Ufuk Topcu

Optimal decentralized protocol for electric vehicle charging

We propose a decentralized algorithm to optimally schedule electric vehicle (EV) charging. The algorithm exploits the elasticity of electric vehicle loads to fill the valleys in electric load profiles. We first formulate the EV charging scheduling problem as an optimal control problem, whose objective is to impose a generalized notion of valley-filling, and study properties of optimal charging profiles. We then give a decentralized algorithm to iteratively solve the optimal control problem. In each iteration, EVs update their charging profiles according to the control signal broadcast by the utility company, and the utility company alters the control signal to guide their updates. The algorithm converges to optimal charging profiles (that are as “flat” as they can possibly be) irrespective of the specifications (e.g., maximum charging rate and deadline) of EVs, even if EVs do not necessarily update their charging profiles in every iteration, and use potentially outdated control signal when they update. Moreover, the algorithm only requires each EV solving its local problem, hence its implementation requires low computation capability. We also extend the algorithm to track a given load profile and to real-time implementation.

Design and Stability of Load-Side Primary Frequency Control in Power Systems

We present a systematic method to design ubiquitous continuous fast-acting distributed load control for primary frequency regulation in power networks, by formulating an optimal load control (OLC) problem where the objective is to minimize the aggregate cost of tracking an operating point subject to power balance over the network. We prove that the swing dynamics and the branch power flows, coupled with frequency-based load control, serve as a distributed primal-dual algorithm to solve OLC. We establish the global asymptotic stability of a multimachine network under such type of load-side primary frequency control. These results imply that the local frequency deviations on each bus convey exactly the right information about the global power imbalance for the loads to make individual decisions that turn out to be globally optimal. Simulations confirm that the proposed algorithm can rebalance power and resynchronize bus frequencies after a disturbance with significantly improved transient performance.

Brief paper: Local stability analysis using simulations and sum-of-squares programming

The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant subsets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite-dimensional polynomial parametrizations for Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates is assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on small examples from the literature and several control oriented systems.

Receding horizon control for temporal logic specifications

In this paper, we describe a receding horizon framework that satisfies a class of linear temporal logic specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. The resulting embedded control software consists of a goal generator, a trajectory planner, and a continuous controller. The goal generator essentially reduces the trajectory generation problem to a sequence of smaller problems of short horizon while preserving the desired system-level temporal properties. Subsequently, in each iteration, the trajectory planner solves the corresponding short-horizon problem with the currently observed state as the initial state and generates a feasible trajectory to be implemented by the continuous controller. Based on the simulation property, we show that the composition of the goal generator, trajectory planner and continuous controller and the corresponding receding horizon framework guarantee the correctness of the system. To handle failures that may occur due to a mismatch between the actual system and its model, we propose a response mechanism and illustrate, through an example, how the system is capable of responding to certain failures and continues to exhibit a correct behavior.

Receding Horizon Temporal Logic Planning

We present a methodology for automatic synthesis of embedded control software that incorporates a class of linear temporal logic (LTL) specifications sufficient to describe a wide range of properties including safety, stability, progress, obligation, response and guarantee. To alleviate the associated computational complexity of LTL synthesis, we propose a receding horizon framework that effectively reduces the synthesis problem into a set of smaller problems. The proposed control structure consists of a goal generator, a trajectory planner, and a continuous controller. The goal generator reduces the trajectory generation problem into a sequence of smaller problems of short horizon while preserving the desired system-level temporal properties. Subsequently, in each iteration, the trajectory planner solves the corresponding short-horizon problem with the currently observed state as the initial state and generates a feasible trajectory to be implemented by the continuous controller. Based on the simulation property, we show that the composition of the goal generator, trajectory planner and continuous controller and the corresponding receding horizon framework guarantee the correctness of the system with respect to its specification regardless of the environment in which the system operates. In addition, we present a response mechanism to handle failures that may occur due to a mismatch between the actual system and its model. The effectiveness of the proposed technique is demonstrated through an example of an autonomous vehicle navigating an urban environment. This example also illustrates that the system is not only robust with respect to exogenous disturbances but is also capable of properly handling violation of the environment assumption that is explicitly stated as part of the system specification.

A simple optimal power flow model with energy storage

The integration of renewable energy generation, such as wind power, into the electric grid is difficult because of the source intermittency and the large distance between generation sites and users. This difficulty can be overcome through a transmission network with large-scale storage that not only transports power, but also mitigates against fluctuations in generation and supply. We formulate an optimal power flow problem with storage as a finite-horizon optimal control problem. We prove, for the special case with a single generator and a single load, that the optimal generation schedule will cross the time-varying demand profile at most once, from above. This means that the optimal policy will generate more than demand initially in order to charge up the battery, and then generate less than the demand and use the battery to supplement generation in final stages. This is a consequence of the fact that the marginal storage cost-to-go decreases in time.

Optimal power flow with large-scale storage integration

Restructuring of the electric power industry along with mandates to integrate renewable energy sources is introducing new challenges for the electric power system. Intermittent power sources, in particular, require mitigation strategies in order to maintain consistent power on the electric grid. We investigate distributed energy storage as one such strategy. Our model for optimal power flow with storage augments the usual formulation by adding simple charge/discharge dynamics for energy storage collocated with load and/or generation buses cast as a finite-time optimal control problem. We first propose a solution strategy that uses a convex optimization based relaxation to solve the optimal control problem. We then use this framework to illustrate the effects of various levels of energy storage using the topology of IEEE benchmark systems along with both time-invariant and demand-based cost functions. The addition of energy storage and demand-based cost functions significantly reduces the generation costs and flattens the generation profiles.

Receding horizon temporal logic planning for dynamical systems

This paper bridges the advances in computer science and control to allow automatic synthesis of control strategies for complex dynamical systems which are guaranteed, by construction, to satisfy the desired properties even in the presence of adversary. The desired properties are expressed in the language of temporal logic. With its expressive power, a wider class of properties than safety and stability can be specified. The resulting system consists of a discrete planner that plans, in the abstracted discrete domain, a set of transitions of the system to ensure the correct behaviors and a continuous controller that continuously implements the plan. To address the computational difficulties in the synthesis of a discrete planner, we present a receding horizon based scheme for executing finite state automata that essentially reduces the synthesis problem to a set of smaller problems.

Exact Convex Relaxation of Optimal Power Flow in Radial Networks

The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks.

TuLiP: a software toolbox for receding horizon temporal logic planning

This paper describes TuLiP, a Python-based software toolbox for the synthesis of embedded control software that is provably correct with respect to an expressive subset of linear temporal logic (LTL) specifications. TuLiP combines routines for (1) finite state abstraction of control systems, (2) digital design synthesis from LTL specifications, and (3) receding horizon planning. The underlying digital design synthesis routine treats the environment as adversary; hence, the resulting controller is guaranteed to be correct for any admissible environment profile. TuLiP applies the receding horizon framework, allowing the synthesis problem to be broken into a set of smaller problems, and consequently alleviating the computational complexity of the synthesis procedure, while preserving the correctness guarantee.