Transient Stability Analysis of AC-DC Hybrid Power Systems Using Direct Method

This paper presents an overview about the main advances which occurred in the application of a direct method for transient stability analysis. The text is mainly focused on the potential energy boundary surface (PEBS) and boundary controlling unstable (BCU) method. The author's opinion about future perspectives and research areas of interest are given at the end of the text.

Transient stability domain estimation of AC/DC systems considering HVDC switching characteristics based on the polynomial Lyapunov function method

Attempts to complement the theoretical foundation of direct methods for transient stability analysis of structure preserving models made by H.D. Chiang et al. (see IEEE Trans. Circuits Syst., vol.CAS-34, p.160-73, 1987) by treating the model as a set of differential-algebraic equations that are not reduced to a set of pure differential equations. The implications of stability analysis on structure preserving models of power systems are explored. The model includes nonlinear load models and exciter dynamics. A practical controlling unstable equilibrium point method tailored to structure preserving models is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability analysis programs are a primary tool used by power system planning and operating engineers to predict the response of the system to various disturbances.Important conclusions and decisions are made based on the results of stability studies.The conventional method of analyzing stability is to calculate the transient behaviour of generators due to a given disturbance.Direct methods of stability analysis identify whether or not the system will remain stable once the disturbance is removed by comparing it with a calculated threshold value.Direct methods not only avoid the time consuming solutions required in the conventional method, but also provide a quantitative measure of the degree of system stability.This additional information makes direct methods very attractive when the relative stability of different plans must be compared or when stability limits must be calculated quickly.Direct methods of transient stability analysis of a multi machine power system, using a function describing the system's transient energy, are discussed.By examining the trajectory of the disturbed system, the following fundamental questions are dealt with: the concept of a controlling unstable equilibrium point (U.E.P), the manner in which some generators tend to lose synchronism, and identifying the energy directly responsible for system separation.Resolving this issue will substantially improve transient stability analysis by direct method.

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.

The work presented in this paper describes a scheme for rescheduling pool generation and adjusting contract-transactions for dynamic security enhancement when necessary, using a power market auction mechanism. The procedure is based on the transient energy margin concept, which is estimated using the corrected hybrid method of transient stability analysis. This index is selected because of useful linearity properties which it possesses with respect to certain important problem control variables. The proposed scheme brings together both technical and economic considerations and the procedure is illustrated using the New England System data set.

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.

The method of generalized equal-area criterion (GEAC) for transient stability analysis of power systems and its recent generalization to cover a wider range of faults are explained. The method is based on an exact mathematical transformation of the time-invariant dynamical equations of an n-machine system into an equivalent single-machine-infinite-bus (SMIB) system equation with time-varying parameters. Further approximations are made to assign appropriate constant values to the SMIB parameters, thus enabling the use of a modified version of the well-known equal-area criterion. An approximate stability index is then defined to yield the degree of stability/instability. GEAC and time simulation results showed excellent agreement in the majority of cases; in the worst case the difference did not exceed 7%. Some tests results are presented. Potential applications of the GEAC method for online transient stability assessment are discussed. >

Recent efforts to apply direct methods of transient stability analysis to multimachine power systems have used the so-called "energy functions." These functions describe the system transient energy causing the synchronous generators to depart from the initial equilibrium state, and the power network's ability to absorb this energy so that the synchronous machines may reach a new post-disturbance equilibrium state. Recent results have shown that not all the transient energy contributes to system separation. Indeed it has become increasingly evident that system separation depends on the energy of certain individual machines or groups of machines, which comprise the critical group, and which tend to separate from the rest of the machines (which make up the noncritical group). Thus there is a need for generating energy functions for individual machines (or for groups of machines). Using a center of inertia frame of reference, the energy function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_{i}</tex> for machine <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</tex> is derived. A procedure for first swing transient stability assessment is developed using the energy function of individual machines and groups of machines. The method is tested extensively on two realistic power networks (the 20-generator IEEE System and the 17-generator reduced Iowa System). An analytical justification for using the critical energy of individual machines in stability assessment is provided using an invariance principle for ordinary differential equations. Power system transient stability is analyzed using the energy function of the critical group of machines. This energy function is dependent on all state variables of the power system, and satisfies the hypotheses of the invariance theorem of La Salle, enabling us to deduce the asymptotic stability of the post-disturbance equilibrium of the entire power system. It also enables us to obtain an estimate of the domain of attraction of this equilibrium of the entire power system. The methodology advanced herein, which combines computer-aided techniques with analytical tools, yields less conservative results than were obtained in previous works that used total system energy. It is to be noted that the present results are preliminary in the sense that the mechanism of separation of the critical group of machines from the rest of the system needs further investigation.

A new decomposition-aggregation approach is developed to perform transient stability analysis of an N-machine power system with a speed governor. The system decomposition is performed so that every subsystem includes four machines, instead of only two or three machines as considered in other work. The system model is derived and decomposed into (N − 1)/3 11th-order interconnected subsystems considering transfer conductances, nonuniform mechanical damping, electromagnetic damping and speed governor action. Each of these subsystems is decomposed into a free subsystem containing 12 nonlinearities and interconnections. A square aggregation matrix of order (N − 1)/3 is obtained instead of orders N and (N + 1)/2 for the pair-wise and triple-wise decompositions, respectively. The approach is applied to a 10-machine power system and an estimate for the system asymptotic stability domain is determined. System transient stability computations are carried out considering a three-phase short circuit fault, with successful reclosure, near a system bus or a sudden loss of one of the system loads. The approach is used to determine a reclosure time for the faulted line and a reconnection time for the lost load required for the system to regain its prefault (normal) conditions. The approach developed is suitable and can be easily used for stability analysis of power systems (the number of machines may be more than 10). The developed approach can also reduce the conservativeness of the decomposition-aggregation method.

Nowadays, integration of large-scale wind farms (WFs) into power systems is experiencing rapid growth. As this rapid integration can affect transient stability significantly, employing doubly fed induction generator (DFIG)-based wind turbines, which have shown better behavior regarding system stability, has attracted much attention. This research contributes to the literature by investigating the transient stability of the power system with increasing penetration of DFIG-based WFs. In the proposed framework, the current-balance form is utilized for the network equations, and in this way, transient stability is performed using time-domain simulation. According to the simulation results, when the rate of wind power generation exceeds 0.7 per-unit, the increasing trend of the critical clearing time (CCT) is reversed and the CCT decreases greatly with the increased wind power penetration. In addition, the reactive power compensation by DFIG, the gearbox ratio, the power system strength, and DFIG parameters are comprehensively investigated as effective parameters on transient stability. Since the rated rotor speed of DFIG significantly impacts the electrical torque and machine currents, the reduction of the rated rotor speed due to the change of the gearbox ratio has been investigated as one of the effective factors to improve the transient stability. The simulation results demonstrate the effectiveness of the proposed approach in improving power system transient stability.

The wide application of WAMS (Wide Area Measurement System) provided a new thinking for transient stability analysis of power system. Based on real-time measurement information from WAMS, a method to quickly analysis power system transient stability that does not depend on network structure, model and parameters of power system is proposed in this paper. Firstly, the parameters of system are identified online by improved least squares method on basis of that the multi-machine power system is equivalently reduction to one machine infinity bus system. The equilibrium point and stability margin of equivalent system are rapidly computed, and then the stability of system is quickly judged. The simulation results show that the algorithm can accurately judge transient stability of system and has better antidisturbance ability and robustness. The issue of dependence of transient stability analysis on system model and parameter is solved. The adverse influences of data lose and measurement errors in actual measurement of the WAMS on analysis results are avoided effectively. Keywords-power system; wide-area measurement system; parameter identification; energy function; transient stability analysis

Practical applications of Lyapunov's direct method to transient stability analyses of multimachine power systems have been obstructed by the well-known conservative nature and the computational difficulty accompanying the usual critical value of Lyapunov function. These problems have been solved in this paper by introducing a new critical value for the first swing stability, and by developing a efficient method of calculating it as well as one of taking account of transfer conductances. These methods have been applied to a transient stability analysis of a 10-machine power system, and yielded results of practical significance.

Parallel time domain simulation is one of the reliable and potential methods that might realize the real-time online transient stability analysis of power system. In the paper, a new parallel calculation method, based on waveform relaxation method, is proposed for power system transient stability analysis. In the method, the entire transmission network is first divided into several subsystems by the geographical location; for each subsystem, its neighboring systems are represented as equivalent voltage sources at the boundary buses; the tie line flows are considered as the communication waveform among the subsystems; then, time domain simulation for each subsystem is performed in parallel. The test result of the practical system indicates that the new parallel algorithm completely achieves the on-line real-time or even over-real-time calculation speed and could be applied to the on-line transient stability analysis of practical system.

This paper proposes a method for power system stability monitoring and analysis through Phasor Measurement Units' (PMUs) measurements (i.e., bus voltage magnitudes and angles). Real-time stability monitoring can be achieved by observing the behavior of the measurement data's frequency spectra. In addition, a modified Thevenin equivalent-based model is proposed to analyze the system small-signal stability and transient stability. The model's parameters are estimated based on the phasor measurements. We verify our proposed method through simulations on a RTDS/PMU/PDC testbed and perform analyses on real PMU data.