Artificial Intelligence-Based Power System Stabilizers for Frequency Stability Enhancement in Multi-machine Power Systems

Low frequency oscillations (LFOs) occur in a system of interconnected generators connected by weak interconnection. A power system stabilizer (PSS) is commonly used to improve the capacity of the power system dampening. Under a variety of operating conditions, traditional PSSs fail to deliver superior damping. To address this issue, a Farmland Fertility Algorithm (FFA-PSSs controller) was used to solve an optimization problem for optimal design of PSSs system parameters, and its performance efficiency was compared to GA and PSO-based PSSs controllers. In addition to PSS, flexible current transmission (FACTS) devices are widely used. PSSs controllers and FACTS devices are frequently constructed in tandem to improve the dampening efficiency of the system. In this study, an Interline Power Flow Controller (IPFC) FACTS device will be added to the PSSs controller to improve the power system’s oscillatory stability. PSSs optimal design and supplemental controller of power fluctuations for IPFC were conducted out on WSCC multi-machine test systems using a system linear model. Using time-domain simulations and quantitative analysis, the proposed IPFC model was compared to the FFA-PSSs controller in terms of performance and efficiency. The main disadvantage of this technique is the difficulty in designing a dynamic IPFC model in test systems, as well as the burden of IPFC coordinated PSSs optimization. In both PSSs design using FFA method and FFA-optimized PSS with IPFC cases, rise in the computational and simulation costs was found unavoidable. To compensate for these flaws and obtain the research contribution, this paper proposes a Neuro-Fuzzy Controller (NFC) developed as a damping controller that can take the place of the two controllers (research objectives three). The application of the NFC substitute the computational and simulation cost involved in designing multi-machine PSS and IPFC-FACTS systems simultaneously. With the availability of NFC in SIMULINK, a dynamic model of theWSCC three-machine system was developed under a variety of operating situations. Quantitative analysis results from the WSCC test system simulation show that when comparing the proposed NFC model to the IPFC model for the WSCC test system, the proposed NFC model was found to be 149 percent and 0 percent efficient in terms of the time to settle of rotor angle respond for G2 and G3, respectively, but 394 percent efficient when compared to the uncontrolled model. The decreased settling time values ensured the proposed NFC model’s efficacy in damping down the LFO and achieving superior stability over the two controllers. The proposed NFC model has shown significant performance improvement in both the transient and steady-state areas than when the system was design with the two damping controllers. The associate editor coordinating the review of this manuscript and approving it for publication was Dazhong Ma . VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 1 A. Sabo et al.: AI-Based PSSs for Frequency Stability Enhancement in Multi-Machine Power Systems INDEX TERMS Low frequency oscillations, power system stabilizers, farmland fertility algorithm, interline power flow controller, neuro-fuzzy controller. ABBREVIATIONS LFO Low Frequency Oscillation. AVR Automatic Voltage Regulator. FACTS Flexible AC Transmission Systems. GA Genetic Algorithm. NFC Neuro-Fuzzy Controller. NN Neural Network. WSCC Western System Coordinated. SVC Static Var Compensator. UPFC Unified Power Flow Controller. SMIB Single Machine Infinite Bus. STATCOM Static Compensatory. PID Proportional Integral Derivative. PIs Performance Indices. DC Direct Current. AC Alternating Current. MBPSS Multi-Band PSS. VSI Voltage Source Inverter. PSO Particle Swarm Optimization. ANFIS Adaptive Neuro-Fuzzy Inference System. FFA Farmland Fertility Algorithm. PSS Power System Stabilizer. IPFC Interline Power flow Controller. SVD Singular Value Decomposition. KF Kalman Filter. TCSC Thyristor Controlled Series Capacitors. VSC Voltage Source Converters. IEEE Institute of Electrical and Electronics Engineers. SSSC Static Synchronous Series Compensator. POD Power Oscillation Dampers. MF Membership Function. EMs Electromechanical modes. ANN Artificial Neural Network. FO Fractional-order. RBF Radial Basis Function.


I. INTRODUCTION
In the past, electrical power systems were relatively local and simple [1]. Today's power systems are complex with complicated architecture of the networks of transmission lines that connect generator to substations and load centers [2]. One of the outcomes of this linked network is low frequency oscillations (LFOs) with frequencies ranging from 0.2 to 3 Hz [3]. To better understand the causes of LFOs on power system. The literature [4] explains that, generators and loads are interconnected via a network in a power system, and the generators are operated in synchronization at a fixed system frequency. The power change impacts all other generators in the system if one generators speed deviates from the synchronous speed. When this occurs, the system maintains synchronous speed by taking the appropriate control action, such as changing the exciter or turbine controllers. LFO on the other hand, can occur if the controller's settings or the networks status are insufficient. The high-speed excitation mechanism, in particular, weakens the damping properties of LFOs (used to minimize the loss of synchronizing torque and increase transient stability). However, for the case of impedance-mismatch as reported by [5], In power electronics converters with regulated output voltage, negative incremental input impedance is present, resulting in constant power load behavior. Oscillations and overvoltage may arise as a result of a large number of constant power loads in an electrical system, potentially culminating in a system shutdown. Smaller electrical systems, such as planes, ships, and microgrids, cannot handle a large number of loads with negative input impedance. Smallsignal stability is determined by the source to load impedance ratio at any given interface, as it is for both dc and ac systems [1], [6]. When LFOs occurs, the oscillation continues for a while and then goes away, or it increases steadily, causing the system to collapse [3]. A significant fault in the system's performance, such as a three-phase short circuit to the ground or the tripe of a transmission line, might cause the power system to oscillate [7]. Therefore, if power fluctuations cause the collapse of a power system, it can be due to the problem of the stabilization of the angle of the large or small perturbation rotor of the power system [8]. The oscillation of the power system is a term used to describe this type of stability. The North American Power Grid's oscillations were first noticed in October 1964 during the north's network of power testing links to the Southern Power Grid [9]. Power oscillation at a frequency of 0.1 Hz was noticed after the connecting line, and the connecting line was tripped after a time.
Moreover, some cases of power system fluctuation in transmission network of many countries have been observed and reported. Examples include: The Great British power grid experienced power fluctuations on the path from Scotland to England in the late 1970s and early 1980s.
When power transmission is transferred, these oscillations are quite high, according to practical experience. The results of a series of studies conducted in 1980 and 1985 showed that these fluctuations occur when the power transfer level is significantly adjusted and the oscillation frequency of these power fluctuations was 0.5 Hz. The installation of power system stabilizers (PSSs) in numerous power facilities in Scotland effectively addressed this issue [10]. Continuous system fluctuations in Taiwan's power grid were reported in 1984, the damping of power fluctuations was found effectively improved by successfully installing PSSs in selected locations [11]. Power oscillations were the direct cause of the North American WSCC network's demise on August 10, 1996. (with frequencies between 0.2 and 0.3 Hz). Lines and generators were expanded with tripping, eventually leading to the western system coordinated council (WSCC) network becoming four islands. These effect left over 5.7 million consumers in total blackout for nine hours, resulting in significant economic losses [12].
The installation of supplementary excitation control, also known as PSSs, is used to regulate the volatility of power systems in order to maximize the damping of oscillations and improve the oscillation sustainability of power systems [13]. PSSs are a simple, effective, and cost-efficient technique [14]- [17]. PSSs have been installed in most electric power facilities in several countries so far [18]. Installing PSS, on the other hand, does not necessarily give a convincing solution to the power system volatility problem [19], [20]. The PSSs creates a positive component of phase torque with vetting changes in speed on the rotor, thus removing the negative damping torque effect by providing additional damping [21], [22]. The system is deemed to be stable and the power system has good oscillation damping when the system damping improves fast with a damping ratio larger than 0.1 and if there is a LFOs for a certain period (several seconds to ten seconds) and finally disappears, then the power system has oscillation power, but the damping of volatility is weak [23]. Nowadays, the volatility factor of the weak damping of power system known as electromechanical oscillating modes (EMs). Researchers and power system engineers are looking for a viable alternative to installing additional transmission lines for regulating and utilizing the power system. FACTS (Flexible AC Transmission Systems) and ESS (Energy Storage Systems) are two new developing innovations in power system applications that aim to improve the systems reliability and flexibility [23]. Several PSS may not be able to offer enough damping for power fluctuation dampening. As a result, power system engineers and academics are always seeking for novel PSS alternatives to successfully remove power system volatility [24]. Furthermore, traditional PSSs are built using frequency domain phase correction techniques and are based on a linearized model of the power system, which results in reduced performance and does not ensure good operation over a larger range of operating circumstances [25]. In order to enhance power system stability, several optimization techniques have been utilized in the literature to optimize PSS parameter values [2]. For single machine infinite bus (SMIB) systems, artificial intelligence (AI) techniques such as neural networks and fuzzy systems have been suggested, which has recently been broadened to incorporate multi-machine power systems [26]. Various tuning approaches have been offered to alleviate the disadvantages in intelligent systems. Many heuristic optimization methods, such as particle swarm optimization (PSO), genetic algorithm (GA), evolutionary algorithm (EA), have been developed and effectively used in optimization [26]. However, utilizing traditional PSS to dampen low frequency power oscillations is still a work in progress. Other alternative solutions must be revealed in order to address this problem. However, tuning PSS parameter values is a difficult task which possess heavy optimization process and sometimes the PSSs design solution does not always provide a satisfactory solution [27]. This can make the PSSs design to be re-designed again and again.
The FACTS devices, in addition to PSS, are frequently employed. PSSs controller and FACTS devices are often designed simultaneously to further improve the system's dampening efficiency [28]. An Interline Power Flow Controller (IPFC) FACTS device will be connected to PSSs controller in this investigation to further increase the oscillatory stability of the power system [19]. IPFC stabilizer was recently developed for the control of LFOs, with less attention in its implementation. Indeed, IPFC is a new concept adopted in overcoming and managing specific limitations of power line flow in multiple-line transmission systems [29], [30]. Although so many FACTS device example unified power flow controller (UPFC) has been widely developed as oscillatory stabilizers, very few entries have addressed IPFC [30]. The primary distinction between FACTS and PSS stabilizations is that FACTS stabilizations are generally deployed at the power system's critical transmission line. For example, in two-zone connection lines and long power transmission routes are installed for purposes such as load adjustment and voltage control [28]. Therefore, in certain cases, FACTS stabilizations can be easily implemented and effectively eliminate the volatility of the power system. For this reason, the sustained control of power system fluctuations by FACTS has become the subject of recent research and many researchers have been following it since the 1980s [31]. These FACTS stabilizers techniques are usually designed with the coordination of optimized PSSs on the test systems for effective damping. The major drawback of this procedure is difficulty in developing the dynamic IPFC model in the test systems and involves IPFC coordinated PSSs optimization burden.
PSSs controllers based on artificial intelligence (AI) have become a popular research topic in recent years. These intelligent controllers have the capacity to learn from the environment in which they are used to enhance their performance. The literatures have suggested Fuzzy Logic PSSs (FLPSSs), which can be type-1 fuzzy (T1FLS), type-2 fuzzy (T2FLS), or adaptive fuzzy sliding mode PSS, Neural Network PSSs (NNPSSs), Adaptive Neuro-Fuzzy Inference System PSSs (ANFIS-PSSs) [32] etc. were proposed in the literatures. For the FLPSS was found robust and their lower computation burden. It does, however, have a few bottlenecks, such as the development of membership functions, rule selection, and rule construction, which are often handled by trial and error or by human specialists. As a result, designing it is a difficult and time-consuming process. In the same way as the FACTS stabilizers, AI stabilizers techniques are also designed with the coordination of PSSs on the test systems. Designing the PSS parameters utilizing a strong optimization process has shown to be an efficient approach of running the PSS. As a result, a stabilizer must be developed to replace the usual optimized PSSs and FACTS, removing the need for system PSSs design modeling and complexities.
Thus, this paper proposes a stabilizer using Neuro-Fuzzy Controller (NFC) that can replace the work of PSSs and VOLUME 9, 2021 provide superior properties than the conventional PSSs and FACTS stabilizers in controlling low frequency oscillations in power system. The main contributions of this paper are: • A metaheuristic FFA technique is proposed for designing PSSs controller on WSCC IEEE test power system. The main contribution is to design dynamic gain parameters of controller in order to handle the system uncertainties and to enhance the steady state and transient performance indices. A considerable contribution is made in this field to enhance the computational cost and convergence for ill-conditioned system operating under multiple working point.
• An eigenvalue placement index was defined for designing the proposed optimal mode feedback and implemented as an optimization problem using FFA. Unlike the classical mode feedback design techniques which requires a conditional condition, the proposed method employs the single value decomposition (SVD) as an analysis tool to determine the appropriate signals for use in the feedback design process. Main contribution of this includes reduced number of parameters of the state feedback matrix, reduced number of control variables, reduced the design time and considering several work points in the design makes the proposed mode feedback resistant to permanent changes in the system. The proposed mode feedback was evaluated on WSCC test systems.
• Since designing dynamic PSSs control parameters give rise to heavy optimization process also, developing dynamic IPFC model in the test systems give rise to heavy system modelling and involves IPFC coordinated PSSs optimization burden, an efficient robust NFC damping controller was proposed to substitute the optimized PSSs and optimized IPFC on the systems. Since PI and PID controllers require a mathematical model of a plant or are model based controllers, NFC in this case is a model-free design because it only depends on expert information and experience. This is an important feature of this controller. Another significant features is that, the proposed NFC model does not require a mathematical model of the test system to be controlled and is operated independent of coordination with conventional optimized PSSs to avoid optimization burden. This paper is organized: Section II explains the modeling of IEEE 9-bus system model equipped with IPFC and also, the proposed FFA design implementation. Section III explains the proposed methodology for the NFC design. The simulation results obtained to validate the PSSs design, IPFC design and the proposed NFC design on WSCC test system respectively is discussed in section IV with conclusion and future scope of this work presented in last section.

II. SYSTEM MODEL STUDIED
This section shows the overall structure and methodology applied for this work. Figure 1 shows the framework for overall structure of this study which includes selection of PSSs for power system applications and selecting the intelligent approach for designing the multi-machine PSSs. FFA optimization method was a key player in this research. The three objectives of this study are PSSs design using the FFA method, FFA optimized PSSs with IPFC and the proposed NFC design using the FFA method respectively. First the power system nonlinear dynamic equations are modeled using MATLAB/Simulink software. The dynamic modeling has been validated using numerical simulation on IEEE WSCC three-machine benchmark test power system, has been selected for numerical simulation. A PSSs has been designed optimally using FFA optimization method for the test system. The performance evaluation of the FFA-PSSs controller was compared with existing search methods of PSO and GA for PSSs design.
Then, the methodological procedure for obtaining objectives two which is the dynamic modeling of IPFC will be studied and developed. Power system nonlinear dynamic equations equipped with the IPFC device has been implemented in Simulink environment of MATLAB software and its state Equations have been obtained. FFA-based mode feedback is proposed and designed as a supplementary controller for the IPFC device in order to increase the system damping status. In this optimization problem, the objective function of replacing eigenvalues and preventing their drift to the right-hand side is studied to improve the electromechanical modes (EMs) damping status for a set of conditions using the power systems. The performance and efficiency of the proposed IPFC model was compared with the FFA-PSSs method. Lastly, the methodology for attaining objectives three which is the dynamic modeling of NFC was studied and established in the studied test system. Power system nonlinear dynamic equations equipped with the NFC device has been implemented in Simulink environment of MATLAB software. Then the FFA method was used to determine the NFC control parameters. Unlike the PSSs and IPFC stabilizers, the NFC damping controller implementation execute the LFOs control without a linearized mathematical model of the system as such makes the system less complicated and cumbersome. The performance and effectiveness of the proposed NFC model was compared with the two controllers.

III. SIMULATION RESULTS AND DISCUSSION OBTAINED TO VALIDATE PSSs AND IPFC DESIGN ON WSCC TEST SYSTEM A. SIMULATION RESULTS OF PSSs USING FFA DESIGN METHOD
This section explains the objectives one methodological process for designing the PSSs system for the WSCC three-machine test system considered in Figure 2. In order to obtain permanent conditions, the power system of the Newton-Raphson power distribution program was implemented [112]. To obtain the systems initial conditions, the power system dynamic equations were solved nonlinearly. Also, using Simulink, the internal system characteristics of the state matrix, eigenvalues, rate of system damping, oscillation frequency and the participation coefficients of the state variables in creating modes were extracted and listed in Table 1.
Based on the results obtained from Table 1, it can be seen that modes 1 and 2 are affected by the speed and angle of the rotor of the second and third generators. Since these modes are caused by rotor angle of the generator, they are called electromechanical mode (EM) and since they are caused by several generators, EM is also called inter-region. Similar arguments can be made for modes 3 and 4. Modes 1 to 4 have a damping ratio of less than 0.1 in terms of the sustainability of low frequency fluctuations are not in a favorable condition and need compensation and control. The results of transient simulations also emphasize on it. Therefore, it is mandatory to add a supplementary controller for this system. Mode number 12 with an eigenvalue equal to zero has appeared in the results. This mode is due to the selection of the angle of the first generator rotor as the reference angle during the implementation of the simulations in this thesis. To improve the damping rate of EMs values to more than 0.1, a damping device called PSS has been installed to the system. Based on the participation coefficients calculated in Table 1, Generator No. 2 has the most effect on EMs, so PSS for this generator is installed. In this study, a speed signal stabilization which is very common has been used. The frequency conversion VOLUME 9, 2021 TABLE 1. EMs parameters obtained from the linearization of WSCC test system. FIGURE 2. WSCC system line diagram [33]. function of this system is given in Equation (1).
The input of which changes are modified is the speed and the output of the voltage that is added to the simulation. In order to facilitate the design of the PSS frequency conversion function is re-written as Equation (2).
For this study, the design of PSSs has become an optimization problem and is solved using Farmland Fertility Algorithm (FFA) evolutionary optimization algorithm. In this study, the following optimization model is proposed in Equation (3): The first expression in the objective function maximizes the damping of electromechanical and inter-zone modes while the second expression prevents the creation of unstable modes and prevents the drift of eigenvalues to the right hand of the complex zone. The K P variable is the participation coefficient for creating positive values. During this season simulations, the K P variable value is 50 and similar to [34] the range of optimization parameters for K G is [0.001-50], for T i [0.001-1] was designed for the objective function of a software and simulation was designed using the FFA search algorithm.

B. FFA FOR PSSs DESIGN
Farmers used the FFA search model to divide their farmed area into numerous sections and assess the soil quality in each of these agricultural regions [35]. Each piece of farming area has a particular soil quality that varies. The quality of soil in these agricultural fields is improved by introducing a variety of specific ingredients known as fertilizers. By doing so, the process can be repeated until it reaches a suitable level of quality. It's worth mentioning that the technique for assessing the quality of the labor process and the recovery results at each step is developed using local or national memory, enabling the farmer to select how much repetition and how much addition is chosen in the best quality [36]. The remaining farm regions solutions, i.e. (the lowest quality section of the agricultural areas, the present global memory solutions), are combined with the remainder of the available solutions in the exploration space to enhance outcomes [37]. After each agricultural area altered outcomes using global memory and arbitrary results in the exploration regions, farmers eventually resolved to combine some soil in each farmland portion in terms of the ideal achievable results from its local memory. FFA algorithm is usually broken down into six stages.
Step 1: Population production is determined by the amount of agricultural land sections and the number of solutions accessible in each sector. Equation (8) represents the starting population number.
In Equation (8), N signifies the total population of the search area in Equation (8). The number of data points in the optimal problem is denoted by K .
Step 2: After assessing the solutions' applicability and determining each agricultural land portion, all possible search space solutions are adapted.
Step 3: The local and global memories of each section are modified after the solutions for each segment of farmland are determined and combined. To calculate some of the best of each segment's local memory stores, as well as the best of all segment's global memory stores, the quantity of the best local and global memory with statistical relationships is utilized.
Step 4: More changes will occur to the lowest sections, and the solution combination is now in the search area.
Step 5: The knowledge stored in local and global memory is highly suitable to deciding and combining.   Step 6: The best solution is to evaluate the various solutions, determine your level of fitness, and keep working continuously.
The relevant FFA techniques parameters for the algorithm are described in Table 2. These characteristics let the sought technique achieve a high rate of convergence and a low computational load [38]. The search model was terminated after a certain number of iterations, and it is commendable to note that the PSS design approach was established and ran several times until the optimum PSSs characteristics were determined [39].
FFA with a primary population of 50 and a repeat number of 100 was executed. Table 3, 4 and 5 shows the three optimization pseudo algorithms for better understanding of their differences.  Figure 3 explains the optimization structure of obtaining the optimal PSSs parameters using the three optimization techniques. Table 6 provides the PSSs optimal parameters VOLUME 9, 2021   while Table 7 illustrates the system eigenvalues obtained for the WSCC test system via the FFA method.
To analyze the simulation work of WSCC, the linearization of the system from Table 1, first the dynamic model of power system was developed in MATLAB/Simulink software. An optimal method for the PSSs design is proposed to prevent the drift of eigenvalues to the right during the design and by increasing the damping of oscillations, the system will be lowered to a favorable condition in terms of the sustainability of frequency fluctuations. Based on the participation coefficients calculated in Table 1, the second generator was selected as the suitable place for installing PSS. According to Table 1, the minimum damping for EMs is 0.0148 for modes 3 and 4. By installing optimal PSS in the second generator location, this index was impressively improved to 0.3200 for the desired modes. As can be seen, this index has improved dramatically. Figure 4 shows the PSS design convergence index comparing FFA, GA, and PSO. The rate of convergence for the FFA was determined to be quicker at 41 iterations than the GA and PSO convergence.
Several potential operating conditions on the test system were examined to satisfy the research objectives. For the first objective, there will be two cases considered for the WSCC test systems. They are: Case 1: Three-phase symmetric fault at bus 9 were applied to the system for 100 milliseconds in one second with no change in system loading.   Case 2: For 100 milliseconds in one second, an adjustment of 5% increments were applied to the third generator excitation voltage reference.
Case 1 Without FFA Controller: The efficiency of FFAbased PSSs design techniques was compared to PSO and GA-based PSSs design methods as follows. The uncontrolled generator 2 rotor angle δ 2 relative to δ 1 (δ 2 − δ 1 ) and the uncontrolled generator 3 rotor angle δ 3 relative to δ 1 (δ 3 − δ 1 ) is presented in Figure 5 while the uncontrolled speed of the three generators are displayed in Figure 6. These results are consequences of no PSSs installed in the systems.  Several Using the FFA, GA, and PSO developed PSSs controllers, several time domain simulations were run to evaluate the power system's performance.
Case 1 With FFA Controller: The controlled generator 2 rotor angle δ 2 relative to δ 1 (δ 2 − δ 1 ) and the controlled generator 3 rotor angle δ 3 relative to δ 1 (δ 3 − δ 1 ) is presented in Figure 7 while the controlled speed of the three generators are displayed in Figure 8. These outcomes are the result of PSSs FFA-based design method.
The optimization issue was addressed and controller settings were found using the FFA method. The FFA-based PSSs approach decreases low frequency fluctuations and enhances the damping ratio of local EMs more effectively than the GA and PSO-based PSSs, according to simulation findings on the WSCC three-machine power system. Case 2 Without FFA Controller: The uncontrolled generator 2 rotor angle δ 2 relative to δ 1 (δ 2 − δ 1 ), the uncontrolled generator 3 rotor angle δ 3 relative to δ 1 (δ 3 − δ 1 ) and the uncontrolled speed of the three generators are shown in the sequence of Figures 9, 10, and 11 respectively.

C. QUANTITATIVE PERFORMANCE EVALUATION COMPARISON FOR PSSs DESIGN
The findings based on the suggested model are compared to the reference results [40] to demonstrate the efficacy of the proposed strategy in contrast to previous approaches. PSSs are used in this reference to enhance the dampening of power fluctuations for generators 2 and 3. Table 8 compares the findings of the proposed model with the reference model [40] in terms of EM damping in a three-machine power system. In this example, the eigenvalues and minimum damping ratio in Table 9, which includes the suggested model, and the literature published models in [40] with the same operating conditions, were gathered for comparison purposes.    The suggested technique lowers the damping of EMs generated by generators 2 and 3 from 0.0536 to 0.3200 and 0.0148 to 0.4442, respectively, as shown in Table 4.8. In other words, compared to the uncontrolled condition, it enhances damping by 497% and 96.6%, respectively, and by 17.9% and 127.7%, respectively, compared to the reference approach [40]. Both the referenced and constructed models had higher damping ratios than the uncontrolled model. The greater damping ratio value ensured the   suggested model's effectiveness in dampening down the LFO and achieving superior stability over the conventional model.
In addition, a transient response study for FFA-based PSSs was performed in comparison to GA and PSO-based PSSs. When the system is uncontrolled, this analysis compares the performance of the FFA-based PSSs to the GA and PSO-based PSSs, as well as the three optimized PSSs techniques. For uncontrolled, PSO, GA-based PSS, and FFA-PSS conditions, Table 10 examines how the first machine reacts to a brief disturbance based on system time to settle in seconds and time to rise in seconds. When the FFA-based PSS design is employed, the rotor speed for G1 is increased by a whopping 82.68 percent. This improvement is based on the time it takes for the system to settle in contrast to when it is uncontrolled. Because G1 is the reference machine, the rotor angle response of G1 is zero. Table 11 shows that the time to settle for rotor speed G2 using FFA was improved by 79.48 percent when compared to when the system is uncontrolled, while Table 12 shows that the time to settle for rotor speed G3 using FFA was improved by 79.70 percent when compared to when the system is uncontrolled.

D. MODELING AND SIMULATION RESULTS OF IPFC USING FFA DESIGN METHOD
The primary goal of power distribution control between lines is to distribute power between lines of the transmission system on which it is installed. Other functions, such as dampening power fluctuations in a power system, can be accomplished utilizing various controls on IPFC at the same time. The dynamic power system model is determined by algebraic-differential equations. Generators and their excitation control systems, as well as IPFC, are related to differential equations. This section looks at the fourth-order generator excitation system as well as the first-order generator excitation system. The mechanical power of generators is considered to be constant [34], [41]. The DC link voltage of its inverters is represented by the differential IPFC equations. Each VSCs are considered as a load, and the line network is used to obtain the Y new equivalent admittance matrix. By absorbing loads in the network as constant impedance and obtaining load voltage, generator currents and injectable currents, IPFC branches will be obtained. Assuming that the generators in the first 1st m are repeatedly in m + 1 to n and IPFC-related system are also n+1 and n+2. Then the voltage and current interface will be as follows.
By absorbing loads as constant impedance to the admittance matrix in relationships (10), (11) and (12) the Y new equivalent admittance will be obtained as: The relationship between algebraic equations of the network (new admin matrix) and stator equations is formed by defining relationships (13), (14), and (15), and the DAEs equations of the network are entirely solved. Figure 15 shows the test system equipped with IPFC device. Now, by linearization of nonlinear DAEs governing the system behavior, its state equations are obtained as Equation (16).
The following is a list of vector-based system mode variables: A proportional-integral controller (PI) is used to change the voltage of the dc link, hence x PI in the state variables refers to the PI controller mode. Equation (18) considers the transfer function for the PSSs as well as the IPFC supplemental controller in this work. It has five settings that can be changed. The additional pre-phase controller is given as Equation (18): Changes in the generator's normalized angular velocity are regarded the local input signal in the PSS transfer function, and its output is a voltage signal that is added to the generator's stimulation. The IPFC supplementary controller is also considering a similar transfer function. The IPFC controller input can be considered as a combination of local and remote inputs, such as real line power changes and generator speed changes. The output of the supplementary controller can also be applied to each of the IPFC VSCs' amplitude and phase angle inputs. VOLUME 9, 2021 FIGURE 16. WSCC system equipped with IPFC control [29].
PSS and POD design have been turned into an optimization problem in this study, and their parameters were obtained using FFA. The following is the proposed objective function for this optimization problem: where, K min The first statement from the objective function equation increases the damping of electromechanical and inter-zone modes, while the second sentence prevents unstable modes from forming. The K P variable is an integer coefficient value that is positive and equal to 50. The range of optimization parameters for K G is considered as [0.001-50] and for T i as [0.001-1] for PSS and POD respectively [42]. For numerical simulations, the WSCC multi-machine test system was chosen. Simulation of time-domain nonlinearity on the WSCC test system using the IPFC-FFA stabilizer was executed. To find permanent conditions, the system of the Newton-Raphson load distribution program was implemented [43]. To obtain the point of operating, nonlinear equations were solved using Simulink and dynamic equations were linearized and state equations were extracted. Using the extracted state equations, eigenvalues and participation coefficients of all eigenvalues were obtained. EMs in the system are in accordance with Table 13 which shows the EMs of the system without power fluctuations.
With the fast and correct altering of the line power flow with respect to power swings in the system, the system  stability margin and damping of critical modes are increased [44]. Installation of IPFC with flexible operation and correct series converter control appears to be the best solution to this problem. It is feasible to balance both actual and reactive power of several tie lines between two locations with different lengths using IPFC program [45]. In the power system, the proposed IPFC design is depicted in Figure 16. The IPFC location is chosen based on both static and dynamic objective functions study through detailed load flow and stability analysis [46]. Then, based on the dynamic objective function evaluation, which includes the speed difference of generators and active power oscillations parameters between areas, the best location for stability increase is chosen [46]. The IPFC series converters are best located between buses 5 and 6. An IPFC with two branches is installed in lines 5-7 and 6-9. The control system applied to IPFC is shown in Figure 16. Generators 1, 2, and 3 are responsible for the EMs with the lowest damping ratio, as seen in Table 13. In other words, this system contains a mix of local and inter-regional EMs. To improve the damping profile of these EMs, a PSSs was installed in the generator 2 with a POD on the IPFC installed in line 5-7, according to the existing participation coefficients in Table 13. Similarly, a PSSs was installed in generator 3 with a POD on the IPFC installed in line 6-9, according to the existing participation coefficients Table 13. The good reason for installing the IPFC between line 6 and 9 is because of simplicity of local signal availability compared to the distant signal, only the signal of real power changes passing through line 6-9 is considered as an entry for POD [30]. The second transducer angle modulator's input was supplemented with additional controller output. The proposed objective function was simulated using the FFA algorithm with initial population of    Figure 17 explains the optimization structure of obtaining the optimal PSSs and POD parameters using the proposed FFA optimization technique.
Several potential operating conditions on the test system were examined to satisfy the research objectives. For the second objective, there will be two cases considered for the WSCC test systems. They are: Case 1: The third generator excitation voltage reference was subjected to small variations of 5% increments for 100 milliseconds in one second.
Case 2: Three-phase symmetric fault at bus 9 were applied to the system for 100 milliseconds in one second with no change in system loading.
Case 1 IPFC-FFA-PSS Controller: The controlled generator 2 rotor angle δ 2 relative to δ 1 (δ 2 − δ 1 ), the controlled generator 3 rotor angle δ 3 relative to δ 1 (δ 3 −δ 1 ) and the controlled speed of the three generators are illustrated in the sequence of Figures 18, 19, and 20 respectively. These results are the outcome of the system's IPFC-based FFA stabilizer being installed.
Case 2 With IPFC-FFA-PSS Controller: Following the IPFC-FFA-based PSSs design, controlled generator 2 rotor angle δ 2 relative to δ 1 (δ 2 − δ 1 ), the controlled generator 3 rotor angle δ 3 relative to δ 1 (δ 3 − δ 1 ) and the controlled   speed of the three generators are illustrated in the sequence of Figures 21, 22, and 23 respectively. The installation of an IPFC-based FFA stabilizer on the system yielded these findings.
The supplemental controller built utilizing FFA was found capable to regulate low frequency fluctuations, according to simulation findings obtained for the validation of IPFC-based FFA stabilizer on the multi-machine test system.

E. QUANTITATIVE PERFORMANCE EVALUATION COMPARISON FOR IPFC DESIGN
The results from the proposed model are compared to the reference results to demonstrate the effectiveness of the proposed technique in contrast to other approaches [47] VOLUME 9, 2021  considering operating condition case two. Comparing the results of the proposed model and reference model [47] in the damping of EMs in the three-machine power system is listed in Table 14. The eigenvalues in the Table 14 for three examples, including the proposed model, and the literature published models in [47] with the identical operating circumstances, were gathered in this case for comparative reasons. The reference model utilized Bees search method to optimize the PSS with UPFC, SSSC, TCSC, STATCOM and SVC controls while the proposed model utilized FFA to optimized PSS with IPFC.
The proposed method reduces the damping of EMs caused by the generators. The given eigenvalues for all of the approaches were found on the left half-plane, as shown in the Table 14. Based on this, it can be observed that the proposed method is more effective than current methods. IPFC-based FFA stabilizer was compared with the optimized FFA-based PSSs and when the system is not controlled. A transient response analysis was also carried out for the IPFC's PSS-based stabilizer in comparison to the optimized one. The first machine reacts to momentary disturbance based on the system time to settle in seconds and time to rise in seconds for uncontrolled, FFA-based PSS and IPFC-FFA-PSS circumstances respectively is shown in Table 15. IPFC-FFA-PSS design improves rotor speed G1 transient reaction by an amount of 5.07% and 17.64% respectively. The improvement is based on time to settle and time to rise in comparison to   when the system is uncontrolled. Similarly, Table 16 shows the time to settle for rotor speed G2 using the IPFC-FFA stabilizer was improved by 5.40% compared to when the system is uncontrolled. Table 17 records an improvement of 13.62% for time to settle of rotor speed G3 using the FACTS stabilizer.
IPFC method controls magnitude and direction of power flow. It's overcome specific limitation of lines, extend the usable transmission limits, enhance grid reliability. No need to check the control or visible power system and reduce number of control variables in the control design problem. The results of numerical simulations show many advantages for the IPFC method. IPFC-based FFA stabilizer design reduces the low frequency fluctuations well and increases the damping ratio of local electromechanical modes in an effective way, according to simulation results. The IPFC device dampens the systems LFOs effectively when coordinated with the optimized PSSs in the system than when there was no coordination. This is a major drawback of the FACTS stabilizer as they require a complementary controller. It makes the system more cumbersome and takes a lot of time to achieve final solution.

IV. PROPOSED NFC METHODOLOGY
This section contains a demonstration of the proposed controller structure and how it was used in this study. To create fuzzy IF-THEN rules and explain membership functions for input and output system parameters, the suggested control model was trained from the start [51]. The back-propagation method is used to train this structure, which is essentially a multi-layer NN [13], [33] and [51]. When input-output is provided for training, the back-propagation algorithm measures the system's output and compares it to the preferred output of the training example to illustrate how the neurofuzzy system operates. From the output to the entry layer, the error is sent backwards through the device network. When a mistake is communicated, the activation processes of neurons are altered. By differentiating the activation functions of the neurons, the algorithm now calculates the needed changes. The following section looks at the sugeno type's fuzzy laws logical ambiguity [48]: (20) The input and output variables are x and y, respectively. Figure 24 shows the diagram assembly of the proposed controller in use in the control system [49], [51].
The proposed controller structure's inputs are specified. The (e) and change in error ( e) inputs of NFC are determined. Layer-1, also known as the Fuzzification layer, selects three Gaussian Membership Functions (MFs) for each input. For Gaussian MF, write the following mathematical expression [13], [51].
where, σ and m present the standard deviation and mean of MF. Firing strengths in the layer-2, also called rule layer, are obtained from membership degrees calculated in the layer-1 as: The normalization layer is the third layer, and it determines the normalized firing powers for each rule. The output of this layer is represented by Equation (23). The defuzzification layer is the fourth layer, and it computes the rules weighted values for each node as follows: Here, (k 1 + k 2 + k 0 ) are the parameter sets. The output layer is labeled layer-5 and is written as follows: The squared error (E) in Equation (26) decreases tracking error (e) and is expressed as [48], [51]. In order to update the antecedent and consequent part parameters by backpropagation algorithm, the squared error (E) in Equation (26) lowers tracking error (e) and is expressed as [51]: The following equation can be used to update the parameters of the proposed controller structure if the parameter to be adapted is determined as ϑ.
The variable η is referred to as the learning rate. The partial derivative is calculated using the chain rule [13], [51]. The derivative chain up to the NFC's output is as follows: The FFA algorithm is used to obtain the parameters K 1 , K 2 , and K 3 in the proposed controller structure as shown in Figure 25. The NFC scale or control parameters are the names given to these parameters. As a result, a more powerful controller was obtained. The proposed controller receives the machine rotor speed deviation dω as an input for controlling the system LFOs. The proposed controller generates a reference signal V nfcs . This signal is sent to the excitation system model, which generates the appropriate signals for dampening the system's LFOs.

V. SIMULATION RESULTS AND DISCUSSION OBTAINED TO VALIDATE THE PROPOSED NFC DESIGN ON WSCC TEST SYSTEM
To find the WSCC system working point, nonlinear equations were solved using Simulink, dynamic equations were VOLUME 9, 2021  linearized, and state equations were extracted. The eigenvalues and participation coefficients of all eigenvalues were calculated using the extracted state equations. The system's EMs are in accordance with Table 18, which characterizes the system's EMs without power fluctuations.
The results in Table 18 show that the speed and angle of the second and third generators' rotors have an effect on modes 1 and 2. These modes are known as electromechanical modes (EM) because they are created by the generator's rotor angle, and they are also known as inter-regional modes since they are caused by many generators. Modes 3 and 4 can be argued in the same way. Modes 1 to 4 have a damping ratio of less than 0.1 in terms of low frequency fluctuations long-term stability, and so require compensation and control. The results of transient simulations also emphasize on it. As a result, a supplemental controller for this system is required. Mode number 12 with an eigenvalue equal to zero has appeared in the results. This mode is due to the selection of the angle of the first generator rotor as the reference angle during the implementation of the simulations in this thesis. NFC damping controller has been added to the system in order to increase the damping rate of EMs to a value greater than 0.1. Generator No. 2 has the greatest effect on EMs, according to the participation coefficients calculated in Table 18, hence NFC is installed for this generator. Table 19 illustrates the new eigenvalues and participation coefficients of all eigenvalues obtained after the WSCC test system was equipped with the proposed NFC stabilizer.
From Table 18, the weak modes of the eigenvalues were increased by a damping ratio greater than 0.1.  Several potential operating conditions on the test system were examined to satisfy the research objectives. For the third objective, there will be three cases considered for the WSCC test systems. They are: Case 1: Three-phase symmetric fault at bus 9 were applied to the system with no change in the system loading.
Case 2: A symmetrical three-phase fault at bus 9 with a 120% increase in active power on generator 2 and generator 3.
Case 3: A symmetrical three-phase fault at bus 9 with an 80% decrease in active power on generator 2 and generator 3.
Case 1 With NFC Controller: The controlled generator 2 rotor angle δ 2 relative to δ 1 (δ 2 − δ 1 ) and the controlled generator 3 rotor angle δ 3 relative to δ 1 (δ 3 − δ 1 ) is obtainable in Figure 26 while the controlled speed of the three generators are displayed in Figure 27. These outcomes are the result of the NFC stabilizer that was placed in the system. Case 2 With NFC Controller: A comparative result between the system with uncontrolled, with FFA-PSS controlled and with the proposed NFC controlled was evaluated. The controlled generator 2 rotor angle δ 2 relative to δ 1 (δ 2 −δ 1 ), the controlled generator 3 rotor angle δ 3 relative to δ 1 (δ 3 −δ 1 ) are explain in Figures 28 and 29 while the controlled generator 2 rotor speed ω 2 relative to ω 1 (ω 2 − ω 1 ), the controlled generator 3 rotor speed ω 3 relative to ω 1 (ω 3 − ω 1 ) are explained in the order of Figures 30 and 31 respectively.     These design results were obtained after equipping the system with the proposed NFC stabilizer.
Case 3 With NFC Controller: After installing the NFC model in the system, a symmetrical three-phase fault for 100 milliseconds has been simulated and the results have been   obtained. Comparative results show the controlled generator 2 rotor angle δ 2 relative to δ 1 (δ 2 − δ 1 ), the controlled generator 3 rotor angle δ 3 relative to δ 1 (δ 3 − δ 1 ) are explain in Figures 32 and 33 respectively. The controlled generator 2 rotor speed ω 2 relative to ω 1 (ω 2 − ω 1 ) and the controlled generator 3 rotor speed ω 3 relative to ω 1 (ω 3 − ω 1 ) are explained in the order of Figures 34 and 35      and time to increase in seconds. When the NFC stabilizer was employed, the rotor speed G1 transient responsiveness was improved by 66.57 percent in terms of time to settle and 64.70 percent in terms of time to rise. In comparison to when the system is uncontrolled, this improvement is based on time to settle and time to rise. Because G1 was used as the reference machine, the rotor angle response of G1 is zero. Table 21 shows that the time to settle for rotor speed G2 using the NFC stabilizer was improved by 69.66 percent when compared to when the system is uncontrolled, while Table 22 shows that the time to settle for rotor speed G3 using the NFC stabilizer was improved by 75.70 percent when compared to when the system is uncontrolled. The results of the proposed model are compared with the results in the reference model [52] to show the effectiveness of the new approach. The reference model [52] examines the design of WSCC PSSs systems utilizing two-level fuzzy PSSs (TLFPSS) and two-level ANFIS PSSs (TLAFPSS). Table 23 compares the numerical results of the proposed model and reference model [52] of G2 and G3 in the damping of EMs in the WSCC test power system for case 1 in the damping of EMs. The reference model [52] has the same operational conditions as the proposal model, which were obtained in this case for comparison purposes. For that specific generator, the technique with lower values of time to settle provides strong stability qualities.
It can be shown from Table 23 that the proposed method minimizes the EM damping caused by the G2 and G3. In other words, it improves the time to settle for EMs generated by the generator 2 by 389 percent when compared to the uncontrolled state, 61.7 percent when compared to the TLFPSS reference model [52], and 51.9 percent when compared to the TLAFPSS reference model [52]. In addition, the suggested model saw a 55.9% and 53.4 percent reduction in settling time for EMs produced by generator 3 when compared to the TLFPSS reference model [52] and the TLAFPSS controlled reference model [52], respectively. On the other hand, the suggested models exhibited effective action on the electric network, placing the eigenvalues in better places than the uncontrolled and referenced models. The reduced settling time values ensured the suggested model's effectiveness in damping down the LFO and achieving improved stability over the reference model.

VI. WSCC TEST SYSTEM QUANTITATIVE PERFORMANCE EVALUATION COMPARISON OF PSS, IPFC, AND NFC DESIGN RESULTS FOR CASE 1
Considering the WSCC system, the effectiveness of the proposed technique in comparison with other approaches for WSCC test system, the quantitative EMs and damping ratio results based on the proposed NFC model are compared with

VII. SENSITIVITY ON THE APPLICATION OF THE PROPOSED NFC MODEL WITH THE FFA-PSSs AND MULTI-BAND PSSs
Conventional PSSs (CPSS) structures (IEEE PSS2B and IEEE PSS3B) are meant to provide the stabilizing signal by passing only a single frequency band. In this regard, IEEE Std. 421.5 [53] introduced a novel PSS structure called as a multiband PSS (MBPSS). This new MBPSS is unique in that it addresses the three distinct frequency bands for more effective dampening of various power system oscillation types [54], [55]. To establish the NFC stabilizer effects on the improvement of the system dynamic response and the relevance of the proposed FFA optimization method in achieving robustness, a reference model in [56] that studied different number of PSSs was considered. The reference model [56] considers a conventional multi-band PSSs (CMBPSS), a fractional-order (FO) multi-band PSSs (PSO-FO-MBPSS) and a Fractional-order lead-lag compensator-based MBPSS design using a hybrid dynamic GA-PSO method. For WSCC test system, the quantitative EMs and damping ratio results based on the proposed NFC model are compared with the FFA based conventional PSS (FFA-CPSS) design results and the results from the reference model [56]. Table 25 compares the proposed NFC model's EMs and damping ratio numerical results with the FFA-CPSS design results and the results of the reference model [56] for no change in loading circumstances case 1 in the damping of EMs in the WSCC test power system. For comparison purposes, the FFA-CPSS design operating points, the proposed NFC model and that of the reference model [56] have identical operating conditions. From the system eigenvalues and damping ratios of the mechanical mode in Table 25 for normal loading conditions, the proposed NFC model damping rate values where found 36.73% efficient when compare to the DGA-PSO-FO-MBPSS reference model [56] and 41.30% efficient compared to the PSO-FO-MBPSS model [56]. These values of the damping ratios are significantly improved by the proposed NFC model. It is also clear that the eigenvalues associated with the electromechanical modes have been shifted to the left of the s-plane with the proposed controller compared to the reference model [56] controllers.

VIII. CONCLUSION
In this study, research objectives one was obtained by designing a WSCC multi-machine PSSs system using Farmland Fertility Algorithm (FFA-PSSs controller) and its performance efficiency was compared to GA and PSO-based PSSs controllers. Research objectives two was obtained by adding an Interline Power Flow Controller (IPFC) FACTS device to the PSSs controller to improve the power system's oscillatory stability. The application of the FFA-optimized PSSs with IPFC was achieved in coordinated operation. PSSs optimal design and supplemental controller of power fluctuations for IPFC were conducted out on WSCC multi-machine test systems using a system linear model. Using time-domain simulations and quantitative analysis, the performance and efficiency of the proposed FFA-optimized PSSs with IPFC model was compared to the FFA-PSSs controller. From the simulations and quantitative analysis outcomes, it was found that the coordination of the FFA-optimized PSSs with the IPFC model was found superior than the FFA-PSSs controller in LFOs mitigation. However, in both PSSs design the rise in the computational and simulation costs was found unavoidable. This is a major drawback. To compensate and overcome these drawbacks, this paper proposed a Neuro-Fuzzy Controller (NFC) developed as a damping controller that can take the place of the two controllers. Quantitative analysis results from the WSCC test system simulation show that in terms of settling time G1 rotor speed respond, the proposed NFC model was found to be 480 percent efficient when compared to the uncontrolled model and 0 percent efficient when compared to the FFA-PSS and the FFA optimized PSS with IPFC controller. Similarly, the proposed NFC model was shown to be 390 percent efficient when compared to the uncontrolled model and 0 percent efficient when compared to the FFA-PSS and the FFA optimized PSS with IPFC controller, respectively, based on the settling time G2 rotor angle response. Furthermore, the proposed NFC model was found to be 216 percent efficient when compared to the uncontrolled model, 0 percent efficient when compared to the FFA-PSSs design technique, and 149 percent efficient when compared to the FFA optimized PSS with IPFC controller. Finally, the proposed NFC model was shown to be 0% efficient when compared to FFA-PSSs and FFA optimized PSS with IPFC controllers, but 394 percent efficient when compared to the uncontrolled model using G3 settling time for rotor speed data. The same goes to the time to settle for the rotor angle respond only the uncontrolled model was found efficient (130%) when NFC model was used with the two controllers 0% efficient. These quantitative simulation outcomes justifies the proposed controllers capacity in substituting the roles of the two damping controllers at the same time overcoming the computational and simulation cost involved when the system is design using the two damping controllers.