Abstract
The frequency security problem becomes a critical concern in power systems when the system inertia is lowered due to the high penetration of renewable energy sources (RESs). A wind-storage system (WSS) controlled by power electronics can provide the virtual inertia to guarantee the fast frequency response after a disturbance. However, the provision of virtual inertia might be affected by the variability of wind power generation. To address this concern, we propose a two-stage chance-constrained stochastic optimization (TSCCSO) model to find the optimal thermal unit commitment (i.e., economic operation) and the optimal placement of virtual inertia (i.e., frequency stability) in a power grid using representative power system operation scenarios. An enhanced bilinear Benders decomposition method is employed with strong valid cuts to effectively solve the proposed optimization model. Numerical results on a practical power system show the effectiveness of the proposed model and solution method.

Abstract
This article presents a contingency-based stochastic security-constrained unit commitment to address the integration of wind power producers to the joint energy and reserve markets. The model considers ancillary services as a solution to cope with the uncertainties of the problem. In this regard, a comprehensive model is considered that maintains the profit of supplementary services. The contingency ranking is a popular method for reducing the computation burden of the unit commitment problem, but performing the contingency analysis changes the high-impact events in previous ranking methods. This article employs an intelligent contingency ranking technique to address the above issue and to find the actual top-ranked outages based on the final solution. The proposed algorithm simultaneously clears the energy and reserve based on the mechanism of the day-ahead market. The main idea of this article is to develop a framework for considering the most effective outages in the presence of the uncertainty of wind power without a heavy computation burden. Also, energy storage systems are considered to evaluate the impact of the scheduling of storage under uncertainties. Also, an accelerated Benders decomposition technique is applied to solve the problem. Numerical results on a six-bus and the IEEE 118-bus test systems show the effectiveness of the proposed approach. Furthermore, it shows that utilizing both wind farms and storage devices will reduce the total operational cost of the system, while the intelligent contingency ranking analysis and enough reserves ensure the security of power supply.

Abstract
This paper presents an effective hybrid supercapacitor-battery energy storage system (SC-BESS) for the active power management in a wind-diesel system using a fuzzy type distributed control system (DCS) to optimally regulate the system transient. It addresses a new online intelligent approach by using a combination of the fuzzy logic and DCS based on the particle swarm optimization techniques for optimal tuning and reduce the design effort of the control system. This mechanism combines the features of online fuzzy theory and distributed control system (DOFCS), which has a flexible structure. The proposed energy management algorithm for the hybrid SCBESS is well able to repel the peak-impact of the battery storage system during the wind speed and load changes. The high performance of the suggested methodology is represented on a typical wind-diesel test system.

Abstract
The coordination between distribution system and transmission system operation in the presence of distributed energy resources (DERs) is a new framework that needs appropriate modeling. Moreover, local energy market models are emerging, and there is the need to describe the decision-making occurring in active distribution systems including the distribution company (Disco) and the DER aggregators. This paper investigates the coordination between transmission, distribution, and DER aggregators that interact in a local market model. The individual objectives of the decision-makers are conflicting with each other. For this purpose, a bi-level optimization approach is proposed, in which the operation problem of the Disco and the day-ahead market clearing managed by the wholesale market operator are considered as the upper- and lower-levels problems, respectively. Moreover, to model the uncertainties of output power of renewable energy sources in the Disco's problem, the information gap decision theory is used. The resulting model is a non-linear bi-level problem, which is transformed into a linear single-level one through the exploitation of the Karush-Kuhn-Tucker conditions and the duality theory. To investigate the effectiveness of the model, two case studies are defined in which the IEEE 33-bus and a real 43-bus distribution systems are connected to the RTS 24-bus power system.

Abstract
With the mushrooming of distributed renewable generation, energy storage unit (ESU) is becoming increasingly important in residential energy systems. This letter proposes a fractional programming model to determine the optimal power, and energy capacities of residential ESUs. The objective function maximizes the ratio between the reduced electricity tariff, and the investment cost of ESU, ensuring the minimal payback time. A decomposition algorithm is developed to solve the fractional program based on convex optimization; the subproblem is a dual convex quadratic program which provides cutting planes, and the master problem comes down to a linear program after variable transformations. Compared to the widely used cost-minimum method, the proposed model is cost-efficient: it enjoys a higher rate of return which is usually welcomed by small consumers.

Abstract
This paper presents an optimal framework for the resilience-oriented design (ROD) in distribution networks to protect these grids against extreme weather events such as earthquakes and floods. This strategy minimizes the summation of daily investment and repair costs of back up distributed generation (DG), hardening and tie lines, operation cost of network and DGs, and load shedding cost. Also, it considers AC power flow equations, system operation limits and planning and reconfiguration constraints. This problem is generally a mixed integer nonlinear programming (MINLP) problem, but it is converted to a mixed integer linear programming (MILP) problem to achieve a globally optimal solution with a low computation time. Moreover, the Benders decomposition (BD) approach is used for the proposed problem to obtain higher computation speed in large scale networks. In addition, this problem includes uncertain parameters such as load, energy price, and availability of network equipment in the case of extreme weather conditions. Hence, a scenario-based stochastic programming (SBSP) approach is used to model these uncertain parameters in the proposed ROD method, based on a hybrid approach, including roulette wheel mechanism (RWM) and the simultaneous backward method. The proposed problem is simulated on 33-bus and large-scale 119-bus distribution networks to prove its capabilities in different case studies.