Neural-network-based Lagrange multiplier selection for distributed demand response in smart grid

As a general difficult problem, the slow convergence of existing distributed demand response methods greatly hinders the reliable applications in smart grid. To overcome this problem, this paper proposes a new distributed method, namely the neural-network-based Lagrange multiplier selection (NN-LMS), to prominently reduce the iterations and avoid an oscillation. The key improvement lies in the forecast strategy of a load serving entity (LSE), who applies a specially designed neural network to capture the users' price response features. A novel Lagrange multiplier selection model, the NN-LMS model, is formulated to optimize the iterative step sizes. This complex model is then solved by a two-stage NN-LMS algorithm, containing the interval bisection method and improved sensitivity method in the first and second stages, respectively. In addition, the data selection, batch normalization and additional network are applied to boost the performance of neural networks. Case studies validate the optimality, improved convergence and numerical stability of the proposed method, and demonstrate its great potential in distributed demand response and other smart grid applications.