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This paper summarises the model reduction techniques used for the reduction of large-scale linear and nonlinear dynamic models, described by the differential and algebraic equations that are commonly used in control theory. The groups of methods discussed in this paper for reduction of the linear dynamic model are based on singular perturbation analysis, modal analysis, singular value decomposition, moment matching and methods based on a combination of singular value decomposition and moment matching. Among the nonlinear dynamic model reduction methods, proper orthogonal decomposition, the trajectory piecewise linear method, balancing-based methods, reduction by optimising system matrices and projection from a linearised model, are described. Part of the paper is devoted to the techniques commonly used for reduction (equivalencing) of large-scale power systems, which are based on coherency, synchrony, singular perturbation analysis, modal analysis and identification. Two (most interesting) of the described techniques are applied to the reduction of the commonly used New England 10-generator, 39-bus test power system.

This paper examines the influence of correlated pseudo measurements on the three-phase (sequence component-based) micro-grid state estimation. Pseudo measurements are used as the external inputs to replace the unavailable real-time measurements on distributed generation (DG) units and loads to provide the minimum bus observability. Output powers of unmonitored DG (photovoltaic and wind-based) units and loads are evaluated using the weather (either measured or forecasted) data, historically recorded state estimation patterns and available real-time measurements. The historical data are classified into clusters by the Self-Organization Map Artificial Neural Network (SOM ANN). The correlation coefficients between dependent pseudo measurements are calculated from clustered weather data and corresponding powers from DG units or loads, where the Feed Forward Artificial Neural Networks (FF ANNs) with backpropagation are used for approximating the output active power of unmonitored elements. The results and practical aspects of the proposed three-phase state estimation methodology with correlated measurements are demonstrated on two (benchmark and real-world) micro-grids. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Planning for contingencies typically results in the use of more expensive facilities before disruptions. It leads to different prices and energy availability at various network locations depending on how the contingency analysis is performed. In this paper we present a two-stage stochastic programming model for incorporating contingencies. The model is computationally demanding, and made tractable by using an interior-point log-barrier method coupled with Benders decomposition. The second-stage optimal recourse function (RF) defines the most economically efficient actions in the post-contingency state for returning the system back to normal operating conditions. The approach is illustrated with for two examples: small (with 8 buses/11 branches) and IEEE medium-scale (with 300 buses/411 branches). [ABSTRACT FROM AUTHOR]

In this paper, we address the issue of quantifying model uncertainties in a deregulated power market. We are interested in a worst-case analysis of effects of network parameter uncertainties on optimization problems that are solved on the level of an independent system operator (ISO). The focus is on linear programming (LP) formulations because of their practical relevance. After briefly reviewing applications of different interval analysis tools (interval matrix inversion and various contractors and solvers for systems of interval equations), we propose two tailored algorithms. In the first (basic LP approach), we propose another solver for a system of linear interval equations, while in the second (power system-customized LP approach), we use features of the power system model to reduce the width of the interval solution. The interval-based results are compared with a deterministic robust noninterval matrix inversion-based solution of a model of the benchmark 68-node New England/New York interconnected power system. Presented analyzes demonstrate that even small parameter variations can have significant impact on optimization. [ABSTRACT FROM AUTHOR]

In this paper, we address the issue of quantifying effects of model uncertainty on transmission security in a power market. The paper addresses two types of uncertainties: 1) structural (e.g., branch outages), which are modeled by contingency scenarios, and 2) perturbations of model parameters (e.g., branch impedance), which are described by sensitivity analysis. The paper embeds these considerations in an optimization procedure that checks if transmission security is maintained and, when necessary, generates minimal corrections in existing contractual transactions that ensure security. Given our interest in real-time applications, we consider problem formulations guaranteeing solution existence and global optimality. A detailed sensitivity analysis based on approximate matrix inversion and linear programming perturbation theory is performed. The paper proposes a linearized ac power flow model to describe the transmission network. The model is studied on a benchmark example of the New England/New York interconnection with 68 nodes. [ABSTRACT FROM AUTHOR]

The paper addresses practical capabilities of artificial neural networks (ANNs) in developing measurement-based continuous-time dynamic equivalents for power systems. Our method is based on a set of measurements at boundary nodes between a subsystem that is to be modeled in detail ("retained" portion of the system) and the part that is to be replaced by a simplified ("equivalent") model. We are particularly interested in combining standard physics-based models with signal-based models derived from measurements. We utilize a color-coding scheme to distinguish between physics-based models (clear or white box) at one end, the signal-based models (opaque or black box) at the opposite end, and mixed (gray box) models in the middle. The paper also proposes a way for combining classical and ANN-based equivalents in a hybrid model implemented in a standard software environment for transient analysis (in this case, ETMSP). Our conclusions are based on simulations performed on a model of a benchmark multimachine power system derived from the WSCC system. [ABSTRACT FROM AUTHOR]

The paper proposes an artificial neural network (ANN)-based strategy for identification of reduced-order dynamic equivalents of power systems. This large-signal model is formulated in continuous-time and is therefore compatible with standard models of power system components. In a departure from previous works on the subject, we do not postulate a particular model structure for the equivalent, hence the label nonparametric. The approach uses only measurements at points where internal (retained) and external (reduced) systems are interfaced, and requires no knowledge of parameters and topology of the external subsystem. The procedure consists of two conceptual steps: 1) the first ("bottleneck") ANN is used to extract "states" of the reduced-order equivalent; and 2) the second (recurrent) ANN is embedded in an ordinary differential equations (ODEs) solver, and trained to approximate the "right-hand side," using the states extracted at the first step. We also describe an extension in which a third ANN is used to synthesize missing interface measurements from a historical database of system responses to various disturbances. We illustrate the capabilities of the approach on a multimachine benchmark example derived from the WSCC system. [ABSTRACT FROM AUTHOR]

In this paper, a fuzzy algorithm for integrated state estimation and load flow analysis in the distribution networks is presented. The algorithm uses an available set of historical data and real-time measurements. The influence of historical data and participation of consumer categories in the node load, as well as influence of real-time measurements on the load estimation, are linguistically described using fuzzy set notation. The corrective fuzzy estimation for minimization of uncertainty fuzzy variables is based on available real-time measurements. Fuzzy solutions can be used directly, as input data for other distribution management system (DMS) fuzzy applications, or indirectly, in the classical algorithms (after the defuzzification is performed). The results and practical aspects of the proposed methodology application on two characteristic real-life distribution networks are presented. [ABSTRACT FROM AUTHOR]