Damping Power System Electromechanical Oscillations Using Time Delays

This paper proposes to utilize intentional time delays as part of controllers to improve the damping of electromechanical oscillations of power systems. Through stability theory, the control parameter settings for which these delays in Power System Stabilizers (PSSs) improve the small signal stability of a power system are systematically identified, including the key parameter settings for which stability regions in the parameter plane remain connected for effective operation. The paper shows that PSSs with two control channels can be effectively designed to achieve best damping characteristics for a wide range of delays. Analytical results are presented on the One-Machine Infinite-Bus (OMIB) electromechanical power system model. To demonstrate the opportunities in more realistic dynamic models, our results are then implemented via numerical analysis on the IEEE standard 14-bus system.Science Foundation Irelan

Sampled-data implementation of derivative-dependent control using artificial delays

We study a sampled-data implementation of linear controllers that depend on the output and its derivatives. First, we consider an LTI system of relative degree $r\ge 2$ that can be stabilized using $r-1$ output derivatives. Then, we consider PID control of a second order system. In both cases, the Euler approximation is used for the derivatives giving rise to a delayed sampled-data controller. Given a derivative-dependent controller that stabilizes the system, we show how to choose the parameters of the delayed sampled-data controller that preserves the stability under fast enough sampling. The maximum sampling period is obtained from LMIs that are derived using the Taylor's expansion of the delayed terms with the remainders compensated by appropriate Lyapunov-Krasovskii functionals. Finally, we introduce the event-triggering mechanism that may reduce the amount of sampled control signals used for stabilization

Improved sampled-data implementation of derivative-dependent control

We consider an LTI system of relative degree two that can be stabilized using the output and its derivative. The derivative is approximated using a finite difference, what leads to a time-delayed feedback. This feedback is analyzed using a Lyapunov-Krasovskii functional that compensates the derivative approximation error presented in an integral form. We show that if the derivative-dependent control exponentially stabilizes the system, then one can use consecutively sampled measurements to approximate the derivative and this approximation will preserve the stability if the sampling period is small enough. We provide linear matrix inequalities that allow to find admissible sampling period and can be used for robustness analysis with respect to system uncertainties. The results are demonstrated by two examples: 2D uncertain system and the Furuta pendulum

An improved time-delay implementation of derivative-dependent feedback

We consider an LTI system of relative degree that can be stabilized using output derivatives. The derivatives are approximated by finite differences leading to a time-delayed feedback. We present a new method of designing and analyzing such feedback under continuous-time and sampled measurements. This method admits essentially larger time-delay/sampling period compared to the existing results and, for the first time, allows to use consecutively sampled measurements in the sampled-data case. The main idea is to present the difference between the derivative and its approximation in a convenient integral form. The kernel of this integral is hard to express explicitly but we show that it satisfies certain properties. These properties are employed to construct the Lyapunov–Krasovskii functional that leads to LMI-based stability conditions. If the derivative-dependent control exponentially stabilizes the system, then its time-delayed approximation stabilizes the system with the same decay rate provided the time-delay (for continuous-time measurements) or the sampling period (for sampled measurements) are small enough

On qualitative properties of single-delay linear retarded differential equations: Characteristic roots of maximal multiplicity are necessarily dominant

International audienceThis paper presents necessary and sufficient conditions for the existence of a real root of maximal multiplicity in the spectrum of a linear time-invariant single-delay equation of retarded type. We also prove that this root is always strictly dominant, and hence determines the asymptotic behavior of the system. These results are based on improved a priori bounds on the imaginary part of roots on the complex right half-plane

Robust and Optimal PID Controller Synthesis for Linear Time Invariant Systems

We dealt with new approaches to the design of Proportional-Integral-Derivative (PID) controllers and solved three important open problems: 1) Optimal design of H∞ continuous time controllers 2) Optimal design of H∞ discrete time controllers and 3) Design of PID controllers for prescribed settling time. We also deal with optimal Dynamic Compensator design for controllable and observable systems. The main result of the first problem is a constructive determination of the set Sγ of stabilizing continuous PI and PID controllers achieving an H∞ norm bound of γ on the error transfer function. This result utilizes the computation of the complete stabilizing set S. We also point out connections between this H∞ design and Gain and Phase Margin designs. The main result of the second problem is a constructive characterization of the set Sγ of stabilizing digital controllers achieving a prescribed bound γ on the error transfer function. This is accomplished by utilizing the computation of S, the set of all PID stabilizing controllers. The minimum achievable γ, denoted γ∗ is also determined. The main result of the third problem is a constructive determination of the set S(σ) of stabilizing PI and PID controllers with closed loop poles having real parts less than −σ. The signature method is applied to obtain the set S(σ) in the controller parameter space. The maximum achievable σ for a given plant is also determined. The main result of the last problem is a new approach to design an optimal dynamic compensator. The system is augmented with a proper number of integrators and the state feedback of the augmented system is considered with a design parameter. The dynamic compensator is then designed such that the eigenvalues of the augmented system is identical to the closed loop specboundtrum of the implemented system with the compensator. By sweeping over the design parameter, multiple design specifications are compared within achievable boundary of performances

Robust and Optimal PID Controller Synthesis for Linear Time Invariant Systems

We dealt with new approaches to the design of Proportional-Integral-Derivative (PID) controllers and solved three important open problems: 1) Optimal design of H∞ continuous time controllers 2) Optimal design of H∞ discrete time controllers and 3) Design of PID controllers for prescribed settling time. We also deal with optimal Dynamic Compensator design for controllable and observable systems. The main result of the first problem is a constructive determination of the set Sγ of stabilizing continuous PI and PID controllers achieving an H∞ norm bound of γ on the error transfer function. This result utilizes the computation of the complete stabilizing set S. We also point out connections between this H∞ design and Gain and Phase Margin designs. The main result of the second problem is a constructive characterization of the set Sγ of stabilizing digital controllers achieving a prescribed bound γ on the error transfer function. This is accomplished by utilizing the computation of S, the set of all PID stabilizing controllers. The minimum achievable γ, denoted γ∗ is also determined. The main result of the third problem is a constructive determination of the set S(σ) of stabilizing PI and PID controllers with closed loop poles having real parts less than −σ. The signature method is applied to obtain the set S(σ) in the controller parameter space. The maximum achievable σ for a given plant is also determined. The main result of the last problem is a new approach to design an optimal dynamic compensator. The system is augmented with a proper number of integrators and the state feedback of the augmented system is considered with a design parameter. The dynamic compensator is then designed such that the eigenvalues of the augmented system is identical to the closed loop specboundtrum of the implemented system with the compensator. By sweeping over the design parameter, multiple design specifications are compared within achievable boundary of performances

Linear time-delay systems: the complete type functionals approach

[EN] Recent results on Lyapunov-Krasovskii functionals of complete type for linear time-delay systems are presented. The main concepts and results are introduced for the single delay system case, and necessary and sufficient stability conditions expressed in terms of the Lyapunov delay matrix are explained. The use of complete type functionals in analysis and controller design is discussed. The contribution focuses mainly at results of researchers in Mexico.[ES] Se introducen resultados recientes del enfoque de funcionales de Lyapunov-Krasovski de tipo completo para sistemas lineales con retardos. Se explican brevemente los principales conceptos y resultados para el caso de sistemas con un retardo así como las condiciones necesarias y suficientes de estabilidad expresadas en terminos del análogo de la matriz de Lyapunov. Las extensiones  de este tipo de condiciones de estabilidad a otras clases de sistemas con retardos son expuestas brevemente. Tambien se presentan aplicaciones existentes del efoque de funcionales de tipo completo a problemas de analisis y de diseño de controladores. El trabajo se enfoca a contribuciones de investigadores de Mexico a este tema de estudio.Este trabajo ha sido realizado parcialmente gracias al apoyo del Conacyt, México, Proyecto A1-S-24796.Mondié, S.; Gomez, M. (2022). Contribuciones al estudio de sistemas lineales con retardos: el enfoque de funcionales de tipo completo. Revista Iberoamericana de Automática e Informática industrial. 19(4):381-393. https://doi.org/10.4995/riai.2022.16828OJS38139319

MOD-1 Wind Turbine Generator Analysis and Design Report, Volume 2

The MOD-1 detail design is appended. The supporting analyses presented include a parametric system trade study, a verification of the computer codes used for rotor loads analysis, a metal blade study, and a definition of the design loads at each principal wind turbine generator interface for critical loading conditions. Shipping and assembly requirements, composite blade development, and electrical stability are also discussed