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Photovoltaic (PV) inverters typically have a multiloop control architecture to facilitate extraction of maximum possible dc-side power and its transfer to an ac-side grid interconnection. In this paper, we integrate dc-side controls that modulate the dc-link voltage for peak PV power harvest with an ac-side dispatchable virtual oscillator controller (dVOC) that synchronizes to the grid. In particular, maximum power point tracking is realized via integral control which then generates a dc-link voltage command. From there, dc-side voltage regulation is achieved by modulating the power reference sent to the ac-side dVOC. The dVOC yields an ac voltage command which is tracked with nested voltage- and current-control loops in the synchronous reference frame. Ac-side functions are topped off with an ac-side current limiter to ensure proper operation during large grid transients. We then analyze the eigenvalues of this interconnected system and its participation factors to demonstrate timescale separation of the various control loops. The proposed framework is substantiated via simulations and experiments.

Three-level neutral-point clamped inverter (3LNPCI) is a widely popular topology in the realm of multi-level inverters. The low frequency third-harmonic neutral-point (NP) current in a 3L-NPCI and the corresponding NP-voltage oscillations on the DC-side are known characteristics of the 3L-inverter. In this paper, a quantitative analysis is presented for characterizing the DC-side third-harmonic phenomena observed in 3LNPCI. Departing from the traditional space-vector perspective, an alternate formulation based on time-domain functions and Fourier-series is adopted, and an analytical expression for the 3rd harmonic NP-current is derived as a function of inverter modulation index and load power factor–this is applicable for all conventional carrier-based PWM techniques employed on 3LNPCIs. The corresponding NP-voltage variation on the DC-side and its translation onto the AC-side as low-frequency harmonic distortions in the inverter output voltage are analytically quantified. Based on this, a model-based observer is designed to mitigate the AC side distortions through accurate estimation of the disturbance variables and feed-forward cancellation. Experimental results along with a full-order switched model simulation of a three-phase 3L-NPCI system validate the theoretical analysis and mitigation technique proposed in this paper.

This paper presents a hybrid analog/digital computing circuit that solves a form of the selective harmonic minimization problem in a fast and scalable manner. Voltages in the circuit represent variables in the optimization problem, and, in steady state, converge to the optimal solution of the problem. A digital microcontroller sets voltages at particular nodes in the circuit as to program the cost function and other inputs to the optimization. We present a specific realization of the computing circuit that solves for eight independent switching angles for a quarter-wave symmetric PWM driven two-level single-phase inverter. This realization minimizes seven undesired harmonics while also maintaining control of the modulation index. The simulation results demonstrate that the proposed circuit can converge to the optimal solution in less than 5.0 ms. Our survey of prior methods indicates that this is substantially faster than existing published methods in the literature.

This paper demonstrates how equivalent-circuit representations of grid-following power-electronic inverters can be realized within a SPICE-based development environment using common circuit components and VerilogA code. This facilitates computationally lean simulations of inverter networks leveraging the strengths of SPICE in large-scale simulations. We validate the approach with time-domain simulations for a modified version of the IEEE standard 118-bus system modeled in Virtuoso (a SPICE-based solver). Simulation results are compared—focusing on accuracy and computation speed—with results from a commonly used power-electronics simulation package. We note a significant decrease in simulation time with comparable signal resolution when simulating the network in SPICE.

Virtual oscillator control (VOC) is a time-domain strategy for regulating the operation of grid-forming (GFM) inverters. The premise of this method is to leverage the dynamics of nonlinear oscillator circuits to realize controllers; the time-domain nature of the resulting implementation is starkly different from classical droop control methods. This paper considers VOC realized with the dynamics of the Andronov-Hopf oscillator, a second-order nonlinear dynamical system that enables GFM inverters to be dispatched and generate low-harmonic outputs while not compromising dynamic performance. Leveraging an equilibrium analysis of the involved dynamics and small-signal models, we put forth a side-by-side comparison of dynamic performance and small-signal stability with classical droop control. The results demonstrate superior dynamic performance of VOC, and broadly, the paper furthers efforts focused on modeling and analysis of this general class of GFM controllers.

Voltage controlled inverters in ac systems are susceptible to damage if the controller is not properly initialized before startup. Since currents are not controlled explicitly, the voltage reference of the controller must be closely aligned with the point of common coupling voltage to prevent large current transients when power delivery begins. In this paper, we are focused on a particular control strategy called virtual oscillator control and propose a pre-synchronization method that guarantees graceful addition of units into an existing ac system. The proposed method is generalized and can be used to add oscillator-controlled inverters to a stiff grid or an islanded microgrid with other inverters. An equivalent circuit model of the pre-synchronization control is derived along with its dynamical properties, design guidelines are given, and experimental results are shown for a 1.5kW inverter.

This paper outlines a combination of two data-driven approaches leveraging sum-of-squares (SoS) optimization to: i) learn the power-voltage (p - v) characteristic of photovoltaic (PV) arrays, and ii) rapidly regulate operation of the companion PV inverter to a desired power setpoint. Estimation of available headroom in PV systems is critical to the task of providing ancillary services, and the proposed method puts forth a computationally tractable solution with minimal data needs for the same. In addition to providing this key contribution to application, from an algorithmic vantage point, we present an interior-point method to solve a linear regression reformulation of the original polynomial fitting problem with SoS constraints. We validate the proposed algorithms through time-domain numerical simulations (incorporating the PV source and a 15-th order inverter model) for a variety of large-signal disturbances (step changes in real-power demand, rapid changes in irradiance) and demonstrate that the method provides an effective strategy to concomitantly discover the p - v curve and seamlessly regulate operation to a desired setpoint.

In this work, we aim to minimize the cost of generation in a power system while meeting demand in near-to real time. The proposed architecture is composed of two sub-problems: continuous-time economic dispatch (CTED) and optimal automatic generation control (OAGC). In its original form, the CTED problem incorporates generator aggregate-frequency dynamics, and it is infinite-dimensional. However, we present a computationally tractable function space-based solution method for the proposed problem. We also develop an optimization-based control algorithm for implementing OAGC. Theoretical considerations for decoupling the two problems are explored. We validate the economic efficiency and frequency performance of the proposed method through simulations of a representative power network.

This paper discusses methods for model reduction of power system dynamics. Dynamical models for realistic power-systems can very easily contain several thousands of states. The dimensionality increases further when considering the dynamics of distributed energy resources; these systems are typically smaller in power rating, so many more are installed at the grid edge to scale capacity. Computationally efficient models that capture the dominant modes of the system are important for all aspects of power-system operation, control, and analysis. In this paper, we analyze two data-driven methods for model reduction of power systems: i) proper orthogonal decomposition, which is based on singular value decomposition, and ii) a constrained convex-optimization framework with stability guarantees. Advantages and disadvantages of both of these methods are discussed. Exhaustive numerical simulations for a low-inertia system with mixed synchronous generator and wind energy conversion system resources are provided to verify the accuracy of the model-reduction methods.

Optimization problems are commonplace across energy, manufacturing, and communication industries. Efforts across academia are largely centered on theoretical properties and solution algorithms for optimization problems. Limited attention has been paid to systematically address challenges involved in implementing algorithms on end-use hardware platforms that are typically resource and power constrained. Through this paper, we seek to uncover the link between algorithmic considerations (e.g., convergence, precision) and hardware resources (e.g., memory utilization, gate usage) when optimization problems are deployed on general-purpose microcontrollers: a class of embedded systems with low power consumption and high configurability. Without loss of generality, we focus our attention on first-order optimization methods implemented on the popular MSP430 microcontroller architecture. We outline a strategy to architect bespoke microcontrollers that are optimized to improve cost, power, and other performance metrics for a particular algorithm. In so doing, we take a critical step in bridging the gap between theoretical properties of optimization problems, algorithmic considerations in algorithms, and design goals for computer architecture.

In this paper, we present a virtual oscillator control (VOC) strategy for power inverters to operate in either grid-connected or islanded settings. The proposed controller is based on the dynamics of the nonlinear Andronov-Hopf oscillator and it provides voltage regulation, frequency support in islanded mode. It also features the potential to respond to real- and reactive-power setpoints for dispatchability in grid-connected mode. In contrast to early VOC incarnations which exhibit undesirable harmonics, the proposed controller offers a sinusoidal ac limit cycle as well as improved dynamic performance. Moreover, the proposed controller intrinsically generates orthogonal signals which facilitate implementation in three-phase systems. We study the controller dynamical model and outline a systematic design procedure such that the inverter satisfies standard ac performance specifications. Numerical simulations validate the analytical developments.

This paper outlines an approach to perform small-signal stability analysis of a power network with conventional synchronous generators and a wind farm composed of Type-3 wind turbines as the number of turbines in the farm is varied. An enabling ingredient to perform this analysis is a dynamic reduced-order aggregate model for a wind farm that preserves the model order and structure of individual wind turbines. This facilitates stability analysis since the number of wind turbines can be varied with ease and small-signal stability of the mixed machine and inverter-interfaced turbines can be examined systematically. Although there is a vast body of literature on small-signal stability of wind farms, penetration level of wind farms is significantly less studied in this context; this paper introduces a systematic approach for such an analysis. Case studies for a modified Kundur two-area system with an integrated wind farm indicate that as the number of wind turbines is increased to a point that the penetration level is approximately 25%, there is a loss of small-signal stability. We validate this with time-domain simulations for the nonlinear system dynamics and also propose a redesign strategy grounded in a system-theoretic analysis of the dynamical models.

This paper presents a model to capture the electromechanical dynamics of a wind turbine with hydrostatic transmission (HST) coupled to the electrical grid through a synchronous generator. The HST is a continuously variable transmission that decouples the generator from the wind-turbine rotor shaft, which allows it to rotate at its synchronous speed. The topology does not include any power-electronics interfaces for energy conversion. The dynamic model of the HST and synchronous generator are used to examine the performance of the system under various disturbances in incident wind through detailed time-domain simulations. We find that with the proposed topology, the terminal voltage and frequency of the generator can be well regulated under a variety of large-signal disturbances.

This paper presents an aggregate reduced-order model for a wind farm composed of identical parallel-connected Type-3 wind turbines. The model for individual turbines includes mechanical dynamics (arising from the turbine and doubly fed induction generator) and electrical dynamics (arising from the rotor-side and grid-side converters and associated filters). The proposed aggregate wind-farm model is structure preserving, in the sense that the parameters of the model are derived by scaling corresponding ones from the individual turbines. The aggregate model hence maps to an equivalent--albeit fictitious--wind turbine that captures the dynamics corresponding to the entire wind farm. The reduced-order model has obvious computational advantages, but more importantly, the presented analysis rigorously formalizes parametric scalings for aggregate wind-turbine models that have been applied with limited justification in prior works. Exhaustive numerical simulations validate the accuracy and computational benefits of the proposed reduced-order model.

This paper proposes a strategy to regulate active-and reactive-power injections of a collection of dispatchable inverters so that the distribution feeder where they are installed can, in aggregate, track active-and reactive-power regulation signals issued by a higher-level aggregator. At its core, the proposed method relies on the linear mapping of nodal active-and reactive-power injections to the active and reactive power injected into the bulk transmission grid and a linear-quadratic-regulator (LQR) controller. We demonstrate the effectiveness of the proposed LQR controller using regulation signals from Pennsylvania-New Jersey-Maryland Interconnection (PJM) for a collection of 15 inverters (each with a 15th-order model capturing phase locked loop, LCL filter, power-and current-controller dynamics) installed in a modified IEEE 37-bus distribution feeder. We also evaluate the ability of the proposed controller to track regulation signals with different sampling and dispatch rates.

In this paper, we introduce a method to analyze three-phase inverters with current control as equivalent circuits. In contrast to existing methods, both the averaged power stage model and its closed-loop controller are represented as a single unified circuit. Since the complete system can be examined as one equivalent circuit, we can glean several insights on design and operation; particularly relating to the time scales at which the controller tracks reference signals and the ability to reject disturbances. We leverage the insights afforded by this general approach to outline design strategies for controllers in both synchronous and stationary reference frames.

Ratings of utility-scale grid-tied photovoltaic (PV) inverters are typically no more than 1 MVA. This implies that a large number of inverters are usually installed in utility-scale PV energy-conversion systems. Given the complexity of inverter dynamic models (typical models are high dimension and nonlinear), reduced-order models for inverters are critical for performance assessment and accurate representation of PV-system dynamics in the bulk power grid with limited computational burden. In this paper, we formulate a reduced-order model for parallel- connected grid-tied three-phase PV inverters that has the same structure and model order as a single inverter. We adopt a singlediode model for the PV modules, and each inverter is assumed to be a single-stage dc-ac voltage-source converter with an input dc- link capacitor and an LCL output filter. The control architecture includes a maximum power point tracking (MPPT) algorithm, a dc-link voltage controller, a reactive power controller, a current controller, and a phase-locked loop for grid synchronization. Numerical simulations demonstrate the computational benefits and accuracy of the reduced-order model.

Virtual oscillator control (VOC) is a decentralized time-domain control technique for ac microgrids where inverters are regulated to emulate the dynamics of weakly nonlinear oscillators. VOC enables the design of modular and scalable systems where inverters can synchronize and share power without communication and in near real-time. In this paper, we show how off-the-shelf commercial inverters with current control can be reprogrammed to behave as voltage sources with virtual oscillator dynamics for deployment in islanded settings. We focus on commercial grid-tied inverters that have an inner current-control loop and show how the outer-loop controls can be straightforwardly modified to enable voltage-control-mode operation. To illustrate the practicality and ease of our approach, the proposed strategy was implemented on a 3.2 kVA experimental test bed composed of 10 SunPower-brand micro-inverters with special firmware for VOC implementation. Results from the experiments not only demonstrate feasibility of the proposed dual-loop VOC architecture on a hardware setup but also show improved voltage regulation due to the additional voltage control loop.

We study the dynamics of Van der Pol oscillators in a class of electrical networks with the goal of synthesizing feedback strategies to stabilize either phase-synchronized or phase-balanced motions. The electrical networks are composed of transmission lines with series R-L circuit models that are uniform, by which we mean that the R-to-L ratios of all lines are the same. The oscillators are coupled through linear filters on their output currents to nodes in the network. Our main results illustrate how the signs of the local feedback gains determine the stability of either phase-synchronized or phase-balanced trajectories. The results have implications on (and indeed, the paper is motivated by) decentralized control of power converters: synchronized solutions are of interest in parallel-connected dc-ac inverters and phase-balanced solutions are of interest in interleaving switching waveforms for multiphase dc-dc converters.

We present a small-signal stability study of a coupled synchronous generator and inverter system, where the inverter is controlled by virtual oscillator control (VOC). VOC is a recently proposed grid-forming inverter control strategy, which acts on faster time scales compared to droop control. In our study, we leverage a scalable VOC controller (that is by design agnostic of power levels) to test the system's small-signal stability at different inverter penetration levels. The impact of rotational inertia, reactive power support, and filter parameters on stability is then investigated. Results highlight possible issues that might arise in these mixed machine-inverter systems further motivating the need to develop next generation stabilizing grid-forming controllers.

This paper describes a virtual oscillator based approach to synchronize series-connected single-phase inverters. Each inverter controller includes a digital implementation of a Van der Pol oscillator. When connected in series, such inverters synchronize automatically, without the need for a central controller, communication channels, phase locked loops, or additional hardware such as powerline communication. A linearization-based analysis is used to prove system stability of the synchronized state. The approach is experimentally verified on a 180 W system consisting of three 60 W inverters.

This paper introduces a reduced-order aggregated model for parallel-connected inverters controlled with virtual oscillator control (VOC). The premise of VOC is to modulate inverter dynamics to emulate those of nonlinear oscillators with the goal of realizing a stable ac microgrid in the absence of communication, synchronous generation, or a stiff grid. To obtain a reduced-order model for a system of parallel-connected inverters with VOC, we first formulate a set of scaling laws that describe how the controller and filter parameters of a given inverter depend on its voltage and power rating. Subsequently, we show that $N$ parallel inverters which adhere to this scaling law can be modeled with the same structure and hence the same computational burden of the model of a single inverter. The proposed aggregate model is experimentally validated on a system of three parallel inverters with heterogeneous power ratings.

This paper introduces the notion of minimum distortion point tracking (MDPT): a control paradigm for input- or output-parallel connected dc-dc converters where switching waveforms are optimally phase shifted to minimize the total dc-bus ripple power. In a sense, MDPT generalizes the ubiquitous concept of interleaving in balanced multiphase dc-dc converters to a broad class of asymmetric input- or output-parallel connected dc-dc converters. Realizing power-quality improvement with control design implies that a drastic reduction in passive input or output filters can be achieved. This paper presents the mathematical characterization of the minimum distortion point (MDP) and a technique for MDPT. An experimental case study for three 600 W dc-dc converters demonstrates a 3× reduction in the bus voltage ripple, convergence to a static MDP in 40 ms, and the ability to dynamically track a time-varying MDP.

Motivated by potential applications for power-electronic converters in microgrids, we study the problem of global asymptotic synchronization of Lienard-type nonlinear oscillators in heterogenous LTI electrical networks with series R-L circuits modeling interconnections. By heterogeneous, we mean that the resistance-to-inductance ratios of the lines are not all the same. Building on our previous work, we derive sufficient conditions for global asymptotic synchronization by using a first-order filter on the outputs of the oscillators. Our approach leverages a coordinate transformation to a system that emphasizes signal differences and the use of passivity based arguments to establish synchronization of the network of oscillators asymptotically. The analysis subsumes and generalizes previous conditions that have been derived for Lienard oscillators in homogeneous electrical networks. Numerical simulations are provided to validate the results.

We synthesize a feedback for a fully connected network of identical Liénard-type oscillators such that the phase-balanced equilibrium - the mode where the centroid of the coupled oscillators in polar coordinates is at the origin - is asymptotically stable, and the phase-synchronized equilibrium is unstable. Our approach hinges on a coordinate transformation of the oscillator dynamics to polar coordinates, and periodic averaging theory to simplify the examination of multiple time-scale behavior. Using Lyapunov- and linearization-based arguments, we demonstrate that the oscillator dynamics have the same radii and balanced phases in steady state for a large set of initial conditions. Numerical simulation results are presented to validate the analyses.

This paper presents a continuous-time semidefinite-programming method for bounding statistics of stochastic processes governed by stochastic differential-algebraic equations with trigonometric and polynomial nonlinearities. Upper and lower bounds on the moments are then computed by solving linear optimal control problems for an auxiliary linear control system in which the states and inputs are systematically constructed vectors of mixed algebraic-trigonometric moments. Numerical simulations demonstrate how the method can be applied to solve moment-closure problems in representative systems described by stochastic differential algebraic equation models.

Synchronous machines have traditionally acted as the foundation of large-scale electrical infrastructures and their physical properties have formed the cornerstone of system operations. However, with the increased integration of distributed renewable resources and energy-storage technologies, there is a need to systematically acknowledge the dynamics of power-electronics inverters — the primary energy-conversion interface in such systems — in all aspects of modeling, analysis, and control of the bulk power network. In this paper, we assess the properties of coupled machine-inverter systems by studying an elementary system comprised of a synchronous generator, three-phase inverter, and a load. The inverter model is formulated such that its power rating can be scaled continuously across power levels while preserving its closed-loop response. Accordingly, the properties of the machine-inverter system can be assessed for varying ratios of machine-to-inverter power ratings. After linearizing the model and assessing its eigenvalues, we show that system stability is highly dependent on the inverter current controller and machine exciter, thus uncovering a key concern with mixed machine-inverter systems and motivating the need for next-generation grid-stabilizing inverter controls.

Next-generation power networks will contain large numbers of grid-connected inverters satisfying a significant fraction of system load. Since each inverter model has a relatively large number of dynamic states, it is impractical to analyze complex system models where the full dynamics of each inverter are retained. To address this challenge, we derive a reduced-order structure-preserving model for parallel-connected grid-tied three-phase inverters. Here, each inverter in the system is assumed to have a full-bridge topology, LCL filter at the point of common coupling, and the control architecture for each inverter includes a current controller, a power controller, and a phase-locked loop for grid synchronization. We outline a structure-preserving reduced-order inverter model with lumped parameters for the setting where the parallel inverters are each designed such that the filter components and controller gains scale linearly with the power rating. By structure preserving, we mean that the reduced-order three-phase inverter model is also composed of an LCL filter, a power controller, current controller, and PLL. We show that the system of parallel inverters can be modeled exactly as one aggregated inverter unit and this equivalent model has the same number of dynamical states as any individual inverter in the system. Numerical simulations validate the reduced-order model.

The existing transmission network is becoming increasingly overloaded due to rapidly growing electricity demand, deregulation, and limited investment in transmission network expansion. This paper presents a state-space model-based control design for regulating line active-power flows in AC electric power systems using linear-quadratic-Gaussian (LQG) control. At its core, the proposed method relies on the linear mapping of nodal active- and reactive-power injections to active-power line flows. Building on this, we outline a combined linear-quadratic regulator and Kalman-filter design to optimally dispatch generators and controllable loads to maintain line flows while ensuring power balance. We demonstrate the utility of the proposed LQG controller with a representative congestion-management application.

Virtual oscillator control (VOC) and droop control are distinct methods to ensure synchronization and power sharing of parallel inverters in islanded systems. VOC is a control strategy where the dynamics of a nonlinear oscillator are used to derive control states to modulate the switch terminals of an inverter. Since VOC is a time-domain controller that reacts to instantaneous measurements with no additional filters or computations, it provides a rapid response during transients and stabilizes volatile dynamics. In contrast, droop control regulates the inverter voltage in response to the measured average real and reactive power output. Given that real and reactive power are phasor quantities that are not well-defined in real time, droop controllers typically use multiplicative operations in conjunction with low-pass filters on the current and voltage measurements to calculate such quantities. Since these filters must suppress low frequency ac harmonics, they typically have low cutoff frequencies that ultimately impede droop controller bandwidth. Although VOC and droop control can be engineered to produce similar steady-state characteristics, their dynamic performance can differ markedly. This paper presents an analytical framework to characterize and compare the dynamic response of VOC and droop control. The analysis is experimentally validated with three 120 V inverters rated at 1kW, demonstrating that for the same design specifications VOC is roughly 8 times faster and presents almost no overshoot after a transient.

We present a decentralized control strategy that yields switch interleaving among parallel-connected dc-dc buck converters. The proposed method is based on the digital implementation of the dynamics of a nonlinear oscillator circuit as the controller. Each controller is fully decentralized, i.e., it only requires the locally measured output current to synthesize the pulse width modulation (PWM) carrier waveform and no communication between different controllers is needed. By virtue of the intrinsic electrical coupling between converters, the nonlinear oscillator-based controllers converge to an interleaved state with uniform phase-spacing across PWM carriers. To the knowledge of the authors, this work presents the first fully decentralized strategy for switch interleaving in paralleled dc-dc buck converters.

Power networks have to withstand a variety of disturbances that affect system frequency, and the problem is compounded with the increasing integration of intermittent renewable generation. Following a large-signal generation or load disturbance, system frequency is arrested leveraging primary frequency control provided by governor action in synchronous generators. In this work, we propose a framework for distributed energy resources (DERs) deployed in distribution networks to provide (supplemental) primary frequency response. Particularly, we demonstrate how power-frequency droop slopes for individual DERs can be designed so that the distribution feeder presents a guaranteed frequency-regulation characteristic at the feeder head. Furthermore, the droop slopes are engineered such that injections of individual DERs conform to a well-defined fairness objective that does not penalize them for their location on the distribution feeder. Time-domain simulations for an illustrative network composed of a combined transmission network and distribution network with frequency-responsive DERs are provided to validate the approach.

This paper considers power distribution systems featuring renewable energy sources (RESs), and it develops a distributed optimization method to steer the RES output powers to solutions of AC optimal power flow (OPF) problems. The design of the proposed method leverages suitable linear approximations of the AC power-flow equations, and it is based on the alternating direction method of multipliers (ADMM). Convergence of the RES-inverter output powers to solutions of the OPF problem is established under suitable conditions on the stepsize as well as mismatches between the commanded setpoints and actual RES output powers. In a broad sense, the methods and results proposed here are also applicable to other distributed optimization problem setups with ADMM and inexact dual updates.

Low-inertia AC microgrids are a collection of heterogeneous renewable-energy resources and energy-storage devices (such as photovoltaic arrays, batteries, fuel cells) that are interfaced to a distribution system through power-electronic inverters. In this work, we focus on islanded microgrids that are controlled and operated independently from the bulk power system. Such systems are envisioned to play a key role in increasing electricity access in unserved (and under served) portions of the world; as well as in applications such as disaster relief. Voltage source inverters play the role of the energy-conversion interface between low-inertia DC-energy resources and the AC electrical network in such systems. (See Fig. 1.)

This paper presents a convex-optimization-based method to estimate maximum and minimum bounds on state variables in the power flow problem while acknowledging worst-case parametric and input uncertainties in the model. The approach leverages a second-order Taylor-series expansion of the states around a nominal (known) power-flow solution. Maximum and minimum bounds are then estimated from semidefinite relaxations of quadratically constrained quadratic programs. The objective of these problems is to maximize / minimize the quadratic approximation of the states recovered from the Taylor series expansion over the convex set in which the uncertainties lie. Numerical case studies validate the approach for the IEEE 118-bus system.

This paper focuses on power distribution networks featuring distributed energy resources (DERs), and develops controllers that drive the DER output powers to solutions of time-varying AC optimal power flow (OPF) problems. The design of the controllers is grounded on primal-dual-type methods for regularized Lagrangian functions, as well as linear approximations of the AC power-flow equations. Convergence and OPF-solution-tracking capabilities are established while acknowledging: i) communication-packet losses, and ii) partial updates of control signals. The latter case is particularly relevant since it enables an asynchronous operation of the controllers where the DER setpoints are updated at a fast time scale based on local voltage measurements, and information on the network state is utilized if and when available, based on communication constraints. As an application, the paper considers distribution systems with a high penetration level of photovoltaic systems, and demonstrates that the proposed framework provides fast voltage-regulation capabilities, while enabling the near real-time pursuit of AC OPF solutions., Paper accepted and presented at the IEEE Conference on Decisions and Control 2016. In this version, a typo in the Figure 3 is corrected. arXiv admin note: text overlap with arXiv:1601.07263

This paper proposes a set-theoretic method to estimate feasible nodal injections (generation or load) in a distribution network, while respecting power system performance requirements. In the setting that we study, performance requirements are constraints in the form of interval ranges on the values that line flows can take, which are modelled by a convex poloytope. At its core, the proposed method relies on the solution of a linearly constrained least-squares optimization problem, which is formulated using sensitivity factors computed by linearizing the power flow equations around the operating point. Since this optimization problem admits a linear closed-form solution, the polytope of permissible line flows is propagated through the solution, via set operations, to obtain the set of feasible nodal injections.

This paper presents a condition for global asymptotic synchronization of Lienard-type nonlinear oscillators in uniform LTI electrical networks with series R-L circuits modeling interconnections. By uniform electrical networks, we mean that the per-unit-length impedances are identical for the interconnecting lines. We derive conditions for global asymptotic synchronization for a particular feedback architecture where the derivative of the oscillator output current supplements the innate current feedback induced by simply interconnecting the oscillator to the network. Our proof leverages a coordinate transformation to a set of differential coordinates that emphasizes signal differences and the particular form of feedback permits the formulation of a quadratic Lyapunov function for this class of networks. This approach is particularly interesting since synchronization conditions are difficult to obtain by means of quadratic Lyapunov functions when only current feedback is used and for networks composed of series R-L circuits. Our synchronization condition depends on the algebraic connectivity of the underlying network, and reiterates the conventional wisdom from Lyapunov- and passivity-based arguments that strong coupling is required to ensure synchronization.

This paper presents analytical closed-form expressions that map the contributions of nodal active- and reactive-power injections to the branch active- and reactive-power flows in an AC electrical network that is operating in sinusoidal steady state. We term these as the power divider laws, since they are derived leveraging, and their form and functionality are similar to, the ubiquitous current divider law. Distinct from the current divider law that only depends on the topology and constitution of the electrical network, the power divider laws are a function of the topology as well as the sinusoidal-steady-state voltage profile of the network.

This paper outlines an optimization-based method to estimate the reach set of a system while acknowledging unknown-but-bounded input and parametric uncertainty in the underlying dynamical model. The approach is grounded in a second-order Taylor-series expansion of the system's state variables along the solution trajectories as a function of the uncertain elements. Subsequently, over the time horizon of interest, Quadratically Constrained Quadratic Programs (QCQPs) are formulated to estimate maximum and minimum bounds on the state variables to recover the reach set. To contend with the nonconvexity of the QCQPs, Lagrangian relaxations are leveraged to formulate Semidefinite Programs (SDPs) that provide guaranteed bounds to the solutions of the QCQPs. Applications of the method to quantify the impact of uncertain power injections in power-system dynamic models are demonstrated with numerical examples.

This paper develops a structured optimal-control framework to design coupling gains for synchronization of weakly nonlinear oscillator circuits connected in resistive networks with arbitrary topologies. The oscillators are modeled as weakly nonlinear Lienard-type circuits, and the coupling gain amounts to the current gain which scales the output current of the oscillator. The structured optimal-control problem allows us to seek a decentralized control strategy (equivalently, a diagonal feedback matrix) that precludes communications between oscillators. To this end, a sparsity-promoting optimal control algorithm is developed to tune the optimal diagonal feedback-gain matrix with minimal performance sacrifice. This involves solving an ℋ2 optimal control problem with l1 regularization by applying the alternating direction method of multipliers (ADMM). Simulation studies with application to voltage regulation in islanded networks composed of power-electronic inverters are provided to validate the approach.

Analytic methods to quantify power systems stability margins while acknowledging uncertainty will be critical in dynamic security assessment due to the integration of renewable resources and uncontrollable loads. Lyapunov's direct method provides a mathematical framework to assess stability margins. However, analytical construction of Lyapunov functions are limited to very restrictive settings and cannot be extended to accommodate the impact of uncertainty. This paper focuses on the algorithmic construction of Lyapunov functions and the estimation of the robust Region-Of-Attraction (ROA) with sum-of-squares (SOS) optimization programs which can be translated into semidefinite problems and then solved with readily available software. Key to the proposed approach is the formulation of computationally tractable polynomial differential equation models that are affine in parametric/input uncertainty. Numerical case studies for a prototypical power system model validate the accuracy of the polynomial approximations and compare the ROA and the robust ROA with results from repeated time-domain simulations.

This paper offers a suite of extensions to Virtual Oscillator Control — a time-domain control method for islanded inverters whereby they are controlled to emulate the dynamics of weakly nonlinear limit-cycle oscillators. First, we develop a coordinate transformation to derive the PWM switching signals from the oscillator dynamic states in a manner that allows the inverter terminal-voltage amplitude and frequency to be traded off against a parametric linear combination of average active and reactive power. Additionally, we compare the time-domain performance of VOC to droop control for parallel connected inverters in two cases: synchronization from a cold start and inverter addition. Finally, with a view towards developing outputfilter-design strategies as well as outlining strategies for grid-connected operations, we derive a sufficient condition for a Virtual-Oscillator-controlled inverter to be entrained to a stiff voltage source.

In this paper we examine the amplitude and phase dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of a class of weakly nonlinear Lienard-type oscillators. The general strategy of controlling inverters to emulate the behavior of Lienard-type oscillators is termed Virtual Oscillator Control (VOC), and it presents a compelling time-domain alternative to ubiquitous droop control methods which linearly trade off voltage frequencies and magnitudes with active and reactive power injections. In comparison to droop control, which assumes a priori that the network operates in a quasi-stationary sinusoidal steady state, VOC is a time-domain control strategy that globally stabilizes a desired sinusoidal steady state. The main, and somewhat surprising, result of this paper is that—when reduced to the sinusoidal steady state—the VOC dynamics correspond to those of droop control. Hence, VOC is a globally stabilizing control strategy that can deal with higher-order harmonics and includes droop control in the harmonic steady state. The results are intriguing, in that they suggest that droop control laws can be recovered from averaging the complex dynamics of a class of weakly nonlinear limit-cycle oscillators.

We examine the steady-state behavior of DC distribution systems with arbitrary topologies that couple a heterogeneous collection of power-electronic circuits modeled as parallel connections of resistances, and constant current and power sources (or loads). For this system, we provide analytical closed-form expressions for sensitivities that capture variations of line power flows due to: i) changes in nodal power injections, and ii) line outages. Our results follow from a perturbative analysis of the network power-balance expressions, and the approach leverages contemporary results from circuit theory and structural properties of the network conductance matrix. Simulations from illustrative networks confirm the validity and accuracy of the analytical expressions in estimating the impact of nodal power injections and line outages.

We study the problem that arises in a class of stochastic processes referred to as Stochastic Hybrid Systems (SHS) when computing the moments of the states using the generator of the process and Dynkin's formula. We focus on the case when the SHS is at equilibrium or approaching equilibrium. We present a family of such processes for which infinite-dimensional linear-system analysis tools are ineffective, and discuss a few differing perspectives on how to tackle such problems by assuming that the SHS state distribution is such that its entropy is maximum. We also provide a numerical algorithm that allows us to efficiently compute maximum entropy solutions, and compare results with Monte Carlo simulations for some illustrative SHS.

In this paper, the three-port Cuk converter interfaces one unidirectional input power port (envisioned to be a DC power source such as PV, or fuel cell) and two bidirectional output ports, representing the grid-tied inverter dc bus and a storage port respectively, and combines all the magnetics into a single core. The well-known property of the basic Cuk converter that emulates an ideal dc-dc transformer (zero ripple terminal currents) is extended to three ports and is analyzed in detail. Two methods, one involving the physical structure of the core, and the other, a circuit-based dual approach, which is directly related to the core structure, are applied to solve the zero-ripple problem, and the accuracy of one of them over the other is verified with simulation results. Three different power transfer modes in this three-port converter are compared using the two methods mentioned above.

Synchronization of coupled oscillators is a pervasive theme of multi-disciplinary research. Focused on circuit-theoretic applications, in this paper, we derive sufficient conditions for global asymptotic synchronization in a system of identical nonlinear circuits coupled through linear time-invariant (LTI) electrical networks. The nonlinear circuits are composed of a parallel combination of passive LTI circuit elements and a nonlinear voltage-dependent current source with finite gain. The terminals of the nonlinear circuits are coupled through LTI networks characterized by either identical per-unit-length impedances or identical effective impedances between any two terminals. This setup is motivated by a recently proposed control strategy for inverters in microgrids. We analyze synchronization by means of an input-output analysis of a coordinate-transformed system that emphasizes signal differences. To apply the synchronization analysis to a broad class of networks, we leverage recent results on Kron reduction-a circuit reduction and transformation procedure that reveals the interactions of the nonlinear circuits. We illustrate our results with simulations in networks of coupled Chua's circuits.