According to the conclusions above, the instability causes for the system in [40] can be dug deeper, where the converter switching frequency f sw is 4 kHz and the control delay is 0.5T sw . Besides, f r is 729 Hz which is smaller than 2 kHz. Therefore, the harmonic instability issues would happen within (729 Hz, 2 kHz), which matches with the current waveforms with 830 Hz resonance as shown in Fig. 5.
Following the same approach, the HF-NPR of currenttype VSCs with an L filter is identified to be ( f sw 4k , 3f sw 4k ) using the output admittance Y o2 (s) as shown in Fig. 6(b) [35], [42], [47]. And the HF-NPR of voltage-type VSCs is identified to be ( f sw 4k , 3f sw 4k ) with an examination on phase angles of converter output impedance Z o (s) as shown in Fig. 6(c), which is analogous to the L-filtered current-type VSCs [37], [48], [49]. When the control delay is small enough, e.g., k = 0.5, the converter could be passive up to Nyquist frequency 0.5f sw , which means there would be no harmonic stability issues if connecting the converter to another passive grid. Plus, if the converter is implemented with silicon-carbide devices instead of silicon devices with a higher switching frequency, the converter passivity could also be guaranteed to a higher absolute value of frequency range and system stability could be improved. Therefore, to eliminate the control-delay-related converterdriven stability, one direct method is to use advanced controllers to achieve small control delays. Other than that, system stability can also be enhanced by some passivity compensation methods. For example, for current-type VSCs, there are voltage feedforward control [35], [43], [46], leadlag control [45], active damping [41], [43], [46], passivitybased robust control [44], and adaptive bandpass-filter-based compensation control [50]; for voltage-type VSCs, there are adaptive notch-filter-based compensation control [50], and voltage feedforward control with virtual impedance control block [48], [49]. Note that virtual impedance control may also affect system slow-interaction converter-driven stability. Therefore, the outer loop needs to be refined accordingly.

B. INNER LOOP CONTROL (FAST INTERACTION)
In addition to the control delays as the root cause for system harmonic instability issues, the inner loop control bandwidth will also have some impacts since the control delays typically add negative damping into the alternating current control (ACC) loops of PECs [49], [51]. For example, in a system with multiple paralleled LCL-filtered current-type VSCs, the interactions among the ACC loops with larger control bandwidth will cause the interactive circulating currents to arise, because the resonance frequency tends to shift to the negative damping region caused by control delays when control bandwidth is increased [52]. A direct solution is to limit the inner current control bandwidth, which may sacrifice the current control dynamics. Apart from this, a multisampling approach can be used [53]. But harmonic instability driven by switching actions would be introduced, causing a distorted grid current with low-frequency aliasing. Hence, a repetitive filter to eliminate the multi-sampling-induced harmonics is also needed.

C. CONVERTER SWITCHING ACTIONS (FAST INTERACTION)
For parallel converters with asynchronous carriers, the pulsewidth-modulation (PWM) block generates sideband harmonics which may cause system harmonic instability [54], [55]. Fig. 7 shows the harmonic current waveforms in a system with two-parallel current-type VSCs.
To eliminate the f sw sideband harmonics, a global synchronization of all PWMs through a communication-based central controller is needed. Another way is to add active damping or passive damping into the system to damp the high-frequency oscillations. Plus, the increasing parasitic resistance at a higher frequency due to the skin effect of the output inductor L can provide additional passive damping which is good for system stability. Therefore, the effects of controllers on system stability above Nyquist frequency (f sw /2) may be negligible in some cases [56].

D. OUTER LOOP CONTROL (SLOW INTERACTION)
Slow-interaction converter-driven instabilities are also observed in power systems as shown in Fig. 8, which are also called sub-synchronous oscillations (SSO) [57]. The main reason for SSO has been identified as the interactions between the outer control loops of the converters and grid strength (defined by short circuit ratio -SCR).

1) PLL CONTROL
For current-type VSCs, the slow-interaction converter-driven instability is mainly due to the asymmetrical PLL dynamics, i.e., only regulating q-axis PCC voltage introducing positive feedback into the system [58]- [60]. By examining the closedloop poles of current-type VSCs, it is found that there is one pair of complex poles (P 1,2 ) that have the low-frequency dynamics related to system fundamental frequency sideband oscillations [58]. The root-locus approach is applied to analyze the locations of the poles to study the impact of the PLL (proportional gain K pll_P and integral gain K pll_I ) as shown in Fig. 9. For the PLL control parameters, a decrease of proportional gain K pll_P (star line in Fig. 9) and an increase of integral gain K pll_I (circle line) will move the SSO moderelated pole to the unstable region. It is also observed that reduction of the ACC integral gain K CC_I (square line) will have minor impacts on system SSO stability. But the impact of ACC proportional gain K CC_P on system SSO is negligible. Using the impedance-based Nyquist stability analysis approach can draw the same conclusions as discussed in [59,60]. Additionally, it is found in [63] that the ACC loop may accelerate the equivalent motion of PLL in the first swing, which will worsen system transient stability by enlarging the mismatch between the accelerating and decelerating area in the power angle curve of the analogized synchronous machine model of the current-type VSC.
The PLL control blocks in LCC-HVDC and VSC-HVDC have similar impacts on systems stability. For the LCC-HVDC, a study was conducted based on the smallsignal model and eigenvalue analysis to investigate the impacts of PLL and LCC controllers in [38]. First, the PLL bandwidth has significant impacts on system stability. Too large PLL control bandwidth will cause system SSO, especially under weak ac grids. Considering PLL gain stabil- ity boundary with different types of LCC controls, the stable region of PLL gain is larger with CDVC than with CEAC. Second, in CEAC controller G γ , smaller proportional gain K p and larger integral gain K I can help improve system stability. While in CDVC controller G dcv, larger K p and smaller K I can enhance system stability. Third, there is a close coupling between PLL and LCC control loops, which indicates that the instability caused by larger PLL gain can be eliminated by properly tuning LCC controllers. For the VSC-HVDC, based on the eigenvalue analysis of the corresponding smallsignal model, the PLL impacts on system stability can be obtained as shown in Fig. 10. It is seen that when the SCR is larger than 1.32, there will be no stability issues for any value of K pll_P . However, in a system with lower SCR, there will be a maximum K pll_P limitation for system stability. Note that the K pll_I is assumed as c times of K pll_P for simplicity. Another study on a windfarm-connected HVDC transmission is conducted with the impedance-based stability analysis in [39]. It is also found that increasing the voltage loop crossover frequency or reducing the PLL control bandwidth can improve system slow-interaction converter-driven stability.
The PLL-related converter-driven instabilities can be directly solved by tuning PLL control parameters, e.g., reducing PLL bandwidth to limit the effective frequency range of the harmful positive feedback. Another approach is to add active damping, e.g., virtual impedance [34], [64] or feedforward control [61], [65].

2) DROOP CONTROL
In voltage-type VSCs, droop control strategies are normally adopted for power regulation and system synchronization. A complex-value-based output impedance model in the stationery frame is built in [62] to study the impacts of the control loops. It is revealed the interactions of the droop control loops and voltage control loop tend to cause system instability issues. Moreover, a comparative study is conducted in [66] to investigate the differences between multi-loop droop (with inner V -I loop as shown in Fig. 2) and single-loop droop (without inner V -I loop). Fig. 11 shows the results of smallsignal stability boundaries under different grid equivalent impedances [66]. It is found that the voltage-loop will make the converter prone to be less damped and lose system stability more easily since the stable region is reduced with inner V -I control. Besides, it is found in [36] that a larger voltage control bandwidth may enhance system SSO stability. Additionally, the Q-v droop impact on system stability is weaker than the p-f droop. Based on these findings, the droopinduced slow-interaction converter-driven instability can be eliminated by tuning the parameters of the more sensitive control blocks, i.e., p-f droop and voltage control.

III. MECHANISM OF GRID CONDITION-INDUCED CONVERTER-DRIVEN STABILITY ISSUES
In addition to various converter control loops, converterdriven stability issues are also dependent on system interactions and operating conditions.

A. GRID STRENGTH (SLOW-AND FAST-INTERACTIONS)
As shown in Fig. 9, Fig. 10, and Fig. 11, the slow-interaction converter-driven stability not only relies on the converter control loops but also depends on the grid strength. In converters with PLL control block, the instabilities would be more likely to be stringent under weak grid conditions. As shown in Fig. 9, an increase of L g (diamond line), i.e., a weaker grid, will also make P 1 be an RHP pole and cause SSO instability. Note that a weak grid is defined as an ac power system with a low SCR and/or inadequate mechanical inertia by IEEE standard 1204-1997 [67]. It is also worth mentioning that in the LCC-HVDC system, a weak system means an SCR < 2.5. While in VSC-HVDC systems, the SCR for ''weak'' or ''strong'' system boundary is suggested to be 1.3-1.6 as implied by Fig. 10 [33]. However, in converters with droop control, the smaller the grid-impedance is, the smaller the allowed maximum p-f droop gain would be as shown in Fig. 11. That means the SSO instability tends to happen in a strong grid under the same droop gains in voltagetype VSCs, which coincides with results in [36], [62].
The fast-interaction stability may also be affected by the grid strength. For example, if the magnitude of the grid-side impedance intersects with that of converter impedance in the HF-NPR, and the phase difference at the intersection does not meet the stability criterion, then the harmonic instability issues will exhibit [48]. A grid impedance away from the HF-NPR can help eliminate the harmonic instability issues.

B. CONVERTER-INTERFACED LOADS (FAST-AND SLOW-INTERACTION)
The converter-interfaced loads will have very different frequency and voltage characteristics from conventional resistive loads or motor loads. Under some circumstances, the CILs can be considered as current-type VSCs as discussed in Section II-A. It is revealed for simplicity that the CILs exhibit constant power characteristics when the control bandwidth is high enough in some studies [68]- [70]. Therefore, negative incremental impedances will be introduced by the constant power loads (CPLs) across the entire frequency range, and both fast-and slow-interaction converter-driven stability will be affected by this negative damping. Similar findings have been obtained by a microgrids study in [71] with different solutions such as using passive damping, active damping, or more advanced control strategies. One should note that although the CPL assumption is dynamic-wise (i.e., simplifying the load dynamics), it may not always be the worst-case condition for system stability from a control standpoint [72].

C. OPERATING CONDITIONS (FAST-AND SLOW-INTERACTION)
System operating conditions also affect the converter-driven stability, including both fast-and slow-interactions. For example, a theory for harmonics created by resonance in [73] shows that the harmonics may not happen in normal mode, but may suddenly occur and grow before it reaches a certain value if operating conditions change as shown in Fig. 12. The main reason for this phenomenon is that the converter impedance depends on both the operating points and harmonic components. To solve this kind of issue, the focus should be on utilizing passive elements or control strategies to provide more damping to reshape the system impedance.
Moreover, slow-interaction converter-driven stability will also be affected by system operating conditions as shown in Fig. 9 that a larger current I ref (bar line) will induce SSO with higher oscillation frequency. Hence, a proper design of converter impedance characteristics under different operating conditions should be examined to guarantee system stability.

IV. CASE STUDIES OF INSTABILITY PHENOMENA IN PEGs
To illustrate the different types of instability phenomena described above, a notional scale-down two-area system interconnected by VSC-HVDC as shown in Fig. 13 was built in MATLAB/Simulink. In each area, a three-bus system is investigated, where G x1 and G x2 work as voltage-type generators, G x3 works as current-type generator/load (x represents Area 1 or Area 2). And G x1 provides voltage references for each sub-system. The system is designed to be stable first. Then, based on the review of the possible causes for system instability issues, some typical impact factors are studied by changing the corresponding parameters, such as the inner control, the outer control, or the grid strength. Note that the control and hardware parameters for the stable operations are regarded as benchmark conditions (defined with subscript ''BM'' in the following text).
Three case studies are conducted in this paper through both time-domain simulations and the Norton admittance matrix (NAM)-based stability analysis with the characteristic loci of the system eigenvalues [74]. The reasons that the NAM-based approach is adopted in these case studies are summarized as follows. First, there are generally two types of modeling approaches for system stability analysis. One is the state-space approach, and the other is the impedancebased approach [26], [75]. The state-space approach is suitable for system low-frequency dynamics modeling and can be used to identify the oscillation modes through eigenvalue analysis. However, if the fast dynamics in the system are considered, the model will become a high-order matrix which might be difficult to compute. Additionally, information of the entire system is required to derive the model. While the impedance-based approach is to analyze the system stability through the interactions between different subsystems, which only needs the terminal characteristics and can be used to identify the impact of each subsystem on system stability. Therefore, an impedance-based approach is adopted in this VOLUME 9, 2022 FIGURE 13. Configuration of the test system.
paper. Second, the impedance-based stability criteria can be further categorized into three types, including the Nyquistbased stability analysis, the loop-based stability analysis, and the NAM-based stability analysis [74]. The Nyquistbased approach analyzes system stability through an openloop model at one partition point. Therefore, the open-loop RHP poles need to be checked first, and the analysis results are sensitive to the partition point. The loop-based approach analyzes the system stability through the closed-loop model, so there is no need to check the open-loop RHP poles and it is insensitive to the system partition point. However, it depends on the circuit operation, and it cannot be used to identify the weak point in the system. The NAM-based approach analyzes the system stability through the closed-loop model with overall system structure, so there is no need to check the open-loop RHP poles. Also, it is insensitive to either the system partition point or circuit operations. It can also be used to identify the weak point and the oscillation frequency in the system by analyzing the characteristic loci of the system return ratio matrix [76], [77]. Therefore, the NAM-based approach is adopted in this paper.

A. CASE I: IMPACT OF INNER CONTROL PARAMETERS
In Case I, Area 1 and Area 2 work independently with VSC-HVDC disconnected, that is no power flowing between Area 1 and Area 2. And the transmission lines in both Area 1 and Area 2 are kept the same as the benchmark system. But the inner control of G 13 is changed to be 5 times of the benchmark parameters to have a faster inner loop design. Consequently, a 480 Hz harmonic instability issue is observed on B 13 and the NAM-based stability analysis result also predicts such an oscillation through the characteristic loci as shown in Fig. 14 (420 Hz + 60 Hz).
To eliminate this instability issue, the control bandwidth of the inner loops should be limited as reviewed in Section II. With a slower inner loop, the system can be stabilized as shown in Fig. 15. Note that in the following case studies, only the unstable waveforms will be given considering the page limits.

B. CASE II: IMPACT OF OUTER CONTROL PARAMETERS
First, the PLL control parameters of G 13 in Area 1 are changed to be K pll_p = 0.01 * K pll_p,BM and K pll_I = 5 * K pll_I ,BM , and the other parameters are kept the same as the benchmark system. Also, all the parameters in Area 2 remain the same as the benchmark system. The VSC-HVDC is disconnected. It can then be found that due to the improper PLL parameter design, there will be low-frequency oscillations in Area 1 as shown in Fig. 16. The phase voltage of B 13 shows a 68Hz resonant frequency which matches with the analysis result.
The PLL control blocks in VSC-HVDC will also have a similar impact on system stability as that in current-type VSCs. When there is power flowing from Area 2 to Area 1 through the VSC-HVDC connection, and the parameters in both Area 1 and Area 2 are kept the same as the benchmark system, except the PLL parameters in VSC-HVDC are changed to be K pll_p = 0.05 * K pll_p,BM . It can then be observed in Fig. 17 that there will be low-frequency oscillations in both the inverter station and the rectifier station. To remove the slow-interaction instability issues, an increase of K pll_p and a decrease of K pll_I can help as reviewed in Section II.

C. CASE III: IMPACT OF GRID STRENGTH
In Case III, Area 1 and Area 2 work independently with VSC-HVDC disconnected. The transmission line parameters in Area 2 stay unchanged compared with the benchmark system so it is stable, while L 113 is increased to 5 times of L 113,BM and L 123 changes to 5 times of L 123,BM in Area 1 (i.e., weaker connection). It can then be seen from Fig. 18 that a 216 Hz harmonic issue occurs in Area 1. And the impedance-based stability analysis approach also predicts this harmonic resonant frequency. According to the review in Section III, to remove this instability issue, a stronger grid connection is expected.
The other causes reviewed in Section II and Section III, such as the control delay or the loads, can also be studied following the same method used in the case studies above.

V. OPEN RESEARCH ISSUES AND CHALLENGES
With the understanding of the impacts of PECs on power system stability, future all power electronics-based grids can be envisioned. But there are still some challenges going forward.

A. STABILITY ANALYSIS AND IMPROVEMENTS OF LARGE-SCALE PEGs
There have been many papers studying the converter-driven stability issues in small-scale PEGs following the common practice: building system models → applying stability analysis approaches → developing stability improvement methods → conducting simulation/experimental validations [74], [78]. The system model is normally a state-space model or an impedance model, and the corresponding stability analysis is eigenvalue-based analysis or Nyquist criterion. The stability improvement method is usually to improve converter control or to add extra damping. And the analysis results can be simulated by PSCAD, MATLAB, or other software. It is also feasible to build a hardware platform for the small-scale PEGs for further analysis. However, for large-scale PEGs, there is no such study yet. Although people have studied high PE penetrations (e.g., 80%) in the VOLUME 9, 2022 large-scale system, the stability analysis mainly focuses on the classic power system stability study in the range of 0.1 Hz −5 Hz [21]. If directly applying the approaches for the smallscale system to large-scale PEGs, there will be many issues: (1) A very large state-space matrix or NAM model has to be built first. And when applying the stability analysis approaches, the matrix may not be solvable due to the huge computation burden of the excess matrix dimensions. One may use the Nyquist stability criterion to study the impedance ratio L AC = Z source /L load , which is normally a one-or twoorder matrix, by simply dividing the system into the source subsystem (Z source ) and the load subsystem (L load ). However, this approach is sensitive to the partition point and can only reveal the interactive stability of two subsystems at this given point. Therefore, the NAM model is preferred since it can preserve the structure of the entire system and be less sensitive to circuit operations [74], [79].
(2) It is time-consuming to simulate a large-scale PEG on a personal computer. For example, in a case study with 32 Type-III WTGs (48 generators in total) in PSCAD, to investigate 8 seconds system response using average models for the PECs at one operating point, it will take about 20 hours to run the entire simulation with regular Intel R Core (TM) i7-7700 CPU @ 3.60 GHz, not to say using converter switching models. Besides, it is also challenging to build a hardware platform for a large-scale power system.
The solutions for the challenges in studying large-scale PEGs can be considered from either top-down or bottomup angles [80]. The top-down approach has a global view of the system. First, it is expected to have a generic converter model to cover a wide variety of PECs to simplify the entire system model, which could keep all the important intrinsic characteristics of the PECs and meanwhile simplify the calculation process. Some latest studies have developed generic models for PECs, such as a generic model for wind power plants [81], [82], or the data-driven-based power electronic converter modeling approach [83]. Second, the stability analysis approach should be improved to relax the huge computation burden for a large-scale system, such as the partition-based nodal admittance matrix model for smallsignal stability analysis of large-scale PEGs in [77]. Third, for the system simulation, a more powerful computer station with multicores calculated simultaneously can be adopted to speed up the process. While the bottom-up approach starts with the local converter. It is desired that the decentralized control for smart converters [84] can ensure system stability. The passivity-based control can be applied for converter design to enhance system stability. The existing works mainly aim at improving fast-interaction converter-driven stability, but a general solution for slow-interaction stability regarding converter synchronization is still unclear since the low-frequency behavior highly depends on system operating points. Therefore, a decentralized converter control for large-scale system stability under variable working conditions is desired.

B. STABILITY ANALYSIS CONSIDERING SYSTEM NONLINEARITIES
The converter-driven stability analysis for either small-scale or large-scale PEGs above is mainly focused on smallsignal stability with system linearization. However, a PEG is inherently a nonlinear system [85], such as large disturbances in systems, power/current limits, or control saturations. To study the system large-signal stability considering all the nonlinearities, a common approach is to use timedomain simulation tools to reflect the system response under some disturbances. Typically, many simulations under different types of disturbances (e.g., faults, generations, or loads dispatch) are needed to characterize system characteristics. There have been some studies focused on large-signal stability analysis on PEGs, such as the converter-level large-signal stability analysis of GFMs or GFLs in grid-connected conditions [86]- [89], or the system-level large-signal analysis on dc microgrids [90]. However, a systematical large-signal stability analysis approach for ac PEGs is still lacking. Therefore, a system-level large-signal stability analysis method for future PEGs considering all the nonlinear effects, especially for large-scale PEGs, should be developed.

VI. CONCLUSION
Power electronics-based grids represent the trend for future electric power systems. New system stability issues like harmonic stability or subsynchronous oscillations, could arise along with the impacts on classical power system stability. This paper presents a comprehensive analysis of the converter-driven stability issues (fast-and slow-interactions) in power systems with root cause analysis. The results show that the converter control, grid strength, CILs, and system operating conditions all affect system stability. The case studies of a two-area PEG verified these instabilities with illustrative and intuitive explanations. Control and design challenges for future PEGs are also presented.

NOTICE OF COPYRIGHT
This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).