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
2552794833 2015555034 2331891307 2962806981 2551993261
The problem of dynamically pricing of electricity by a retailer for customers in a demand response program is considered. It is assumed that the retailer obtains electricity in a two-settlement wholesale market consisting of a day ahead market and a real-time market. Under a day ahead dynamic pricing mechanism, the retailer aims to learn the aggregated demand function of its customers while maximizing its retail profit. A piecewise linear stochastic approximation algorithm is proposed. It is shown that the accumulative regret of the proposed algorithm grows with the learning horizon T at the order of O(log T). It is also shown that the achieved growth rate cannot be reduced by any piecewise linear policy. 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. 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. We propose an algorithm for distributed charging control of electric vehicles (EVs) using online learning and online convex optimization. Many distributed charging control algorithms in the literature implicitly assume fast two-way communication between the distribution company and EV customers. This assumption is impractical at present and also raises security and privacy concerns. Our algorithm does not use this assumption; however, at the expense of slower convergence to the optimal solution and by relaxing the sense of optimality. The proposed algorithm requires one-way communication, which is implemented through the distribution company publishing the pricing profiles for the previous days. We provide convergence results for the algorithm and illustrate the results through numerical examples. In this paper, we apply an emerging method, online learning with dynamics, to deduce properties of distributed energy resources (DERs) from coarse measurements, e.g., measurements taken at distribution substations, rather than household-level measurements. Reduced sensing requirements can lower infrastructure costs associated with reliably incorporating DERs into the distribution network. We specifically investigate whether dynamic mirror descent (DMD), an online learning algorithm, can determine the real-time controllable demand served by a distribution feeder using feeder-level active power demand measurements. In our scenario, DMD incorporates various controllable demand and uncontrollable demand models to generate real-time controllable demand estimates. In a realistic scenario, these estimates have an RMS error of 8.34 of the average controllable demand, which improves to 5.53 by incorporating more accurate models. We propose topics for additional work in modeling, system identification, and the DMD algorithm itself that could improve the RMS errors.