Johanna L. Mathieu

Quantifying Changes in Building Electricity Use, With Application to Demand Response

We present methods for analyzing commercial and industrial facility 15-min-interval electric load data. These methods allow building managers to better understand their facilitys electricity consumption over time and to compare it to other buildings, helping them to “ask the right questions” to discover opportunities for demand response, energy efficiency, electricity waste elimination, and peak load management. We primarily focus on demand response. Methods discussed include graphical representations of electric load data, a regression-based electricity load model that uses a time-of-week indicator variable and a piecewise linear and continuous outdoor air temperature dependence and the definition of various parameters that characterize facility electricity loads and demand response behavior. In the future, these methods could be translated into easy-to-use tools for building managers.

State Estimation and Control of Heterogeneous Thermostatically Controlled Loads for Load Following

Thermostatically controlled loads (TCLs), such as refrigerators, air conditioners, and electric water heaters, can be aggregated and used to deliver power systems services. The effectiveness of control strategies depends on the level of infrastructure and communications. This paper explores the use of TCLs for load following when measured state information is not available in real time. We use Markov Chain models to describe the temperature state evolution of populations of TCLs, and Kalman filtering techniques for both state estimation and joint parameter/state estimation. We find power tracking RMS errors in the range of 2-16% of the aggregate steady state power consumption of the TCL population. Results depend upon the information available for system identification, state estimation, and control. If high precision tracking is not required, TCLs may not need to be metered to provide state information to the central controller in real time or at all.

Arbitraging Intraday Wholesale Energy Market Prices With Aggregations of Thermostatic Loads

We investigate the potential for aggregations of residential thermostatically controlled loads (TCLs), such as air conditioners, to arbitrage intraday wholesale electricity market prices via non-disruptive load control. We present two arbitrage approaches: 1) a benchmark that gives us an optimal policy but requires local computation or real-time communication and 2) an alternative based on a thermal energy storage model, which relies on less computation/communication infrastructure, but is suboptimal. We find that the alternative approach achieves around 60%-80% of the optimal wholesale energy cost savings. We use this approach to compute practical upper bounds for savings via arbitrage with air conditioners in Californias intraday energy market. We investigate six sites over four years and find that the savings range from

Examining uncertainty in demand response baseline models and variability in automated responses to dynamic pricing

2-

Modeling options for demand side participation of thermostatically controlled loads

37 per TCL per year, and depend upon outdoor temperature statistics and price volatility.

A framework for and assessment of demand response and energy storage in power systems

Controlling electric loads to deliver power system services presents a number of interesting challenges. For example, changes in electricity consumption of Commercial and Industrial (C&I) facilities are usually estimated using counterfactual baseline models, and model uncertainty makes it difficult to precisely quantify control responsiveness. Moreover, C&I facilities exhibit variability in their response. This paper seeks to understand baseline model error and demand-side variability in responses to open-loop control signals (i.e. dynamic prices). Using a regression-based baseline model, we define several Demand Response (DR) parameters, which characterize changes in electricity use on DR days, and then present a method for computing the error associated with DR parameter estimates. In addition to analyzing the magnitude of DR parameter error, we develop a metric to determine how much observed DR parameter variability is attributable to real event-to-event variability versus simply baseline model error. Using data from 38 C&I facilities that participated in an automated DR program in California, we find that DR parameter errors are large. For most facilities, observed DR parameter variability is likely explained by baseline model error, not real DR parameter variability; however, a number of facilities exhibit real DR parameter variability. In some cases, the aggregate population of C&I facilities exhibits real DR parameter variability, resulting in implications for the system operator with respect to both resource planning and system stability.

Maximizing the potential of energy storage to provide fast frequency control

Residential thermostatically controlled loads (TCLs) have potential for participation in electricity markets. This is because we can control a large group of these loads to achieve aggregate system behavior such as providing frequency reserves while ensuring the control actions are non-disruptive to the end users. A main challenge in controlling aggregations of TCLs is developing dynamical system models that are simple enough for optimization and control, but rich enough to capture the behavior of the loads. In this work, we propose three classes of models that approximate aggregate TCL dynamics. We analyze these models in terms of their accuracy and computational tractability. The models demonstrate a progression from models that help us analyze and predict TCL population behavior to those that help us develop large-scale automatic control strategies. Specifically, we demonstrate how formal methods from computer science and optimal control can be used to derive bounds on model error, guarantees for trajectory tracking, and algorithms for price arbitrage. We find that the accuracy of the analytic results decreases as TCL parameter heterogeneity is introduced. Thus, we motivate further development of analytical tools and modeling approaches to investigate realistic TCL behavior in power systems.

Stochastic Optimal Power Flow with Uncertain Reserves from Demand Response

The shift in the electricity industry from regulated monopolies to competitive markets as well as the widespread introduction of fluctuating renewable energy sources bring new challenges to power systems. Some of these challenges can be mitigated by using demand response (DR) and energy storage to provide power system services. The aim of this paper is to provide a unified framework that allows us to assess different types of DR and energy storage resources and determine which resources are best suited to which services. We focus on four resources: batteries, plug-in electric vehicles, commercial buildings, and thermostatically controlled loads. We define generic power system services in order to assess the resources. The contribution of the paper is threefold: (i) the development of a framework for assessing DR and energy storage resources; (ii) a detailed analysis of the four resources in terms of ability for providing power system services, and (iii) a comparison of the resources, including an example case for Switzerland. We find that the ability of resources to provide power system services varies largely and also depends on the implementation scenario. Generally, there is large potential to use DR and energy storage for providing power system services, but there are also challenges to be addressed, for example, adequate compensation, privacy, guaranteeing costumer service, etc.

Uncertainty in the flexibility of aggregations of demand response resources

Due to their fast responsiveness, energy storage units such as batteries can provide fast frequency control to power systems. However, when the control signal is biased or substantially autocorrelated, they cannot provide services for extended periods of time because they have limited energy capacities. To improve the ability of batteries to provide frequency control, we can offset their frequency response so that they only respond to fast and zero-mean frequency deviations, while passing slower and biased deviations to other resources. We propose two new heuristics to offset frequency control signals, and a method to compare these heuristics to previously developed heuristics. This method allows us to quantify the heuristics from the point of view of both the storage unit operator (return on investment, ROI) and the transmission system operator (impact on the power system). Considering battery degradation, the new heuristics yield better ROIs, and we find that our results are not very sensitive to the batterys energy-to-power ratio around its optimum. We also find that the best choice of heuristic depends on what impact matters most to the transmission system operator.

Modeling, Analysis, and Control of Demand Response Resources

Demand response (DR) can provide reserves in power systems but a fundamental challenge is that the amount of capacity available from DR is time-varying and uncertain. We propose a stochastic optimal power flow (OPF) formulation that handles uncertain energy from wind and uncertain reserves provided by DR. To handle the uncertainty, we formulate chance constraints and use a scenario based methodology to solve the stochastic OPF problem. This technique allows us to provide a-priori guarantees regarding the probability of constraint satisfaction. Additionally, we devise a strategy for the reserves, provided either by the generators or the loads, that could be deployed in real time operation. To evaluate the effectiveness of our methodology, we carry out a simulation based analysis on the IEEE 30-bus network. Our case studies show that optimizing over the reserves provided by DR, even though they are uncertain, results in lower total cost compared to the case where only generation side reserves are taken into account. We also carry out a Monte Carlo analysis to empirically estimate the probability of constraint satisfaction and demonstrate that it is within the theoretical limits.