Incentivizing Reliable Demand Response with Customers' Uncertainties and Capacity Planning

One of the major issues with the integration of renewable energy sources into the power grid is the increased uncertainty and variability that they bring. If this uncertainty is not sufficiently addressed, it will limit the further penetration of renewables into the grid and even result in blackouts. Compared to energy storage, Demand Response (DR) has advantages to provide reserves to the load serving entities (LSEs) in a cost-effective and environmentally friendly way. DR programs work by changing customers' loads when the power grid experiences a contingency such as a mismatch between supply and demand. Uncertainties from both the customer-side and LSE-side make designing algorithms for DR a major challenge. This paper makes the following main contributions: (i) We propose DR control policies based on the optimal structures of the offline solution. (ii) A distributed algorithm is developed for implementing the control policies without efficiency loss. (iii) We further offer an enhanced policy design by allowing flexibilities into the commitment level. (iv) We perform real world trace based numerical simulations which demonstrate that the proposed algorithms can achieve near optimal social cost. Details can be found in our extended version.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0453

Harnessing Flexible and Reliable Demand Response Under Customer Uncertainties

Demand response (DR) is a cost-effective and environmentally friendly approach for mitigating the uncertainties in renewable energy integration by taking advantage of the flexibility of customers' demands. However, existing DR programs suffer from either low participation due to strict commitment requirements or not being reliable in voluntary programs. In addition, the capacity planning for energy storage/reserves is traditionally done separately from the demand response program design, which incurs inefficiencies. Moreover, customers often face high uncertainties in their costs in providing demand response, which is not well studied in literature. This paper first models the problem of joint capacity planning and demand response program design by a stochastic optimization problem, which incorporates the uncertainties from renewable energy generation, customer power demands, as well as the customers' costs in providing DR. We propose online DR control policies based on the optimal structures of the offline solution. A distributed algorithm is then developed for implementing the control policies without efficiency loss. We further offer enhanced policy design by allowing flexibilities into the commitment level. We perform real world trace based numerical simulations. Results demonstrate that the proposed algorithms can achieve near optimal social costs, and significant social cost savings compared to baseline methods

Data-Driven Chance-Constrained Design of Voltage Droop Control for Distribution Networks

This paper addresses the design of local control methods for voltage control in distribution networks with high levels of distributed energy resources (DERs). The designed control methods modulate the active and reactive power output of DERs proportional to the deviation of the local measured voltage magnitudes from a reference voltage, which is referred to as droop control; thus, the design focuses on determining the droop characteristics that satisfy network-wide voltage magnitude constraints. The uncertainty and variability of DERs renders the design of optimal droop controls very challenging; hence, this paper proposes chance constraints to limit the risk from intermittent DERs by designing droop control coefficients that guarantee the satisfaction of network operational constraints with a specific probability. In addition, the proposed approach relies entirely on historical data rather than assuming knowledge of the probability distributions that characterize the uncertainty of DERs. The efficacy of the proposed method is demonstrated on a 37-bus distribution feeder

Time-Varying Feedback Optimization for Quadratic Programs with Heterogeneous Gradient Step Sizes

Online feedback-based optimization has become a promising framework for real-time optimization and control of complex engineering systems. This tutorial paper surveys the recent advances in the field as well as provides novel convergence results for primal-dual online algorithms with heterogeneous step sizes for different elements of the gradient. The analysis is performed for quadratic programs and the approach is illustrated on applications for adaptive step-size and model-free online algorithms, in the context of optimal control of modern power systems

Using Predictions in Online Optimization: Looking Forward with an Eye on the Past

We consider online convex optimization (OCO) problems with switching costs and noisy predictions. While the design of online algorithms for OCO problems has received considerable attention, the design of algorithms in the context of noisy predictions is largely open. To this point, two promising algorithms have been proposed: Receding Horizon Control (RHC) and Averaging Fixed Horizon Control (AFHC). The comparison of these policies is largely open. AFHC has been shown to provide better worst-case performance, while RHC outperforms AFHC in many realistic settings. In this paper, we introduce a new class of policies, Committed Horizon Control (CHC), that generalizes both RHC and AFHC. We provide average-case analysis and concentration results for CHC policies, yielding the first analysis of RHC for OCO problems with noisy predictions. Further, we provide explicit results characterizing the optimal CHC policy as a function of properties of the prediction noise, e.g., variance and correlation structure. Our results provide a characterization of when AFHC outperforms RHC and vice versa, as well as when other CHC policies outperform both RHC and AFHC

Using Predictions in Online Optimization: Looking Forward with an Eye on the Past

We consider online convex optimization (OCO) problems with switching costs and noisy predictions. While the design of online algorithms for OCO problems has received considerable attention, the design of algorithms in the context of noisy predictions is largely open. To this point, two promising algorithms have been proposed: Receding Horizon Control (RHC) and Averaging Fixed Horizon Control (AFHC). The comparison of these policies is largely open. AFHC has been shown to provide better worst-case performance, while RHC outperforms AFHC in many realistic settings. In this paper, we introduce a new class of policies, Committed Horizon Control (CHC), that generalizes both RHC and AFHC. We provide average-case analysis and concentration results for CHC policies, yielding the first analysis of RHC for OCO problems with noisy predictions. Further, we provide explicit results characterizing the optimal CHC policy as a function of properties of the prediction noise, e.g., variance and correlation structure. Our results provide a characterization of when AFHC outperforms RHC and vice versa, as well as when other CHC policies outperform both RHC and AFHC