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A tie-line security region provides all possible tie-line power injections with which constraints in a regional network will not be violated. With the high penetration of renewables, a sharp increase or decrease of renewable power requires a good depiction of the tie-line security region considering time coupling. However, the tie-line power security region with time coupling is a high-dimension polytope, which leads to a considerable computational burden. This paper presents a fast algorithm to approximate the original high-dimension tie-line security region considering time coupling. A few lower-dimension polytopes associated with combinations of different periods are calculated for the approximation. An evaluation method with clear physical explanations is established to measure the accuracy of the approximation. The method converts the evaluation to two linear programming problems based on the mathematical relationship between optimal points and polytope vertices. Under a Monte Carlo framework, the statistical analysis is employed to measure the accuracy using five presented indices. The performance of the proposed methods is verified by the case studies on the IEEE 118-bus test system and a 661-bus utility system. [ABSTRACT FROM AUTHOR]

Linear power flow models are widely used in power system analysis because it brings huge computational benefits, especially for power system optimization problems. The improvement of the linearization accuracy is greatly beneficial to the power system operation considering the large amount of power scheduled based on linear power flow models. We find that the linearization error substantially changes with different selections of the variable space. In this paper, we formulate a model to find the linear power flow model with the minimized linearization error based on the optimal selection of the variable space. The expression of the variable space is generalized as a polynomial function. A simplified model of power losses is proposed. The difference between the selection of the variable space and the common hot-start approaches is illustrated. The effectiveness of the proposed linear power flow model is verified by power flow calculation and optimal power flow (OPF) calculation in the IEEE and Polish test systems. [ABSTRACT FROM AUTHOR]

Contingency screening is vital for maintaining the transmission system reliability. Bilevel programming is a powerful tool for the accurate identification of critical events. To accelerate the contingency screening with bilevel programming, this study proposes a root-event-based dynamic space pruning algorithm. A root event is an event in which all the failed components have contributions to the event impact. Considering the fact that numerous N − k events describe the same critical scenario, the proposed space pruning principles partition the N − k event space into the subspace of root events and the complement subspace. To accelerate the screening of subspace of root events, bilevel programming is constructed to identify new critical events having high risk and causing more severe load shedding than the root event. Besides, relaxed bilevel programming is proposed to accelerate the screening of the complement subspace. The relaxed scheme replaces the constraints of power flow by constraints of transmission capacity, and enables the identification of most of the critical events in the complement subspace with a low computational cost. Case studies on the IEEE RTS and a provincial grid in China indicate that the proposed algorithm significantly accelerates the screening process without missing critical events. [ABSTRACT FROM AUTHOR]

Reliability evaluation of bulk power systems (BPSs) has inherent computational complexity due to the numerous system states and the time‐consuming system state analysis, including power flow calculation, load curtailment, recognition of split power systems and network reconfiguration. In this study, a novel uniform‐design based method is proposed to improve the computational efficiency of power system reliability evaluation. The main idea is that the uniform‐design technique is used to generate the system states in reliability evaluation, which makes the sampled states more uniform and representative in the overall state space compared to the enumerated system states in an analytical method or the random‐generated system states in Monte Carlo simulation. As a result, the sample size and the computational time can be significantly reduced. In addition, the confidence intervals of the reliability indices, such as LOLP, FLOL and EENS, are given. And the estimation errors of reliability indices are discussed. The proposed method is tested on several BPSs, including the IEEE‐RTS79, IEEE‐RTS96 and a real BPS in China. All the case studies indicate that the proposed technique can significantly improve the computational efficiency of BPS reliability evaluation. [ABSTRACT FROM AUTHOR]

Linear power flow models are widely used in power systems to simplify the nonlinear power flow equations. The DC power flow model is one of the representatives. There are many other linear power flow models that improve the DC power flow model with the inclusion of $\boldsymbol{Q}$ and $\boldsymbol{v}$. However, existing linear models are derived based on empirical mathematical approximation without a general methodology guidance. In this paper, we found that the fundamental difference among different linear power flow models lies in the formulation of “independent variables.” Based on this finding, a general formulation of linear power flow models is proposed. The linearization error is theoretically analyzed. In particular, the case when $\boldsymbol{ \theta }$ and $\boldsymbol{v^{\scriptscriptstyle k}}$ are regarded as independent variables is thoroughly investigated. Method for finding the linear power flow with the minimum error is presented. The formulation of the independent variables associated with the minimum linearization error is determined by the distribution of state variables $\boldsymbol{v}$ and $\boldsymbol{\theta }$. It is shown that the linearization error when $\boldsymbol{v^{\scriptscriptstyle 2}}$ is regarded as an independent variable is normally smaller than that for $\boldsymbol{v}$ because of the special properties of the distribution of $\boldsymbol{v}$ in power grids. [ABSTRACT FROM AUTHOR]