Performance Assessment of Linear Models of Hydropower Plants

TL;DR

This paper evaluates linearized models of hydropower plants, proposing strategies to simplify complex nonlinear dynamics for improved control applications using convex optimization techniques.

Contribution

It introduces new linearization methods for plant head, discharge, and turbine torque, enhancing the accuracy and applicability of models for control purposes.

Findings

Linearization of hydroacoustic resistance improves model simplicity.

Numerical linearization of turbine torque via Taylor expansion.

Models tested on medium- and low-head HPPs with positive results.

Abstract

This paper discusses linearized models of hydropower plants (HPPs). First, it reviews state-of-the-art models and discusses their non-linearities, then it proposes suitable linearization strategies for the plant head, discharge, and turbine torque. It is shown that neglecting the dependency of the hydroacoustic resistance on the discharge leads to a linear formulation of the hydraulic circuits model. For the turbine, a numerical linearization based on a first-order Taylor expansion is proposed. Model performance is evaluated for a medium- and a low-head HPP with a Francis and Kaplan turbine, respectively. Perspective applications of these linear models are in the context of efficient model predictive control of HPPs based on convex optimization.