Stability Of Multi-machine Power System Research Articles

Enhancing Transient Stability in Multi-Machine Power Systems through a Model-Free Fractional-Order Excitation Stabilizer

Enhancing Transient Stability in Multi-Machine Power Systems through a Model-Free Fractional-Order Excitation Stabilizer

On the optimal multi-objective design of fractional order PID controller with antlion optimization

This study introduces an optimal multi-objective design approach for a robust multimachine Fractional Order PID Controller (FOPID) using the Antlion algorithm. The research focuses on the need for effective stabilizers in multimachine power systems by employing traditional speed-based lead-lag FOPID controllers. The study formulates a multi-objective problem, optimizing the damping factor and damping ratio of lightly damped electromechanical modes to maximize a composite set of objective functions, tackled through the Antlion algorithm. Stability analysis of Single-Machine Infinite-Bus (SMIB) and multimachine power systems is conducted based on rotor speed and power deviation minimization in the time domain response, along with damping ratio and eigenvalue analysis. The proposed approach is implemented and tested on three IEEE test cases, showcasing significant improvements in stability through the reduction of maximum overshoot (Mp) and settling time (ts) of speed deviation. Comparative analysis with other optimization-based FOPID controllers underscores the superiority of the proposed approach in enhancing stability in multimachine power systems. The main impact of this research lies in its contribution to the advancement of stability enhancement techniques in multimachine power systems, offering a systematic framework for optimal FOPID controller design and empowering decision-making processes in power engineering.

Robust multi-machine power system stabilizer design using bio-inspired optimization techniques and their comparison

This paper reports a comparative study among four bio-inspired meta-heuristic techniques i.e. Sooty-Tern Optimization (STO), Grey Wolf Optimization (GWO), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) to tune the robust Power System Stabilizer (PSS) parameters of the multi-machine power system. These approaches are successfully tested on two bench-mark systems: sixteen-machine, sixty-eight-bus New England Extended Power Grid (NEEPG) and three-machine, nine-bus Western System Coordinating Council (WSCC). The efficacy of planned PSS via STO and GWO is validated by extensive non-linear simulations, eigenvalue analysis, and performance indices for numerous operating conditions under decisive perturbations, and outcomes are matched with those of GA and PSO techniques. In addition, the robustness is also tested for these algorithms. The results indicate that the PSS design using STO and GWO improves the small-signal stability and damping performance for mitigating inter-area and local area modes of low-frequency oscillations compared to GA and PSO.

Artificial Eco-System-Based Optimization Algorithm for Optimal Design of Single-Machine Infinite Bus and Multi-Machine Power System Stabilizers

Artificial Eco-System-Based Optimization Algorithm for Optimal Design of Single-Machine Infinite Bus and Multi-Machine Power System Stabilizers

A New Self-Tuning Deep Neuro-Sliding Mode Control for Multi-Machine Power System Stabilizer

In order to increase the accuracy and improve the performance of the power system stabilizer (PSS) controller compared to the methods presented in other studies, this paper presents a new method for tuning sliding mode control (SMC) parameters for a PSS using a deep neural network. This controller requires fast switching which can create unwanted signals. To solve this problem, a boundary layer is used. First, the equations of a multi-machine power system are converted into the standard form of sliding mode control, and then the sliding surfaces are determined with three unknown parameters. Calculating and determining the optimal values (at any moment) for these parameters are fundamental challenges. A deep neural network can overcome this challenge and adjust the control system regularly. In the simulation, a power system with 4 machines and 11 buses is implemented and both phase-to-ground and three-phase errors are applied. The simulation results clearly show the good performance of the proposed method and especially the importance of the deep neural network in the SMC structure compared to other methods.

Implementing Optimization Techniques in PSS Design for Multi-Machine Smart Power Systems: A Comparative Study

This study performed a comparative analysis of five new meta-heuristic algorithms specifically adopted based on two general classifications; namely, nature-inspired, which includes artificial eco-system optimization (AEO), African vulture optimization algorithm (AVOA), gorilla troop optimization (GTO), and non-nature-inspired or based on mathematical and physics concepts, which includes gradient-based optimization (GBO) and Runge Kutta optimization (RUN) for optimal tuning of multi-machine power system stabilizers (PSSs). To achieve this aim, the algorithms were applied in the PSS design for a multi-machine smart power system. The PSS design was formulated as an optimization problem, and the eigenvalue-based objective function was adopted to improve the damping of electromechanical modes. The expressed objective function helped to determine the stabilizer parameters and enhanced the dynamic performance of the multi-machine power system. The performance of the algorithms in the PSS’s design was evaluated using the Western System Coordinating Council (WSCC) multi-machine power test system. The results obtained were compared with each other. When compared to nature-inspired algorithms (AEO, AVOA, and GTO), non-nature-inspired algorithms (GBO and RUN) reduced low-frequency oscillations faster by improving the damping of electromechanical modes and providing a better convergence ratio and statistical performance.

Coherence indicators of generators for express assessment of electric power system transient stability

A brief overview of the generator coherence indicators is presented, the areas and limitations of their applicability are indicated. The application of the area method for the rapid assessment of the transient stability of complex multi-machine electric power system based on the features of the dynamics of the system behavior, determined by the heterogeneous structure of the electrical network, is considered. A distinctive feature of the proposed approach is the use of the characteristics of the heterogeneity of the power system structure, which determine the presence of weak links (or cut-sets) of the electrical network, which are critical from the point of view of a possible violation of the system stability.

Application of Improved Quasi-Affine Transformation Evolutionary Algorithm in Power System Stabilizer Optimization

This paper proposes a parameter coordination optimization design of a power system stabilizer (PSS) based on an improved quasi-affine transformation evolutionary (QUATRE) algorithm to suppress low-frequency oscillation and improve the dynamic stability of power systems. To begin, the simulated annealing (SA) algorithm randomly updates the globally optimal solution of each QUATRE iteration and matches the inferior solution with a certain probability to escape the local extreme point. This new algorithm is first applied to the power system. Since the damping ratio is one of the criteria with which to measure the dynamic stability of the power system, this paper sets the objective function according to the principle of maximization of the damping coefficient of the electromechanical mode, and uses SA-QUATRE to search a group of global optimal PSS parameter combinations to improve the safety factor of the system as much as possible. Finally, the method’s rationality and validity were validated by applying it to the simulation examples of the IEEE 4-machine 2-area system with different operation states. The comparison with the traditional optimization algorithm shows that the proposed method has more advantages for multi-machine PSS parameter coordination optimization, can restrain the low-frequency oscillation of the power system more effectively and can enhance the system’s stability.

Implementation of Modified Multi-Objective Particle Swarm Optimization to multi-machine power system stability

This paper addresses a coordinated wind turbine equipped with a doubly fed induction generator, photovoltaic plant, and a fractional lead-lag stabilizer to enhance the low-frequency oscillation (LFO) in response to their effects on the power system under load conditions. To achieve better stability in the power system, the DFIG wind turbine and PV plant are equipped with a power oscillation damper (POD) in a practical form by single-input signal output. Although power system stabilizers (PSSs) are the first choice offered for multimachine power system stability, they cannot guarantee power system stability with different types of power plants and their interconnections. To get the high-speed response and the least steady-state error, the fractional-order lead-lag stabilizer is suggested. To save the initial price of equipping all generators with the stabilizer, only the best locations are selected using a probabilistic method formulated in the frequency domain. The optimal tuning of FL-L and POD variables is formulated by the optimization problem, and the developed version of particle swarm optimization is used to solve it. Finally, the suggested coordinated controller is implemented in the MATLAB tool. Moreover, the suggested controller is compared to other available controllers by several indices. The simulation results show that the proposed controller can provide acceptable performance in low frequency oscillation in large scale power systems. According to the simulation results, the damping ratio was modified from 0.1343 to 0.5773. It leads to a reduction in the settlement time from 3.65 s to 2.14 s. Also, the proposed modified optimization algorithm makes a faster and better global and local search compared to other optimization algorithms.

Control and modelling of multi-machine power system stabilizer with FACTS

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Control of PV Systems for Multimachine Power System Stability Improvement

The goal of achieving decarbonized operation of power systems in response to climate change has led to an increase in the number of sources connected to electrical grids through inverters, of which photovoltaic systems are an example. The operating characteristics of these systems in steady-state or transient operation are different from those of synchronous machines, giving rise to issues related to power system stability. The vast majority of grid codes stipulate that fault ride-through operating requirements should be enabled during severe contingencies in the transmission network, prioritizing delivery of reactive power to the power system to support voltage stability. However, this control action may contribute to rapid collapse of the system voltage under adverse operating conditions, such as when the critical voltage in the power vs. voltage curve is near the reliable voltage operating bound. Supporting power system stability under these circumstances represents a new challenge for inverter control schemes. This paper adapts a recently published fault ride-through control scheme for PV inverters for use in a multimachine power system and shows that the scheme can successfully maintain transient and voltage stability even under adverse voltage operating conditions.

Dynamic stability of wind farm multi-machine power system

Since it is difficult to store electrical energy, production, and consumption must be in equilibrium under constant voltage and frequency. The producers, the receivers, and the electrical networks that connect them, have mechanical and electrical inertias which disturb this balance. Faced with a variation in power, the electrical system, after oscillations, returns to a stable state. In some cases, the oscillatory regime may diverge. Studies are being carried out to remedy this problem and ensure the stability of the electricity network. This manuscript focuses on FACTS regulation which helps electrical systems, subjected to strong disturbances, to maintain their stability. Magnetic Energy Storage Superconductor (SMES) contains a short-circuited superconducting coil on itself, which injects or absorbs active and reactive power into the system, thereby improving the stability of electrical systems.

A coordinated strategy for multi-machine power system stability

Owing to the fast growth of the energy demand, the current power system may reach the marginal operating design resulting in unfavourable frequency/voltages conditions, the timeframe of stability and unexpected faults. Therefore, it is necessary to use all capacity without any additional development costs and having a secure and safe system. Hereby, this study addresses a novel coordination strategy for improving low-frequency oscillations in multi-machine models under various operating conditions. To achieve this goal, the proposed solution is divided into three main parts, the first part presents eigenvalues and time-domain analyzes to extract the unstable modes for a nonlinear model of multi-machine to capture a real-world problem. The second part proposes two controllers based on fuzzy theory and thyristor controlled series compensator (TCSC) with power oscillation damper (POD) structure to reach considerable damping of low-frequency oscillations. Since an uncoordinated design between two controllers in the power system aggravated instability, therefore, the last part proposes a modified virus colony search (VCS) to optimally adjust the decision variables with two conflicting objectives based on time and frequency domains. To demonstrate the proposed coordinated strategy, the well-known two-area and four-machine test system have been selected and the obtained results are compared in several loading conditions such as ±20 load changing, with other available controllers through several analysing indices. According to numerical results, the proposed design can improve the statical indices such as integral of time multiplied absolute value of the error (ITAE) and figure of demerit (FD) about 12 and 11%, respectively. Also, the eigenvalues can be collected between the damping ratio 0.2 and real part -1.0.

Local Search-based Non-dominated Sorting Genetic Algorithm for Optimal Design of Multimachine Power System Stabilizers

This study presents a metaheuristic method for the optimum design of multimachine Power System Stabilizers (PSSs). In the proposed method, referred to as Local Search-based Non-dominated Sorting Genetic Algorithm (LSNSGA), a local search mechanism is incorporated at the end of the second version of the non-dominated sorting genetic algorithm in order to improve its convergence rate and avoid the convergence to local optima. The parameters of PSSs are tuned using LSNSGA over a wide range of operating conditions, in order to provide the best damping of critical electromechanical oscillations. Eigenvalue-based objective functions are employed in the PSS design process. Simulation results based on eigenvalue analysis and nonlinear time-domain simulation proved that the proposed controller provided competitive results compared to other metaheuristic techniques.

An intelligent Hybrid Wind–PV farm as a static compensator for overall stability and control of multimachine power system

The paper demonstrates the potential of a hybrid Wind–PV farm as STATCOM (Static Synchronous Compensator) for damping and control of overall chaotic oscillations in a two-area power system. Kundur’s modified system associated with a hybrid Wind–PV farm is simulated in MATLAB to demonstrate the detailed performance assessment of the hybrid farm. A unique controller is deployed to regulate the AC and DC currents of the STATCOM using two PI controllers. A swarm-based hybrid metaheuristic optimizer PSO-BFOA optimally tunes and controls the PI controller parameters. The system is compensated to an optimum level of 85% and exposed to a 3-phase fault. Zero dampings are accompanied by additional disturbances of a 20% change in electric torque and the reference voltage. The disturbances are made to model the worst conditions to examine the rigorous performance of the hybrid Wind–PV​ farm in alleviating the overall chaotic oscillations. The simulation results for the performance assessment in different cases, i.e., without control, with Wind-STATCOM, with PV-STATCOM, and with the hybrid Wind–PV-STATCOM, reveal the potential of the hybrid Wind–PV Farm as STATCOM in alleviating the overall chaotic oscillations.

A non‐linear adaptive excitation control scheme for feedback linearized synchronous generations in multimachine power systems

A new adaptive scheme is proposed in this paper to design excitation controllers for feedback linearized models of synchronous generators in multimachine power systems in order to ensure the stability during large disturbances. The proposed scheme uses speed deviations of synchronous generators, readily available measured physical properties of multimachine power systems, to make all generators within a power network as partially linearized as well as to provide more damping. An adaptive scheme is then used to estimate all unknown parameters which appear in the partial feedback linearizing excitation controllers in order to avoid parameter sensitivities of existing feedback linearization techniques. The overall stability of multimachine power systems is ensured through the excitation control and parameter adaptation laws. The Lyapunov stability theory is used to theoretically analyse the stability of multimachine power systems with the proposed scheme. Simulation studies are presented to evaluate the performance of the proposed excitation control scheme for two different test systems by different operating conditions including short‐circuit faults on key locations along with variations in parameters for a large duration. Furthermore, comparative results are presented to highlight the superiority of the proposed adaptive partial feedback linearizing excitation control scheme over an existing partial feedback linearizing excitation controllers.

Genetic-TLBO Algorithm for Power System Stabilizer

Background: A large number of nature-based optimization methods have been proposed to use as efficient tools in scientific studies. Genetic Algorithm (GA), which operates based on human genetical evolution, has been an outstanding mostly used solver in a wide range of applications. This algorithm reflects the process of natural selection where the fittest individuals are selected for reproduction in order to produce offspring of the next generation. Initialization, selection, crossover, and mutation are the main parts of the GA population-based method which enables GA to have a prominent explorative feature. On the other hand, the Teaching Learning Based Optimization algorithm (TLBO) is of great performance during searching for the optimum solution among individuals. Therefore, it is expected that the combination of both algorithms in a certain logical way improves the optimization time. Objective: The study intends to determine ways of improving performance of the TLBO algorithm to solve a complex non-linear problem. Power system studies are one of the most complex problems for analysis. Therefore, a powerful heuristic optimization procedure would have a valuable contribution in solving such problems. In addition, the proposed heuristic algorithm will help scientists to apply the technique to their problems. Materials and Methods: According to the aforementioned explanation, a new efficient optimization approach is proposed which optimizes the parameters of multi-machine power system stabilizers (PSSs). The TLBO algorithm includes two different stages in its main structure, which are aptly called teacher and student stages. The student stage of TLBO is replaced by the genetic algorithm in order to improve the explorative feature of the main TLBO. The PSS parameters are obtained for four PSSs which are connected to four generators. Results: The performance of the proposed stabilizer is compared with other formerly designed stabilizers reported in the literature consisting of multi-band PSSs for two areas four-machine power system. Simulation results demonstrate the effectiveness and robustness of the proposed PSS in damping local and inter-area oscillation modes under various disturbances and confirm its superiority in comparison with the other types of PSSs. Conclusion: : A search heuristic method like the genetic algorithm can dramatically improve the performance of meta-heuristic optimization technique. In actuality, the TLBO as a meta-heuristic optimization technique suffers from a direct search of random solutions in its primary stage. Then, the TLBO relinquishes some parts of search space which may restrict the algorithm to find absolute maximums or minimums. In this condition, the GA with a great ability in searching the whole search space effectively improves the TLBO. According to the obtained results, the proposed algorithm, named Genetic-TLBO, obviates the conventional TLBO flaws successfully.

Adaptive Sliding Mode Control for Multi-machine Power Systems under Normal and Faulted Conditions

This paper proposes a new adaptive sliding mode (ASM) decentralized excitation controller to improve the stability of multi-machine power systems under different perturbations such as system’ parametric and structural uncertainties. The stability of the closed-loop system is proved by Lyapunov stability theory. The proposed controller is evaluated through simulation on the standard IEEE 33-bus-bar power system which contains 6 synchronous machines and a HVDC-link. The simulation results indicate good robustness and satisfactory performance of the proposed controller. Moreover, in this paper, using the space-phasor based sequence networks method, a procedure for the dynamic analysis of modern power systems under the transient asymmetrical faults is presented. The method considers the complete dynamics of the synchronous machines and the HVDC-link and provides the possibility of taking into account the sequence networks dynamics.

Fixed-Time Fractional-Order Sliding Mode Controller for Multimachine Power Systems

This paper proposes a fractional-order sliding mode controller (FOSMC) for fixed-time stability of multimachine power systems. Fractional calculus has been applied in sliding mode control (SMC) to design FOSMC which can better suppress the chattering phenomenon than the traditional integer-order SMC. Hence, a FOSMC is proposed to regulate the excitation of synchronous generators to improve the transient stability of the power system. In addition, the FOSMC can maintain the multimachine power systems stabilization in an upper bound and measurable convergence time independent of the initial operating conditions of the power system. The Lyapunov function is implemented to demonstrate the stability of multimachine power systems under the FOSMC, and the upper bound convergence time of the power system is generally estimated. The New England 10-machine 39-bus power system is taken into simulation to test the effectiveness and superior performances of the FOSMC than the existing control methods under different operating conditions. Meanwhile, the FOSMC with different orders are presented to verify that the FOSMC can better restrain the chattering phenomenon than traditional integer-order SMC. Simulation results show that the FOSMC can effectively reduce the chattering phenomenon and ensure the power system stabilization in an upper bound time, thus enhancing the dynamic performances of the power system.

Application of Neuro-Fuzzy Controller to Replace SMIB and Interconnected Multi-Machine Power System Stabilizers

In this research, an effective application and performance assessment of the Neuro-Fuzzy Controller (NFC) damping controller is designed to replace a single machine infinite bus (SMIB) power system stabilizer (PSS), and coordinated multi PSSs in large interconnected power systems are presented. The limitation of the conventional PSSs on SMIB and interconnected multi-machine test power systems are exposed and disclosed by the proposed NFC stabilizer. The NFC is a nonlinear robust controller which does not require a mathematical model of the test power system to be controlled, unlike the conventional PSSs’ damping controller. The Proposed NFC is designed to improve the stability of SMIB, an interconnected IEEE 3-machine, 9-bus power system, and an interconnected two-area 10-machine system of 39-bus New England IEEE test power system under multiple operating conditions. The proposed NFC damping controller performance is compared with the conventional PSS damping controller to confirm the capability of the proposed stabilizer and realize an improved system stability enhancement. The conventional PSSs’ design problem is transformed into an optimization problem where an eigenvalue-based objective function is developed and applied to design the SMIB-PSS and the interconnected multi-machine PSSs. The time-domain phasor simulation was done in the SIMULINK domain, and the simulation results show that the transient responses of the system rise time, settling time, peak time, and peak magnitude were all impressively improved by an acceptable amount for all the test system with the proposed NFC stabilizer. Thus, the NFC was able to effectively control the LFOs and produce an enhanced performance compared to the conventional PSS damping controller. Similarly, the result validates the effectiveness of the proposed NFC damping controller for LFO control, which demonstrates more robustness and efficiency than the classical PSS damping controller. Therefore, the application and performance of the NFC has appeared as a promising method and can be considered as a remarkable method for the optimal design damping stabilizer for small and large power systems.