Hydro-thermal Electric Power System Research Articles

Optimal scheduling of large-scale hydrothermal power systems using the Lagrangian relaxation technique

This paper describes a method for scheduling large-scale hydrothermal power systems based on the Lagrangian relaxation technique. Lagrangian multipliers are introduced to decompose the original problem into small independent subproblems one for each generating unit, which are solved through a three level calculation structure. Using this approach, a large-scale hydrothermal electric power system could be treated as a precise general problem that takes into account the following among other factors: (a) random load demand; (b) non-linear cost function of thermal production; (c) variations of water head in hydroelectric plants; (d) non-linear function of hydroelectric output; (e) a system of cascaded hydroelectric plants including regulation reservoirs with limited spillage capacity. An economic interpretation of the results is given and an illustrative application of the technique is presented.

Selection of objectives in minimum loss power flow in hydrothermal electric power systems

Two formulations of the optimal minimum loss hydrothermal power flow problem in electric power systems are discussed. The formulations — one based on Kron's loss objective function and the other a network-based loss formulation — are treated in detail and the results of the two approaches are compared using two standard test systems. For the systems investigated, Kron's loss minimization schedules higher thermal generation than that required by the network loss minimization during lower demand. Kron's loss minimization involves lower active power transmission losses than those involved by the network-based loss minimization during low demand, and higher active power transmission losses than those required by the network-based loss minimization during higher demand. The total energy loss involved in the outcome of the Kron's loss minimization results is higher than that due to the network-based loss minimization schedule. There is a negligible difference in voltage magnitudes. Reactive power generation results favour the network-based loss approach. On the basis of the experiments, it is concluded that a network-based loss model is preferable in this application.

Minimum loss power flow in hydrothermal electric power systems

Abstract Optimal hydrothermal power flow in electric power systems is considered in this paper on the basis of the minimum loss formulation of the objective function. The computational implementation is based on Newton's iterative procedure, with special initial guess and sparsity-based matrix manipulations to obtain improved convergence properties. The proposed method is tested using three standard test systems, and the effect of the volume of water availability on the optimal solutions is explored. The active thermal generation decreases and the reactive generation at the slack bus increases as the volume of water available increases. Moreover, losses, water worth, and costs decrease as the volume of water available increases. As the active hydro generation increases, the corresponding reactive power generation is decreased. As a general rule, load voltage magnitudes increase with an increase in water availability, with the exception of some buses. The voltage differences are not appreciable in a normally loaded system, but have been observed to be significant when the load at the end of long lines is increased.

COMPARATIVE STUDY OF DIFFERENT FORMULATIONS IN HYDRO-THERMAL OPTIMAL LOAD FLOW PROBLEM

Abstract This paper deals with the optimal power flow problem in a fixed-head hydrothermal electric power system. As the hydro generation is energy limited, a dynamic optimization problem involving the daily scheduling of the system is encountered. This dynamic optimal power flow problem requires a solution of a large scale set of non-linear simultaneous equations. Newton-Raphson's method has been implemented to obtain the optimal operational strategy. Due to the large scale nature of the problem, we have adopted a sparse matrix solution to the problem. Three different formulations involving (1) Polar form (2) Rectangular form and (3) Current mismatch form have been developed. We have developed an algorithm with three different versions. Implementation of these methods is detailed in this paper. The algorithms have been successfully executed for six different IEEE test systems varying in size from 5-bus to 118-bus systems. The test results and CPU times are detailed. A comparative study of the performance...

Main Design Parameters Optimization of a Large Hydro-Thermal Electric Power System

Abstract This paper presents a nonlinear programming model and a solution technique for optimizing such main design parameters of a large hydro-thermal electric power system as total storage, dead storage and installed capacity of each station. This technique uses an augmented Lagrangian algorithm with a new approach to save computer core storage. Application of this model to Yunnan Province (P.R.C.) hydro-thermal electric power system which involves five reservoirs, eleven hydropower stations and several thermal stations is summarized.

OPTIMAL ECONOMIC OPERATION OF THERMAL AND VARIABLE HEAD HYDRO SYSTEMS USING HAMILTON-LAMONT'S MODEL AND NEWTON-RAPHSON METHOD

ABSTRACT In this paper, optimum scheduling of an integrated hydro-thermal electric power systems with variable head hydro plants, is treated. The scheduling problem is solved by the use of coordination equations developed by Ricard and Kron. There are many reported models to represent the performance of a hydro plant, and here Hamilton-Lamont's model is used to derive specific optimality conditions for the problem. Using Newton-Raphson method, an algorithm is developed for solving iteratively the problem of optimal power scheduling. The iterative method is implemented using a specially designed initial guess estimator based on the physical properties of the problem to generate a set of feasible initial estimates of the unknowns to speed up the process. A number of example systems are used to test the performance of the algorithm. Successful convergence of the algorithm is reported in this paper and results for one sample test system are given.

Optimal hydrothermal load flow: Formulation and a successive approximation solution for fixed head systems

AbstractThis paper deals with the optimal load flow problem in a fixed‐head hydrothermal electric power system. Equality constraints on the volume of water available for active power generation at the hydro plants as well as inequality constraints on the reactive power generation at the voltage controlled buses are imposed. Conditions for optimal load flow are derived and a successive approximation algorithm for solving the optimal generation schedule is developed. Computer implementation of the algorithm is discussed, and the results obtained from the computer solution of test systems are presented.

Optimal Load Flow in Hydro-Thermal Systems: Computational Experience with Newton's Method

ABSTRACT In this paper the problem of optimal load flow in a hydro-thermal electric power system is considered. It is assumed that the hydro generation resources are energy limited. As a result, a dynamic optimization problem involving the daily schedule of the system is encountered. The scheduling problem requires the solution of a large scale set of nonlinear simultaneous equations. In this paper Newton's method is used to solve the scheduling problem. The algorithm has been successfully tested with five test systems varying in size from a 5 bus system to a 57 bus system. Results of the computational experience are summarized in this paper.

The Hydrothermal Optimal Load Flow, A Practical Formulation and Solution Techniques Using Newton's Approach

This paper is concerned with the problem of optimal power flow in a hydro-thermal electric power system (HTOPF). The formulation and optimality conditions for systems with fixed head hydro-plants subject to an energy limited constraint are presented. The solution to obtain the optimal operational strategy is implemented using Newton's method. Due to the large scale nature of the problem, special sparsity oriented and structural property enhancements are explored and four versions for algorithmic implementation are detailed in the paper. Special attention is paid to finding realistic initial guess estimates for the algorithms reported. Results of computational experience with six standard test systems are reported in the paper.

Optimal Parameter Estimation for Hydro-Plant Performance Models in Economic Operation Studies

Optimal Economic Operational schedules in hydro-thermal electric power systems are obtained on the basis of models of the various subsystems involved. In this paper we are concerned with models of hydro-plant performance characteristics. Due to the diversity of plant types and installations, a number of models have been proposed in developing optimal operational strategies over the years. Here we choose four commonly used models. The problem of finding optimal estimates of model parameters is investigated for the Glimn-Kirchmayer model, the Hildebrand model, the Hamilton-Lamont model and the Arvanitidis-Rosing model. We develop the optimal estimator equations for each model using the weighted-least-squares approach. The result for three of the models is a set of nonlinear equations in the unknown parameters. We adopt Newton's method for actually implementing the optimal estimators. Due to the sensitivity of the algorithm's convergence characteristics to the initial guess of the unknowns, we explore and present procedures for generating initial guess values to improve the procedure's performance. Computational experience with the techniques is given in the paper to confirm its feasibility using test data from existing hydro-plants. The paper proposes and examines some extensions to the classical models to improve the accuracy of the modeling process.

Long-term expansion planning for hydrothermal electric power systems

This paper shows some aspects of the applicability of mixed integer programming (MIP) in expansion planning for regional electric utility systems, considering both power plants and the transmission network. The hydrothermal generation system may include significant run-of-river and reservoir power stations, and also pumped storage stations. Some essential elements of the model are explained to demonstrate the MIP modelling. The application of the model to the long-term expansion planning problem of a hydrothermal power system is also described.

An Application of Powell's Hybrid Method to Optimum Operation of Fixed-Head Hydro-Thermal Electric Power Systems

Basic requirements of any proposed algorithm for implementing optimum operation strategies in integrated electric power systems are speed, efficiency and reliable convergence. A powerful candidate for this is Newton-Raphson Method for solving nonlinear equations which has quadratic convergence properties. However, this classical iteration can fail to converge and in this case alternate methods should be sought. Among the possible candidates is a Hybrid Method due to M.J.D. Powell which provides reliable convergence. In this paper we detail the application of Powell’s Method to the problem of implementing the coordination equations for hydrothermal electric power systems with fixed head hydro plants. Results pertaining to utility systems are presented and an evaluation of the method’s performance is given.

Optimal operation of multi-chain hydro-thermal power systems

This paper considers the problem of optinal operation of hydro-thermal electric power systems. A system with a general configuration of multi-chains of reservoirs hydro sybsystem is treated. Optimal operation strategies developed using the minimum norm problem formulation of functional analytic optimization are given. The computational aspects of actually inplementing the strategies are discussed. In particular a general modified contraction mapping algorithm is treated. Computational experiments with a number of algorithms are reported for a sample system. Convergence characteristics of each algorithm are discussed.

Application of functional analysis to optimization of electric power systems†

In this paper the hydro-thermal scheduling problem is discussed. An interconnected hydro-thermal electric power system is scheduled such that maximum economy is achieved. The schedules obtained are designed to meet a specified active power demand and simultaneously to satisfy energy constraints imposed on the hydro-plants generations. The scheduling problem is solved by the use of functional analysis and, in this case, the minimum norm problem formulation is employed. It is emphasized that the optimal solution found here is guaranteed to be the unique optimal solution. The practical implementation of finding the generation schedule is illustrated by way of two examples.

Verification of Prediction and Economic Operation in Hydrothermal Electric Power System

Verification of Prediction and Economic Operation in Hydrothermal Electric Power System

On Some Consideration and Solution Method of the Economic Operation Problem of Hydro-Thermal Electric Power System.

On Some Consideration and Solution Method of the Economic Operation Problem of Hydro-Thermal Electric Power System.