Book•
Nonlinear control systems and power system dynamics
01 Jan 2001-
TL;DR: This book discusses the design Principles of Single-Input Single-Output Nonlinear Control Systems and their applications in Electric Power Systems and Nonlinear Excitation Control of Large Synchronous Generators.
Abstract: Preface. 1. Introduction. 2. Basic Concepts of Nonlinear Control Theory. 3. Design Principles of Single-Input Single-Output Nonlinear Control Systems. 4. Design Principles of Multi-Input Multi-Output Nonlinear Control Systems. 5. Basic Mathematical Descriptions for Electric Power Systems. 6. Nonlinear Excitation Control of Large Synchronous Generators. 7. Nonlinear Steam Valving Control. 8. Nonlinear Control of HVDC Systems. 9. Nonlinear Control of Static Var Systems. 10. Nonlinear Robust Control of Power Systems. Index.
Citations
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TL;DR: By modeling the disturbances and parameter uncertainties into the LFC model, an adaptive supplementary control scheme for the power system frequency regulation is proposed and an improved sliding mode control (SMC) is employed as the basic controller.
Abstract: Randomness from the power load demand and renewable generations causes frequency oscillations among interconnected power systems. Due to the requirement of synchronism of the whole grid, load frequency control (LFC) has become one of the essential challenges for power system stability and security. In this paper, by modeling the disturbances and parameter uncertainties into the LFC model, we propose an adaptive supplementary control scheme for the power system frequency regulation. An improved sliding mode control (SMC) is employed as the basic controller, where a new sliding mode variable is specifically proposed for the LFC problem. The adaptive dynamic programming strategy is used to provide the supplementary control signal, which is beneficial to the frequency regulation by adapting to the real-time disturbances and uncertainties. The stability analysis is also provided to guarantee the reliability of the proposed control strategy. For comparison, a particle swarm optimization-based SMC scheme is developed as the optimal parameter controller for the frequency regulation problem. Simulation studies are performed on single-area and multiarea benchmark systems, and comparative results illustrate the favorable performance of the proposed adaptive approach for the frequency regulation under load disturbances and parameter uncertainties.
167 citations
Cites methods from "Nonlinear control systems and power..."
...Several control methods have been used in this topic [3], [5], [7]–[9], such as proportional–integral (PI) control, internal model control, fuzzy logic control, intelligent control, etc....
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TL;DR: In this article, a nonlinear controller is designed based on the proposed model to prolong the stack life of the PEM fuel cells, which is known that large deviations between hydrogen and oxygen partial pressures can cause severe membrane damage in the fuel cell.
Abstract: This paper presents a dynamic nonlinear model for polymer electrolyte membrane fuel cells (PEMFCs). A nonlinear controller is designed based on the proposed model to prolong the stack life of the PEM fuel cells. Since it is known that large deviations between hydrogen and oxygen partial pressures can cause severe membrane damage in the fuel cell, feedback linearization is applied to the PEM fuel cell system so that the deviation can be kept as small as possible during disturbances or load variations. A dynamic PEM fuel cell model is proposed as a nonlinear, multiple-input multiple-output system so that feedback linearization can be directly utilized. During the control design, hydrogen and oxygen inlet flow rates are defined as the control variables, and the pressures of hydrogen and oxygen are appropriately defined as the control objectives. The details of the design of the control scheme are provided in the paper. The proposed dynamic model was tested by comparing the simulation results with the experimental data previously published. The simulation results show that PEMFCs equipped with the proposed nonlinear controls have better transient performances than those with linear controls.
156 citations
Cites background from "Nonlinear control systems and power..."
...More details of nonlinear control based on differential geometry are available in [26]–[28], [34]....
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TL;DR: In this article, a nonlinear excitation controller design to enhance transient stability of multimachine power systems is presented, where a linear state feedback stabilizing controller is designed for the reduced-order linear part using optimal control theory to enhance the stability of the whole system.
Abstract: In this paper a new nonlinear excitation controller design to enhance transient stability of multimachine power systems is presented Partial feedback linearization is first used to transform the nonlinear power system model into a partially linear system comprising a reduced-order linear part and a nonlinear dynamic autonomous part Then a linear state feedback stabilizing controller is designed for the reduced-order linear part using optimal control theory to enhance the stability of the whole system In this way, the performance of the stabilizing controller would be independent of the operating points of the power system and therefore is superior to those designed for completely linearized systems It is shown that the controller design method ensures the stability of the nonlinear dynamic autonomous part The design method is applicable to multimachine power systems but tested on a 3-machine 11-bus two-area test system The performance of the proposed control scheme to large disturbances is evaluated, through computer simulation, and compared with a conventional power system stabilizer and an exact feedback linearizing controller
140 citations
Cites methods from "Nonlinear control systems and power..."
...If we chose the last transformation as [51]...
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...For a multimachine power system, the exact feedback linearizing control law can be written as follows [51]:...
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DOI•
15 Apr 2003TL;DR: In this paper, a framework for optimal load-frequency control (LFC) in deregulated environments is proposed, where the objective function of optimisation incorporates both the indices of economy and stability with their own physical meanings.
Abstract: A framework for optimal load-frequency control (LFC) in deregulated environments is proposed. The objective function of optimisation incorporates both the indices of economy and stability with their own physical meanings. Under this framework, the problem of market-based optimal LFC is formulated to be an optimisation problem of functional extremum. Since the structure-preserving model of power systems is adopted in order to consider the characteristics of loads, the optimisation problem is constrained by differential algebraic-equation systems (DAEs). Then a quasi-Newton algorithm is put forward to solve the formulated optimal DAEs-constrained optimisation problem. Simulation is carried out on the IEEE 30-bus system with different market structures. It is shown that the proposed framework and the corresponding algorithm are effective, and can achieve optimal operation of power systems in terms of both security and economy.
131 citations
TL;DR: To control the grid current and dc-link voltage, the zero dynamic design approach of feedback linearization is used, which linearizes the system partially and enables controller design for reduced-order PV system.
Abstract: This paper presents a new approach to control the grid current and dc-link voltage for maximum power point tracking and improvement of the dynamic response of a three-phase grid-connected photovoltaic (PV) system. To control the grid current and dc-link voltage, the zero dynamic design approach of feedback linearization is used, which linearizes the system partially and enables controller design for reduced-order PV system. This paper also describes the zero dynamic stability of the three-phase grid-connected PV system, which is a key requirement for the implementation of such controllers. Simulation results on a large-scale grid-connected PV system show the effectiveness of the proposed control scheme in terms of delivering maximum power into the grid.
126 citations
Cites background from "Nonlinear control systems and power..."
...This needs to be selected in such a way that it must satisfy the following conditions [21]:...
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References
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TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
Abstract: Simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: For a given number gamma >0, find all controllers such that the H/sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma . It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma /sup 2/. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable, free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e. H/sub 2/) theory. This paper is intended to be of tutorial value, so a standard H/sub 2/ solution is developed in parallel. >
5,272 citations
TL;DR: In this paper, a general theory of dissipative dynamical systems is presented, where dissipativeness is defined in terms of an inequality involving the storage function and the supply function, which is bounded from below by the available storage and from above by the required supply.
Abstract: The first part of this two-part paper presents a general theory of dissipative dynamical systems. The mathematical model used is a state space model and dissipativeness is defined in terms of an inequality involving the storage function and the supply function. It is shown that the storage function satisfies an a priori inequality: it is bounded from below by the available storage and from above by the required supply. The available storage is the amount of internal storage which may be recovered from the system and the required supply is the amount of supply which has to be delivered to the system in order to transfer it from the state of minimum storage to a given state. These functions are themselves possible storage functions, i.e., they satisfy the dissipation inequality. Moreover, since the class of possible storage functions forms a convex set, there is thus a continuum of possible storage functions ranging from its lower bound, the available storage, to its upper bound, the required supply. The paper then considers interconnected systems. It is shown that dissipative systems which are interconnected via a neutral interconnection constraint define a new dissipative dynamical system and that the sum of the storage functions of the individual subsystems is a storage function for the interconnected system. The stability of dissipative systems is then investigated and it is shown that a point in the state space where the storage function attains a local minimum defines a stable equilibrium and that the storage function is a Lyapunov function for this equilibrium. These results are then applied to several examples. These concepts and results will be applied to linear dynamical systems with quadratic supply rates in the second part of this paper.
3,124 citations
TL;DR: The theory of dissipative systems in the context of finite dimensional stationary linear systems with quadratic supply rates has been studied in this paper, where a necessary and sufficient frequency domain condition for dissipativeness is derived.
Abstract: This paper presents the theory of dissipative systems in the context of finite dimensional stationary linear systems with quadratic supply rates. A necessary and sufficient frequency domain condition for dissipativeness is derived. This is followed by the evaluation of the available storage and the required supply and of a time-domain criterion for dissipativeness involving certain matrix inequalities. The quadratic storage functions and the dissipation functions are then examined. The discussion then turns to reciprocal systems and it is shown that external reciprocity and dissipativeness imply the existence of a state space realization which is also internally reciprocal and dissipative. The paper proceeds with an examination of reversible systems and of relaxation systems. In particular, it is shown how a unique internal storage function may be defined for relaxation systems. These results are applied to the synthesis of electrical networks and the theory of linear viscoelastic materials.
1,061 citations
TL;DR: In this article, a technique for generating Lyapunov functions for a broad class of nonlinear systems represented by state equations is presented, where dissipativeness is characterized by the existence of a computable function which can be interpreted as the stored energy of the system.
Abstract: This short paper presents a technique for generating Lyapunov functions for a broad class of nonlinear systems represented by state equations. The system, for which a Lyapunov function is required, is assumed to have a property called dissipativeness. Roughly speaking, this means that the system absorbs more energy from the external world than it supplies. Different types of dissipativeness can be considered depending on how one chooses to define "power input." Dissipativeness is shown to be characterized by the existence of a computable function which can be interpreted as the "stored energy" of the system. Under certain conditions, this energy function is a Lyapunov function which establishes stability, and in some cases asymptotic stability, of the isolated system.
1,032 citations