arXiv subjects

Emiliano Dall'Anese

Publications and source records attributed to Emiliano Dall'Anese.

At least 91 records · Page 5Linked to original sources

arXiv2017

Stochastic Dual Algorithm for Voltage Regulation in Distribution Networks with Discrete Loads

This paper considers power distribution networks with distributed energy resources and designs an incentive-based algorithm that allows the network operator and customers to pursue given operational and economic objectives while concurrently ensuring that voltages are within prescribed limits. Heterogeneous DERs with continuous and discrete control commands are considered. We address four major challenges: discrete decision variables, non-convexity due to a Stackelberg game structure, unavailability of private information from customers, and asynchronous operation. Starting from a non-convex setting, we develop a distributed stochastic dual algorithm that solves a relaxed problem, and prove that the proposed algorithm achieves the global optimal solution of the original problem on average. Feasible values for discrete decision variables are also recovered. Stability of the algorithm is analytically established and numerically corroborated.

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arXiv2017

Network-Cognizant Voltage Droop Control for Distribution Grids

This paper examines distribution systems with a high integration of distributed energy resources (DERs) and addresses the design of local control methods for real-time voltage regulation. Particularly, the paper focuses on proportional control strategies where the active and reactive output-powers of DERs are adjusted in response to (and proportionally to) local changes in voltage levels. The design of the voltage-active power and voltage-reactive power characteristics leverages suitable linear approximations of the AC power-flow equations and is network-cognizant; that is, the coefficients of the controllers embed information on the location of the DERs and forecasted non-controllable loads/injections and, consequently, on the effect of DER power adjustments on the overall voltage profile. A robust approach is pursued to cope with uncertainty in the forecasted non-controllable loads/power injections. Stability of the proposed local controllers is analytically assessed and numerically corroborated.

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arXiv2017

An Incentive-Based Online Optimization Framework for Distribution Grids

This paper formulates a time-varying social-welfare maximization problem for distribution grids with distributed energy resources (DERs) and develops online distributed algorithms to identify (and track) its solutions. In the considered setting, network operator and DER-owners pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. The proposed algorithm affords an online implementation to enable tracking of the solutions in the presence of time-varying operational conditions and changing optimization objectives. It involves a strategy where the network operator collects voltage measurements throughout the feeder to build incentive signals for the DER-owners in real time; DERs then adjust the generated/consumed powers in order to avoid the violation of the voltage constraints while maximizing given objectives. The stability of the proposed schemes is analytically established and numerically corroborated.

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arXiv2017

Engineering Inertial and Primary-frequency Response for Distributed Energy Resources

We propose a framework to engineer synthetic-inertia and droop-control parameters for distributed energy resources (DERs) so that the system frequency in a network composed of DERs and synchronous generators conforms to prescribed transient and steady-state performance specifications. Our approach is grounded in a second-order lumped-parameter model that captures the dynamics of synchronous generators and frequency-responsive DERs endowed with inertial and droop control. A key feature of this reduced-order model is that its parameters can be related to those of the originating higher-order dynamical model. This allows one to systematically design the DER inertial and droop-control coefficients leveraging classical frequency-domain response characteristics of second-order systems. Time-domain simulations validate the accuracy of the model-reduction method and demonstrate how DER controllers can be designed to meet steady-state-regulation and transient-performance specifications.

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arXiv2017

Prediction-Correction Algorithms for Time-Varying Constrained Optimization

This paper develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do not require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.

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arXiv2016

Design of Distributed Controllers Seeking Optimal Power Flow Solutions Under Communication Constraints

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.

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arXiv2016

Beyond Relaxation and Newton-Raphson: Solving AC OPF for Multi-phase Systems with Renewables

This paper focuses on the AC Optimal Power Flow (OPF) problem for multi-phase systems. Particular emphasis is given to systems with high integration of renewables, where adjustments of the real and reactive output powers from renewable sources of energy are necessary in order to enforce voltage regulation. The AC OPF problem is known to be nonconvex (and, in fact, NP-hard). Convex relaxation techniques have been recently explored to solve the OPF task with reduced computational burden; however, sufficient conditions for tightness of these relaxations are only available for restricted classes of system topologies and problem setups. Identifying feasible power-flow solutions remains hard in more general problem formulations, especially in unbalanced multi-phase systems with renewables. To identify feasible and optimal AC OPF solutions in challenging scenarios where existing methods may fail, this paper leverages the Feasible Point Pursuit - Successive Convex Approximation algorithm -- a powerful approach for general nonconvex quadratically constrained quadratic programs. The merits of the approach are illustrated using single- and multi-phase distribution networks with renewables, as well as several transmission systems.

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arXiv2016

Optimal Power Flow Pursuit

This paper considers distribution networks featuring inverter-interfaced distributed energy resources, and develops distributed feedback controllers that continuously drive the inverter output powers to solutions of AC optimal power flow (OPF) problems. Particularly, the controllers update the power setpoints based on voltage measurements as well as given (time-varying) OPF targets, and entail elementary operations implementable onto low-cost microcontrollers that accompany power-electronics interfaces of gateways and inverters. The design of the control framework is based on suitable linear approximations of the AC power-flow equations as well as Lagrangian regularization methods. Convergence and OPF-target tracking capabilities of the controllers are analytically established. Overall, the proposed method allows to bypass traditional hierarchical setups where feedback control and optimization operate at distinct time scales, and to enable real-time optimization of distribution systems.

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arXiv2015

Photovoltaic Inverter Controllers Seeking AC Optimal Power Flow Solutions

This paper considers future distribution networks featuring inverter-interfaced photovoltaic (PV) systems, and addresses the synthesis of feedback controllers that seek real- and reactive-power inverter setpoints corresponding to AC optimal power flow (OPF) solutions. The objective is to bridge the temporal gap between long-term system optimization and real-time inverter control, and enable seamless PV-owner participation without compromising system efficiency and stability. The design of the controllers is grounded on a dual epsilon-subgradient method, and semidefinite programming relaxations are advocated to bypass the non-convexity of AC OPF formulations. Global convergence of inverter output powers is analytically established for diminishing stepsize rules and strictly convex OPF costs for cases where: i) computational limits dictate asynchronous updates of the controller signals, and ii) inverter reference inputs may be updated at a faster rate than the power-output settling time. Although the focus is on PV systems, the framework naturally accommodates different types of inverter-interfaced energy resources.

math.OC↗

arXiv2015

Regulation of Dynamical Systems to Optimal Solutions of Semidefinite Programs: Algorithms and Applications to AC Optimal Power Flow

This paper considers a collection of networked nonlinear dynamical systems, and addresses the synthesis of feedback controllers that seek optimal operating points corresponding to the solution of network-wide constrained optimization problems. Particular emphasis is placed on the solution of semidefinite programs (SDPs). The design of the feedback controller is grounded on a dual epsilon-subgradient approach, with the dual iterates utilized to dynamically update the dynamical-system reference signals. Global convergence is guaranteed for diminishing stepsize rules, even when the reference inputs are updated at a faster rate than the dynamical-system settling time. The application of the proposed framework to the control of power-electronic inverters in AC distribution systems is discussed. The objective is to bridge the time-scale separation between real-time inverter control and network-wide optimization. Optimization objectives assume the form of SDP relaxations of prototypical AC optimal power flow problems.

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arXiv2014

Optimal Dispatch of Residential Photovoltaic Inverters Under Forecasting Uncertainties

Efforts to ensure reliable operation of existing low-voltage distribution systems with high photovoltaic (PV) generation have focused on the possibility of inverters providing ancillary services such as active power curtailment and reactive power compensation. Major benefits include the possibility of averting overvoltages, which may otherwise be experienced when PV generation exceeds the demand. This paper deals with ancillary service procurement in the face of solar irradiance forecasting errors. In particular, assuming that the forecasted PV irradiance can be described by a random variable with known (empirical) distribution, the proposed uncertainty-aware optimal inverter dispatch (OID) framework indicates which inverters should provide ancillary services with a guaranteed a-priori risk level of PV generation surplus. To capture forecasting errors, and strike a balance between risk of overvoltages and (re)active power reserves, the concept of conditional value-at-risk is advocated. Due to AC power balance equations and binary inverter selection variables, the formulated OID involves the solution of a nonconvex mixed-integer nonlinear program. However, a computationally-affordable convex relaxation is derived by leveraging sparsity-promoting regularization approaches and semidefinite relaxation techniques. The proposed scheme is tested using real-world PV-generation and load-profile data for an illustrative low-voltage residential distribution system.

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arXiv2014

Decentralized Optimal Dispatch of Photovoltaic Inverters in Residential Distribution Systems

Decentralized methods for computing optimal real and reactive power setpoints for residential photovoltaic (PV) inverters are developed in this paper. It is known that conventional PV inverter controllers, which are designed to extract maximum power at unity power factor, cannot address secondary performance objectives such as voltage regulation and network loss minimization. Optimal power flow techniques can be utilized to select which inverters will provide ancillary services, and to compute their optimal real and reactive power setpoints. Leveraging advances in semidefinite relaxation techniques and sparsity-promoting regularizations, such problems can be solved with reduced computational burden and with optimality guarantees. To enable large-scale implementation, a novel algorithmic framework is introduced - based on the so-called alternating direction method of multipliers - by which the optimal power flow problem in this setting can be systematically decomposed into sub-problems that can be solved in a decentralized fashion by the utility and customer-owned PV systems with limited exchanges of information. Since the computational burden is shared among multiple devices and the requirement of all-to-all communication can be circumvented, the proposed optimization approach scales to large distribution networks.

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arXiv2014

Risk-Constrained Microgrid Reconfiguration Using Group Sparsity

The system reconfiguration task is considered for existing power distribution systems and microgrids, in the presence of renewable-based generation and load foresting errors. The system topology is obtained by solving a chance-constrained optimization problem, where loss-of-load (LOL) constraints and Ampacity limits of the distribution lines are enforced. Similar to various distribution system reconfiguration renditions, solving the resultant problem is computationally prohibitive due to the presence of binary line selection variables. Further, lack of closed form expressions for the joint probability distribution of forecasting errors hinders tractability of LOL constraints. Nevertheless, a convex problem re-formulation is developed here by resorting to a scenario approximation technique, and by leveraging the underlying group-sparsity attribute of currents flowing on distribution lines equipped with tie and sectionalizing switches. The novel convex LOL-constrained reconfiguration scheme can also afford a distributed solution using the alternating direction method of multipliers, to address the case where multi-facilities are managed autonomously from the rest of the system.

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arXiv2014

Sparsity-leveraging Reconfiguration of Smart Distribution Systems

A system reconfiguration problem is considered for three-phase power distribution networks featuring distributed generation. In lieu of binary line selection variables, the notion of group sparsity is advocated to re-formulate the nonconvex distribution system reconfiguration (DSR) problem into a convex one. Using the duality theory, it is shown that the line selection task boils down to a shrinkage and thresholding operation on the line currents. Further, numerical tests illustrate the ability of the proposed scheme to identify meshed, weakly-meshed, or even radial configurations by adjusting a sparsity-tuning parameter in the DSR cost. Constraints on the voltages are investigated, and incorporated in the novel DSR problem to effect voltage regulation.

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arXiv2014

Distributed Optimal Power Flow for Smart Microgrids

Optimal power flow (OPF) is considered for microgrids, with the objective of minimizing either the power distribution losses, or, the cost of power drawn from the substation and supplied by distributed generation (DG) units, while effecting voltage regulation. The microgrid is unbalanced, due to unequal loads in each phase and non-equilateral conductor spacings on the distribution lines. Similar to OPF formulations for balanced systems, the considered OPF problem is nonconvex. Nevertheless, a semidefinite programming (SDP) relaxation technique is advocated to obtain a convex problem solvable in polynomial-time complexity. Enticingly, numerical tests demonstrate the ability of the proposed method to attain the globally optimal solution of the original nonconvex OPF. To ensure scalability with respect to the number of nodes, robustness to isolated communication outages, and data privacy and integrity, the proposed SDP is solved in a distributed fashion by resorting to the alternating direction method of multipliers. The resulting algorithm entails iterative message-passing among groups of consumers and guarantees faster convergence compared to competing alternatives

math.OC↗

arXiv2014

Optimal Dispatch of Photovoltaic Inverters in Residential Distribution Systems

Low-voltage distribution feeders were designed to sustain unidirectional power flows to residential neighborhoods. The increased penetration of roof-top photovoltaic (PV) systems has highlighted pressing needs to address power quality and reliability concerns, especially when PV generation exceeds the household demand. A systematic method for determining the active- and reactive-power set points for PV inverters in residential systems is proposed in this paper, with the objective of optimizing the operation of the distribution feeder and ensuring voltage regulation. Binary PV-inverter selection variables and nonlinear power-flow relations render the novel optimal inverter dispatch problem nonconvex and NP-hard. Nevertheless, sparsity-promoting regularization approaches and semidefinite relaxation techniques are leveraged to obtain a computationally feasible convex reformulation. The merits of the proposed approach are demonstrated using real-world PV-generation and load-profile data for an illustrative low-voltage residential distribution system.

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arXiv2012

Economic Dispatch in Unbalanced Distribution Networks via Semidefinite Relaxation

The economic dispatch problem is considered for unbalanced three-phase power distribution networks entailing both non-deferrable and elastic loads, and distributed generation (DG) units. The objective is to minimize the costs of power drawn from the main grid and supplied by the DG units over a given time horizon, while meeting the overall load demand and effecting voltage regulation. Similar to optimal power flow counterparts for balanced systems, the resultant optimization problem is nonconvex. Nevertheless, a semidefinite programming (SDP) relaxation technique is advocated to obtain a (relaxed) convex problem solvable in polynomial-time complexity. To promote a reliable yet efficient feeder operation, SDP-compliant constraints on line and neutral current magnitudes are accommodated in the optimization formulated, along with constraints on the power factor at the substation and at nodes equipped with capacitor banks. Tests on the IEEE 13-node radial feeder demonstrate the ability of the proposed method to attain the globally optimal solution of the original nonconvex problem.

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arXiv2012

Dynamic Network Delay Cartography

Path delays in IP networks are important metrics, required by network operators for assessment, planning, and fault diagnosis. Monitoring delays of all source-destination pairs in a large network is however challenging and wasteful of resources. The present paper advocates a spatio-temporal Kalman filtering approach to construct network-wide delay maps using measurements on only a few paths. The proposed network cartography framework allows efficient tracking and prediction of delays by relying on both topological as well as historical data. Optimal paths for delay measurement are selected in an online fashion by leveraging the notion of submodularity. The resulting predictor is optimal in the class of linear predictors, and outperforms competing alternatives on real-world datasets.

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