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This paper evaluates the real-time price-based demand response (DR) management for residential appliances via stochastic optimization and robust optimization approaches. The proposed real-time price-based DR management application can be imbedded into smart meters and automatically executed on-line for determining the optimal operation of residential appliances within 5-minute time slots while considering uncertainties in real-time electricity prices. Operation tasks of residential appliances are categorized into deferrable/non-deferrable and interruptible/non-interruptible ones based on appliances' DR preferences as well as their distinct spatial and temporal operation characteristics. The stochastic optimization adopts the scenario-based approach via Monte Carlo (MC) simulation for minimizing the expected electricity payment for the entire day, while controlling the financial risks associated with real-time electricity price uncertainties via the expected downside risks formulation. Price uncertainty intervals are considered in the robust optimization for minimizing the worst-case electricity payment while flexibly adjusting the solution robustness. Both approaches are formulated as mixed-integer linear programming (MILP) problems and solved by state-of-the-art MILP solvers. The numerical results show attributes of the two approaches for solving the real-time optimal DR management problem for residential appliances. Index Terms-Deferrable task, interruptible task, real-time price-based demand response management, residential appliances, robust optimization, stochastic optimization. NOMENCLATURE Variables:Electricity price forecast of time in scenario .Electricity payment of scenario from to the end of the day.Available energy in battery of plug-in electric vehicle (PEV) at time in scenario . Time required to finish task of appliance . Index of appliances.Commitment status of appliance at current time .Commitment of appliance at time in scenario . Indices of tasks.Volume of water heater tank at time in scenario .Power consumption of appliance at current time .Power consumption of appliance at time in scenario .Binary indicator to identify risks in scenario at current time .Relative error of scenario cost values at time slot .Risk in scenario at time slot .Index of scenarios.Indices of time slots. Index of current time slot.Indoor temperature at time in scenario .Binary variables indicating temperature and volume status at time in scenario .Auxiliary variable.Dual variables.Binary variable indicating the operation status of task for appliance at time in scenario .Binary variable indicating the operation status of task for appliance at time . Sets and Parameters:The set of all appliances.Real-time electricity price of current time slot announced by ISO in real-time market.Target daily electricity cost pre-defined by consumer.Energy requirement of appliance .Desired charging energy for a PEV.Minimum battery capacity of a PEV.Maximum battery capacity of a PEV.Number of time slots required by appliance to finish its ...

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Title: Optimal sizing and siting of grid-scale battery energy storage systems to reduce cost by grid restrictions in the Colombian electrical systemIn this document, a method to find the best siting and sizing of battery energy storage systems (BESS) to reduce the cost from restrictions in the Colombian power system is proposed. The method is expresed as a mixed-integer linear programming (MILP) formulation, initially with a deterministic approach, but later improving it using a scenario-based approach, to consider uncertainties in some parameters of the model. Optimization models were written in the programming language Python, using the Pyomo package. The different development stages were tested in a 6-bus test system, a simplified 15-bus system of Colombia, and the Colombian national transmission system, using real data of the Colombian system for the last two systems. Results have been assessed by comparing costs from restrictions with and without BESS under different conditions, identifying additional benefits of integrating BESS in the studied systems.