203 research outputs found
A Lyapunov Approach to Control of Microgrids with a Network-Preserved Differential-Algebraic Model
We provide sufficient conditions for asymptotic stability and optimal resource allocation for a networkpreserved microgrid model with active and reactive power loads. The model considers explicitly the presence of constantpower loads as well as the coupling between the phase angle and voltage dynamics. The analysis of the resulting nonlinear differential algebraic equation (DAE) system is conducted by leveraging incremental Lyapunov functions, definiteness of the load flow Jacobian and the implicit function theorem
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
Stabilization of structure-preserving power networks with market dynamics
This paper studies the problem of maximizing the social welfare while
stabilizing both the physical power network as well as the market dynamics. For
the physical power grid a third-order structure-preserving model is considered
involving both frequency and voltage dynamics. By applying the primal-dual
gradient method to the social welfare problem, a distributed dynamic pricing
algorithm in port-Hamiltonian form is obtained. After interconnection with the
physical system a closed-loop port-Hamiltonian system of differential-algebraic
equations is obtained, whose properties are exploited to prove local asymptotic
stability of the optimal points.Comment: IFAC World Congress 2017, accepted, 6 page
Gather-and-broadcast frequency control in power systems
We propose a novel frequency control approach in between centralized and
distributed architectures, that is a continuous-time feedback control version
of the dual decomposition optimization method. Specifically, a convex
combination of the frequency measurements is centrally aggregated, followed by
an integral control and a broadcast signal, which is then optimally allocated
at local generation units. We show that our gather-and-broadcast control
architecture comprises many previously proposed strategies as special cases. We
prove local asymptotic stability of the closed-loop equilibria of the
considered power system model, which is a nonlinear differential-algebraic
system that includes traditional generators, frequency-responsive devices, as
well as passive loads, where the sources are already equipped with primary
droop control. Our feedback control is designed such that the closed-loop
equilibria of the power system solve the optimal economic dispatch problem
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
Stability and Frequency Regulation of Inverters with Capacitive Inertia
In this paper, we address the problem of stability and frequency regulation
of a recently proposed inverter. In this type of inverter, the DC-side
capacitor emulates the inertia of a synchronous generator. First, we remodel
the dynamics from the electrical power perspective. Second, using this model,
we show that the system is stable if connected to a constant power load, and
the frequency can be regulated by a suitable choice of the controller. Next,
and as the main focus of this paper, we analyze the stability of a network of
these inverters, and show that frequency regulation can be achieved by using an
appropriate controller design. Finally, a numerical example is provided which
illustrates the effectiveness of the method
Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Trade-Offs
Frequency restoration in power systems is conventionally performed by
broadcasting a centralized signal to local controllers. As a result of the
energy transition, technological advances, and the scientific interest in
distributed control and optimization methods, a plethora of distributed
frequency control strategies have been proposed recently that rely on
communication amongst local controllers.
In this paper we propose a fully decentralized leaky integral controller for
frequency restoration that is derived from a classic lag element. We study
steady-state, asymptotic optimality, nominal stability, input-to-state
stability, noise rejection, transient performance, and robustness properties of
this controller in closed loop with a nonlinear and multivariable power system
model. We demonstrate that the leaky integral controller can strike an
acceptable trade-off between performance and robustness as well as between
asymptotic disturbance rejection and transient convergence rate by tuning its
DC gain and time constant. We compare our findings to conventional
decentralized integral control and distributed-averaging-based integral control
in theory and simulations
Distributed Optimal Frequency Control Considering a Nonlinear Network-Preserving Model
This paper addresses the distributed optimal frequency control of power
systems considering a network-preserving model with nonlinear power flows and
excitation voltage dynamics. Salient features of the proposed distributed
control strategy are fourfold: i) nonlinearity is considered to cope with large
disturbances; ii) only a part of generators are controllable; iii) no load
measurement is required; iv) communication connectivity is required only for
the controllable generators. To this end, benefiting from the concept of
'virtual load demand', we first design the distributed controller for the
controllable generators by leveraging the primal-dual decomposition technique.
We then propose a method to estimate the virtual load demand of each
controllable generator based on local frequencies. We derive incremental
passivity conditions for the uncontrollable generators. Finally, we prove that
the closed-loop system is asymptotically stable and its equilibrium attains the
optimal solution to the associated economic dispatch problem. Simulations,
including small and large-disturbance scenarios, are carried on the New England
system, demonstrating the effectiveness of our design
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