7 research outputs found
A modular design of incremental Lyapunov functions for microgrid control with power sharing
In this paper we contribute a theoretical framework that sheds a new light on the problem of microgrid analysis and control. The starting point is an energy function comprising the kinetic energy associated with the elements that emulate the rotating machinery and terms taking into account the reactive power stored in the lines and dissipated on shunt elements. We then shape this energy function with the addition of an adjustable voltage-dependent term, and construct incremental storage functions satisfying suitable dissipation inequalities. Our choice of the voltage-dependent term depends on the voltage dynamics/controller under investigation. Several microgrids dynamics that have similarities or coincide with dynamics already considered in the literature are captured in our incremental energy analysis framework. The twist with respect to existing results is that our incremental storage functions allow for an analysis of the coupled microgrid obviating the need for simplifying linearization techniques and for the restrictive decoupling assumption in which the frequency dynamics is fully separated from the voltage one
A power consensus algorithm for DC microgrids
A novel power consensus algorithm for DC microgrids is proposed and analyzed.
DC microgrids are networks composed of DC sources, loads, and interconnecting
lines. They are represented by differential-algebraic equations connected over
an undirected weighted graph that models the electrical circuit. A second graph
represents the communication network over which the source nodes exchange
information about the instantaneous powers, which is used to adjust the
injected current accordingly. This give rise to a nonlinear consensus-like
system of differential-algebraic equations that is analyzed via Lyapunov
functions inspired by the physics of the system. We establish convergence to
the set of equilibria consisting of weighted consensus power vectors as well as
preservation of the weighted geometric mean of the source voltages. The results
apply to networks with constant impedance, constant current and constant power
loads.Comment: Abridged version submitted to the 20th IFAC World Congress, Toulouse,
Franc
A unifying energy-based approach to stability of power grids with market dynamics
In this paper a unifying energy-based approach is provided to the modeling
and stability analysis of power systems coupled with market dynamics. We
consider a standard model of the power network with a third-order model for the
synchronous generators involving voltage dynamics. By applying the primal-dual
gradient method to a social welfare optimization, a distributed dynamic pricing
algorithm is obtained, which can be naturally formulated in port-Hamiltonian
form. By interconnection with the physical model a closed-loop port-Hamiltonian
system is obtained, whose properties are exploited to prove asymptotic
stability to the set of optimal points. This result is extended to the case
that also general nodal power constraints are included into the social welfare
problem. Additionally, the case of line congestion and power transmission costs
in acyclic networks is covered. Finally, a dynamic pricing algorithm is
proposed that does not require knowledge about the power supply and demand.Comment: 11 pages, submitted to TAC, accepted. arXiv admin note: text overlap
with arXiv:1510.0542
A modular design of incremental Lyapunov functions for microgrid control with power sharing
In this paper we contribute a theoretical framework that sheds a new light on the problem of microgrid analysis and control. The starting point is an energy function comprising the kinetic energy associated with the elements that emulate the rotating machinery and terms taking into account the reactive power stored in the lines and dissipated on shunt elements. We then shape this energy function with the addition of an adjustable voltage-dependent term, and construct incremental storage functions satisfying suitable dissipation inequalities. Our choice of the voltage-dependent term depends on the voltage dynamics/controller under investigation. Several microgrids dynamics that have similarities or coincide with dynamics already considered in the literature are captured in our incremental energy analysis framework. The twist with respect to existing results is that our incremental storage functions allow for an analysis of the coupled microgrid obviating the need for simplifying linearization techniques and for the restrictive decoupling assumption in which the frequency dynamics is fully separated from the voltage one
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