Optimal decentralized control of a wind turbine and diesel generator system

This article presents a decentralized optimal controller design technique for the frequency and power control of a coupled wind turbine and diesel generator. The decentralized controller consists of two proportional-integral (PI)-lead controllers which are designed and optimized simultaneously using a quasi-Newton based optimization technique, namely, Davidon–Fletcher–Powell algorithm. The optimal PI-lead controllers are designed in such a way that there are no communication links between them. Simulation results show the superior performance of the proposed controller with a lower order structure compared to the benchmark decentralized linear-quadratic Gaussian integral controllers of orders 4 and 11. It is also shown that the proposed controller demonstrates an effective performance in damping the disturbances from load and wind power, as well as a robust performance against the parameter changes of the power system.     

Model predictive and linear quadratic Gaussian control of a wind turbine

Model Predictive and linear quadratic Gaussian controllers are designed for a 5MW variable‐speed pitch‐regulated wind turbine for three operating points – below rated wind speed, just above rated wind speed, and above rated wind speed. The controllers are designed based on two different linear dynamic models (at each operating point) of the same wind turbine to study the effect of utilising different control design models (i.e. the model used for designing a model‐based controller) on the control performance. The performance of the LQG controller is enhanced by improving the robustness, achieved by replacing the Kalman filter with a modified Luenberger observer, whose gain is obtained to minimise the effect of uncertainty and disturbance. Copyright © 2016 John Wiley & Sons, Ltd.     

Wind time series modeling and stochastic optimal control for a grid‐connected permanent magnet wind turbine generator

In this paper, the control system of a permanent‐magnet synchronous machine wind turbine generator connected to the grid is studied. A set of wind speed time series is used to model the rapidly changing wind speed component as a stochastic process. Several control laws, including the nonlinear stochastic optimal controller, are developed, and their efficiency is examined comparatively and under various conditions. Also, the effect of parameter uncertainty to the system efficiency is shown through simulations. The results show that the system efficiency increase obtained by the use of sophisticated control techniques, although not dramatic, is not negligible. Copyright © 2015 John Wiley & Sons, Ltd.     

Gap metric–based model bank construction for wind turbine predictive control

This paper presents a novel model bank construction method for the multiple model predictive control of wind turbine system. The gap metric is used to measure the dynamic difference between the linearized models of the wind turbine system at different wind speed. Two algorithms are then proposed to divide the wind speed range in different operating regions. Meanwhile, a complete and nonredundant linear model bank is established to approximate the wind turbine system in the whole operating region. We take the robust model predictive control algorithm to design the local controller and utilize the wind speed as the switching criterion to combine the submodels. The simulation study on a 5‐MW wind turbine verifies the efficiency of the proposed method.     

Load frequency predictive control for power systems concerning wind turbine and communication delay

This article addresses a model predictive control (MPC) technique for load frequency control (LFC) system in the presence of wind power, communication delay, and denial-of-service (DoS) attack. In this article, communication delay is incorporated into a single area control error transmission for simplicity, wind power and load disturbance are regarded as Lipschitz nonlinear terms, as for the randomly occurring DoS attack, it is modeled as Bernoulli processes with known conditional probability. Thinking all these adverse factors to stability and the limitation of input constraint synthetically, the stability of LFC system can be guaranteed by delay-dependent Lyapunov function lemma and a state feedback MPC controller is designed to solve the LFC problems by minimizing the infinite-horizon objective function. Although some scholars have studied the performance degradation and instability of LFC system caused by cyber attack and/or communication delay and some very nice results have been addressed, limited works have considered the MPC approach to deal with both the problems of cyber attack and communication delay which explicitly considers the physical constraints. In addition, the delay-dependent Lyapunov function is adopted to deal with the problem of communication delay, which results in less conservatism of the presented method. Finally, the optimization problem with input constraint is solved and proven to be recursive feasibility, and the closed-loop system turns out to be stable. The reasonability and validity of the provided strategy is verified through several groups of simulation experiments. It illustrates that the proposed control method can keep the system frequency steady in the standard range in spite of various attack conditions.     

Hybridized gravitational search algorithm tuned sliding mode controller design for load frequency control system with doubly fed induction generator wind turbine

In this paper, the load frequency regulation problem of 2‐area interconnected power system is resolved using the sliding mode control (SMC) methodology. Interconnected 2‐area power systems with and without doubly fed induction generator wind turbines are considered for implementing the proposed optimal control methodology. Here, a heuristic gravitational search algorithm (GSA) and its variants such as opposition learning–based GSA (OGSA), disruption‐based GSA (DGSA), and disruption based oppositional GSA (DOGSA) are employed to optimize the switching vector and feedback gains of SMC. In order to overcome the inherent chattering problem in SMC, the control signals are considered in the objective function. The robustness of optimized SMC is analyzed by the inclusion of nonlinearities such as generation rate constraint (GRC), governor deadband, and time delay during the signal processing between the control areas, which are present in the real‐time power system. The insensitiveness of the optimal controller is shown by variation in system parameters like loading condition, speed governor constant, turbine constant, and tie‐line power coefficient. Further, the optimal SMC has been studied with significant load variations and wind power penetration levels in the control areas. The potential of proposed SMC design with chattering reduction feature is shown and validated by comparing the results obtained with the other reported methods in the literature.     

Optimal control of electrical vehicle incorporated hybrid power system with second order fractional-active disturbance rejection controller

This article proposes a novel control methodology employing a fractional-active-disturbance-rejection-controller for the combined operation of load frequency control and automatic voltage regulator of a hybrid power system. A two area hybrid power system with diverse energy sources like solar-thermal, conventional-thermal and wind sources equipped with appropriate system nonlinearities is investigated. In order to ascertain the role of modern-day electric-vehicle (EV), the hybrid power system is incorporated with EVs in both the areas. To establish an effective frequency, voltage and tie line power control of the hybrid power system, a second order fractional-active-disturbance-rejection-controller with fractional-extended state observer is modeled as secondary controller. Magnetotactic-bacteria-optimization (MBO) technique is applied to obtain optimal values of the controller gains and the hybrid system parameters. The robustness of the controller gains is tested under different system parameter changes from their nominal values. In addition, the effect of incorporating a power system stabilizer on the hybrid power system is evaluated. Further, the impact of integrating renewable sources and EVs in the hybrid power system is explored. Moreover, the stability of the hybrid power system is monitored with the inclusion of FACTS device. The developed controller operates encouragingly with reference to system stability, rapidity and accuracy in comparison to testified control strategies available in the literature. The robustness test under load-perturbation, solar-insolation, wind input variations also proves the efficiency of MBO optimized second order fractional-active-disturbance-rejection-controller gains.     

Optimal control of a parabolic distributed parameter system via orthogonal polynomials

A class of optimal control of systems with distributed parameters is considered. The process of the systems under consideration is governed by a linear parabolic partial differential equation. By use of the modal space technique, the optimal control of a distributed parameter system is simplified into the optimal control of a linear time-invariant lumped-parameter system. Next, a direct computational method for evaluating the modal optimal control and trajectory of the linear time-invariant lumped-parameter is suggested. The method is based on using finite interpolating orthogonal polynomials to approximate modal state variables. The formulation is straightforward and convenient for digital computation. An illustrative example is given to demonstrate the advantage of this method. © 1998 John Wiley & Sons, Ltd.     

Optimal control of a production system with periodic maintenance

In this paper we consider a production system consisting of one machine for which maintenance is performed on a periodic basis. When the machine is undergoing maintenance, the system is shut down and cannot produce. One part-type is produced and the demand rate is assumed to be constant. In order to make on-time delivery, the objective is to produce following the demand as closely as possible. However, the maintenance disruptions make the production deviate from the demand. We formulate the production flow control problem as an optimal control model and use Pontryagin's minimum principle to solve the special case of one up-down cycle. We then solve the general N-cycle problem based on the one-cycle solution.     

Optimal control of innate immune response

Treatment of a pathogenic disease process is interpreted as the optimal control of a dynamic system. Evolution of the disease is characterized by a non‐linear, fourth‐order ordinary differential equation that describes concentrations of pathogens, plasma cells, and antibodies, as well as a numerical indication of patient health. Without control, the dynamic model evidences sub‐clinical or clinical decay, chronic stabilization, or unrestrained lethal growth of the pathogen, depending on the initial conditions for the infection. The dynamic equations are controlled by therapeutic agents that affect the rate of change of system variables. Control histories that minimize a quadratic cost function are generated by numerical optimization over a fixed time interval, given otherwise lethal initial conditions. Tradeoffs between cost function weighting of pathogens, organ health, and use of therapeutics are evaluated. Optimal control solutions that defeat the pathogen and preserve organ health are demonstrated for four different approaches to therapy. It is shown that control theory can point the way toward new protocols for treatment and remediation of human diseases. Copyright © 2002 John Wiley & Sons, Ltd.     

Design of a chattering-free integral terminal sliding mode approach for DFIG-based wind energy systems

This article proposes a Fuzzy Second Order Integral Terminal Sliding Mode (FSOITSM) control approach for DFIG-based wind turbines subject to grid faults and parameter variations. Since traditional terminal sliding mode control (SMC) suffers from singularity, a novel integral terminal sliding manifold is proposed to eliminate chattering and improve the wind turbine's performance in the presence of faults and disturbances. A fuzzy system is proposed to auto-tune the controllers' gains and ensures the invariance of the sliding surfaces even under heavy uncertainties, thus further improving the reliability and performance of the proposed controller. The performance of the proposed approach was assessed under various operating conditions. A comparison analysis with a standard SMC approach as well as the state of the art in voltage sag mitigation was also carried over. Reliability, robustness, and power availability under faulty grid conditions are among the main features of the proposed approach. In addition, the proposed approach exhibited chattering free dynamics and enabled the finite time convergence of the sliding manifold and overcame the singularity problem associated with standard TSMC.     

High‐order observers‐based LQ control scheme for wind speed and uncertainties estimation in WECSs

Tip speed ratio control is a popular method in wind energy conversion systems in order to capture the maximum power. This method, however, requires wind speed information, which is difficult in practice to accurately measure it. Therefore, estimation methods are usually applied, where a high‐precision estimate leads to a high‐efficient system. Based on the fact that the wind speed varies in a random way, this paper proposes a generalized high‐order observer to estimate the aerodynamic torque and the wind speed accordingly. This observer algorithm releases the assumption that the wind speed should be slowly varying, which is required in previous observer designs. Moreover, two other generalized high‐order observers are also applied to estimate the uncertainties, which depend on state variables and cannot be considered as slow‐varying disturbances. Using the outputs of these observers, a robust high‐performance optimal control system is developed for the rotor speed to keep the optimal tip speed ratio. The stability analysis of the designed control system is fully presented. The effectiveness of the proposed technique is validated via simulation studies.     

Optimal production rates in a deterministic two‐product manufacturing system

This paper is concerned with explicit optimal control for a deterministic manufacturing system consisting of a single reliable machine and producing two part types studied by Connolly (Master Thesis, Operations Research Center, MIT, Cmbridge, 1992) and Gershwin (Manufacturing Systems Engineering, Prentice‐Hall: Englewood Cliffs, NJ, 1994). Using the verification theorem, we show the uniqueness of the optimal control under some conditions. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimal control of nonlinear aeroelastic system with non-semi-simple eigenvalues at Hopf bifurcation points

This study discusses an efficient method of the Hopf bifurcation control for nonlinear aeroelastic system. The nonlinear aeroelastic system whose linear part has multiple non-semi-simple eigenvalues at critical point gives rise to Hopf bifurcations. The method of the multiple scales and the well-known linear quadratic regulator method are used to deal with the optimal control of the nonlinear system at Hopf bifurcation points. The modal optimal control equation and modal Riccati equation of the nonlinear system are developed to simplify the computations. The conventional Potter's algorithm is extended to solve modal Riccati equation for the modal Riccati matrix of the Hopf bifurcation control. The first-order approximation solutions are developed, which include the gain vectors and inputs. By the way of optimal control, the admissible control input and trajectory of the linear part of the nonlinear aeroelastic system are obtained to minimize the performance measure. Then, we set the appropriate first-order gain vector to adjust the convergence speed of this nonlinear system.     

An improved neuro-adaptive-optimal control for oscillation damping in wind-integrated power systems

This article proposes an improved neuro-adaptive-optimal control scheme, based on online system identification and simultaneous control, to replace power system stabilizer in the renewable-energy-penetrated power systems. A simple, linear neural identifier, with a few adjustable connection weights is used, which ensures minimal computational burden, reduced development time, and makes the controller practically realizable. An adaptive learning rate, derived using Lyapunov stability theorems, guarantees stability of convergence of the learning algorithm as well as an optimal speed of convergence. It is demonstrated that a simple linear neural identifier, which approximates a local linear model of a system, by adjustment of its parameters online, is faithfully able to track the varying dynamics of the system. Improved oscillation-damping performance over a wide range of operating conditions and disturbances, in comparison with a well-established IEEE-PSS1A and fuzzy-logic-control-based PSS, was validated through simulation studies on a single-machine infinite-bus power system and a wind-integrated two-area power system. The computational superiority of the proposed scheme in comparison to complex and non-linear neural networks and fuzzy-logic-based control was also established. The novelty of the controller lies in its structure which, in-spite of being purely linear, performs robustly for highly complex and non-linear power system models.     

Optimal control of a revenue management system with dynamic pricing facing linear demand

This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time‐varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two‐product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two‐product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright © 2006 John Wiley & Sons, Ltd.     

Optimal control approach for discontinuous dynamical systems

In this work, we consider a wide class of discontinuous dynamical systems, discontinuity of which is based on the sign (for short sgn) function. We propose a smooth optimal control problem to solve the main discontinuous system. By solving some numerical examples in mechanical engineering, we show the efficiency of our approach with respect to 2 smoothing methods for discontinuous systems.     

Optimal operation of a grid-connected battery energy storage system over its lifetime

This paper deals with the optimal control of grid-connected Battery Energy Storage Systems (BESSs) operating for energy arbitrage. An important issue is that BESSs degrade over time, according to their use, and thus they are usable only for a limited number of cycles. Therefore, the time horizon of the optimization depends on the actual operation of the BESS. We focus on Li-ion batteries and use an empirical model to describe battery degradation. The BESS model includes an equivalent circuit for the battery and a simplified model for the power converter. In order to model the energy price variations, we use a linear stochastic model that includes the effect of the time-of-the-day. The problem of maximizing the revenues obtained over the BESS lifetime is formulated as a stochastic optimal control problem with a long, operation-dependent time horizon. First, we divide this problem into a finite set of subproblems, such that for each one of them, the State of Health (SoH) of the battery is approximately constant. Next, we reformulate approximately every subproblem into the minimization of the ratio of two long-time average-cost criteria and use a value-iteration-type algorithm to derive the optimal policy. Finally, we present some numerical results and investigate the effects of the energy loss parameters, degradation parameters, and price dynamics on the optimal policy.