Control of large-scale dynamic systems by aggregation
TL;DR: Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived and questions of performance degradation and of stability of such suboptimally controlled systems are answered.
Abstract: A method is proposed to obtain a model of a dynamic system with a state vector of high dimension. The model is derived by "aggregating" the original system state vector into a lower-dimensional vector. Some properties of the aggregation method are investigated in the paper. The concept of aggregation, a generalization of that of projection, is related to that of state vector partition and is useful not only in building a model of reduced dimension, but also in unifying several topics in the control theory such as regulators with incomplete state feedback, characteristic value computations, model controls, and bounds on the solution of the matrix Riccati equations, etc. Using the quantitative definition of weak coupling proposed by Milne, a suboptimal control policy for the weakly coupled system is derived. Questions of performance degradation and of stability of such suboptimally controlled systems are also answered in the paper.
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Dissertation•
01 Jan 2014
TL;DR: In this article, the development of dynamic equivalent models for large scale wind power plants is presented for large-scale wind power systems. But the model is not suitable for wind power generation.
Abstract: Development of Dynamic Equivalent Models for Large Scale Wind Power Plants
1 citations
Cites background from "Control of large-scale dynamic syst..."
...Notes [67]–[69] explain the main concept of model equivalencing....
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TL;DR: In this paper, the first and second-order eigenvalue sensitivities of aggregated models with respect to the parameters of the original high-order system were derived and it was shown that these sensitivities are identical with the corresponding sensitivities in the original system and independent of the choice of the aggregation matrix.
Abstract: Analytical expressions are derived for first- and second-order eigenvalue sensitivities of aggregated models with respect to the parameters of the original high-order system. It is shown that these sensitivities are identical with the corresponding sensitivities of the original system and independent of the choice of the aggregation matrix. A numerical example is included to illustrate the results.
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TL;DR: In this article , an effective frequency control strategy is proposed for emulating sufficient inertia power and improving frequency stability, which is based on applying virtual inertia control with superconducting magnetic energy storage (SMES) instead of a traditional energy storage system (ESS) to compensate for the system inertia during the high penetration of renewable energy sources, taking into account the role of the controller in the secondary control loop (SCL).
Abstract: In this paper, an effective frequency control strategy is proposed for emulating sufficient inertia power and improving frequency stability. The developed technique is based on applying virtual inertia control (VIC) with superconducting magnetic energy storage (SMES) instead of a traditional energy storage system (ESS) to compensate for the system inertia during the high penetration of renewable energy sources, taking into account the role of the controller in the secondary control loop (SCL). Unlike previous studies that depended on the designer experience in selecting the parameters of the inertia gain or the parameters of the SMES technology, the parameters of the proposed strategy are selected using optimization techniques. Moreover, an improved optimization algorithm called Improved Social Network Search algorithm (ISNS) is proposed to select the optimal parameters of the proposed control strategy. Moreover, the ISNS is improved to overcome the demerits of the traditional SNS algorithm, such as low speed convergence and global search capability. Accordingly, the ISNS algorithm is applied to a hybrid two-area power grid to determine the optimal parameters of the proposed control technique as follows: the proportional-integral derivative (PID) controller in the SCL. Additionally, the ISNS is applied to select the optimal control gains of the VIC-based SMES technology (e.g., the inertia gain, the proportional gain of the SMES, and the negative feedback gain of the SMES). Furthermore, the effectiveness of the proposed ISNS algorithm is validated by comparing its performance with that of the traditional SNS algorithm and other well-known algorithms (i.e., PSO, TSA, GWO, and WHO) considering different standard benchmark functions. Formerly, the effectiveness of the proposed frequency control technique was confirmed by comparing its performance with the system performance based on optimal VIC with ESS as well as without VIC considering different operating situations. The simulation results demonstrated the superiority of the proposed technique over other considered techniques, especially during high penetration of renewable power and lack of system inertia. As a result, the proposed technique is credible for modern power systems that take into account RESs.
1 citations
01 Dec 1981
TL;DR: In this article, a unified treatment of aggregability, lumpability, coherency and similar properties allowing model simplification is presented, where each of the N groups of states is represented by one aggregate variable and an aggregate model is formed.
Abstract: This paper presents a unified treatment of aggregability, lumpability, coherency and similar properties allowing model simplification. Each of the N groups of states is represented by one aggregate variable and an aggregate model is formed. Interpretation is given when groups are coherent, but not aggregable and vice-versa. In a class of systems aggregability and coherency hold simultaneously.
1 citations
TL;DR: An overview of a recently proposed computer-science perspective to ODE reduction is recast to finding an appropriate equivalence relation over ODE variables, akin to classical models of computation based on labelled transition systems.
Abstract: Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of effectively performing analyses. This has motivated a large body of research, across many disciplines, into abstraction techniques that provide smaller ODE systems while preserving the original dynamics in some appropriate sense. In this paper we give an overview of a recently proposed computer-science perspective to this problem, where ODE reduction is recast to finding an appropriate equivalence relation over ODE variables, akin to classical models of computation based on labelled transition systems.
1 citations
Cites background from "Control of large-scale dynamic syst..."
...Here, starting from the seminal paper [1], many approaches have been proposed to reduce the original model in a way that preserves controllability, i....
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TL;DR: A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations.
Abstract: A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations. The coordinating program generates at each cycle new objective forms for each part, and each part generates in turn from its optimal basic feasible solutions new activities columns for the interconnecting program. Viewed as an instance of a “generalized programming problem” whose columns are drawn freely from given convex sets, such a problem can be studied by an appropriate generalization of the duality theorem for linear programming, which permits a sharp distinction to be made between those constraints that pertain only to a part of the problem and those that connect its parts. This leads to a generalization of the Simplex Algorithm, for which the decomposition procedure becomes a special case. Besides holding promise for the efficient computation of large-scale systems, the principle yields a certain rationale for the “decentralized decision process” in the theory of the firm. Formally the prices generated by the coordinating program cause the manager of each part to look for a “pure” sub-program analogue of pure strategy in game theory, which he proposes to the coordinator as best he can do. The coordinator finds the optimum “mix” of pure sub-programs using new proposals and earlier ones consistent with over-all demands and supply, and thereby generates new prices that again generates new proposals by each of the parts, etc. The iterative process is finite.
2,281 citations
01 Jan 1960
TL;DR: In this article, the authors considered the problem of least square feedback control in a linear time-invariant system with n states, and proposed a solution based on the concept of controllability.
Abstract: THIS is one of the two ground-breaking papers by Kalman that appeared in 1960—with the other one (discussed next) being the filtering and prediction paper. This first paper, which deals with linear-quadratic feedback control, set the stage for what came to be known as LQR (Linear-Quadratic-Regulator) control, while the combination of the two papers formed the basis for LQG (Linear-Quadratic-Gaussian) control. Both LQR and LQG control had major influence on researchers, teachers, and practitioners of control in the decades that followed. The idea of designing a feedback controller such that the integral of the square of tracking error is minimized was first proposed by Wiener [17] and Hall [8], and further developed in the influential book by Newton, Gould and Kaiser [12]. However, the problem formulation in this book remained unsatisfactory from a mathematical point of view, but, more importantly, the algorithms obtained allowed application only to rather low order systems and were thus of limited value. This is not surprising since it basically took until theH2-interpretation in the 1980s of LQG control before a satisfactory formulation of least squares feedback control design was obtained. Kalman’s formulation in terms of finding the least squares control that evolves from an arbitrary initial state is a precise formulation of the optimal least squares transient control problem. The paper introduced the very important notion of c ntrollability, as the possibility of transfering any initial state to zero by a suitable control action. It includes the necessary and sufficient condition for controllability in terms of the positive definiteness of the Controllability Grammian, and the fact that the linear time-invariant system withn states,
1,451 citations
TL;DR: A method is proposed for reducing large matrices by constructing a matrix of lower order which has the same dominant eigenvalues and eigenvectors as the original system.
Abstract: Often it is possible to represent physical systems by a number of simultaneous linear differential equations with constant coefficients, \dot{x} = Ax + r but for many processes (e.g., chemical plants, nuclear reactors), the order of the matrix A may be quite large, say 50×50, 100×100, or even 500×500. It is difficult to work with these large matrices and a means of approximating the system matrix by one of lower order is needed. A method is proposed for reducing such matrices by constructing a matrix of lower order which has the same dominant eigenvalues and eigenvectors as the original system.
614 citations
TL;DR: In this article, a constructive design procedure for the problem of estimating the state vector of a discrete-time linear stochastic system with time-invariant dynamics when certain constraints are imposed on the number of memory elements of the estimator is presented.
Abstract: The paper presents a constructive design procedure for the problem of estimating the state vector of a discrete-time linear stochastic system with time-invariant dynamics when certain constraints are imposed on the number of memory elements of the estimator. The estimator reconstructs the state vector exactly for deterministic systems while the steady-state performance in the stochastic case may be comparable to that obtained by the optimal (unconstrained) Wiener-Kalman filter.
68 citations
67 citations