Cascading Failure Analysis With DC Power Flow Model and Transient Stability Analysis

Probabilistic Reliability Management Approach and Criteria for power system real-time operation

“…In the second step of our solution approach, and particularly the computation of the residual risk for the evaluation of (8), we have implemented the cascading failure simulator presented in [14], which is a modified version of the model originally introduced in [15]. Referring the interested reader to [14], [15] for a detailed presentation of this simulation model, we should briefly introduce that this DC power flow based algorithm starts from any triggering event and involves the sequential simulation of relay-based trippings of overloaded branches, generator trippings and load shedding events, while taking into account the accumulated overloading of any branch over time to define the temporal characteristics of the cascade evolution process.…”

“…Referring the interested reader to [14], [15] for a detailed presentation of this simulation model, we should briefly introduce that this DC power flow based algorithm starts from any triggering event and involves the sequential simulation of relay-based trippings of overloaded branches, generator trippings and load shedding events, while taking into account the accumulated overloading of any branch over time to define the temporal characteristics of the cascade evolution process.…”

Analysis and Modeling of Advanced Power Control and Protection Requirements for Integrating Renewable Energy Sources in Smart Grid,

“…In order to solve the two players' optimal strategies of a stochastic game in the normal form Π, one popular solution is that of a Nash equilibrium in mixed strategies [181], in which it is a state of the game such that no player can increase its reward by unilaterally deviating from this equilibrium state. For mixed strategies, the strategies for generating severe multi-failure events and corresponding response mechanisms are defined as probability distributions over their space F and D, respectively.…”

“…Using the minimax Q-learning algorithm presented in [181], the operator's Nash equilibrium strategies can be derived recursively through the following dynamic programming approach. At time step t, the optimal discounted sum of expected rewards Q * , for a given state s and a pair action (f, d), can be devised iteratively by the following recursions…”

Analysis and Modeling of Advanced Power Control and Protection Requirements for Integrating Renewable Energy Sources in Smart Grid,

“…Although the existence of the Nash equilibrium for static games is guaranteed by the Nash's theorem [181], in the case of stochastic games, the possible number of strategies is infinite and is known only in very special cases of stochastic games. However, in this game, we limit our study to stationary optimal strategies by solving the mixed strategies for both sides of the game in each state, instead of each time step, where…”