Short-term hydro scheduling of a variable speed pumped storage hydropower plant considering head loss in a shared penstock

J Kong,H Abgottspon,H I Skjelbred

doi:10.1088/1755-1315/240/8/082002

J Kong, H Abgottspon + Show 1 more

Open Access

https://doi.org/10.1088/1755-1315/240/8/082002

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Abstract

In this paper we present in detail how to handle the nonlinear and state-dependent elements in the power consumption function (PCF) of a variable speed pump (VP). The function is formulated by piecewise linear approximations with dynamically specified breakpoints. In the proposed method, the head variation resulting from the change in the water level of the upstream and downstream reservoirs and head loss caused by the friction of water on the penstock wall are both considered. Furthermore, we put forward a heuristic to incorporate the head loss in a penstock shared by multiple VPs in a short-term hydro scheduling tool used for daily operation in the real world. The case study is taken from the Limmern pumped storage hydropower plant with 4×250 MW reversible Francis pump-turbines with variable speed technology. Each penstock is shared by two of the four units. The numerical results demonstrate that the appropriate formulation of the PCF and the accurate representation of the head loss in a shared penstock are crucial for obtaining realistic and optimal scheduling for VPs.

Highlights

With the increasing generation from intermittent renewable energies, pumped hydroelectric energy storage is widely adopted as a way to accommodate the power fluctuations of the system
In this paper we present in detail how to handle the nonlinear and state-dependent elements in the power consumption function (PCF) of a variable speed pump (VP)
The function is formulated by piecewise linear approximations with dynamically specified breakpoints

Summary

Introduction

With the increasing generation from intermittent renewable energies, pumped hydroelectric energy storage is widely adopted as a way to accommodate the power fluctuations of the system. We propose a heuristic to solve the problem: when building the I/O curve for one VP, we firstly do not include penstock head loss It leads to the underrated power consumption for the given pumped water flow. The main goals and contributions of this paper are: 1) to convert the nonlinear PCF of a VP into a piecewise linear unit I/O curve; 2) to explicitly formulate the head loss in a shared penstock for a VP; 3) to propose the heuristic that can (nearly) optimally solve the nonlinearity and state-dependency. Mathematical formulation we mainly present the two main issues addressed in the paper: 1) how the nonlinear PCF is incorporated with a MILP framework; 2) how the power loss in a shared penstock is formulated, piecewise linearized and added to the energy balance constraint. The reader interested in the formulation of the power compensation in a shared penstock caused by the hydraulic short-circuit operation is referred to [16]

Sets and Indices

Objective function

Formulate the consumption power loss in a shared penstock

Conclusion