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We propose a novel state estimation algorithm for consensus dynamics subject to measurement error. We first demonstrate that with properly tuned parameters, our algorithm attains the same equilibrium value that would be attained using the traditional algorithm based on local state feedback (nominal consensus). We then show that our approach improves consensus performance in a particular class of problems by reducing the state error (i.e., the difference between the agent states and the consensus value). A numerical example compares the performance of the distributed algorithm we propose to that of the traditional local feedback scheme. The results show that the proposed algorithm significantly reduces the state error. 

Voltage collapse is a type of blackout-inducing dynamic instability that occurs when the power demand exceeds the maximum power that can be transferred through the network. The traditional (preventive) approach to avoid voltage collapse is based on ensuring that the network never reaches its maximum capacity. However, such an approach leads to inefficiencies as it prevents operators to fully utilize the network resources and does not account for unprescribed events. To overcome this limitation, this paper seeks to initiate the study of voltage collapse stabilization. More precisely, for a DC star network, we formulate the problem of voltage stability as a dynamic problem where each load seeks to achieve a constant power consumption by updating its conductance as the voltage changes. We show that such a system can be interpreted as a game, where each player (load) seeks to myopically maximize their utility using a gradient-based response. Using this framework, we show that voltage collapse is the unique Nash Equilibrium of the induced game and is caused by the lack of cooperation between loads. Finally, we propose a Voltage Collapse Stabilizer (VCS) controller that uses (flexible) loads that are willing to cooperate and provides a fair allocation of the curtailed demand. Our solution stabilizes voltage collapse even in the presence of non-cooperative loads. Numerical simulations validate several features of our controllers. 

This work investigates local and global measures of disorder in large-scale directed networks of double-integrator systems connected over a multi-dimensional torus. We quantify these performance measures in systems subjected to distributed disturbances using an H2 norm with outputs corresponding to local state errors or deviations from the global average. We consider two directed uni-directional state feedback inter- connections that correspond to relative position and relative velocity feedback in vehicle network applications. Our main result reveals that absolute state feedback plays a critical role in system robustness when local state measurements are uni- directional. Specifically, if absolute measurements of either state variable are available, then systems with uni-directional relative feedback perform as well as their symmetric bi-directional counterparts but have the advantage of reduced communication requirements. However in the absence of absolute feedback their performance is worse; in fact, it is impossible to maintain stability (i.e. a finite H2 norm) with uni-directional state mea- surements for arbitrarily large networks. Numerical examples illustrate the theory. 

The AC frequency in electrical power systems is conventionally regulated by synchronous machines. The gradual replacement of these machines by asynchronous renewable-based generation, which provides] little or no frequency control, increases system uncertainty and risk of instability. This poses hard limits on the proportion of renewables that can be integrated into the system. To address this issue, in this paper, we develop a framework for performing frequency control in power systems with arbitrary mixes of conventional and renewable generation. Our approach is based on a robust stability criterion that can be used to guarantee the stability of a full power system model based on a set of decentralised tests, one for each component in the system. It can be applied even when using detailed heterogeneous component models and can be verified using several standard frequency response, state-space, and circuit theoretic analysis tools. By designing decentralised controllers for individual components to meet these decentralised tests, strong apriori robust stability guarantees, that hold independently of the operating point and remain valid even as components are added to and removed from the grid, can be given. This allows every component to contribute to the regulation of system frequency in a simple and provable manner. Notably, our framework certifies the stability of several existing (non-passive) power system control schemes and models, and allows for the study of robustness with respect to delays. 

This paper characterizes synchronization perfor- mance and total transient power losses in droop-controlled microgrids with heterogeneously rated inverters. We consider frequency and voltage dynamics for a Kron-reduced network model with highly inductive lines in the presence of impulse disturbances. We quantify the total transient frequency and voltage deviations from synchrony and the associated total transient resistive losses through the L 2 norm of the system output. We derive closed-form expressions for this norm that depend on the heterogeneous droop gains and properties of the network. Our results indicate the importance of inertia in mitigating transient frequency deviations. We also show that if disturbances are uniform, the transient resistive losses are given by a monotonically decreasing function of the active power droop gains regardless of the network topology. Numerical examples further analyze these losses, revealing that they can be amplified by high droop gain heterogeneity. This relationship indicates that non-uniform power sharing requirements can limit performance. 

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. 

Consensus algorithms constitute a powerful tool for computing average values or coordinating agents in many distributed applications. Unfortunately, the same property that allows this computation (i.e., the nontrivial nullspace of the state matrix) leads to unbounded state variance in the presence of measurement errors. In this work, we explore the trade-off between relative and absolute communication (feedback) in the presence of measurement errors. We evaluate the robustness of first and second-order integrator systems under a parameterized family of controllers (homotopy), that continuously trade between relative and absolute feedback interconnections, in terms of the H 2 norm of an appropriately defined input-output system. Our approach extends the previous H 2 norm-based analysis to systems with directed feedback interconnections whose underlying weighted graph Laplacians are diagonalizable. Our results indicate that any level of absolute communication is sufficient to achieve a finite H 2 norm, but purely relative feedback can only achieve finite norms when the measurement error is not exciting the subspace associated with the consensus state. Numerical examples demonstrate that smoothly reducing the proportion of absolute feedback in double integrator systems smoothly decreases the system performance (increases the H 2 norm) and that this performance degradation is more rapid in systems with relative feedback in only the first state (position). 

We consider the problem of designing a feedback controller that guides the input and output of a linear time-invariant system to a minimizer of a convex optimization problem. The system is subject to an unknown disturbance that determines the feasible set defined by the system equilibrium constraints. Our proposed design enforces the Karush-Kuhn-Tucker optimality conditions in steady-state without incorporating dual variables into the controller. We prove that the input and output variables achieve optimality in equilibrium and outline two procedures for designing controllers that stabilize the closed-loop system. We explore key ideas through simple examples and simulations.