Enhancing Grid Stability through an Adaptive Genetic Optimization Framework for Power System Stabilizer Control

Enhancing Grid Stability through an Adaptive Genetic Optimization Framework for Power System Stabilizer Control

Anusiyaayodhi A

Department of Electrical and Electronics Engineering, Vikrant University, Gwalior, Madhyapradesh, India.

Dr. Brijendra Mishra

Department of Electrical and Electronics Engineering, Vikrant University, Gwalior, Madhyapradesh, India.

Abstract

Power system stabilizers (PSS) play a crucial role in damping low-frequency oscil-lations and maintaining dynamic stability in modern electrical grids. However, conventional PSS tuning methods often struggle to adapt to varying operating conditions and the increasing complexity introduced by renewable energy inte-gration. This paper presents an adaptive genetic optimization framework for PSS parameter tuning that enhances grid stability across diverse operating scenarios. The proposed approach employs a multi-objective genetic algorithm (GA) that simultaneously optimizes damping ratio, settling time, and overshoot char- acteristics while accounting for system nonlinearities and uncertainties. An adaptive mechanism continuously monitors grid conditions and triggers real-time parameter adjustment when significant deviations are detected, ensuring robust performance under changing load profiles and network configurations.

The framework incorporates a comprehensive fitness function that evaluates system responses to various disturbances, including three-phase faults, load variations, and generator outages. To assess the effectiveness of the proposed technique, a comprehensive evaluation is performed using MATLAB/Simulink-based simulations. Simulation studies conducted on test system demonstrate that the proposed adaptive GA-based PSS controller achieves superior damping performance compared to conventional PSS and fixed-parameter GA-tuned con-trollers, reducing settling times by up to 40% and improving damping ratios by 25-35% s.

The results validate the frameworks effectiveness in maintaining stability under

dynamic conditions, offering a promising solution for modern power systems facing unprecedented operational challenges.

‌Keywords: Power System Stabilizer (PSS), Adaptive Control, Genetic Algorithm (GA), Multi-Objective Optimization, Small-Signal Stability, Eigenvalue Analysis, Damping Enhancement, Synchronous Generator

1. ‌Introduction

   1. Background and Motivation

      Power systems are increasingly exposed to low-frequency oscillations arising from high loading, weak grid conditions, and the widespread penetration of renewable energy sources (RESs). These oscillations pose a significant t hreat t o s ystem stabil- ity, often degrading damping characteristics and risking inter-area instability. Power System Stabilizers (PSS) have traditionally been deployed to enhance the damping of electromechanical oscillations by modulating generator excitation. However, the effectiveness o f c onventional P SS t uning d iminishes u nder v arying o perating condi- tions, nonlinear system dynamics, and uncertainties introduced by renewable energy integration and changing network configurations [ 1, 2].

      Most utilities still rely on classical tuning methods such as phase compensation or fixed-parameter o ptimization, w hich a re d esigned a round a l imited n umber o f oper- ating points. As a consequence, these tuned PSS settings may become suboptimal or even destabilizing when subjected to disturbances, topology changes, or shifting generation patterns [3]. The need for adaptive and robust tuning methodologies is therefore more critical than ever. Recent studies have explored intelligent and evolu- tionary optimization techniques to improve PSS performance in complex, nonlinear, and time-varying environments [4, 5]. Among these, Genetic Algorithms (GAs) have emerged as a promising approach due to their global search ability, robustness against non-convexity, and suitability for multi-objective optimization.

      ‌Nevertheless, existing GA-based approaches typically rely on offline tuning and do not adapt in real time to system variations. Their lack of responsiveness to dynamic changes in grid conditions restricts their effectiveness in modern power networks char- acterized by rapid fluctuations a nd w ide o perational u ncertainty [ 6]. T his motivates the development of an adaptive optimization mechanism that continuously evaluates system performance and updates controller parameters to ensure consistent damping behavior across operating scenarios.

   2. Literature Review

      A wide range of methodologies have been explored to improve PSS performance, including fuzzy logic controllers [7], model predictive controllers [8], hybrid neuro- fuzzy techniques [9], and heuristic optimization-based tuning [10]. While these methods

      demonstrate improved performance over classical designs, many suffer from compu- tational complexity, slow convergence, or lack of real-time adaptability. Evolutionary algorithms such as Particle Swarm Optimization (PSO), Differential Evolution (DE), Ant Colony Optimization (ACO), and Genetic Algorithms (GA) have shown substan- tial success in optimizing PSS parameters under nonlinear and uncertain environments [11, 12].

      Recent advancements propose multi-objective optimization frameworks that con- sider time-domain indices, frequency-domain damping ratios, and robustness against load variations [13]. However, these methods generally remain offline, limiting their ability to respond to disturbances or continuously changing grid behavior. Few studies attempt adaptive or online evolutionary tuning, and those that do often face challenges with computational burden, convergence reliability, or stability guarantees [14].

      ‌Given these limitations, a structured adaptive GA-based tuning framework that integrates real-time monitoring, multi-objective fitness evaluation, and robust search operators is essential for modernizing PSS control. Such a framework would bridge the gap between offline optimization and online adaptability while retaining algorithmic simplicity and computational efficiency.

   3. Key Contributions

      This work proposes an Adaptive Genetic Optimization Framework for enhancing the damping performance of Power System Stabilizers in multi-area power networks. The main contributions are summarized as follows:

      1. A novel adaptive genetic optimization architecture is developed for real-time PSS tuning. The proposed method enables continuous parameter adjustment based on operating-point deviations, ensuring improved damping under dynamic grid conditions.

      2. A multi-objective GA formulation is introduced for simultaneously optimizing damping ratio, overshoot, settling time, and robustness to uncertainties. The fitness function integrates both time-domain and frequency-domain performance metrics, making the optimization comprehensive and resilient.

      3. A disturbance-sensitive adaptation mechanism is incorporated that triggers GA re- optimization during significant deviations such as load changes, generator outages, or inter-area oscillatory events.

      4. Extensive simulations on a two-area benchmark power system validate the effec- tiveness of the proposed approach. Comparative studies show that the adaptive GA-PSS significantly enhances oscillation damping and reduces settling times compared to conventional fixed-parameter PSS and offline GA-tuned controllers. The remainder of this paper is oranized as follows: Section II presents the mathe-

      matical model of the two-area test system and PSS structure. Section III introduces the

      proposed adaptive genetic optimization framework. Section IV discusses stability and performance analysis. Section V provides simulation results, followed by concluding remarks in Section VI.

2. ‌System Modeling and Problem Formulation‌

   1. Power System Dynamic Model

      The synchronous generator is modeled using the classical nonlinear electromechanical swing dynamics. The rotor angle () and rotor speed () relative to the synchronous reference (s) evolve according to the well-known swing equations:

      where (): generator electrical rotor angle (rad), (): mechanical rotor speed (rad/s), (s): synchronous reference speed (rad/s), (H): inertia constant (s), (Tm): mechanical input torque (p.u.), (Te): electromagnetic torque (p.u.), (D): mechanical damping coefficient (p.u.).

      The electromagnetic torque is expressed using the standard Park-transformed fluxcurrent interaction:

      Te = diq qid (3)

      where (d, q): (dq)-axis stator flux linkages (p.u.), (id, iq): (dq)-axis stator currents (p.u.).

      The generator electrical dynamics follow the two-axis representation:

      1. PSS F

      where (VR): regulator output (p.u.), (TA): amplifier time constant (s), (KA): ampli- fier gain, (Vref ): reference voltage (p.u.), (Vt): generator terminal voltage magnitude

      (p.u.), (VP SS): supplementary PSS stabilizing signal (p.u.), (VF ): stabilizing feedback signal from exciter feedback loop (p.u.).

      The exciter field voltage dynamics are:

      dEfd =

      where (Efd): exciter field voltage (p.u.), (KE): exciter gain, (TE): exciter time

      constant (s).

      The exciter stabilizing feedback loop is modeled by:

      ‌dRF dt

      where (RF ): feedback compensator state (p.u.), (KF , TF ): stabilizer gain and time

      constant.

      ‌where (Ra): stator resistance (p.u.), (vd, vq): stator terminal voltages in (dq) frame (p.u.), (Rfd): field winding resistance (p.u.), (fd): field flux linkage (p.u.), (ifd): field current (p.u.), (vfd): field voltage applied through the excitation system (p.u.).

      These differential relationships collectively govern the synchronous generators electromechanical and electromagnetic interactions.

      1. Excitation System Model

         The IEEE Type-1 Automatic Voltage Regulator (AVR) and exciter system is modeled using a controlled amplifierexciterfeedback loop. The amplifier output (VR) follows:

      1. 2.1.3 Network Model and Load Representation

         The power network is represented using the nodal admittance formulation:

         where (Ii): injected current at bus i, (Yij): element of the network admittance matrix, (Vj): complex voltage at bus j.

         Real and reactive power flow at bus i are expressed as:

   2. Power System Stabilizer Structure

      1. LeadLag PSS Configuration

         The PSS provides supplementary damping through a washout filter and cascaded leadlag compensators:

         The phase compensator network contributes:

      2. ‌2.2.2 Signal Processing and Output Limits‌

         ‌To prevent AVR saturation and instability, the PSS output is limited as:

         VPSS,min VPSS VPSS,max (18)

   3. Linearized System Model for Stability Analysis

      1. State-Space Representation

         The nonlinear model is linearized around an equilibrium operating point to obtain:

         x = Ax + Bu (19)

         y = Cx + Du (20)

         ‌with state vector:

         x = [, , d, q, Efd, VR, RF , xP SS]T

         Each state corresponds to the small-signal deviation of a physical quantity.

      2. Eigenvalue Characterization

         The system eigenvalues are computed from:

         det(I A) = 0 The oscillatory modes take the form:

         with oscillation frequency:

         ‌A minimum stability requirement enforces:

   4. Problem Formulation

      1. Control Objective

         The PSS parameter set is defined as:

      2. ‌2.4.2 Multi-Objective Optimization

         with bounds:

         KPSS,min KPSS KPSS,max (28)

         Ti,min Ti Ti,max, i = 1, . . . , 4 Minimum damping constraint:

3. Proposed Adaptive Genetic Optimization Framework

   ‌This section presents the complete design methodology of the proposed adaptive PSS tuning framework, which integrates offline multi-objective genetic optimization with an online condition-monitoring mechanism for parameter adaptation. The formulation explicitly links PSS parameterization with the closed-loop linearized model, enabling systematic eigenvalue shaping and time-domain enhancement under varying operating conditions.

   1. PSS Parameterization

      The optimization vector collects all stabilizer coefficients as

      which fully characterizes the washoutleadlag PSS structure.

      For a given candidate , the linearized synchronous generatorAVRPSS model introduced in Section II is augmented to incorporate the stabilizer dynamics. The resulting closed-loop matrix is expressed as

      This formulation explicitly reflects the influence of KP SS and the compensator time constants on the small-signal behavior, ensuring that each candidate solution can be directly evaluated through modal analysis.

   2. ‌Multi-Objective Fitness Formulation‌

      The tuning objective seeks to enhance damping, transient speed, oscillation suppres- sion, and robustness margins simultaneously. To capture all relevant performance indices, a unified multi-objective structure is adopted.

      1. Damping Ratio Objective

         The eigenvalues of the closed-loop system are written as

         Modes with inadequate damping degrade electromechanical stability; therefore, a penaty function is introduced:

      2. 3.2.2 Settling Time and Overshoot Objectives

      3. ‌Eigenvalue Stability Margin

      4. Combined Fitness Function

         ‌F () = w1J + w2Jts + w3JOS + w4J (41a)

         F () = w1J + w2Jts + w3JOS + w4J

   3. 3.3 Genetic Algorithm Operations

      Selection probability:

      Arithmetic crossover:

   4. Adaptive Monitoring Mechanism

      3.5 Parameter Update and Deployment

4. ‌Results and Analysis

   1. System Under Study

      The system considered in this study is a single-machine infinite-bus ( SMIB) configu- ration equipped with a conventional IEEE-type exciter and a power system stabilizer (PSS), as illustrated in Figure 1. The generator is modeled using the classical 4th-order synchronous machine model, incorporating both electromechanical swing dynamics and field winding dynamics to capture low-frequency oscillatory behavior.

      The stabilizer input is derived from speed deviation, which is processed through a washout stage and a dual-stage leadlag compensator. The proposed adaptive Genetic Algorithm (GA)-based PSS continuously monitors system operating condi- tions and adjusts key stabilizer parametersgain, phase-compensation time constants, and washout parametersto maximize damping performance.

      The infinite bus is represented using a Thevenin equivalent, while the transmission system is modeled using standard -line parameters to ensure accurate representation of electrical interactions. Disturbances such as three-phase faults, load perturbations, and parametric variations are applied to test the robustness of the stabilizer. This SMIB configuration remains the most widely accepted benchmark for oscillation damp- ing performance evaluation, providing clear visibility into generator dynamics and control interactions.

      ‌Fig. 1 System Under Study

   2. Output Power Response

      ‌Figure 2 illustrates the generator electromagnetic output power response following a disturbance. Without adaptive tuning, the system exhibits low-frequency oscillations characterized by slow damping and elevated oscillatory magnitude. With the proposed adaptive GA-based PSS, the oscillations decay significantly faster, demonstrating the stabilizers ability to inject supplementary damping torque in phase with the speed deviation. The GA-optimized leadlag structure provides accurate phase compensation across the oscillatory frequency range, thereby increasing the effective damping ratio of the dominant electromechanical mode. Consequently, the system reaches steady-state output power more rapidly, with minimized overshoot and reduced transient energy exchange between mechanical and electrical subsystems.

   3. Rotor Speed Dynamics

      Figure 3 shows the rotor speed dynamics, which represent the generators iner- tial response. Under conventional PSS tuning, the rotor speed displays oscillatory swings driven by the mismatch between mechanical input and electrical output dur- ing disturbance recovery. The adaptive GA-based PSS significantly e nhances rotor speed stabilization by dynamically updating stabilizer parameters according to pre- vailing system conditions. This prevents parameter drift under varying load levels and transmission network changes. The improved damping performance ensures that

      Fig. 2 Output power response of the system

      Fig. 3 Rotor Speed

      ‌rotor speed quickly converges to synchronous value, suppressing prolonged oscilla- tory motion and preventing rotor-angle divergence. This confirms that the proposed method strengthens the systems synchronous stability margin.

   4. Speed Deviation Performance

The speed deviation () response presented in Figure 4 further validates the con- trollers ability to suppress low-frequency electromechanical oscillations. Under the proposed stabilizer, oscillations exhibit a steep decay profile, reflecting significantly enhanced modal damping. The adaptive mechanism ensures that the PSS gain and compensator time constants remain optimal even when system nonlinearities, loading

Fig. 4 speed deviation Response to a time change

Fig. 5 Stator voltage

‌conditions, or operating points shift. This real-time optimization capability is particu- larly beneficial under stressed grid conditions, where conventional fixed-parameter PSS typically loses effectiveness. A s a r esult, t he s peed d eviation s ettles w ithin a shorter time interval, demonstrating improved transient stability performance and enhanced resilience against fault-induced disturbances.

4.5 Stator Terminal Voltage Response

Figure 5 presents the stator terminal voltage (Vt) behavior following a disturbance. Voltage oscillations represent the interaction between the excitation system and the generators internal reactances. Traditional PSS designs often provide limited damping

to voltage-related oscillations due to fixed parameterization. The proposed GA-based stabilizer improves voltage regulation by enhancing damping of both electrical and electromechanical modes. The voltage reaches steady-state more rapidly, with reduced oscillatory amplitude, demonstrating effective c oordination b etween t he P SS and the automatic voltage regulator (AVR). This improvement contributes to superior dynamic voltage stability, preventing undesirable interactions such as exciter-induced oscillations or control-loop interference common in high-gain excitation systems.

Conclusion

This paper presented an adaptive genetic algorithm-based framework for power system stabilizer (PSS) parameter tuning, aimed at enhancing damping of low- frequency oscillations and maintaining dynamic stability in modern power grids. The proposed approach effectively c ombines m ulti-objective o ptimization w ith real-time adaptability, enabling the PSS to respond to varying operating conditions, network uncertainties, and disturbances such as faults and load variations. Simulation results on the test system demonstrated that the adaptive GA-based PSS significantly out- performs conventional and fixed-parameter G A-tuned c ontrollers, a chieving faster settling times, higher damping ratios, and improved overall system stability. These findings validate the effectiveness and robustness of the proposed method, highlighting its potential as a practcal solution for modern power systems integrating renewable energy sources and facing increasingly complex operational challenges.

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Declarations

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

The authors confirm that the data supporting the findings of this study are available within the article and raw data that support the findings of this study are available from the corresponding author upon reasonable request.