Design of a Wide Area Controller Using Eigenstructure Assignment in Power Systems

Small signal stability has become a major concern for power system operators around the world. This has resulted from constantly evolving changes in the power system ranging from increased number of interconnections to ever increasing demand of power. In highly stressed operating conditions, even a small disturbance such as a load change can make the system unstable resulting in small signal instability. The main reason for small signal instability in power systems is an inter-area mode/s becoming unstable. Inter-area modes involve a group of generators oscillating against each other. Traditionally, power system stabilizers installed on the synchrous machines were used to damp the inter-area modes. However, they may not be very suitable to perform the job since they use local I/O signals which do not have a good controllability/observability of the inter-area modes. Recent advancements in phasor measurement technology has resulted in fast acquisition of time-synchronized measurements throughout the system. Thus, instead of using local controllers, an idea of a wide area controller (WAC) was proposed by the power systems community that would use global signals. This dissertation demonstrates the design of a WAC using eigenstructure assignment technique. This technique provides the freedom to assign a few eigenvalues and corresponding left or right eigenvectors for Multi-Input-Multi-Output (MIMO) systems. This technique forms a good match for designing a WAC since a WAC usually uses multiple I/O signals and a power system only has a few inter-area modes that might lead to instability. The last chapter of this dissertation addresses an important aspect of controller design, i.e., robustness of the controller to uncertainties in operating point and time delay of feedback signals. The operating point of a power system is highly variable in nature and thus the designed WAC should be able to damp the inter-area modes under these variations. Also, a transmission delay is associated due to routing of remote signals. This time delay is known to deteriorate the performance of the controller. A single controller will be shown to achieve robustness against both these uncertainties

Pole Placement and Reduced-Order Modelling for Time-Delayed Systems Using Galerkin Approximations

The dynamics of time-delayed systems (TDS) are governed by delay differential equa- tions (DDEs), which are infinite dimensional and pose computational challenges. The Galerkin approximation method is one of several techniques to obtain the spectrum of DDEs for stability and stabilization studies. In the literature, Galerkin approximations for DDEs have primarily dealt with second-order TDS (second-order Galerkin method), and the for- mulations have resulted in spurious roots, i.e., roots that are not among the characteristic roots of the DDE. Although these spurious roots do not affect stability studies, they never- theless add to the complexity and computation time for control and reduced-order modelling studies of DDEs. A refined mathematical model, called the first-order Galerkin method, is proposed to avoid spurious roots, and the subtle differences between the two formulations (second-order and first-order Galerkin methods) are highlighted with examples. For embedding the boundary conditions in the first-order Galerkin method, a new pseudoinverse-based technique is developed. This method not only gives the exact location of the rightmost root but also, on average, has a higher number of converged roots when compared to the existing pseudospectral differencing method. The proposed method is combined with an optimization framework to develop a pole-placement technique for DDEs to design closed-loop feedback gains that stabilize TDS. A rotary inverted pendulum system apparatus with inherent sensing delays as well as deliberately introduced time delays is used to experimentally validate the Galerkin approximation-based optimization framework for the pole placement of DDEs. Optimization-based techniques cannot always place the rightmost root at the desired location; also, one has no control over the placement of the next set of rightmost roots. However, one has the precise location of the rightmost root. To overcome this, a pole- placement technique for second-order TDS is proposed, which combines the strengths of the method of receptances and an optimization-based strategy. When the method of receptances provides an unsatisfactory solution, particle swarm optimization is used to improve the location of the rightmost pole. The proposed approach is demonstrated with numerical studies and is validated experimentally using a 3D hovercraft apparatus. The Galerkin approximation method contains both converged and unconverged roots of the DDE. By using only the information about the converged roots and applying the eigenvalue decomposition, one obtains an r-dimensional reduced-order model (ROM) of the DDE. To analyze the dynamics of DDEs, we first choose an appropriate value for r; we then select the minimum value of the order of the Galerkin approximation method system at which at least r roots converge. By judiciously selecting r, solutions of the ROM and the original DDE are found to match closely. Finally, an r-dimensional ROM of a 3D hovercraft apparatus in the presence of delay is validated experimentally

Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey

The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out

Optimal Pole Assignment of Linear Systems by the Sylvester Matrix Equations

The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach

Multirate sampled-data yaw-damper and modal suppression system design

A multirate control law synthesized algorithm based on an infinite-time quadratic cost function, was developed along with a method for analyzing the robustness of multirate systems. A generalized multirate sampled-data control law structure (GMCLS) was introduced. A new infinite-time-based parameter optimization multirate sampled-data control law synthesis method and solution algorithm were developed. A singular-value-based method for determining gain and phase margins for multirate systems was also developed. The finite-time-based parameter optimization multirate sampled-data control law synthesis algorithm originally intended to be applied to the aircraft problem was instead demonstrated by application to a simpler problem involving the control of the tip position of a two-link robot arm. The GMCLS, the infinite-time-based parameter optimization multirate control law synthesis method and solution algorithm, and the singular-value based method for determining gain and phase margins were all demonstrated by application to the aircraft control problem originally proposed for this project

Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system

Optimal actuation in active vibration control using pole-placement

The purpose of this study was to find and demonstrate a method of optimal actuation in a mechanical system to control its vibration response. The overall aim is to develop an active vibration control method with a minimum control effort, allowing the smallest actuators and lowest control input. Mechanical systems were approximated by discrete masses connected with springs and dampers. Both numerical and analytical methods were used to determine the optimum force selection vector, or input vector, to accomplish the pole placement, finding the optimal location of actuators and their relative gain so that the control effort is minimized. The problem was of finding the optimal input vector of unit norm that minimizes the norm of the control gain vector. The methods of pole placement and partial pole placement were introduced, and used to solve various problems, including the active natural frequency modification problem associated with resonance avoidance in undamped systems, and the single-input-multiple-output pole assignment problem for second order systems. Both full and limited controllability were addressed. During the numerical analysis, it was discovered that the system is uncontrollable if a control input vector is chosen that is mathematically orthogonal to an eigenvector associated with a reassigned eigenvalue. Conversely, the optimal input vector was discovered to be mathematically parallel to an eigenvector. This was proven analytically through mathematical proofs and demonstrated with various examples. Simulations were performed in MATLAB and Maple to verify the results numerically. An example using realistic units was developed to show the order of magnitude improvement expected by using this method of optimization. All initial conditions and system parameters were held the same, but the input vector was changed. The optimal input vector provided an order of magnitude improvement over an evenly distributed input vector. The principal conclusion was that by choosing a state feedback input vector that is mathematically parallel to the eigenvector associated with the open-loop eigenvalue to be reassigned, or in the case of multiple assignments, in the subspace of the eigenvectors, the control effort to accomplish pole placement can be reduced to its minimal value