arXiv subjects

Nima Monshizadeh

Publications and source records attributed to Nima Monshizadeh.

47 records · Page 3Linked to original sources

arXiv2017

Conditions on Shifted Passivity of Port-Hamiltonian Systems

In this paper, we examine the shifted passivity property of port-Hamiltonian systems. Shifted passivity accounts for the fact that in many applications the desired steady-state values of the input and output variables are nonzero, and thus one is interested in passivity with respect to the shifted signals. We consider port-Hamiltonian systems with strictly convex Hamiltonian, and derive conditions under which shifted passivity is guaranteed. In case the Hamiltonian is quadratic and state dependency appears in an affine manner in the dissipation and interconnection matrices, our conditions reduce to negative semidefiniteness of an appropriately constructed constant matrix. Moreover, we elaborate on how these conditions can be extended to the case when the shifted passivity property can be enforced via output feedback, thus paving the path for controller design. Stability of forced equilibria of the system is analyzed invoking the proposed passivity conditions. The utility and relevance of the results are illustrated with their application to a 6th order synchronous generator model as well as a controlled rigid body system.

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arXiv2017

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.

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arXiv2017

Exponential convergence under distributed averaging integral frequency control

We investigate the performance and robustness of distributed averaging integral controllers used in the optimal frequency regulation of power networks. We construct a strict Lyapunov function that allows us to quantify the exponential convergence rate of the closed-loop system. As an application, we study the stability of the system in the presence of disruptions to the controllers' communication network, and investigate how the convergence rate is affected by these disruptions.

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arXiv2017

Stability and optimality of distributed secondary frequency control schemes in power networks

We present a systematic method for designing distributed generation and demand control schemes for secondary frequency regulation in power networks such that stability and an economically optimal power allocation can be guaranteed. A dissipativity condition is imposed on net power supply variables to provide stability guarantees. Furthermore, economic optimality is achieved by explicit decentralized steady state conditions on the generation and controllable demand. We discuss how various classes of dynamics used in recent studies fit within our framework and give examples of higher order generation and controllable demand dynamics that can be included within our analysis. In case of linear dynamics, we discuss how the proposed dissipativity condition can be efficiently verified using an appropriate linear matrix inequality. Moreover, it is shown how the addition of a suitable observer layer can relax the requirement for demand measurements in the employed controller. The efficiency and practicality of the proposed results are demonstrated with a simulation on the Northeast Power Coordinating Council (NPCC) 140-bus system.

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arXiv2016

A Novel Reduced Model for Electrical Networks with Constant Power Loads

We consider a network-preserved model of power networks with proper algebraic constraints resulting from constant power loads. Both for the linear and the nonlinear differential algebraic model of the network, we derive explicit reduced models which are fully expressed in terms of ordinary differential equations. For deriving these reduced models, we introduce the "projected incidence" matrix which yields a novel decomposition of the reduced Laplacian matrix. With the help of this new matrix, we provide a complementary approach to Kron reduction which is able to cope with constant power loads and nonlinear power flow equations.

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arXiv2016

Bregman storage functions for microgrid control

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 a large signal 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 complete Lyapunov stability analysis of the various systems is carried out along with a discussion on their active and reactive power sharing properties.

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arXiv2016

A Communication-Free Master-Slave Microgrid with Power Sharing

In this paper a design of a master-slave microgrid consisting of grid-supporting current source inverters and a synchronous generator is proposed. The inverters are following the frequency of the grid imposed by the synchronous generator. Hence, the proposed structure of the microgrid is steadily synchronized. We show that the method achieves power sharing without the need of communication. Furthermore, no change in operation mode is needed during transitions of the microgrid between islanded and grid-connected modes.

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arXiv2016

Nonlinear Analysis of an Improved Swing Equation

In this paper, we investigate the properties of an improved swing equation model for synchronous generators. This model is derived by omitting the main simplifying assumption of the conventional swing equation, and requires a novel analysis for the stability and frequency regulation. We consider two scenarios. First we study the case that a synchronous generator is connected to a constant load. Second, we inspect the case of the single machine connected to an infinite bus. Simulations verify the results.

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arXiv2015

Output agreement in networks with unmatched disturbances and algebraic constraints

This paper considers a problem of output agreement in heterogeneous networks with dynamics on the nodes as well as on the edges. The control and disturbance signals entering the nodal dynamics are "unmatched" meaning that some nodes are only subject to disturbances, and are deprived of actuating signals. To further enrich our model, we accommodate (solvable) algebraic constraints in a subset of nodal dynamics. We show that appropriate dynamic feedback controllers achieve output agreement on a desired vector. We also investigate the case of an optimal steady-state control over the network. The proposed results are applied to a heterogeneous microgrid.

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arXiv2014

Structure-preserving model reduction of physical network systems by clustering

In this paper, we establish a method for model order reduction of a certain class of physical network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the same class. To capture the physical properties of the network, we allow for weights associated to both the edges as well as the vertices of the graph. We extend the notion of almost equitable partitions to this class of graphs. Consequently, an explicit model reduction error expression in the sense of H2-norm is provided for clustering arising from almost equitable partitions. Finally the method is extended to second-order systems.

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arXiv2014

Zero forcing sets and controllability of dynamical systems defined on graphs

In this paper, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established. To illustrate the proposed results, special cases including path, cycle, and complete graphs are discussed. Moreover, as shown for graphs with a tree structure, the proposed results of the present paper together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases.

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