Systems and methods for managing power generation and storage resources

1. A non-transitory, computer-readable storage medium comprising instructions configured to cause a computing device to perform operations for power system management, the operations comprising:

modeling energy trajectory characteristics of respective energy storage units, comprising charging, discharging, and ramping constraints of the respective energy storage units;

determining a schedule for the energy storage units during an operating period of the power system, the schedule comprising:

configuring the energy storage units to selectively draw power from the power system and supply power to the power system at designated times during the operating period;

adapting the schedule for the energy storage units to balance a net load forecast for the operating period and generation trajectories of power generating units scheduled to supply power to the power system during the operating period; and

configuring the energy storage units to operate in accordance with the determined schedule during the operating period.

2. The non-transitory computer-readable storage medium of claim 1 , wherein:

the schedule determined for the energy storage units define energy trajectories of the respective energy storage units, and

determining the schedule for the energy storage units comprises configuring the energy trajectories of the respective energy storage units to comply with the charging, discharging, and ramping characteristics of the respective energy storage units.

3. The non-transitory computer-readable storage medium of claim 1 , further comprising:

determining generation trajectories for the power generating units that comply with generation and ramping constraints of the respective power generating units.

4. The non-transitory computer-readable storage medium of claim 1 , wherein determining the schedule for the energy storage units comprises:

determining utility functions for the continuous-time charging trajectories of the respective energy storage units.

5. The non-transitory computer-readable storage medium of claim 4 , wherein determining the schedule for the energy storage units further comprises:

maximizing the utility functions over the operating period while balancing the net load forecast with power being supplied to the power system.

6. The non-transitory computer-readable storage medium of claim 4 , wherein determining the schedule for the energy storage units further comprises:

determining cost functions for the continuous-time discharging trajectories of the energy storage units.

7. The non-transitory computer-readable storage medium of claim 6 , wherein determining the schedule for the energy storage units further comprises:

minimizing a sum of cost functions determined for the continuous-time generation trajectories of the power generation units and the cost functions for the continuous-time discharging trajectories of the energy storage units less the utility functions for the continuous time charging trajectories of the energy storage units.

8. The non-transitory computer-readable storage medium of claim 7 , wherein determining the schedule for the energy storage units further comprises modeling the continuous-time generation trajectories, charging trajectories, and discharging trajectories in a function space.

9. The non-transitory computer-readable storage medium of claim 8 , wherein determining the schedule for the energy storage units further comprises determining an optimal solution of a function space optional control problem.

10. A system, comprising:

a computing device communicatively coupled to a plurality of energy storage units, the computing device comprising:

a modeler configured to determine model continuous-time ramping trajectories of the energy storage units in a function space;

a processor configured to:

approximate nonlinear charging utility functions of the energy storage units in terms of first auxiliary variables of the function space,

approximate nonlinear discharging cost functions of the energy storage units in terms of second auxiliary variables of the function space, and

determine an optimal configuration of the energy storage units during an operating period by minimizing the nonlinear discharging cost functions of the energy storage units less the nonlinear charging utility functions of the energy storage units over the operating period; and

a controller configured to operate the energy storage units in accordance with the determined optimal configuration during the operating period.

11. The system of claim 10 , wherein the modeler is further configured to:

model a continuous-time net load trajectory in the function space; and

model continuous-time generation trajectories of respective power generating units in the function space.

12. The system of claim 11 , wherein the processor is further configured to:

determine an optimal configuration of the power system, comprising the optimal configuration of the energy storage units, the optimal configuration adapted to minimize a total operating cost metric over the operating period, the total operating cost comprising a sum of the approximated nonlinear discharging cost functions and cost functions corresponding to the continuous-time generation trajectories of the respective power generating units less the approximated nonlinear charging utility functions of the energy storage units.

13. The system of claim 10 , wherein the processor is configured to convert a continuous-time optimization control problem to minimize a sum of generation cost functions of continuous-time generation trajectories of respective power generating units and the nonlinear discharging cost functions of the energy storage units less the nonlinear charging utility functions of the energy storage units over the operating period into a Mixed Integer Linear Programing (MLP) problem.

14. The system of claim 13 , wherein the processor is configured to determine an optimal solution to the MILP problem, comprising generation trajectories for the power generation units and the optimal configuration of the energy storage units.

15. A computer-implemented method for managing a power system, comprising:

formulating a continuous-time optimal control problem comprising:

a sum of generation cost functions of continuous-time generation trajectories of respective power generating units, discharge cost functions of continuous-time discharging trajectories of respective energy storage units, and charge utility functions of continuous-time charging trajectories of the respective energy storage units; and

a continuous-time power balance constraint to balance a continuous-time net load trajectory with the generation, discharging, and charging trajectories;

converting the continuous-time optimal control problem into a Mixed Integer Linear Programming (MILP) system;

solving the MILP system to determine an optimal configuration of the power system over the operating period; and

configuring the power system to operate in accordance with the optimal configuration during the operating period.

16. The computer-implemented method of claim 15 , further comprising:

projecting the continuous-time net load forecast into a function space corresponding to the MILP system.

17. The computer-implemented method of claim 16 , further comprising:

projecting the continuous-time generation trajectories into the function space.

18. The computer-implemented method of claim 16 , further comprising:

projecting the continuous-time charging trajectories and the discharging trajectories into the function space.