Abstract

An essential challenge in generation scheduling (GS) problems of hydrothermal power systems is the inclusion of adequate modeling of the hydroelectric production function (HPF). The HPF is a nonlinear and nonconvex function that depends on the head and turbined outflow. Although the hydropower plants have multiple generating units (GUs), due to a series of complexities, the most attractive modeling practice is to represent one HPF per plant, i.e., a single function is built for representing the plant generation instead of the generation of each GU. Furthermore, due to the computation time constraints and representation of nonlinearities, the HPF must be given by a piecewise linear (PWL) model. This paper presented some continuous PWL models to include the HPF per plant in GS problems of hydrothermal systems. Depending on the type of application, the framework allows a choice between the concave PWL for HPF modeled with one or two variables and the nonconvex (more accurate) PWL for HPF dependent only on the turbined outflow. Basically, in both PWL models, offline, mixed-integer linear (or quadratic) programming techniques are used with an optimized pre-selection of the original HPF dataset obtained through the Ramer-Douglas-Peucker algorithm. As a highlight, the framework allows the control of the number of hyperplanes and, consequently, the number of variables and constraints of the PWL model. To this end, we offer two possibilities: (i) minimizing the error for a fixed number of hyperplanes, or (ii) minimizing the number of hyperplanes for a given error. We assessed the performance of the proposed framework using data from two large hydropower plants of the Brazilian system. The first has 3568 MW distributed in 50 Bulb-type GUs and operates as a run-of-river hydro plant. In turn, the second, which can vary the reservoir volume by up to 1000 hm3, possesses 1140 MW distributed in three Francis-type units. The results showed a variation from 0.040% to 1.583% in terms of mean absolute error and 0.306% to 6.356% regarding the maximum absolute error even with few approximations.

Highlights

  • We presented two different methods of partitioning the hydroelectric production function (HPF) domain: (i) the most used in the literature which is based on uniform discretization, i.e., the domain is subdivided into a grid of equidistantly spaced points, and (ii) in which an optimal partition of the domain is performed using the Ramer‐Douglas‐Peucker algorithm (RDP) algorithm which, in general terms, searches for a curve with a higher concentration of points in regions of pronounced nonlinearity of the HPF

  • The data sets were taken from two Hydropower Plant (HP) in Brazil: Santo Antônio Hydropower Plant (SAHP) and Machadinho Hydropower Plant (MAHP)

  • This paper proposed a framework to obtain piecewise linear approximations for plant‐based HPF supported by recent mathematical contributions in the literature

Read more

Summary

Introduction

The electricity industry in the world has gone through significant transitions regarding the digitalization of electric networks, management and automation of industries, expansion in the use of renewable sources, and improvement of decentralized energy generation technologies. This process is synthesized in the so‐called three Ds: decarbonization, digitization, and decentralization. In this context, Brazil, for example, has a privileged position, having, in 2020, about 83% of the electrical power system made up of renewable energy resources. In the case of markets with centralized dispatch, i.e., the tight‐

Objectives
Results
Conclusion
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call