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Equations (32)–(34) describe the iterative processes of the ADMM, and when the convergence condition (35) is satisfied, iteration can be stopped.
We establish two convergence theorems for iterative processes of the type x n + 1 = f x n, n = 0, 1, 2, …, (1.2).
Recently, Proinov [17 19] has developed a general convergence theory for iterative processes of the type x_{k+1} = Tx_{k}, quad k = 0,1,2,ldots, (2.1) where ({T colon D subset X to X}) is an iteration function in a cone metric space X.
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The iterative process of the algorithm is presented in [22].
Open image in new window Fig. 2 Iterative process of the electricity price of each MG.
The five parameters generated during the iterative process of the algorithm are shown in Table 1.
Open image in new window Fig. 7 Iterative process of the variables of MG1.
The iterative process of the secondary order moment autocorrelation function is shown in Fig. 4.
Open image in new window Fig. 3 Iterative process of the trading energy quantity of MG1 Open image in new window Fig. 4 Iterative process of the trading energy quantity of MG2 Open image in new window Fig. 5 Iterative process of the trading energy quantity of MG3.
The iterative process of the energy trading between MGs is shown in Figs. 3, 4 and 5.
Fuzzy control theory is used to decide the constraint method for each iterative process of the algorithm.
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