#### Date on Master's Thesis/Doctoral Dissertation

8-2020

#### Document Type

Doctoral Dissertation

#### Degree Name

Ph. D.

#### Department

Industrial Engineering

#### Degree Program

Industrial Engineering, PhD

#### Committee Chair

Bai, Lihui

#### Committee Member

Gentili, Monica

#### Committee Member

Saleem, Jason

#### Committee Member

McIntyre, Michael

#### Author's Keywords

demand side management; dynamic programming, mixed integer linear programming, bi-section search, bi-level optimization, trust-region

#### Abstract

Development of smart grids along with communication technologies have led to the increased attention and adoption of demand side management (DSM) in the residential sector. Among various DSM schemes, demand response (DR) is a market- based mechanism to shave peak electricity consumption at the system level. In the past decade, the academia has seen a growing literature studying load management methodologies for residential consumers. A typical demand response program has three important facets: the energy cost, comfort of the consumers and overall system efficiency. In this dissertation, we investigate and develop models for effective load control to minimize energy cost and for understanding electricity consumer behavior so as to best design DR schemes. Participation in a real-world field demonstration not only stimulated our motivation for these studies, but also provided us with real- world data to validate the developed models and analyses. This in fact makes the dissertation distinct from current academic literature. We first develop a control algorithm for Heating Ventilation Air-Conditioning (HVAC) systems in households during a peak period. The dynamic programming based model can determine the optimal temperature set-points of a thermostat given the lower and upper limits of temperature that household feels comfortable and the desired duration of the control. The temperature limits act as a quantitative metric for the comfort level of consumers. The objective is to minimize the energy consumption. The model is particularly suitable for DR programs with critical peak pricing, in which a higher electricity rate occurs during the peak period. When deployed separately during the peak and adjoining two periods, the model can keep the inside temperature within the given limits while consuming minimal energy during the peak period. This ensures that the HVAC system would have minimal usage during the peak period as the temperature is kept within the limits. In addition, we show that alternative start and end times of the control algorithm can be tested for each home. Analyses of the alternative options provide us with information about the insulation of the building. We perform computational experiments with real-world data to show the efficacy of the proposed methodology. Second, we propose a mixed-integer linear fractional programming (MILFP) model to optimally deploy the dynamic programming based HVAC controllers among a pool of homes in a staggered fashion. Doing so, the model aims to flatten the demand curve over time thus maximizing the load factor for the entire distribution network. In addition, we develop a reformulation of the MILFP model into an MILP model which significantly reduces computational time for medium-scale instances. Furthermore, for large-scale instances, excessive computational times by general purpose solvers motivate us to develop a customized bi-section search algorithm. Our extensive computational experiments conclude that the customized algorithm is able to solve real-world as well as randomly generated instances in reasonable CPU times. In another effort, we study the behavior of consumers when subject to dynamic pricing under a DR program. We model the price-responsive behavior with utility functions and develop a bi-level programming model to estimate the coefficients of such a function utilizing consumption data from advanced metering infrastructure (AMI) from the field demonstration project mentioned previously. The upper level objective is to minimize the estimation error between the measured data and the optimum consumption while the lower level is for each household/consumer to maximize their total utility of energy consumption. We propose a trust-region algorithm to solve the non-linear bi-level utility estimation (BLUE) model after employing linear and quadratic approximation for the upper and lower level objective function, respectively. A mathematical property of the optimal solution is exploited to develop a cut that has significantly improved the computational time. Numerical experiments with real world data are conducted to validate the proposed models. In addition, we show the strong positive correlation between the utility coefficients and the widely used price elasticity property. Finally, this dissertation also presents several empirical models to assess the effect of smart technologies on electricity consumption under a demand charge dynamic pricing rate. The models developed here were being utilized in the aforementioned demand response pilot study. We present a statistical test based model to estimate the change of coincident load of residential consumers with the installation of efficient appliances including heat pump water heaters, smart thermostats, and battery storage units. The method utilizes a day matching algorithm to pair days with similar weather conditions. The consumption data from the two paired up days are used to conduct a paired t-test to evaluate the statistical significance of the changes. The results reveal that insulation plays an important role in energy savings along with battery systems.

#### Recommended Citation

Roy, Arnab, "Mathematical models and analysis for demand side management in residential electricity distribution networks." (2020). *Electronic Theses and Dissertations.* Paper 3504.

Retrieved from https://ir.library.louisville.edu/etd/3504