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Hydro generation scheduling: non-linear programming and optimality conditions

Hydro generation scheduling: non-linear programming and optimality conditions

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A mathematical analysis based on hydroelectric plant characteristics, i.e. reservoir and tailrace geometry, is the central chapter's subject. Deterministic mid-short term scheduling planning could be solved to optimality if generation function is at least biconcave, i.e. a discontinuous reservoir and a uniform tailrace. Although the formulation is not proved to be unimodal, a B&B method based on concave envelope relaxation converges to global optimum. In a broader sense, increasing property is established for hydro-generation function. As the formulation is linearly constrained, i.e. only linear inequalities, special algorithms could exploit boundary of the feasible set (a polytope) to find a global optimum. Unimodularity property could also be studied in general case, i.e. arbitrary reservoir and tailrace height.

Chapter Contents:

  • 8.1 Introduction
  • 8.2 Hydropower generation function
  • 8.2.1 Physical properties of geometric functions
  • 8.2.1.1 Increasing property
  • 8.2.1.2 Convexity and concavity
  • 8.2.2 Special cases of geometric functions
  • 8.2.2.1 Examples
  • 8.2.3 Mathematical properties
  • 8.2.3.1 Run-off-the-river plant with variable tailrace height
  • 8.2.3.2 Storage plant with constant tailrace height
  • 8.2.3.3 Stair-like reservoir with a uniform tailrace
  • 8.2.3.4 Storage plant with variable tailrace height
  • 8.3 Water conservation and discharge limits
  • 8.3.1 Head sensitive discharge limits
  • 8.4 Cascade D-HGS formulation
  • 8.5 Global optimization approach
  • 8.5.1 Computational results
  • 8.6 Conclusions
  • References

Inspec keywords: power generation planning; reservoirs; power generation scheduling; hydroelectric power stations; nonlinear programming; hydroelectric generators

Other keywords: unimodularity property; linear inequalities; B&B method; nonlinear programming; tailrace height; mathematical analysis; tailrace geometry; deterministic mid-short term scheduling planning; hydroelectric plant characteristics; discontinuous reservoir; hydro generation scheduling; hydro-generation function; arbitrary reservoir; concave envelope relaxation; optimality conditions; uniform tailrace

Subjects: Hydroelectric power stations and plants; Power system management, operation and economics; Power system planning and layout; Optimisation techniques

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