With a fast-growing electricity demand and a larger proportion of intermittent energy sources follows a greater need for flexible and balancing sources of electricity, such as hydropower. Planning of hydropower production is considered to be a difficult problem to solve due to several nonlinearities, combinatorial properties and the fact that it is a large scale system with spatial-temporal coupling. Optimization approaches are used for solving such problems and a common simplification is to disregard the effect of head variation on the power output. This thesis presents two methods for modeling the head dependency in optimization models for hydropower river systems, the Triangulation method and the Bilinear method. The Triangulation method implements a three-dimensional interpolation technique called triangulation, using a MILP formulation. This is a commonly used method found in the literature. The Bilinear method is a novel approach that applies a piecewise bilinear approximation of the power production function, resulting in a BLP problem. Also, a strategy for selecting which hydropower stations to include head dependence for is provided. The performance of the methods was evaluated on authentic test cases from Lule River and compared to results obtained by Vattenfall's current model without head dependency. The Triangulation method and the Bilinear method give higher accuracy, and are therefore considered more realistic, than the current model. Further, the results indicate that it is sufficient to include head dependence for a subset of stations since the error is significantly reduced. Mid- to long-term scenarios were solved with high accuracy when a subset of the stations was modeled as head dependent. Overall, the Bilinear method had a significantly shorter computational time than the Triangulation method.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:liu-186934 |
| Date | January 2022 |
| Creators | Larsson, Lina, Lindberg, Mikaela |
| Publisher | Linköpings universitet, Tillämpad matematik, Linköpings universitet, Tekniska fakulteten |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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