Robust Decentralized Control of Power Systems: A Matrix Inequalities Approach

This dissertation presents an extension of robust decentralized control design techniques for power systems, with special emphasis on design problems that can be expressed as minimizing a linear objective function under linear matrix inequality (LMI) in tandem with nonlinear matrix inequality (NMI) constraints. These types of robust decentralized control design problems are generally nonconvex optimizations, and are proven to be computationally challenging. Therefore, this dissertation proposes alternative computational schemes using: i) bordered-block diagonal (BBD) decomposition algorithm for designing LMI based robust decentralized static output feedback controllers, ii) sequential LMI programming method for designing robust decentralized dynamic output feedback controllers, and, iii) generalized parameter continuation method involving matrix inequalities for designing reduced-order decentralized dynamic output feedback controllers. First, this dissertation considers the problem of designing robust decentralized static output feedback controllers for power systems that guarantee connective stability despite the presence of uncertainties among the interconnected subsystems. The design problem is then solved using BBD decomposition algorithm that clusters the state, input and output structural information for the direct computation of the appropriate gain matrices. Moreover, the approach is flexible enough to allow the inclusion of additional design constraints such as the size of the gain matrices and the degree of robust stability while at the same time maximizing the tolerable upper bounds on the class of perturbations. Second, this research considers the problem of designing a robust decentralized fixed-order dynamic output feedback controller for power systems that is formulated as a nonconvex optimization problem involving LMIs coupled through bilinear matrix equation. In the design, the robust connective stability of the overall system is guaranteed while the upper bounds of the uncertainties arising from the interconnection of the subsystems as well as nonlinearities within each subsystem are maximized. The (sub)-optimal robust decentralized dynamic output feedback control design problem is then solved using sequential LMI programming method. Moreover, the local convergence property of this algorithm has shown the effectiveness of the proposed approach for designing (sub)-optimal robust decentralized dynamic output feedback controllers for power systems. Third, this dissertation considers the problem of designing a robust decentralized structure-constrained dynamic output feedback controller design for power systems using LMI-based optimization approach. The problem of designing a decentralized structure-constrained H2/Hinf controller is first reformulated as an extension of a static output feedback controller design problem for the extended system. The resulting nonconvex optimization problem which involves bilinear matrix inequalities (BMIs) is then solved using the sequentially LMI programming method. Finally, the research considers the problem of designing reduced-order decentralized Hinf controllers for power systems. Initially a fictitious centralized Hinf robust controller, which is typically high-order controller, is designed to guarantee the robust stability of the overall system against unstructured and norm bounded uncertainties. Then the problem of designing a reduced-order decentralized controller is reformulated as an embedded parameter continuation problem that homotopically deforms from the centralized controller to the decentralized controller as the continuation parameter monotonically varies. The design problem, which guarantees the same robustness condition of the centralized controller, is solved using a two-stage iterative matrix inequality optimization algorithm. Moreover, the approach is flexible enough to allow designing different combinations of reduced-order controllers between the different input/output channels. The effectiveness of these proposed approaches are demonstrated by designing realistic power system stabilizers (PSSs) for power system, notably so-called reduced-order robust PSSs that are linear and use minimum local-feedback information. Moreover, the nonlinear simulation results have confirmed the robustness of the system for all envisaged operating conditions and disturbances. The proposed approaches offer a practical tool for engineers, besides designing reduced-order PSSs, to re-tune PSS parameters for improving the dynamic performance of the overall system

Algorithms for output feedback, multiple-model, and decentralized control problems

The optimal stochastic output feedback, multiple-model, and decentralized control problems with dynamic compensation are formulated and discussed. Algorithms for each problem are presented, and their relationship to a basic output feedback algorithm is discussed. An aircraft control design problem is posed as a combined decentralized, multiple-model, output feedback problem. A control design is obtained using the combined algorithm. An analysis of the design is presented

A distributed accelerated gradient algorithm for distributed model predictive control of a hydro power valley

A distributed model predictive control (DMPC) approach based on distributed optimization is applied to the power reference tracking problem of a hydro power valley (HPV) system. The applied optimization algorithm is based on accelerated gradient methods and achieves a convergence rate of O(1/k^2), where k is the iteration number. Major challenges in the control of the HPV include a nonlinear and large-scale model, nonsmoothness in the power-production functions, and a globally coupled cost function that prevents distributed schemes to be applied directly. We propose a linearization and approximation approach that accommodates the proposed the DMPC framework and provides very similar performance compared to a centralized solution in simulations. The provided numerical studies also suggest that for the sparsely interconnected system at hand, the distributed algorithm we propose is faster than a centralized state-of-the-art solver such as CPLEX

Deep neural learning based distributed predictive control for offshore wind farm using high fidelity LES data

The paper explores the deep neural learning (DNL) based predictive control approach for offshore wind farm using high fidelity large eddy simulations (LES) data. The DNL architecture is defined by combining the Long Short-Term Memory (LSTM) units with Convolutional Neural Networks (CNN) for feature extraction and prediction of the offshore wind farm. This hybrid CNN-LSTM model is developed based on the dynamic models of the wind farm and wind turbines as well as higher-fidelity LES data. Then, distributed and decentralized model predictive control (MPC) methods are developed based on the hybrid model for maximizing the wind farm power generation and minimizing the usage of the control commands. Extensive simulations based on a two-turbine and a nine-turbine wind farm cases demonstrate the high prediction accuracy (97% or more) of the trained CNN-LSTM models. They also show that the distributed MPC can achieve up to 38% increase in power generation at farm scale than the decentralized MPC. The computational time of the distributed MPC is around 0.7s at each time step, which is sufficiently fast as a real-time control solution to wind farm operations

Review of trends and targets of complex systems for power system optimization

Optimization systems (OSs) allow operators of electrical power systems (PS) to optimally operate PSs and to also create optimal PS development plans. The inclusion of OSs in the PS is a big trend nowadays, and the demand for PS optimization tools and PS-OSs experts is growing. The aim of this review is to define the current dynamics and trends in PS optimization research and to present several papers that clearly and comprehensively describe PS OSs with characteristics corresponding to the identified current main trends in this research area. The current dynamics and trends of the research area were defined on the basis of the results of an analysis of the database of 255 PS-OS-presenting papers published from December 2015 to July 2019. Eleven main characteristics of the current PS OSs were identified. The results of the statistical analyses give four characteristics of PS OSs which are currently the most frequently presented in research papers: OSs for minimizing the price of electricity/OSs reducing PS operation costs, OSs for optimizing the operation of renewable energy sources, OSs for regulating the power consumption during the optimization process, and OSs for regulating the energy storage systems operation during the optimization process. Finally, individual identified characteristics of the current PS OSs are briefly described. In the analysis, all PS OSs presented in the observed time period were analyzed regardless of the part of the PS for which the operation was optimized by the PS OS, the voltage level of the optimized PS part, or the optimization goal of the PS OS.Web of Science135art. no. 107