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Transmission networks and generating units must be reinforced to satisfy the ever-increasing demand for electricity and to keep power system reliability within an acceptable level. According to the standards, the planned power system must be able to supply demand in the case of outage of a single element (N − 1 security criteria), and the possibility of cascading failures must be minimized. In this paper, we propose a risk-based dynamic generation and transmission expansion planning model with respect to the propagating effect of each contingency on the power system. Using the concept of risk, post-contingency load-shedding penalty costs are obtained and added in the objective function to penalize high-risk contingencies more dominantly. The McCormick relaxation is tailored to alter the objective function into a linear format. To keep the practicality of the proposed model, a second-order cone programming model is applied for power flow representation, and the problem is modeled in a dynamic time frame. The proposed model is formulated as a mixed-integer second-order cone programming problem. The numerical studies on the RTS 24-bus test system illustrate the efficacy of the proposed model. 

Distributed optimization algorithms are proposed to, potentially, reduce the computational time of large-scale optimization problems, such as security-constrained economic dispatch (SCED). While various geographical decomposition strategies have been presented in the literature, we proposed a temporal decomposition strategy to divide the SCED problem over the considered scheduling horizon. The proposed algorithm breaks SCED over the scheduling time and takes advantage of parallel computing using multi-core machines. In this paper, we investigate how to partition the overall time horizon. We study the effect of the number of partitions (i.e., SCED subproblems) on the overall performance of the distributed coordination algorithm and the effect of partitioning time interval on the optimal solution. In addition, the impact of system loading condition and ramp limits of the generating units on the number of iterations and solution time are analyzed. The results show that by increasing the number of subproblems, the computational burden of each subproblem is reduced, but more shared variables and constraints need to be modeled between the subproblems. This can result in increasing the total number of iterations and consequently the solution time. Moreover, since the load behavior affects the active ramping between the subproblems, the breaking hour determines the difference between shared variables. Hence, the optimal number of subproblems is problem dependent. A 3-bus and the IEEE 118-bus system are selected to analyze the effect of the number of partitions. 

Distributed optimization is becoming popular to solve a large power system problem with the objective of reducing computational complexity. To this end, the convergence performance of distributed optimization plays an important role to solve an optimal power flow (OPF) problem. One of the critical factors that have a significant impact on the convergence performance is the reference bus location. Since selecting the reference bus location does not affect the result of centralized DC OPF, we can change the location of the reference bus to get more accurate results in distributed optimization. In this paper, our goal is to provide some insights into how to select reference bus location to have a better convergence performance. We modeled the power grid as a graph and based on some graph theory concepts, for each bus in the grid a score is assigned, and then we cluster buses to find out which buses are more suitable to be considered as the reference bus. We implement the analytical target cascading (ATC) on the IEEE 48-bus system to solve a DC OPF problem. The results show that by selecting a proper reference bus, we obtained more accurate results with an excellent convergence rate while improper selection may take much more iterations to converge.