Probatilistic Available Transmission Capability Calculation Of Power System Based On Polynomial Chaos Expansion

The large-scale development and utilization of renewable energy is conducive to achieving the clean and low-carbon transformation of the power system,and is an important technical means to achieve the national strategic goal of "carbon peaking,carbon neutrality".Due to the randomness and intermittency of renewable energy output,the operation of the power system presents greater uncertainty,and the operating state of the system is also more complex,posing higher requirements for the safety and stability of the power system.The Available Transfer Capability(ATC)of the power system is an important indicator for evaluating the security and economy of the power system.The strong uncertainty and randomness of wind power output make the available transmission capability between regions present a high probability characteristic,while increasing the risk of power system flow exceeding the limit.This poses a new challenge for quickly and accurately evaluating the available transmission capability between regions of the power system.Research on a new method for probabilistic ATC evaluation considering wind power output uncertainty and opportunity constraints,obtaining ATC results that balance power system safety and economy,is of great significance for ensuring the operation scheduling,stability analysis,and reliability evaluation of power systems.To handle this challenge,a Polynomial Chaos Expansion(PCE)based chance-constrained PATC calculation method is developed in this paper,this article mainly completed the following research work:First of all,establish a wind farm output prediction model corrected for wind power output prediction error as an uncertainty input to the power system,and study the impact of wind power output uncertainty on the evaluation of available transmission capacity of the power system;To solve the problem of power system PATC based on chance constraints,from the perspective of controlling the risk of power system power flow out of limit caused by the uncertainty of wind power output,on the basis of the traditional optimal power flow ATC calculation model in Cartesian coordinate system,considering the strong uncertainty of wind power output,the generator output constraints,node voltage amplitude constraints and branch thermal stability constraints are transformed into chance constraints,Construct a PATC evaluation model for power systems based on opportunity constraints.Then,based on the basic principle of Polynomial Chaos Expansion,according to the probability distribution characteristics of wind power output prediction errors,the corresponding orthogonal polynomials are selected as orthogonal basis functions to approximate wind power output prediction errors and other random variables associated with them in the power network;Further,the probabilistic equality constraints and opportunity constraints of the constructed PATC evaluation model for power systems with opportunity constraints are converted into deterministic constraints using random Galerkin projection and chance constraint transformation methods based on first and second moments,respectively,to achieve the transformation of the PATC evaluation model for power systems with opportunity constraints into a deterministic single optimization model that is easy to solve,Then,the PATC model with chance constraints is solved;The proposed PATC evaluation model for power systems based on PCE was validated and analyzed using the modified PJM-5 test system and the modified IEEE-118 test system,respectively.The results were compared and analyzed with the results of traditional Monte Carlo simulation methods to verify the accuracy and effectiveness of the PATC evaluation model based on PCE.The results show that the proposed PATC evaluation model for power systems based on PCE can effectively and accurately achieve deterministic transformation of the opportunity constrained model,providing a new idea for the opportunity constrained ATC calculation method.Finally,based on the PCE PATC evaluation model for power systems,the problem of solving the probabilistic ATC evaluation model with chance constraints is transformed into the problem of solving the optimal approximation coefficients of various variables in the system network,and then the problem of solving the optimal polynomial approximation coefficients of the PATC model is realized;Further,based on the obtained optimal polynomial approximation coefficients and the selected orthogonal basis functions,the evaluation of power system PATC taking into account wind power uncertainty is realized;The proposed PCE-based PATC evaluation method for power systems is validated and analyzed through the modified PJM-5 test system,the modified IEEE-118 test system,and the actual system of West Power Grid in a certain province.The results are compared and analyzed with the results of traditional Monte Carlo simulation methods to verify the accuracy and effectiveness of the proposed method.The results show that the proposed PCE based PATC evaluation method for power systems can quickly and accurately evaluate PATC,providing strong support for power system operation scheduling,stability analysis,and reliability evaluation.