Research On Interval Analysis Method For Uncertain Power Flowin Distribution Network With Renewable Energy

Smart distribution network for high-ratio renewable energy consumption has become one of the important trends in the development of future power systems.With the increasing uncertainties in source,network and loads and its deep coupling with information systems and external heterogeneous energy systems,operational uncertainty will become one of significant characteristics in smart distribution network.Power flow analysis and optimizaiton are the basic electrical calculations for studying and adjusting the steady-state operation of power systems,but in this context its rationality premise is more and more difficult to be satisfied.Therefore in order to ensure the safe and stable ecnomic operation of smart distribution networks,it is very necessary to develop the power flow analysis and optimization method under uncertainty.The main research contents of intervl analysis for smart distribution network are carried out as below.1)Interval power flow algorithm applied to distribution network with high proportion renewable energyFor the weakly meshed distribution network with multiple types of distributed generations(DG),through the loop analysis by path matrix and two-step correction by reactive power sensitivity matrix and voltage sensitivity matrix,a back/forward sweep affine power flow algorithm for meshed network is developed to.consider the impacts of DG local control.For AC/DC hybrid distribution network,Combining the nonlinear programming-based equivalent and alternate iterative method,an algorithm of equivalent interval power flow applied to voltage interval calucation in hybrid distribution networks is further designed.Through Monte Carlo simulation-based probabilistic load flow(MCS-PLF),the comparison results demonstrate that,the number of loops,system size and the uncertainty of loads have little effect on the convergence performance.The nonlinear programming-based equivalent is exact for radial AC distribution networks and DC distribution networks,thus avoiding the coservertive problem of interval/affine arithmetic-based interval power flow calculation.2)Interval algorithm of online contingency analysis applied to DC distribution networkTo realize the online contingency analysis in DC distribution network in an uncertain environment,an interval power flow model with N-1 line outage is detrived.Based on the ecpressions of voltage change intervals and current change upper bounds derived by interval matrix norm,a contingency filter has been developed based on to quickly select the contingency with violation risk in the post-outage period.The nonlinear programming-based equivalent and affine arithmetic are further employed to construct the equivalent model for detailed assessment,and then the successive linear programming are used to solve the equivalent model efficiently.Combining the reformulation-linearization technique,the proposed contingency filter and the detailed assessment,an two-stage online contingency analysis algorithm incorporating interval uncertainty is designed.The comporison with MCS-PF and line outage distribution factor(LODF)-based method violates the effectiveness of the online algorithm.The proposed contingency filter provides an accurate but conservative bound result for voltage changes in post-outage period,and enables one to identify contingencies which cause violations on node voltage and branch current,thus making the efficient dietailed assessment and online process possible.3)Linear analysis model for nonlinear mapping relationship between power injection and node voltageTo quantitatively assessing the impact of uncertainties on node voltage in a distribution network,the feasibility and requirements of the linear quantitative description is discussed,and then a linear analysis model for the nonlinear mapping relationship between power injcetions and node voltages is developed.By the point-estimation method and elastic net regression,a method to identify the parameters of the linear analysis model is also proposed.To further illustrate the practical application of the linear model,a coordinated optimal configuration method for DG storage is presented to take count of the voltage quality,which can make the power fluctuation and voltage fluction governed jointly.Benchmarked against MCS-PLF,electromagnetic transient simulation and sensitivity analysis,the test results demonstrate the effectivenss and accuracy of the proposed linear model,as well as the rationality of the application case.4)Interval analysis model for nonlinear mapping relationship between power injection and node voltageTo quantitatively assess the impact boundaries of uncertainties on node voltages,the linear analysis model is extended to an interval analysis model.By using the interval/affine power flow,two solution methods of interval regression based on quadratic programming and stochastic programming are proposed respectively to meet the different demand of solving efficiency and conservative level for parameter identification.To further illustrate the practical application of the interval model,an optimal location method for energy storage based on set pair analysis is presented,which can be used to take count of the certainty and ucnertainty in voltage fluctuation suppression.Benchmarked against MCS-PLF,electromagnetic transient simulation and sensitivity analysis,the test results demonstrate the effectivenss and accuracy of the proposed interval model,as well as the rationality of the application case.5)Analytical model of interval optimal powre flow and its modification methodTo efficiently solve the problem of optimal power flow(OPF)incorporating interval uncertainty,its modeling characteristics are analyzed firstly and then an analytical model that can be solved in numerical approachs is derived by employing the affine arithmetic and first-order Taylor inclusion function.To improve solution accuracy,a modification method taking account of the high-order information is designed.According to the multi-period optimization of dynamic optimal power flow(DOPF),an interval DG model that describes the uncertainty of control and an analytical model for interval DOPF are derived in turn.Tests on a modified 33-bus system and a real 113-bus distribution network violate their effectiveness and applicability of the proposed model and modification method,as compared to MCS-PLF,OPF,stochastic OPF,etc.