Adaptive power grid restoration
A method of self-healing power grids after power outages includes providing an Adaptive Restoration Decision Support System (ARDSS) for generating a restoration solution using static and dynamic input data from power generator(s) powering transmission lines, from the transmission lines and loads. At a beginning of a restoration period a two-stage problem is solved including a first and second-stage problem with an optimal planning (OP) function as a mixed-integer linear programming (MILP) problem using initial static and dynamic data to determine start-up times for the power generator and energization sequences for transmission lines involved in the power outage. Only the second-stage problem is again solved with an optimal real-time (OR) function using the start-up times and energization sequences along with updated static and dynamic data to determine operating parameters for the grid. The restoration solution is implemented over restoration time steps until all loads involved in the power outage are recovered.
1. A method of self-healing an electrical power grid including transmission lines and loads after a power outage, comprising:
providing an Adaptive Restoration Decision Support System (ARDSS) for generating a restoration solution from said power outage by using received static and dynamic input data from at least one power generator providing power to said power grid, from said transmission lines, and from said loads;
at a beginning of a restoration period that is triggered following said power outage solving a two-stage problem including a first-stage problem and a second-stage problem with optimal planning (OP) function as a mixed-integer linear programming (MILP) problem using initial said static and dynamic input data to determine start-up times for said power generators when involved in said power outage and energization sequences for ones of said transmission lines involved in said power outage;
solving only said second-stage problem again with optimal real-time (OR) function using said start-up times and energization sequences along with updated said static and dynamic input data to determine a plurality of operating parameters for said power grid, and
implementing said restoration solution over a plurality of restoration time steps until all said loads involved in said power outage are recovered.
2. The method of claim 1 , wherein said OR function comprises a simplified version said OP function, and wherein a computation time for solving only said second-stage problem with said OR function is less than a computation time for solving said two-stage problem using said OR function.
3. The method of claim 1 , wherein said solving said second-stage problem further comprises solving additional sub-problems including computing initial conditions for said power generator using non-linear algebraic equations, solving a linear optimization problem that calculates a frequency response of said power grid as one of said plurality of operating parameters and determines pickup locations and sizes for said loads as others of said plurality of operating parameters.
4. The method of claim 1 , wherein said ARDSS is integrated into an energy management system (EMS) that is in a control room a power system including said power grid.
5. The method of claim 3 , wherein said plurality of operating parameters further comprise a dynamic reserve allocation of said power generator, a voltage profile of said power grid, a power flow for said transmission lines, an optimal power output for said power generator, and real and reactive power losses.
6. The method of claim 1 , wherein said OP function is again executed to resolve said two-stage problem responsive to a contingency occurring during said restoration period.
7. The method of claim 1 , wherein said ARDSS comprises an integer L-shaped algorithm, and auxiliary variables and optimality cuts are included in said second-stage problem.
8. The method of claim 1 , wherein said static inputs include power system topological information including parameters from said transmission lines and said power generator, and said dynamic inputs are states of a power system including said power grid updated in real-time with said updated dynamic input data provided by phasor measurement units (PMUs) or a supervisory control and data acquisition (SCADA) system.
9. An adaptive restoration decision support system (ARDSS) for implementing a method of self-healing an electrical power grid by generating a restoration solution from a power outage in said electrical power grid powered by at least one power generator comprising transmission lines and loads, said ARDSS comprising:
a computer system comprising a processor having an associated memory or digital logic for implementing said method, said method comprising:
said ARDSS generating said restoration solution from said power outage by using received static and dynamic input data from said power generator, from said transmission lines, and from said loads;
at a beginning of a restoration period that is triggered following said power outage solving a two-stage problem including a first-stage problem and a second-stage problem with optimal planning (OP) function as a mixed-integer linear programming (MILP) problem using initial said static and dynamic input data to determine start-up times for said power generators when involved in said power outage and energization sequences for ones of said transmission lines involved in said power outage;
solving only said second-stage problem again with optimal real-time (OR) function using said start-up times and energization sequences along with updated said static and dynamic input data to determine a plurality of operating parameters for said power grid, and
implementing said restoration solution over a plurality of restoration time steps until all said loads involved in said power outage are recovered.
10. The system of claim 9 , wherein said OR function comprises a simplified version said OP function, and wherein a computation time for solving only said second-stage problem with said OR function is less than of a computation time for solving said two-stage problem using said OR function.
11. The system of claim 9 , wherein said solving said second-stage problem further comprises solving additional sub-problems including computing initial conditions for said power generator using non-linear algebraic equations, solving a linear optimization problem that calculates a frequency response of said power grid as one of said plurality of operating parameters and determines pickup locations and sizes for said loads as others of said plurality of operating parameters.
12. The system of claim 9 , wherein said ARDSS is integrated into an energy management system (EMS) that is in a control room a power system including said power grid.
13. The system of claim 11 , wherein said plurality of operating parameters further comprise a dynamic reserve allocation of said power generator, a voltage profile of said power grid, a power flow for said transmission lines, an optimal power output for said power generator, and real and reactive power losses.
14. The system of claim 9 , wherein said OP function is again executed to resolve said two-stage problem responsive to a contingency occurring during said restoration period.
15. The system of claim 9 , wherein said ARDSS comprises an integer L-shaped algorithm, and auxiliary variables and optimality cuts are included in said second-stage problem.
16. The system of claim 9 , wherein said static inputs include power system topological information including parameters from said transmission lines and said power generator, and said dynamic inputs are states of said power system including said power grid updated in real-time with said updated dynamic input data provided by phasor measurement units (PMUs) or a supervisory control and data acquisition (SCADA) system.