Studies On Optimal Power Flow Calculation Of Active Distribution Network Based On Second-Order Cone Programming

With the access of a large number of distributed generatation and the enhancement of automation level of distribution network,the traditional distribution network is rapidly developing to the active distribution network which can take active control and management,and controllable components in the distribution network increase.By rationally scheduling active components at all levels,it can effectively reduce the network loss of the distribution network and improve reliability,realize optimal power flow distribution in distribution network.Optimal power flow,which is a classic tool for analyzing optimal distribution of power flow,can fully coordinate the economy and safety of the distribution system,thus has been widely used in power systems.But compared with transmission grids,the optimal power flow of distribution network lacks effective calculation methods.Besides,the addition of controllable element models and the uncertainty of distributed generation make the calculation of optimal power flow more difficult.Therefore,it is very necessary to explore a more accurate and efficient optimal power flow calculation method in the context of active distribution network.The structural parameter characteristics of the distribution network and the access of controllable components and distributed generation bring many difficulties to the optimal power flow calculation of the distribution network.First,the non-convex nonlinearity of the optimal power flow model of the distribution network makes it difficult to be solved efficiently and precisely.Second,discrete variables such as capacitors increase the computational difficulty.Third,the new controllable components need to be modeled accurately.Fourth,the uncertainty of load and distributed generation output makes the optimal power flow problem need to be solved by reasonable uncertainty calculation method.For the first problem,based on the branch flow model and the second-order cone programming theory,the optimal power flow model for the second-order cone programming of the distribution network is established.The method is based on the branch flow model.The non-convex nonlinear distribution optimal power flow model is transformed into a second-order cone programming model by phase angle relaxation and second-order cone relaxation.The relaxed model can be efficiently solved by the convex optimization algorithm package and the global optimal solution can be obtained.For the optimal power flow problem with discrete variables such as capacitors,based on the theory of Lp norm sphere and Boolean encoding,an integer programming model based on Lp-box is established,and based on L1-box and second-order cone relaxation methods,Optimal power flow model for active distribution network with distributed generations and multiple controllable components.The model replaces the variables with constraints and uses second-order cone relaxation method to transform the original model into a second-order cone scheme with only continuous variables,the relaxed model is solved by commercial algorithm package such as Gurobi.The effectiveness and exactness of the proposed method is verified by modified IEEE33 bus system and the P&G69 bus system.A new type of controllable component,the power flow router,was introduced and applied to the distribution network.The mathematical model of the power flow router is established,and an improved branch power flow model for the power distribution network is proposed.Based on this,the optimal power flow model of the distribution network with power flow router is established.The second-order cone relaxation is performed on the model,and the relaxed model is solved by a commercial algorithm package such as Gurobi.Considering the uncertainty of the load and distributed generation output,a probabilistic optimal power flow method combining Latin hypercube sampling and second-order cone programming is proposed.The effectiveness and exactness of the proposed method is verified by a modified IEEE33 node system.