| Weather uncertainties make it difficult to accurately predict the power generation capacity of new energy sources such as wind power and photovoltaic.As a result,the power generation output of new energy sources has obvious randomness and intermittency.As more and more new energy power generation is connected to the power system,the uncertainties of the power system present characteristics of strong degree,large scale,and high complexity.Probability analysis is the main method of uncertainty analysis in power systems.However,probabilistic analysis often requires a large amount of sample data to accurately establish the probability distribution of uncertain variables,which is difficult to meet in some practical applications.As an effective complementary tool for probabilistic analysis,interval analysis requires only a small amount of sample data to determine the boundaries of non probabilistic convex models,making modeling relatively simple.However,there are some problems in current interval analysis of power systems that are difficult to meet the increasingly complex uncertainty analysis needs.Considering uncertainties brought by wind power generation to power systems,this paper uses non probabilistic convex models as uncertainty modeling methods,and linear cone optimization as the basis of interval analysis methods,conducting research from three aspects:power flow calculation,static voltage stability analysis,and optimal power flow,proposing an interval cone optimization analysis method for power systems considering uncertainties.The main work is as follows:(1)An affine cone optimization algorithm for interval power flow based on ellipsoidal box hybrid convex model is proposed to solve the problem of uncertain power flow calculation in power systems.Firstly,for wind farm outputs with a Weibull distribution of wind speed and correlation,the ellipsoidal model and the parallelepiped model were compared and analyzed.An Ellipsoidal Box Hybrid Convex Model(EBHCM)was proposed to describe both independent and related uncertainties.Then,the EBHCM is embedded into the affine nonlinear optimization model of interval power flow based on affine arithmetic in the form of second-order cone constraints and linear inequality constraints.Finally,the objective function is transformed into a linear form through affine arithmetic and first order Taylor approximation,and the ellipsoidal constraint is transformed into a second order cone constraint.An affine cone optimization model for interval power flow is proposed.The simulation results show that when the wind speed follows the Weibull distribution and has a strong correlation,compared to the box model and the parallelepiped model,the EBHCM is less conservative in describing the uncertainty of wind farm output and calculating the interval power flow.(2)To solve the problem of calculating the static voltage stability limit(SVSL)fluctuation interval of radiation networks,a SVSL fluctuation interval algorithm based on positive semi definite relaxation is proposed.Firstly,an extended power flow optimization model with load parameters is established based on rectangular coordinates to calculate SVSL.Then,the extended power flow optimization model is subjected to semi definite relaxation,and the proposed EBHCM is used as an uncertainty modeling method.Two two-level optimization models,min-min and max-min,are established to calculate the upper and lower bounds of the SVSL fluctuation interval,respectively.Finally,based on the strong duality theorem,the two-level optimization is transformed into a single-layer optimization,and the optimization model is transformed into a linear cone optimization model through Taylor approximation.A method for tracking the fluctuation region of the PV curve is given.Test results on seven IEEE radiation network systems show that the proposed algorithm has improved computational accuracy,robustness,and efficiency compared to other algorithms such as affine algorithms.(3)Based on the aforementioned linear cone optimization model of SVSL fluctuation interval for radial networks,a SVSL interval algorithm based on second-order cone optimization iteration is further proposed,extending its application scope to ring networks.Firstly,considering the reactive power limitation of generators,an extended power flow optimization model in polar coordinates is established.Then,based on second-order cone relaxation,an extended second-order cone optimization model is proposed,and loop closure constraints are added to ensure that the voltage phase angles at the loop closure points of the loop network are completely consistent,indicating that a series of linear cone optimizations can be used to solve the loop network SVSL.Finally,based on the extended second-order cone optimization model,two two-level optimization models are proposed to calculate the SVSL interval,and the fluctuation interval of the loop network SVSL is solved by alternately optimizing the uncertain variables of the upper-level programming and the dual variables of the lower-level optimization.The simulation results show that the proposed method is suitable for calculating the SVSL interval of the loop network while retaining high computational accuracy,and can track the limit induced bifurcation points on the PV curve caused by generator reactive power exceeding the limit.(4)Aiming at the uncertain optimal power flow problem,a radial network interval optimal power flow model considering the uncertainty of irregular distribution is proposed.Firstly,the impact of wind turbine control strategies on wind turbine output is analyzed,indicating that wind turbine control strategies can cause the uncertainty of wind turbine output to exhibit a discontinuous characteristic.A discontinuous interval is proposed to describe the discontinuous uncertainty of wind turbine output.Then,considering three different wind turbine operation modes,an interval optimal power flow model including two two-level optimizations is proposed.The inner layer optimization is transformed into a linear cone optimization using a convex relaxation technique,and sufficient conditions for accurate relaxation are given in theory.The outer layer uses Monte Carlo method to generate sample points with discontinuous characteristics,and finally uses linear cone optimization to obtain the interval of interval optimal power flow state variables.The calculation results of the proposed algorithm in five IEEE standard test systems show that the proposed convex relaxation is accurate in radiation networks,with a maximum relaxation gap of no more than 0.22%.The results of interval optimal power flow show that discontinuous uncertainties may lead to discontinuous changes in the boundary of state variables.The proposed method can effectively analyze the impact of discontinuous uncertainties on optimal power flow. |
PDF Full Text Request