Abstract
The close interaction between the electricity market and the end-users can assist the demand response (DR) aggregator in handling and managing various uncertain parameters simultaneously to reduce their effect on the aggregator's operation. As the DR aggregator's main responsibility is to aggregate the obtained DR from individual consumers and trade it into the wholesale market. Another responsibility of the aggregator is proposing the DR programs (DRPs) to the end-users. This article proposes a model to handle these uncertainties through the development of a novel hybrid stochastic-robust optimization approach that incorporates the uncertainties around wholesale market prices and the participation rate of consumers. The behavior of the consumers engaging in DRPs is addressed through stochastic programming. Additionally, the volatility of the electricity market prices is modeled through a robust optimization method. Two DRPs are considered in this model to include both time-based and incentive-based DRPs, i.e., time-of-use and incentive-based DR program to study three sectors of consumers, namely industrial, commercial, and residential consumers. An energy storage system is also assumed to be operated by the aggregator to maximize its profit. The proposed mixed-integer linear hybrid stochastic-robust model improves the evaluation of DR aggregator's scheduling for the probable worst-case scenario. Finally, to demonstrate the effectiveness of the proposed approach, the model is thoroughly simulated in a real case study.

Abstract
This paper proposes a two-objective linearized resilient architecture (LRA) model for distribution networks to achieve a strictly resilient network during natural disasters like earthquakes and floods. To obtain this goal, the proposed LRA framework is based on the planning of the energy storage system (ESS), hardening and tie lines, and backup distributed generation (DG). Therefore, the proposed model minimizes the sum of planning and expected operation costs in the first objective function, and the total load shedding and repair costs originates from earthquakes and floods in the second objective function. Also, it constraints to the network planning model, linearized equations of the system operation, and system reconfiguration formulation. Moreover, stochastic programming models the uncertain availability of the network equipment during the natural disaster condition, the load and electricity price. In the next step, the e-constraint-based Pareto optimization is used to achieve an equivalent single-objective LRA model and obtain the best compromise solution. Finally, the proposed strategy is applied to a standard test distribution network. Numerical simulation confirms the capability of the proposed method in obtaining a resilient distribution network during natural disasters.

Abstract
This article proposes a risk constrained decision-making problem for wind power producers (WPPs) in a competitive environment. In this problem, the WPP opts to maximize its likely profit whereas aggregators want to minimize their payments. So, this bilevel problem is converted to a single level one. Then, the WPP offers proper prices to the aggregators to attract them to supply their demand. Also, these aggregators can procure reserve for the WPP to compensate its uncertainties. Therefore, through a peer-to-peer (P2P) trading mechanism, the WPP requests the aggregators to allocate reserve to cover the uncertainties of the wind generation. Also, due to the presence of uncertain resources of the problem, a risk measurement tool is applied to the problem to control the uncertainties. The effectiveness of the model is assessed on realistic data from the Nordpool market and the results show that as the loads become responsive, more loads are allowed to choose their WPP to supply their load. Also, the reserve that is provided by these responsive loads to the WPP increases.

Abstract
Optimal dispatch of modern power systems often entails efficiently solving large-scale optimization problems, especially when generators have to respond to the fast fluctuation of renewable generation. This paper develops a method to learn the optimal strategy from a mixed-integer quadratic program with time-varying parameters, which can model many power system operation problems such as unit commitment and optimal power flow. Different from existing machine learning methods that learn a map from the parameter to the optimal action, the proposed method learns the map from the parameter to the optimal integer solution and the optimal basis, forming a discrete pattern. Such a framework naturally gives rise to a classification problem: the parameter set is partitioned into polyhedral regions; in each region, the optimal 0-1 variable and the set of active constraints remain unchanged, and the optimal continuous variables are affine functions in the parameter. The outcome of classification is compared with analytical results derived from multi-parametric programming theory, showing interesting connections between traditional mathematical programming theory and the interpretability of the learning-based method. Tests on a small-scale problem demonstrate the partition of the parameter set learned from data meets the theoretical outcome. More tests on the IEEE 57-bus system and a real-world 1881-bus system validate the performance of the proposed method with a high-dimensional parameter for which the analytical method is intractable.

Abstract
This paper presents a scenario-based framework for energy hub (Ell) design considering the variable efficiencies of gas-fired converters, wind turbines and integrated demand response (MR) programs. The proposed hub is able to meet the electrical, heating and cooling demands and is also equipped with a power-to-gas (P2G) system. Electrical, cooling, and heating loads uncertainties have been taken into account and the final problem is modeled as a mixed-integer non-linear programming (MINLP) problem. The P2G system is precisely modeled and its impacts on hub planning, emission, and the efficiency of gas-fired converters are thoroughly investigated. The results demonstrate that the P2G system reduced CO2 emissions by 37.4% by consuming CO2 emitted by gas-fired units. In addition, the results indicate that the P2G system injects hydrogen into the gas-fired units and increases their efficiencies. Therefore, the generation rate of these units has increased and consequently a smaller capacity has been installed for them. Numerical results illustrate that the presence of the P2G system has led to a reduction of 7.7% and 16.2% of investment and operation costs, respectively. Finally, the results indicate that the implementation of the IDR program reduces the installed capacity of the equipment, thereby reducing 3.3% of total cost. Overall, the results prove that the implementation of IDR programs along with the installation of the P2G system lead to reduce costs and CO2 emissions.

Abstract
Transmission expansion planning (TEP) is an important part of power system expansion planning. In TEP, optimal number of new transmission lines and their installation time and place are determined in an economic way. Uncertainties in load demand, place of power plants, and fuel price as well as voltage level of substations influence TEP solutions effectively. Therefore, in this paper, a scenario based-model is proposed for evaluating the fuel price impact on TEP considering the expansion of substations from the voltage level point of view. The fuel price is an important factor in power system expansion planning that includes severe uncertainties. This factor indirectly affects the lines loading and subsequent network configuration through the change of optimal generation of power plants. The efficiency of the proposed model is tested on the real transmission network of Azerbaijan regional electric company using a discrete artificial bee colony (DABC) and quadratic programming (QP) based method. Moreover, discrete particle swarm optimization (DPSO) and decimal codification genetic algorithm (DCGA) methods are used to verify the results of the DABC algorithm. The results evaluation reveals that considering uncertainty in fuel price for solving TEP problem affects the network configuration and the total expansion cost of the network. In this way, the total cost is optimized more and therefore the TEP problem is solved more precisely. Also, by comparing the convergence curve of the DABC with that of DPSO and DCGA algorithms, it can be seen that the efficiency of the DABC is more than DPSO and DCGA for solving the desired TEP problem.