Gustav S. Christensen

Optimal filtering of linear discrete dynamic systems based on least absolute value approximations

This paper offers a new formulation for optimal linear filtering of dynamic systems based on Weighted Least Absolute Value (WLAV) approximations. We start, in this paper, with a single stage process as an introduction to the multistage processes. Given the initial estimation x(0) prior to the measurement at the initial stage, we calculate the error in each measurement. We choose from the set of measurement a number of observations which having the smallest residuals equal to the rank of the matrix H, n, provided that the number of measurements, m, is greater than the number of unknowns (m > n). This set of measurements is used to estimate the unknown n states. It has been shown that the best WLAV is superior to the best Weighted Least Squares (WLS), when estimating the true form of data that contain some very inaccurate observations.

Extensions to Functional Optimization of Common-Flow Hydro-Thermal Systems

The problem of optimum scheduling of hydro-thermal power systems is considered. A functional analytic optimization technique is applied to a general system. The power system considered contains (n-m) hydro-plants on the same stream. The time delay of the flow between upstream and downstream plants is taken into consideration. This is an extension of the results reported in [1]. Optimal solutions to some special cases of this problem are given and shown to agree with results obtained earlier using other techniques. The resulting optimal schedule can be easily incorporated in existing economy dispatch program that neglect the hydraulic coupling.

Functional Optimization of Common-Flow Hydro-Thermal Systems

A functional analytic optimization technique is applied to the Problem of optimum scheduling of hydro-thermal power systems. The power system considered contains two hydro-plants on the same stream. The time delay of flow between upstream and downstream plants is taken into consideration. The problem is formulated as an abstract minimum norm problem. The optimal solution found here satisfies the necessary conditions of variational calculus for control problems with delayed arguments. A generalized contraction mapping technique is applied to a sample system to illustrate the results obtained.

Dynamic Optimal Load Flow

The load flow problem in an electric power system is concerned with solving a set of static nonlinear equations describing the electric network performance. The problem is formulated on the basis of Kirchhoff’s laws in terms of active and reactive power injections and voltages at each node in the system. Presently, the load flow program is a major tool for the electric power systems engineer in carrying out diverse functions in the planning and operation of the system. This topic is treated in detail in many introductory electric power systems textbooks (Refs. 3.1–3.4).

Optimal filtering for continuous linear dynamic systems based on WLAV approximations

Abstract In this paper, we offer a new formulation for optimal filtering of continuous linear dynamic systems based on Weighted Least Absolute Value (WLAV) approximations. This filter may be better than a Kalman filter for continuous systems, since the Kalman filter algorithm was obtained by minimizing a Weighted Least Square cost functional (WLS), while the proposed filter algorithm is obtained by equating to zero the sum of the absolute error in the measurements. It is shown that the best WLAV approximations are superior to the best WLS approximations when estimating the true form of data that contain some very inaccurate observations. This paper is an extension to the work that has been done in a companion paper by the same two authors for discrete dynamic systems.

Optimization of hydropower systems operation with a quadratic model

Abstract This paper is devoted to the development and application of a reservoir optimization model that yields monthly release policies. The generalization consists of the capability to handle nonlinear energy generation rates in the objective function (maximization of system annual energy generation). A quadratic model for the elevation-storage (average storage) curve is used. The optimization problem is described and formulated as the optimal control of a multivariable state-space model in which the state and control vectors are constrained by sets of equality and inequality relations. Lagrange and Kuhn-Tucker multipliers are used to adjoin these equality and inequality constraints to the objective functions. The resulting cost functional is maximized by using the minimum norm formulation of the functional analysis. Numerical results are reported for a real system in operation consisting of three rivers; each river has two series reservoirs.

Optimal Control of Turboalternators

This chapter is devoted to the solution of the problem of optimal control of synchronous turboalternators. In the first section of this chapter the optimal torque and voltage control of a large turbogenerator connected to an infinite bus is found by using the minimum norm formulation. In the second section the optimal control of a system with two identical interconnected turbogenerators connected to an infinite bus is considered. Control of the generators is effected through control of field voltages and turbine torques. Finally, in the last section a realistic feedback control of two interconnected turbogenerators is considered.

Some Optimal Control Techniques

The intent of this chapter is to introduce fundamental concepts of optimal control theory that are relevant to the applications treated in the following Chapters. Emphasis will be given to clear, methodical development rather than rigorous formal proofs. The fundamental conditions of the variational calculus for dynamic system optimization are discussed in Section 2.2. A brief summary of Pontryagin’s maximum principle is given in Section 2.3. In Section 2.4 the functional analytic technique of formulating optimization problems in the minimum norm form is dealt with. A brief treatment of some basic concepts from functional analysis is given prior to stating one powerful version of minimum norm problems.

Economic Coordination of Hydrothermal—Nuclear Systems

It is the purpose of this chapter (1) to formulate the problem of optimal short-term operation of hydrothermal-nuclear systems, (2) to obtain the solution by using a functional analytic optimization technique that employs the minimum norm formulation, and (3) to propose an algorithm suitable for implementing the optimal solution.

Optimal Tie-Line Control

For more than two decades, the problem of load frequency control (LFC) using conventional or advanced-control theory has been the subject of numerous studies. The conventional LFC approach often employs what is called the tie-line bias concept to design a system controller that has a proportional-plus-integral (PI) action. This type of control is used extensively in practice in preference to all the techniques that have been proposed recently, employing modern control theory. The reason for that is that most recent techniques have developed linear feedback controls that are functions of all the system state variables as well as the system disturbances (Refs. 5.1, 5.2). Therefore, it was necessary to design an observer to realize these kind of controls (Ref. 5.3). Once an observer is introduced into the system, the cost is increased, and the control is no longer optimal (Ref. 5.4). Another important reason is that a control that depends upon all the system states needs some of these state variables to be telemetered, since the areas of interconnected power systems (IPS) are spread over large geographical territories. This is why, in practice, control engineers prefer to use the conventional control to the advanced one, in spite of the contention that the latter improves the system transient performance.