Research On Probabilistic Optimal Power Flow Problem In Power System Considering Random Variation Of Load And Wind Power

The optimal power flow (OPF), considering the system economical efficiency and security, has been commonly used as an efficient method in the power system analysis and optimization. It is applied widely in power system safety operation, the economic operation, reliability analysis, energy and power management and electricity price, etc. In the environment of power market, OPF not only provide the optimal decision for power market operator and make a decision process more transparent and more fair, so it is also applied widely in power market congestion management, load management, spot price, reactive power pricing and available transfer capability etc. The previous OPF methods are mostly based on the determinate network topological structure, the system component parameters and operation conditions. However, the quantities above mentioned are uncertain or random. In addition, the more and more random wind powers are connected into power system. It makes the uncertainties of system increase continually and the uncertainties bright the new challenges to the OPF analysis. The probabilistic optimal power flow (POPF) problem considering the random variation of load and wind farm output is researched in the dissertation. The main contents of the dissertation are as follows:Firstly, the probabilistic load flow (PLF) calculation methods are researched and compared. The influence of the correlated nodal injections on the PLF is researched. Results show that the correlation among nodal injections should be considered in PLF analysis. It is introduced for the basic theory of the first-order second-moment method (FOSMM), the linearized model, the approximate second order model considering the correction of covariance and the two-point estimate method (2PEM), and it is determined for the calculation models and steps of the methods with the assumption of the independent and correlated nodal injections. The methods are verified on a 24-bus system. The results obtained from the methods are compared against more accurate results obtained from Monte Carlo simulation (MCS). Numerical results show that the approximate second order model is more accurate than the other algorithms with higher computation burden. The influence of the correlation on the PLF is demonstrated, which shows the correlation among nodal injections should be considered in PLF analysis. The errors will increase if ignoring the influence. The contents not only can be for reference for other researchers when selecting the PLF methods, but also provide the basis for considering the correlation among nodal injections in PLF analysis.Secondly, due to wind power outputs varying with random wind, a probabilistic wind farm model considering the reactive power-slip characteristic is proposed. Then, a combined iteration method for the PLF state variables and the slip, applied to grid-connected induction wind power system, is presented. In the probabilistic model for wind farm, the uncertainties of wind speed is takes into account, and the real power injected and reactive power absorbed by the wind turbine are described as the function of the voltage magnitude, the slip of the induction machine and the circuit parameters of the wind turbines. In the unified iteration method, the slip of induction machine is introduced as the new correction value. The Newton-Raphson algorithm is used to solve the unified iteration of state variable and slip. Thus, the proposed method retains the quadratic convergence of the Newton-Raphson algorithm. With wind speed described as Weibull probability density function (PDF) and load described as normal distribution, the PLF is performed on the modified IEEE 14-bus system using MCS method. The results show the effectiveness of the proposed method, and show that the appropriate wind power capacity can improve the voltage profile. The different ratio of wind farm capacity with respect to the system overall real power load is researched. The results show that inappropriate wind farm capacity can lead to the exceptional power flow results.Thirdly, based on the subdifferential, a semismooth Levenberg-Marquardt (L-M) method is successfully used to solve and the OPF problem. By introducing the nonlinear complementarity problem (NCP) function, the Karush-Kuhn-Tucker (KKT) conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by a semismooth L-M method based on the subdifferential. The method belongs to Newton-type method. It can ensure the positive defmitiveness of the iterative coefficient matrix by using the L-M parameter, which avoids the ill-conditioning of iterative equations. The method, requiring only the approximate solution of a linear system at each iteration, is quite applicable to the large-scale cases. The feasibility of the proposed method for solving the nondifferentiable problem is verified on Kojima-Shindo problem, and the effectiveness of the proposed method is demonstrated by analyzing the convergence characteristic and computational precision of the method on the IEEE test systems. Fourthly, owing to the impact of uncertain parameters on the system optimization results, a POPF algorithm based on the FOSMM is presented considering the uncertainty of correlated load. The POPF is first shown as the stochastic nonlinear programming problem. By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth L-M method based on the subdifferential. The proposed algorithm is verified by three test systems, i.e., the five-bus system, IEEE 30-bus and 118-bus systems. Results are compared with the 2PEM and MCS method. The proposed method has minor computational expense regardless of the number of uncertain variables and is computationally faster than the 2PEM and MCS method. The proposed method shows good performance when no line current is at its limit. If the case appears, the proposed method may not provide the explicit PDF curves of spot prices due to the exceptional spot prices caused by the congestion.Finally, facing the increasing uncertain problem of system operation condition brought by more and more wind farms connected directly into power grid, the POPF calculation for grid-connected induction wind power system is researched, and the uncertainty of wind power is considered by the FOSMM. In the POPF model, wind farm is modeled by the probabilistic wind farm model considering the reactive power-slip characteristic, and the inequality constraints include not only the unit output constraints, the ratio constraints, the voltage constraints and the line current constraints but also the reactive compensation capacity constraints in wind farm and the system climbing capacity constraints per minute. By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth Newton-type method based on the subdifferential. The proposed algorithm is verified by the modified IEEE 30-bus system. Compared with the MCS method, the proposed method shows good performance. Results also show that the appropriate wind farm capacity can save the system fuel cost, and the changements of the costs and nodal spot prices keep the reasonable agreement with related theories. However, with the increasement of wind farm capacity, the reliability cost caused by wind power grows higher and higher and wind power value grows smaller and smaller.