A Recent Review on Approaches to Design Power System Stabilizers: Status, Challenges and Future Scope

Modern power system networks are complex and subjected to several uncertainties. Due to the complexity and uncertainties involved in power system operation, the networks are prone to instabilities. Rotor-angle instability is one such issue that, if not addressed properly, may lead to system collapse. A power system stabilizer (PSS) is primarily a power oscillation damping (POD) controller used to dampen power oscillations, thereby improving rotor angle stability. The proper design of PSSs is a challenging task and is essential for the secure and reliable operation of power systems. In the past, many power system instability events occurred, resulting in cascading failures and even blackouts. In the literature, several methods are proposed for the efficient design of PSSs or POD controllers. In this contribution, a recent review on the design of PSS is presented, along with challenges and the future scope of research in this field. On the basis of this review, it can be concluded that there is ample scope for designing PSS in a more efficient and robust manner, considering several uncertainties that may occur during the operation of modern power systems.


I. INTRODUCTION
Presently, power system networks are exceedingly complicated and non-linear due to increased interconnections between different areas and capacity expansions [1]. As a matter of consequence, the power system may experience transient events leading to cascading outages and, in turn, the total collapse of the system [2]. Thus, one of the most difficult challenges with interconnected power networks is to maintain secure and reliable operation of the power system [3]. Instability issues that may arise during operation of a power system can be classified as voltage instability, rotor angle instability, and frequency instability. Rotor-angle instability is caused when the angle separation of the rotors of different generators in a system increases beyond a permissible limit due to an unwanted transient event, which may result in increased power oscillations and lead to total collapse of the system [2]. In 1985, at the Akosombo plant in Ghana-Ivory Coast, the The associate editor coordinating the review of this manuscript and approving it for publication was Shadi Alawneh .
power system was unstable due to low-frequency oscillation (0.6-0.7 Hz), so power system stabilizer (PSS) tuning was performed in one generating plant to mitigate the problem. In order to tackle the aforementioned instability issue, power oscillation damping is inevitably required. For this purpose, PSSs are generally utilized in the power system network to provide appropriate damping of power oscillations [4]. Conventional PSSs with fixed parameters can dampen local power oscillations but are not capable of damping inter-area oscillations efficiently [1]. Therefore, several research are carried out towards the efficient design of PSSs to dampen power oscillations and are well documented in the literature.
Power oscillations occur due to rotor angle deviations between generators in the system caused by transient events like transmission line faults, increased loading, etc. The frequency range of power oscillations lies between 0.1 and 3 Hz. For local oscillations, the range of frequency is 0.7 × 3 Hz, and for inter-plant oscillations, the range of frequency is 0.1 × 0.7 Hz [5]. One of the causes of power oscillation is the presence of weak power transfer tie lines. Heavy power circulation all over grid line interfaces due to severely imbalanced regional power as well as pumped storage units in pumping operation mode seem to be common causes of power oscillations reported in the literature survey. References [6], [7]. Some power system instabilities result in a series of failures, which may lead to significant blackouts. Though PSSs are capable of damping out power oscillations to a great extent and enhancing overall stability of the whole power system but, in case of cascading events and any other severe disturbances, PSSs will not be able to prevent total voltage collapse or blackouts.
Power oscillations in earlier power systems were negligible because the generator and load were closer together and the power system was small. But, presently, the structure of a modern power system is complex due to the widespread interconnection of numerous systems. As a result, maintaining consistent stability in the grid is a major concern, and there is every likelihood of the occurrence of power oscillations that may lead to power outages [5], [7]. Throughout the world, many real-time instances of power system instability issues that resulted in total collapses or blackouts occurred. Fig 1 depicts recent events of power system instability that occurred on a year-to-year basis. Table 1 lists the total population affected by the aforementioned events. On December 3, 2021, Colombo, a city in Sri Lanka, had a blackout that affected 21 million people [8]. The outage was triggered by the breakdown of a critical transmission line, which prompted total power loss [8], [11].
Previously, on August 17, 2020, the same type of electrical blackout occurred at the Kerawalapitiya Grid-substation, affecting 21 million people [18]. On May 21, 2021, a blackout occurred in Amman, a city in Jordan's Hashemite Kingdom, affecting 10 million people. The power outage has been triggered by a technical electrical breakdown in the Jordanian-Egyptian energy interconnection, which resulted in an outage in high-voltage grid systems and a widespread power loss across the Kingdom. Jordan has experienced two power outages in the past, in 2014 and 2004, owing to a fault in one of the energy-producing stations, as well as a major power loss caused by a technical failure in the Aqaba thermal power station [9].
The biggest blackout in Pakistan history occurred on Saturday, January 9, 2021. This blackout affected Pakistan's largest cities, including residents of Karachi, Rawalpindi, Lahore, Islamabad, and Multan. Approximately 200 million people (almost 90 percent of Pakistan's population) were affected [10]. This event has occurred as a result of a malfunction in the national power distribution system in certain regions. The problem happened at 11.41 p.m. at the Guddu power plant in Sindh province, tripping the high transmission lines and causing the national power distribution system's frequency to drop from 50 Hz to zero in less than a second, forcing power plants to shut down. It was like a cascading effect that shut down the power grid, cutting off around 10,320 megawatts of electricity [19].
On August 4, 2019, a severe power outage occurred in Jakarta, Indonesia, affecting 100 million people. It has been caused by malfunctioning transmission circuits on the Ungaran-Pemalang power line in central Java, which caused voltage drops that affected electrical networks in the provinces of Jakarta, West Java, and Banten [12], [13]. Venezuela experienced blackouts on March 7, 2019, owing to the breakdown of the Simon Bolivar hydroelectric plant (Guri dam), as well as ageing infrastructure and inadequate maintenance in the state of Bolvar, which impacted 32 million people [14], [15]. In Indonesia, due to a power outage on November 15, 2018, 9 million people were affected in south Sulawesi, west Sulawesi, and sections of central Sulawesi. The blackout has been caused by interference with the Makale-Palopo transmission line [16].
One more power outage affected a large part of Brazil on March 21, 2018, impacting 10 million people, primarily in the northern and northeastern areas. The blackout has occurred due to the failure of a transmission line near the massive Belo Monte hydroelectric station [17]. Similarly, from time to time, power system instability occurs in several nations. The majority of the causes of previous blackouts have been frequency instability caused by power oscillations in the local area as well as inter-area transmission issues [7], [22].
Several preventive measures are taken to reduce the occurrence of blackouts, such as the addition of an advanced power system stabilizer in the system to eliminate power oscillations, smart grid optimization with the addition of modern technologies, the use of advanced relay systems, and so on [22], [23].
The rest of the article is structured as follows: Section II introduces the fundamentals of power system stability, including rotor angle instability, rotor angle dynamics, and an overview of conventional power system stabilizers. Section III introduces a detailed overview of control and optimization-based techniques. Section IV provides a detailed overview of a wide area-based power oscillation damping controller. Section V introduces a detailed overview VOLUME 11, 2023   of the penetration of renewable sources. Section VI provides a detailed overview of FACTS devices with PSS coordination and their control. Section VII provides a detailed overview of artificial intelligence and fuzzy-based PSS coordination and their control. Finally, the concluding remarks and future challenges are illustrated in Section VIII, respectively.

II. STABILITY IN POWER SYSTEM: THE FUNDAMENTALS
The classification of power system stability is shown in Fig. 2 [1]. The key problem in sustaining the secure operation of an interconnected power system is its stability. Primarily, rotor-angle instability occurs during the transfer of power through a transmission line due to rotor-angle fluctuation between two generators caused by large perturbations at the load side. The fluctuations can be easily transferred to power, resulting in increased oscillations. Large fluctuations may lead to loss of synchronizm between generators [24]. Therefore, it is essential to dampen power oscillations in order to make the system as efficient and stable as possible [22].

A. ROTOR ANGLE INSTABILITY
Before discussing rotor angle instability, let us first define rotor angle stability, which is the capacity of a synchronous generator to retain synchronizm even after being subjected to oscillations [25]. Since the relationship between electrical and mechanical power, i.e., (P elec and P mech ) is the same under normal operating conditions because electrical and mechanical torque, i.e., (τ elec and τ mech ) are the same, P elec ∝τ elec and P mech ∝τ mech . Here, the angular speed (ω r ) and the rated angular speed (ω 0 ) are equal, so that the angular rotor speed deviation ( ω r ) is minimal [3]. As a result, if the rotor speed deviation ( ω r ) is small, the synchronous generator will operate at its synchronous speed. In synchronous machines, a change in electrical torque causes disturbances that can be divided into two categories: the synchronous torque component, which is in phase with the rotor angle, and the damping torque component, which is in phase with the rotor speed deviation [2], [26].
Furthermore, rotor angle instability occurs as a small oscillation caused by consistent load changes or as a large oscillation due to severe transmission line failures [22]. The rate of change of rotor angle ( dδ dx ) is determined by the difference between the rotor's angular speed (ω r ) and the rated angular speed (ω 0 ), and this difference has been referred to as the rotor speed deviation (Deltaomega r ). Accordingly, it can be deduced that if the rotor angle changes, the rotor speed will fluctuate, and if the rotor speed fluctuates, the generator will oscillate, and if the generator oscillates, the system may become unstable. The cycle of the factors that cause power oscillations is depicted in Fig 3 [23].

B. ROTOR ANGLE DYNAMICS
In this section, the effect of rotor angle variation and its dynamics according to the swing equation have been discussed. A synchronous machine prime mover applies a mechanical torque (τ mech ) to the machine shaft, and then the machine generates an electromagnetic torque. In the event of a disturbance, electromagnetic torque (τ elec ) is less than mechanical torque (τ mech ) [2], so the accelerating torque (τ acc ) is, Now, τ acc has an inertia J (kg * m 2 ) which has been produced from prime mover so the equation becomes, where, t is time (in seconds). We know that, where θ mech is machine mechanical angle (rad), θ elec is machine electrical angle (rad) and p is field poles. Now substituting Eq. (3) in Eq. (2) we get, Multiply both side by ω sm in Eq. (4) we get, we know that, where, ω sm is angular speed of prime mover in mechanical quantity (mech.rad/s). As torque (τ ) is a mechanical quantity, it has multiplied with a mechanical quantity (ω sm ). Then, rewrite Eq. (5) we get, Therefore, where, where ω 0 is the rated angular speed. Therefore, rewrite Eq. (7) we get, we know that, Consequently, Eq. (8) can be written as, As per the relationship between fixed reference and rotor axis of synchronous generator, θ elec is, where δ elec is electrical rotor angle in elec.rad. Differentiate Eq. (10) with respect to t we get, where, ω r = dθ elec dt = Angular speed of rotor (elec.rad/s) After taking double differentiation of Eq. (10) we get, Substitute Eq. (12) in Eq. (9) to get, Hence, Eq. (13) is called as swing equation. The above equation states that, if a system is to be stable during disturbances, the rotor angle must oscillate around an equilibrium point. Furthermore, if the rotor angle continues to oscillate endlessly without reaching a new state of equilibrium, the machine is deemed to be in a transiently unstable [2], [3].
In normal operating condition, τ mech = τ elec means P mech = P elec which means ω 0 = ω r . Therefore, it can be concluded that, under normal operating conditions, the angular rotor speed is the same as the rated angular speed of the rotor. However, if the rotor angle between two generators fluctuates, the rotor speed will fluctuate too, resulting in rotor speed deviation. Therefore, rotor angle must be maintained within a permissible limit in order to attain system stability [1], [26].

C. OVERVIEW OF CONVENTIONAL POWER SYSTEM STABILIZER 1) SMALL SIGNAL STABILITY ANALYSIS OF MULTI-MACHINE POWER SYSTEM
Small signal stability analysis of multi-machine power system (MMPS) is discussed in this section. The fundamental approach of small signal stability analysis in context of power oscillations in power system networks are mathematically deduced below. Following are the differential equations of MMPS [27], where, ω r,i is angular rotor speed deviation of i th generator. As G i is the gain of i th generator and E ′ d,i and E ′ q,i are the voltages proportional to d-axis and q-axis flux linkages of i th generator, respectively. I d,i and I q,i are the direct and quadrature axis currents of i th generator and x d,i and x q,i are the direct and quadrature axis synchronous reactances of i th generator, respectively. If the terminal voltage for direct axis component is V td,i = V t,i sin(δ i − θ i ) and for quadrature axis component is V tq,i = V t,i cos(δ i − θ i ) then the electrical output power is, (18) Consequently, the network equations are represented in the network reference frame as, where, [I ] and [V ] are the current and voltage vectors in the network reference frame with the components ( To understand the concept of power oscillation damping in MMPS more clearly, the Kundur two-area, four-machine, 11-bus system illustrated in Fig. 4 is examined. For damping power oscillation, Multi-band PSS (MB-PSS) and Delta ω PSS are preferred for power oscillation damping due to the fact that their input is rotor angular speed deviation ( ω r ). The structures of Delta ω PSS and MB-PSS are depicted in Fig. (6) and Fig. (5), respectively. To comprehend the behaviour of CPSS present in the system, some simulation results of the system are obtained, as shown in Fig. (7). The results in the figure show that in a system without PSS, oscillations are extreme, which means that the system becomes unstable and there is a maximum possibility of a power outage. The peak overshoot, peak undershoot, and curve shape of the MB-PSS are superior to those of ω-PSS. Furthermore, the damping strength of MB-PSS is greater than ω-PSS in single-line-to-ground fault conditions. MB-PSS stabilizes power oscillations more quickly and efficiently compared to ω-PSS.

2) INCLUSION OF PSS IN EXCITATION SYSTEM
The system provides additional dynamics if a PSS is used [27].
where, K stab is the stabilizing gain of PSS and x t 1   are augmented differential equations from Eq. (14) to Eq. (17) for each machine. If there is only one stage in the lead-lag network, Eq. (23) can be eliminated by setting τ 3 = τ 4 and x t 2 = x t 3 [27]. Then the following equations are formed: Consequently, the linearized output of a two-stage PSS is given by, Thus, the output of PSS with a single stage is given by, where, V s Â is the change in stabilizing voltage signal which is the output signal of the PSS and fed into the excitation system.

III. CONTROL AND OPTIMIZATION BASED TECHNIQUES
Control-based techniques require exact configuration of the system, whereas optimization techniques, which require additional computational time and a well-formulated objective function, are proposed in [28]. In [29], a decentralized proportional integral derivative (PID)-PSS has been developed using an iterative method based on linear matrix inequality (LMI) techniques.
In [30], two iterative LMI techniques have been proposed to examine the problem of quadratic stability in polytopic systems with the utilization of static output feedback (SOF) controllers. H 2 controller-based LMI technique designed to damp low-frequency oscillation (LFO) has been proposed in [31]. Here, the damping performance of this controller is superior to that of CPSS across a wide range of conditions. PSS is designed in [32] on the basis of a linear optimum feedback controller (LOFCD), which has been proposed to provide a step-by-step process for deriving PID parameters without the use of the trial-and-error (TAR) method.
For designing PSS, [33] proposed a system identification method based on determining the Eigenvalue Sensitivity Function. This technique calculates the effect of errors in the mathematical model. Here, the automatic voltage regulator (AVR) enhances the steady-state stability of the power system. In practice, the TAR method outperforms the Zeigler-Nichols method Â [33].
In [34], a robust control technique based on the concept of loop shaping known as H ∞ robust control optimization method has been presented and then applied to the AVR-PSS system in order to optimize the transient and dynamic stability of a turbo alternator coupled to a single machine infinite bus system (SMIB). In [35], a robust PSS-based particle swarm optimization (PSO) with mixed sensitivity H ∞ is designed using the LMI method. [36] describes and designs a proportional integral (PI) PSS-based controller. This technique improves the mathematical calculation and computational time of the system. Also, a 2-level control technique is discussed in [36] to minimise the LFO. This technique is superior to the genetic algorithm (GA), PSO, bacterial foraging optimization (BFO), and some other CPSS.
To overcome the challenges of rotor-angle stability, a cascaded control approach based on a PID controller and the marine predator algorithm (MPA) has been proposed in [37]. Here, MPA is more efficient and effective than traditional controllers with respect to rotor angle stability. A mechanism for explicit self-tuning control (ESTC) has been proposed in [38] to improve the stability and damping of the LFO. Here, the structure of the proposed controller, which acts as an adaptive PSS, depends on the principle of recursive least squares (RLS).
In [39], robust robust-PSS-based programming of a sequential conic has been designed to solve the problems of tuning PSS gain (TPG) and tuning PSS parameters (TPP). Here, the simulation results are tested on a 68-B test system.
A CPSS-based quantum-behaved PSO has been presented in [40] in order to reliably tune PSS parameters (TPP) and mitigate the overall LFO of the system using an eigenvalueobjective function. In [41], a probabilistic PSS based on recursive GA has been designed for optimizing PSS parameters and overcoming PSS design challenges.
CPSS-based GA has been developed in [42] for effectively damping LFO and TPP. The simulation results are tested in this case using the 10M-39B New England Test System (NETS). Reference [43] proposed an improved modified PSO by passive congregation with chaos integration to design a PSS for TPP. PSS based fuzzy logic (FL) incorporation with chaotic ant swarm optimization (CASO) technique is designed for effectively TPP has been presented in [44]. A PSS-based improved PSO algorithm designed for damping the LFO to optimize convergence speed and search space more effectively has been proposed in [45]. Here, the simulation results are tested on a 2-A test system.
A cultural algorithm (CA)-based PSS designed to dampen LFO has been presented in [46]. A modified MB-PSS technique that incorporates PSO, CA, and co-evolutionary (CE) algorithms for optimally damping LFO and TPP has been proposed in [47]. According to [48], a CPSS-based bat algorithm (BA) has been designed to tune the pole zero and gain parameters to damp an LFO.
PSS-based ant colony optimization (ACO) designed to improve the number of iterations and damping performance has been presented in [49]. Here, the simulation result is tested on the 3M-9B and 8M-36B test systems. Reference [50] proposes a honeybee mating optimization (HBMO) technique based on CPSS for optimising parameters and determining the optimal location to damp LFO. In [51], a PSS-based Cuckoo Search Algorithm (CSA) designed to increase the robustness of PSS parameters and improve the performance of the damping LFO has been presented. A PID-PSS-based BA designed to increase the robustness of PID-PSS parameters and to enhance the performance of damping LFO has been presented in [52].
PSS-based CSA is designed to enhance the damping of LFO and has been presented in [53]. Here, the robustness of the system is tested under the 3M-9B system. PSS-based PID inclusion with PSO, according to [54], is intended to optimise the parameter affected by incoming uncertainties. In [55], a robust PID-PSS-based bacterial foraging optimization (BFO) technique for inclusion with PSO has been proposed to improve the damping performance and TPP of the system. In [56], a fractional order (FO)-PID-PSS-based BA is designed to enhance the damping of LFO. In [57], modified PSO algorithms are designed to improve the TPP, and a damping LFO has been presented. Here, the simulation results are tested on the 3M-9B system.
PSS-based CSA is designed to dampen the LFO and TPP of the system by evaluating its efficacy, as presented in [58]. A controller based on a static synchronous series compensator (SSSC) typed FO-single output multi-input (SOMI) is designed for inclusion with the whale optimization algorithm (WOA) to damp out electromagnetic LFO and TPP, as well discussed in [59]. In [60], a PSS-PID-based modified PSO has been designed to reduce the influence of computation time and improve the damping performance of the system.
A damping LFO has been proposed in [61], PSS-based WOA is designed to TPP. Here, the simulation results are tested in the 3M-9B system, the 2A-4M system, and the 10M-39B NETS. In [62], a PSS-based stability nonlinearity index (SN) has been designed using a newly developed SN-PSS-Hyper-spherical search (HSS) optimization algorithm to maximise the damping ratio coefficients and minimize the non-linearity index (NI) of the dominant electro-mechanical mode. Here, the simulation results are tested on the 2A-4M-11B and IEEE 10M-39B test systems. A PSS-based improved WOA has been designed in [63] to improve damping performance and finely control the PSS parameters. Here, the simulation results are tested under 3M-9B, 2A-4M, and 10M-39B NETS.
PSS based on simulated annealing (SA) and the atom search algorithm (ASO) has been designed and has been proposed in [64]. Here, the balance between the exploration and exploitation phases is excellent, with optimal TPP and damping LFO. Furthermore, the simulation results of the system are tested in the Heffronâ Phillips SMIB model, and the results are compared with PSO, GA, SA, ASO, and gravitational search algorithms (GSA). In [65], modified grey wolf optimization (GWO) is designed to improve the TPP, and damping LFO has been proposed. Table 2 shows an overview of the methodologies for PSS controller parameter tuned through optimization techniques.  [70]. In [69], a unique approach for calculating the delay-dependent stability criteria on the basis of Lyapunov stability theory (LST) theory and the Schur model reduction technique (SMRT) method has been proposed to optimize the low-order system. Furthermore, LMI methods are used to achieve the delay margin with less conservatism. As discussed in [69], there is an increase in delay margin, the damping performance of a conventional wide area damping controller (WADC) degrades, and the gain margin decreases. Consequently, the simulation results are tested under 2A-4M system.

Reference [69] proposes a Wide Area
Reference [70] proposed an adaptive delay compensator (ADC) with synthesis (H 2 /H ∞ ) approach to compensate for time delay disturbances and optimise the performance of a WADC based on WAMS. Here, the compensator is capable of successfully compensating phase angle deviations that are induced by various time delays, and the system is tested in 2A-4M and IEEE 39-Bus NETS.
In [71], a novel computation of the damping factor used to design WADC based on time delay margin has been presented. Here, LST and integral inequality methods are employed for determining the delay margin. Also, calculation speed is increased, conservatism is reduced, and the balance between signal transmission delay and damping performance is maintained in [71].
In [72], a wide area measurement system-based damping controller is designed to damp inter-area oscillation mode and compensate the remote feedback communication time delay (CTD) signal. In [73], a WADC is designed with a hardware-in-the-loop real-time (HILRT) simulation system to eliminate the disturbances from inter-area oscillations and to compensate the time-varying delay signal from the widearea transmission line.
In [74], WAPSS-based synchrophasor measurement technique has been designed to damp inter-area oscillation and compensate for CTD. Here, the Jaya algorithm (JA) is used to strengthen the parameters of wide area PSS (WAPSS), and geometric measures were taken to obtain the input signal. A WADC-based power oscillation damper with time delay compensator (TDC) has been designed in [75] to reduce the attenuation effect caused by noise pollution in wide area signals.
In [76], a compact WADC with a classic-PSS structure has been designed for use with a unified residue (UR) approach to dampen the LFO with parallel balance time delay compensation (TDC) and to maintain the balance between time delays. In [77], WADC based on the LMI approach has been designed to enhance the performance of WADC. Here, uncertainties in CTD and permanent system failures occur whenever there is 34052 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. a chance of a cyberattack on the phasor measurement units (PMU) of WADC channels.
In [78], a novel method of WAMS-based fractional order (FO)-PID controller as an auxiliary controller is designed for large-scale photovoltaic (PV) farms to improve the performance of LFO damping and reduce the uncertainties in system parameters. In [79], a delay margin-based PI controller has been designed for compensating and predicting accurate CTD to improve system stability. Here, a novel smith predictor (SP) based WAPSS with discrete hidden markov model (DHMM) has been developed.
Reference [80] developed a multi-objective optimization function to robustly improve WAPSS damping performance, solve small and large disturbance angular instability problems, minimise eigenvalue sensitivity to small disturbances, and vary WADC time delay. The simulation results were validated using the 16M-68B New York Power System (NYPS) and NETS. In [81], a WADC-based HY-PSO algorithm has been designed to improve the performance of the proposed system and reduce uncertainties in the operating point, variations in the time delay, and the failure of CCN due to a cyberattack. Table 3 shows an overview of the literature survey of WAPSS.

V. RENEWABLE SOURCE PENETRATION
In recent years, researchers have been attracted towards renewable energy source (RES) integration in grid-connected networks [82]. In [83], a WAPSS for a wind-integrated system incorporating stochastically tuned conventional structured phase-lead-lag to dampen or overcome the inter-area LFO as a system facing enormous stochastic variation in the steady state while determining the operating point has been designed. In [84], a PSS-based energy storage system (ESS) has been designed to choose the optimal installation location and feedback signal by dampening torque indices (DTI).
In [85], PSS-based conventional-PSO passive congregation has been designed, which is an evolutionary algorithm inclusion with doubly fed induction generators (DFIG) on wind turbines (WT) to improve LFO damping. In [86], a hierarchical wide area controller (WAC) is designed to maximise damping performance while providing a proper control signal between the synchronous generator and RES controller. A gain-scheduling WADC has been designed for the RES integration in [87] to improve the damping performance of wide area transmission line signals.Â Reference [88] has designed a wide-area power oscillation damper (POD)-based DFIG-based wind farm to compute the gain scheduling WADC using an LMI approach and the staircase basis function method. Here, a tensor product model is converted into a linear parameter based on a parallel distributed compensation (PDC) controller. Also, it compensates the dropouts of packet data signals, CTDs, and inter-area oscillations from wide-area transmission line signals. In [89], type-II-FL based PSS has been designed to compensate the high level wind penetration. Fig 8 shows the block diagram   FIGURE 8. Two-area, four-machine, 11-bus test system with DFIG wind turbine integration. of a two-area, four-machine, 11-bus test system with the integration of a DFIG wind turbine.
In [90], an optimal oscillation damping controller (OODC) based on a reduced-order model (ROM) is designed for DFIG-WT to provide appropriate control signals. In [91], an adaptive dynamics programming technique was used in the policy iteration algorithm (PIA) for DFIG-WT solved by riccati equations (ARE) to design a damping controller based on an improved efficient cubature-Kalman filter (CKF). Here, the simulation results were tested in a modified IEEE-WSCC-9B system, and the effectiveness is observed by comparing it with an optimally tuned conventional damping controller and a traditional linear quadratic regulator (LQR).
An ADC-based WADC has been designed using the synthesis H i nfty/H 2 approach for the coordination of a flexible AC transmission system (FACTS) and wind farm to provide appropriate scheduling and CTD and to dampen the uncertainties from oscillations, as proposed in [92]. In [93], the effect of incorporating power oscillation damping and an inertia controller into the structure of the WT system has been examined. This will affect the drivetrain, blades, and tower and also have a marginal effect on POD performance. The simulation results are validated using a 2A-4M-11B test system equipped with a full-scale converter (FCT)-WT.
In [94], a Youla-Kucera-polytopic linear parameter varying (LPV) has been designed for DFIG integrated with the power grid and virtual inertia control (VIC) to suppress subsynchronous oscillation under the abnormal fluctuation of the operating point. Also, its structure ensures the reduction of calculation time while providing efficient damping and maintaining its nonlinear dynamic characteristics. Here, the simulation results were tested under the IEEE-39B system integrated with 2-WT. Furthermore, improved-PSO is intended to solve the problem of optimal power flow through a transmission line for a hybrid system by estimating output power using lognormal and weibull probability distribution functions (PDF) and lowering total generation cost, as proposed in [95].
The method of estimating the percentage of deloading for large-scale PV plants integrated in the transmission network using multiple linear regression analysis (MLRA) has been discussed in [96]. In this case, the simulation results are validated using a modified IEEE 39B test system. Also, by comparing the proposed method with a battery energy storage system (BESS) and a synchronous condenser, which are installed in a PV integrated grid system, effectiveness is observed.
In [97], estimation method for optimal reactive power dispatch (ORPD) has been proposed for inclusion with the techniques of inheritance-non-dominated sorting genetic algorithm (i-NSGA-II) and roulette wheel selection to improve the performance of an integrated wind power system. The simulation results were validated using IEEE 33B and 69B test systems, as well as a modified Gilbert network.
A quantitative transient stability evaluation study framework was developed using a method of quantitatively estimating the influence of RES participation in power transmission lines on transient stability, as proposed in [98]. Table 4 summarises the literature review on renewable energy penetration.

VI. FACTS DEVICES WITH PSS COORDINATION AND THEIR CONTROL
CPSS is not able to damp both inter-area and intra-area oscillations simultaneously in an effective manner due to the limited observability of the system. PSS has a remarkable ability to effectively dampen power oscillations, whereas FACTS controllers are specifically intended to provide necessary reactive power, which eliminates the inter-area oscillations [99]. As a result, researchers are keen to develop advanced technology and controllers based on FACTS devices with PSS [99], [100]. Fig 9 depicts the block diagram of a two-area, four-machine 11-bus test system with a FACTS compensator [99].
In [99], a multi-input hierarchical FL PSS-based SVC (Static Var Compensator) has been designed for MMPS. Whereas, a hierarchical FL system has the quality of having a reduced number of rules as it consists of a number of lowdimensional FL systems in the form of a hierarchical structure. Here, SVC is the most efficient device for reactive power compensation, and its ability to provide a constant voltage supply has been proposed in [99]. Furthermore, as examined in [99], the multi-input hierarchical FL-PSS-based SVC performance outperforms CPSS, and the simulation results were tested on the 2A-4M-11B system.
In [100], WADC-based FACT devices (i.e., SVC) have been designed to damp inter-area oscillations in remote area signals where CTD is obtained from WAMS. Here, system feasibility is practically demonstrated and verified in a complex power system. Also, the simulation results were tested in 2A-4M power system, 10M-39B NETS, and 16M-68B power system. In [101] and [102], a decentralised Takagi Sugeno FL-WADC-based FACT controller is designed with the use of the probability collocation method for DFIG-WT to reduce the uncertainties from load parameters. Here, the simulation results were tested on a very large power system with 1332 buses and 39 buses of NETS.
A WADC-based STATCOM is designed in [103] to dampen the LFO by supplying appropriate auxiliary signals so that the generator rotor angle receives an appropriate signal to minimise speed deviation. A novel FL lead-lag controller-based static synchronous series compensator has been designed to boost the stability of the power system [104]. In [105] and [106], the coordination of PSS and FACT devices with IPGSA and MTT has been proposed to improve the damping controller parameters, which optimize the damping ratio.
In [107], ACO-static synchronous compensator (STATCOM)-based voltage source converter is designed to damp a sub-synchronous LFO to improve the gain parameters of the controller. However, Fig 9 depicts a similar tested system block diagram [107].
In [108], a PSS-based GA and Grasshopper Optimization Algorithm (GOA) have been designed in order to optimize the parameters of the system. In [109] and [110], a PSS-based FACT device has been designed with a synchrosqueezed wavelet transform (SWT) and stochastic subspace identification (SSI) algorithm to deal with the LFO of a largescale power system. Here, the controller parameters are to be optimized by the modified fruit fly optimization (FFO) algorithm as well as the Prony and UR methods.
To improve the damping performance of the LFO, [111] designed a PSS-based FFA and an IPFC as a supplementary controller. In [112], a PSS-based SVC with a UR-based approach has been designed to enhance the damping LFO. Here, the UR-based method is used to determine the optimal location of the proposed PSS. In order to optimise system performance, a FACTS device (SSSC) has been designed in collaboration with the POD controller as a supplementary controller [113].
Here, the geometric measure of observability (GMO) provides the information of a feedback signal and improves the performance of the system. Whereas, the simulation of the system is evaluated in 2A-4M-11B with the integration of TCSC. Table 5 shows an overview of the literature survey of FACTS devices in coordination with PSS.

VII. ARTIFICIAL INTELLIGENCE AND FUZZY BASED PSS COORDINATION AND THEIR CONTROL
Nowadays, artificial intelligence (AI) is very popular due to the exponential increase in the strength of its prediction and forecasting [110]. [110] also demonstrated a PSS based on the farmland fertility algorithm (FFA) with interline power flow controllers (IPFC). Here, a neuro-fuzzy controller (NFC) has been developed as a damping controller to optimize the computational time. An artificial neural network (ANN) is trained by a large amount of data over a period of time, and then it can only predict the optimal parameters. But, still, neural networks are popular because they solve complex problems without any mathematical support [131].
In [115], an indirect adaptive FLPSS is designed to dampen inter-area oscillations. Here, PSO tunes the controller gain to ensure system stability and minimize the sum of the squares of speed variations. In [44], a single-input and dual-input PSS-based CASO algorithm is designed with the adoption of FL for very fast on-line, off-nominal feedback to improve the stabilizer parameters at various operating conditions.
In [116], a unique adaptive PSS based on both synergetic control and FL systems has been designed with LST to improve system stability. in addition to the adoption of a chatter-free continuous control rule, which simplifies the controller implementation. In [117], a PSS-based adaptive fuzzy sliding mode controller (AFSMC) has been designed to improve the transient dynamics and oscillation damping in a SMIB and MMPS.
Reference [118] developed a novel PSS-based AFSMC that employs Nussbaum gain on a nonlinear model subjected to a three-phase fault-enhancing damping LFO and transient dynamics. In [119], a PSS-based type-2 FL has been designed with a DE approach to optimize the system characteristics and rule. Here, the simulation results were tested in SMIB. A robust PSS-based indirect AFSMC has been designed that incorporates a PI controller and a sliding mode controller for damping local and inter-area oscillation modes for MMPS [120].
In [121], a hybrid strategy for tuning PSS in MMPS with an objective function to reduce LFO and enhance power system dynamic stability across a wide range of power systems has been proposed. In [122], a FL-PSS-based harmony search algorithm (HSA) has been designed to increase the input output scaling factors of the FL controller across a wide range of operating conditions. Here, the objective function for the optimization problem is the minimization of the integral square error. In addition, the performance indices of both systems (HSA and FL-PSS) have been examined.
Reference [124] designed an intelligent controller based on an AFSMC with a PI switching surface to minimise inter-area oscillations and damp the system's LFO. In [125], an adaptive FL-PSS has been designed by robust synergetic control theory and terminal attractor techniques to enhance damping LFO. Here, the performance of proposed stabilizers has been examined for SMIB and MMPS under various types of disturbances.
In [126], PSS-based conventional FL-PID and type-1-FL controller has been designed to improve the stability of SMIB and MMPS under various loading conditions. In [127], a FL-PSS-based krill herd algorithm (KHA) to dampen LFO has been proposed.
In [128], PSS-based FL controller has been designed to improve the performance of damping LFOs and tune the PSS parameters. Here, the advantage of this technique over conventional FL-PSS with constant parameters is that it optimizes the behaviour of a dynamic system. In [129], an AI-PID-PSS-based approach to an artificial bee colony (ABC) has been designed to minimize objective function by TPP and to provide suitable low-frequency mode damping. In [130], a PSS-based artificial immune system (AIS) has been designed to dampen LFO.
However, in order to successfully implement the framework of control design in power oscillations, numerous challenges of technology integration must be overcome. Table 6 shows an overview of the literature survey of artificial intelligence based PSS.

VIII. CURRENT ISSUES AND FUTURE CHALLENGES
Numerous research regarding the efficient design of PSSs have been reported. Several challenges have been observed in the development of PSSs. First, appropriate selection of controller parameters is a challenge since modern power systems are highly non-linear and uncertain. The suggested solution for the aforementioned problem is to design an advanced damping controller for modern power systems. Second, modeling of time-varying delay compensation and its consideration in design of wide-area power system stabilizers is one of the key challenges. Third, mitigating the effects of the penetration level of renewable energy sources and its coordination with existing PSS is a challenging task. The suggested solutions for the aforementioned problem are to optimize devices that facilitate the control of voltage fluctuations in grid and improve the variable renewable energy (VRE) forecasting technology. Fourth, fast continuous control of power flow in the transmission system by controlling voltages at critical buses is one of the key challenges for the application of FACTS damping controllers, which are coordinated with PSS for damping enhancement in the power system network. The suggested solution for the aforementioned problem is to develop advanced controller-based FACT devices to improve stability of the modern power systems. Further, a challenge with AI approaches is that they can only approximate future output if the training network is given ideal input and output. In addition, AI techniques require more computational  time to predict the outcome, which is one of the challenges. The suggested solution for the aforementioned problem is to develop some hybrid AI-based technique so that the prediction capability of AI becomes more accurate.

IX. CONCLUSION
Modern day power systems are structurally complex. It is highly susceptible to transient events like faults and outages, which may eventually lead to the instability of the system. Therefore, secure and reliable operation of the power system is highly desirable. Rotor angle instability is one such instability that may disrupt a secure and reliable power supply. Consequently, the problem of rotor angle instability must be tackled efficiently. PSSs are devices that are capable of damping power oscillations in the systems, thereby reducing the impact of rotor angle instabilities. However, designing a VOLUME 11, 2023 34057 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
robust and efficient PSS is currently a difficult task. Several techniques are reported in the literature for the design of PSSs. However, the increase in complexities in modern power systems compels more efficient designs of PSSs that can tackle modern day uncertainties. In the present study, techniques developed to design PSSs are categorically discussed, and future challenges are highlighted.