With the expansion of power grids and the growth of renewable energy generation, more uncertainties of topology (e.g. components outages) and injection (e.g. renewable energy outputs variations) need to be analyzed. As a result, large numbers of system states have to be evaluated by optimal power flow (OPF) and this brings a significant challenge to the efficiency of reliability assessment. To address this, a Lagrange-multiplier-based reliability assessment method (LM-T&I) is proposed to accelerate the evaluation of system states. The Lagrange-multiplier-based function is constructed to obtain the optimal load shedding of topology changes and injection variations, avoiding time-consuming OPF computations. Moreover, combined with the impact-increment-based state enumeration method (IISE), the computational efficiency can be further improved. Case studies are conducted on the RTS-79 and IEEE 118-bus systems. The scalability of the LM-T&I method is verified on the practical Brazilian system. The results demonstrate that the LM-T&I method has a superior performance on the reliability assessment compared with traditional methods.

With the integration of multiple types of loads and renewable generations, the number of system states significantly grows. As a result, running optimal power flow (OPF) to analyze a myriad of system states is challenging and this seriously restricts the efficiency of the state enumeration method. To address that, this paper proposes a Lagrange Multiplier based State Enumeration (LMSE) approach to accelerate the analysis without loss of accuracy. The core idea is to directly obtain the optimal load shedding of contingency states by Lagrange multiplier-based functions, rather than the time-consuming OPF algorithms. This approach can also be conveniently integrated with the impact-increment method and the clustering technique for further efficiency enhancement. Case studies are performed on the RTS-79 and IEEE 118-bus systems considering multiple types of loads, photovoltaics (PVs), and wind turbines (WTs). Results indicate that the proposed method can significantly reduce the computing time without compromising the calculation accuracy.

With the ever-increasing penetration of renewable resources, more complexities and uncertainties are introduced in power system reliability assessment. This entails an enormous number of contingency states to represent the characteristics of renewable energy. As a result, the unbearable computation burden is the main challenge toward the efficiency of the state enumeration (SE) method. To address that, this paper proposes an improved reliability evaluation approach that can not only increase the accuracy but also accelerate the analysis. In detail, the impact increment method is first employed to decrease the proportion of higher-order contingency states, leading to accuracy improvement. Then, the shadow price is used to solve the optimal power flow (OPF) problem in a faster manner. This shadow price (SP) method allows us to obtain the optimal load curtailment directly from linear functions rather than the time-consuming OPF algorithms. In addition, one hundred percent criterion is used to match shadow-price-based linear functions with system states. Case studies are performed on the RTS-79 system and IEEE 118-bus system, in which test scenarios include loads, photovoltaics (PV), and wind turbines (WT). Results indicate that the proposed method can significantly ease the computation burden and outperform traditional reliability assessment methods in terms of both computing time and accuracy.

The increasing penetration of intermittent renewable generators and the uncertainty of loads have brought significant challenges to the power system reliability assessment, as large numbers of optimal power flow (OPF) tasks need to be repetitively solved considering these uncertainties. To deal with that, this paper proposes a state-similarity-based (SS) approach to replace the computationally demanding AC OPF. It is observed that the active constraints related to the least load curtailment typically remain consistent across varying system states. Following this, the active constraints are used to represent the state similarity, and then nonlinear equations are derived to replace the original AC OPF problems. Thereafter, an alternating iterative approach is developed to obtain the minimal load curtailment instead of calculating the time-consuming optimization. An optimality criterion is developed to exclude the majority of mismatched solutions, thereby minimizing potential inaccuracies in the reliability assessment. Case studies conducted on the RTS-79, IEEE 118-bus, and Brazilian systems demonstrate that the proposed methods can significantly enhance computational efficiency with minimal errors. In some instances, these methods can outperform traditional reliability assessment methods by over 10 times.