We use online convex optimization (OCO) for setpoint tracking with uncertain, flexible loads. We consider full feedback from the loads, bandit feedback, and two intermediate types of feedback: partial bandit where a subset of the loads are individually observed and the rest are observed in aggregate, and Bernoulli feedback where in each round the aggregator receives either full or bandit feedback according to a known probability. We give sublinear regret bounds in all cases. We numerically evaluate our algorithms on examples with thermostatically controlled loads and electric vehicles.
Online learning has also been used in models of price-based DR. Reference @cite_22 uses a continuum-armed bandit to do real-time pricing of price responsive dynamic loads. Reference @cite_8 uses OCO and conditional random fields to predict the price sensitivity of Electric Vehicles (EVs). This model was then used as input to compute real-time prices. Using OCO, @cite_36 develops real-time pricing algorithms to flatten the aggregate load consumption. They later apply their algorithm to EVs charging. OCO was also used in @cite_6 to flatten the aggregated power consumption using EVs charging scheduling. @cite_10 used OCO to identify the controllable portion of demand in real-time from aggregate measurements.
@cite_22 @cite_8 @cite_36 @cite_6 @cite_10
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While electric vehicles (EVs) are expected to provide environmental and economical benefit, judicious coordination of EV charging is necessary to prevent overloading of the distribution grid. Leveraging the smart grid infrastructure, the utility company can adjust the electricity price intelligently for individual customers to elicit desirable load curves. In this context, this paper addresses the problem of predicting the EV charging behavior of the consumers at different prices, which is a prerequisite for optimal price adjustment. The dependencies on price responsiveness among consumers are captured by a conditional random field (CRF) model. To account for temporal dynamics potentially in a strategic setting, the framework of online convex optimization is adopted to develop an efficient online algorithm for tracking the CRF parameters. The proposed model is then used as an input to a stochastic profit maximization module for real-time price setting. Numerical tests using simulated and semi-real data verify the effectiveness of the proposed approach. The Information and Communication Technologies (ICT) that are currently under development for future smart grid systems can enable load aggregators to have bidirectional communications with both the grid and Electric Vehicles (EVs) to obtain real-time price and load information, and to adjust EV charging schedules in real time. In addition, Energy Storage (ES) can be utilized by the aggregator to mitigate the impact of uncertainty and inaccurate prediction. In this paper, we study a problem of scheduling EV charging with ES from an electricity market perspective with joint consideration for the aggregator energy trading in the day-ahead and real-time markets. We present a Mixed Integer Linear Programming (MILP) model to provide optimal solutions as well as a simple polynomial-time heuristic algorithm based on LP rounding. In addition, we present a communication protocol for interactions among the aggregator, the ES, the power grid, and EVs, and demonstrate how to integrate the proposed scheduling approach in real-time charging operations. Extensive simulation results based on real electricity price and load data have been presented to justify the effectiveness of the proposed approach and to show how several key parameters affect its performance. We consider a queuing model with applications to electric vehicle (EV) charging systems in smart grids. We adopt a scheme where an Electric Service Company (ESCo) broadcasts a one bit signal to EVs, possibly indicating ‘on-peak’ periods during which electricity cost is high. EVs randomly suspend resume charging based on the signal. To model the dynamics of EVs we propose an M M ∞ queue with random interruptions, and analyze the dynamics using time-scale decomposition. There exists a trade-off: one may postpone charging activity to ‘off-peak’ periods during which electricity cost is cheaper, however this incurs extra delay in completion of charging. Using our model we characterize achievable trade-offs between the mean cost and delay perceived by users. Next we consider a scenario where EVs respond to the signal based on the individual loads. Simulation results show that peak electricity demand can be reduced if EVs carrying higher loads are less sensitive to the signal. Real-time price setting strategies are investigated for use by demand response programs in future power grids. The major challenge is that consumers have varying degrees of responsiveness to price adjustments at different time instants, which must be learned and accounted for by demand response initiatives. To this end, an online learning approach is developed here offering strong performance guarantees with minimal assumptions on the dynamics of load levels and consumer elasticity, even when consumers are adversarial and take actions strategically. The developed algorithms can determine electricity prices sequentially so as to elicit desirable usage behavior and flatten load curves, while implicitly learning individual consumers’ price elasticity based on available feedback information. Two feedback structures are considered: 1) a full information setup, where aggregate load levels as well as individual price elasticity parameters are directly available, and 2) a partial information (bandit) case, where only the aggregate load levels are revealed. Fairness and sparsity constraints are also incorporated via appropriate regularizers. Numerical tests verify the effectiveness of the proposed approach.