Static Equivalent Modelling Method Considering The Uncertainty Of Renewable Energy Sources

By simplifying the power grid,the static equivalent modelling method can provide an equivalent grid model that is similar to the original system but in a smaller scale.Based on the equivalent model,the analysis and calculation of the power grid have lower memory requirement and have higher computation speed,which can reduce the computation burden brought by the analysis tasks and lower the chance of divergence in calculation.In addition,static equivalent modelling method can be applied to scenarios containing the decentralized operation of interconnected power grids.The information exchange between sub-grids in different regions only involves equivalent models,which can be used to guarantee the security and independency of operation.Therefore,the static equivalent modelling method in the power grid is an effective approach to perform analysis and calculation in the interconnected power grid.The existing static equivalent modelling methods are dependent much on the current operating state and may produce large errors when the system operation deviates from the basic operating point.This may leads to large deviations in the security analysis of the power grid,which might endanger the safe operation of power grid.For this problem,this paper demonstrates the principles of classical Ward equivalent method and the extended Ward equivalent method in detail,and analyses the cause of errors in Ward-type equivalent methods from a theoretical level.From this analysis,a modified Ward equivalent method based on the external to boundary sensitivity matrix is proposed in this paper.Utilizing the fast decoupled power flow equations and the decomposition of interconnected power grid,the external-to-boundary sensitivity matrices of phase angles,voltage magnitudes and reactive power are derived,respectively.One advantage of the modified Ward equivalent method is that it can track and update the state variables of the external network based on the boundary voltage,which substantially reduces the dependency on the base operating point.Finally,a series of tests of static security analysis are conducted in the IEEE 39-bus system to validate the effectiveness of Ward equivalent method and assess its accuracy.Simulation studies show that the equivalent model given by the modified Ward method has high accuracy in both nodal voltage and power flow on transmission lines,better than the classical Ward equivalent method and the extended Ward method.Results show that the proposed modified Ward method is suitable for the static security analysis under various operating conditions including power output fluctuation,load fluctuation and line outage.As the large-scale renewable energy distributed generation is integrated into the distribution network,the traditional distribution network is gradually changing into the active distribution network.Active distribution networks often have a high proportion of renewable energy generation.However,the existing researches on the equivalent modelling of active distribution networks rarely consider the probabilistic characteristics and correlation of renewable energy sources.To tackle this problem,this paper builds the models of uncertain sources in the active distribution network,such as the solar radiation,wind speed and load,hence the probabilistic modelling of power injection in the active distribution network is built.The approximate linear relationship of the external to boundary power transfer is derived from the nodal voltage equation.And the probabilistic equivalent model is built based on the cumulants of random variables.Furthermore,for the correlation between random variables,the Gaussian copula function are used to calculate the joint cumulants of power output of renewable energy sources.The orthogonal transformation is used to modify the coefficient matrices,thereby taking the correlation bewteen random variables into account.The application of the probabilistic equivalent model in the probabilistic power flow algorithms that are based on cumulant and Monte Carlo simulation respectively is given in the paper.Simulation studies are carried out on the coupling system composed of an IEEE 30-bus transmission network and an IEEE 34-bus distribution network.Simulation results demonstrate the effectiveness of the probabilistic equivalent modelling method for the active distribution network and show that the accuracy of probabilistic equivalent model can be improved with involvement of the correlation of random variables.