Constrained Cost Optimization Under Uncertainty for an Incompletely-Connected Electric Utility System

Andrew Howe, Chris Humphries
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In this case study, we build a stochastic model to perform cost optimization and investment decision modeling for a system of interconnected power grids.

The modeled utility system is composed of four independent power-generating regions. Each region has its own power demand and portfolio of types of power generating plants. Because of the variation in generating assets, the generation cost profile can vary dramatically by region. Power transmission lines connect the four regions subject to the constraints that some regions are not connected at all, and the amount of power that is allowed to flow over each boundary is limited. Furthermore, power plant availability and total generating capacity vary stochastically, as a function of many factors.

First we mathematically define an optimization problem that allows us to meet the aggregate demand of all regions under these transmission constraints while minimizing the total cost. This is then implemented under the framework of uncertain generation capacity so we can make prob- abilistic statements about the costs and other relevant quantities. Ultimately, this optimization model can be used to guide and inform capacity and transmission expansion investment-related decisions. Our model is developed using Microsoft Excel and the @Risk and Evolver tools from Palisade’s Decision Tools Suite.


constrained optimization; utility cost modeling; decision support system; investment analysis

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