The auxiliary problem principle has been widely applied in power systems to solve the multi-area economic dispatch problem. Although the effectiveness and correctness of the auxiliary problem principle method have been demonstrated in relevant literatures, the aspect connected with accurate estimate of its convergence rate has not yet been established. In this paper, we prove the O(1/n) convergence rate of the auxiliary problem principle method.

With the proportion of wind power in the power systems increasing, consideration must be given to the fact that the randomness and volatility of wind power output will inevitably affect the stable operation of power grid. One of the effective ways to solve this problem is to forecast the output of wind power. In this paper, we employ the method of BP neural network to predict the wind power output in a period of time. To discuss the predictive performance of BP neural networks, we set different number of input variables to observe the prediction effect of BP neural network. We find that it’s not that the more input information, the better the prediction effect. The data with strong correlation can be used as input to achieve better results.

The alternating direction method has been used widely in the power systems field for solving the multiarea dispatch problem. However, experience with applications has shown that the convergence rate of the alternating direction method depends significantly on the selection of the penalty parameter of the linear consistency constraint. Typically, it is difficult to obtain the optimal penalty parameter in advance. In this paper, for the purpose of solving this problem, we propose centralized and distributed self-adaptive penalty parameter strategies that allow the value of the penalty parameter to increase or decrease based on the information from each iteration. Simulation results illustrate that the proposed centralized and distributed self-adaptive methods are superior to the traditional alternating direction method in terms of robustness and convergence rate.

With the continuous development of the world economy, the development and utilization of environmentally friendly and renewable energy have become the trend in many countries. In this paper, we study the dynamic economic dispatch with wind integrated. Firstly, we take advantage of the positive and negative spinning reserve to deal with wind power output prediction errors in order to establish a dynamic economic dispatch model of wind integrated. The existence of a min function makes the dynamic economic dispatch model nondifferentiable, which results in the inability to directly use the traditional mathematical methods based on gradient information to solve the model. Inspired by the aggregate function, we can easily transform the nondifferentiable model into a smooth model when parameter p tends to infinity. However, the aggregate function will cause data overflow when p tends to infinity. Then, for solving this problem, we take advantage of the adjustable entropy function method to replace of aggregate function method. In addition, we further discuss the adjustable entropy function method and point out that the solution generated by the adjustable entropy function method can effectively approximate the solution of the original problem without parameter p tending to infinity. Finally, simulation experiments are given, and the simulation results prove the effectiveness and correctness of the adjustable entropy function method.

Summary In this paper, a novel with respect to economic dispatch of large‐scale multi‐area power systems is formulated and studied based on decomposition and coordination algorithm. More precisely, auxiliary problem principle (APP) is applied to overcome the defects of augmented Lagrangian relaxation technology with nonlinear inseparable quadratic terms. The main purpose of this paper is to investigate the intrinsic relationship between APP control parameters and convergence speed, and develop a general criterion that ensures that a suitable control parameter set referring to the implemented APP can be effectively estimated. Theoretical and experimental results of this paper are consistent with each other based on the verification of proposed numerical results. Copyright © 2013 John Wiley & Sons, Ltd.

Abstract:The auxiliary problem principle is a powerful tool for solving multi-area economic dispatch problem. One of the main drawbacks of the auxiliary problem principle method is that the convergence performance depends on the selection of penalty parameter. In this paper, we propose a self-adaptive strategy to adjust penalty parameter based on the iterative information, the proposed approach is verified by two given test systems. The corresponding simulation results demonstrate that the proposed self-adaptive auxiliary problem principle iterative scheme is robust in terms of the selection of penalty parameter and has better convergence rate compared with the traditional auxiliary problem principle method.

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