  Continuous-time optimization models have successfully been used to capture
the impact of ramping limitations in power systems. In this paper, the
continuous-time framework is adapted to model flexible hydropower resources
interacting with slow-ramping thermal generators to minimize the hydrothermal
system cost of operation. To accurately represent the non-linear hydropower
production function with forbidden production zones, binary variables must be
used when linearizing the discharge variables and the continuity constraints on
individual hydropower units must be relaxed. To demonstrate the performance of
the proposed continuous-time hydrothermal model, a small-scale case study of a
hydropower area connected to a thermal area through a controllable high-voltage
direct current (HVDC) cable is presented. Results show how the flexibility of
the hydropower can reduce the need for ramping by thermal units triggered by
intermittent renewable power generation. A reduction of 34% of the structural
imbalances in the system is achieved by using the continuous-time model.

Optimization and Control