Transient Stability Studies Research Articles

Computing the Network’s Equilibrium Point at the Fault Clearing Instant in Transient Stability Studies

This paper proposes an approach for computing the network’s equilibrium point related to the fault clearing time in transient stability studies. The computation of this point is not a trivial task, particularly when the algebraic network’s equations are expressed in the power balance form. A natural attempt to solve this problem is using Newton’s method. However, convergence issues are found because of the lack of a general strategy for initializing nodal voltages at the clearing time. This problem has not been widely discussed in the existing literature and, therefore, is comprehensively analyzed in this paper. Furthermore, the paper proposes the use of a network’s model based on current injections and an extended admittance matrix to overcome the problem. This model is efficiently solved via the fixed-point iteration method, which involves factorization of the extended admittance matrix into the product of a lower triangular matrix [L] and an upper triangular matrix [U]. This solution executes a just once and only forward–backward substitution during the iterative solution process. Case studies clearly demonstrate the proposal’s effectiveness in computing the equilibrium point in operating conditions where Newton’s method fails to converge.

The effects of various distributed generating types on the smart grid have been demonstrated using transient stability study and steady state voltage analysis

Renewable energy and smart grid technologies are crucial in the modern era due to climate change and the need for secure energy sources. To address concerns regarding energy security, efficiency and aging energy infrastructure, it is necessary to move away from centralized power generation and embrace decentralized distributed generation and smart grid technologies. This transformation will meet the increasing demand for electricity, improve the quality of service, and reduce pollution. However, there are technical challenges to overcome, such as maintaining system stability when incorporating distributed generation into the smart grid. This research focuses on evaluating the impact of distributed generation on the smart grid, especially the system stability after integrating distributed generation. System stability was evaluated and confirmed using Dig-SILENT Power Factory V 13.2 software, which simulates connection issues and failures.

A Study of Multi-objective Transient Stability Constrained Optimal Power Flow based on Reduced-Space Interior Point Method

A Study of Multi-objective Transient Stability Constrained Optimal Power Flow based on Reduced-Space Interior Point Method

A new single modulating and single carrier signal based control technique for symmetrical and asymmetrical multilevel inverter topology

Abstract In literature, to generate gate pulses for any inverter topology, most of the authors are using a single modulating signal with (level-1) or (level-1)/2 carrier-based pulse width modulation (PWM) techniques and single carrier (SC) signal with (level-1)/2 modulating signal based PWM techniques. Then, while going to higher-level inverter topologies, the complexity of the PWM control approach in both cases can increase. To reduce the control complexity, few authors have reported a single modulating signal with single carrier-based PWM techniques. However, these techniques need more mathematical equations and if-else loops. This article proposes a new single-modulating and single-carrier signal-based generalized PWM control approach using floor function (FF). This technique has been verified by considering one of the single-phase conventional symmetrical and asymmetrical multilevel inverter (MLI) topologies. Generally, FF rounds the value to the nearest integer towards the negative infinity. The proposed PWM control implementation process is very simple and suitable for both high switching frequency (HSF) and low switching frequency (LSF) operations. The proposed control technique (PCT) has been experimentally verified with different steady-state and transient-state studies of results under standalone operation.

Deep Learning-Based Equivalent Modelling of Hybrid RES Plant for Efficient, Repetitive Power System Transient Stability Studies

The paper presents the methodology for dynamic equivalent modelling of hybrid renewable energy source (HRES) plant with the aim of obtaining highly accurate time domain HRES plant power responses at any time during the year. The focus is on equivalent modelling for transient stability studies. Historical HRES plant production dataset and transmission network short-circuit fault statistical data, along with unsupervised data mining and deep learning techniques, represent a basis of the modelling procedure. Dynamic equivalent model (DEM) is developed in the form of deep Long Short Term Memory network. Real and imaginary parts of voltage at the point of common coupling (PCC) are model inputs, while real and reactive power at the PCC are model outputs. The paper also proposes a practical approach for selecting the adequate DEM at any time in a year based on the forecasted HRES plant operating scenario only. Model performance is evaluated on a large number of case studies using the HRES plant consisting of three renewable energy sources. The results have shown that only a few DEMs are required for representing the annual HRES plant dynamic performance and obtaining reliable transient system stability results.

Synthesis Load Model With Renewable Energy Sources for Transient Stability Studies

Increased penetration of renewable energy sources (RES) has brought challenges to load modelling techniques. This paper proposes a synthesis load model with RES (SLMR), and elaborates related industrial practice conducted by China Electric Power Research Institute. Several practical issues are addressed in designing and implementing SLMR, such as load survey and representation of different types of RESs. Besides, three new modelling concerns brought by RESs are novelly addressed in the paper, i.e., aggregation of various RES parameters, consideration of various RES terminal voltage, and additional line loss due to RES response. Parameterization of the SLMR calibrates widely varied node voltage in distribution grid, and aggregates them to one equivalent node. The proposed SLMR is practically applied in industrial works, which is demonstrated in the paper.

Enhancement of power transfer capacity of transmission network using multilevel multifunction inverter

This article presents a multilevel multifunction inverter (MLMFI) with a novel controller for the grid-connection of a solar array. The aim of this work is to improve the technology of the power transfer capacity of existing transmission lines in order to alleviate the current energy crisis. An effective mathematical modelling of an MLMFI configuration having two series-connected H-bridges per phase with isolated solar arrays is presented. A novel closed-loop controller is proposed for reference signal generation using the PWM technique. With the proposed controller, the power flow in a transmission line is analysed for daytime and nighttime conditions. The proposed controller performance was tested on a realistic single-machine infinite-bus power system with midpoint MLMFI using MATLAB simulation software. The proposed MLMFI-based solar array enhanced the stable power transfer limit of a transmission line. A comparative analysis between conventional and proposed controllers for power flow and transient stability studies was also presented. The proposed MLMFI results were validated by developing an experimental model.

Design of a computer code to evaluate the influence of the harmonics in the transient stability studies of electrical networks

Design of a computer code to evaluate the influence of the harmonics in the transient stability studies of electrical networks

Approaching the Transient Stability Boundary of a Power System: Theory and Applications

Estimating the stability boundary is a fundamental and challenging problem in transient stability studies. It is known that a proper level set of a Lyapunov function or an energy function can provide an inner approximation of the stability boundary, and the estimation can be expanded by trajectory reversing methods. In this paper, we streamline the theoretical foundation of the expansion methodology, and generalize it by relaxing the request that the initial guess should be a subset of the stability region. We investigate topological characteristics of the expanded boundary, showing how an initial guess can approach the exact stability boundary locally or globally. We apply the theory to power system transient stability assessment, and propose expansion algorithms to improve the well-known Potential Energy Boundary Surface (PEBS) and Boundary of stability region based Controlling Unstable equilibrium point (BCU) methods. Case studies on the IEEE 39-bus system well verify our results and demonstrate that estimations of the stability boundary and the critical clearing time can be significantly improved with modest computational cost. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the problem of determining whether a power system can retain transient stability subject to large disturbances such as short-circuit fault and generator tripping. The most well-known approaches to such a problem are the direct methods that can avoid time-costly simulations and “directly” determine the transient stability by estimating the stability boundary. Nevertheless, such estimations are generally too conservative. This paper proposes a new expansion method to improve the direct methods, which allows the initial estimation to lie partially outside the real boundary and hence enables applications to both global and local direct methods. Our method can expand the initial estimation towards the real stability boundary, thus reducing the conservativeness and providing a more accurate stability assessment such as the critical clearing time (CCT) of a fault. In this paper, we first mathematically establish the expansion theory and then propose numerical algorithms for power system applications. Simulations on the IEEE 39-bus benchmark verify our approach and show that the conservativeness can be significantly reduced with modest computational cost. Our approach can be further extended to scenarios where a valid Lyapunov (energy) function is unavailable.

Open Source High Fidelity Modeling of a Type-5 Wind Turbine Drivetrain

The increasing integration of renewable energy resources in evolving bulk power system (BPS) is impacting the system inertia. Type-5 wind turbine generation has the potential to behave like a traditional synchronous generator and can help mitigate the impact on system inertia. A hydraulic torque converter (TC) and gearbox with torque limiting feature are integral parts of a Type-5 wind turbine unit. A high fidelity model of Type-5 wind turbine drivetrain is not openly and widely available for grid integration and transient stability studies. This hinders appropriate assessment of Type-5 wind power plant’s contribution to bulk grid resilience. This work develops and validates a TC model based on those generally used in automobile’s transmission system. Moreover, the concept of torsional coupling is leveraged to integrate the TC and gearbox system dynamics. The entire integrated model will be open sourced and publicly available for grid integration studies.

The Central American Power System: Achievements, Challenges, and Opportunities for a Green Transition

Over the past few decades, Central American countries have seen a steady increase in their energy needs. Luckily, the region has abundant renewable energy resources and, as a result, has been busy constructing wind and photovoltaic power facilities. However, while these renewable sources are promising, they come with some risks—mainly, their variable power generation can pose a challenge to the interconnected regional system. This paper explores the current state of the Central American power system and the obstacles it faces as it strives to transition to a more environmentally-friendly energy system. To do so, the authors employed power flow analysis and transient stability studies, which were conducted using ETAP (Electrical Transient Analyzer Program) to model and simulate the power system. Their study revealed that the Central American power system is at risk of instability, and they suggest that integrating ancillary services and storage solutions could strengthen its resilience. Additionally, the authors advocate for the development of microgrids, energy management, and sustainable decarbonization plans. Lastly, the authors emphasize the importance of short-, medium-, and long-term power planning to make better decisions.

Revamped Sine Cosine Algorithm Centered Optimization of System Stabilizers and Oscillation Dampers for Wind Penetrated Power System

The mapping of damping ratios and damping factors by Sine-Cosine Algorithm (SCA) is significant in the analysis of low frequency oscillations generated in an integrated network having multiple conventional and renewable energy sources. Multiple random models with unknown search spaces and uncertain conditions and constraints, which incorporate the fluctuation of solutions towards or outwards at the initial stage for solving real-time problems can be analyzed by a revamped sine-cosine algorithm (RSCA) model. In this paper, the SCA has been revamped to explore the stability threshold for a stable system under dynamic nonlinear operating conditions. It is achieved with the infusion of suitable mathematical functions for optimizing the parameters of Power System Stabilizers (PSSs) and Doubly Fed Induction Generator (DFIG) system-based oscillation dampers to enhance the Small Signal Stability of power systems through effective damping of low-frequency oscillations (LFOs). These LFOs weaken the effective power generation and demand management cycle in conventional power systems when the system faces conditions like intermittent renewable energy sources, overloading conditions, impulsive faults etc. The small-signal and transient stability studies for various disturbances and different operating conditions are investigated, and the performance of the proposed RSCA for optimized parameter tuning of system stabilizers and oscillation dampers are analyzed on the modified benchmarking systems with wind generators using MATLAB Ⓡ simulations. The efficiency and robustness of the proposed algorithm has been verified under selective critical operating conditions, line outages, and load uncertainties to prove that the low frequency modes are damped with an elevated positive damping ratio and rapid settling time with reduced oscillations. The application of system stabilizers and oscillation dampers optimized through the proposed RSCA shows a reduced settling time in the LFOs created and improved damping ratio of 0.22 for an increase in 20% loading and 50% of wind power generation in the case study of Two Area Four Machine System.

A Machine Learning-Based Method for Identifying Critical Distance Relays for Transient Stability Studies

Protective relays play a crucial role in defining the dynamic responses of power systems during and after faults. Therefore, modeling protective relays in stability studies is crucial for enhancing the accuracy of these studies. Modeling all the relays in a bulk power system is a challenging task due to the limitations of stability software and the difficulties of keeping track of the changes in the setting information of these relays. Distance relays are one of the most important protective relays that are not properly modeled in current practices of stability studies. Hence, using the Random Forest algorithm, a fast machine learning-based method is developed in this paper that identifies the distance relays required to be modeled in stability studies of a contingency, referred to as critical distance relays (CDRs). GE positive sequence load flow analysis (PSLF) software is used to perform stability studies. The method is tested using 2018 summer peak load data of Western Electricity Coordinating Council (WECC) for various system conditions. The results illustrate the great performance of the method in identifying the CDRs. They also show that to conduct accurate stability studies, only modeling the CDRs suffices, and there is no need for modeling all the distance relays.

" Transient stability Studies of series FACT Device: A Comparative Study of GCSC and TSSC "

" Transient stability Studies of series FACT Device: A Comparative Study of GCSC and TSSC "

Transient Stability of Multi-Machine Wind Turbine Generators System Connected to the Power Network

currently worldwide installed capacity of the network connected wind generators grows rapidly; this rise of integration rate of wind energy could lead to circulation of transient stability and could potentially cause local or system wide blackout. This paper presents a recovery strategy that enables the system of HVDC transmission systems based on voltage source converter, which transmit electrical power from the wind turbines to the power network, to ride-through different positions of ac faults with smallest amount current and voltage stresses on the converter switching devices. Issue such as control strategies for a VSC-HVDC conduction system connecting offshore wind farms to the power network is discussed. The results show that the transient stability study of the system is widely different when the faults occur in neither wind side nor power network side. The DC link voltage behaves similarly to the AC voltage. However when the AC fault occurs in the wind side stations either for ac voltage or DC voltage the system behavior does not return to its normal operation after the fault is cleared. A reduced network model has been implemented in MATLAB/ SIMULINK to assess control performance during the fault.

An Analytical Approach for Frequency Estimation of Modern Power Grid

This letter proposes an analytical method to estimate the frequency of buses of transmission grid based on updated generator speed, internal generator voltages, admittance matrix and bus voltages. The proposed method estimates the buses frequency which are much more reliable, accurate and efficient for transient stability studies in contrast to other existing methods. To demonstrate the efficiency of the proposed approach, the method is applied on IEEE 39 bus test system for frequency support and is compared to other existing methods.

An approach for the aggregation of power system controllers with different topologies

This paper proposes an approach to aggregate non-structured power system controllers preserving the dynamical characteristics of the original devices. The method is based on linear operations that use the frequency response of the elements, resulting in an accurate input–output description of the equivalent controller when compared to the original ones. The developed method was applied to a model of the future interconnected Paraguayan-Argentinean power system to produce a dynamic equivalent used in a real-time simulator to test the special protection scheme needed for the safe operation of the this future system. Transient and small-signal stability studies presented matching simulation results in the time domain with significantly reduced computational burden and processing time.

A review of power system dynamic equivalents for transient stability studies

The increasing complexity of interconnected power system has brought challenges to detailed dynamic simulation in terms of computational effort. Therefore, for transient stability assessment, dynamic equivalents of parts of large-scale system are required to capture the electromagnetic transients. This paper presents a review of past research on dynamic equivalencing using coherency-based methods and system identification methods. Future topics are discussed to improve the state-of-art approaches.

Overcurrent Relays Coordination Considering Transient Stability Study of Induction Generator Using a Method Based on Terminal Voltage

Nowadays, with increasing penetration of Induction Generators (IG) in the electricity grid, it is of great importance that IG be connected to the grid in the fault conditions. In this paper, a terminal voltage based method for transient stability study of IG is proposed. For this purpose, an improved analytical method is used to determine Critical Clearing Time (CCT) of IG in the state of grid fault, including near and non-near faults. For the faults occurring far from the terminal of generator, electromagnetic torque is not equal to zero during fault. Hence, equivalent circuit model of IG and network is used to calculate the CCT. A new formulation based on terminal voltage of IG is presented to consider the stability constraint on Over Current Relay (OCR) coordination, to prevent disconnecting of IG in grid fault condition. Simulations are carried out on two samples network, and the results demonstrate the efficiency of proposed method.

Transient Stability Assessment for Current-Constrained and Current-Unconstrained Fault Ride Through in Virtual Oscillator-Controlled Converters

Unified virtual oscillator controller (uVOC) inherits the rigorous analytical foundation offered by oscillator based grid-forming (GFM) controllers and enables fast over-current limiting and fault ride-through (FRT). Control design for effective FRT requires transient stability analysis. Existing transient stability analysis methods and studies are limited in either considering only current unconstrained scenarios or neglecting the simultaneous power angle and voltage dynamics. Under current-constrained faults, the voltage and power angle dynamics are strongly coupled and both play critical roles in determining transient stability. Therefore, decoupled analysis of the two, typically used in transient stability studies, does not offer comprehensive insight into the system dynamics. In this work, a comprehensive modeling and analysis method for transient stability in uVOC based converters is developed under both current-saturated and unsaturated symmetrical AC faults. We utilize phase-plane analysis of the overall system in a single graphical representation to obtain holistic insights into the coupled voltage and power angle dynamics. The FRT controller and the analysis method have been validated through simulations and hardware experiments. The results demonstrate that uVOC is not constrained by a critical clearing angle unlike droop and virtual synchronous machine (VSM) type second order controllers.