Simulation of Complex Tunnel Systems in Short-term Hydro Scheduling

The goal of short-term hydro scheduling is to find optimal production plans that can be used to operate real-world cascaded watercourses in an efficient way. In Northern and Central Europe, many of these watercourses include complex, pressurized tunnel systems between multiple reservoirs and hydropower plants. Determining the feasibility of a production plan in such systems is a fundamental challenge for hydropower producers. In this paper we propose a new simulation method aimed at solving this task. It is currently in operational use by the largest hydropower producer in Norway. The first part of the paper explains the basic principles, on which the method is founded.

1. By simulating the system with very fine time resolution, results with sufficiently high precision are obtained. The outcome from one time period will be immediately used to facilitate the calculation at the next time period. Continuous updating of information within short intervals not only advances the convergence but also allows the simulator to capture the nonlinear dynamics of complex tunnel systems. This design choice results in a decomposable problem structure that can exploit parallellized computation resources on modern hardware.

2. To meet the requirements for low calculation time, the solutions of non-linear flow equations are stored for re-use in subsequent calculations. This decreases the computational effort in each time step, and makes it possible to process the entire analysis period within acceptable time.

A set of simplified test cases is constructed to highlight the basic properties of the simulation algorithm. Results are compared to more traditional simulation methods that rely on solving a set of dynamic equations for each time step. Real-world case studies demonstrate superior results of the proposed simulation method in terms of both precision and calculation time. Suggestions are given for new areas of application, including water budgeting and manual re-scheduling.