Method of dynamic economic dispatch

1. 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:

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(

ρ

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unit

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=

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unit

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;

Dn

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P

unit

Dn

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ρ

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{

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∑

allunits

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C

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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.

2. The method of claim 1 , further comprising:

obtaining an identity of each of the committed electrical power generating units.

3. The method of claim 1 , further comprising:

obtaining a commitment status of each of the committed electrical power generating units.

4. The method of claim 1 , further comprising:

determining the consecutive set of time intervals.

5. The method of claim 1 , further comprising:

obtaining the predetermined consecutive set of time intervals.

6. The method of claim 1 , further comprising:

obtaining a predicted system load profile for the predetermined consecutive set of time intervals.

7. The method of claim 1 , further comprising:

obtaining a predicted system load profile for the predetermined consecutive set of time intervals from a Very Short Term Load Predictor.

8. The method of claim 1 , further comprising:

obtaining the integrated cost of system power output.

9. The method of claim 1 , further comprising:

obtaining the system reserve requirement.

10. The method of claim 1 , further comprising:

obtaining an optimal electrical generation output temporal trajectory for each committed electrical power generating unit.

11. The method of claim 1 , further comprising:

obtaining an ACE.

12. The method of claim 1 , further comprising:

regulating an ACE to within a predetermined range around zero.

13. The method of claim 1 , further comprising:

minimizing a count of unit reversals.

14. The method of claim 1 , further comprising:

enabling a predetermined operating constraint.

15. The method of claim 1 , further comprising:

disabling a predetermined operating constraint.

16. The method of claim 1 , further comprising:

providing the optimal power output temporal trajectoriess to an LFC application.

17. The method of claim 1 , wherein the optimal power output temporal trajectories are optimal via a hierarchical nonlinear optimization technique.

18. The method of claim 1 , wherein the optimal power output temporal trajectories are optimal via a Lagrange Multiplier approach.

19. The method of claim 1 , wherein the optimal power output temporal trajectories are optimal via a Dantzig-Wolfe based optimization approach.

20. The method of claim 1 , wherein the optimal power output temporal trajectories are constrained by a system power balance.

21. The method of claim 1 , wherein the optimal power output temporal trajectories are constrained by a system spinning reserve requirement.

22. The method of claim 1 , wherein the optimal power output temporal trajectories are constrained by generation limits of the committed electrical power generating units.

23. The method of claim 1 , wherein the optimal power output temporal trajectories are constrained by power flow thermal limits of system transmission lines.

24. The method of claim 1 , wherein the optimal power output temporal trajectories are constrained by system power output limits.

25. The method of claim 1 , wherein the optimal power output temporal trajectories are constrained by ramp rate limits of the committed electrical power generating units for the predetermined consecutive set of time intervals.

26. The method of claim 1 , wherein the optimal power output temporal trajectories are constrained by a ramping constraint for the committed electrical power generating units for the predetermined consecutive set of time intervals.

27. A computer readable medium having computer readable instructions embedded therein, which, when executed by a computer, cause the computer to implement a method comprising:

for an electrical system comprising a plurality of committed electrical power generating units;

calculating a power output value for each of the committed electrical power generating units responsive to ramping limits of the committed electrical power generating units, wherein calculating the power output value 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

⁢

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P

unit

Dn

-

ρ

unit

t

,

Up

·

Δ

⁢

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P

unit

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+

min

P

unit

t

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{

∑

i

∈

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∑

allunits

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(

C

unit

⁡

(

P

unit

t

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ρ

unit

t

;

Up

⁡

(

P

unit

t

-

P

unit

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-

1

)

-

ρ

unit

t

;

Dn

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(

P

unit

t

-

P

unit

t

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1

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

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P

unit

t

∈

SCED

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}

,

wherein ρ unit t;Up is a multiplier to 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 uoward 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 t 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;

calculating a power reserve value for each of the committed electrical power generating units; and

assigning each of the corresponding power output values 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.

28. A system comprising:

for an electrical system comprising a plurality of committed electrical power generating units:

a power output processor adapted to calculate a power output value for each of the committed electrical power generating units responsive to ramping limits of the committed electrical power generating units, wherein calculating the power output value 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

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(

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 t 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;

a power reserve processor adapted to calculate a power reserve value for each of the committed electrical power generating units; and

a power output assignment processor adapted to assign each of the corresponding power output values 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.