621 research outputs found
Distributed Discontinuous Coupling for Convergence in Heterogeneous Networks
In this letter, we propose the use of a distributed discontinuous coupling protocol to achieve convergence and synchronization in networks of non-identical nonlinear dynamical systems. We show that the synchronous dynamics is a solution to the average of the nodes' vector fields, and derive analytical estimates of the critical coupling gains required to achieve convergence
Synchrony in networks of Franklin bells
The Franklin bell is an electro-mechanical oscillator that can generate a repeating chime in the presence of an electric field. Benjamin Franklin famously used it as a lightning detector. The chime arises from the impact of a metal ball on a metal bell. Thus, a network of Franklin bells can be regarded as a network of impact oscillators. Although the number of techniques for analysing impacting systems has grown in recent years, this has typically focused on low dimensional systems and relatively little attention has been paid to networks. Here we redress this balance with a focus on synchronous oscillatory network states. We first study a single Franklin bell, showing how to construct periodic orbits and how to determine their linear stability and bifurcation. To cope with the non-smooth nature of the impacts we use saltation operators to develop the correct Floquet theory. We further introduce a new smoothing technique that circumvents the need for saltation and that recovers the saltation operators in some appropriate limit. We then consider the dynamics of a network of Franklin bells, showing how the master stability function approach can be adapted to treat the linear stability of the synchronous state for arbitrary network topolo-gies. We use this to determine conditions for network induced instabilities. Direct numerical simulations are shown to be in excellent agreement with theoretical results
On the Robust Control and Optimization Strategies for Islanded Inverter-Based Microgrids
In recent years, the concept of Microgrids (MGs) has become more popular due to a significant integration of renewable energy sources (RESs) into electric power systems. Microgrids are small-scale power grids consisting of localized grouping of heterogeneous Distributed Generators (DGs), storage systems, and loads. MGs may operate either in autonomous islanded mode or connected to the main power system. Despite the significant benefits of increasing RESs, many new challenges raise
in controlling MGs. Hence, a three layered hierarchical architecture consisting of
three control loops closed on the DGs dynamics has been introduced for MGs. The
inner loop is called Primary Control (PC), and it provides the references for the DG’s
DC-AC power converters. In general, the PC is implemented in a decentralized way
with the aim to establish, by means of a droop control term, the desired sharing of
power among DGs while preserving the MG stability. Then, because of inverterbased DGs have no inertia, a Secondary Control (SC) layer is needed to compensate
the frequency and voltage deviations introduced by the PC’s droop control terms.
Finally, an operation control is designed to optimize the operation of the MGs by
providing power setpoints to the lower control layers.
This thesis is mainly devoted to the design of robust distributed secondary frequency and voltage restoration control strategies for AC MGs to avoid central controllers and complexity of communication networks. Different distributed strategies
are proposed in this work: (i) Robust Adaptive Distributed SC with Communication delays (ii) Robust Optimal Distributed Voltage SC with Communication Delays and (iii) Distributed Finite-Time SC by Coupled Sliding-Mode Technique. In all
three proposed approaches, the problem is addressed in a multi-agent fashion where
the generator plays the role of cooperative agents communicating over a network
and physically coupled through the power system. The first approach provides an
exponentially converging voltage and frequency restoration rate in the presence of
both, model uncertainties, and multiple time-varying delays in the DGs’s communications. This approach consist of two terms: 1) a decentralized Integral Sliding
Mode Control (ISMC) aimed to enforce each agent (DG) to behaves as reference
unperturbed dynamic; 2) an ad-hoc designed distributed protocol aimed to globally, exponentially, achieves the frequency and voltage restoration while fulfilling
the power-sharing constraints in spite of the communication delays. The second
approach extends the first one by including an optimization algorithm to find the
optimal control gains and estimate the corresponding maximum delay tolerated by
the controlled system. In the third approach, the problem of voltage and frequency
restoration as well as active power sharing are solved in finite-time by exploiting
delay-free communications among DGs and considering model uncertainties. In this approach, for DGs with no direct access to their reference values, a finite-time
distributed sliding mode estimator is implemented for both secondary frequency
and voltage schemes. The estimator determines local estimates of the global reference values of the voltage and frequency for DGs in a finite time and provides this
information for the distributed SC schemes.
This dissertation also proposes a novel certainty Model Predictive Control (MPC)
approach for the operation of islanded MG with very high share of renewable energy sources. To this aim, the conversion losses of storage units are formulated by
quadratic functions to reduce the error in storage units state of charge prediction
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