Distributed Economic Dispatch for Smart Grids With Random Wind Power

Abstract

In this paper, we present a distributed economic dispatch (ED) strategy based on projected gradient and finitetime average consensus algorithms for smart grid systems. Both conventional thermal generators and wind turbines are taken into account in the ED model. By decomposing the centralized optimization into optimizations at local agents, a scheme is proposed for each agent to iteratively estimate a solution of the optimization problem in a distributed manner with limited communication among neighbors. It is theoretically shown that the estimated solutions of all the agents reach consensus of the optimal solution asymptomatically. This scheme also brings some advantages, such as plug-and-play property. Different from most existing distributed methods, the private confidential information, such as gradient or incremental cost of each generator, is not required for the information exchange, which makes more sense in real applications. Besides, the proposed method not only handles quadratic, but also nonquadratic convex cost functions with arbitrary initial values. Several case studies implemented on six-bus power system, as well as the IEEE 30-bus power system, are discussed and tested to validate the proposed method.

Agent‐based distributed and economic automatic generation control for droop‐controlled AC microgrids

“…Recently, distributed algorithm is widely applied in smart grid related problems [17][18][19][20][21][22][23][24], due to its advantage of robustness, scalability, and less information requirement. In [17], distributed secondary voltage and frequency restoration control of droop-controlled inverter-based islanded MG are addressed.…”

“…However, the initialisation method for l(0), E(0), and P ref (0) should be properly designed. If w i, j is defined as shown in (13), then W will have the property as given in (19) [34], which means that the summation of all elements of u(0) is preserved by multiply matrix W T for any times…”

“…Let us multiply both sides of the third equation in (11) by 1 T , where 1 is a column vector with value 1 for all its elements. Considering the property of W, as shown in (19), one can derive…”

“…Though the proposed EAGC algorithm needs local communication with its neighbouring agents such as all the other distributed algorithms reported in the literature [18][19][20][21][22], it has many advantages against a centralised control especially when the size of the system is large. For a centralised control, the centralised controller needs to communicate with all the subsystems to acquire the global information, while for the proposed distributed EAGC algorithm, each DG agent only needs to communicate with its neighbouring agents.…”

Global convergence rate of incremental aggregated gradient methods for nonsmooth problems

“…regularized least squares problems that arise in various machine learning applications [7,21], distributed optimization problems that arise in wireless sensor network as well as smart grid applications [11,19] and constrained optimization of separable problems [1]. An important feature of this formulation is that the number of component functions m is large, hence solving this problem using a standard gradient method that involves evaluating the full gradient of f (x), i.e., ∇f (x) = m i=1 ∇f i (x), is costly.…”