Individual risk in mean-field control models for decentralized control, with application to automated demand response

TL;DR

This paper analyzes individual risk in mean-field control models for decentralized energy management, showing how local control can mitigate poor service quality without significantly affecting grid-level performance.

Contribution

It introduces a detailed risk modeling framework and demonstrates how local control strategies can bound individual QoS in mean-field control systems.

Findings

QoS histograms are approximately Gaussian, indicating potential for poor service.

Variance of QoS can be estimated using an extended LTI model with noise.

Local control can truncate QoS distribution, ensuring service bounds.

Abstract

Flexibility of energy consumption can be harnessed for the purposes of ancillary services in a large power grid. In prior work by the authors a randomized control architecture is introduced for individual loads for this purpose. In examples it is shown that the control architecture can be designed so that control of the loads is easy at the grid level: Tracking of a balancing authority reference signal is possible, while ensuring that the quality of service (QoS) for each load is acceptable on average. The analysis was based on a mean field limit (as the number of loads approaches infinity), combined with an LTI-system approximation of the aggregate nonlinear model. This paper examines in depth the issue of individual risk in these systems. The main contributions of the paper are of two kinds: Risk is modeled and quantified: (i) The average performance is not an adequate measure of success. It is found empirically that a histogram of QoS is approximately Gaussian, and consequently each load will eventually receive poor service. (ii) The variance can be estimated from a refinement of the LTI model that includes a white-noise disturbance; variance is a function of the randomized policy, as well as the power spectral density of the reference signal. Additional local control can eliminate risk: (iii) The histogram of QoS is truncated through this local control, so that strict bounds on service quality are guaranteed. (iv) This has insignificant impact on the grid-level performance, beyond a modest reduction in capacity of ancillary service.