108 research outputs found
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Robust Hybrid Linear State Estimator Utilizing SCADA and PMU Measurements
This paper intends to improve the accuracy of power system State Estimation (SE) by introducing a hybrid linear robust state estimator. To this end, automatic bad data rejection is accomplished through an M-estimator, i.e. a Schweppe-type estimator with Huber loss function. The method of Iteratively Reweighted Least Squares (IRLS) is used to maximize the likelihood function in the M-estimator. Leverage measurements are also treated by a simple yet effective formulation. To run the algorithm for real-world large-scale grids, cumbersome construction of the Jacobian matrix at each iteration is avoided. In addition, convergence to the local minima faced in the large-scale Gauss-Newton algorithm is not a concern as the proposed formulation is linear with no approximation. As observability and redundancy considerations mandate SE to take advantage of traditional SCADA measurements along with available PMU measurements, the linearity of the proposed SE formulation is guaranteed regardless of whether PMU-only, SCADA-only or hybrid SCADA/PMU measurements are utilized. In this regard, covariance matrix for measurements weights is derived for both types of measurements. Thanks to the linear formulation and therefore swiftness of the proposed algorithm, SE could be run for different power systems with a few up to thousands of buses
An exact relaxation of AC-OPF problem for battery-integrated power grids
Renewable energy resources and power electronics-interfaced loads introduce
fast dynamics in distribution networks. These dynamics cannot be regulated by
slow conventional solutions and require fast controllable energy resources such
as Battery Energy Storage Systems (BESSs). To compensate for the high costs
associated to BESSs, their energy and power management should be optimized. In
this paper, a convex iterative optimization approach is developed to find the
optimal active and reactive power setpoints of BESSs in active distribution
networks. The objective is to minimize the total cost of energy purchase from
the grid. Round-trip and life-time characteristics of BESSs are modelled
accurately and integrated into a relaxed and exact formulation of the AC power
flow, resulting into a Modified Augmented Relaxed Optimal Power Flow (MAROP)
problem. The feasibility and optimality of the solution under the grid security
limits and technical constraints of BESSs is proven analytically. A 32-bus IEEE
test benchmark is used to illustrate the performance of the developed approach
in comparison to the alternative approaches existing in the literature
Optimal Control of Two-Player Systems with Output Feedback
In this article, we consider a fundamental decentralized optimal control
problem, which we call the two-player problem. Two subsystems are
interconnected in a nested information pattern, and output feedback controllers
must be designed for each subsystem. Several special cases of this architecture
have previously been solved, such as the state-feedback case or the case where
the dynamics of both systems are decoupled. In this paper, we present a
detailed solution to the general case. The structure of the optimal
decentralized controller is reminiscent of that of the optimal centralized
controller; each player must estimate the state of the system given their
available information and apply static control policies to these estimates to
compute the optimal controller. The previously solved cases benefit from a
separation between estimation and control which allows one to compute the
control and estimation gains separately. This feature is not present in
general, and some of the gains must be solved for simultaneously. We show that
computing the required coupled estimation and control gains amounts to solving
a small system of linear equations
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