Systems and methods for microgrids availability evaluation using a markov chain energy storage model

1. A method for availability evaluation of microgrid systems with an energy storage device, comprising:

applying a Markov chain model to model charging and discharging processes in the energy storage device;

determining a transition probability matrix in the Markov chain model as:

P

=

[

k

11

p

1

p

2

…

p

-

1

0

p

1

⁢

⁢

…

p

-

2

p

-

1

…

…

…

…

…

…

p

-

1

0

p

1

p

-

2

p

-

1

k

nn

]

N

×

N

where:

p1 is a probability of transition between consecutive states going from lower to higher states;

p−1 is a probability of transition between consecutive states going from higher to lower states;

p2 is a probability of transition between alternate states going from lower to higher states;

p−2 is a probability of transition between alternate states going from higher to lower states;

k nn is the probability of maintaining the nth state;

N is the number of states;

P is a matrix that contains these probabilities to determine absolute probability of occurrence of each state;

determining an effect of the energy storage device connected to a microgrid with multiple energy sources and loads; and

determining effect of system architectures on the availability of microgrids using minimum cut sets (MCS).

2. The method of claim 1 , comprising generating an energy storage model for reliability evaluation.

3. The method of claim 2 , wherein the model comprises a probabilistic model.

4. The method of claim 1 , comprising applying a Markov Chain based model.

5. The method of claim 4 , wherein the Markov Chain model comprises two states.

6. The method of claim 1 , wherein the Markov Chain model comprises a multi-state model that considers charging and discharging states of a storage device.

7. The method of claim 1 , wherein the model comprises a deterministic model.

8. The method of claim 1 , comprising performing availability evaluation of system architecture.

9. The method of claim 8 , comprising modeling components in parallel or in series or in combination.

10. The method of claim 9 , comprising applying a deterministic model.

11. The method of claim 9 , comprising performing series or parallel modeling.

12. The method of claim 9 , comprising applying a probabilistic model.

13. The method of claim 12 , comprising applying analytical methods including Boolean algebra or a cut set.

14. The method of claim 12 , comprising applying a statistical method.

15. The method of claim 12 , comprising applying a Markov-chain Monte Carlo simulation.

16. The method of claim 12 , comprising applying a sequential simulation.

17. The method of claim 12 , comprising applying an event tree.

18. The method of claim 8 , wherein no modeling is required.

19. The method of claim 1 , comprising:

determining a state space of (X−L) for the energy storage system as

S=[−M Δ,−( M− 1)Δ, . . . ,−2Δ,−Δ,2Δ, . . . ,( M− 1)Δ, MΔ]

where X and L are the total amount of generated power and load, Δ is the amount of exchanged energy and M is the maximum number of steps in the presented Markov chain; and

determining the total capacity of the energy storage system as C=M·Δ.

20. The method of claim 1 , comprising determining a loss of load probability (LOLP) as π E =Σ iε(1,M) p−1×Σ j<L π j where L is an average value of load, π E represents LOLP by multiplying the sum of probabilities of discharging in any amount and the sum of limiting probabilities of states that cannot match the power which a load requires.