Maryam Kamgarpour

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

Convergence properties of a decentralized Kalman filter

2-

Brief paper: On optimal control of non-autonomous switched systems with a fixed mode sequence

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

Modeling options for demand side participation of thermostatically controlled loads

We consider the problem of decentralized Kalman filtering in a sensor network. Each sensor node implements a local Kalman filter based on its own measurements and the information exchanged with its neighbors. It combines the information received from other sensors through using a consensus filter as proposed in [14]. For a time-invariant process and measurement model, we show that this algorithm guarantees that the local estimates of the error covariance matrix converge to the centralized error covariance matrix and that the local estimates of the state converge in mean to the centralized Kalman filter estimates. However, due to the use of the consensus filter, the local estimates of the state do not converge to the least-squares estimate that would be obtained from a centralized Kalman filter.

A descent algorithm for the optimal control of constrained nonlinear switched dynamical systems

We consider differentiability with respect to the switch times of the value function of an optimal control problem for a non-autonomous switched system. The control variables are the switch times between the modes and the input in each mode. We provide a method to compute the derivative of the cost function given a nominal input. Then, we view the optimal control problem as a parametrized optimization problem in which the switch times are the parameters and the optimization is over the set of feasible inputs of each mode. From this point of view, we provide conditions under which the continuity and differentiability of the optimal value function, that is the cost function optimized over the inputs, can be guaranteed.

A Hierarchical Flight Planning Framework for Air Traffic Management

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.

A numerical method for the optimal control of switched systems

One of the oldest problems in the study of dynamical systems is the calculation of an optimal control. Though the determination of a numerical solution for the general non-convex optimal control problem for hybrid systems has been pursued relentlessly to date, it has proven difficult, since it demands nominal mode scheduling. In this paper, we calculate a numerical solution to the optimal control problem for a constrained switched nonlinear dynamical system with a running and final cost. The control parameter has a discrete component, the sequence of modes, and two continuous components, the duration of each mode and the continuous input while in each mode. To overcome the complexity posed by the discrete optimization problem, we propose a bi-level hierarchical optimization algorithm: at the higher level, the algorithm updates the mode sequence by using a single-mode variation technique, and at the lower level, the algorithm considers a fixed mode sequence and minimizes the cost functional over the continuous components. Numerical examples detail the potential of our proposed methodology.

Tracking controllers for small UAVs with wind disturbances: Theory and flight results

The continuous growth of air traffic demand, skyrocketing fuel price, and increasing concerns on safety and environmental impact of air transportation necessitate the modernization of the air traffic management (ATM) system in the United States. The design of such a large-scale networked system that involves complex interactions among automation and human operators poses new challenges for many engineering fields. This paper investigates several important facets of the future ATM system from a systems-level point of view. In particular, we develop a hierarchical decentralized decision architecture that can design 4-D (space +time) path plans for a large number of flights while satisfying weather and capacity constraints of the overall system. The proposed planning framework respects preferences of individual flights and encourages information sharing among different decision makers in the system, and thus has a great potential to reduce traffic delays and weather risks while maintaining safety standards. The framework is validated through a large-scale simulation based on real traffic data over the entire airspace of the contiguous United States. We envision that the hierarchical decentralization approach developed in this paper would also provide useful insights into the design of decision and information hierarchies for other large-scale infrastructure systems.

A stochastic reach-avoid problem with random obstacles

Switched dynamical systems have shown great utility in modeling a variety of systems. Unfortunately, the determination of a numerical solution for the optimal control of such systems has proven difficult, since it demands optimal mode scheduling. Recently, we constructed an optimization algorithm to calculate a numerical solution to the problem subject to a running and final cost. In this paper, we modify our original approach in three ways to make our algorithms application more tenable. First, we transform our algorithm to allow it to begin at an infeasible point and still converge to a lower cost feasible point. Second, we incorporate multiple objectives into our cost function, which makes the development of an optimal control in the presence of multiple goals viable. Finally, we extend our approach to penalize the number of hybrid jumps. We also detail the utility of these extensions to our original approach by considering two examples.

Approximate dynamic programming via sum of squares programming

This work outlines two approaches for small unmanned aerial vehicles (UAVs) performing surveillance with fixed cameras. Small UAVs present significant control challenges, due to relatively low-bandwidth actuation and significant disturbances due to wind. This work features implementations of a spatial sliding mode controller and a receding-horizon kinodynamic controller. The spatial sliding mode controller is designed to follow a desired aircraft path which places the camera-footprint on the desired locations, while the kinodynamic controller is designed to directly track a camera-footprint path. Since our objective is surveillance, we aim to compare the effectiveness of each controller in tracking a desired sensor path. Discussion of each controller is followed by simulation and flight test results.