Probabilistic Energy Flow Of Power Systems With Large-Scale Wind Power And Integrated Electricity And Natural Gas Systems

Both wind energy and natural gas are abundant,safe and clean energy sources.They play an important role in alleviating the problems of energy crisis,environmental pollution and climate change.With wide application of wind power and natural gas power generation technologies,generation mix and network configuration have been changing.In the future power grid,wind energy and natural gas will gradually replace coal as important energy sources in the generation mix,and the power system and natural gas network will be closely coupled.Therefore,it is necessary to analyze the performance of power systems with large-scale wind power(PSLWP)and integrated electricity and natural gas systems(IENGS)in order to ensure the secure,stable,and economical operation of future energy systems.The randomness,intermittence and fluctuations of wind power,and fluctuations of loads introduce many uncertainties into energy systems,which brings great challenges to system planning and operation.The traditional probabilistic methods are not completely suitable for PSLWP and IENGS due to the large fluctuation from large-scale wind power and the feature difference between electricity systems and natural gas networks.Therefore,this paper focuses on studying the probabilistic load flow(PLF)computation.method of PSLWP,the probabilistic optimal power flow(P-OPF)computation method of PSLWP and the probabilistic energy flow(PEF)computation method of IENGS.(1)Large-scale wind power integration brings strongly fluctuating uncertainties into power system planning,resulting in that the traditional analytical methods may produce significant linearization errors.This paper proposes a novel PLF computation method based on a clustering technique and the cumulant method.First,the samples of wind power and loads are generated using the inverse Nataf transformation.Second,the K-means clustering technique is applied to group the generated samples.As a result,the samples in each cluster has smaller fluctuations.Third,in each cluster,the cumulant-based PLF computation method is used to calculate the cumulants of output random variables.According to the law of total probability and the relationship between cumulants and moments,the cumulants obtained in each cluster are converted into the cumulants corresponding to the original total samples.Finally,Gram-Charlier series expansion is applied to calculate probability density functions(PDFs)of output random variables.Case studies on IEEE 9-bus and 118-bus systems with wind farms demonstrate that the proposed method can be used to solve PLF problems of power systems with large-scale wind power.(2)Probabilistic optimal power flow is an important tool to handle uncertainties in system operation.It is also faced with large fluctuations from large-scale wind power.Therefore,this paper proposes a method of combined the clustering technique and the cumulant method to solve P-OPF problems.First,the sensitivity matrix of input variables(wind power and loads)to output variables(the objective function,voltage angles and magnitudes,active and reactive power generation)is developed.Second,based on the developed sensitivity matrix,this paper builds the cumulant-based P-OPF computation model with consideration of wind power integration.Third,the method of combined the clustering technique and the cumulant method is applied to solve P-OPF problems.Consequently,the computational accuracy of the cumulant-based P-OPF under widely fluctuating input random variables is improved.Finally,PDFs of output random variables are calculated using 6-order Cornish-Fisher series expansion.The applicability of the proposed method is validated on IEEE 9-bus and 118-bus systems with large-scale wind power.(3)The high proportion of renewable energies introduces many uncertainties with large fluctuations into IENGS.However,due to the feature difference between electricity systems and natural gas systems,the abovementioned method of combined the conventional clustering technique and the cumulant method is unsuitable for this scenario.Therefore,a novel PEF computation method based on an improved K-means clustering technique and the cumulant method is developed.First,an integrated energy flow model is built considering frequency regulation characteristics of electricity systems.Second,the sensitivity matrix of input variables(wind power,photovoltaic power,electricity loads and natural gas loads)to output variables(voltage angles and magnitudes,active and reactive line flows,pressures at natural gas nodes and pipeline flows)is derived.A cumulant-based PEF computation model is developed based on the sensitivity matrix.Third,an improved K-means clustering technique is proposed by standardizing the input random variable samples and introducing the overall sensitivity coefficients to modify the input random variable samples.The improved K-means clustering technique can incorporate the effects of different fluctuations,scales and sensitivities.The clustering results are beneficial to reduce the overall errors of the cumulant-based PEF.Finally,a novel PEF computation method is proposed by combining the improved K-means clustering technique and the cumulant method.In case studies,a regional IENGS and a multi-regional IENGS are used to verify the proposed PEF computation method.(4)In order to overcome the poor convergence of the natural gas flow model established using the Newton-node method and the difficulty for the cumulant method to accurately obtain PDFs of highly non-normal random variables,a linearized PEF computation model is proposed based on an equivalent loop energy flow model of the natural gas network and the improved K-means clustering technique.First,equivalent models of the natural gas network are built.Based on the Newton-loop method,an equivalent loop energy flow model of the natural gas network is developed.It can not only avoid the problem that the node energy flow model has poor convergence,but also solve the problems that the traditional loop energy flow model is not suitable for loopless networks and has difficulties to handle non-pipe components.Second,an integrated energy flow model for IENGS is established by combining the equivalent loop energy flow model of the natural gas network and the node energy flow model of the electricity system.Finally,according to the idea of conducting linearization calculation for each set of samples at the corresponding clustering center,a linearized probabilistic energy flow calculation method is proposed.Case studies contain two processes:1)The 14-node natural gas network and the 20-node Belgian natural gas network are used as test systems.It is verified that the established equivalent loop energy flow model of the natural gas network has good convergence and accuracy.2)An integrated electricity and natural gas system consisting of the IEEE 39-bus transmission system and the 20-node Belgian natural gas network is used as the test system.It is verified that the proposed PEF computation method has good accuracy and computational efficiency.