Hydroelectric system modelling for cascaded reservoir-type power stations in the Lower Tana River (Seven Forks Scheme) in Kenya

IEEE Trans. Power Syst.

Grève

McCulloch

2018

This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract-In this paper, we propose an optimal dispatch scheme for a cascade hydroelectric power system that maximises the head levels of each dam, and minimises the spillage effects taking into account uncertainty in the net load variations, i.e., the difference between the load and the renewable resources, and inflows to the cascade. By maximising the head levels of each dam the volume of water stored, which is a metric of system resiliency, is maximised. In this regard, the operation of the cascade hydroelectric power system is robust to the variability and intermittency of renewable resources and increases system resilience to variations in climatic conditions. Thus, we demonstrate the benefits of coupling hydroelectric and photovoltaic resources. To this end, we introduce an approximate model for a cascade hydroelectric power system. We then develop correlated probabilistic forecasts for the uncertain output of renewable resources, e.g., solar generation, using historical data based on clustering and Markov chain techniques. We incorporate the generated forecast scenarios in the optimal dispatch of the cascade hydroelectric power system, and define a robust variant of the developed system. However, the robust variant is intractable due to the infinite number of constraints. Using tools from robust optimisation, we reformulate the resulting problem in a tractable form that is amenable to existing numerical tools and show that the computed dispatch is immunised against uncertainty. The efficacy of the proposed approach is demonstrated by means of an actual case study involving the Seven Forks system located in Kenya, which consists of five cascaded hydroelectric power systems. With the case study we demonstrate that the Seven Forks system may be coupled with solar generation since the "price of robustness" is small; thus demonstrating the benefits of coupling hydroelectric systems with solar generation. Permanent repository link

Section: Preliminariesmentioning

confidence: 99%

Section: A Databasementioning

confidence: 99%

See 1 more Smart Citation

Robust Optimization for Hydroelectric System Operation Under Uncertainty

IEEE Trans. Power Syst.

Grève

McCulloch

2018

“…whereP w k (t ) is the power needed to pump the water of pumped storage hydro plant k at time t and w k (t ) is the pumping rate at time t . We represent the intertemporal water balance constraints that relate the charge/discharge decisions, combining (11) and (13)…”

Section: B Cascading Effect Of Hydroelectric Systemmentioning

confidence: 99%

“…In this section, we illustrate the robust optimal dispatch of a pumped storage hydroelectric system with a cascade that contains two hydroelectric power plants, which is a subsystem of the Seven Forks system in Kenya [13]. This system even artificial is driven through data of an actual system.…”

Section: B Equivalent Tractable Reformulationmentioning

confidence: 99%

Optimal Dispatch of Pumped Storage Hydro Cascade Under Uncertainty

Najibi

Alonso

2018 UKACC 12th International Conference on Control (CONTROL)

2018

In this paper, we propose an optimal dispatch scheme for a pumped storage hydro cascade that maximizes the energy per cubic meter of water in the system taking into account uncertainty in the net load variations. To this end, we introduce a model to describe the behaviour of a pumped storage hydro cascade and formulate its optimal dispatch. We then incorporate forecast scenarios in the optimal dispatch, and define a robust variant of the developed system. The resulting optimization problem is intractable due to the infinite number of constraints. Using tools from robust optimization, we reformulate the resulting problem in a tractable form that is amenable to existing numerical tools and show that the computed dispatch is immunised against uncertainty. The efficacy of the proposed approach is demonstrated by means of a realistic case study based on the Seven Forks system located in Kenya.

Optimal Short-Term Operation of a Cascaded Hydro-Solar Hybrid System: A Case Study in Kenya

IEEE Trans. Sustain. Energy

McCulloch

2019

In this paper we propose an optimal dispatch scheme for a cascaded hybrid hydro-solar power system, i.e., a hydroelectric system coupled with solar generation, that maximises the head levels of each dam, and minimises the spillage effects. As a result more water is stored in the dams to meet a given amount of energy providing more flexibility to the system in dry months. This dispatch scheme is based on the development of a simplified hydroelectric power system model which has low computational burden and may be implemented for the short-term operation of a cascaded hydro-solar hybrid power system. To this end, the non-convex relationships that describe the system physical constraints, e.g., hydroelectric power output, are transformed into affine relationships; thus reducing the computational complexity. The transformations are based on the construction of convex envelopes around bilinear functions, piecewise affine functions, and exploitation of optimisation properties. We validate the proposed framework and quantify the benefits of coupling hydroelectric and solar resources in terms of live water volume in dams and amount of solar a system may withstand with the Tana river cascade located in Kenya through an analysis of incorporating actual system data.