Abstract
Accurate and practical load modeling plays a critical role in the power system studies including stability, control, and protection. Recently, wide-area measurement systems (WAMSs) are utilized to model the static and dynamic behavior of the load consumption pattern in real-time, simultaneously. In this article, a WAMS-based load modeling method is established based on a multi-residual deep learning structure. To do so, a comprehensive and efficient load model founded on combination of impedance-current-power and induction motor (IM) is constructed at the first step. Then, a deep learning-based framework is developed to understand the time-varying and complex behavior of the composite load model (CLM). To do so, a residual convolutional neural network (ResCNN) is developed to capture the spatial features of the load at different location of the large-scale power system. Then, gated recurrent unit (GRU) is used to fully understand the temporal features from highly variant time-domain signals. It is essential to provide a balance between fast and slow variant parameters. Thus, the designed structure is implemented in a parallel manner to fulfill the balance and moreover, weighted fusion method is used to estimate the parameters, as well. Consequently, an error-based loss function is reformulated to improve the training process as well as robustness in the noisy conditions. The numerical experiments on IEEE 68-bus and Iranian 95-bus systems verify the effectiveness and robustness of the proposed load modeling approach. Furthermore, a comparative study with some relevant methods demonstrates the superiority of the proposed structure. The obtained results in the worst-case scenario show error lower than 0.055% considering noisy condition and at least 50% improvement comparing the several state-of-art methods.

Abstract
Increasing the penetration of renewable resources has aggravated the operational flexibility at distribution level. In this study, a flexibility-oriented scheduling of microgrids (MGs) is suggested to reduce the power fluctuations in distribution feeders caused by the high penetration of wind turbines (WTs) in MGs. A flexibility constraint as viable and practical solution is used in MG scheduling to address this challenge. The presented scheduling model, implemented using mixed integer linear programming (MILP) and a stochastic framework, exercises risk constraints to capture the uncertainties associated with wind turbines, loads and market prices. The effectiveness of the model is investigated on a MG with high penetration of WTs in the presence of demand response (DR) and energy storage systems (ESSs). Numerical studies show the influence of risk parameters' changing on operation costs. In addition, the flexibility constraint mitigates the sharp variation of the net load at distribution level, which improves the flexibility of the distribution system.

Abstract
The use of data from residential smart meters can help in the management and control of distribution grids. This provides significant benefits to electricity retailers as well as distribution system operators but raises important questions related to the privacy of consumers' information. In this article, an innovative differential privacy (DP) compliant algorithm is developed to ensure that the data from consumer's smart meters are protected. The effects of this novel algorithm on the operation of the distribution grid are thoroughly investigated not only from a consumer's electricity bill point of view but also from a power systems point of view. This method allows for an empirical investigation into the losses, power quality issues, and extra costs that such a privacy-preserving mechanism may introduce to the system. In addition, severalcost allocation mechanisms based on the cooperative game theory are used to ensure that the extra costs are divided among the participants in a fair, efficient, and equitable manner. Overall, the comprehensive results show that the approach provides privacy preservation in line with the consumer's preferences and does not lead to significant cost or loss increases for the energy retailer. In addition, the novel algorithm is computationally efficient and performs very well with a large number of consumers, thus demonstrating its scalability.

Abstract
This paper investigates a fully decentralized model for electricity trading within a transactive energy market. The proposed model presents a peer-to-peer (P2P) trading framework between the clients. The model is incorporated for industrial, commercial, and residential energy hubs to serve their associated demands in a least-cost paradigm. The alternating direction method of multipliers (ADMM) is implemented to address the decentralized power flow in this study. The optimal operation of the energy hubs is modeled as a standard mixed-integer linear programming (MILP) optimization problem. The corresponding decision variables of the energy hubs operation are transferred to the peer-to-peer (P2P) market, and ADMM is applied to ensure the minimum data exchange and address the data privacy issue. Two different scenarios have been studied in this paper to show the effectiveness of the electricity trading model between peers, called integrated and coordinated operation modes. In the integration mode, there is no P2P energy trading while in the coordinated framework, the P2P transactive energy market is taken into account. The proposed model is simulated on the modified IEEE 33-bus distribution network. The obtained results confirm that the coordinated model can efficiently handle the P2P transactive energy trading for different energy hubs, addressing the minimum data exchange issue, and achieving the least-cost operation of the energy hubs in the system. The obtained results show that the total operating cost of the hubs in the coordinated model is lower than that of the integrated model by $590.319, i.e. 11.75 % saving in the costs. In this regard, the contributions of the industrial, commercial, and residential hubs in the total cost using the integrated model are $3441.895, $596.600, and $988.789, respectively. On the other hand, these energy hubs contribute to the total operating cost in the coordinated model by $2932.645, $590.155, and $914.165 respectively. The highest decrease relates to the industrial hub by 14.8 % while the smallest decrease relates to the residential hub by 1 %. Furthermore, the load demand in the integrated and coordinated models is mitigated by 13 % and 17 %, respectively. These results indicate that the presented framework could effectively and significantly reduce the total load demand which in turn leads to reducing the total cost and power losses. (c) 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Abstract
This paper presents a quadratically constrained programming (QCP) model to tackle the optimal power flow (OPF) problem in distribution networks. The proposed model is fast, reliable, and precise enough to be embedded into the multi-emporal power system analysis. The proposed model benefits from a standard QCP to solve the branch active and reactive power flows. The second-order conic programming (SOCP) approach has been applied to address the quadratic constraints. The nonconvex feature of the OPF problem has been relaxed utilizing the McCormick envelopes. To find the minimum current of each branch, the lossless power flow model has been first solved and the obtained results have been considered for solving the OPF problem. The IEEE 33-bus test system has been selected as the benchmark to verify the efficient performance of the proposed OPF model. The simulation study confirms that the McCormick envelopes used in the QCP approach lead to precise results with a very fast convergence time. Overall, the presented model for the OPF can be extended for both planning and operation purposes in distribution system studies.

Abstract
This paper investigates the issue of frequency regulation of a single-area alternating current (AC) power system connected to an electric vehicle (EV) aggregator through a nonideal communication network. It is assumed that the command control action is received by the EV aggregator with constant delay and the power system experiences uncertain parameters. A novel effective iterative algorithm, direct search, is proposed for the time-delayed system to design the gains of a proportional-integral (PI) controller. The proposed direct search algorithm can find a feasible solution whenever at least one solution lays in the space search. Thus, by choosing a wide space search, we can expect that the PI controller assures the closed-loop stability, theoretically. The proposed approach has low conservative results over the existing approaches. For the uncertain time-delayed system, a robust PI controller is designed, which is resilient against the system uncertainties and time delay. Numerical simulations are carried out to show the merits of the developed controller.