Patent ID: 7321810

Claim:
A method, comprising: for an electrical power system comprising a plurality of committed electrical power generating units: for each of the committed electrical power generating units, determining an optimal power output temporal trajectory, the optimal power output temporal trajectory constrained by a ramping limit of the committed electrical power generating unit, wherein determining the optimal power output temporal trajectory for each of the committed electrical power generating units comprises calculating ramping constraints according to a Lagrange relationship: L ⁡ ( ρ unit t : Up , ρ unit t , Dn ) = ρ unit t ; Dn · Δ ⁢ ⁢ P unit Dn - ρ unit t , Up · Δ ⁢ ⁢ P unit Up + min P unit t ⁢ { ∑ i ∈ T ⁢ ⁢ ∑ allunits ⁢ ⁢ ( C unit ⁡ ( P unit t ) + ρ unit t ; Up ⁡ ( P unit t - P unit t - 1 ) - ρ unit t ; Dn ⁡ ( P unit t - P unit t - 1 )  ⁢ P unit t ∈ SCED ′ } , wherein ρ unit t;Up is a multiplier for an upward ramping limit of a unit over a time interval t; ρ unit t;Dn is a multiplier for a downward ramping limit of a unit over the time interval t; ΔP unit Dn is a unit downward ramping limit; ΔP unit Up is a unit upward ramping limit; P unit t is the unit power generation at time interval t; T is a time period comprising consecutive time intervals t; P unit t−1 for t=t 1 represents P unit 0 with t 0 being a current time interval; C unit is the cost of unit power generation; and ℑ SCED t represents static security constrained economic dispatch (SCED) constraints at time interval t; determining an optimal power reserve temporal trajectory for each of the committed electrical power generating units; and assigning each of the optimal power output temporal trajectories to the respective electrical power generating units so that, over a predetermined consecutive set of time intervals, an integrated cost of system power output is minimized and a system reserve requirement is met.