Algorithm 1: Power Restoration Strategy Optimization

1: Procedure: solve power restoration strategy(initial grid data, params) // where ‘initial grid data’ is collected from PMUs.

2:  // Section 1: Initialization and Topological Analysis via BFS

3:   Grid Model ← Initialize Grid Model (Initial grid data)

4:

5:   // Construct a Minimum Spanning Tree (MST) using Breadth-First Search

6:   Start Node ← Find Main Power Source Node(Grid Model)

7:   Queue Q ← [Start Node]

8:   Set Visited Nodes V ← {Start Node}

9:   Tree MST ← $\varnothing$

10:    while Q is not empty do

11:    u ← Dequeue(Q)

12:    for each Branch S connected to u do

13:     v ← Get other end of S

14:     if v $\in$ V then

15:      Add v to V; Enqueue(Q, v); Add S to MST

16:     end if

17:    end for

18:    end while

19:

20:    // Identify Chords and Form Fundamental Loops to Define the Search Space

21:    Chords ← Calculate Set Difference(Grid Model.All Branches, MST)

22:    Loop List ← $\varnothing$

23:    for each Chord R in Chords do

24:    Path ← Find Path in Tree(MST, R.Endpoint1, R.Endpoint2)

25:    New Loop ← Path $\cup$ {R}

26:    Add New Loop to Loop List

27:    end for

28:

29:    // Synergy Point: The output of BFS (Loop List) now directly defines the chromosome structure for AMCGA.

30:    // Chromosome Length = size of Loop List. Each gene corresponds to a loop.and gene values use decimal encoding.

31:

32:    // Section 2: Optimization via Adaptive Modified Genetic Algorithm (AMCGA)

33:    Population ← Generate Random Initial Population(Params.Pop Size, Loop List)

34:    for g ← 1 to $I_{\max }$ do

35:    // Evaluate fitness for each individual solution

36:    for each Chromosome in Population do

37:     // Decode gene values into a set of open branches to form a new topology

38:     Open Branches ← Decode Chromosome(Chromosome, Loop List)

39:     Current Topology ← Calculate Set Difference(Grid Model.All Branches, Open Branches)

40:     // Simulate grid operation over the specified duration to evaluate strategy effectiveness.

41:     Total Score ← 0

42:     for time ← 0 to Simulation Hours do

43:      DG Output ← Get DG Output

44:      Restored Loads ← Calculate Restored Loads(Current Topology, DG Output)

45:      Total Score ← Total Score +Calculate Weighted Score(Restored Loads)

46:     end for

47:     Fitness(Chromosome) ← Total Score

48:    end for

49:

50:    // Evolution using Adaptive Multi-Point Crossover & Mutation

51:    $P_{cross}=P_{c1}+P_{c2}\ast {\displaystyle \frac{\left(I_{\max }-I\right)}{I_{\max }}}$

52:    $P_{mutation}=P_m\ast I_{\max }/\left(I_{\max }-m\ast I\right)$

53:

54:    Parents ← Select(Population, Fitness)

55:    Offspring ← Multi Point Crossover(Parents, $P_{cross}$)

56:    Offspring ← Mutate(Offspring, $P_{mutation}$)

57:    Population ← Update Population(Population, Offspring)

58:    end for

59:

60:    // Section 3: Formulate and Output the Final Strategy

61:    Best Chromosome ← individual with highest Fitness in Population

62:    Final Open Branches ← Decode Chromosome(Best Chromosome, Loop List)

63:    Final Topology ← Calculate Set Difference(Grid Model.All Branches, Final Open Branches)

64:    // The strategy includes the final network structure and could include other operational data.

65:    Optimal Power Restoration Strategy ← Formulate Strategy(Final Topology, Grid Model)

66:    return Optimal Power Restoration Strategy

67:  end Procedure