Long-term optimal operation of a parallel multireservoir power system

Long-term optimal operation of a multireservoir system is complex because it is a dynamic problem (present decisions for one reservoir depend on future decisions for all reservoirs); the optimal operating policy for one reservoir depends not only on its own energy content, but also on the corresponding content of each one of the other reservoirs; it is a highly stochastic problem with respect to the reservoir inflows and it is a nonlinear problem. This paper presents a new method for determining the optimal monthly operating policy of a power system consisting of multireservoirs on a multiriver system taking into account the stochasticity of the river flows. Functional optimization techniques and minimum norm formulation have been used. Results for a numerical example composed of three rivers with four reservoirs, three reservoirs, and two reservoirs on each river, respectively, are presented.This work was supported by the National Research Council of Canada, Grant. No. A4146.     

Optimal long-term operation of a multireservoir power system for critical water conditions

We present in this paper a new method for solving the optimization problem of a variable head multireservoir power system under a critical water condition for long-term regulation. The problem is formulated as a minimum norm problem. The proposed method is efficient in computing time and in calculating the expected benefits from the system during the critical period. Numerical results are presented for a real system in operation consisting of two rivers; each river has two reservoirs connected in a series.This work was supported by the National Research Council of Canada, Grant No. A4146. The authors wish to thank B. C. Hydro for providing the reservoir data.     

Minimum norm approach to optimal long-term operation of multireservoir power systems with specified monthly generation

The aim of this paper is to present a new algorithm to maximize the value of the energy produced from a multireservoir power system, plus the estimated value of water remaining in storage at the end of the 12-month planning period. The systems described here are characterized by having a specified monthly generation, and this generation is equal to a certain percentage of the total generation at the end of the year.The problem is formulated as a minimum norm problem in the framework of analytic optimization. Numerical results are reported for a real system in operation consisting of three rivers; each river has two series reservoirs. The proposed algorithm is efficient in computing time and in calculating the total expected benefits from the system.This work was supported by the National Research Council of Canada, Grant No. A4146. The authors would like to acknowledge data obtained from B.C. Hydro, Vancouver, B.C., Canada.     

Modelling and optimization of reservoirs for long-term regulation with variable head using functional analysis

In this paper, functional analysis and minimum norm formulation are applied to maximize the total benefits from two hydro reservoirs. The hydroelectric power generation is treated as a nonlinear function; water head variation and stochasticity of the river flows are included. The resulting problem has a nonlinear objective function and linear constraints. The proposed method is computationally efficient, compared to previous techniques. Numerical results are presented for widely different water conditions for an actual system in operation.This work was supported by the National Research Council of Canada, Grant No. A4146. The authors wish to thank B. C. Hydro for providing the reservoir data.     

Optimal discrete long-term operation of nuclear-hydrothermal power systems

We discuss in this paper an algorithm for solving the optimal long-term operating problem of a hydrothermal-nuclear power system by application of the minimum norm optimization technique. The algorithm proposed here has the ability to deal with large-scale power systems and with equality and/or inequality constraints on the variables. A discrete model for the xenon and iodine concentrations is used, as well as a discrete model for hydro reservoirs. The optimization is done on a monthly time basis. For simplicity of the problem formulation, the transmission line losses are considered as a part of the load.This work supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A4146.     

Optimum load scheduling of nuclear-hydro-thermal power systems

This paper considers the problem of short-term optimal operation of nuclear-hydro-thermal electric power systems. The solution is obtained by use of a functional analytic optimization technique that employs the minimum norm formulation.A power system with an arbitrary number of generating stations is considered. The limited flexibility exhibited by the thermal nuclear reactors, when operating in a load-following mode, is accounted for by means of a model of the xenon concentration in their cores. The nonlinear effects induced by trapezoidal water reservoirs and the time delay of the water flow between upstream and downstream hydroplants is taken into consideration as well.A two-level iterative scheme of the feasible type is proposed for implementing the optimal solution.This work was supported in part by the National Research Council of Canada, Grant No. A-4146.     

Optimal control of linear time-varying systems via Fourier series

The optimal control of linear time-varying systems with quadratic cost functional is obtained by Fourier series approximation. The properties of Fourier series are first briefly presented and the operational matrix of backward integration together with the product operational matrix are utilized to reduce the optimal control problem to a set of simultaneous linear algebraic equations. An illustrative example is included to demonstrate the validity and applicability of the technique.     

Optimization of the production of hydroelectric power systems with a variable head

We present in this paper a new approach for optimization of the production of hydroelectric power systems with a variable head. The problem is formulated as a minimum norm problem.The method takes into account the water head variation. To avoid underestimation of production for rising water levels and overestimation for falling water level, an average head (of begin and end of time step) is used. The method also takes into account the stochasticity of the river flows. Numerical results for a real system in operation including up to six reservoirs are reported for different water conditions. The proposed method is computationally efficient compared to other approaches.This work was supported by the National Research Council of Canada, Grant No. A-4146. The authors would like to acknowledge the data obtained from British Columbia Hydro.     

Decentralized optimum load frequency control of interconnected power systems

A new approach for designing a linear regulator for the problem of load frequency control (LFC) of interconnected power systems is developed. The control is specified to be of proportional-plus-integral (P-I) form and is only a function of the measurable states. The LFC problem is formulated as a parameter optimization problem.This work was supported in part by the National Research Council of Canada, Grant No. A4146.     

Optimal control of impulsive hybrid systems

In this paper, we deal with optimization techniques for a class of hybrid systems that comprise continuous controllable dynamics and impulses (jumps) in the state. Using the mathematical techniques of distributional derivatives and impulse differential equations, we rewrite the original hybrid control system as a system with autonomous location transitions. For the obtained auxiliary dynamical system and the corresponding optimal control problem (OCP), we apply the Lagrange approach and derive the reduced gradient formulas. Moreover, we formulate necessary optimality conditions for the above hybrid OCPs, and discuss the newly elaborated Pontryagin-type Maximum Principle for impulsive OCPs. As in the case of the conventional OCPs, the proposed first order optimization techniques provide a basis for constructive computational algorithms.     

Optimal feedback control of bilinear systems

Feedback synthesis of optimal constrained controls for single-input bilinear systems is considered. Quadratic cost functionals (with and without quadratic control penalization) are modified by the inclusion of additional nonnegative state penalizing functions in the respective cost integrands. The latter functions are chosen so as to regularize the problems, in the sense that feedback solutions of particularly simple form are obtained. Finite and infinite time horizon problem formulations are treated, and associated aspects of feedback stabilization of bilinear systems are discussed.     

Optimal control of a dynamical system representing a gantry crane

Problems arising in the optimal control of gantry crane instaliations are considered. Continuous controls to minimize a control squared objective function are obtained. The amplitude of in-plane oscillations of the suspended mass is assumed small. The optimal controls are sufficiently simple for practical realization.     

Opticon: An algorithm for the optimal control of nonlinear stochastic models

In this paper we describe the algorithm OPTCON which has been developed for the optimal control of nonlinear stochastic models. It can be applied to obtain approximate numerical solutions of control problems where the objective function is quadratic and the dynamic system is nonlinear. In addition to the usual additive uncertainty, some or all of the parameters of the model may be stochastic variables. The optimal values of the control variables are computed in an iterative fashion: First, the time-invariant nonlinear system is linearized around a reference path and approximated by a time-varying linear system. Second, this new problem is solved by applying Bellman's principle of optimality. The resulting feedback equations are used to project expected optimal state and control variables. These projections then serve as a new reference path, and the two steps are repeated until convergence is reached. The algorithm has been implemented in the statistical programming system GAUSS. We derive some mathematical results needed for the algorithm and give an overview of the structure of OPTCON. Moreover, we report on some tentative applications of OPTCON to two small macroeconometric models for Austria.     

Optimal load frequency control with governor backlash

A new technique is described for designing an optimal controller for a system whose dynamical equations contain a backlash element. The approach is applied to the problem of load frequency control (LFC) of a single area steam power system.This work was supported in part by the National Research Council of Canada, Grant No. A4146.     

Optimal control of infinite-dimensional uncertain systems

In this paper, we consider a minimax problem of optimal control for a class of strongly nonlinear uncertain evolution equations on a Banach space. We prove the existence of optimal controls. A nontrivial example of a class of systems governed by a nonlinear partial differential equation with uncertain spatial parameters is presented for illustration.This work was supported in part by the National Science and Engineering Research Council of Canada under Grant No. A7109 and The Engineering Faculty Development Fund, University of Ottawa.The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.     

Optimal control of heterogeneous systems: Basic theory

A general model of a heterogeneous control system is introduced in the form of a first order distributed system with nonlocal dynamics and exogenous side-conditions. The heterogeneity is represented by a parameter taking values in an abstract measurable space, so that both continuous and discrete heterogeneity, as well as probabilistic heterogeneity without density, are included. A distributed and a lumped controls are involved, the latter appearing also in the side conditions. An existence theorem is proved for the uncontrolled system, and the sensitivity of the solution with respect to the control variables is estimated. The main result is an optimality condition in the form of the Pontryagin local maximum principle. A global maximum principle holds for the distributed control under an additional condition that rules out discrete measurable heterogeneity spaces. A number of possible applications are outlined: age-structured systems, size-structured systems, (nonlocal) advection-reaction equations, static parametric heterogeneity in epidemiology, and two-stage control systems with uncertain switching time.     

Optimal control of semilinear parabolic systems with state constraint

The aim of this work is to obtain the existence of optimal solution and maximum principle for optimal control problem with pointwise type state constraint governed by semilinear parabolic systems with certain polynomial-like nonlinearity. Application to optimal control problems of the phase transition system is given.     

Optimal control of continuous-time deterministic systems with incomplete discrete feedback

Sufficient conditions for optimality are obtained for controls that depend on the current time and values of known functions of the state vector at finite points of the time interval. The equations for finding the required control laws are derived. An example is given for which an exact solution of the problem can be obtained.The author is grateful to Professor R. W. Rishel for his support during the preparation of the paper.     

Optimal control of differential-difference systems with intragroup symmetry

A decomposition method of finding the optimal control of differential-difference systems with intragroup symmetry is presented. The introduction of two forms of motions of coordinates of separate groups allows us to reduce the original optimal control problem to the solution of optimal control problems of order less than the order of the initial problem.     

A control method for speeding up response of hydroelectric station power canals

A control method which, through the suitable servo-operation of the check gates, attains a consistent improvement in the speed of response of hydroelectric power canals is presented. Its application allows the size of the canal headpond to be reduced at the design stage of the power station as well. The proposed method is based on the constant volume control concept and uses a mathematical model of the power canal derived from linearization of the Saint-Venant equations. The results of the computer simulation of a controlled real system's dynamic behavior obtained through the use of the method of characteristics are presented.