Extended Affine Model And Its Application In Power System Interval Power Flow Analysis

With the large-scale integration of renewable energy into grid,both ends of the supply and demand balance in the power system,namely the source and the load,are facing uncertainty disturbances at the same time,which seriously threatens the safe and stable operation of the power system.Accurate analysis and quantitative evaluation of the impact of uncertainty on the steady-state operation of the renewable energy power system can reduce the impact of the source and load side double uncertainties on the safe and reliable operation of the power system,and improve the security and economy of renewable energy generation consumption.The power system uncertainty analysis method based on probability statistics is difficult to obtain a large number of accurate statistical data,leading to the low accuracy of the model,and requires a large number of probability calculation,leading to complicated and complicated solution process,which has been restricting the application of power system uncertainty analysis method based on probability statistics.Under this background,this paper uses affine arithmetic and extended affine arithmetic to construct the affine optimization model and extended affine optimization model of interval power flow respectively to solve the distribution of interval power flow.On this basis,the idea of global sensitivity analysis is introduced to establish the analytical variance contribution decomposition model of uncertainty power flow and static voltage stability assessment,so as to quantify the importance of uncertainty disturbance sources on the steady-state operation of power systems,that is,the ranking of global sensitivity index.The main work and research results of the paper are summarized as follows:(1)In order to avoid the convergence and initial value problems of the interval iteration method,the affine arithmetic is introduced to transform the interval power flow equation into two kinds of affine optimization models.The linear affine optimization model of the interval power flow based on the polar coordinate system and the nonlinear affine optimization model of the interval power flow based on the rectangular coordinate system are constructed systematically.The two kinds of interval power flow affine optimization models are based on the deterministic power flow solution at the midpoint of the interval variable.The affine operator expansions of the system state variables are obtained.Then,the power flow equation are reconstructed to form an optimization model with noise element to reduce the range of noise element,which changes the calculation mode of the traditional iterative interval power flow algorithm and improve the interval power flow calculation accuracy and efficiency.(2)Because the model based on traditional affine arithmetic(or called first-order affine arithmetic)is essentially the first-order interval Taylor expansion approximation of the interval power flow equation,there is inevitably the interval expansion caused by local truncation error.The extended affine arithmetic(or called second-order affine arithmetic)is obtained by using the interval Taylor expansion.The extended affine optimization model of node voltage amplitude/phase angle and branch active/reactive power are derived based on extended affine arithmetic.Combining the quadratic features of the interval power flow equation in the rectangular coordinate system,the problem of solving extended affine coefficients is equivalently transformed into the solution of three deterministic algebraic equations.The extended affine quadratic programming method of interval power flow based on rectangular coordinate system is also a non iterative method,which does not have the problems of convergence and initial value;its calculation accuracy and efficiency are higher than that of the affine nonlinear optimization method of interval power flow based on rectangular coordinate system.(3)The interval power flow distribution can only reflect the joint effect of multiple input interval variables,but can not quantify the impact of each input interval variable on the system output interval results,which is not conducive to identify the leading and secondary factors affecting the static security of power system.By decomposing the variance contribution of the power flow output response,the variance contribution of each input is obtained,and then the importance index of each input,namely the global sensitivity index is obtained.The proposed global sensitivity analysis method based on the extended affine power flow model can obtain the results close to the Monte Carlo method,and the calculation efficiency can be greatly improved due to the analytical calculation,which can be applied to the scene where the input variables are correlated and uncorrelated.(4)The static voltage stability probability evaluation needs an accurate probability model of input variable,and the lack of statistical data often leads to model accuracy problems.By introducing the interval affine method into the uncertainty assessment of static voltage stability,the extended affine model of static voltage stability assessment based on L-index is derived by using the interval Taylor expansion,and the importance of the input variables that affect the static voltage stability of power system is measured by the global sensitivity analysis method based on analytical variance decomposition,and the global sensitivity analysis method for static voltage stability based on extended affine model is proposed.The results of static voltage stability evaluation based on the extended affine model are closer to the Monte Carlo method than the traditional affine method.The global sensitivity analysis based on the extended affine model can identify the key input variables that affect the static voltage stability quickly and effectively.