Hydro-thermal Power System Planning

This tutorial deals with the Brazilian interconnected power system. I suggest readers to go through stage-wise independent finite discrete problem first, in which I give a brief description of the problem and a simple implementation. I simply regard the historical data as the whole sample space. Though it is an unrealistic assumption, the purpose of the notebook is to get you familiar with the problem.

Take a step further. The inflow energy should be a Markovian process. A time series model can be fitted to the historical data. The coefficients of the time series equations are output to the data folder. In order to incorporate this data process into our optimization problem, two approaches are implemented – time series approach and Markov chain approach.

The time series approach adds additional state variables and reformulate the problem into a stage-wise independent form.

For Markov chain approaches, the process of discretization is quite involved. One can certainly make discretization and solve the problem in the same interface using the msppy package (e.g., the portfolio optimization quick start example), but I intentionally separate the routine for illustration purpose.

• Introduction
• Model the uncertain inflow energy
• Approach one: direct calibration without linearization
• Discretize the Markovian continuous uncertainty
• Solve the problem: TS approach
• Solve the problem: Markovian approach
• Solve the problem: Stationary approach