In this paper, we explore the consensus control scheme of stochastic perturbed nonlinear multi-agent systems with impulsive protocol and comparison system method. The effective variable impulsive consensus method is used to remove the restriction of fixed impulsive instants, which is more reliable and flexible in practical applications. From the theory of impulsive differential system, comparison system and stochastic differential system, some sufficient consensus conditions are derived and the relation between the system parameters and impulsive time window is analyzed extensively. The effectiveness of the proposed control method is confirmed by the numerical simulations finally.

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Considering uncertain wind power and dispatchable load, a mixed probabilistic and interval optimal power flow model is proposed, and Monte Carlo sampling and affine arithmetic method are used to solve it. First, an uncertain optimal power flow model with mixed probabilistic variables and interval variables is established by expressing the uncertain dispatchable load as the interval model and the uncertain wind speed and node load as the probabilistic model. Then Monte Carlo sampling is used to sample the probabilistic variables in the proposed model. By this way, the mixed probabilistic and interval optimal power flow can be transformed into interval optimal power flow with sampling points, and the interval optimal power flow of each sampling point can be solved by the affine arithmetic method. Finally, a maximum probability density function and a minimum probability density function are synthesized based on the interval extremum of unknown variables in optimal power flow for each sampling point. The numerical results obtained by the IEEE-118 and IEEE-300 bus systems show that the mixed probabilistic and interval optimal power flow model has the merits of handling the problem including both probabilistic variables and interval variables at the same time, obtaining the probabilistic interval of optimal power flow with any value and learning the maximum probability and minimum probability of the power system's possible operating status. The proposed algorithm has the advantage of high solution efficiency.

It is an important means for knowing something about the influence of uncertain factors on the power flow state to calculate uncertain power flow. In this paper, the uncertain power flow problem considering wind power and photovoltaic power generation is studied. The interval distribution models of wind power and photovoltaic power generation are established by expressing the natural factors such as wind speed and light intensity as interval variables, and an uncertain power flow model of hybrid stochastic and interval variables is established by expressing the node load as the stochastic variable to obey the Gaussian distribution. A double-layer Monte Carlo method is proposed to solve it. The numerical results obtained by the IEEE-30 bus system show that the proposed model and method are effective, by which the maximum and minimum cumulative probability functions of the power flow state can be obtained, thus determining whether the probabilistic interval of the power flow state is out-of-limit (maximum probability and minimum probability). INDEX TERMS Interval variable, stochastic variable, double-layer Monte Carlo method, photovoltaic power generation, wind power generation.

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