Complex Affine Arithmetic Based Analysis And Operational Optimization Of Active Distribution Networks Considering Uncertainties

Facing serious energy and environmental issues,the development of renewable energy has promoted the transformation of traditional distribution networks into active distribution networks.Considering the uncertain fluctuations of distributed generations and loads,active distribution networks operate in complex environments with multiple uncertainties.Based on complex affine arithmetic,this dissertation focuses on the analysis and operational optimization of active distribution networks considering uncertainties.The main contributions are as follows:1)Affine arithmetic is extended to the polar coordinate system and operations of complex affine arithmetic in polar form are developed.Based on the Chebyshev approximation theory and the min-range approximation theory,the affine approximation of trigonometric function and anti-trigonometric function is solved.The arithmetic can take into account the internal correlation of single variable and the correlation among multiple variables.While ensuring completeness,the conservativeness of results is effectively reduced.Combined with complex affine arithmetic in rectangular form,a complete complex affine arithmetic is formed.Complex affine arithmetic can calculate affine values of the real part,imaginary part,magnitude,and angle of uncertain variables.Thus,it provides computational support for the subsequent uncertainty analysis and operational optimization of active distribution networks.2)Considering the correlation and de-redundancy of noise terms,an improved forward and backward sweep power flow algorithm based on complex affine arithmetic is proposed for active distribution networks.As for uncertain models of power flow,the correlation among main noise terms of complex affine variables is taken into account.The uncertain fluctuations of distributed generations and loads,as well as the uncertainty mitigation effects of energy storage systems and static var compensators are fully considered.As for the forward and backward sweep process of power flow,the redundancy of error noise terms of complex affine voltages and currents is removed,which effectively improves computational efficiency.Compared with the original complex affine power flow algorithm,Monte Carlo method and deterministic power flow algorithm,the completeness,accuracy and efficiency of the proposed algorithm are verified.3)An uncertain multi-factor sensitivity analysis method of the voltage fluctuation interval in active distribution networks is proposed,which breaks through the limitation of traditional voltage sensitivity analysis method.Considering the variations of multiple uncertain factors,uncertain sensitivity equations with complex affine variables are built for the voltage fluctuation interval based on the transitivity of noise symbols in affine operations.Uncertain sensitivity indicators of single-factor and multi-factor are defined.Meanwhile,a calculation method for uncertain sensitivity indicators is proposed based on the micro-increments of noise coefficients.Furthermore,a linear calculation method of the voltage fluctuation interval based on uncertain sensitivity indicators is proposed.When uncertain factors change,the proposed method avoids the repeated calculation of power flow.Compared with the continuous utilization of the improved forward and backward sweep power flow algorithm based on complex affine arithmetic,the accuracy and efficiency of the proposed method are verified.4)An uncertain multi-objective optimization method based on affine arithmetic is proposed for active distribution networks with energy storage systems.Considering both operational economy and power quality,an uncertain multi-objective optimization model based on affine arithmetic is established for active distribution networks.The objective function is to minimize affine values of total active power losses and total voltage deviations.And the power outputs of energy storage systems are taken as control variables.Furthermore,an affine arithmetic based elitist non-dominated sorting genetic algorithm(AA-NSGA?)is proposed.As for affine parameters,the problems of fast non-dominated sorting,Pareto optimal solution and crowded distance calculation are solved.The proposed algorithm can effectively deal with uncertain parameters in the optimization model.The convergence,uniformity,span,and uncertainty indicators are defined.And case studies are implemented to verify the superior convergence and diversity of the proposed algorithm.Meanwhile,the uncertainty,seasonality and timing characteristics of distributed generations and loads are considered,which demonstrates the applicability of the proposed method in practical scenarios.