25 research outputs found
Asymptotic convergence of constrained primal–dual dynamics
This paper studies the asymptotic convergence properties of the primal–dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal–dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal–dual optimizers are globally asymptotically stable under the primal–dual dynamics and that each solution of the dynamics converges to an optimizer
Optimal load-side control for frequency regulation in smart grids
Frequency control rebalances supply and demand while maintaining the network
state within operational margins. It is implemented using fast ramping reserves
that are expensive and wasteful, and which are expected to grow with the
increasing penetration of renewables. The most promising solution to this
problem is the use of demand response, i.e. load participation in frequency
control. Yet it is still unclear how to efficiently integrate load
participation without introducing instabilities and violating operational
constraints.
In this paper we present a comprehensive load-side frequency control
mechanism that can maintain the grid within operational constraints. In
particular, our controllers can rebalance supply and demand after disturbances,
restore the frequency to its nominal value and preserve inter-area power flows.
Furthermore, our controllers are distributed (unlike the currently implemented
frequency control), can allocate load updates optimally, and can maintain line
flows within thermal limits. We prove that such a distributed load-side control
is globally asymptotically stable and robust to unknown load parameters. We
illustrate its effectiveness through simulations.Comment: Under revisio
Cooperative Data-Driven Distributionally Robust Optimization
We study a class of multiagent stochastic optimization problems where the objective is to minimize the expected value of a function which depends on a random variable. The probability distribution of the random variable is unknown to the agents. The agents aim to cooperatively find, using their collected data, a solution with guaranteed out-of-sample performance. The approach is to formulate a data-driven distributionally robust optimization problem using Wasserstein ambiguity sets, which turns out to be equivalent to a convex program. We reformulate the latter as a distributed optimization problem and identify a convex-concave augmented Lagrangian, whose saddle points are in correspondence with the optimizers, provided a min-max interchangeability criteria is met. Our distributed algorithm design, then consists of the saddle-point dynamics associated to the augmented Lagrangian. We formally establish that the trajectories converge asymptotically to a saddle point and, hence, an optimizer of the problem. Finally, we identify classes of functions that meet the min-max interchangeability criteria
Energy-based analysis and control of power networks and markets:Port-Hamiltonian modeling, optimality and game theory
This research studies the modeling, control and optimization of power networks. A unifying mathematical approach is proposed for the modeling of both the physical power network as well as market dynamics. For the physical system, several models of varying complexity describing the changes in frequency and voltages are adopted. For the electricity market, various dynamic pricing algorithms are proposed that ensure a optimal dispatch of power generation and demand (via flexible loads). Such pricing algorithms can be implemented in real-time and using only local information that is available in the network (such as the frequency). By appropriately coupling the physical dynamics with the pricing algorithms, stability of the combined physical-economical system is proven. This in particular shows how real-time dynamic pricing can be used as a control method to achieve frequency regulation and cost efficiency in the network