Читать книгу Mathematical Programming for Power Systems Operation - Alejandro Garcés Ruiz - Страница 13

The economic and environmental dispatch of thermal units is one of the most classic problems in power systems operation. It consists of minimizing the operating costs or the total CO₂ emissions, subject to physical constraints such as the power balance and the maximum generation capacity. For the economic dispatch, each generation unit has a cost function fi, which is usually quadratic and depends on the power generated by each unit. Thus, the objective is to minimize the total cost (or emissions), subject to power balance, as presented below:

(1.1)

where pi is the power generated by each thermal unit, and d is the total demand. Environmental dispatch introduces quadratic or exponential functions in the objective function, but the problem’s structure is the same. Moreover, power flow constraints can be introduced into the model, although, in that case, it is more precise to name the problem as an optimal power flow (OPF). Chapter 7 presents the economic and environmental dispatches, while Chapter 10 presents the OPF problem.

Another problem closely related to the economic dispatch of thermal units is the unit commitment. This problem considers not only the operating costs but also the start-up and shut-down costs of thermal units. Therefore, the problem becomes binary and dynamic. This problem is studied in Chapter 8.