Abstract
This paper investigates prosumers' flexibility provision for the optimal operation of active distribution networks in a transactive energy (TE) market. From a prosumer point of view, flexibility can be provided to operators using renewable energy resources (RES) and demand response (DR) through home appliances with the ability to modify their consumption profiles. In the TE market model, the distribution system operator (DSO) is responsible for market-clearing mechanisms and controlling the net power exchange between the distribution network and the upstream grid. The contribution of this work is the enhancement of a strategy to reduce operational costs of an active distribution network by using prosumers' flexibility provision through an aggregator or a smart building coordinator. To this end, a TE market for both energy and flexibility trading at distribution networks is presented, demonstrating the possibility to fulfill DSO requirements through the flexibility contributions in the day-ahead (DA) and real-time (RT) markets.

Abstract
Today's power grid is in a transitional stage to cater to the needs of energy efficiency, climate change, and environmental targets. In the process of designing the future power grid, one of the most fundamental models to be utilized is AC optimal power flow (AC-OPF). Since the feasible space of AC-OPF is non-convex, the optimization models developed using it often result in multiple local minima. To avoid such computational challenges in solving optimization models, various relaxation methods have been developed in the past. In the literature, these relaxation methods are mainly tested on specific networks. However, the scalability of relaxation techniques on branch-flow-based AC-OPF is yet to be explored. In this context, this paper compares the performance of different relaxation methods with the well-established MATPOWER AC-OPF solver in terms of the mean square error (MSE), maximum squared error, minimum and maximum values of voltage magnitude, and the average simulation time. In addition, the scalability of these models is tested on various radial and mesh networks with nodes ranging from 33 to 6655 nodes and 9 to 6515 nodes, respectively. In this manner, the trade-off between computational complexity and solution accuracy is demonstrated and analyzed in depth. This provides an enhanced understanding of the suitability and efficiency of the compared relaxation methods, helping, in turn, the efficiency of optimization models for varying sizes and types (i.e., radial or meshed) of networks.

Abstract
Nowadays, decentralized microgrids (DC-MGs) have become a popular topic due to the effectiveness and the less complexity. In fact, DC-MGs resist to share their internal information with the distribution system operator (DSO) to protect their privacy and compete in the electricity market. Further, lack of information sharing among MGs in normal operation conditions leads to form a competitive market. However, in emergency operation conditions, it results numerous challenges in managing network outages. Therefore, this paper presents a hierarchical model consisting of three stages to enhance the resilience of DC-MGs. In all stages, the network outage management is performed considering the reported data of MGs. In the first stage, proactive actions are performed with the aim of increasing the network readiness against the upcoming windstorm. In the second stage, generation scheduling, allocation of mobile units and distribution feeder reconfiguration (DFR) are operated by DSO to minimize operating costs. In the final stage, the repair crew is allocated to minimize the energy not served (ENS). Un-certainties of load demand, wind speed and solar radiation are considered, and the effectiveness of the proposed model is investigated by integrating to the 118-bus distribution network. Finally, the results of the simulation indicate that DFR and proactive actions decrease the ENS by 19,124 kWh and 4101 kWh, respectively. Further, the sharing of information among MGs leads to a 48.16% growth in the supply service level to critical loads, and consequently a 3.47% increase in the resilience index.

Abstract
This paper presents a mathematical problem formulation for energy management systems for smart homes. The flexibility can be provided by a home energy management system (HEMS) in a local energy community. The main concept is to model the flexibility provision and flexibility procurement within the energy community that can be provided to the aggregator from active consumers. The integrated energy management model is coded as a standard mixed-integer linear programming (MILP) model which can be solved by open-source tools like the PuLP package developed in Python. The simulation results confirm the performance of the proposed model in terms of flexibility provided by the centralized integrated energy system introduced in this paper.

Abstract
Determining the transformer top-oil temperature (TOT) is one of the key issues in determining the transformer insulation life and reliability of the power system. Due to the non-linear nature of the model presented in the IEEE C57.91 standard to determine this temperature, a more precise method is needed to estimate the equation coefficients to estimate the TOT in the future. This paper presents a method for online thermal modelling of the transformer according to the IEEE C57.91 based on the Unscented Kalman filter (UKF). This method can be applied to transformers with a variety of cooling modes and estimates the TOT with an acceptable error. In order to evaluate the proposed method, the practical data of the 800 kVA distribution transformer with unknown equation coefficients and simulated data with known coefficients are used, and finally, by calculating the estimation error, the proper performance of the presented method is proved. It is proved that the proposed method predicts TOT even in the presence of noise with an error of less than 0.5 degrees C and a delay of less than 1.5 h. It makes the proposed method can be implemented for purposes such as load management, and insulation life estimation of the transformer.

Abstract