J. Jesus Rico

Dynamic harmonic evolution using the extended harmonic domain

A novel methodology is presented in this paper for conducting transient and steady-state analysis of electric networks containing nonlinearities and switching plants components. The method is termed the extended harmonic domain (EHD) method as may be seen as an extension of the harmonic domain (HD) method used in steady-state analysis. It is shown in the paper that EHD is a natural approach for conducting dynamic and steady-state studies of the evolution of harmonics in power circuits containing nonlinear components and flexible AC transmission systems (FACTS) devices. It is also shown in the paper that EHD provides a suitable basis for extending the well-known steady-state power quality indices to the transient range. To illustrate the use of the theory, a three-phase linear circuit and a three-phase PWM-STATCOM are modeled using EHD. The results are compared against those provided by industry standard tools as PSCAD/EMTDC and Matlab.

Operational matrices for the analysis of periodic dynamic systems

This letter presents a methodology for the study of periodical dynamic systems. The method is based on the use of orthogonal series expansions and their operational properties. As opposed to the conventional use of the series expansions, in this work it is considered that the expansion coefficients may slowly vary with time. This salient feature allows for traditional steady-state methods such the harmonic domain to be used in dynamical systems. An important use of the method is the analysis of switched networks. The use of the method is illustrated with simple but of practical value systems.

Harmonic modelling in Hartley's domain with particular reference to three phase thyristor-controlled reactors

The main objectives of this paper are to present a new frame-of-reference based on the use of Hartleys transform and to present a three-phase thyristor controlled reactor (TCR) harmonic model which uses Hartleys domain. Solutions using the new frame-of-reference are between two to four times faster than solutions using an established frame-of-reference based on Fouriers transform because Hartleys transform makes use of the real plane as opposed to the complex plane. Harmonic switching vectors in Hartleys domain have been developed for maximum computer efficiency. Their use, combined with discrete convolution operations, provide cleaner and faster operations than those afforded by the fast Hartley transform. The TCR model is completely general and caters for any kind of plant imbalances, e.g. uneven firing angles and inductances. Network imbalances are accounted for via the excitation voltage. The new frame-of-reference accommodates any number of buses, phases, harmonics and cross-couplings between harmonics. It provides a reliable and efficient means for the iterative solution of power systems harmonic problems through a Newton-Raphson method which exhibits quadratic convergence.

Robust inverse optimal control for discrete-time nonlinear system stabilization

Abstract This paper presents an inverse optimal control approach in order to achieve stabilization of discrete-time nonlinear systems, avoiding the need to solve the associated Hamilton–Jacobi–Bellman equation, and minimizing a cost functional. Then, the proposed approach is extended to discrete-time disturbed nonlinear systems. The synthesized stabilizing optimal controller is based on a discrete-time control Lyapunov function. The applicability of the proposed approach is illustrated via simulations.

Harmonic/State Model-Order Reduction of Nonlinear Networks

This paper presents a practical approach to obtain reduced-order models for electric networks expressed in the dynamic harmonic domain (DHD). The proposed method reduces the DHD system of ordinary differential equations first in the harmonic sense via a voltage-based frequency-scan procedure and subsequently in the state sense via truncated balanced realizations. The harmonic-selection and truncation stage substantially reduces the original full-size system. The state-reduction process is applied to the already harmonic-reduced system, achieving further reduction. Two networks are used as case studies to demonstrate the reduction properties of the proposed model-order reduction methodology.

Optimal control for non-polynomial systems

Abstract This paper shows that a large class of nonlinear systems can be recasted into polynomial ones via state variable embedding an idea used by Carleman many decades ago. Then, by representing the original nonlinear system as a polynomial system, one could apply powerful control techniques. In particular, in this work, an infinite-time state-feedback optimal regulator has been synthesized by solving the Hamilton–Jacobi–Bellman equation for the recasted polynomial system, achieving asymptotic stability and minimizing a cost functional. The prowess of the proposal is validated via simulations in the recasting and optimal control of two applications: a pendulum and a synchronous generator connected to an infinite bus.

Optimal and Robust Control in DC Microgrids

This paper presents an optimal and robust nonlinear control scheme to achieve trajectory tracking for disturbed nonlinear systems, which is applied for the control of power converters in dc microgrids. The state-feedback optimal controller synthesis is based on the solution of the Hamilton–Jacobi–Bellman equation, which considers the minimization of a cost functional (performance index), resulting in an efficient control strategy. The proposed methodology is used to efficiently regulate the power flow from renewable resources into the utility grid, to supply energy to loads, and to storage energy. Simulation results are presented to assess the performance of the proposed controller for a case study dc microgrid, where its adequate operation depends on the dc bus voltage regulation; hence, for guaranteeing such voltage regulation through the converter (inverter) connected to the utility grid, the optimal control scheme is in addition combined with a super-twisting controller (a robust sliding mode-based control technique) to enhance the inverter control strategy robustness.

Optimal operation of energy resources in a micro-grid

This paper presents the development of a dynamic optimization model to manage the generated energy in a micro-grid. The micro-grid consists of the following components: a wind energy system, an energy storage element, a load, and the interconnection to the utility grid. The optimization scheme considers the minimization of the associated cost due to the purchase of energy from the utility grid and simultaneously maximizing the profits associated with the sale of the generated energy to the utility grid. The optimization model considers the dynamics of charge and discharge of the storage element, energy prices and forecasting for wind energy, buying and selling prices and load demand energy, such that an efficient use of energy generated in the micro-grid can be achieved. It is important to include the dynamics of the storage element for the development of the optimization model, since it allow us to store or extract energy in accordance of the micro-grid requirements to maximize the profits. The proposed optimization model serves as an automated mechanism to manage the energy in a micro-grid, which decides the amount of energy to be sent or extracted from the utility grid and to the storage element while supplying the local demand with minimum cost.

Optimal operation and control for an electrical micro-grid

This paper presents an optimization and control scheme for power converters in a micro-grid, which is composed of a wind energy system, an energy storage element (supercapacitor), a load and the interconnection to the utility grid. Based on the results of a dynamic optimization model, which establish the energy flow in the micro-grid, an optimal control scheme uses these results of electrical power values as set-points to efficiently integrate renewable energy to/from the utility grid through the optimal control of power converters. A case study micro-grid is used to integrate the energy from renewable resources, with the facility to storage energy, to provide of energy to loads and to provide/consume energy to/from the utility grid. Simulation results are presented to assess the performance of the proposed controller for the case study micro-grid.

Optimized Operation of a Micro-grid for Energy Resources

Abstract This paper presents the development of a dynamic optimization model to manage the generated energy in a micro-grid. Without loss of generality, the micro-grid consists of the following components: a wind energy system, an energy storage element, a load, and the interconnection with the utility grid. The optimization scheme considers the minimization of the associated cost due to the purchase of energy from the utility grid and simultaneously maximizing the profits associated with the sale of the generated energy to the utility grid. This energy generation and optimization schemes could represent the operation of a micro-grid, which considers different renewable resources and its energy management. The optimization model considers the dynamics of charge and discharge of the storage element, energy prices and forecasting for wind energy, buying and selling prices, and load energy demand, such that an efficient use of the generated energy in a micro-grid can be achieved.