Optimal storage sizing for integrating wind and load forecast uncertainties

1. A system to manage energy system, comprising:

means for receiving load forecasts and power generator forecasts with uncertainty specification;

means for performing stochastic optimization on the load and power generation forecasts;

means for determining an optimal storage sizing for energy balancing;

means for validating the optimal storage sizing; and

means for minimizing

C ES ·E S max +C PS ·P S max +C Einit ·E Sinit

∑

k

=

1

N

⁢

[

π

⁢

∑

i

⁢

ρ

W

k

i

⁢

ρ

L

k

i

·

max

⁢

{

0

,

P

L

k

i

-

P

W

k

i

-

P

S

k

}

]

where C ES is an energy component and C PS is a power component,

E S max is a maximum energy limit of a storage unit,

P S max is a maximum rate of charge or discharge from the storage unit,

C Einit is a cost term to reduce the dependence on initial stored energy of the storage unit E Sinit ,

π is a constant penalty term,

Prob

⁡

(

=

P

W

k

i

)

=

ρ

W

k

i

and

Prob

⁡

(

=

P

L

k

i

)

=

ρ

L

k

i

,

P L k is a load in interval k, and

P S k is a power discharged from a storage unit in interval k with a positive value indicating discharge and a negative value indicating charging of the storage unit,

wherein the power generator is connected to an energy storage device with the optimal storage sizing.

2. The system of claim 1 , comprising means for receiving minimum initial stored energy required based on storage characteristics, allowable operational limit.

3. The system of claim 1 , comprising means for analyzing various levels of uncertainty of renewable generation forecasts and load forecasts.

4. The system of claim 1 , comprising means for receiving reliability indices to measure ‘goodness’ values and trade-off assessment.

5. The system of claim 1 , comprising means for determining loss-of-load probability (LOLP).

6. The system of claim 1 , comprising means for determining loss-of-energy probability (LOEP) or spilled-generation-probability (SGP).

7. The system of claim 1 , wherein the optimal storage sizing determination further comprises determining optimal energy capacity or optimal power capacity.

8. The system of claim 1 , wherein the power generator comprises a wind generator or a solar panel.

9. The system of claim 1 , comprising means for applying reliability indices to validate optimal parameters.

10. The system of claim 1 , comprising means for performing stochastic linear programming to solve an optimization problem.

11. The system of claim 1 , comprising means for applying Monte Carlo based simulations to determine all possible states of the system, thus evaluating the reliability indices.

12. The system of claim 1 , comprising means for determining deterministic wind and deterministic load.

13. The system of claim 1 , comprising means for determining or estimating stochastic wind and stochastic load.

14. The system of claim 1 , comprising means for minimizing the under-generation and loss-of-load probability, and simultaneous minimization of both under-generation and wind spillage.

15. The system of claim 1 , comprising code for:

restricting a search space by:

E S k+1 E S k −P S k ∀k= 1,2, . . . N

E S min ≦E S k ≦E S max ∀k=1,2, . . . N

| P S k |≦P S max ∀k= 1,2, . . . N

where P S max is a maximum rate of charge or discharge from the storage unit,

E S max is a maximum energy limit of the storage,

E S k is an energy limit of a storage unit k and E S k+1 is an energy limit of a storage unit k+1, and

E S min is a minimum energy required in the storage unit at the start of the planning horizon.

16. The system of claim 1 , comprising analyzing various levels of uncertainty of renewable generation forecasts and load forecasts.

17. The system of claim 1 , comprising receiving reliability indices to measure a ‘goodness’ of computed values and trade-off assessment.

18. A method to manage energy system, comprising:

receiving load forecasts and power generator forecasts with uncertainty specification;

performing stochastic optimization on the load and power generation forecasts;

determining an optimal storage sizing for energy balancing;

validating the optimal storage sizing;

minimizing

C ES ·E S max +C PS ·P S max +C Einit ·E Sinit

∑

k

=

1

N

⁢

[

π

⁢

∑

i

⁢

ρ

W

k

i

⁢

ρ

L

k

i

⁢



P

L

k

i

-

P

W

k

i

-

P

S

k



]

;

⁢

and

restricting a search space by:

E S k+1 =E S k −P S k ∀k= 1,2 , . . . N

E S min ≦E S k ≦E S max ∀k= 1,2 , . . . N

| P S k ≦P S max ∀k= 1,2 , . . . N

where

Prob

⁡

(

=

P

W

k

i

)

=

ρ

W

k

i

and

rob

⁡

(

=

P

L

k

i

)

=

ρ

L

k

i

,

C ES is an energy component and, C PS is a power component,

E S max is a maximum energy limit of a storage unit,

P S max is a maximum rate of charge or discharge from the storage unit,

C Einit is a cost term to reduce the dependence on initial stored energy of the storage unit E Sinit ,

π is a constant penalty term,

P L k is a load in interval k,

P S k is a power discharged from a storage unit in interval k with a positive value indicating discharge and a negative value indicating charging of the storage unit,

P S max is a maximum rate of charge or discharge from the storage unit,

E S max is a maximum energy limit of the storage, and

E S min is a minimum energy required in the storage unit at the start of the planning horizon,

wherein the power generator is connected to an energy storage device with the optimal storage sizing.

19. The method of claim 18 , comprising receiving minimum initial stored energy required based on storage characteristics, allowable operational limit.