Design of Observer-Based Robust Power System Stabilizers

2016 ◽  
Vol 3 (1) ◽  
pp. 38
Author(s):  
Hisham M. Soliman ◽  
Mahmoud Soliman
Keyword(s):  
Power Systems ◽  
Power System ◽  
Controller Design ◽  
Damping Ratio ◽  
Iterative Solution ◽  
Linear Matrix ◽  
Diagonal Form ◽  
Matrix Inequality ◽  
Great Loss ◽  
Wide Range

<p>Power systems are subject to undesirable small oscillations that might grow to cause system shutdown and consequently great loss of national economy. A model to describe power system dynamics for different loads is derived in the norm-bounded form. The first controller design is based on the derived model to achieve  robust stability against load variation. The design is based on a new Bilinear matrix inequality (BMI) condition. The BMI optimization  is solved interatively in terms of Linear Matrix Inequality (LMI) framework. The condition contains a symmetric positive definite full matrix to be obtained, rather than the commonly used block diagonal form. The difficulty in finding a feasible solution is thus alleviated. The resulting LMI is of small size, easy to solve. The second PSS design shifts the closed loop poles in a desired region so as to achieve a favorite  settling time and damping ratio via a non-iterative solution to a set of LMIs.  Simulation results based on single-machine and multi-machine power system models verify the ability of the proposed PSS to satisfy control objectives for a wide range of load conditions.</p>

scholarly journals Design of Observer-Based Robust Power System Stabilizers

2016 ◽  
Vol 6 (5) ◽  
pp. 1956
Author(s):  
Hisham M. Soliman ◽  
Mahmoud Soliman
Keyword(s):  
Power System ◽  
Linear Matrix Inequality ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Iterative Solution ◽  
Linear Matrix ◽  
Diagonal Form ◽  
Matrix Inequality ◽  
Great Loss ◽  
Wide Range

<p>Power systems are subject to undesirable small oscillations that might grow to cause system shutdown and consequently great loss of national economy. The present manuscript  proposes two  designs for observer-based robust power system stabilizer (PSS) using Linear Matrix Inequality (LMI) approach to damp such oscillations. A model to describe power system dynamics for different loads is derived in the norm-bounded form. The first controller design is based on the derived model to achieve  robust stability against load variation. The design is based on a new Bilinear matrix inequality (BMI) condition. The BMI optimization  is solved interatively in terms of Linear Matrix Inequality (LMI) framework. The condition contains a symmetric positive definite full matrix to be obtained, rather than the commonly used block diagonal form. The difficulty in finding a feasible solution is thus alleviated. The resulting LMI is of small size, easy to solve. The second PSS design shifts the closed loop poles in a desired region so as to achieve a favorite  settling time and damping ratio via a non-iterative solution to a set of LMIs.  The approach provides a systematic way to design a robust output feedback PSS which  guarantees good dynamic performance for different loads. <span style="font-size: 10px;">Simulation results based on single-machine and multi-machine power system models verify the ability of the proposed PSS to satisfy control objectives for a wide range of load conditions.</span></p>

Design of Observer-Based Robust Power System Stabilizers

2016 ◽  
Vol 6 (5) ◽  
pp. 1956
Author(s):  
Hisham M. Soliman ◽  
Mahmoud Soliman
Keyword(s):  
Power System ◽  
Linear Matrix Inequality ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Iterative Solution ◽  
Linear Matrix ◽  
Diagonal Form ◽  
Matrix Inequality ◽  
Great Loss ◽  
Wide Range

<p>Power systems are subject to undesirable small oscillations that might grow to cause system shutdown and consequently great loss of national economy. The present manuscript  proposes two  designs for observer-based robust power system stabilizer (PSS) using Linear Matrix Inequality (LMI) approach to damp such oscillations. A model to describe power system dynamics for different loads is derived in the norm-bounded form. The first controller design is based on the derived model to achieve  robust stability against load variation. The design is based on a new Bilinear matrix inequality (BMI) condition. The BMI optimization  is solved interatively in terms of Linear Matrix Inequality (LMI) framework. The condition contains a symmetric positive definite full matrix to be obtained, rather than the commonly used block diagonal form. The difficulty in finding a feasible solution is thus alleviated. The resulting LMI is of small size, easy to solve. The second PSS design shifts the closed loop poles in a desired region so as to achieve a favorite  settling time and damping ratio via a non-iterative solution to a set of LMIs.  The approach provides a systematic way to design a robust output feedback PSS which  guarantees good dynamic performance for different loads. <span style="font-size: 10px;">Simulation results based on single-machine and multi-machine power system models verify the ability of the proposed PSS to satisfy control objectives for a wide range of load conditions.</span></p>

scholarly journals A Wide Range Robust PSS Design Based on Power System Pole-Placement Using Linear Matrix Inequality

2012 ◽  
Vol 63 (4) ◽  
pp. 233-241 ◽  
Author(s):  
Mohammad Ataei ◽  
Rahmat-Allah Hooshmand ◽  
Moein Parastegari
Keyword(s):  
Power System ◽  
Linear Matrix Inequality ◽  
Controller Design ◽  
Damping Ratio ◽  
Pole Placement ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Matrix Inequality ◽  
Gain Matrix ◽  
Wide Range

A Wide Range Robust PSS Design Based on Power System Pole-Placement Using Linear Matrix InequalityIn this paper, a new method for robust PSS design based on the power system pole placement is presented. In this stabilizer, a feedback gain matrix is used as a controller. The controller design is proposed by formulating the problem of robust stability in a Linear Matrix Inequality (LMI) form. Then, the feedback gain matrix is designed based on the desired region of the closed loop system poles. This stabilizer shifts the poles of the power system in different operational points into the desired regions ins-plane, such that the response of the power system will have proper damping ratio in all the operational points. The uncertainties of the power system parameters are also considered in this robust technique. Finally, in order to show the advantages of the proposed method in comparison with conventional PSS, some simulation results are provided for a power system case study in different operational points.

Robust H2 Output Feedback Controller Design for Damping Power System Oscillations

2017 ◽  
Vol 6 (10) ◽  
pp. 8
Author(s):  
Kho Hie Kwee ◽  
Hardiansyah .
Keyword(s):  
Power System ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Worst Case ◽  
Output Feedback Controller ◽  
Power System Oscillations

This paper addresses the design problem of robust H2 output feedback controller design for damping power system oscillations. Sufficient conditions for the existence of output feedback controllers with norm-bounded parameter uncertainties are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the output feedback controller which minimizes an upper bound on the worst-case H2 norm for a range of admissible plant perturbations. The technique is illustrated with applications to the design of stabilizer for a single-machine infinite-bus (SMIB) power system. The LMI based control ensures adequate damping for widely varying system operating.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

scholarly journals Studying State Convergence of Input-to-State Stable Systems with Applications to Power System Analysis

Energies ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 92 ◽  
Author(s):  
Antonio T. Alexandridis
Keyword(s):  
Nonlinear Systems ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Nonlinear Models ◽  
Sufficient Conditions ◽  
Stability And Convergence ◽  
Convergence To Equilibrium ◽  
Analysis Tool ◽  
Wide Range

In stability studies, the response of a system enforced by external, known or unknown, inputs is of great importance. Although such an analysis is quite easy for linear systems, it becomes a cumbersome task when nonlinearities exist in the system model. Nevertheless, most of the real-world systems are externally enforced nonlinear systems with nonzero equilibriums. Representative examples in this category include power systems, where studies on stability and convergence to equilibrium constitute crucial objectives. Driven by this need, the aim of the present work is twofold: First, to substantially complete the theoretical infrastructure by establishing globally valid sufficient conditions for externally enforced nonlinear systems that converge to nonzero equilibriums and, second, to deploy an efficient method easily applicable on practical problems as it is analyzed in detail on a typical power system example. To that end, in the theoretical first part of the paper, a rigorous nonlinear analysis is developed. Particularly, starting from the well-established nonlinear systems theory based on Lyapunov techniques and on the input-to-state stability (ISS) notion, it is proven after a systematic and lengthy analysis that ISS can also guarantee convergence to nonzero equilibrium. Two theorems and two corollaries are established to provide the sufficient conditions. As shown in the paper, the main stability and convergence objectives for externally enforced systems are fulfilled if simple exponential or asymptotic converging conditions can be proven for the unforced system. Then, global or local convergence is established, respectively, while for the latter case, a novel method based on a distance-like measure for determining the region of attraction (RoA) is proposed. The theoretical results are examined on classic power system generation nonlinear models. The power system examples are suitably selected in order to effectively demonstrate the proposed method as a stability analysis tool and to validate all the particular steps, especially that of evaluating the RoA. The examined system results clearly verify the theoretical part, indicating a rather wide range of applications in power systems.

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