In this paper, an optimal day-ahead scheduling problem is studied for a microgrid with multiple distributed resources. For the sake of coping with the prediction uncertainties of renewable energies and loads and taking advantage of the time-of-use price for buying/selling electricity, an interval-based optimization model for maximum profits is developed. To reduce the computational complexity in solving the model, the possibility degree comparison between an interval and a real number is used to convert the interval constraints into the general ones; meanwhile, some slack variables and complementary conditions are introduced to eliminate the absolute-value operation. Unlike the stochastic optimization, the interval optimization only needs the upper-lower bounds of the uncertain variables instead of their probability distribution functions, which is beneficial to the practical application. Furthermore, the possible profit interval and the expected optimal profit can be determined by solving the optimization model. Numerical simulations are performed on a microgrid system modified from the benchmark low voltage network in the European Union project “Microgrid”, and the results demonstrate the effectiveness of the proposed method.

To deal with the problem of generation rate constraint (GRC) during load frequency control (LFC) design for a multi-area interconnected power system, this paper proposes an anti-windup controller design method. Firstly, an $H_{\infty }$ dynamic controller is designed to obtain robust performance of the closed-loop control system in the absence of the GRC. Then, an anti-windup compensator (AWC) is formulated to restrict the magnitude and rate of the control input (namely power increment) in the prescribed ranges so that the operation of generation unit does not exceed the physical constraints. Finally, the anti-windup LFC is tested on the multi-area interconnected power systems, and the simulation results illustrate the effectiveness of the proposed LFC design method with GRC.

This paper considers the problem of distributed frequency regulation based on the consensus control protocol in smart grids. In this problem, each system component is coordinated to collectively provide active power for the provision of ancillary frequency regulation service. Firstly, an approximate model is proposed for the frequency dynamic process. A distributed control algorithm is investigated, while each agent exchanges information with neighboring agents and performs behaviors based on communication interactions. The objective of each agent is to converge to a common state considering different dynamic load characteristics, and distributed frequency control strategy is developed to enable the agents to provide active power support. Then, the distributed proportional integral controllers with the state feedback are designed considering the consensus protocol with topology . The theory of distributed consensus protocol isfurther developed to prove the stability of the proposed control algorithm. Whenproperly controlled, the controllers can provide grid support services in a distributed manner that turn out the grid balanced globally. Finally, simulations of the proposed distributed control algorithm are tested to validate the availability of the proposed approach and the performance in the electrical networks.

The economic dispatch problem of a virtual power plant (VPP) is becoming non-convex for distributed generators’ characteristics of valve-point loading effects, prohibited operating zones, and multiple fuel options. In this paper, the economic dispatch model of VPP is established and then solved by a distributed randomized gradient-free algorithm. To deal with the non-smooth objective function, its Gauss approximation is used to construct distributed randomized gradient-free oracles in optimization iterations. A projection operator is also introduced to solve the discontinuous variable space problem. An example simulation is implemented on a modified IEEE-34 bus test system, and the results demonstrate the effectiveness and applicability of the proposed algorithm.

Wind power prediction research shows that it is difficult to accurately and effectively estimate the probability distribution (PD) of wind power. When only partial information of the wind power probability distribution function is available, an optimal available transfer capability (ATC) assessment strategy considering the uncertainty on the wind power probability distribution is proposed in this paper. As wind power probability distribution is not accurately given, the proposed strategy can efficiently maximize ATC with the security operation constraints satisfied under any wind power PD function case in the uncertainty set. A distributional robust chance constrained (DRCC) model is developed to describe an optimal ATC assessment problem. To achieve tractability of the DRCC model, the dual optimization, S-lemma and Schur complement are adopted to eliminate the uncertain wind power vector in the DRCC model. According to the characteristics of the problem, the linear matrix inequality (LMI)-based particle swarm optimization (PSO) algorithm is used to solve the DRCC model which contains first and second-order moment information of the wind power. The modified IEEE 30-bus system simulation results show the feasibility and effectiveness of the proposed ATC assessment strategy.