Abstract: Due to the increasing penetration of wind energy, it is
necessary to possess design tools that are able to simulate the impact
of these installations in utility grids. In order to provide a net
contribution to this issue a detailed wind park model has been
developed and is briefly presented. However, the computational costs
associated with the performance of such a detailed model in
describing the behavior of a wind park composed by a considerable
number of units may render its practical application very difficult. To
overcome this problem integral manifolds theory has been applied to
reduce the order of the detailed wind park model, and therefore
create the conditions for the development of a dynamic equivalent
which is able to retain the relevant dynamics with respect to the
existing a.c. system. In this paper integral manifold method has been
introduced for order reduction. Simulation results of the proposed
method represents that integral manifold method results fit the
detailed model results with a higher precision than singular
perturbation method.
Abstract: Recently, genetic algorithms (GA) and particle swarm optimization (PSO) technique have attracted considerable attention among various modern heuristic optimization techniques. The GA has been popular in academia and the industry mainly because of its intuitiveness, ease of implementation, and the ability to effectively solve highly non-linear, mixed integer optimization problems that are typical of complex engineering systems. PSO technique is a relatively recent heuristic search method whose mechanics are inspired by the swarming or collaborative behavior of biological populations. In this paper both PSO and GA optimization are employed for finding stable reduced order models of single-input- single-output large-scale linear systems. Both the techniques guarantee stability of reduced order model if the original high order model is stable. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example from literature and the results are compared with recently published conventional model reduction technique.
Abstract: The authors present an algorithm for order reduction of linear dynamic systems using the combined advantages of stability equation method and the error minimization by Genetic algorithm. The denominator of the reduced order model is obtained by the stability equation method and the numerator terms of the lower order transfer function are determined by minimizing the integral square error between the transient responses of original and reduced order models using Genetic algorithm. The reduction procedure is simple and computer oriented. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The proposed algorithm has also been extended for the order reduction of linear multivariable systems. Two numerical examples are solved to illustrate the superiority of the algorithm over some existing ones including one example of multivariable system.
Abstract: Reduction of Single Input Single Output (SISO) discrete systems into lower order model, using a conventional and an evolutionary technique is presented in this paper. In the conventional technique, the mixed advantages of Modified Cauer Form (MCF) and differentiation are used. In this method the original discrete system is, first, converted into equivalent continuous system by applying bilinear transformation. The denominator of the equivalent continuous system and its reciprocal are differentiated successively, the reduced denominator of the desired order is obtained by combining the differentiated polynomials. The numerator is obtained by matching the quotients of MCF. The reduced continuous system is converted back into discrete system using inverse bilinear transformation. In the evolutionary technique method, Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.
Abstract: The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical examples taken from the literature.
Abstract: In this paper, real-coded genetic algorithm (RCGA) optimization technique has been applied for large-scale linear dynamic multi-input-multi-output (MIMO) system. The method is based on error minimization technique where the integral square error between the transient responses of original and reduced order models has been minimized by RCGA. The reduction procedure is simple computer oriented and the approach is comparable in quality with the other well-known reduction techniques. Also, the proposed method guarantees stability of the reduced model if the original high-order MIMO system is stable. The proposed approach of MIMO system order reduction is illustrated with the help of an example and the results are compared with the recently published other well-known reduction techniques to show its superiority.
Abstract: A computationally simple approach of model order
reduction for single input single output (SISO) and linear timeinvariant
discrete systems modeled in frequency domain is proposed
in this paper. Denominator of the reduced order model is determined
using fuzzy C-means clustering while the numerator parameters are
found by matching time moments and Markov parameters of high
order system.
Abstract: Design of a fixed parameter robust STATCOM controller for a multi-machine power system through an H-? based loop-shaping procedure is presented. The trial and error part of the graphical loop-shaping procedure has been eliminated by embedding a particle swarm optimization (PSO) technique in the design loop. Robust controllers were designed considering the detailed dynamics of the multi-machine system and results were compared with reduced order models. The robust strategy employing loop-shaping and PSO algorithms was observed to provide very good damping profile for a wide range of operation and for various disturbance conditions.