Speed-up the computing efficiency of waveform relaxation method for power system transient stability

Modern electric power systems are large and complicated, and, in many regions, the generation and transmission systems are operating near their limits. Eigenanalysis is one of the tools used to analyze the behavior of these systems. Standard eigenvalue methods require that simplified models be used for these analyses; however, these simplified models do not adequately model all of the characteristics of large power systems. Thus, new eigenanalysis methods that can analyze detailed power system models are required. The primary objectives of the work described in this report were I) to determine the availability of eigenanalysis algorithms that are better than methods currently being applied and that could be used an large power systems and 2) to determine if vector supercomputers could be used to significantly increase the size of power systems that can be analyzed by a standard power system eigenanalysis code. At the request of the Bonneville Power Administration, the Pacific Northwest Laboratory (PNL) conducted a literature review of methods currently used for the eigenanalysis of large electric power systems, as well as of general eigenanalysis algorithms that are applicable to large power systems. PNL found that a number of methods are currently being used for the this purpose, and all seem to work fairly well. Furthermore, most of the general eigenanalysis techniques that are applicable to power systems have been tried on these systems, and most seem to work fairly well. One of these techniques, a variation of the Arnoldi method, has been incorporated into a standard power system eigenanalysis package. Overall, it appears that the general purpose eigenanalysis methods are more versatile than most of the other methods that have been used for power systems eigenanalysis. In addition, they are generally easier to use. For some problems, however, it appears that some of the other eigenanalysis methods may be better. Power systems eigenanalysis requires the computation of eigenvalues of nonsymmetric matrices. Such computations are fairly difficult, however, and they constitute an area of active research. Thus, research in this area should be closely monitored, and, as new methods become available, they should be tested on large power systems. PNL also investigated the use of vector supercomputers to enlarge the size of power systems that can be analyzed by MASS, a standard power system eigenanalysis code. MASS was converted to run on a Cray supercomputer. On a conventional computer, MASS is limited to power system problems with about 500 states because of computer time constraints. Running MASS on a Cray X-MP EA/232, however, PNL found that a problem with about 2200 states could be solved in about 26 minutes. Furthermore, by moving to a larger Cray, it should be possible to use MASS to analyze power systems with 5,000 to 10,000 states. Problems with 5,000 states would probably take about 5 Cray hours, while a problem with 10,000 states would probably take about 43 Cray hours, though the actual execution times will depend on the type of Cray used. Problems requiring 5 Cray hours are not uncommon. Problems requiring 43 Cray hours, however, would be fairly expensive. Thus, power systems with about 5000 states probably represent an upper limit on the size of problems that one would want to routinely solve using a Cray version of MASS.

The present work is based on developing a control strategy to mitigate the impact of reduced inertia due to significant DFIG penetration in a large power system. The paper aims to design a supplementary control for the DFIG power converters such that the effective inertia contributed by these wind generators to the system is increased. The paper also proposes the idea of adjusting pitch compensation and maximum active power order to the converter in order to improve inertial response during the transient with response to drop in grid frequency. Results obtained on a large realistic power system indicate that the frequency nadir following a large power impact in the form of generators dropping out is effectively improved with the proposed control strategy. The proposed control is also validated against the sudden wind speed change in the form of wind gust downs and wind ramp downs occurring in conjunction with the generators dropping out. A beneficial impact in terms of damping power system oscillations is also observed, which is validated by eigenvalue analysis. The affected mode is then excited with a large disturbance in time domain. The damping improvement observed in time domain and subsequent Prony analysis support the result obtained from eigenvalue analysis.

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.

In recent developments of direct methods for power system transient stability analysis, the task of finding the controlling unstable equilibrium point (u.e.p.) of the original system is performed on an artificial, dimension-reduction system for easily computing the controlling u.e.p. It has been shown that if the stable and unstable manifolds of a family of parametrized systems, which relates the original power system and an artificial, dimension-reduction system, satisfy the transversality condition as the parameter varies, then the artificial, dimension-reduction system contains the same set of u.e.p.'s on the stability boundary. In this paper, instead of direct verification of the transversality conditions, we show that under small mechanical power injections, the original power system model and the artificial, dimension-reduction system contain the same unstable equilibrium points on the stability boundary for one machine and two machine power system models.

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 presents a new efficient solution approach for solving the unit commitment schedule of thermal generating units of a realistic large scale power system. The approach is based on the equivalencing like concept of network reduction which reduces the number of units in the large power system to the lowest possible number according to their fuel/generation cost characteristics. The reduced system is then solved and from that overall solution to the original unit commitment problem of the entire system is obtained. Test results for real-life systems of up to 79 units and comparisons with results obtained using Lagrangian relaxation and truncated dynamic programming (DP-TC) are also reported.

This paper investigates the transient stability of power systems co-dominated\nby different types of grid-forming (GFM) devices. Synchronous generators (SGs\nand VSGs) and droop-controlled inverters are typical GFM devices in modern\npower systems. SGs/VSGs are able to provide inertia while droop-controlled\ninverters are generally inertialess. The transient stability of power systems\ndominated by homogeneous GFM devices has been extensively studied. Regarding\nthe hybrid system jointly dominated by heterogeneous GFM devices, the transient\nstability is rarely reported. This paper aims to fill this gap. It is found\nthat the synchronization behavior of the hybrid system can be described by a\nsecond-order motion equation, resembling the swing equation of SGs. Moreover,\ntwo significant differences from conventional power systems are discovered. The\nfirst is that the droop control dramatically enhances the damping effect,\ngreatly affecting the transient stability region. The second is that the\nfrequency state variable exhibits a jump at the moment of fault disturbances,\nthus impacting the post-fault initial-state location and stability assessment.\nThe underlying mechanism behind the two new characteristics is clarified and\nthe impact on the transient stability performance is analyzed and verified. The\nfindings provide new insights into transient stability of power systems hosting\nheterogeneous devices.\n

The quality of power system operating need to assess maturity of small oscillation stability issues of regional power grid thoroughly, analysis level of operating, controller installation allocating and parameter optimization scheme from different develop stage of regional power grid accurately. The assessment scheme is based on damping torque analysis of real large scale power system. Small oscillation stability is to be evaluated through the mechanism of damping torque analysis with automatic voltage regulator and other power system stabilizers. By analyzing the characteristic of the link between damping torque provided or transferred through each generator and the oscillation mode detected in the power system, the maturity indice has been established. This indice may cover the information of the contribution of controllers towards the power system and the dispatching within each generator in power system. Practical application effects in a real large scale power grid indicates this assessment can thoroughly describe the action of control elements in the power grid, help to depict the whole picture of impact applying power system controllers. A novel maturity evaluation of small oscillation in power grid is presented.

This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation problems.

This paper presents transient stability assessment of a large actual power system using the probabilistic neural network (PNN) with enhanced feature selection and extraction method. The investigated large power system is divided into five smaller areas depending on the coherency of the areas when subjected to disturbances. This is to reduce the amount of data sets collected for the respective areas. Transient stability of the power system is first determined based on the generator relative rotor angles obtained from time domain simulations carried out by considering three phase faults at different loading conditions. The data collected from the time domain simulations are then used as inputs to the PNN. An enhanced feature selection and extraction methods are then incorporated to reduce the input features to the PNN which is used as a classifier to determine whether the power system is stable or unstable. It can be concluded that the PNN with enhanced feature selection and extraction methods reduces the time taken to train the PNN without affecting the accuracy of the classification results.

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.

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

A power system is composed of various components such as generators, transformers, transmission lines, switching devices and loads. They have their mathematical model and graphical representation. Sometimes, a power system’s change of topology occurs due to events like short circuits, lightning striking a transformer, or a reconfiguration of the transmission system. In this thesis, a new way of simulating large scale power systems is presented from the modeling point of view. In the literature, a lot of modeling methods and mathematical tools are available to tackle this subject. However, this thesis mainly focuses on the time domain simulation of large scale power systems - and in particular, transients which appear after a change of topology. A change of topology in electrical networks impact time domain simulations on two levels. The first impact is that it is necessary to update or re-compute the set of equations. The computation time of this action on the topology can be significant - especially for large scale power systems. The second impact of this change of topology is the transient that will occur. Usually, this change will impose to numerically compute fast oscillations in currents and voltages until they reach a new steady state...

This paper proposes approaches to estimate the dominant swing mode sensitivity by utilizing Wide Area Measurements. The proposed methods are suitable to situations where availability of information of system model and operating condition is limited to a subsystem in which the control action resides. Modal frequency and mode shape of the dominant swing mode are estimated from a Wide Area Measurement System (WAMS) based mode identification technique. This information is used along with the subsystem model for estimation of eigenvalue sensitivity. Such a scenario is indeed faced in large interconnected power systems, where effect of a control action in the subsystem on a dominant inter-area mode needs to be estimated before actual implementation. Analytical formulations of sensitivity are derived using special modal characteristics (identified based on simplified system models) and a hybrid representation of the system, in which the subsystem is treated as a controller in a feedback loop to the rest of the system. Case studies with detailed models of two area four machine and IEEE 16 machine 68 bus system validate these formulations.

This paper aims at improving the excitation control system for the doubly fed induction generator-based wind farm (WF). The proposed decentralized coordinated neural control is consisted of two controllers, i.e., a multiple model predictive controller (MPC) and an artificial neural network (ANN) controller. The MPC is based on the interaction measurement model and designed to guarantee the performance of system-wide optimization around the chosen operating points, while the ANN controller is used to calculate the weights of MPC controllers and trained to guarantee the control performance over the full operating region. The proposed control strategy allows to reduce the computational cost, and at the same time to take advantage of the distributed nature of the power system. Moreover, a simple, generic hybrid power system is used to demonstrate transient stability contributions. The problems of large-scale WF integration and its impact on transient stabilities of power systems are discussed through the eigenvalue analysis and time domain simulation. The results show that system damping and transient stability of hybrid power system are considerably improved.