Chance-constrained Optimal Power Flow Method And Its Applications:A Data-driven Surrogate-based Approach

To build a clean,low-carbon,and sustainable energy system,developing a power system with a high proportion of renewable energy is becoming an inevitable trend in China and even the world.Due to the random fluctuation of wind power and photovoltaic,the uncertainty of the power system sharply increases.The operation state of the power grid becomes more complex and changeable,leading to a severe threat to the power system operation.Optimal power flow(OPF)is one of the most important tools for power system operation.Renewable energy development makes the traditional deterministic OPF method challenging to consider the uncertainty of renewable energy.It is necessary to study the stochastic optimization method,which can effectively deal with the uncertainty of new energy.As an important branch of the stochastic optimization method,the chance constraint optimization(CCO)ensures that the violation of uncertain constraints is restricted within a preset risk level.,which attracts extensive attention in academia and industry application.The key of the chance-constrained optimal power flow(CC-OPF)is to analytically formulate the system operation chance constraints into deterministic ones with system operation boundary margin.Its essence is to establish the analytical mapping function between the power system decision variables and the system operation boundary margin considering the impact of renewable energy uncertainty on system operation constraints.However,the existing CC-OPF methods still have the following problems: 1)CC-OPF is challenging to be analytically formulated under the arbitrary distribution of renewable energy uncertainty;2)The coupling relationships between power system decision variables and the system operation boundary margin are hard to be modeled in the existing CC-OPF methods;3)Efficient and accurate effectiveness verification and economic signal analysis of CC-OPF need to be studied.In this regard,this article focuses on the CC-OPF problem and develops a data-driven method to construct the analytical surrogate model of system operation boundary margin,including:(1)To overcome the CC-OPF analytical formulation problem under the arbitrary distribution of renewable energy uncertainty,an analytical CC-OPF formulation method is proposed based on the data-driven surrogate model.Firstly,the mathematical essence of CC-OPF is analyzed to establish the mapping relationship between power system decision variables and system operation boundary margin.Then,the key idea of solving CC-OPF based on the data-driven surrogate method is presented.Finally,the chanceconstrained DC optimal power flow is introduced to demonstrate the effectiveness of the proposed method.(2)To overcome the CC-OPF analytical formulation problem considering the influence of generator affine control on the system operation boundary margin,a datadriven CC-OPF method considering generator affine correction control is proposed.Generator affine control is the response behavior of the generator to the uncertainty of renewable energy.Based on a low nonlinear power flow model,a data-driven surrogate model is constructed to learn the mapping relationship between generator affine control variables and system operation boundary margin based on a low nonlinear power flow model.To correct the modeling error introduced by linearization and data-driven training,a data-driven fast iterative algorithm based on the Monte Carlo simulation is proposed to improve the model accuracy of CC-OPF.(3)To overcome the CC-OPF analytical formulation problem considering the singularity of the renewable energy uncertainty distribution caused by the renewable energy power output upper limit control,a two-stage CC-OPF analytical formulation method is proposed based on the data-driven surrogate model.An error correction strategy is also developed by solving a convex linear programming(LP)problem to ensure modeling accuracy.Compared with the existing methods,this paper can effectively consider the influence of the upper limit control of renewable power output on its uncertainty probability distribution.(4)The effectiveness verification of CC-OPF needs to repeatedly solve massive power flow and OPF problems,leading to a high computational burden.To overcome this,a data-driven effectiveness verification of CC-OPF flow is proposed based on the OPF model object feature decomposition.Specifically,the complex OPF model features are decomposed into three stages to correct the learning bias.To further improve the accuracy of effectiveness verification of CC-OPF,a sample pre-classification strategy is proposed based on multi-parametric programming(MPP)theory.(5)To analyze the economic signals provided by the CC-OPF,this article proposes an electricity market pricing method that explicitly considers the characteristics of multiple statistical moments of renewable uncertainty based on the derivation of the Lagrange duality problem.The proposed method solves the problem that the existing deterministic OPF is difficult to calculate the flexible resource cost required to suppress the uncertainty of renewable energy,providing a clear price signal to guide the market resource allocation.In summary,this article proposes a CC-OPF method based on the data-driven surrogate model,which overcomes the Mathematics that the existing CC-OPF method is challenging to deal with the arbitrary distribution of renewable energy uncertainty.In this paper,the data-driven method provides a new idea for solving the technical challenge of chance-constrained optimal power flow,providing a theoretical basis for the practical industrial application of chance-constrained optimal power flow.