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Reactive power optimization is a special kind of optimal power flow for optimizing voltage profile and reactive power flow in the steady state based on deterministic sets of the demand load and generation values, thus minimizing the real power losses or improving the voltage quality of the power grid. However, the input data in power systems have a certain degree of uncertainty that requires the reactive power optimization be solved by means of uncertain nonlinear programming, as advocated in the literature. To address this problem, we represent the uncertain input data as intervals and establish a model of the reactive power optimization that incorporates the interval uncertainties to describe the problem. The linear approximation method is formulated using the interval Taylor extension to help solve this type of problem. To obtain more accurate intervals for the state variables, the affine arithmetic-based power flow calculation is used to solve the interval power flow equation instead of crude computation based on the interval arithmetic, and thus the modified linear approximation method is developed. The proposed methods are presented in detail and the numerical results are analyzed to demonstrate their effectiveness and applicability, especially in comparison to the previously proposed chance constrained programming method.

DC power flow analysis is based on a linear approximation model for AC power flow equations, and represents an efficient approach for acquiring the bus angles and active transmission power of a power grid. However, the input data and network parameters of the power grid are uncertain due to numerous internal and external factors. Therefore, the DC power flow model should be considered as an uncertain problem, which makes deterministic DC power flow analysis methods unworkable. The present work overcomes this problem by regarding uncertain input data and network parameters as interval values, respectively, and establishes the interval DC power flow (IDCPF) models considering interval input data only (denoted as IDCPF01), and IDCPF model including both interval input data and network parameters (denoted as IDCPF02). Analyses based on the IDCPF models seek to obtain conservative ranges of bus angles and active transmission power flow, which can be employed by dispatchers to develop strategies for ensuring the operational security of the power system. The optimizing-scenarios method (OSM) is employed here to solve the IDCPF models. In addition, it is proven that the lower (or upper) bounds of the bus angles of the IDCPF01 model are simultaneously obtained when the injected power is set as its lower (or upper) interval bounds. This fact greatly improves the efficiency of the OSM for solving the IDCPF models. The results obtained by the proposed method are compared with those obtained by Monte Carlo simulation, the AA-based method, and the interval AC power flow method. The overall simulation results demonstrate the effectiveness and robustness of the proposed method.

The reactive power optimisation (RPO) is generally used to design an optimal profile of the voltage and reactive power of power systems in the steady state for deterministic sets of demand loads and generation values, and it is a significant procedure in voltage control. However, the input data of a power system is actually uncertain in practise, which makes RPO an uncertain non-linear programme. To address this problem, the input data were considered as intervals, and the RPO incorporating interval uncertainties model was proposed. To solve this model, the genetic algorithm was employed as the solution algorithm, where the reliable power flow calculation was used to judge the constraints of the model. The Pareto front was established as the solution of the proposed model since it has two objective functions, i.e. the midpoint and radius of real power losses. The application of this technique to the uncertain RPO was explained in detail. Two numerical results were analysed to demonstrate the effectiveness of the proposed method, especially in comparison with the previously proposed chance-constrained programming method.

A rectangular interval power flow (RIPF) method is proposed to evaluate solutions' intervals of power flow including uncertain loads and output of generators. It is based on affine arithmetic which is a more accurate method to compute intervals, and it obtains intervals through optimization methods to enhance efficiency of interval calculation. Because no approximation is used, RIPF can acquire narrower intervals of voltage phase results than polar interval power flow (PIPF), which is an excellent method raised before. However, RIPF is no better than PIPF in estimating intervals of voltage amplitude, since it could not satisfy the voltage equations of interval power flow. Therefore, a mixed interval power flow (MIPF) is established to incorporate merits of RIPF in computing intervals of voltage phase and PIPF's advantages in evaluating intervals of voltage magnitude. The IEEE118 system is analyzed to conclude that MIPF can acquire more accurate power flow intervals than PIPF.

Under the opening environment of the electricity market, it's very important to study bidding strategy to balance the benefit between suppliers and their retailers. At present, machine game is the most popular approach to deal with this problem. However, it's unable to present the practical trade process, for it ignores the humanity of the traders. To overcome this problem, behavior game is used to reflect and trade off the benefit between suppliers and retailers, and experimental economics platform z-Tree is employed to realize this procedure. In this paper, the algorithm based on historical trading data is designed by using z-Tree and simulate the bidding strategies of suppliers and their retailers in different rebate factor. Aforementioned research result shows simulation in z-Tree can reflect the actual electricity market situation and get optimal bidding spread in different rebate factor. It has some significance for suppliers and their retailers for bidding strategies.

With the widely use of wide area measurement system (WAMS), data measured by PMU is becoming more and more important for real-time operation in power system. At present, error warnings and neglect of real alarms problems are produced in WAMS when considering the injection of wrong data. However, state estimation performs poorly in dealing with the wrong data in WAMS causing tremendous computation resources and time. In this paper, a rapid identification and recovery method based on the concept of pattern recognition is put forward. Without repeated iterations and the injection of parameters of power grid, all the wrong data can be easily and quickly identified by changing from feature space to pattern space. To support our conclusion, 90 samples in practical application of WAMS are processed, demonstrating the effectiveness of the proposed method.