Extended Equal Area Criterion Research Articles

Transient stability enhancement control strategy based on grid dispatching for multi-paralleled grid forming inverters during LVRT

In this article, the transient synchronization process of multi-paralleled grid forming (GFM) inverters is studied detailly. Firstly, based on the multi-paralleled inverters control structure and complementary cluster center of inertia relative motion (CCCOI-RM), the single machine infinite bus (SMIB) system is proposed. Subsequently, the power angle characteristic (PAC) equation of multi-paralleled inverters for different dispatching strategies with simplified damping coefficient is built. Meanwhile, a grid dispatching strategy considering communication delay is proposed, which avoiding the cascading failures of grid faults. Furthermore, according to the grid dispatching strategy, a cluster control strategy optimization method including critical cluster identification (CCI) method and transient stability prediction analysis method is designed, which is proposed to identify unstable cluster in multi-paralleled inverters. In addition, the synchronization stability criteria for dispatching strategies of multi-paralleled inverters are obtained based on the PAC equation, in which the transient instability phenomenon and mechanism for different fault stages is explained by extended equal area criterion (EEAC) method. Finally, the simulations results validate the effectiveness of the theoretical analysis and proposed method.

Extended Equal Area Criterion Revisited: A Direct Method for Fast Transient Stability Analysis

For transient stability analysis of a multi-machine power system, the Extended Equal Area Criterion (EEAC) method applies the classic Equal Area Criterion (EAC) concept to an approximate One Machine Infinite Bus (OMIB) equivalent of the system to find the critical clearing angle. The system-critical clearing time can then be obtained by numerical integration of OMIB equations. The EEAC method was proposed in the 1980s and 1990s as a substitute for time-domain simulation for Transmission System Operators (TSOs) to provide fast, transient stability analysis with the limited computational power available those days. To ensure the secure operation of the power system, TSOs have to identify and prevent potential critical scenarios through offline analyses of a few dangerous ones. These days, due to increased uncertainties in electrical power systems, the number of these critical scenarios is increasing, substantially, calling for fast, transient stability analysis techniques once more. Among them, the EEAC is a unique approach that provides not only valuable information, but also a graphical representation of system dynamics. This paper revisits the EEAC but from a modern, functional point of view. First, the definition of the OMIB model of a multi-machine power system is redrawn in its general form. To achieve fast, transient stability analysis, EEAC relies on approximate models of the true OMIB model. These approximations are clarified, and the EAC concept is redefined with a general definition for instability, and its conditions. Based on the defined conditions and definitions, functions are developed for each EEAC building block, which are later put out together to provide a full-resolution, functional scheme. This functional scheme not only covers the previous literature on the subject, but also allows to introduce several possible new EEAC approaches and provides a detailed description of their implementation procedure. A number of approaches are applied to the French EHV network, and the approximations are examined.

Coordination of Resistive SFCL and Additional Power Controller for Transient Stability Enhancement of Virtual Synchronous Generator

Virtual synchronous generator (VSG) techniques are friendly applied in inverter interfaced renewable energy sources (IIRESs), and that enables to recover the rotor inertia and provide the damping support. However, the VSG generally owns weak overcurrent ability, and its transient angle stability (TAS) under faults may be destroyed. For solving the issue, This paper puts forward a coordination method of a resistive superconducting fault current limiter (SFCL) and an additional power controller (APC). The relevant mathematical model is built, and the TAS is probed based on the extended equal area criterion (EEAC). In the coordination philosophy, the SFCL represses the fault current and prevents the disconnection of the VSG, and thereupon the designed APC is to actively adjust the VSG's power reference and positively reduce the acceleration of the virtual rotor. It is aimed to fully realize the transient power balance, and the change of the virtual rotor angle can be mitigated. Furthermore, the MATLAB platform is adopted to create a simulation model. Multiple fault scenarios are simulated, and the findings certify the efficacy and superiority of the proposed approach. The VSG successfully rides through the serious and moderate faults, and meanwhile, its transient angle stability is visibly increased.

An integrated method for critical clearing time prediction based on a model-driven and ensemble cost-sensitive data-driven scheme

The critical clearing time (CCT) is one of the most important indexes for large-disturbance rotor angle stability margin evaluation. In practice, model-driven methods are usually realized based on simplified models to ease the computational burden, but the accuracy is sacrificed. To solve this problem, a data-driven method is adopted in this paper for fast error correction of a model-driven method, creating an integrated method. Both a reliable accuracy and an acceptable computation speed can be achieved with this integrated method. Meanwhile, involvement of model-driven method helps enhance robustness of the integrated method to training sample insufficiency, measurement error and power system scale. In addition, the data-driven method is further transformed on the basis of a cost-sensitive approach where the error tolerance for different actual CCT values should be differentiated during the training process instead of being treated equally in the common data-driven method. To mitigate the negative effect caused by such transformations, an ensemble learning structure is also constructed. In this paper, an integrated extended equal-area criterion (IEEAC) and an extreme learning machine (ELM) are applied as model-driven and data-driven methods, respectively. A genetic algorithm (GA) is used in the ensemble learning structure construction. Validations show that the proposed integrated method with the transformed data-driven method can improve the CCT prediction accuracy and avoid the polarization of the error distribution.

A Flexible Control Strategy to Prevent Sending-End Power System From Transient Instability Under HVDC Repetitive Commutation Failures

High-voltage direct-current (HVDC) transmission systems have been rapidly developing, whereas they also become the crucial factors that affect the power system's stability. The repetitive commutation failures (RCF) of the HVDC link will put the sending-end power system at risk of transient instability, which greatly raises the demand of the system to enhance its ability to cope with such events. This paper proposes a flexible control strategy supported by the fast-acting energy storage system (ESS) based on the combination of the model predictive control (MPC) principle and the extended equal area criterion (EEAC) to ensure transient stability of the sending-end system when RCF occurs in a single HVDC link. The formulas to forecast the system's dynamic behavior are constructed. The optimal power expected to be provided by the ESS for each commutation failure (CF) is obtained by assessing the system stability margin. The proposed strategy is to maintain the system's transient stability by the consecutive appropriate responses of the ESS during RCF. Additionally, the blocking conditions of the HVDC link and the required consequent control are studied. The simulation results demonstrate the ability of the proposed strategy to ensure the transient stability of the sending-end power system when the RCF occurs.

Application of phase sequence exchange in emergency control of a multi-machine system

Phase sequence exchange (PSE) is a recently developed emergency control technology. The effectiveness of PSE in a multi machine system is demonstrated in this paper. Two PSE device installation positions in a multi-machine system are first proposed. The first is at the outlet of each generator, and the second is at the connection lines between two large systems with weak connections. Based on extended equal area criterion (EEAC), a control method is then proposed. After the system out of step, the generator that need PSE and the power angle threshold can be determined quickly. When the threshold value of power angle is reached, the generator in the critical cluster exchanges phase sequence at the same time, which reduces the power angle of the one-machine to infinite bus (OMIB) image by 120° and increases the deceleration area of OMIB image. This prevents out-of-step conditions while maintaining the integrity of the system. The effectiveness of the PSE is verified using Kundur's two-area four-machine power system and the IEEE 39-bus system, and compared with other emergency control methods.

Preventive-Corrective Coordinated Transient Stability Dispatch of Power Systems With Uncertain Wind Power

This paper proposes a new coordinated method for preventive generation rescheduling and corrective load shedding to maintain power system transient stability under uncertain wind power variation. A two-step bi-level optimization model is proposed where generation rescheduling and load shedding are coordinated by a risk coordination parameter, which adjusts the total coordination cost in the upper level. Then, based on Extended Equal Area Criterion (EEAC) and trajectory sensitivities, the non-linear risk and stability constraints are converted into the linear form for generation rescheduling cost and load shedding cost optimization in the lower level, respectively. Uncertain wind power output is modeled as a small number of robust test scenarios. Finally, the golden section search is applied to solve the bi-level problem. The proposed method is validated on the New-England 39-bus system by using commercial grade software. The computational efficiency, economic optimality, and stability robustness under random wind power of the method are demonstrated.

Trajectory sensitivity based preventive transient stability control of power systems against wind power variation

The penetration of high-level wind power has significantly made the power system’s operation complicated. The random power variation of the wind farms may deteriorate the power system’s transient stability degree since it alters the operating state of the power system. In this paper, based on trajectory sensitivity and Extended Equal Area Criterion (EEAC) method, a new preventive control approach is proposed to optimally balance the wind power variation by rescheduling synchronous generators while maintaining the transient stability for credible contingencies. The whole problem is formulated to a programming problem with linear stabilization constraints. The proposed method is validated on the New-England 10-machine 39-bus system by using commercial simulation software Transient Security Assessment Tool (TSAT), and both single- and multiple-contingency cases are tested. Simulation results verify its satisfactory performance on control effectiveness, computational efficiency, transparency, and accuracy.

Effects of cascading failure intervals on synchronous stability

Cascading failure analyses are mainly based on simultaneous or quasi-steady-state (QSS) assumptions, which are inappropriate in cases of rapid cascading failure analysis and control. Fault interval is considered in the stability analysis of cascading failure for the first time in this article. Based on the extended equal area criterion (EEAC), a transient stability analysis method is proposed for cascading failure in consideration of intervals. The results show the periodicity of stable margin variations with intervals. The conclusions are validated in a Hamiltonian system, and the effects of time-varying factors are analyzed. The OMIB case shows that it may be over-optimistic to assess stability levels under simultaneous or QSS assumptions. The validity of all conclusions in this paper is verified with the New England system and with an actual power system.

Coordinated Control of DFIG Based Wind Farms and SGs for Improving Transient Stability

This paper proposes a coordinated control of doubly fed induction generator (DFIG)-based wind farms’ (WFs) post-fault active power and synchronous generators’ (SGs) tripping with the aim of improving transient stability of both the first swing and multi swings. To achieve it, the impact mechanism of the WFs’ post-fault active power and SGs’ tripping on the stability margin of each swing is first presented by using extended equal area criterion (EEAC). Based on this, a principle of the coordinated control is put forward. The WFs’ control period is designed as six stages, and the value of post-fault active power in each stage is suggested to improve the stability of the first five swings and maintain the post-fault steady state. To decrease the tripping amount of the SGs, the SGs are tripped only when WFs’ control effect is not sufficient to avoid the instability. Then, by utilizing an “online pre-decision and real-time matching” scheme, an engineering application method for the control principle is proposed, where the control procedures and detailed parameters calculation are demonstrated. The numerical simulations show that the coordinated control has a better damping effect and a less control cost (less amount of tripped SGs) than the traditional DFIG control or traditional SG tripping.

Adaptive Protection and Control in the Power System for Wide-Area Blackout Prevention

This paper presents a new approach in adaptive out-of-step (OOS) protection settings in power systems in real time. The proposed method uses extended equal area criterion (EEAC) to determine the critical clearing time and critical clearing angle of the system, which are vital information for the OOS protection setting calculation. The dynamic model parameters and the coherency groups of the system for EEAC analysis are determined in real time to ensure that the newly calculated settings suit with the prevalent system operating condition. The effectiveness of the method is demonstrated in simulated data from a 16-machine 68-bus system model.

Impact Study of PMSG-Based Wind Power Penetration on Power System Transient Stability Using EEAC Theory

Wind turbines with direct-driven permanent magnet synchronous generators (PMSGs) are widely used in wind power generation. According to the dynamic characteristics of PMSGs, an impact analysis of PMSG-based wind power penetration on the transient stability of multi-machine power systems is carried out in this paper based on the theory of extended equal area criterion (EEAC). Considering the most severe PMSG integration situation, the changes in the system’s equivalent power-angle relationships after integrating PMSGs are studied in detail. The system’s equivalent mechanical input power and the fault period electrical output power curves are found to be mainly affected. The analysis demonstrates that the integration of PMSGs can cause either detrimental or beneficial effects on the system transient stability. It is determined by several factors, including the selection of the synchronous generators used to balance wind power, the reactive power control mode of PMSGs and the wind power penetration level. Two different simulation systems are also adopted to verify the analysis results.

A Decomposition-Based Practical Approach to Transient Stability-Constrained Unit Commitment

Traditional security-constrained unit commitment (SCUC) considers only static security criteria, which may however not ensure the ability of the system to survive dynamic transition before reaching a viable operating equilibrium following a large disturbance, such as transient stability. This paper proposes a tractable mathematical model for transient stability-constrained unit commitment (TSCUC) and a practical solution approach. The problem is modeled without explicit differential-algebraic equations, reducing the problem size to one very similar to a conventional SCUC. The whole problem is decomposed into a master problem for UC and a range of subproblems for steady-state security evaluation and transient stability assessment (TSA). Additional constraints including Benders cut and so-named stabilization cut are generated for eliminating the security/stability violations. The extended equal-area criterion (EEAC) is used for fast TSA and analytically deriving the stabilization cut, wherein multiple contingencies having common instability mode can be simultaneously stabilized by one cut. The proposed approach is demonstrated on the New England 10-machine system and the IEEE 50-machine system, reporting very high computational efficiency and high-quality solutions.

Stability-based minimization of load shedding in weakly interconnected systems for real-time applications

Abstract The transient stability of power systems is highly affected by the changes in the power generation and load levels. Due to the variability of the generating resources, the system stability can be provoked and the system stability limits can be reached as a result of certain sudden drop in the power generation. In these cases, the load shedding can act as an effective emergency corrective action for keeping system stability; however, over-shedding of loads results in severe economical as well as social security problems. Therefore, minimization of the load shedding required for the restoration of the system stability is one of the main objectives of this paper. Another critical issue related to successful load shedding is the fast assessment of the system stability, and the amount of the load shedding as well as the implementation of the load shedding corrective action. Therefore, this paper presents a fast method of stability assessment and load shedding requirements in the weakly interconnected power system. The method is an improved form of the extended equal area criterion (EEAC) where the required system equivalence is based on the availability of wide area monitoring (WAM) devices in modern power systems. The paper also investigates the impact of the implementation duration of the required load shedding. The results are verified through time domain simulations which confirm the accuracy of the presented method and its suitability for real-time applications.

Transient Stability Analysis and Enhancement of IEEE- 9 Bus System

System stability study is the important parameter of economic, reliable and secure power system planning and operation. Power system studies are important during the planning and conceptual design stages of the project as well as during the operating life of the plant periodically. This paper presents the power system stability analysis for IEEE- 9 bus test system. The fault is created on different busses and transient stability is analyzedfor different load and generation conditions. The critical clearing time (CCT) is calculated by using time domain classical extended equal area criterion method. The system frequency and voltage variation is observed for different fault locations and CCT. The IEEE-9 bus test system is simulated and stability is analyzed on ETAP software.

A Research on Emergency DC Power Support Based on DCOI

An integrated scheme of emergency DC power support which is based on dominant center of Inertia DCOI is proposed to improve power system transient stability. The inter-area speed differences equivalent by dominant center of inertia alleviates the main weakness of the traditional signal which is made of the frequencies at both sides and is represent of abnormal information of the nonlinear dynamic behavior of the power system based on a model in which two AC systems are connected by a HVDC Link. Sichuan Power Grid connected with Southwest Power Grid by Deyang-Baoji HVDC project is used to testify the method. The simulation results show that the control strategy can significantly advance the transient stability of AC/DC system through extended equal area criterion (EEAC).

An Improved Iterative Method for Assessment of Multi-Swing Transient Stability Limit

This paper addresses the issue of improving the conventional iterative method used for integrated extended equal area criterion (IEEAC) and single machine equivalent (SIME) for multi-swing transient stability limit analysis in power system operation. Effects of the complicated phenomena on the conventional method, i.e., nonmonotonic variation of the stability margin and the isolated stability domain (ISD), are studied. Accordingly, the conventional method is improved for both efficiency and accuracy. With this knowledge, an improved sensitivity-based iterative method for searching multi-swing transient stability limit is proposed. The advantage of this method is that the complicated phenomena are fully considered and their effects are either overcome or avoided as much as possible. Case studies on the ten-generator New England power system are presented to verify the effectiveness and efficiency of this improved method.

Transient Stability Ranking Technique based on System Parameter Estimation and Extended Equal-Area Criterion

The on-line TSC (Transient Stability Control) system is the world's first online-type stabilization system for electric power systems, which realizes optimum stabilized control of moment-by-moment power system conditions by obtaining power system information online and carrying out stability calculations at certain intervals.This paper discusses the new transient stability ranking method for severity of each contingency, which will be introduced to the new on-line TSC system of Chubu Electric Power Company. The ranking method is based on system parameter estimation and the Extended Equal Area Criterion. The method can be applied to unbalanced fault.

Power system transient stability analysis software tool for an undergraduate curriculum

AbstractThis paper describes, a technique of the transient stability assessment, known as the Extended Equal Area Criterion (EEAC) as applied to a multimachine power system. The EEAC is implemented using the MATLAB program to provide a software tool with GUI. The software tool of the EEAC is developed to incorporate the transient stability analysis, into an undergraduate curriculum in power engineering. Another criterion for developing this software is to reduce the effort normally associated with the instruction of the complex theory of the transient stability and the use of the software in an undergraduate classroom environment. The results obtained from the MATLAB software on two multimachine power systems are compared with the traditional time domain analysis technique for verification purposes. © 2001 John Wiley & Sons, Inc. Comput Appl Eng Educ 9: 37–48, 2001

Integrated Direct Methods for Transient Stability Analysis

In this paper, three direct methods (i.e., Controlling Unstable Equilibrium Point (CUEP) method, Potential Energy Boundary Surface (PEBS) method, and Extended Equal Area Criterion (EEAC) method) for power system transient stability analysis have been reviewed and compared. Their analysis accuracy and their error sources are investigated. Then, an integrated direct method with much higher accuracy and reliability is proposed. The proposed method has been applied to two Chinese power systems for transient stability analysis of more than two thousand cases under large disturbances of symmetrical and unsymmetrical faults and autoreclosure operating sequence disturbances. Statistical results clearly illustrate the effectiveness of the proposed method.