Mahdieh Sadat Sadabadi

Plug-and-Play Voltage Stabilization in Inverter-Interfaced Microgrids via a Robust Control Strategy

This paper proposes a decentralized control strategy for the voltage regulation of islanded inverter-interfaced microgrids. We show that an inverter-interfaced microgrid under plug-and-play (PnP) functionality of distributed generations (DGs) can be cast as a linear time-invariant system subject to polytopic-type uncertainty. Then, by virtue of this novel description and use of the results from theory of robust control, the microgrid control system guarantees stability and a desired performance even in the case of PnP operation of DGs. The robust controller is a solution of a convex optimization problem. The main properties of the proposed controller are that: 1) it is fully decentralized and local controllers of DGs that use only local measurements; 2) the controller guarantees the stability of the overall system; 3) the controller allows PnP functionality of DGs in microgrids; and 4) the controller is robust against microgrid topology change. Various case studies, based on time-domain simulations in MATLAB/SimPowerSystems Toolbox, are carried out to evaluate the performance of the proposed control strategy in terms of voltage tracking, microgrid topology change, PnP capability features, and load changes.

An LMI formulation of fixed-order H ∞ and H 2 controller design for discrete-time systems with polytopic uncertainty

In this paper, a new approach to fixed-order H∞ and H2 output feedback control of MIMO discrete-time systems with polytopic uncertainty is proposed. The main idea of this approach is based on the definition of SPR-pair matrices and the use of some instrumental matrices which operates as a tool to overcome the original non-convexity of fixed-order controller design. Then, stability condition as well as H∞ and H2 performance constraints are presented by a set of linear matrix inequalities with linearly parameter dependent Lyapunov matrices. An iterative algorithm for update on the instrumental matrices is developed, that monotonically converges to a suboptimal solution. Simulation results show the effectiveness of the proposed approach.

Fixed-order Controller Design for State Space Polytopic Systems by Convex Optimization

In this paper, a new method for fixed-order controller design of systems with polytopic uncertainty in their state space representation is proposed. The approach uses the strictly positive realness (SPRness) of some transfer functions, as a tool to decouple the controller parameters and the Lyapunov matrices and represent the stability conditions and the performance criteria by a set of linear matrix inequalities. The quality of this convex approximation depends on the choice of a central state matrix. It is shown that this central matrix can be computed from a set of initial fixed-order controllers computed for each vertex of the polytope. The stability of the closed-loop polytopic system is guaranteed by a linear parameter dependent Lyapunov matrix. The results are extended to fixed-order H infinity controller design for SISO systems.

From Static Output Feedback to Structured Robust Static Output Feedback: A Survey

This paper reviews the vast literature on static output feedback design for linear time-invariant systems including classical results and recent developments. In particular, we focus on static output feedback synthesis with performance specifications, structured static output feedback, and robustness. The paper provides a comprehensive review on existing design approaches including iterative linear matrix inequalities heuristics, linear matrix inequalities with rank constraints, methods with decoupled Lyapunov matrices, and non-Lyapunov-based approaches. We describe the main difficulties of dealing with static output feedback design and summarize the main features, advantages, and limitations of existing design methods. Keywords: Static output feedback (SOF), structured static output feedback , robustness, convex optimization, linear matrix inequality (LMI), bilinear matrix inequality (BMI), non-smooth non-convex optimization.

Determination of the Two-Dimensional ARMA Model Order Using Rank Test Based Approach

Determination of the order of a two-dimensional (2-D) ARMA model is a key first step toward the goal of modeling a process. In this paper, a rank test approach for 2-D ARMA model order determination is proposed. This method shows that the information of AR and MA orders are implicitly contained in two different correlation matrices and the AR and MA orders of the 2-D ARMA model can be independently determined before parameter estimation. In the proposed method, the model is assumed causal, stable, linear, and spatial shift-invariant with P1times P2 quarter plane (QP) support. Analysis and simulation results demonstrate the applicability of this approach.

Plug-and-Play Robust Voltage Control of DC Microgrids

The purpose of this paper is to explore the applicability of linear time-invariant dynamical systems with polytopic uncertainty for modeling and control of islanded dc microgrids under plug-and-play (PnP) functionality of distributed generations (DGs). We develop a robust decentralized voltage control framework to ensure robust stability and reliable operation for islanded dc microgrids. The problem of voltage control of islanded dc microgrids with PnP operation of DGs is formulated as a convex optimization problem with structural constraints on some decision variables. The proposed control scheme offers several advantages including decentralized voltage control with no communication link, transient stability/performance, PnP capability, scalability of design, applicability to microgrids with general topology, and robustness to microgrid uncertainties. The effectiveness of the proposed control approach is evaluated through simulation studies carried out in MATLAB/SimPowerSystems Toolbox.

Fixed-order control of LTI systems subject to polytopic uncertainty via the concept of Strictly Positive Realness

This paper deals with the problem of fixed-order controller design of LTI continuous-time and discrete-time polytopic systems via homogeneous polynomially parameter-dependent Lyapunov matrices. The proposed method is based on the concept of Strictly Positive Realness (SPRness) of a transfer function depending on a parameter-dependent gain. To convert the problem to a set of LMI conditions, the parameter-dependent gain is determined a priori by means of a parameter-dependent state feedback controller. Simulation results and a comparison with recent existing methods demonstrate the effectiveness of the proposed approach.

Nonlinear Identification of Synchronous Generator Using Hammerstein Model with Piecewise Linear Static Maps

The new approach for identification of synchronous generator using Hammerstein model and with piecewise linear map is investigated in this paper. In this method, synchronous generator model consists of a linear-dynamic block and a nonlinear-static block. The identification method simultaneously approximates these blocks without requiring prior assumptions on the form of the static non-linearity. In this study, the field voltage is considered as the input and the active output power and the terminal voltage are considered as the outputs of the synchronous generator. Experimental results show good accuracy of the identified model.

Robust Performance Analysis of Affine Single Parameter-dependent Systems with Polynomially Parameter-dependent Lyapunov Matrices

This paper addresses the problem of H-infinity and H-2 performance analysis of continuous-time affine single parameter-dependent systems with polynomially parameter-dependent Lyapunov matrices. First, some necessary and sufficient conditions in terms of linear matrix inequalities (LMIs) are provided using (D,G) scaling approach. Then, the results are used to deal with the problem of fixed-order H-infinity and H-2 controller design via bilinear matrix inequalities (BMIs) in a nonconservative way. Simulation results demonstrate the effectiveness of the proposed approach.

Fixed-structure Sparse Control of Interconnected Systems with Polytopic Uncertainty

This paper deals with the problem of sparse H-infinity dynamic output-feedback control of LTI interconnected systems with polytopic uncertainty. The main objective is to find a controller structure with minimum information exchange between subsystems and local controllers such that stability condition as well as an H-infinity performance criterion are satisfied. To this end, an optimization problem is defined which is the minimization of the cardinality of a special matrix subject to an H-infinity performance constraint. Then, the problem is approximated by a convex optimization. The effectiveness of the proposed approach is evaluated through some simulation results.