Typical paper for preserving nonlinear algorithm are:
1. The paper [Probabilistic power flow calculation of power system with nonlinearity preserved] puts forward its application in probabilistic power flow calculation of power system. In this paper, a new probabilistic power flow calculation method is proposed, which retains the nonlinearity of power flow equation and adopts P-Q decoupling method, so the mathematical model has high accuracy, while retaining the advantages of P-Q decoupling, which is beneficial to the random power flow calculation of large power grid. A typical system is calculated by this method, and its numerical value is verified by MonteCarlo random simulation, and satisfactory results are obtained.
2. Literature [A fast P-Q decoupled power flow calculation method based on system partition and keeping nonlinearity] analyzes and studies the fast P-Q decoupled power flow calculation method keeping nonlinearity. In this paper, a new state estimation algorithm is proposed, which not only retains the nonlinearity of the measurement equation, but also adopts the fast P-Q decomposition method, so the mathematical model has high accuracy, retains the advantages of fast P-Q decomposition, and improves the calculation accuracy and speed of state estimation. The large-scale system is divided into several small systems by system segmentation method, and the state estimation results of each small system are coordinated. Obtaining the state estimation results of the whole system with the same reference nodes can greatly improve the calculation speed of state estimation and is beneficial to the state estimation of large power grids. The digital simulation experiment of 18 bus system verifies the effectiveness of this method. Iwamoto Shinichi proposed a nonlinear fast power flow calculation method, but this method uses rectangular coordinate system, so it can't use P-Q decoupling. In order to be more conducive to power flow calculation of large power grid, this principle is extended to P-Q decoupling. In this way, not only the fast algorithm to keep nonlinear is used, but also the constant Jacobian matrix is used in the iteration, which retains the advantages of P-Q decoupling.
For some ill-conditioned systems, the application of nonlinear power flow calculation method often leads to oscillation or non-convergence in the calculation process. Mathematically, the nonlinear power flow calculation equation is essentially insoluble. In this way, people put forward the problem of constructing the power flow equation into a function and finding the minimum value of this function, which is called the calculation method of nonlinear programming power flow. The advantage is that the calculation process will never diverge in principle. If the mathematical programming principle is organically combined with Newton power flow algorithm, it is the optimal multiplier method. In addition, in order to optimize the operation of the system, the optimal power flow problem that meets certain index requirements is selected from all feasible power flow solutions. Optimal power flow is a power grid analysis and optimization problem that takes into account both economy and security. OPF has been widely used in safe operation, economic dispatch, reliability analysis, energy management and electricity price formulation of power system.
Typical papers on optimal power flow are:
1. Literature [Research on New Algorithm of Optimal Power Flow in Power System] Based on NCP method, a new algorithm for solving optimal power flow-projective asymptotic semi-smooth Newton algorithm is proposed. Based on NCP method, this paper presents a new algorithm for solving OPF-projective asymptotic semi-smooth Newton algorithm. According to the characteristics of power system, the research work of this paper is as follows: 1. A semi-smooth equations with bound constraints equivalent to KKT system of OPF problem is established. Compared with the existing NCP method, the new model reduces the dimension of the problem because it does not need to consider the dual variable (multiplier variable) corresponding to the bound constraint, so it is suitable for solving large-scale power system problem 2. Based on the new model, this paper proposes a new Newton-type algorithm. On the one hand, the algorithm maintains the compatibility of bound constraints, on the other hand, it has good global and local superlinear convergence, and the algorithm is simple in structure and easy to implement. 3. Considering the inherent weak coupling characteristics of power system, inspired by the traditional decoupling optimal power flow method, a new Newton-type decomposition method is designed. The new method realizes the algorithm based on decoupling-correction strategy, which not only makes full use of the weak coupling characteristics of the system, but also ensures the theoretical convergence of the decomposition algorithm. 4. According to the two proposed algorithms, numerical experiments are carried out on the standard IEEE power test system and compared with other existing methods. The results show that the new algorithm has good convergence and calculation effect, and has broad application prospects in power system planning and operation.
2. According to the literature [Research on Optimal Power Flow Based on Trust Region Interior Point Method], OPF interior point method has the advantages of strong convergence and polynomial time complexity, and it is one of the excellent algorithms with great potential.
With the continuous development of power system, OPF algorithm ranks among the extremely difficult non-convex large-scale nonlinear programming. Trust region and linear search method are two technologies to ensure the global convergence performance of optimization algorithm. Combining interior point method with trust region and linear search method to construct a new optimization algorithm is a research hotspot in the field of mathematical programming.
Typical documents in this regard are:
1. Literature [Research on transmission capacity adequacy based on optimal power flow in power market environment] Firstly, the optimal power flow is used as a tool to select the key lines in the system as the research object of transmission capacity adequacy. From the perspective of power grid operation safety and reliability, the influence of transmission line stability limit on transmission capacity adequacy is systematically studied, and it is pointed out that the product of stability limit factor and shadow price can directly reflect the economic value of stability limit level, and at the same time, it can better show the relative safety and economy of system operation.
2. Literature [Research on node real-time electricity price and power purchase share based on optimal power flow in power market environment] In order to provide price reference for the optimal power purchase model of distribution companies, a real-time electricity price model is established with the minimum generation cost as the objective function and the influence of price elasticity of power demand considered. Predictive correction primal dual interior point method is used to solve the model, and the feasibility of the model is verified by taking IEEE30-bus system as an example.
3. Literature [Research on Dynamic Optimal Power Flow Model and Algorithm of Power System] points out that dynamic optimal power flow of power system is an effective tool for unified optimization of system state during dispatching period, which has important theoretical and practical significance for ensuring safe and economic operation of power system. Based on interior point method and immune genetic algorithm, the algorithms of classical dynamic optimal power flow problem and dynamic reactive power optimization problem are deeply studied, and new algorithms are proposed. A dynamic optimal power flow model including voltage stability constraints, reactive discrete variables and unit start-stop variables is established, and the new algorithm is extended to various new models, which expands the research field of dynamic optimal power flow.
For some special power flow calculation problems, there are DC power flow calculation method, random power flow calculation method and three-phase power flow calculation method. DC power flow calculation method, the document [AC /DC power flow calculation based on improved Broyden method] mainly introduces the unified iterative method for power flow calculation of AC /DC hybrid system by using improved Broyden method and improved Broyden method for solving nonlinear equations on the basis of analyzing Broyden method, designs the concrete implementation steps of the algorithm, and carries out simulation calculation with IEEE9-node correction system. The results show that the improved Broyden method adopted in this paper is effective and feasible. Document [Identification Technology of Brittle Source of Three-bus System Based on DC Power Flow and Distribution Factor] proposes a method and steps to quickly find the brittle source of the system based on the combination of DC Power Flow and Distribution Factor Method. The effectiveness of this method is proved by identifying the brittle source of 3-node power system. The influence of variable speed constant frequency doubly-fed generator wind farm on voltage quality is studied in the document [Random power flow calculation of power system considering internal equivalent circuit of doubly-fed wind turbine]. Based on the simplified equivalent circuit of doubly-fed generator, the deterministic power flow model of wind farm is established, and the stochastic analysis model of wind turbine is established. On this basis, the stochastic power flow based on semi-invariant method is used to calculate. The paper "Stochastic Power Flow Calculation of Distribution System Considering Distributed Generation" puts forward the stochastic power flow calculation of distribution system considering distributed generation.