An approach to the direct analysis of transient stability

The increasing proportion of renewable energy has seriously affected the stable operation of the power system, especially the transient stability. Here, a Transient Energy Function (TEF) based method for the transient stability analysis of the multi-machine system with Permanent Magnet Synchronous Generator (PMSG) involved is studied. First, the TEF of power system with PMSG is derived on the basis of its network structure-preserving mode. Next, the trapezoidal integral path is adopted to calculate the TEF of the disturbed power system approximately, and TEF based criteria are further obtained to analyze its transient stability. At last, the multi-machine system with PMSG involved is employed to verify the effectiveness of the proposed method.

In this paper, a transient energy function for AC/DC power systems is used to evaluate critical clearing times with consideration of the DC dynamics. The generator angular speeds, rotor angles and voltages at the HVDC link's AC buses are explicit variables in the transient energy function. A method for computing the transient energy function numerically is proposed. In the method, the angular speeds and rotor angles deemed as slow dynamics are integrated along sustained fault trajectories, and the integral path of the DC dynamics treated as fast dynamics are acquired by some modifications. The problems in applying potential energy boundary surface (PEBS) method to the computation of critical clearing time are also discussed. The critical clearing times for 4-generator and 10-generator AC/DC systems obtained using the transient energy function approximate well to those with the step-by-step time simulation.

A reliable and accurate direct procedure for fast transient stability assessment is proposed. Its main idea lies in the correction of the potential energy boundary surface (PEBS) method. The main problem of all other direct methods is determining the correct critical value of the Lyapunov function (system separation) determination, resulting from the nonlinear power system and different fault locations. After fault critical clearing time (CCT) estimation by the PEBS method, the direction of the postfault system trajectory is observed and a decision is made about the correct CCT assessment. >

Real-time transient stability detection in the power system with high penetration of DFIG-based wind farms using transient energy function

In this paper, a new method is proposed for dynamic security dispatch. The idea of coherent behavior of generators is used to find a new generation configuration with better transient stability behavior. Rescheduling the generation in the power system improves system security by increasing the critical clearing time or the transient energy margin without changing total generation. The calculation in the proposed method is simple and direct; the generation rescheduling depends only on the original generation and inertia constants of the machines, and their rotor speeds at the fault clearing time. In this work, the transient energy function (TEF) method is used to check the dynamic security of the system by analyzing all credible three phase faults with single line outages. If the worst energy margin is not acceptable, the proposed rescheduling is done, and the security is checked again. The method has been tested on the Ontario Hydro 55-bus 11-generator system, the IEEE 145-bus 50-generator system and the IEEE 162-bus 17-generator system. Results on several loading levels of the 162-bus 17-generator system are also shown.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper attempts to study the transient stability of a two machine infinite bus system when affected by large disturbances, by comparison of time domain approach vs. transient energy function. Then the decentralized nonlinear controller is embedded within the power system and simulation results show that the transient stability has been greatly enhanced. Based on the existing transient energy function of uncontrolled power system, the controlled power system has been represented as a forced Hamiltonian system. The Lyapunov function which is suitable for transient stability analysis of this controlled power system has been used for stability assessment. Simulations in different operating points show the enhancement of transient stability of power system with controller in both time domain approach and energy function method.

Fast contingency screening and efficient preventive control are two of the necessary integral functions of dynamic security analysis (DSA). Contingency screening requires the use of severity indices, and for DSA such an index should be a measure of system stability. In this paper, three time-domain simulation based indices are proposed for ranking of contingencies and generation rescheduling in DSA. These indices are energy margin index (EMI) based on hybrid extended equal area criteria (EEAC), transient energy index (TEI) based on hybrid transient energy function (TEF), and critical clearing time (CCT). Results on realistic power systems are presented to show their relative merit for use in contingency screening and generation rescheduling.

This paper proposes a decoupling based direct method to analyze the post-contingency transient stability for a general multi-machine power system. A linear decoupling transformation is used to construct the same number of independent single machine infinite bus (SMIB) power systems as oscillation modes. Each SMIB system carries stability information regarding one oscillation mode of the original system at the equilibrium. Then, the transient energy function method is applied on all decoupled SMIB systems to calculate stability margins, the smallest of which indicates the stability margin of the original system. Case studies on an IEEE 9-bus power system and a WECC 179-bus power system demonstrate the validity of the proposed method.

To ensure stable operation of a power system, it is necessary to analyse the power system performance under various operating conditions. Analysis includes studies such as power flow and both steady-state and transient stability. To perform such studies requires knowledge about the models used to represent the various components that constitute an integrated power system. In situations where there is a risk of loss of stability, it is necessary to apply controls that can ensure stable and uninterrupted supply of electricity following a disturbance. The subject of stability thus encompasses modelling, computation of load flow in the transmission grid, stability analysis under both steady-state and disturbed conditions, and appropriate controls to enhance stability. All these topics are covered in this book, providing a comprehensive treatment of the overall subject of stability of power systems. Topics covered include modelling of the synchronous machine; the synchronous machine connected to power systems; modelling of transformers, transmission lines and loads; power flow analysis; optimal power flow; small signal stability; transient stability; transient energy function methods; artificial intelligent techniques; power system stabilizers; series compensation; shunt compensation; compensation devices; and recent technologies. The subject matter is covered at a level that is suitable for students, scientists and engineers involved in the study, design, analysis and control of power systems.

Changing the steady state parameters of power system before fault occurrence is a new approach for increasing the transient stability of the system. With the presence of PMUs in smart grid and the possession of system information at any given time, FACTS devices can be set up online so that total critical clearing time (CCT) of the network is maximized as the most accurate transient stability criterion, by changing the system's steady state variables before the fault occurrence. Calculation of CCT requires iterative fault analysis and time-domain simulation of the network. In this paper, a novel prefault online optimal FACTS tuning is presented for transient stability enhancement of smart grid by CCT maximizing. Also the optimal type, number and location of FACTS devices are determined for long term planning. FACTS devices modeling and New England 39-bus system simulation are done by DIgSILENT software. DPL is used for CCT calculation and proposed approach implementation based on PSO algorithm. Also investment cost of these devices are considered for determining the optimal number of them.

With the increase in penetration level of wind generation in modern electrical power systems, the accurate analysis of transient stability of wind turbine will become more crucial. For this purpose, an appropriate model of doubly fed induction generator (DFIG) for transient stability analysis is required. This paper focuses on the development of approximate model of DFIG for the determination of transient stability using transient energy functions (TEF). The transient stability of the wind turbine during three phase short circuit fault is simulated for a 2-machine test system to verify the effectiveness of TEF for determining the stability of the power system.

Today’s power systems are operated closer to their stability limits due to the continuously growing load demands, interface to open markets, and integration of more renewable energies. In order to provide operators with clear insight on the current system situation, near real-time power systems dynamic security assessment tools are required. One of the core elements of near real-time dynamic security assessment tools is contingency screening and ranking. Most of the commercially available tools screen and rank contingencies by using the traditional numerical integration or Transient Energy Functions (TEFs) or hybrid methods. The traditional numerical integration method is accurate but computationally intensive and has a slow assessment speed which makes it difficult to identify any insecure contingency before it happens. Despite the TEF method of transient stability analysis being relatively fast, it develops less accurate results due to models simplification and assumptions. This paper introduces transient stability based on fast and robust contingency screening and ranking using an Adaptive step-size Differential Transformation (AsDTM) method. Based on the most current snapshot from Supervisory Control and Data Accusation (SCADA) data, the proposed method triggers AsDTM-based transient stability simulation for each credible contingency and evaluates Transient Stability Indices (TSI) as the normalized weighted sum of squares of errors derived from state variables and complex bus voltages at every simulation time step. Finally, contingencies are ranked based on these TSI and the worst contingency is identified for the next detail assessment. The method is tested on IEEE 9 bus and 39 bus test systems. Test results reveal that the proposed method is faster, robust, and can be used in near real-time dynamic security assessment sessions.

In recent years, power systems have become larger and more complicated. Deregulation of electric power industries has begun in some countries, and power system operations have become more difficult. However, the stability of the power supply is the most important consideration for customers. Therefore, power system operators should consider not only economic load dispatch but also on-line stability aspects. In this paper, the authors pay attention to one of the most important transient stability indices [critical clearing time (CCT)] and propose a new transient stability preventive control method using linear relationships between CCTs and generator rotor angles. At first, CCT calculations, as contingency screenings, are carried out to find contingencies that have smaller CCTs than predefined target values. The target values are taken as larger values than the actual circuit breaker operating times in the power system. A preventive control to achieve a more stable power system operating point is carried out by generator output rescheduling and generator terminal voltage control, which are determined using the relationships between CCTs and generator rotor angles. This proposed method is demonstrated using a Japanese standard power system called the IEE of Japan (IEEJ) EAST 10 machine system.

This study presents transient stability analysis to determine the value of critical clearing time (CCT) by considering the increased load and the addition of the transmission line from the 150 kV Malang interconnection system. These considerations are carried out because the Malang interconnection system is only centered on the Kebonagung substation. Therefore, the continuous increase in load will result in overcapacity at the substation. For this reason, the system must be tested by transient stability to determine the critical clearing time due to the 3-phase fault. Critical clearing time is the time the system determinant returns to its stable state or not. Determination of the CCT value can be obtained using the Runge-Kutta 4th Order method. In the calculation results, the smallest CCT value is 0.410 seconds when an error occurs on the Pakis-Infinite bus which is close to the Pakis bus with the value of critical clearing angle in the range 16.808° to 16.910° for the Wlingi generator and 46.970° to 47.183° for the Sutami generator.

Transient stability analysis of a grid-connected type-4 wind turbine with grid-forming control during the fault