14 research outputs found
A Local Control Approach to Voltage Regulation in Distribution Networks
This paper address the problem of voltage regulation in power distribution
networks with deep penetration of distributed energy resources (DERs) without
any explicit communication between the buses in the network. We cast the
problem as an optimization problem with the objective of minimizing the
distance between the bus voltage magnitudes and some reference voltage profile.
We present an iterative algorithm where each bus updates the reactive power
injection provided by their DER. The update at a bus only depends on the
voltage magnitude at that bus, and for this reason, we call the algorithm a
local control algorithm. We provide sufficient conditions that guarantee the
convergence of the algorithm and these conditions can be checked a priori for a
set of feasible power injections. We also provide necessary conditions
establishing that longer and more heavily loaded networks are inherently more
difficult to control. We illustrate the operation of the algorithm through case
studies involving 8-,34- and 123-bus test distribution systems.Comment: shorter version submitted to NAPS 201
Convex relaxation of Optimal Power Flow in Distribution Feeders with embedded solar power
AbstractThere is an increasing interest in using Distributed Energy Resources (DER) directly coupled to end user distribution feeders. This poses an array of challenges because most of today's distribution feeders are designed for unidirectional power flow. Therefore when installing DERs such as solar panels with uncontrolled inverters, the upper limit of installable capacity is quickly reached in many of today's distribution feeders. This problem can often be mitigated by optimally controlling the voltage angles of inverters. However, the optimal power flow problem in its standard form is a large scale non-convex optimization problem, and thus can’t be solved precisely and also is computationally heavy and intractable for large systems. This paper examines the use of a convex relaxation using Semi-definite programming to optimally control solar power inverters in a distribution grid in order to minimize the global line losses of the feeder. The mathematical model is presented in details. Further, case studies are completed with simulations involving a 15-bus radial distribution system. These simulations are run for 24 hour periods, with actual solar data and demand data
An Optimal and Distributed Method for Voltage Regulation in Power Distribution Systems
This paper addresses the problem of voltage regulation in power distribution
networks with deep-penetration of distributed energy resources, e.g.,
renewable-based generation, and storage-capable loads such as plug-in hybrid
electric vehicles. We cast the problem as an optimization program, where the
objective is to minimize the losses in the network subject to constraints on
bus voltage magnitudes, limits on active and reactive power injections,
transmission line thermal limits and losses. We provide sufficient conditions
under which the optimization problem can be solved via its convex relaxation.
Using data from existing networks, we show that these sufficient conditions are
expected to be satisfied by most networks. We also provide an efficient
distributed algorithm to solve the problem. The algorithm adheres to a
communication topology described by a graph that is the same as the graph that
describes the electrical network topology. We illustrate the operation of the
algorithm, including its robustness against communication link failures,
through several case studies involving 5-, 34-, and 123-bus power distribution
systems.Comment: To Appear in IEEE Transaction on Power System
Novel insights into lossless AC and DC power flow
A central question in the analysis and operation of power networks is feasibility of the power flow equations subject to security constraints. For large-scale networks the solution of the nonlinear AC power flow equations can be constructed only numerically or approximated through the linear DC power flow. The latter serves as well-used approximation to obtain the phase angle differences near an acceptable operating point, but the accuracy of the DC approximation drops in a stressed grid. Here, we propose a modified DC approximation that applies to lossless networks with parametric uncertainties and with voltage magnitudes bounded within security constraints. We show that the phase angle differences can xbe well approximated by the solution to a set of linear and interval-valued equations reminiscent of the DC power flow equations. Our proposed approximation improves upon the standard DC approximation, is computationally attractive and provably exact for a broad range of network topologies and parameters. We validate the accuracy of our approximation through standard power network test cases with randomized power demand at the loads
Synchronization in Complex Oscillator Networks and Smart Grids
The emergence of synchronization in a network of coupled oscillators is a
fascinating topic in various scientific disciplines. A coupled oscillator
network is characterized by a population of heterogeneous oscillators and a
graph describing the interaction among them. It is known that a strongly
coupled and sufficiently homogeneous network synchronizes, but the exact
threshold from incoherence to synchrony is unknown. Here we present a novel,
concise, and closed-form condition for synchronization of the fully nonlinear,
non-equilibrium, and dynamic network. Our synchronization condition can be
stated elegantly in terms of the network topology and parameters, or
equivalently in terms of an intuitive, linear, and static auxiliary system. Our
results significantly improve upon the existing conditions advocated thus far,
they are provably exact for various interesting network topologies and
parameters, they are statistically correct for almost all networks, and they
can be applied equally to synchronization phenomena arising in physics and
biology as well as in engineered oscillator networks such as electric power
networks. We illustrate the validity, the accuracy, and the practical
applicability of our results in complex networks scenarios and in smart grid
applications