Reformulations And Efficient Algorithms For Chance-constrained Optimal Power Flow Based On Linearized Network Models

With the large-scale access of renewable energy,its intermittent and random characteristics force the power system to withstand increasingly strong uncertainties.At the same time,the Voltage Source Control-Multiple Terminal Direct Current system(VSC-MTDC)has also been widely integrated into the large AC power grid.In order to enable the power grid to operate in security and economy under large-scale renewable energy integrating scenarios,it is of great practical significance to perform stochastic optimization analysis on pure AC power grids and AC/VSC-MTDC hybrid power grids in random scenarios.Although the stochastic optimization algorithms for pure AC power grids have been studied for many years with fruitful results,there are still many challenges;in addition,there are few studies on the stochastic optimization analysis of AC/VSC-MTDC hybrid power grids.The existing problems mainly include: how to model the stochastic optimization problem and obtain its easy-to-handle reformulated form,how to reduce the complexity of the optimization model,improve the solution efficiency while taking into account the accuracy,how to balance the accuracy and speed of uncertainty evaluation,and how to extend the stochastic optimization problem to AC/VSC-MTDC hybrid power grid.Linearization is one of the commonly used and efficient methods in optimization modeling.Its scalability and applicability play an important role in optimization problems.There are many advantages in applying the linearization method to the stochastic optimization analysis of pure AC power grids and AC/VSC-MTDC hybrid power grids.According to its characteristics,this article improves the existing models and algorithms from the following aspects:Firstly,aiming at the efficiency and accuracy of traditional AC and DC power flow models,this paper proposes a novel chance-constrained optimal power flow model based on the linearized network model.This model significantly reduces the complexity of the AC model,while maintaining explicit constraints on the voltage magnitude,reactive power and branch apparent power flow of the power system.From the perspective of the model,the computational performance that the linear-constrained optimization model should have can be achieved.In particular,the linearization of the non-linear apparent power flow on the branch will trigger a joint chance constraint,which makes it difficult to perform the deterministic reformulation of the chance constraint.Therefore,this paper uses an improved Boole’s inequality to approximately split the joint chance constraint,and the decomposed single chance constraints can be transformed into deterministic constraints with other single chance constraints.Secondly,since the analytical reformulation method and the simulation method cannot juggle the accuracy and efficiency of the uncertainty evaluation at the operating point.This paper combines the three-point estimation(TPE)method in the probabilistic power flow with the Cornish-Fisher series expansion(CFE)and introduces the Nataf transformation to effectively evaluate the probabilistic uncertainty of the feasibility recovered solution of the AC power flow.At the same time,an iterative solution process is adopted,which can decouple the chance-constrained optimization into deterministic optimization,AC feasibility recovery,and uncertainty evaluation process.Thirdly,for the AC/VSC-MTDC hybrid power grid under high-dimensional and related random scenarios,the chance-constrained optimization problem based on its linearized network model is proposed.Unlike pure AC power grids,the AC/VSC-MTDC hybrid power grid integrates converters and DC power grids.In existing stochastic optimization problems,the modeling of the converter station is generally incomplete and the loss of the VSC converter is arbitrarily neglected.This paper considers the complete converter model,whose VSC converter loss has a high degree of non-linearity.In this paper,the non-linear loss is attributed to a constant loss and the non-linear power flow loss of the added virtual branch,and uses the linearized network model to deal with this loss.Finally,based on the improved IEEE 39 and IEEE 118-bus system,the effectiveness,superiority and applicability of the proposed chance-constrained optimal power flow modeling and solution methods are verified.Moreover,based on the improved IEEE 39-bus system,the optimal operation of the AC/DC hybrid power grid in random scenarios is analyzed.On the basis of verifying the effectiveness and superiority of the proposed models and algorithms,the influence of the optimization of the control parameters of the AC/DC hybrid system on the results is further analyzed.