Search

To determine the stability of a power system integrated with numerous wind power generators, considering the stochastic fluctuation of wind power output, this paper mainly studies the stability criterion of power systems under stochastic continuous disturbances (SCDs). The dynamic performance of a power system under SCDs is described through stochastic differential equations (SDEs) based on nonlinear state equations. Under the framework of SDEs, a criterion for determining the mean square stability of a power system under SCDs is proposed, and it is proved that the proposed stability criterion is a necessary and sufficient condition for determining the mean square stability. In addition, the bi-level nonlinear semidefinite programming (NLSDP) problem in the stability criterion is transformed into a single-level NLSDP problem by using the improved Karush–Kuhn–Tucker condition of the inner-layer problem, and an extended primal-dual interior point algorithm is proposed to solve the single-level NLSDP problem. In addition, the optimal objective value calculated from the proposed stability criterion is used to quantify the stability degree of the system under SCDs. Finally, case studies on the modified IEEE-39 and 118 bus systems, and an actual provincial power grid demonstrate the correctness and effectiveness of the proposed stability criterion and solution algorithm.

The stochastic energy management (SEM) of power systems is computationally intractable due to its randomness, nonconvexity, and nonlinearity. To solve this problem, a response surface method (RSM)-based approximate dynamic programming (ADP) algorithm is proposed in this paper. Since the value function can be directly obtained by RSM, the proposed algorithm does not need to iteratively approach them as existing ADP algorithms, which facilitates reducing the computing time. In addition, an improved generalized polynomial chaos (IgPC) method (i.e., an extension of RSM) is proposed to calculate the expectation of the value function of ADP in the stochastic environment. Compared with the Monte Carlo method, which is commonly used in existing ADP algorithms, IgPC requires fewer sampling scenarios while providing similar results. Simulation results with two modified IEEE test systems and a real 2778-bus system demonstrate the effectiveness of the proposed algorithm in terms of accuracy and computation efficiency.

In this paper, an improved dynamic programming (IDP)-based decentralized algorithm is proposed for the AC-optimal power flow (AC-OPF) of radially connected transmission-distribution-microgrid networks (RCTDMNs). Most of the existing decentralized algorithms need to iterate among networks, which may lead to additional computational and information exchange burden. Different from these algorithms, we decompose the original AC-OPF problem into small-scale subproblems based on dynamic programming (DP) theory, and then solve them in a decentralized manner without iteration among networks. In order to improve the computational performance of DP, its value functions are directly obtained by solving Galerkin projection equations (GPEs) instead of traversing the whole state space. Moreover, a parallel technique is proposed to further accelerate the proposed IDP algorithm when dealing with the AC-OPF problem of RCTDMNs. Case studies on various test systems demonstrate the effectiveness of the proposed method.