Power System Small-disturbance Stability Research Articles

Power system small-disturbance stability analysis and control design: A characteristic locus method

A characteristic locus method developed from the celebrated generalized Nyquist criterion is proposed for power systems small-disturbance stability analysis and control design in this paper. First, a loop transformation is introduced to re-formulate the familiar Heffron-Phillips model. The new model has a feedback control structure so that the generalized Nyquist criterion is applicable when concluding the stability of the closed-loop system. Subsequently, the relationship between generalized Nyquist curve and characteristic loci is utilized to acquire a new stability margin. The effectiveness of the stability margin is demonstrated using Cassini Oval Theorem. An analytical expression of the stability margin is derived as well. It is convenient to quantify the effects of control loops on stability margin by applying this expression. Moreover, the analytical relationship between stability margin and frequency responses of controllers provides information for the design of the controllers. The utility of the proposed method is confirmed through case studies.

Ellipsoidal Design of Robust Stabilization of Power Systems Exposed to a Cycle of Lightning Surges Modeled by Continuous-Time Markov Jumps

Power system stability is greatly affected by two types of stochastic or random disturbances: (1) topological and (2) parametric. The topological stochastic disturbances due to line faults caused by a series of lightning strikes (associated with circuit breaker, C.B., opening, and auto-reclosing) are modeled in this paper as continuous-time Markov jumps. Additionally, the stochastic parameter changes e.g., the line reactance, are influenced by the phase separation, which in turn depends on the stochastic wind speed. This is modeled as a stochastic disturbance. In this manuscript, the impact of the above stochastic disturbance on power system small-disturbance stability is studied based on stochastic differential equations (SDEs). The mean-square stabilization of such a system is conducted through a novel excitation control. The invariant ellipsoid and linear matrix inequality (LMI) optimization are used to construct the control system. The numerical simulations are presented on a multi-machine test system.

Application of game theoretic approaches for identification of critical parameters affecting power system small-disturbance stability

This paper evaluates a number of game theoretic (GT) approaches with the aim of assessing their suitability to identify the most influential parameters affecting the small-disturbance stability of a power system. Identification of the most influential parameters affecting system stability will facilitate cost-effective operation and control of a power system in general as it would require limited network monitoring, control and modelling effort by system operators and stakeholders. After identifying the most influential parameters the financial and human resources could be adequately prioritised and deployed to solve or prevent power system stability problems. A priority ranking procedure based on a GT approach has the advantage, compared to other techniques, of considering simultaneously the effect of individual and all possible combinatorial effects of the uncertain parameters (or players in a game context). In this study, the most influential players have been identified through a multi-level approach considering the power flow in the network (by optimal power flow), small disturbance stability aspects (by modal analysis), rational behavior of individual players (by a sensitivity technique) and formation of groups between players (by cooperative game theory). Various GT approaches have been considered namely Shapley Value, Aumann Shapley, Nucleolus, and τ-value approach in order to compare and assess their suitability for power system applications. The results are illustrated using two test networks and considering several approaches of sensitivity analysis and different degrees of variability in the considered uncertainties.

Priority Ranking of Critical Uncertainties Affecting Small-Disturbance Stability Using Sensitivity Analysis Techniques

This paper critically evaluates a number of sensitivity analysis (SA) techniques to identify the most influential parameters affecting power system small-disturbance stability. SA of uncertain parameters has attracted increased attention with the adoption of deregulated market structure, intermittent energy resources, and new types of loads. Identification of the most influential parameters affecting system stability using SA techniques will facilitate better operation and control with reduced monitoring (only of the parameters of interest) by system operators and stakeholders. In total, nine SA techniques have been described, implemented, and compared in this paper. These can be categorized into three different types: local, screening, and global SA. This comparative analysis highlights their computational complexity and simulation time. The methods have been illustrated using a two-area power system and 68 bus NETS-NYPS test system. The priority ranking of all uncertain parameters has been evaluated, identifying the most critical parameters with respect to the small-signal stability of the test systems. It is shown that for many applications, the Morris screening approach is most suitable, providing a good balance between accuracy and efficiency.

The Influence of Wind Power Grid to Power System Small Disturbance Stability Study

Setting up a practical power system containing wind farm small disturbance stability mathematical model, and the linearized equation of wind turbines and original equations of linear system, power system containing wind turbines augmented state formation matrix, turn the inverse iteration with PSASP software Rayleigh (Rayleigh quotient iterative algorithm and sparse matrix technique for large state matrix eigenvalues. In this paper, the Inner Mongolia power grid, wind power access to power system oscillation mode and the influence of the oscillation characteristics and meet the requirements of small disturbance stability of wind scale and operation control scheme. The influence of the wind farm is proposed for power system damping characteristics will not greater than the same capacity of synchronous generator's point of view.

Power system voltage small-disturbance stability studies based on the power flow equation

This study first studies power system small-disturbance stability at the operating point where the power flow (PF) equation encounters a saddle-node bifurcation. The authors demonstrate that the linearised model of the differential-algebraic equation (DAE) that describes the power system dynamics will have a zero eigenvalue at the equilibrium precisely when the PF Jacobian is singular. Note that the PF equation and DAE models are general ones. This clarifies a point in previous contributions on this relationship. Numerical results for two power system examples are used to demonstrate the theory, and finally the extension of the theory is discussed for the limit-induced bifurcation associated with the PF equation when some generators reach their reactive power limits.

Optimisation-based control coordination of PSSs and FACTS devices for optimal oscillations damping in multi-machine power system

An optimal procedure for designing co-ordinated controllers of power system stabiliser and flexible ac transmission system devices is developed for achieving and enhancing small-disturbance stability in multi-machine power systems. A constrained optimisation approach is applied for minimising an objective function formed from selected eigenvalues of the power systems state matrix. The eigenvalue–eigenvector equations associated with the selected modes form a set of equality constraints in the optimisation. There is no need for any standard eigenvalue calculation routines, and the use of sparse Jacobian matrix in the case of large system for forming the eigenvalue–eigenvector equations leads to the sparsity formulation. Inequality constraints include those for imposing bounds on the controller parameters. Constraints which guarantee that the modes are distinct ones are derived and incorporated in the control coordination formulation using the property that eigenvectors associated with distinct modes are linearly independent. The robustness of the controllers is achieved very directly through extending the sets of equality constraints and inequality constraints in relation to selected eigenvalues and eigenvectors associated with the state matrices of power systems with loading conditions and/or network configurations different from that of the base case. Simulation results of a multi-machine power system confirm that the procedure is effective in designing controllers that guarantee and enhance the power system small-disturbance stability.

Identification of Electromechanical Modes and Placement of PSSs Using Relative Gain Array

The paper investigates the possibility to use relative gain array (RGA) for power system small-disturbance stability analysis. The RGA has been successfully used in the past as steady state measure of interactions for multivariable, decentralized control in chemical and process engineering. The effectiveness of the RGA in identifying electromechanical modes and selecting the optimal location for placement of PSSs is compared with the conventional approach that uses transfer function residues, eigenvalues and participation factors. Two different multimachine power systems are used for the case studies. Limitations and advantages of the use of RGA in this purpose are clearly indicated in the paper.

Revealing loads having the biggest influence on power system small disturbance stability

The paper presents a novel approach to reveal loads having the biggest impact on damping of small-disturbed oscillations in power systems. The technique is based on a quasi-optimisation procedure with the cost function reflecting shifts of selected eigenvalues along the real axis when all unknown load parameters are varied within their constraints. The cost function takes into consideration a variety of power system operating conditions. All points of the cost function steepest descent trajectory, obtained in the space of unknown load parameters, correspond locally to biggest shifts of eigenvalues. Participation factors of load parameters are computed along the steepest descent trajectory, and they give ranks of load importance. Small ranks indicate loads which have no influence on damping of selected modes. Big ranks reveal loads whose parameters cause the biggest change in damping under the most unfavourable combination of unknown parameters. Parameters with biggest ranks should be measured first of all to avoid mistakes in evaluation of damping properties and power system stability margins.

Characterization of power system small disturbance stability with models incorporating voltage variation

The small disturbance (SD) stability of a power system is studied with the model including generator swing equations, the real and reactive power flow equations. The effects of voltage variation and reactive power constraints are thus explicitly represented in the model. It is shown that the necessary and sufficient condition for an operating point to be SD stable is that the reduced matrix from the power flow Jacobian is positive definite. A sufficient condition is that the power flow Jacobian itself is positive definite. The result is compared to the one obtained from the constant voltage model and the latter is shown to be more optimistic. Also derived are conditions for steady-state security regions to be SD stable.