**Cascading Failures**

**Introduction**

The complex structure and wide interconnections of power grids make them vulnerable to disturbances such as faults, loss of transmission lines (TLs), etc. This complexity makes the control strategies more sophisticated and costly in order to maintain the stability and reliability of power grids during contingencies. For instance, the 2003 North American blackout initiated by a fault in a transmission line and the lack of rapid and appropriate actions from the grid components imposed extravagant cost of maintenance and restoration on the government and the electric power industry. Due to all technical and financial issues such as instability, unreliability, maintenance and restoration costs caused by outages, several research efforts have been done recently to mitigate this catastrophic phenomenon. Many different approaches and methods have been recently proposed and developed for analysing, modelling, and controlling cascading failures based on deterministic or probabilistic dynamic mathematical models and simulations . Authors introduced SASE model based on reduced dynamic model of an extensive power system by considering limited state variables that depict crucial characteristics of the grid. The system is modelled using Markov chain in continuous time structure. This stochastic model predicts the growth of blackout possibility. The drawback of this model is that all the state variables are not considered for modelling of the system dynamics. An assessment method was suggested in to investigate the effects of N-1 criterion policies on the uncertainty of consecutive line outages by considering aspects of both long term transmission line expansion planning and cascading issues. In another work, CASCADE probabilistic model was presented based on load dependency . In this model, all components in a system are assumed identical and failure of each component has equal effect on the other components. Branching Process is another probabilistic model for cascading failures analysis . This model demonstrates the probability distribution for all component failures. In addition to probabilistic models, several research works have been proposed based on deterministic modelling. For instance, proposed cascading failure model based on complex network structure. The authors focused more on communication network failures and congestions in power grids. DeMarco in utilized a deterministic hybrid model based on Lyapunov method. This model is a nonlinear system-based model that investigates the dynamics of cascading failures which occur because of transient circumstances in power grids. The main problem with this method is that it is not expandable to a large scale power grid. In addition to the above mentioned methods in modelling of cascading failure characteristics for utilizing predictable control methods, some of the recent research works have been presented based on load shedding strategies for cascading failure prevention . The main challenge associated with the load shedding method is that many utility customers will be deprived of power which makes the various stakeholders in the power industry incur losses. On the other hand, some emerging algorithms in Artificial Intelligence (AI) and machine learning such as the multi-agent systems have been widely utilized recently to enhance the power system stability, reliability, and performance . The main characteristics of intelligent systems are controllability, adaptability, simplicity, and fast response even for complicated structures. Among the machine learning methods, the reinforcement learning (RL) approach is a powerful method that has various applications in power system control . Literature reviews demonstrate that using AI methods for managing cascading failure and blackout is a very novel topic and is in its early steps of development and there are very few research works in this area of study . the authors used neural network concept for early detection and warning system and authors in used support vector machine (SVM) and communication structure between relays to mitigate occurrence of blackouts. This method mainly reduces the probability of blackouts for only few locations with high risk of incorrect tripping. Besides load shedding, most of the research works are focused either on modelling or early detection of cascading failures and blackouts. In this work, we are proposing to halt the cascading event after it is initiated and when there is a little or no option for the operator to take besides cutting customers off the grid. The idea is to intelligently adjust the generating units relative to each other instead of a pre-planned load shedding scheme.

**Literature Review and Background**

The following section presents the current research advances and summarizes the gap and limitations in all the areas involved in the proposed dissertation. This includes deterministic approaches, probabilistic (stochastic) methods, intelligent early warning systems and monitoring, and load shedding strategies for modeling, risk analysis and prevention of cascading failures and blackouts in power systems.

**Probabilistic (Stochastic) Methods for Modeling and Analysis of Cascading ****Failures**

a scalable and analytically tractable probabilistic model for the cascading failure dynamics in power grids was proposed considering operating characteristics of the power grid. Authors introduced SASE model based on reduced dynamic model of an extensive power system by a continuous-time Markov chain and considering limited state variables that depict crucial characteristics of the grid comprising loading level, error in transmission-capacity estimation, and constraints in performing load shedding. This stochastic model predicts the growth of blackout possibility in time. The drawback of this model is that all the state variables are not considered for modelling of the system dynamics. An assessment method was suggested to investigate the effects of N-1 criterion policies on the uncertainty of consecutive line outages by considering aspects of both long term transmission line expansion planning and cascading issues. The long-term effects of these policies on the probability distribution of outage size and the grid utilization were computed in a large-scale system. introduced an interaction model for cascading failures. This probabilistic model identifies the critical components of the system that propagate cascading failures and an interaction matrix is acquired based on component failures interactions. The model investigates the risk of cascading failures and provides online decision-making. In the OPA model , the cascading failure was approximated by considering the dynamics of demands and DC load flow. Linear programming was utilized to re-dispatch the generation and loads after a random line outage. The drawback of the OPA model is that the timing of failures is ignored which cannot be suitable for the protective coordination. The CASCADE model was based on load dependency. In this model, all elements of power system are considered to be identical and failure of each element has equal impact on the other elements. The CASCADE model does not include all electrical features of the grid and time sequence of the event is not considered and the model is not robust enough for protective coordination. Branching Process is another probabilistic model for analyzing cascading failures. This model relies on the probability distribution for investigating the total component failures. This model does not provide complete dynamic independent variables to include all dynamic features associated with cascading failures and blackouts in power systems. a new numerical metric defined as the critical moment (CM) is compared with the validity of a typical DC power flow-based cascading failure simulator (CFS) in cascading failure analysis. The main issue with this work is that due to the complex nature of the power system and cascading failures, the underlying assumptions in DC power flowbased cascading failure simulators (CFS) may fail to hold during the development of cascading failures.

**Deterministic Methods for Modeling and Analysis of Cascading Failures**

In addition to probabilistic methods mentioned in previous section, several researches have been done based on deterministic-based approaches to analyse and investigate cascading failures. it is shown that how the breakdown of a single node is sufficient to collapse the entire system simply because of the dynamics of redistribution of flows on the network. In this work, cascading failure is modelled based on complex network structure and graph theory. The authors focused more on communication network failures and congestions in power grids. the role of transient dynamic response following a specified initiating disturbance is captured and subsequent (“cascading”) element failures are examined that are induced when operating thresholds for individual elements are exceeded along the state trajectory. Author in this work utilized a deterministic hybrid model based on Lyapunov method. This model is a nonlinear system-based model that investigates the dynamics of cascading failures which occur because of transient circumstances in power grids. The main problem with this method is that it is not expandable to a large scale power grid. line outages in the transmission network of the power grid are considered, specifically those caused by natural disasters or large-scale physical attacks. In this work,authors show how to identify the most vulnerable locations in the network by performing extensive numerical experiments with real grid data to estimate the effects of geographically correlated outages. In this model, a circular and deterministic failure model of cascading outage is considered, where all lines and nodes within a radius r of the failure’s epicenter are removed.

**Power System Simulation-based methods for preventing Cascading Failures**

Another research direction for modeling and analysis of cascading failures and blackouts is based on power system simulation studies. Besides of mathematical deterministic or probabilistic models stated in previous sections, this part is dedicated to power system simulation-based strategies. Many methods and paradigms have been developed using power system simulations for investigating the behavior of the cascading failures for early warning detection systems and development and preventing cascading failure propagation. a simulation of an upgrading power transmission system is utilized to investigate how the complexity of system dynamics impact the assessment and mitigation of blackout risk by estimating the frequency and cost of blackout. This approach uses the NERC data to estimate blackout risk and cost base on unserved energy and the number of customers disconnected and blackout duration. This complex system approach to risk analysis, analyzes the long-term, steady state risk of failure in a system that is dynamically evolving as the system is upgrading in response to increasing demand a method based on composite power system reliability evaluation through sequential Monte Carlo simulation is proposed since cascading failures involve sequences of dependent outages. Then, importance sampling (IS) and importance sampling and antithetic variates (IS-AV) techniques using the Weibull distribution are utilized and applied to power generator outages to overcome large computational burden involved by the simulations., an optimal plan for expanding the capacity of a power grid is determined in order to minimize the likelihood of a large cascading blackout. Capacity-expansion decisions considered in this work considering the addition of new transmission lines and the addition of capacity to existing lines. An Optimization model is used to minimize the probability of a large blackout subject to a budget constraint using Monte Carlo simulation. Moreover, variance-reduction technique is used to provide results in a reasonable time frame. a novel method is proposed for N-k induced cascading contingency screening based on random vector functional- link (RVFL) neural network and quantum inspired multi-objective evolutionary algorithm (QMEA). This method can conduct reliable and simultaneous screening for various N-k contingencies and early warning monitoring and detection based on intelligent algorithms. a multi agent system (MAS) based wide area protection and control scheme is proposed to deal with the long term voltage instability induced cascading trips. Based on sensitivity analysis between the relay operation margin and power system state variables, an optimal emergency control strategy is defined to adjust the emergency states timely and prevent the unexpected relay trips and cascading outages. In order to supervise the control process and minimize the load loss, an agent based process control is adopted to monitor the states of distributed controllers and adjust the emergency control strategy. three load shedding strategies are proposed and investigated to prevent cascading failures in power grid. The first strategy is a base line case called the homogeneous load shedding strategy. It reduces load homogeneously in all the buses of the system. This strategy is extremely simple and fast. Second strategy is to accurately find the location and amount of load shedding by a linear optimization formulation which is much more efficient in overall load shedding in the system. Third, a novel tree heuristic is proposed to overcome the drawbacks of the optimization, namely fairness and scalability.The tree heuristic is linear and very simple to implement. The results of the tree strategy are compared with that of another existing heuristic and it is found that the tree performs equal to or better than the existing heuristic for all cases. a distributed multi-agent-based load shedding algorithm is proposed, which can make efficient load shedding decision based on discovered global information to prevent cascading outages. To improve the speed of the algorithm, particle swarm optimization (PSO) is used. The information discovery algorithm is represented as a discrete time linear system and the stability of which is analyzed according to averageconsensus theorem.support vector machine (SVM) and communication structure between relays and the supervisory control and data acquisition (SCADA) are utilized to mitigate occurrence of blackouts. This method mainly reduces the probability of blackouts for only few locations with high risk of incorrect tripping. Based on the research gaps identified in the literature, three different intelligent and machine learning-based approaches are proposed in this research work to manage congestion in transmission lines and prevent cascading failure and blackout at early stages of their occurrence after unplanned critical N-1 and N-1-1 contingencies in the system. The three different and distinct intelligent frameworks are:

** Multi-Agent Systems (MAS) Approach**

** Supervised learning Approach based on Artificial Neural Network (ANN)**

** Reinforcement learning Approach**

These proposed methods will provide a learning platform for the power system on how to manage the congestion by intelligent re-dispatch of power through frequency control of the generators. These methods will satisfy the constraints of voltage, frequency, and power flow during the cascading failure events. Another gap mentioned in the literature was the lack of practical and experimental implementation of the proposed mathematical algorithms. In order to fill the research gap in terms of experimental implementation, a real-time and experimental testbed is designed and developed in the smart grid laboratory based on two-way communication infrastructure including hardware setup, software setups, SCADA and monitoring, and real-time interface. The experimental implementation of the proposed intelligent methods is investigated in real-time. The developed experimental power testbed emulates the real behavior of the power system in a complete dynamic and interactive manner.In addition to the experimental implementation, the developed algorithms are implemented offline on a large-scale power systems through computer simulation in MATLAB/Simulink environment. The main purpose is to evaluate the performance of the proposed methods in terms of robustness, effectiveness, and functionality in a large-scale power testbed. Therefore, the proposed approaches are implemented on the IEEE 118-bus standard test system for multiple critical contingency conditions