Studies On Linear Three-phase Power Flow Method Considering Uncertainties For Power Distribution Networks

With the increase of connected-grid intermittent renewable resources and rapid growing of new loads,the impacts of uncertainty on power systems become significant.Power flow calculation is the most fundamental part in power system analysis,the approaches for handling power flow uncertainties become hot spots and research trends.The unbalance problem is prevalent in distribution networks.To reasonably analyze the distribution network,a three-phase power flow calculation method is needed.In this paper,the three-phase model of main components of distribution network were estabilished,deterministic linear three-phase power flow(LTPF),interval linear three-phase power flow considering interval uncertainties and linear three-phase power flow considering multiple mixed uncertainties for power distribution networks were studied.Three-phase model of distribution lines based on port equation is researched;the topology structure of three-phase network is analyzed.The calculation method for forming three-phase correlation matrix and matrix-form based formula of three-phase node admittance matrix were given.A supplementation for resolving singularity problem of admittance of existing three-phase transformer model was made.Admittance model of wye connected,open-delta connected and delta connected three-phase regulator were deliberated in details.The ZIP load model based on current injection was discussed,the formula of node admittance of shunt capacitors was given.Simplification conditions for distribution network was analyzed quantitatively based on the characteristics of high R/X ratio of typical distribution networks.Two simplification methods were used to linearize ZIP load model,and two versions of linear ZIP load model based three-phase power flow method were presented.Several balanced and unbalanced distribution systems were used to test and compare the performance of two simplification method based power flow methods,their application scope were also discussed.Combining the affine inversion method with the linear three-phase power flow algorithm,a non-iterative affine inverse operation based interval linear three-phase power flow method for power distribution networks was proposed.The interval variables in systems were represented by affine numbers,linear three-phase power flow equations were transformed into affine equations,and the formula of affine node voltage was derived by applying the inverse operation method of affine matrix and conservative estimation of affine equations.Probability,interval and fuzzy model were used to model different types of variables,a linear three-phase power flow algorithm considering multiple mixed uncertainties was proposed.On the basis of affine node voltage equations,the concept of bound influences(BI)of interval variables was given.Probability variables were handled by transfering to interval numbers.By removing the self bound influence of probabilistic variables(SBI-PV),the accuracy of bound influences of interval variables were improved.The probability-interval power flow solutions were obtained by the superposition of BI of interval variables on operation point,and probability-interval-fuzzy power flow were obtained by compositing two probability-interval power flow solutions.