Abstract (from our first paper on randomized policies): Renewable energy sources such as wind and solar power have a high degree of unpredictability and time-variation, which makes balancing demand and supply challenging.  One possible way to address this challenge is to harness the inherent flexibility in demand of many types of loads. We focus on pool pumps, and how they can be used to provide ancillary service to the grid for maintaining demand-supply balance.

One Million Pools in Florida that would consume one gigawatt of electricity if they all operate at once.

The control solution is based on the following steps

1. A Markov Decision Process (MDP) model is introduced for an individual pool pump.
2. Motivated by Todorov’s formulation, a randomized control architecture is proposed, motivated by the need for decentralized decision making, and the need to avoid synchronization that can lead to large and detrimental spikes in demand.
3. An aggregate model for a large number of pools is obtained from a mean field limit.
4. A linearization of the eigenvector problem in (2) provides an LTI-system approximation of the aggregate nonlinear model, with a scalar signal as the input and a measure of the aggregate demand as the output.

The final approximation is convenient for control design at the grid level.  Simulations are provided to illustrate the accuracy of the models and effectiveness of the proposed control approach.

Journal version link here

See bibliography below, and also: From the Sunshine State to the Solar State; Gator Engineers have a plan

2013 Tutorial at Cambridge – link here

A high-level view of our work is contained in barbusmey14

The paper meybarbusyueehr14 (on which the abstract above is based) focuses on performance at the grid level, and only evaluates the average quality of service (QoS) to loads.

The sequel yuemeybus13 is an in-depth analysis of the impact of service to an individual load. Additional mechanisms are introduced to ensure strict constraints on QoS. State estimation questions are considered in  chebusmey15b and chebusmey16b

Another sequel busmey14 helps to explain why the grid-level control problem is easy!  Under certain conditions on the nominal model, the input-output system seen at the grid level is passive – a valuable property for control.

It is shown in busmey16a that passivity can be achieved by design

State estimation and Mean-Field Control with application to demand dispatch

Much more has been done since 2016, which means it is too hard to keep this page up to date!  

@misc{busmeyPatent15,
author = {Bu\v{s}i\'{c}, Ana and Meyn, Sean},
howpublished = {{US Patent 10,692,158 (submitted July, 2015)}},
title = {Using loads with discrete finite states of power to provide ancillary services for a power grid},
year = {2020}}

@phdthesis{NeilCammardellaThesis21,
address = {Gainesville, FL, USA},
author = {Neil Cammardella},
school = {University of Florida},
title = {Creating Virtual Energy Storage Through Optimal Allocation And Control Of Flexible Power Consumption},
year = {2021}}

@phdthesis{JoelMathiasThesis21,
address = {Gainesville, FL, USA},
author = {Joel Mathias},
school = {University of Florida},
title = {Balancing the power grid with distributed control of flexible loads},
year = {2021}}

@phdthesis{BobMoyeThesis21,
address = {Gainesville, FL, USA},
author = {Robert Walton Moye},
school = {University of Florida},
title = {Resource investments in organized markets: a case for central planning},
year = {2021}}

Florida is the sunshine state – why is there so little solar energy?  Why do we import natural gas and coal, when we have so much indigenous energy?

• Use the techniques described in our recent papers to smooth out all of the volatility on time scales less than a few hours.  This is a significant claim – this “regulation” amounts to 10% of the electricity market in regions such as Texas.

There is harmony in this approach – in the case of climate control, the air conditioners gently ramp up when the sun is shining.

Bibliography