Real-Time Pricing-Based Scheduling Strategy in Smart Grids: A Hierarchical Game Approach

Algorithm 1

Distributed electricity scheduling.

Input:  𝐿_𝑘(1) = 0.1; 𝑥₂(1) = 0.1; 𝑛=0; 𝑚=0; 𝑡=0;

 𝑅_𝐾={1,2,…,𝐾};𝑅_𝑁={1,2,…,𝑁};

Output: Optimal 𝑝^∗; 𝐿^∗_𝑘; 𝑥^∗_𝑖;

 While  𝑡<24  do

  𝑡←𝑡+1

  While  𝐿_𝑘(𝑛+1)−𝐿_𝑘(𝑛)<𝜀  do

    𝑛←𝑛+1;

    𝑝(𝑛)=𝑝₀(1−𝜆)Σ_{𝑅𝑘∈𝐾}𝐿_𝑘(𝑛);

    for all  𝑘∈𝑅_𝐾  do

     𝐿_𝑘(𝑛+1)=𝐿_𝑘(𝑛)+𝜇ℎ_𝑘(𝐋)⁺;

    end for

  end while

  while  𝑥_𝑖(𝑚+1)−𝑥_𝑖(𝑚)<𝜀  do

   𝑚←𝑚+1;

   𝑝(𝑚)=𝑝₀(Σ_{𝑖∈𝑅𝑁}𝑥_𝑖(𝑚)−𝜆Σ_{𝑘∈𝑅𝐾}𝐿^∗_𝑘));

   for all  𝑖∈𝑅_𝑁  do

    𝑥_𝑖(𝑚+1)=𝑥_𝑖(𝑚)+𝜃ℎ_𝑖(𝐱)⁺;

   end for

  end while

end while